Finite Group Databasebeta

← C3×#10595453 #13175050

Subgroups — C3×#10595453 #13175050

Order 1728.

1376 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D3×#41C211yesmaximal, characteristic, complemented
2C3×D3×#235C211yesmaximal, characteristic, complemented
3C3×#64159C211yesmaximal, characteristic, complemented
4C32×#950C211yesmaximal, characteristic, complemented
5C3×#63948C211yesmaximal, characteristic, complemented
6C3×#63946C211yesmaximal, characteristic, complemented
7C3×#63943C211yesmaximal, characteristic, complemented
8C3×#63939C211yesmaximal, characteristic, complemented
9C3×#63934C211yesmaximal, characteristic, complemented
10C3×#63932C211yesmaximal, characteristic, complemented
11C3×#63929C211yesmaximal, characteristic, complemented
12C3×#63925C211yesmaximal, characteristic, complemented
13C3×#63829C211yesmaximal, characteristic, complemented
14C3×#63822C211yesmaximal, characteristic, complemented
15C2×C3×#3711C211yesmaximal, characteristic, complemented
16C3×#5822—31nomaximal
17C3×#5768—31nomaximal
18#10595453C311yesmaximal, characteristic, direct product factor
19C33×#41C2211yescharacteristic, complemented
20C3×#3828C2211yescharacteristic, complemented
21C32×#239C2211yescharacteristic
22C32×D3×Q8C2211yescharacteristic, complemented
23C32×#237—21no—
24C32×#237C2211yescharacteristic
25C32×D3×D4—21no—
26C32×D3×D4C2211yescharacteristic, complemented
27C32×#235—21no—
28C32×#235C2211yescharacteristic, complemented
29C32×#235C2211yescharacteristic, complemented
30C2×C32×C4×D3—21no—
31C2×C32×C4×D3C2211yescharacteristic
32C3×D3×#67—21no—
33C3×#3804—21no—
34C3×D3×D12C2211yescharacteristic, complemented
35C3×C4×D32—21no—
36C3×#3799C2211yescharacteristic
37C3×#3798—21no—
38C3×#3795C2211yescharacteristic
39C3×D3×Dic6C2211yescharacteristic, complemented
40C3×#3756C2211yescharacteristic, complemented
41C3×#3755C2211yescharacteristic, complemented
42C3×#3754C2211yescharacteristic, complemented
43C3×#3753C2211yescharacteristic, complemented
44C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
45C32×#216C2211yescharacteristic, complemented
46C32×#215C2211yescharacteristic, complemented
47C32×#214C2211yescharacteristic, complemented
48C32×#213C2211yescharacteristic, complemented
49C2×C32×C3⋊C8C2211yescharacteristic, complemented
50C3×#3719C2211yescharacteristic, complemented
51C3×#3718C2211yescharacteristic, complemented
52C3×#3717C2211yescharacteristic, complemented
53C3×#3716C2211yescharacteristic, complemented
54C3×#3715C2211yescharacteristic, complemented
55C3×#3715C2211yescharacteristic, complemented
56C3×#3714C2211yescharacteristic, complemented
57C3×#3713C2211yescharacteristic, complemented
58C3×#3711C2211yescharacteristic, complemented
59C3×#3711C2211yescharacteristic, complemented
60C3×#3711C2211yescharacteristic, complemented
61C3×#3711C2211yescharacteristic, complemented
62C2×C32×#41—31no—
63C3×D3×#41—21no—
64C3×D3×#41—31no—
65C3×D3×#41D311yescharacteristic, complemented
66C3×D3×#41C2×C311yescharacteristic, complemented
67C2×C3×#235—31no—
68D3×#235C2×C311yescharacteristic, complemented
69C32×#135—31no—
70#64159C2×C311yescharacteristic, complemented
71C3×#951—31no—
72C3×#951—31no—
73C3×#950—21no—
74C3×#950—31no—
75C3×#950—31no—
76C3×#950—31no—
77C3×#950—31no—
78C3×#950—31no—
79C3×#950—61no—
80C3×#950D311yescharacteristic, complemented
81C3×#950C2×C311yescharacteristic, complemented
82C3×#949—31no—
83C3×#949—31no—
84C3×#942—31no—
85C3×#942—31no—
86C3×#932—31no—
87C3×#932—31no—
88C2×C3×#208—31no—
89C3×#918—31no—
90C3×#918—31no—
91C3×#915—31no—
92C3×#915—31no—
93C3×#914—31no—
94C3×#914—31no—
95C3×#911—31no—
96C3×#911—31no—
97C3×#904—31no—
98C2×C3×ΓL(1,𝔽25)—31no—
99#63948C2×C311yescharacteristic, complemented
100#63946C2×C311yescharacteristic, complemented
101#63943C2×C311yescharacteristic, complemented
102#63939C2×C311yescharacteristic, complemented
103#63934C2×C311yescharacteristic, complemented
104#63932C2×C311yescharacteristic, complemented
105#63929C2×C311yescharacteristic, complemented
106#63925C2×C311yescharacteristic, complemented
107#63829C2×C311yescharacteristic, complemented
108#63822C2×C311yescharacteristic, complemented
109C2×#3711C2×C311yescharacteristic, complemented
110C22×C32×D3—21no—
111C22×C32×D3D411yescharacteristic
112C2×C3×D32—21no—
113C33×Q8C2311yescharacteristic
114C33×D4—21no—
115C33×D4C2311yescharacteristic
116C2×C33×C4—21no—
117C2×C33×C4C2311yescharacteristic
118C3×#638—21no—
119C3×C4⋊(C3⋊D3)C2311yescharacteristic
120C3×C4×C3⋊D3—21no—
121C3×#634C2311yescharacteristic
122C32×#67—21no—
123C32×#67—21no—
124C32×#67—21no—
125C32×#67—21no—
126C2×C32×Dic3—21no—
127C2×C32×Dic3D411yescharacteristic
128C32×D12—21no—
129C32×D12C2311yescharacteristic
130C32×D12C2311yescharacteristic
131C32×C4×D3—21no—
132C32×C4×D3—21no—
133C32×C4×D3—21no—
134C32×C4×D3—21no—
135C32×C4×D3D411yescharacteristic
136C32×C4×D3D411yescharacteristic
137C32×C4×D3C2311yescharacteristic
138C32×C4×D3C2311yescharacteristic
139C32×Dic6—21no—
140C32×Dic6C2311yescharacteristic
141C32×Dic6C2311yescharacteristic
142C3×#627—21no—
143C3×#626—21no—
144C3×#626—21no—
145C3×#625—21no—
146C3×#624—21no—
147C3×D3×Dic3—21no—
148C3×D3×Dic3—21no—
149C3×C3⋊(C3⋊C8)C2311yescharacteristic
150C3×C3⋊(C3⋊C8)C2311yescharacteristic
151C32×C3⋊C8C2311yescharacteristic
152C32×C3⋊C8C2311yescharacteristic
153C3×#575—91no—
154#5822—31no—
155#5768—31no—
156C32×#41—21no—
157C32×#41—21no—
158C32×#41—21no—
159C32×#41—31no—
160C32×#41—31no—
161C32×#41—31no—
162C32×#41—31no—
163C32×#41—41no—
164C32×#41—61no—
165C32×#41—61no—
166C32×#41C2×D311yescharacteristic, complemented
167C32×#41C2×D311yescharacteristic, complemented
168C32×#41C22×C311yescharacteristic, complemented
169C2×C32×Q8—31no—
170C2×C32×D4—31no—
171C2×C32×D4—61no—
172C22×C32×C4—31no—
173C22×C32×C4—61no—
174#3828C22×C311yescharacteristic, complemented
175C2×C3×#67—61no—
176C3×#239—21no—
177C3×#239—31no—
178C3×#239C2×D311yescharacteristic
179C3×#239C22×C311yescharacteristic
180C3×D3×Q8—21no—
181C3×D3×Q8—31no—
182C3×D3×Q8C2×D311yescharacteristic, complemented
183C3×D3×Q8C22×C311yescharacteristic, complemented
184C3×#237—22no—
185C3×#237—21no—
186C3×#237—21no—
187C3×#237—21no—
188C3×#237—31no—
189C3×#237—61no—
190C3×#237C2×D311yescharacteristic
191C3×#237C22×C311yescharacteristic
192C3×D3×D4—22no—
193C3×D3×D4—21no—
194C3×D3×D4—21no—
195C3×D3×D4—21no—
196C3×D3×D4—31no—
197C3×D3×D4—61no—
198C3×D3×D4C2×D311yescharacteristic, complemented
199C3×D3×D4C22×C311yescharacteristic, complemented
200C3×#235—22no—
201C3×#235—21no—
202C3×#235—21no—
203C3×#235—21no—
204C3×#235—21no—
205C3×#235—31no—
206C3×#235—31no—
207C3×#235—31no—
208C3×#235—31no—
209C3×#235—61no—
210C3×#235—61no—
211C3×#235—61no—
212C3×#235—61no—
213C3×#235C2×D311yescharacteristic, complemented
214C3×#235C2×D311yescharacteristic, complemented
215C3×#235C22×C311yescharacteristic, complemented
216C3×#235C22×C311yescharacteristic, complemented
217C2×C3×D12—31no—
218C2×C3×C4×D3—22no—
219C2×C3×C4×D3—21no—
220C2×C3×C4×D3—21no—
221C2×C3×C4×D3—21no—
222C2×C3×C4×D3—61no—
223C2×C3×C4×D3—61no—
224C2×C3×C4×D3C2×D311yescharacteristic
225C2×C3×C4×D3C22×C311yescharacteristic
226C2×C3×Dic6—31no—
227D3×#67—21no—
228#3804—21no—
229D3×D12C22×C311yescharacteristic, complemented
230C4×D32—21no—
231#3799C22×C311yescharacteristic
232#3798—21no—
233#3795C22×C311yescharacteristic
234D3×Dic6C22×C311yescharacteristic, complemented
235C32×Q16—31no—
236C32×SD16—31no—
237C32×SD16—31no—
238C32×D8—31no—
239C2×C32×C8—31no—
240#3756C22×C311yescharacteristic, complemented
241#3755C22×C311yescharacteristic, complemented
242#3754C22×C311yescharacteristic, complemented
243#3753C22×C311yescharacteristic, complemented
244C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
245C3×#216—21no—
246C3×#216—31no—
247C3×#216—31no—
248C3×#216—31no—
249C3×#216—31no—
250C3×#216—31no—
251C3×#216—61no—
252C3×#216C2×D311yescharacteristic, complemented
253C3×#216C22×C311yescharacteristic, complemented
254C3×#215—21no—
255C3×#215—31no—
256C3×#215—31no—
257C3×#215—31no—
258C3×#215—31no—
259C3×#215—31no—
260C3×#215—61no—
261C3×#215C2×D311yescharacteristic, complemented
262C3×#215C22×C311yescharacteristic, complemented
263C3×#214—21no—
264C3×#214—31no—
265C3×#214—31no—
266C3×#214—31no—
267C3×#214—31no—
268C3×#214—31no—
269C3×#214—61no—
270C3×#214C2×D311yescharacteristic, complemented
271C3×#214C22×C311yescharacteristic, complemented
272C3×#213—21no—
273C3×#213—31no—
274C3×#213—31no—
275C3×#213—31no—
276C3×#213—31no—
277C3×#213—31no—
278C3×#213—61no—
279C3×#213C2×D311yescharacteristic, complemented
280C3×#213C22×C311yescharacteristic, complemented
281C3×#208—31no—
282C3×#208—31no—
283C3×#208—31no—
284C3×#208—31no—
285C2×C3×C3⋊C8—21no—
286C2×C3×C3⋊C8—31no—
287C2×C3×C3⋊C8—31no—
288C2×C3×C3⋊C8—61no—
289C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
290C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
291C3×Dic12—31no—
292C3×D24—31no—
293C3×#204—31no—
294C3×#204—31no—
295C3×ΓL(1,𝔽25)—31no—
296C3×ΓL(1,𝔽25)—31no—
297C3×ΓL(1,𝔽25)—31no—
298C3×ΓL(1,𝔽25)—31no—
299#3719C22×C311yescharacteristic, complemented
300#3718C22×C311yescharacteristic, complemented
301#3717C22×C311yescharacteristic, complemented
302#3716C22×C311yescharacteristic, complemented
303#3715C22×C311yescharacteristic, complemented
304#3715C22×C311yescharacteristic, complemented
305#3714C22×C311yescharacteristic, complemented
306#3713C22×C311yescharacteristic, complemented
307#3711C22×C311yescharacteristic, complemented
308#3711C22×C311yescharacteristic, complemented
309#3711C22×C311yescharacteristic, complemented
310#3711C22×C311yescharacteristic, complemented
311C22×C33—21no—
312C22×C33C2×D411yescharacteristic
313C2×C3×C3⋊D3—21no—
314C2×C32×D3—21no—
315C2×C32×D3—21no—
316C2×C32×D3—41no—
317C2×C32×D3—42no—
318C2×C32×D3C2×D411yescharacteristic
319C2×C32×D3C2×D411yescharacteristic
320C3×D32—42no—
321C33×C4—21no—
322C33×C4C2×D411yescharacteristic
323C33×C4C2411yescharacteristic
324C3×C3⋊Dic3—21no—
325C32×Dic3—21no—
326C32×Dic3—21no—
327C32×Dic3C2×D411yescharacteristic
328C32×Dic3C2×D411yescharacteristic
329C2×C3×#41—31no—
330C2×C3×#41—31no—
331C2×C3×#41—61no—
332C2×C3×#41—91no—
333D3×#41—31no—
334D3×#41C3×D311yescharacteristic, complemented
335C2×#235—31no—
336C3×#137—91no—
337C3×#137—91no—
338C3×#137—91no—
339C3×#137—91no—
340C3×AGL(1,ℤ/8)—91no—
341C3×AGL(1,ℤ/8)—91no—
342C3×AGL(1,ℤ/8)—91no—
343C3×AGL(1,ℤ/8)—91no—
344C3×#135—31no—
345C3×#135—31no—
346C3×#135—61no—
347C3×#135—91no—
348C3×#135—91no—
349C3×#135—91no—
350C2×C3×M16—91no—
351#951—31no—
352#951—31no—
353#950—31no—
354#950—31no—
355#950—31no—
356#950—31no—
357#950—31no—
358#950—61no—
359#950C3×D311yescharacteristic, complemented
360#949—31no—
361#949—31no—
362#942—31no—
363#942—31no—
364#932—31no—
365#932—31no—
366C2×#208—31no—
367#918—31no—
368#918—31no—
369#915—31no—
370#915—31no—
371#914—31no—
372#914—31no—
373#911—31no—
374#911—31no—
375#904—31no—
376C2×ΓL(1,𝔽25)—31no—
377C23×C32—31no—
378C23×C32—61no—
379C22×C3×D3—22no—
380C22×C3×D3—21no—
381C22×C3×D3—21no—
382C22×C3×D3—21no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3#6711yescharacteristic
386C22×C3×D3C3×D411yescharacteristic
387C2×D32—21no—
388C32×Q8—21no—
389C32×Q8—21no—
390C32×Q8—21no—
391C32×Q8—31no—
392C32×Q8—31no—
393C32×Q8—41no—
394C32×Q8—61no—
395C32×Q8C22×D311yescharacteristic
396C32×Q8C22×D311yescharacteristic
397C32×Q8C23×C311yescharacteristic
398C32×D4—21no—
399C32×D4—22no—
400C32×D4—21no—
401C32×D4—21no—
402C32×D4—21no—
403C32×D4—21no—
404C32×D4—21no—
405C32×D4—31no—
406C32×D4—31no—
407C32×D4—41no—
408C32×D4—41no—
409C32×D4—41no—
410C32×D4—42no—
411C32×D4—61no—
412C32×D4—61no—
413C32×D4—61no—
414C32×D4—61no—
415C32×D4—61no—
416C32×D4C22×D311yescharacteristic
417C32×D4C22×D311yescharacteristic
418C32×D4C23×C311yescharacteristic
419C2×C32×C4—21no—
420C2×C32×C4—22no—
421C2×C32×C4—21no—
422C2×C32×C4—21no—
423C2×C32×C4—21no—
424C2×C32×C4—21no—
425C2×C32×C4—21no—
426C2×C32×C4—31no—
427C2×C32×C4—31no—
428C2×C32×C4—31no—
429C2×C32×C4—31no—
430C2×C32×C4—31no—
431C2×C32×C4—41no—
432C2×C32×C4—41no—
433C2×C32×C4—41no—
434C2×C32×C4—42no—
435C2×C32×C4—61no—
436C2×C32×C4—61no—
437C2×C32×C4—61no—
438C2×C32×C4—61no—
439C2×C32×C4—61no—
440C2×C32×C4C22×D311yescharacteristic
441C2×C32×C4C22×D311yescharacteristic
442C2×C32×C4C23×C311yescharacteristic
443#638—21no—
444C4⋊(C3⋊D3)C23×C311yescharacteristic
445C4×C3⋊D3—21no—
446#634C23×C311yescharacteristic
447C3×#67—22no—
448C3×#67—22no—
449C3×#67—22no—
450C3×#67—21no—
451C3×#67—21no—
452C3×#67—21no—
453C3×#67—21no—
454C3×#67—21no—
455C3×#67—21no—
456C3×#67—21no—
457C3×#67—21no—
458C3×#67—41no—
459C3×#67—61no—
460C3×#67—61no—
461C3×#67—61no—
462C3×#67—61no—
463C3×#67—61no—
464C3×#67—61no—
465C3×#67—121no—
466C2×C3×Dic3—22no—
467C2×C3×Dic3—21no—
468C2×C3×Dic3—21no—
469C2×C3×Dic3—21no—
470C2×C3×Dic3—61no—
471C2×C3×Dic3—61no—
472C2×C3×Dic3#6711yescharacteristic
473C2×C3×Dic3C3×D411yescharacteristic
474C3×D12—22no—
475C3×D12—21no—
476C3×D12—21no—
477C3×D12—21no—
478C3×D12—21no—
479C3×D12—31no—
480C3×D12—31no—
481C3×D12—61no—
482C3×D12—61no—
483C3×D12—61no—
484C3×D12C22×D311yescharacteristic
485C3×D12C22×D311yescharacteristic
486C3×D12C23×C311yescharacteristic
487C3×D12C23×C311yescharacteristic
488C3×C4×D3—22no—
489C3×C4×D3—22no—
490C3×C4×D3—22no—
491C3×C4×D3—21no—
492C3×C4×D3—21no—
493C3×C4×D3—21no—
494C3×C4×D3—21no—
495C3×C4×D3—21no—
496C3×C4×D3—21no—
497C3×C4×D3—21no—
498C3×C4×D3—21no—
499C3×C4×D3—21no—
500C3×C4×D3—21no—
501C3×C4×D3—21no—
502C3×C4×D3—21no—
503C3×C4×D3—41no—
504C3×C4×D3—61no—
505C3×C4×D3—61no—
506C3×C4×D3—61no—
507C3×C4×D3—61no—
508C3×C4×D3—61no—
509C3×C4×D3—61no—
510C3×C4×D3—121no—
511C3×C4×D3#6711yescharacteristic
512C3×C4×D3#6711yescharacteristic
513C3×C4×D3C3×D411yescharacteristic
514C3×C4×D3C3×D411yescharacteristic
515C3×C4×D3C22×D311yescharacteristic
516C3×C4×D3C22×D311yescharacteristic
517C3×C4×D3C23×C311yescharacteristic
518C3×C4×D3C23×C311yescharacteristic
519C3×Dic6—22no—
520C3×Dic6—21no—
521C3×Dic6—21no—
522C3×Dic6—21no—
523C3×Dic6—21no—
524C3×Dic6—31no—
525C3×Dic6—31no—
526C3×Dic6—61no—
527C3×Dic6—61no—
528C3×Dic6—61no—
529C3×Dic6C22×D311yescharacteristic
530C3×Dic6C22×D311yescharacteristic
531C3×Dic6C23×C311yescharacteristic
532C3×Dic6C23×C311yescharacteristic
533#627—21no—
534#626—21no—
535#626—21no—
536#625—21no—
537#624—21no—
538D3×Dic3—21no—
539D3×Dic3—21no—
540C32×C8—31no—
541C32×C8—31no—
542C3⋊(C3⋊C8)C23×C311yescharacteristic
543C3⋊(C3⋊C8)C23×C311yescharacteristic
544C3×C3⋊C8—21no—
545C3×C3⋊C8—21no—
546C3×C3⋊C8—31no—
547C3×C3⋊C8—31no—
548C3×C3⋊C8—31no—
549C3×C3⋊C8—31no—
550C3×C3⋊C8—61no—
551C3×C3⋊C8—61no—
552C3×C3⋊C8C22×D311yescharacteristic
553C3×C3⋊C8C22×D311yescharacteristic
554C3×C3⋊C8C23×C311yescharacteristic
555C3×C3⋊C8C23×C311yescharacteristic
556#575—91noSylow
557C2×C33—21no—
558C2×C33—41no—
559C2×C33C22×D411yescharacteristic
560C3×C3⋊D3—41no—
561C32×D3—21no—
562C32×D3—21no—
563C32×D3—41no—
564C32×D3—41no—
565C3×#41—21no—
566C3×#41—21no—
567C3×#41—21no—
568C3×#41—31no—
569C3×#41—31no—
570C3×#41—31no—
571C3×#41—31no—
572C3×#41—31no—
573C3×#41—31no—
574C3×#41—31no—
575C3×#41—31no—
576C3×#41—41no—
577C3×#41—61no—
578C3×#41—61no—
579C3×#41—61no—
580C3×#41—61no—
581C3×#41—61no—
582C3×#41—61no—
583C3×#41—62no—
584C3×#41—61no—
585C3×#41—61no—
586C3×#41—62no—
587C3×#41—91no—
588C3×#41—91no—
589C3×#41—91no—
590C3×#41—181no—
591C3×#41—181no—
592C3×#41D3211yescharacteristic, complemented
593C3×#41C2×C3×D311yescharacteristic, complemented
594C3×#41C2×C3×D311yescharacteristic, complemented
595C2×C3×Q8—31no—
596C2×C3×Q8—31no—
597C2×C3×Q8—61no—
598C2×C3×Q8—91no—
599C2×C3×D4—31no—
600C2×C3×D4—31no—
601C2×C3×D4—61no—
602C2×C3×D4—61no—
603C2×C3×D4—61no—
604C2×C3×D4—62no—
605C2×C3×D4—91no—
606C2×C3×D4—181no—
607C22×C3×C4—31no—
608C22×C3×C4—31no—
609C22×C3×C4—61no—
610C22×C3×C4—61no—
611C22×C3×C4—61no—
612C22×C3×C4—62no—
613C22×C3×C4—181no—
614C2×#67—61no—
615#239—31no—
616#239C2×C3×D311yescharacteristic
617D3×Q8—31no—
618D3×Q8C2×C3×D311yescharacteristic, complemented
619#237—21no—
620#237—31no—
621#237—61no—
622#237C2×C3×D311yescharacteristic
623D3×D4—21no—
624D3×D4—31no—
625D3×D4—61no—
626D3×D4C2×C3×D311yescharacteristic, complemented
627#235—21no—
628#235—31no—
629#235—31no—
630#235—31no—
631#235—31no—
632#235—61no—
633#235—61no—
634#235—61no—
635#235—61no—
636#235C2×C3×D311yescharacteristic, complemented
637#235C2×C3×D311yescharacteristic, complemented
638C2×D12—31no—
639C2×C4×D3—21no—
640C2×C4×D3—61no—
641C2×C4×D3—61no—
642C2×C4×D3C2×C3×D311yescharacteristic
643C2×Dic6—31no—
644C3×Q16—31no—
645C3×Q16—31no—
646C3×Q16—61no—
647C3×Q16—91no—
648C3×Q16—91no—
649C3×Q16—91no—
650C3×SD16—31no—
651C3×SD16—31no—
652C3×SD16—31no—
653C3×SD16—31no—
654C3×SD16—61no—
655C3×SD16—61no—
656C3×SD16—91no—
657C3×SD16—91no—
658C3×SD16—91no—
659C3×SD16—91no—
660C3×SD16—91no—
661C3×SD16—91no—
662C3×D8—31no—
663C3×D8—31no—
664C3×D8—61no—
665C3×D8—91no—
666C3×D8—91no—
667C3×D8—91no—
668C3×M16—91no—
669C3×M16—91no—
670C3×M16—91no—
671C3×M16—91no—
672C2×C3×C8—31no—
673C2×C3×C8—31no—
674C2×C3×C8—61no—
675C2×C3×C8—91no—
676#216—31no—
677#216—31no—
678#216—31no—
679#216—31no—
680#216—31no—
681#216—61no—
682#216C2×C3×D311yescharacteristic, complemented
683#215—31no—
684#215—31no—
685#215—31no—
686#215—31no—
687#215—31no—
688#215—61no—
689#215C2×C3×D311yescharacteristic, complemented
690#214—31no—
691#214—31no—
692#214—31no—
693#214—31no—
694#214—31no—
695#214—61no—
696#214C2×C3×D311yescharacteristic, complemented
697#213—31no—
698#213—31no—
699#213—31no—
700#213—31no—
701#213—31no—
702#213—61no—
703#213C2×C3×D311yescharacteristic, complemented
704#208—31no—
705#208—31no—
706#208—31no—
707#208—31no—
708C2×C3⋊C8—31no—
709C2×C3⋊C8—31no—
710C2×C3⋊C8—61no—
711C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
712Dic12—31no—
713D24—31no—
714#204—31no—
715#204—31no—
716ΓL(1,𝔽25)—31no—
717ΓL(1,𝔽25)—31no—
718ΓL(1,𝔽25)—31no—
719ΓL(1,𝔽25)—31no—
720C22×C32—21no—
721C22×C32—22no—
722C22×C32—21no—
723C22×C32—21no—
724C22×C32—21no—
725C22×C32—21no—
726C22×C32—21no—
727C22×C32—31no—
728C22×C32—31no—
729C22×C32—41no—
730C22×C32—41no—
731C22×C32—41no—
732C22×C32—42no—
733C22×C32—61no—
734C22×C32—61no—
735C22×C32—121no—
736C22×C32—122no—
737C22×C32D3×D411yescharacteristic
738C22×C32C2×#6711yescharacteristic
739C22×C32C2×C3×D411yescharacteristic
740C2×C3⋊D3—21no—
741C2×C3×D3—22no—
742C2×C3×D3—21no—
743C2×C3×D3—21no—
744C2×C3×D3—21no—
745C2×C3×D3—21no—
746C2×C3×D3—21no—
747C2×C3×D3—21no—
748C2×C3×D3—41no—
749C2×C3×D3—41no—
750C2×C3×D3—41no—
751C2×C3×D3—42no—
752C2×C3×D3—44no—
753C2×C3×D3—42no—
754C2×C3×D3—42no—
755C2×C3×D3—61no—
756C2×C3×D3—61no—
757C2×C3×D3—121no—
758C2×C3×D3—122no—
759C2×C3×D3—122no—
760C2×C3×D3C2×#6711yescharacteristic
761C2×C3×D3C2×#6711yescharacteristic
762C2×C3×D3C2×C3×D411yescharacteristic
763C2×C3×D3C2×C3×D411yescharacteristic
764D32—42no—
765C32×C4—21no—
766C32×C4—22no—
767C32×C4—21no—
768C32×C4—21no—
769C32×C4—21no—
770C32×C4—21no—
771C32×C4—21no—
772C32×C4—21no—
773C32×C4—21no—
774C32×C4—21no—
775C32×C4—31no—
776C32×C4—31no—
777C32×C4—41no—
778C32×C4—41no—
779C32×C4—41no—
780C32×C4—41no—
781C32×C4—42no—
782C32×C4—61no—
783C32×C4—61no—
784C32×C4D3×D411yescharacteristic
785C32×C4C2×#6711yescharacteristic
786C32×C4C2×C3×D411yescharacteristic
787C32×C4C23×D311yescharacteristic
788C32×C4C23×D311yescharacteristic
789C32×C4C24×C311yescharacteristic
790C3⋊Dic3—21no—
791C3×Dic3—22no—
792C3×Dic3—21no—
793C3×Dic3—21no—
794C3×Dic3—21no—
795C3×Dic3—21no—
796C3×Dic3—21no—
797C3×Dic3—21no—
798C3×Dic3—41no—
799C3×Dic3—61no—
800C3×Dic3—61no—
801C3×Dic3—121no—
802C3×Dic3C2×#6711yescharacteristic
803C3×Dic3C2×#6711yescharacteristic
804C3×Dic3C2×C3×D411yescharacteristic
805C3×Dic3C2×C3×D411yescharacteristic
806C2×#41—31no—
807C2×#41—91no—
808#137—91no—
809#137—91no—
810#137—91no—
811#137—91no—
812AGL(1,ℤ/8)—91no—
813AGL(1,ℤ/8)—91no—
814AGL(1,ℤ/8)—91no—
815AGL(1,ℤ/8)—91no—
816#135—31no—
817#135—91no—
818#135—91no—
819#135—91no—
820C2×M16—91no—
821C33#57511yescharacteristic, complemented, Sylow
822C23×C3—31no—
823C23×C3—31no—
824C23×C3—61no—
825C23×C3—61no—
826C23×C3—61no—
827C23×C3—62no—
828C23×C3—181no—
829C22×D3—21no—
830C22×D3—61no—
831C22×D3—61no—
832C22×D3C3×#6711yescharacteristic
833C3×Q8—21no—
834C3×Q8—21no—
835C3×Q8—21no—
836C3×Q8—31no—
837C3×Q8—31no—
838C3×Q8—31no—
839C3×Q8—31no—
840C3×Q8—41no—
841C3×Q8—61no—
842C3×Q8—61no—
843C3×Q8—61no—
844C3×Q8—61no—
845C3×Q8—62no—
846C3×Q8—91no—
847C3×Q8—181no—
848C3×Q8C2×D3211yescharacteristic
849C3×Q8C22×C3×D311yescharacteristic
850C3×Q8C22×C3×D311yescharacteristic
851C3×D4—22no—
852C3×D4—21no—
853C3×D4—21no—
854C3×D4—21no—
855C3×D4—21no—
856C3×D4—21no—
857C3×D4—21no—
858C3×D4—31no—
859C3×D4—31no—
860C3×D4—31no—
861C3×D4—31no—
862C3×D4—41no—
863C3×D4—41no—
864C3×D4—42no—
865C3×D4—41no—
866C3×D4—61no—
867C3×D4—61no—
868C3×D4—61no—
869C3×D4—61no—
870C3×D4—62no—
871C3×D4—61no—
872C3×D4—61no—
873C3×D4—61no—
874C3×D4—61no—
875C3×D4—62no—
876C3×D4—62no—
877C3×D4—62no—
878C3×D4—61no—
879C3×D4—61no—
880C3×D4—61no—
881C3×D4—61no—
882C3×D4—91no—
883C3×D4—121no—
884C3×D4—181no—
885C3×D4—181no—
886C3×D4—181no—
887C3×D4—181no—
888C3×D4C2×D3211yescharacteristic
889C3×D4C22×C3×D311yescharacteristic
890C3×D4C22×C3×D311yescharacteristic
891C2×C3×C4—22no—
892C2×C3×C4—21no—
893C2×C3×C4—21no—
894C2×C3×C4—21no—
895C2×C3×C4—21no—
896C2×C3×C4—21no—
897C2×C3×C4—21no—
898C2×C3×C4—31no—
899C2×C3×C4—31no—
900C2×C3×C4—31no—
901C2×C3×C4—31no—
902C2×C3×C4—31no—
903C2×C3×C4—31no—
904C2×C3×C4—31no—
905C2×C3×C4—31no—
906C2×C3×C4—31no—
907C2×C3×C4—31no—
908C2×C3×C4—41no—
909C2×C3×C4—41no—
910C2×C3×C4—42no—
911C2×C3×C4—41no—
912C2×C3×C4—61no—
913C2×C3×C4—61no—
914C2×C3×C4—61no—
915C2×C3×C4—61no—
916C2×C3×C4—61no—
917C2×C3×C4—61no—
918C2×C3×C4—61no—
919C2×C3×C4—61no—
920C2×C3×C4—61no—
921C2×C3×C4—62no—
922C2×C3×C4—62no—
923C2×C3×C4—62no—
924C2×C3×C4—61no—
925C2×C3×C4—61no—
926C2×C3×C4—62no—
927C2×C3×C4—61no—
928C2×C3×C4—61no—
929C2×C3×C4—61no—
930C2×C3×C4—61no—
931C2×C3×C4—121no—
932C2×C3×C4—181no—
933C2×C3×C4—181no—
934C2×C3×C4—181no—
935C2×C3×C4—181no—
936C2×C3×C4C2×D3211yescharacteristic
937C2×C3×C4C22×C3×D311yescharacteristic
938C2×C3×C4C22×C3×D311yescharacteristic
939#67—21no—
940#67—21no—
941#67—21no—
942#67—21no—
943#67—61no—
944#67—61no—
945#67—61no—
946#67—61no—
947#67—61no—
948#67—61no—
949#67—121no—
950C2×Dic3—21no—
951C2×Dic3—61no—
952C2×Dic3—61no—
953C2×Dic3C3×#6711yescharacteristic
954D12—21no—
955D12—31no—
956D12—31no—
957D12—61no—
958D12—61no—
959D12—61no—
960D12C22×C3×D311yescharacteristic
961D12C22×C3×D311yescharacteristic
962C4×D3—21no—
963C4×D3—21no—
964C4×D3—21no—
965C4×D3—21no—
966C4×D3—61no—
967C4×D3—61no—
968C4×D3—61no—
969C4×D3—61no—
970C4×D3—61no—
971C4×D3—61no—
972C4×D3—121no—
973C4×D3C3×#6711yescharacteristic
974C4×D3C3×#6711yescharacteristic
975C4×D3C22×C3×D311yescharacteristic
976C4×D3C22×C3×D311yescharacteristic
977Dic6—21no—
978Dic6—31no—
979Dic6—31no—
980Dic6—61no—
981Dic6—61no—
982Dic6—61no—
983Dic6C22×C3×D311yescharacteristic
984Dic6C22×C3×D311yescharacteristic
985C3×C8—31no—
986C3×C8—31no—
987C3×C8—31no—
988C3×C8—31no—
989C3×C8—61no—
990C3×C8—61no—
991C3×C8—91no—
992C3×C8—91no—
993C3⋊C8—31no—
994C3⋊C8—31no—
995C3⋊C8—31no—
996C3⋊C8—31no—
997C3⋊C8—61no—
998C3⋊C8—61no—
999C3⋊C8C22×C3×D311yescharacteristic
1000C3⋊C8C22×C3×D311yescharacteristic
1001C2×C32—21no—
1002C2×C32—21no—
1003C2×C32—21no—
1004C2×C32—21no—
1005C2×C32—21no—
1006C2×C32—21no—
1007C2×C32—41no—
1008C2×C32—41no—
1009C2×C32—41no—
1010C2×C32—41no—
1011C2×C32—41no—
1012C2×C32—42no—
1013C2×C32—41no—
1014C2×C32—41no—
1015C2×C32—61no—
1016C2×C32—61no—
1017C2×C32—81no—
1018C2×C32—81no—
1019C2×C32—81no—
1020C2×C32—82no—
1021C2×C32—121no—
1022C2×C32—121no—
1023C2×C32C2×D3×D411yescharacteristic
1024C2×C32C22×#6711yescharacteristic
1025C2×C32C22×C3×D411yescharacteristic
1026C3⋊D3—41no—
1027C3×D3—22no—
1028C3×D3—21no—
1029C3×D3—21no—
1030C3×D3—21no—
1031C3×D3—21no—
1032C3×D3—41no—
1033C3×D3—42no—
1034C3×D3—41no—
1035C3×D3—41no—
1036C3×D3—41no—
1037C3×D3—41no—
1038C3×D3—81no—
1039C3×D3—121no—
1040C3×D3—121no—
1041C3×D3—241no—
1042#41—31no—
1043#41—31no—
1044#41—31no—
1045#41—31no—
1046#41—61no—
1047#41—61no—
1048#41—91no—
1049#41—91no—
1050#41—91no—
1051#41—181no—
1052#41—181no—
1053#41C3×D3211yescharacteristic, complemented
1054C2×Q8—31no—
1055C2×Q8—91no—
1056C2×D4—31no—
1057C2×D4—61no—
1058C2×D4—91no—
1059C2×D4—181no—
1060C22×C4—31no—
1061C22×C4—61no—
1062C22×C4—181no—
1063Q16—31no—
1064Q16—91no—
1065Q16—91no—
1066Q16—91no—
1067SD16—31no—
1068SD16—31no—
1069SD16—91no—
1070SD16—91no—
1071SD16—91no—
1072SD16—91no—
1073SD16—91no—
1074SD16—91no—
1075D8—31no—
1076D8—91no—
1077D8—91no—
1078D8—91no—
1079M16—91no—
1080M16—91no—
1081M16—91no—
1082M16—91no—
1083C2×C8—31no—
1084C2×C8—91no—
1085C22×C3—22no—
1086C22×C3—21no—
1087C22×C3—21no—
1088C22×C3—21no—
1089C22×C3—21no—
1090C22×C3—21no—
1091C22×C3—21no—
1092C22×C3—31no—
1093C22×C3—31no—
1094C22×C3—31no—
1095C22×C3—31no—
1096C22×C3—41no—
1097C22×C3—41no—
1098C22×C3—42no—
1099C22×C3—41no—
1100C22×C3—61no—
1101C22×C3—61no—
1102C22×C3—62no—
1103C22×C3—61no—
1104C22×C3—61no—
1105C22×C3—61no—
1106C22×C3—61no—
1107C22×C3—121no—
1108C22×C3—121no—
1109C22×C3—121no—
1110C22×C3—122no—
1111C22×C3—124no—
1112C22×C3—122no—
1113C22×C3—122no—
1114C22×C3—181no—
1115C22×C3—362no—
1116C22×C3D3×#6711yescharacteristic
1117C22×C3C3×D3×D411yescharacteristic
1118C22×C3C2×C3×#6711yescharacteristic
1119C2×D3—21no—
1120C2×D3—21no—
1121C2×D3—41no—
1122C2×D3—42no—
1123C2×D3—61no—
1124C2×D3—61no—
1125C2×D3—121no—
1126C2×D3—122no—
1127C2×D3—122no—
1128C2×D3C2×C3×#6711yescharacteristic
1129C2×D3C2×C3×#6711yescharacteristic
1130C3×C4—22no—
1131C3×C4—21no—
1132C3×C4—21no—
1133C3×C4—21no—
1134C3×C4—21no—
1135C3×C4—21no—
1136C3×C4—21no—
1137C3×C4—21no—
1138C3×C4—21no—
1139C3×C4—21no—
1140C3×C4—31no—
1141C3×C4—31no—
1142C3×C4—31no—
1143C3×C4—31no—
1144C3×C4—41no—
1145C3×C4—41no—
1146C3×C4—42no—
1147C3×C4—41no—
1148C3×C4—41no—
1149C3×C4—61no—
1150C3×C4—61no—
1151C3×C4—62no—
1152C3×C4—61no—
1153C3×C4—61no—
1154C3×C4—61no—
1155C3×C4—61no—
1156C3×C4—121no—
1157C3×C4—181no—
1158C3×C4D3×#6711yescharacteristic
1159C3×C4C3×D3×D411yescharacteristic
1160C3×C4C2×C3×#6711yescharacteristic
1161C3×C4C22×D3211yescharacteristic
1162C3×C4C23×C3×D311yescharacteristic
1163C3×C4C23×C3×D311yescharacteristic
1164Dic3—21no—
1165Dic3—21no—
1166Dic3—61no—
1167Dic3—61no—
1168Dic3—121no—
1169Dic3C2×C3×#6711yescharacteristic
1170Dic3C2×C3×#6711yescharacteristic
1171C32—21no—
1172C32—21no—
1173C32—21no—
1174C32—41no—
1175C32#576811yescharacteristic, complemented
1176C32#582211yescharacteristic, complemented
1177C32C3×#57511yescharacteristic, complemented
1178C23—31no—
1179C23—61no—
1180C23—181no—
1181Q8—31no—
1182Q8—31no—
1183Q8—61no—
1184Q8—91no—
1185Q8—181no—
1186Q8C2×C3×D3211yescharacteristic
1187D4—21no—
1188D4—31no—
1189D4—31no—
1190D4—61no—
1191D4—61no—
1192D4—61no—
1193D4—61no—
1194D4—61no—
1195D4—91no—
1196D4—181no—
1197D4—181no—
1198D4—181no—
1199D4—181no—
1200D4C2×C3×D3211yescharacteristic
1201C2×C4—21no—
1202C2×C4—31no—
1203C2×C4—31no—
1204C2×C4—31no—
1205C2×C4—31no—
1206C2×C4—31no—
1207C2×C4—61no—
1208C2×C4—61no—
1209C2×C4—61no—
1210C2×C4—61no—
1211C2×C4—61no—
1212C2×C4—181no—
1213C2×C4—181no—
1214C2×C4—181no—
1215C2×C4—181no—
1216C2×C4C2×C3×D3211yescharacteristic
1217C8—31no—
1218C8—31no—
1219C8—91no—
1220C8—91no—
1221C2×C3—21no—
1222C2×C3—21no—
1223C2×C3—21no—
1224C2×C3—21no—
1225C2×C3—21no—
1226C2×C3—21no—
1227C2×C3—41no—
1228C2×C3—41no—
1229C2×C3—41no—
1230C2×C3—42no—
1231C2×C3—41no—
1232C2×C3—41no—
1233C2×C3—41no—
1234C2×C3—41no—
1235C2×C3—62no—
1236C2×C3—61no—
1237C2×C3—61no—
1238C2×C3—61no—
1239C2×C3—61no—
1240C2×C3—81no—
1241C2×C3—81no—
1242C2×C3—81no—
1243C2×C3—82no—
1244C2×C3—121no—
1245C2×C3—122no—
1246C2×C3—121no—
1247C2×C3—121no—
1248C2×C3—121no—
1249C2×C3—121no—
1250C2×C3—241no—
1251C2×C3—361no—
1252C2×C3C2×D3×#6711yescharacteristic
1253C2×C3C2×C3×D3×D411yescharacteristic
1254C2×C3C22×C3×#6711yescharacteristic
1255D3—21no—
1256D3—21no—
1257D3—41no—
1258D3—41no—
1259D3—121no—
1260D3—121no—
1261D3—241no—
1262C22—21no—
1263C22—31no—
1264C22—31no—
1265C22—61no—
1266C22—61no—
1267C22—121no—
1268C22—122no—
1269C22—181no—
1270C22—362no—
1271C22C3×D3×#6711yescharacteristic
1272C4—21no—
1273C4—31no—
1274C4—31no—
1275C4—61no—
1276C4—61no—
1277C4—181no—
1278C4C3×D3×#6711yescharacteristic
1279C4C22×C3×D3211yescharacteristic
1280C3—21no—
1281C3—21no—
1282C3—21no—
1283C3—41no—
1284C3#1059545311yescharacteristic, direct product factor
1285C3C3×#576811yescharacteristic, complemented
1286C3C3×#582211yescharacteristic, complemented
1287C2—21no—
1288C2—41no—
1289C2—61no—
1290C2—61no—
1291C2—121no—
1292C2—121no—
1293C2—361no—
1294C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC3×C4D3×#67
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C3×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×D3×#41C2semidirect
2. C3×D3×#235C2semidirect
3. C3×#64159C2semidirect
4. C32×#950C2semidirect
5. C3×#63948C2semidirect
6. C3×#63946C2semidirect
7. C3×#63943C2semidirect
8. C3×#63939C2semidirect
9. C3×#63934C2semidirect
10. C3×#63932C2semidirect
11. C3×#63929C2semidirect
12. C3×#63925C2semidirect
13. C3×#63829C2semidirect
14. C3×#63822C2semidirect
15. C2×C3×#3711C2semidirect
18. #10595453C3direct (N × H)
19. C33×#41C22semidirect
20. C3×#3828C22semidirect
22. C32×D3×Q8C22semidirect
26. C32×D3×D4C22semidirect
28. C32×#235C22semidirect
29. C32×#235C22semidirect
34. C3×D3×D12C22semidirect
39. C3×D3×Dic6C22semidirect
40. C3×#3756C22semidirect
41. C3×#3755C22semidirect
42. C3×#3754C22semidirect
43. C3×#3753C22semidirect
44. C2×C3×C3⋊(C3⋊C8)C22semidirect
45. C32×#216C22semidirect
46. C32×#215C22semidirect
47. C32×#214C22semidirect
48. C32×#213C22semidirect
49. C2×C32×C3⋊C8C22semidirect
50. C3×#3719C22semidirect
51. C3×#3718C22semidirect
52. C3×#3717C22semidirect
53. C3×#3716C22semidirect
54. C3×#3715C22semidirect
55. C3×#3715C22semidirect
56. C3×#3714C22semidirect
57. C3×#3713C22semidirect
58. C3×#3711C22semidirect
59. C3×#3711C22semidirect
60. C3×#3711C22semidirect
61. C3×#3711C22semidirect
65. C3×D3×#41D3semidirect
66. C3×D3×#41C2×C3semidirect
68. D3×#235C2×C3semidirect
70. #64159C2×C3semidirect
80. C3×#950D3semidirect
81. C3×#950C2×C3semidirect
99. #63948C2×C3semidirect
100. #63946C2×C3semidirect
101. #63943C2×C3semidirect
102. #63939C2×C3semidirect
103. #63934C2×C3semidirect
104. #63932C2×C3semidirect
105. #63929C2×C3semidirect
106. #63925C2×C3semidirect
107. #63829C2×C3semidirect
108. #63822C2×C3semidirect
109. C2×#3711C2×C3semidirect
166. C32×#41C2×D3semidirect
167. C32×#41C2×D3semidirect
168. C32×#41C22×C3semidirect
174. #3828C22×C3semidirect
182. C3×D3×Q8C2×D3semidirect
183. C3×D3×Q8C22×C3semidirect
198. C3×D3×D4C2×D3semidirect
199. C3×D3×D4C22×C3semidirect
213. C3×#235C2×D3semidirect
214. C3×#235C2×D3semidirect
215. C3×#235C22×C3semidirect
216. C3×#235C22×C3semidirect
229. D3×D12C22×C3semidirect
234. D3×Dic6C22×C3semidirect
240. #3756C22×C3semidirect
241. #3755C22×C3semidirect
242. #3754C22×C3semidirect
243. #3753C22×C3semidirect
244. C2×C3⋊(C3⋊C8)C22×C3semidirect
252. C3×#216C2×D3semidirect
253. C3×#216C22×C3semidirect
261. C3×#215C2×D3semidirect
262. C3×#215C22×C3semidirect
270. C3×#214C2×D3semidirect
271. C3×#214C22×C3semidirect
279. C3×#213C2×D3semidirect
280. C3×#213C22×C3semidirect
289. C2×C3×C3⋊C8C2×D3semidirect
290. C2×C3×C3⋊C8C22×C3semidirect
299. #3719C22×C3semidirect
300. #3718C22×C3semidirect
301. #3717C22×C3semidirect
302. #3716C22×C3semidirect
303. #3715C22×C3semidirect
304. #3715C22×C3semidirect
305. #3714C22×C3semidirect
306. #3713C22×C3semidirect
307. #3711C22×C3semidirect
308. #3711C22×C3semidirect
309. #3711C22×C3semidirect
310. #3711C22×C3semidirect
334. D3×#41C3×D3semidirect
359. #950C3×D3semidirect
592. C3×#41D32semidirect
593. C3×#41C2×C3×D3semidirect
594. C3×#41C2×C3×D3semidirect
618. D3×Q8C2×C3×D3semidirect
626. D3×D4C2×C3×D3semidirect
636. #235C2×C3×D3semidirect
637. #235C2×C3×D3semidirect
682. #216C2×C3×D3semidirect
689. #215C2×C3×D3semidirect
696. #214C2×C3×D3semidirect
703. #213C2×C3×D3semidirect
711. C2×C3⋊C8C2×C3×D3semidirect
821. C33#575semidirect
1053. #41C3×D32semidirect
1175. C32#5768semidirect
1176. C32#5822semidirect
1177. C32C3×#575semidirect
1284. C3#10595453direct (N × H)
1285. C3C3×#5768semidirect
1286. C3C3×#5822semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×D3×#412
C3×D3×#2352
C3×#641592
C32×#9502
C3×#639482
C3×#639462
C3×#639432
C3×#639392
C3×#639342
C3×#639322
C3×#639292
C3×#639252
C3×#638292
C3×#638222
C2×C3×#37112
C3×#58223
C3×#57683
#105954533