Finite Group Databasebeta

← C3×#10594745 #13174342

Subgroups — C3×#10594745 #13174342

Order 1728.

1258 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64319C211yesmaximal, characteristic, complemented
2C3×D3×#237C211yesmaximal, characteristic, complemented
3C3×#64124C211yesmaximal, characteristic, complemented
4C32×#916C211yesmaximal, characteristic, complemented
5C32×#914C211yesmaximal, characteristic, complemented
6C3×#63951C211yesmaximal, characteristic, complemented
7C3×#63947C211yesmaximal, characteristic, complemented
8C3×#63943C211yesmaximal, characteristic, complemented
9C3×#63933C211yesmaximal, characteristic, complemented
10C3×#63932C211yesmaximal, characteristic, complemented
11C3×#63927C211yesmaximal, characteristic, complemented
12C3×#63807C211yesmaximal, characteristic, complemented
13C3×#63800C211yesmaximal, characteristic, complemented
14C3×#63798C211yesmaximal, characteristic, complemented
15C3×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16C3×#5773—31nomaximal
17C3×#5768—31nomaximal
18#10594745C311yesmaximal, characteristic, direct product factor
19C3×Q8×C3⋊D3C2211yescharacteristic, complemented
20C3×#3830C2211yescharacteristic
21C32×#239C2211yescharacteristic
22C32×#239C2211yescharacteristic, complemented
23C32×#237C2211yescharacteristic, complemented
24C32×D3×D4C2211yescharacteristic, complemented
25C3×D3×#67—21no—
26C3×#3805—21no—
27C3×#3804—21no—
28C2×C3×D3×Dic3—21no—
29C3×#3802—21no—
30C3×#3802C2211yescharacteristic, complemented
31C3×C4×D32—21no—
32C3×C4×D32C2211yescharacteristic
33C3×#3796C2211yescharacteristic
34C3×#3795—21no—
35C3×#3795—21no—
36C3×#3795C2211yescharacteristic
37C3×#3795C2211yescharacteristic, complemented
38C3×#3795C2211yescharacteristic, complemented
39C3×D3×Dic6C2211yescharacteristic, complemented
40C33×SD16C2211yescharacteristic, complemented
41C3×#3756C2211yescharacteristic, complemented
42C3×#3754C2211yescharacteristic, complemented
43C3×#3746C2211yescharacteristic, complemented
44C3×#3743C2211yescharacteristic, complemented
45C32×#216C2211yescharacteristic, complemented
46C32×#215C2211yescharacteristic, complemented
47C32×#213C2211yescharacteristic, complemented
48C32×#213C2211yescharacteristic, complemented
49C32×D24C2211yescharacteristic, complemented
50C32×#204C2211yescharacteristic, complemented
51C32×ΓL(1,𝔽25)C2211yescharacteristic, complemented
52C32×D3×C8C2211yescharacteristic, complemented
53C3×#3719C2211yescharacteristic, complemented
54C3×#3716C2211yescharacteristic, complemented
55C3×#3716C2211yescharacteristic, complemented
56C3×#3716C2211yescharacteristic, complemented
57C3×#3715C2211yescharacteristic, complemented
58C3×#3713C2211yescharacteristic, complemented
59C3×#3712C2211yescharacteristic, complemented
60C3×#3711C2211yescharacteristic, complemented
61C3×D3×C3⋊C8C2211yescharacteristic, complemented
62C3×D3×#41—31no—
63C3×D3×#41—31no—
64C3×D3×#41—31no—
65C2×C3×#237—31no—
66#64319C2×C311yescharacteristic, complemented
67D3×#237C2×C311yescharacteristic, complemented
68C32×AGL(1,ℤ/8)—31no—
69C32×#135—31no—
70#64124C2×C311yescharacteristic, complemented
71C3×#951—31no—
72C3×#950—31no—
73C3×#950—31no—
74C3×#932—31no—
75C3×#918—31no—
76C3×#918—31no—
77C3×#916—21no—
78C3×#916—31no—
79C3×#916D311yescharacteristic, complemented
80C3×#916C2×C311yescharacteristic, complemented
81C3×#915—31no—
82C3×#915—31no—
83C3×#915—31no—
84C3×#915—31no—
85C3×#915—61no—
86C3×#914—21no—
87C3×#914—31no—
88C3×#914D311yescharacteristic, complemented
89C3×#914C2×C311yescharacteristic, complemented
90C3×#912—31no—
91C3×#912—31no—
92C3×#911—31no—
93C3×#911—31no—
94C3×#911—31no—
95C3×#911—31no—
96C3×#909—31no—
97C3×D3×M16—31no—
98C3×#904—31no—
99C2×C3×ΓL(1,𝔽25)—31no—
100#63951C2×C311yescharacteristic, complemented
101#63947C2×C311yescharacteristic, complemented
102#63943C2×C311yescharacteristic, complemented
103#63933C2×C311yescharacteristic, complemented
104#63932C2×C311yescharacteristic, complemented
105#63927C2×C311yescharacteristic, complemented
106#63807C2×C311yescharacteristic, complemented
107#63800C2×C311yescharacteristic, complemented
108#63798C2×C311yescharacteristic, complemented
109D3×ΓL(1,𝔽25)C2×C311yescharacteristic, complemented
110C22×C32×D3—21no—
111C2×C3×D32—21no—
112C2×C3×D32D411yescharacteristic
113C33×Q8C2311yescharacteristic
114C33×D4C2311yescharacteristic
115C3×#638—21no—
116C2×C3×C3⋊Dic3—21no—
117C3×C4×C3⋊D3—21no—
118C3×C4×C3⋊D3C2311yescharacteristic
119C3×#634—21no—
120C3×#634C2311yescharacteristic
121C3×#634C2311yescharacteristic
122C32×#67—21no—
123C32×#67—21no—
124C2×C32×Dic3—21no—
125C32×D12—21no—
126C32×D12—21no—
127C32×D12C2311yescharacteristic
128C32×D12C2311yescharacteristic
129C32×D12C2311yescharacteristic
130C32×C4×D3—21no—
131C32×C4×D3—21no—
132C32×C4×D3C2311yescharacteristic
133C32×C4×D3C2311yescharacteristic
134C32×Dic6C2311yescharacteristic
135C3×#627—21no—
136C3×#626—21no—
137C3×#625—21no—
138C3×#625—21no—
139C3×#625—21no—
140C3×#625—21no—
141C3×#624D411yescharacteristic
142C3×D3×Dic3—21no—
143C3×D3×Dic3—21no—
144C3×D3×Dic3—21no—
145C3×D3×Dic3—21no—
146C3×D3×Dic3—21no—
147C3×D3×Dic3D411yescharacteristic
148C3×D3×Dic3D411yescharacteristic
149C33×C8C2311yescharacteristic
150C3×C3⋊(C3⋊C8)C2311yescharacteristic
151C32×C3⋊C8C2311yescharacteristic
152C32×C3⋊C8C2311yescharacteristic
153C3×#575—91no—
154#5773—31no—
155#5768—31no—
156C32×#41—31no—
157C32×#41—31no—
158C32×#41—31no—
159C2×C32×D4—31no—
160Q8×C3⋊D3C22×C311yescharacteristic, complemented
161#3830C22×C311yescharacteristic
162C2×C3×#67—61no—
163C22×C3×Dic3—61no—
164C3×#239—21no—
165C3×#239—21no—
166C3×#239—31no—
167C3×#239C2×D311yescharacteristic
168C3×#239C2×D311yescharacteristic, complemented
169C3×#239C22×C311yescharacteristic
170C3×#239C22×C311yescharacteristic, complemented
171C3×D3×Q8—31no—
172C3×D3×Q8—31no—
173C3×D3×Q8—31no—
174C3×D3×Q8—61no—
175C3×#237—21no—
176C3×#237—31no—
177C3×#237—31no—
178C3×#237—31no—
179C3×#237—31no—
180C3×#237—31no—
181C3×#237—31no—
182C3×#237—61no—
183C3×#237—61no—
184C3×#237—61no—
185C3×#237—61no—
186C3×#237—61no—
187C3×#237—61no—
188C3×#237C2×D311yescharacteristic, complemented
189C3×#237C22×C311yescharacteristic, complemented
190C3×D3×D4—21no—
191C3×D3×D4—31no—
192C3×D3×D4—31no—
193C3×D3×D4—61no—
194C3×D3×D4—61no—
195C3×D3×D4—61no—
196C3×D3×D4C2×D311yescharacteristic, complemented
197C3×D3×D4C22×C311yescharacteristic, complemented
198C3×#235—31no—
199C3×#235—31no—
200C3×#235—31no—
201C3×#235—61no—
202C3×#235—61no—
203C3×#235—61no—
204C2×C3×C4×D3—31no—
205C2×C3×C4×D3—31no—
206C2×C3×C4×D3—61no—
207C2×C3×C4×D3—61no—
208C2×C3×C4×D3—61no—
209C2×C3×Dic6—31no—
210D3×#67—21no—
211#3805—21no—
212#3804—21no—
213C2×D3×Dic3—21no—
214#3802—21no—
215#3802C22×C311yescharacteristic, complemented
216C4×D32—21no—
217C4×D32C22×C311yescharacteristic
218#3796C22×C311yescharacteristic
219#3795—21no—
220#3795—21no—
221#3795C22×C311yescharacteristic
222#3795C22×C311yescharacteristic, complemented
223#3795C22×C311yescharacteristic, complemented
224D3×Dic6C22×C311yescharacteristic, complemented
225C32×Q16—31no—
226C32×SD16—21no—
227C32×SD16—21no—
228C32×SD16—21no—
229C32×SD16—31no—
230C32×SD16—31no—
231C32×SD16—41no—
232C32×SD16C2×D311yescharacteristic, complemented
233C32×SD16C2×D311yescharacteristic, complemented
234C32×SD16C22×C311yescharacteristic, complemented
235C32×D8—31no—
236C32×D8—31no—
237C32×D8—31no—
238C32×M16—31no—
239C2×C32×C8—31no—
240#3756C22×C311yescharacteristic, complemented
241#3754C22×C311yescharacteristic, complemented
242#3746C22×C311yescharacteristic, complemented
243#3743C22×C311yescharacteristic, complemented
244C3×#216—21no—
245C3×#216—31no—
246C3×#216—31no—
247C3×#216—31no—
248C3×#216—61no—
249C3×#216C2×D311yescharacteristic, complemented
250C3×#216C22×C311yescharacteristic, complemented
251C3×#215—21no—
252C3×#215—31no—
253C3×#215C2×D311yescharacteristic, complemented
254C3×#215C22×C311yescharacteristic, complemented
255C3×#214—31no—
256C3×#214—31no—
257C3×#214—31no—
258C3×#214—31no—
259C3×#214—31no—
260C3×#214—31no—
261C3×#214—61no—
262C3×#213—21no—
263C3×#213—21no—
264C3×#213—31no—
265C3×#213—31no—
266C3×#213C2×D311yescharacteristic, complemented
267C3×#213C2×D311yescharacteristic, complemented
268C3×#213C22×C311yescharacteristic, complemented
269C3×#213C22×C311yescharacteristic, complemented
270C3×#208—31no—
271C2×C3×C3⋊C8—31no—
272C3×Dic12—31no—
273C3×Dic12—31no—
274C3×Dic12—31no—
275C3×Dic12—61no—
276C3×D24—21no—
277C3×D24C2×D311yescharacteristic, complemented
278C3×D24C22×C311yescharacteristic, complemented
279C3×#204—21no—
280C3×#204—31no—
281C3×#204—31no—
282C3×#204—31no—
283C3×#204C2×D311yescharacteristic, complemented
284C3×#204C22×C311yescharacteristic, complemented
285C3×ΓL(1,𝔽25)—21no—
286C3×ΓL(1,𝔽25)—31no—
287C3×ΓL(1,𝔽25)—31no—
288C3×ΓL(1,𝔽25)—31no—
289C3×ΓL(1,𝔽25)—31no—
290C3×ΓL(1,𝔽25)—31no—
291C3×ΓL(1,𝔽25)—61no—
292C3×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
293C3×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
294C3×D3×C8—21no—
295C3×D3×C8—31no—
296C3×D3×C8C2×D311yescharacteristic, complemented
297C3×D3×C8C22×C311yescharacteristic, complemented
298#3719C22×C311yescharacteristic, complemented
299#3716C22×C311yescharacteristic, complemented
300#3716C22×C311yescharacteristic, complemented
301#3716C22×C311yescharacteristic, complemented
302#3715C22×C311yescharacteristic, complemented
303#3713C22×C311yescharacteristic, complemented
304#3712C22×C311yescharacteristic, complemented
305#3711C22×C311yescharacteristic, complemented
306D3×C3⋊C8C22×C311yescharacteristic, complemented
307C22×C33—21no—
308C2×C3×C3⋊D3C2×D411yescharacteristic
309C2×C32×D3—21no—
310C2×C32×D3—21no—
311C2×C32×D3—21no—
312C2×C32×D3—42no—
313C2×C32×D3C2×D411yescharacteristic
314C2×C32×D3C2×D411yescharacteristic
315C3×D32—41no—
316C3×D32—42no—
317C33×C4—21no—
318C33×C4C2411yescharacteristic
319C3×C3⋊Dic3—21no—
320C3×C3⋊Dic3—21no—
321C3×C3⋊Dic3C2×D411yescharacteristic
322C32×Dic3—21no—
323C32×Dic3C2×D411yescharacteristic
324C32×Dic3C2×D411yescharacteristic
325C2×C3×#41—91no—
326C2×C3×#41—91no—
327D3×#41—31no—
328D3×#41—31no—
329D3×#41—31no—
330C2×#237—31no—
331C3×#137—91no—
332C3×#137—91no—
333C3×#137—91no—
334C3×#137—91no—
335C3×AGL(1,ℤ/8)—31no—
336C3×AGL(1,ℤ/8)—31no—
337C3×AGL(1,ℤ/8)—61no—
338C3×AGL(1,ℤ/8)—91no—
339C3×AGL(1,ℤ/8)—91no—
340C3×AGL(1,ℤ/8)—91no—
341C3×#135—31no—
342C3×#135—31no—
343C3×#135—61no—
344C3×#135—91no—
345C3×#135—91no—
346C3×#135—91no—
347C2×C3×M16—91no—
348#951—31no—
349#950—31no—
350#950—31no—
351#932—31no—
352#918—31no—
353#918—31no—
354#916—31no—
355#916C3×D311yescharacteristic, complemented
356#915—31no—
357#915—31no—
358#915—31no—
359#915—31no—
360#915—61no—
361#914—31no—
362#914C3×D311yescharacteristic, complemented
363#912—31no—
364#912—31no—
365#911—31no—
366#911—31no—
367#911—31no—
368#911—31no—
369#909—31no—
370D3×M16—31no—
371#904—31no—
372C2×ΓL(1,𝔽25)—31no—
373C23×C32—61no—
374C22×C3×D3—21no—
375C22×C3×D3—21no—
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—41no—
379C22×C3×D3—61no—
380C22×C3×D3—61no—
381C2×D32—21no—
382C2×D32C3×D411yescharacteristic
383C32×Q8—21no—
384C32×Q8—21no—
385C32×Q8—21no—
386C32×Q8—31no—
387C32×Q8—41no—
388C32×Q8C22×D311yescharacteristic
389C32×Q8C22×D311yescharacteristic
390C32×Q8C23×C311yescharacteristic
391C32×D4—21no—
392C32×D4—21no—
393C32×D4—21no—
394C32×D4—31no—
395C32×D4—31no—
396C32×D4—31no—
397C32×D4—41no—
398C32×D4—61no—
399C32×D4—61no—
400C32×D4—61no—
401C32×D4—61no—
402C32×D4C22×D311yescharacteristic
403C32×D4C22×D311yescharacteristic
404C32×D4C23×C311yescharacteristic
405C2×C32×C4—31no—
406C2×C32×C4—31no—
407C2×C32×C4—61no—
408C2×C32×C4—61no—
409C2×C32×C4—61no—
410#638—21no—
411C2×C3⋊Dic3—21no—
412C4×C3⋊D3—21no—
413C4×C3⋊D3C23×C311yescharacteristic
414#634—21no—
415#634C23×C311yescharacteristic
416#634C23×C311yescharacteristic
417C3×#67—21no—
418C3×#67—21no—
419C3×#67—21no—
420C3×#67—21no—
421C3×#67—41no—
422C3×#67—41no—
423C3×#67—61no—
424C3×#67—61no—
425C3×#67—61no—
426C3×#67—61no—
427C3×#67—61no—
428C3×#67—61no—
429C3×#67—61no—
430C3×#67—61no—
431C3×#67—61no—
432C3×#67—61no—
433C3×#67—61no—
434C3×#67—121no—
435C2×C3×Dic3—21no—
436C2×C3×Dic3—21no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—41no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—61no—
443C2×C3×Dic3—61no—
444C2×C3×Dic3—61no—
445C2×C3×Dic3—61no—
446C2×C3×Dic3—61no—
447C2×C3×Dic3—121no—
448C3×D12—21no—
449C3×D12—21no—
450C3×D12—21no—
451C3×D12—21no—
452C3×D12—21no—
453C3×D12—21no—
454C3×D12—21no—
455C3×D12—41no—
456C3×D12—41no—
457C3×D12—61no—
458C3×D12C22×D311yescharacteristic
459C3×D12C22×D311yescharacteristic
460C3×D12C22×D311yescharacteristic
461C3×D12C23×C311yescharacteristic
462C3×D12C23×C311yescharacteristic
463C3×D12C23×C311yescharacteristic
464C3×C4×D3—21no—
465C3×C4×D3—21no—
466C3×C4×D3—21no—
467C3×C4×D3—21no—
468C3×C4×D3—21no—
469C3×C4×D3—21no—
470C3×C4×D3—31no—
471C3×C4×D3—31no—
472C3×C4×D3—31no—
473C3×C4×D3—31no—
474C3×C4×D3—31no—
475C3×C4×D3—31no—
476C3×C4×D3—41no—
477C3×C4×D3—41no—
478C3×C4×D3—61no—
479C3×C4×D3—61no—
480C3×C4×D3—61no—
481C3×C4×D3—61no—
482C3×C4×D3—61no—
483C3×C4×D3—61no—
484C3×C4×D3—61no—
485C3×C4×D3—61no—
486C3×C4×D3—121no—
487C3×C4×D3C22×D311yescharacteristic
488C3×C4×D3C22×D311yescharacteristic
489C3×C4×D3C23×C311yescharacteristic
490C3×C4×D3C23×C311yescharacteristic
491C3×Dic6—21no—
492C3×Dic6—31no—
493C3×Dic6—31no—
494C3×Dic6—31no—
495C3×Dic6—31no—
496C3×Dic6—61no—
497C3×Dic6—61no—
498C3×Dic6—61no—
499C3×Dic6—61no—
500C3×Dic6—61no—
501C3×Dic6—61no—
502C3×Dic6—121no—
503C3×Dic6C22×D311yescharacteristic
504C3×Dic6C23×C311yescharacteristic
505#627—21no—
506#626—21no—
507#625—21no—
508#625—21no—
509#625—21no—
510#625—21no—
511#624C3×D411yescharacteristic
512D3×Dic3—21no—
513D3×Dic3—21no—
514D3×Dic3—21no—
515D3×Dic3—21no—
516D3×Dic3—21no—
517D3×Dic3C3×D411yescharacteristic
518D3×Dic3C3×D411yescharacteristic
519C32×C8—21no—
520C32×C8—21no—
521C32×C8—21no—
522C32×C8—31no—
523C32×C8—31no—
524C32×C8—41no—
525C32×C8C22×D311yescharacteristic
526C32×C8C22×D311yescharacteristic
527C32×C8C23×C311yescharacteristic
528C3⋊(C3⋊C8)C23×C311yescharacteristic
529C3×C3⋊C8—21no—
530C3×C3⋊C8—21no—
531C3×C3⋊C8—31no—
532C3×C3⋊C8—31no—
533C3×C3⋊C8—61no—
534C3×C3⋊C8C22×D311yescharacteristic
535C3×C3⋊C8C22×D311yescharacteristic
536C3×C3⋊C8C23×C311yescharacteristic
537C3×C3⋊C8C23×C311yescharacteristic
538#575—91noSylow
539C2×C33—41no—
540C2×C33C22×D411yescharacteristic
541C3×C3⋊D3—21no—
542C32×D3—21no—
543C32×D3—21no—
544C32×D3—41no—
545C32×D3—41no—
546C32×D3—41no—
547C3×#41—31no—
548C3×#41—31no—
549C3×#41—31no—
550C3×#41—31no—
551C3×#41—31no—
552C3×#41—31no—
553C3×#41—61no—
554C3×#41—61no—
555C3×#41—61no—
556C3×#41—91no—
557C3×#41—91no—
558C3×#41—91no—
559C3×#41—91no—
560C3×#41—91no—
561C3×#41—181no—
562C3×#41—181no—
563C3×#41—181no—
564C3×#41—181no—
565C2×C3×Q8—91no—
566C2×C3×Q8—91no—
567C2×C3×D4—31no—
568C2×C3×D4—31no—
569C2×C3×D4—61no—
570C2×C3×D4—91no—
571C2×C3×D4—181no—
572C2×C3×D4—181no—
573C22×C3×C4—91no—
574C22×C3×C4—181no—
575C22×C3×C4—181no—
576C2×#67—61no—
577C22×Dic3—61no—
578#239—31no—
579#239C2×C3×D311yescharacteristic
580#239C2×C3×D311yescharacteristic, complemented
581D3×Q8—31no—
582D3×Q8—31no—
583D3×Q8—31no—
584D3×Q8—61no—
585#237—31no—
586#237—31no—
587#237—31no—
588#237—31no—
589#237—31no—
590#237—31no—
591#237—61no—
592#237—61no—
593#237—61no—
594#237—61no—
595#237—61no—
596#237—61no—
597#237C2×C3×D311yescharacteristic, complemented
598D3×D4—31no—
599D3×D4—31no—
600D3×D4—61no—
601D3×D4—61no—
602D3×D4—61no—
603D3×D4C2×C3×D311yescharacteristic, complemented
604#235—31no—
605#235—31no—
606#235—31no—
607#235—61no—
608#235—61no—
609#235—61no—
610C2×C4×D3—31no—
611C2×C4×D3—31no—
612C2×C4×D3—61no—
613C2×C4×D3—61no—
614C2×C4×D3—61no—
615C2×Dic6—31no—
616C3×Q16—31no—
617C3×Q16—31no—
618C3×Q16—61no—
619C3×Q16—91no—
620C3×Q16—91no—
621C3×Q16—91no—
622C3×SD16—21no—
623C3×SD16—21no—
624C3×SD16—21no—
625C3×SD16—31no—
626C3×SD16—31no—
627C3×SD16—31no—
628C3×SD16—31no—
629C3×SD16—41no—
630C3×SD16—61no—
631C3×SD16—61no—
632C3×SD16—91no—
633C3×SD16—91no—
634C3×SD16—91no—
635C3×SD16—91no—
636C3×SD16—91no—
637C3×SD16D3211yescharacteristic, complemented
638C3×SD16C2×C3×D311yescharacteristic, complemented
639C3×SD16C2×C3×D311yescharacteristic, complemented
640C3×D8—31no—
641C3×D8—31no—
642C3×D8—31no—
643C3×D8—31no—
644C3×D8—31no—
645C3×D8—31no—
646C3×D8—61no—
647C3×D8—61no—
648C3×D8—61no—
649C3×D8—91no—
650C3×M16—31no—
651C3×M16—31no—
652C3×M16—61no—
653C3×M16—91no—
654C3×M16—91no—
655C3×M16—91no—
656C2×C3×C8—31no—
657C2×C3×C8—31no—
658C2×C3×C8—61no—
659C2×C3×C8—91no—
660#216—31no—
661#216—31no—
662#216—31no—
663#216—61no—
664#216C2×C3×D311yescharacteristic, complemented
665#215—31no—
666#215C2×C3×D311yescharacteristic, complemented
667#214—31no—
668#214—31no—
669#214—31no—
670#214—31no—
671#214—31no—
672#214—31no—
673#214—61no—
674#213—31no—
675#213—31no—
676#213C2×C3×D311yescharacteristic, complemented
677#213C2×C3×D311yescharacteristic, complemented
678#208—31no—
679C2×C3⋊C8—31no—
680Dic12—31no—
681Dic12—31no—
682Dic12—31no—
683Dic12—61no—
684D24C2×C3×D311yescharacteristic, complemented
685#204—31no—
686#204—31no—
687#204—31no—
688#204C2×C3×D311yescharacteristic, complemented
689ΓL(1,𝔽25)—31no—
690ΓL(1,𝔽25)—31no—
691ΓL(1,𝔽25)—31no—
692ΓL(1,𝔽25)—31no—
693ΓL(1,𝔽25)—31no—
694ΓL(1,𝔽25)—61no—
695ΓL(1,𝔽25)C2×C3×D311yescharacteristic, complemented
696D3×C8—31no—
697D3×C8C2×C3×D311yescharacteristic, complemented
698C22×C32—21no—
699C22×C32—21no—
700C22×C32—21no—
701C22×C32—31no—
702C22×C32—31no—
703C22×C32—41no—
704C22×C32—41no—
705C22×C32—41no—
706C22×C32—61no—
707C22×C32—61no—
708C22×C32—61no—
709C22×C32—81no—
710C22×C32—122no—
711C2×C3⋊D3C2×C3×D411yescharacteristic
712C2×C3×D3—21no—
713C2×C3×D3—21no—
714C2×C3×D3—21no—
715C2×C3×D3—21no—
716C2×C3×D3—21no—
717C2×C3×D3—21no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—31no—
721C2×C3×D3—31no—
722C2×C3×D3—41no—
723C2×C3×D3—41no—
724C2×C3×D3—41no—
725C2×C3×D3—42no—
726C2×C3×D3—42no—
727C2×C3×D3—61no—
728C2×C3×D3—82no—
729C2×C3×D3—121no—
730C2×C3×D3—121no—
731C2×C3×D3—122no—
732C2×C3×D3—122no—
733C2×C3×D3D3×D411yescharacteristic
734C2×C3×D3D3×D411yescharacteristic
735C2×C3×D3C2×C3×D411yescharacteristic
736C2×C3×D3C2×C3×D411yescharacteristic
737D32—41no—
738D32—42no—
739C32×C4—21no—
740C32×C4—21no—
741C32×C4—21no—
742C32×C4—21no—
743C32×C4—21no—
744C32×C4—21no—
745C32×C4—31no—
746C32×C4—31no—
747C32×C4—41no—
748C32×C4—41no—
749C32×C4—41no—
750C32×C4—41no—
751C32×C4—61no—
752C32×C4—81no—
753C32×C4C23×D311yescharacteristic
754C32×C4C23×D311yescharacteristic
755C32×C4C24×C311yescharacteristic
756C3⋊Dic3—21no—
757C3⋊Dic3—21no—
758C3⋊Dic3C2×C3×D411yescharacteristic
759C3×Dic3—21no—
760C3×Dic3—21no—
761C3×Dic3—21no—
762C3×Dic3—21no—
763C3×Dic3—31no—
764C3×Dic3—31no—
765C3×Dic3—41no—
766C3×Dic3—61no—
767C3×Dic3—61no—
768C3×Dic3—61no—
769C3×Dic3—61no—
770C3×Dic3—61no—
771C3×Dic3—121no—
772C3×Dic3—121no—
773C3×Dic3D3×D411yescharacteristic
774C3×Dic3D3×D411yescharacteristic
775C3×Dic3C2×C3×D411yescharacteristic
776C3×Dic3C2×C3×D411yescharacteristic
777C2×#41—91no—
778C2×#41—91no—
779#137—91no—
780#137—91no—
781#137—91no—
782#137—91no—
783AGL(1,ℤ/8)—31no—
784AGL(1,ℤ/8)—91no—
785AGL(1,ℤ/8)—91no—
786AGL(1,ℤ/8)—91no—
787#135—31no—
788#135—91no—
789#135—91no—
790#135—91no—
791C2×M16—91no—
792C33#57511yescharacteristic, complemented, Sylow
793C23×C3—61no—
794C23×C3—61no—
795C23×C3—91no—
796C23×C3—121no—
797C23×C3—181no—
798C22×D3—21no—
799C22×D3—31no—
800C22×D3—31no—
801C22×D3—61no—
802C22×D3—61no—
803C3×Q8—21no—
804C3×Q8—21no—
805C3×Q8—21no—
806C3×Q8—31no—
807C3×Q8—31no—
808C3×Q8—41no—
809C3×Q8—61no—
810C3×Q8—91no—
811C3×Q8—91no—
812C3×Q8—181no—
813C3×Q8—181no—
814C3×Q8C2×D3211yescharacteristic
815C3×Q8C22×C3×D311yescharacteristic
816C3×Q8C22×C3×D311yescharacteristic
817C3×D4—21no—
818C3×D4—21no—
819C3×D4—21no—
820C3×D4—31no—
821C3×D4—31no—
822C3×D4—31no—
823C3×D4—31no—
824C3×D4—31no—
825C3×D4—31no—
826C3×D4—41no—
827C3×D4—61no—
828C3×D4—61no—
829C3×D4—61no—
830C3×D4—61no—
831C3×D4—61no—
832C3×D4—61no—
833C3×D4—61no—
834C3×D4—61no—
835C3×D4—61no—
836C3×D4—61no—
837C3×D4—61no—
838C3×D4—121no—
839C3×D4—121no—
840C3×D4—121no—
841C3×D4—121no—
842C3×D4—181no—
843C3×D4—181no—
844C3×D4—181no—
845C3×D4—181no—
846C3×D4—181no—
847C3×D4—181no—
848C3×D4C2×D3211yescharacteristic
849C3×D4C22×C3×D311yescharacteristic
850C3×D4C22×C3×D311yescharacteristic
851C2×C3×C4—31no—
852C2×C3×C4—31no—
853C2×C3×C4—31no—
854C2×C3×C4—31no—
855C2×C3×C4—61no—
856C2×C3×C4—61no—
857C2×C3×C4—61no—
858C2×C3×C4—61no—
859C2×C3×C4—61no—
860C2×C3×C4—61no—
861C2×C3×C4—61no—
862C2×C3×C4—61no—
863C2×C3×C4—91no—
864C2×C3×C4—91no—
865C2×C3×C4—91no—
866C2×C3×C4—91no—
867C2×C3×C4—121no—
868C2×C3×C4—121no—
869C2×C3×C4—121no—
870C2×C3×C4—181no—
871C2×C3×C4—181no—
872C2×C3×C4—181no—
873C2×C3×C4—181no—
874C2×C3×C4—181no—
875C2×C3×C4—181no—
876C2×C3×C4—181no—
877#67—21no—
878#67—21no—
879#67—61no—
880#67—61no—
881#67—61no—
882#67—61no—
883#67—61no—
884#67—61no—
885#67—61no—
886#67—61no—
887#67—61no—
888#67—61no—
889#67—61no—
890#67—121no—
891C2×Dic3—21no—
892C2×Dic3—31no—
893C2×Dic3—31no—
894C2×Dic3—61no—
895C2×Dic3—61no—
896C2×Dic3—61no—
897C2×Dic3—61no—
898C2×Dic3—61no—
899C2×Dic3—61no—
900C2×Dic3—61no—
901C2×Dic3—121no—
902D12—21no—
903D12—21no—
904D12—61no—
905D12C22×C3×D311yescharacteristic
906D12C22×C3×D311yescharacteristic
907D12C22×C3×D311yescharacteristic
908C4×D3—21no—
909C4×D3—21no—
910C4×D3—31no—
911C4×D3—31no—
912C4×D3—31no—
913C4×D3—31no—
914C4×D3—31no—
915C4×D3—31no—
916C4×D3—61no—
917C4×D3—61no—
918C4×D3—61no—
919C4×D3—61no—
920C4×D3—61no—
921C4×D3—61no—
922C4×D3—61no—
923C4×D3—61no—
924C4×D3—121no—
925C4×D3C22×C3×D311yescharacteristic
926C4×D3C22×C3×D311yescharacteristic
927Dic6—31no—
928Dic6—31no—
929Dic6—31no—
930Dic6—31no—
931Dic6—61no—
932Dic6—61no—
933Dic6—61no—
934Dic6—61no—
935Dic6—61no—
936Dic6—61no—
937Dic6—121no—
938Dic6C22×C3×D311yescharacteristic
939C3×C8—21no—
940C3×C8—21no—
941C3×C8—21no—
942C3×C8—31no—
943C3×C8—31no—
944C3×C8—31no—
945C3×C8—31no—
946C3×C8—41no—
947C3×C8—61no—
948C3×C8—61no—
949C3×C8—91no—
950C3×C8C2×D3211yescharacteristic
951C3×C8C22×C3×D311yescharacteristic
952C3×C8C22×C3×D311yescharacteristic
953C3⋊C8—31no—
954C3⋊C8—31no—
955C3⋊C8—61no—
956C3⋊C8C22×C3×D311yescharacteristic
957C3⋊C8C22×C3×D311yescharacteristic
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—21no—
961C2×C32—41no—
962C2×C32—41no—
963C2×C32—41no—
964C2×C32—41no—
965C2×C32—61no—
966C2×C32—61no—
967C2×C32—81no—
968C2×C32—81no—
969C2×C32—81no—
970C2×C32—121no—
971C2×C32—121no—
972C2×C32—121no—
973C2×C32—161no—
974C2×C32C2×D3×D411yescharacteristic
975C2×C32C2×D3×D411yescharacteristic
976C2×C32C22×C3×D411yescharacteristic
977C3⋊D3—21no—
978C3×D3—21no—
979C3×D3—21no—
980C3×D3—21no—
981C3×D3—21no—
982C3×D3—41no—
983C3×D3—41no—
984C3×D3—41no—
985C3×D3—41no—
986C3×D3—41no—
987C3×D3—41no—
988C3×D3—41no—
989C3×D3—41no—
990C3×D3—61no—
991C3×D3—61no—
992C3×D3—81no—
993C3×D3—81no—
994C3×D3—81no—
995C3×D3—121no—
996#41—31no—
997#41—31no—
998#41—31no—
999#41—91no—
1000#41—91no—
1001#41—91no—
1002#41—91no—
1003#41—91no—
1004#41—181no—
1005#41—181no—
1006#41—181no—
1007#41—181no—
1008C2×Q8—91no—
1009C2×Q8—91no—
1010C2×D4—31no—
1011C2×D4—91no—
1012C2×D4—181no—
1013C2×D4—181no—
1014C22×C4—91no—
1015C22×C4—181no—
1016C22×C4—181no—
1017Q16—31no—
1018Q16—91no—
1019Q16—91no—
1020Q16—91no—
1021SD16—31no—
1022SD16—31no—
1023SD16—91no—
1024SD16—91no—
1025SD16—91no—
1026SD16—91no—
1027SD16—91no—
1028SD16C3×D3211yescharacteristic, complemented
1029D8—31no—
1030D8—31no—
1031D8—31no—
1032D8—91no—
1033M16—31no—
1034M16—91no—
1035M16—91no—
1036M16—91no—
1037C2×C8—31no—
1038C2×C8—91no—
1039C22×C3—21no—
1040C22×C3—21no—
1041C22×C3—21no—
1042C22×C3—31no—
1043C22×C3—31no—
1044C22×C3—31no—
1045C22×C3—31no—
1046C22×C3—41no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—61no—
1050C22×C3—61no—
1051C22×C3—61no—
1052C22×C3—61no—
1053C22×C3—61no—
1054C22×C3—61no—
1055C22×C3—61no—
1056C22×C3—61no—
1057C22×C3—81no—
1058C22×C3—91no—
1059C22×C3—121no—
1060C22×C3—121no—
1061C22×C3—121no—
1062C22×C3—122no—
1063C22×C3—122no—
1064C22×C3—242no—
1065C22×C3—361no—
1066C22×C3—362no—
1067C2×D3—21no—
1068C2×D3—21no—
1069C2×D3—21no—
1070C2×D3—31no—
1071C2×D3—31no—
1072C2×D3—42no—
1073C2×D3—61no—
1074C2×D3—121no—
1075C2×D3—121no—
1076C2×D3—122no—
1077C2×D3—122no—
1078C2×D3C3×D3×D411yescharacteristic
1079C2×D3C3×D3×D411yescharacteristic
1080C3×C4—21no—
1081C3×C4—21no—
1082C3×C4—21no—
1083C3×C4—21no—
1084C3×C4—21no—
1085C3×C4—21no—
1086C3×C4—31no—
1087C3×C4—31no—
1088C3×C4—31no—
1089C3×C4—31no—
1090C3×C4—41no—
1091C3×C4—41no—
1092C3×C4—41no—
1093C3×C4—41no—
1094C3×C4—61no—
1095C3×C4—61no—
1096C3×C4—61no—
1097C3×C4—61no—
1098C3×C4—81no—
1099C3×C4—91no—
1100C3×C4—121no—
1101C3×C4—181no—
1102C3×C4—181no—
1103C3×C4C22×D3211yescharacteristic
1104C3×C4C23×C3×D311yescharacteristic
1105C3×C4C23×C3×D311yescharacteristic
1106Dic3—21no—
1107Dic3—31no—
1108Dic3—31no—
1109Dic3—61no—
1110Dic3—61no—
1111Dic3—61no—
1112Dic3—61no—
1113Dic3—61no—
1114Dic3—121no—
1115Dic3—121no—
1116Dic3C3×D3×D411yescharacteristic
1117Dic3C3×D3×D411yescharacteristic
1118C32—21no—
1119C32—21no—
1120C32—21no—
1121C32—41no—
1122C32#576811yescharacteristic, complemented
1123C32#577311yescharacteristic, complemented
1124C32C3×#57511yescharacteristic, complemented
1125C23—61no—
1126C23—91no—
1127C23—181no—
1128Q8—31no—
1129Q8—91no—
1130Q8—91no—
1131Q8—181no—
1132Q8—181no—
1133Q8C2×C3×D3211yescharacteristic
1134D4—31no—
1135D4—31no—
1136D4—31no—
1137D4—61no—
1138D4—61no—
1139D4—61no—
1140D4—61no—
1141D4—181no—
1142D4—181no—
1143D4—181no—
1144D4—181no—
1145D4—181no—
1146D4—181no—
1147D4C2×C3×D3211yescharacteristic
1148C2×C4—31no—
1149C2×C4—31no—
1150C2×C4—61no—
1151C2×C4—61no—
1152C2×C4—61no—
1153C2×C4—91no—
1154C2×C4—91no—
1155C2×C4—91no—
1156C2×C4—91no—
1157C2×C4—181no—
1158C2×C4—181no—
1159C2×C4—181no—
1160C2×C4—181no—
1161C2×C4—181no—
1162C2×C4—181no—
1163C2×C4—181no—
1164C8—31no—
1165C8—31no—
1166C8—91no—
1167C8C2×C3×D3211yescharacteristic
1168C2×C3—21no—
1169C2×C3—21no—
1170C2×C3—21no—
1171C2×C3—41no—
1172C2×C3—41no—
1173C2×C3—41no—
1174C2×C3—41no—
1175C2×C3—61no—
1176C2×C3—61no—
1177C2×C3—61no—
1178C2×C3—61no—
1179C2×C3—81no—
1180C2×C3—81no—
1181C2×C3—81no—
1182C2×C3—121no—
1183C2×C3—121no—
1184C2×C3—121no—
1185C2×C3—121no—
1186C2×C3—121no—
1187C2×C3—121no—
1188C2×C3—121no—
1189C2×C3—121no—
1190C2×C3—161no—
1191C2×C3—181no—
1192C2×C3—241no—
1193C2×C3—241no—
1194C2×C3—241no—
1195C2×C3D32×D411yescharacteristic
1196C2×C3C2×C3×D3×D411yescharacteristic
1197C2×C3C2×C3×D3×D411yescharacteristic
1198D3—21no—
1199D3—21no—
1200D3—41no—
1201D3—41no—
1202D3—41no—
1203D3—61no—
1204D3—61no—
1205D3—121no—
1206C22—21no—
1207C22—31no—
1208C22—31no—
1209C22—61no—
1210C22—61no—
1211C22—61no—
1212C22—91no—
1213C22—122no—
1214C22—361no—
1215C22—362no—
1216C4—21no—
1217C4—31no—
1218C4—31no—
1219C4—61no—
1220C4—91no—
1221C4—181no—
1222C4—181no—
1223C4C22×C3×D3211yescharacteristic
1224C3—21no—
1225C3—21no—
1226C3—21no—
1227C3—41no—
1228C3#1059474511yescharacteristic, direct product factor
1229C3C3×#576811yescharacteristic, complemented
1230C3C3×#577311yescharacteristic, complemented
1231C2—41no—
1232C2—61no—
1233C2—61no—
1234C2—121no—
1235C2—121no—
1236C2—121no—
1237C2—181no—
1238C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×SD16C22
socleC2×C33C22×D4
hypercenterC3×SD16D32
hypocenterC32C3×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#64319C2semidirect
2. C3×D3×#237C2semidirect
3. C3×#64124C2semidirect
4. C32×#916C2semidirect
5. C32×#914C2semidirect
6. C3×#63951C2semidirect
7. C3×#63947C2semidirect
8. C3×#63943C2semidirect
9. C3×#63933C2semidirect
10. C3×#63932C2semidirect
11. C3×#63927C2semidirect
12. C3×#63807C2semidirect
13. C3×#63800C2semidirect
14. C3×#63798C2semidirect
15. C3×D3×ΓL(1,𝔽25)C2semidirect
18. #10594745C3direct (N × H)
19. C3×Q8×C3⋊D3C22semidirect
22. C32×#239C22semidirect
23. C32×#237C22semidirect
24. C32×D3×D4C22semidirect
30. C3×#3802C22semidirect
37. C3×#3795C22semidirect
38. C3×#3795C22semidirect
39. C3×D3×Dic6C22semidirect
40. C33×SD16C22semidirect
41. C3×#3756C22semidirect
42. C3×#3754C22semidirect
43. C3×#3746C22semidirect
44. C3×#3743C22semidirect
45. C32×#216C22semidirect
46. C32×#215C22semidirect
47. C32×#213C22semidirect
48. C32×#213C22semidirect
49. C32×D24C22semidirect
50. C32×#204C22semidirect
51. C32×ΓL(1,𝔽25)C22semidirect
52. C32×D3×C8C22semidirect
53. C3×#3719C22semidirect
54. C3×#3716C22semidirect
55. C3×#3716C22semidirect
56. C3×#3716C22semidirect
57. C3×#3715C22semidirect
58. C3×#3713C22semidirect
59. C3×#3712C22semidirect
60. C3×#3711C22semidirect
61. C3×D3×C3⋊C8C22semidirect
66. #64319C2×C3semidirect
67. D3×#237C2×C3semidirect
70. #64124C2×C3semidirect
79. C3×#916D3semidirect
80. C3×#916C2×C3semidirect
88. C3×#914D3semidirect
89. C3×#914C2×C3semidirect
100. #63951C2×C3semidirect
101. #63947C2×C3semidirect
102. #63943C2×C3semidirect
103. #63933C2×C3semidirect
104. #63932C2×C3semidirect
105. #63927C2×C3semidirect
106. #63807C2×C3semidirect
107. #63800C2×C3semidirect
108. #63798C2×C3semidirect
109. D3×ΓL(1,𝔽25)C2×C3semidirect
160. Q8×C3⋊D3C22×C3semidirect
168. C3×#239C2×D3semidirect
170. C3×#239C22×C3semidirect
188. C3×#237C2×D3semidirect
189. C3×#237C22×C3semidirect
196. C3×D3×D4C2×D3semidirect
197. C3×D3×D4C22×C3semidirect
215. #3802C22×C3semidirect
222. #3795C22×C3semidirect
223. #3795C22×C3semidirect
224. D3×Dic6C22×C3semidirect
232. C32×SD16C2×D3semidirect
233. C32×SD16C2×D3semidirect
234. C32×SD16C22×C3semidirect
240. #3756C22×C3semidirect
241. #3754C22×C3semidirect
242. #3746C22×C3semidirect
243. #3743C22×C3semidirect
249. C3×#216C2×D3semidirect
250. C3×#216C22×C3semidirect
253. C3×#215C2×D3semidirect
254. C3×#215C22×C3semidirect
266. C3×#213C2×D3semidirect
267. C3×#213C2×D3semidirect
268. C3×#213C22×C3semidirect
269. C3×#213C22×C3semidirect
277. C3×D24C2×D3semidirect
278. C3×D24C22×C3semidirect
283. C3×#204C2×D3semidirect
284. C3×#204C22×C3semidirect
292. C3×ΓL(1,𝔽25)C2×D3semidirect
293. C3×ΓL(1,𝔽25)C22×C3semidirect
296. C3×D3×C8C2×D3semidirect
297. C3×D3×C8C22×C3semidirect
298. #3719C22×C3semidirect
299. #3716C22×C3semidirect
300. #3716C22×C3semidirect
301. #3716C22×C3semidirect
302. #3715C22×C3semidirect
303. #3713C22×C3semidirect
304. #3712C22×C3semidirect
305. #3711C22×C3semidirect
306. D3×C3⋊C8C22×C3semidirect
355. #916C3×D3semidirect
362. #914C3×D3semidirect
580. #239C2×C3×D3semidirect
597. #237C2×C3×D3semidirect
603. D3×D4C2×C3×D3semidirect
637. C3×SD16D32semidirect
638. C3×SD16C2×C3×D3semidirect
639. C3×SD16C2×C3×D3semidirect
664. #216C2×C3×D3semidirect
666. #215C2×C3×D3semidirect
676. #213C2×C3×D3semidirect
677. #213C2×C3×D3semidirect
684. D24C2×C3×D3semidirect
688. #204C2×C3×D3semidirect
695. ΓL(1,𝔽25)C2×C3×D3semidirect
697. D3×C8C2×C3×D3semidirect
792. C33#575semidirect
1028. SD16C3×D32semidirect
1122. C32#5768semidirect
1123. C32#5773semidirect
1124. C32C3×#575semidirect
1228. C3#10594745direct (N × H)
1229. C3C3×#5768semidirect
1230. C3C3×#5773semidirect

Maximal subgroups

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

subgroupindex
C3×#643192
C3×D3×#2372
C3×#641242
C32×#9162
C32×#9142
C3×#639512
C3×#639472
C3×#639432
C3×#639332
C3×#639322
C3×#639272
C3×#638072
C3×#638002
C3×#637982
C3×D3×ΓL(1,𝔽25)2
C3×#57733
C3×#57683
#105947453