Finite Group Databasebeta

← C3×#10594766 #13174363

Subgroups — C3×#10594766 #13174363

Order 1728.

1190 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64316C211yesmaximal, characteristic, complemented
2C3×#64315C211yesmaximal, characteristic, complemented
3C3×#64127C211yesmaximal, characteristic, complemented
4C32×#918C211yesmaximal, characteristic, complemented
5C32×D3×Q16C211yesmaximal, characteristic, complemented
6C3×#63950C211yesmaximal, characteristic, complemented
7C3×#63949C211yesmaximal, characteristic, complemented
8C3×#63948C211yesmaximal, characteristic, complemented
9C3×#63946C211yesmaximal, characteristic, complemented
10C3×#63944C211yesmaximal, characteristic, complemented
11C3×D3×#216C211yesmaximal, characteristic, complemented
12C3×#63811C211yesmaximal, characteristic, complemented
13C3×#63806C211yesmaximal, characteristic, complemented
14C3×#63804C211yesmaximal, characteristic, complemented
15C3×#63801C211yesmaximal, characteristic, complemented
16C3×#5779—31nomaximal
17C3×#5766—31nomaximal
18#10594766C311yesmaximal, characteristic, direct product factor
19C3×#3832C2211yescharacteristic
20C3×Q8×C3⋊D3C2211yescharacteristic
21C32×#239C2211yescharacteristic
22C32×D3×Q8C2211yescharacteristic
23C32×D3×Q8C2211yescharacteristic
24C32×D3×Q8C2211yescharacteristic
25C3×#3799—21no—
26C3×#3799—21no—
27C3×#3799C2211yescharacteristic
28C3×#3799C2211yescharacteristic
29C3×#3798—21no—
30C3×#3798—21no—
31C3×#3798C2211yescharacteristic
32C3×#3797—21no—
33C3×#3797C2211yescharacteristic
34C3×#3796—21no—
35C3×#3796C2211yescharacteristic
36C3×#3795—21no—
37C3×#3795C2211yescharacteristic
38C3×D3×Dic6—21no—
39C3×D3×Dic6C2211yescharacteristic
40C33×Q16C2211yescharacteristic
41C3×#3756C2211yescharacteristic
42C3×#3755C2211yescharacteristic
43C3×#3744C2211yescharacteristic
44C3×#3743C2211yescharacteristic
45C32×#216C2211yescharacteristic
46C32×#216C2211yescharacteristic
47C32×#216C2211yescharacteristic
48C32×#215C2211yescharacteristic
49C32×Dic12C2211yescharacteristic
50C32×#204C2211yescharacteristic
51C32×ΓL(1,𝔽25)C2211yescharacteristic
52C32×D3×C8C2211yescharacteristic
53C3×#3719C2211yescharacteristic
54C3×#3719C2211yescharacteristic
55C3×#3718C2211yescharacteristic
56C3×#3717C2211yescharacteristic
57C3×#3715C2211yescharacteristic
58C3×#3714C2211yescharacteristic
59C3×#3711C2211yescharacteristic
60C3×#3710C2211yescharacteristic
61C3×D3×C3⋊C8C2211yescharacteristic
62C3×#1010—31no—
63C3×#1007—31no—
64C3×#1007—31no—
65C3×#1007—31no—
66#64316C2×C311yescharacteristic, complemented
67#64315C2×C311yescharacteristic, complemented
68C32×#137—31no—
69C2×C32×Q16—31no—
70#64127C2×C311yescharacteristic, complemented
71C3×#950—31no—
72C2×C3×#216—31no—
73C3×#942—31no—
74C3×#942—31no—
75C3×#919—31no—
76C3×#919—31no—
77C3×#918—21no—
78C3×#918—31no—
79C3×#918—31no—
80C3×#918—31no—
81C3×#918—31no—
82C3×#918—31no—
83C3×#918—61no—
84C3×#918D311yescharacteristic, complemented
85C3×#918C2×C311yescharacteristic, complemented
86C3×D3×Q16—21no—
87C3×D3×Q16—31no—
88C3×D3×Q16—31no—
89C3×D3×Q16—31no—
90C3×D3×Q16D311yescharacteristic, complemented
91C3×D3×Q16C2×C311yescharacteristic, complemented
92C3×#916—31no—
93C3×#916—31no—
94C3×#915—31no—
95C3×#915—31no—
96C3×#909—31no—
97C3×#907—31no—
98C3×#904—31no—
99C3×#901—31no—
100#63950C2×C311yescharacteristic, complemented
101#63949C2×C311yescharacteristic, complemented
102#63948C2×C311yescharacteristic, complemented
103#63946C2×C311yescharacteristic, complemented
104#63944C2×C311yescharacteristic, complemented
105D3×#216C2×C311yescharacteristic, complemented
106#63811C2×C311yescharacteristic, complemented
107#63806C2×C311yescharacteristic, complemented
108#63804C2×C311yescharacteristic, complemented
109#63801C2×C311yescharacteristic, complemented
110C33×Q8C2311yescharacteristic
111C33×Q8C2311yescharacteristic
112C3×C4⋊(C3⋊D3)—21no—
113C3×C4⋊(C3⋊D3)C2311yescharacteristic
114C3×C4×C3⋊D3—21no—
115C3×C4×C3⋊D3—21no—
116C3×C4×C3⋊D3C2311yescharacteristic
117C3×#634—21no—
118C3×#634C2311yescharacteristic
119C32×D12—21no—
120C32×D12C2311yescharacteristic
121C32×C4×D3—21no—
122C32×C4×D3—21no—
123C32×C4×D3—21no—
124C32×C4×D3—21no—
125C32×C4×D3C2311yescharacteristic
126C32×C4×D3C2311yescharacteristic
127C32×Dic6—21no—
128C32×Dic6—21no—
129C32×Dic6—21no—
130C32×Dic6C2311yescharacteristic
131C32×Dic6C2311yescharacteristic
132C32×Dic6C2311yescharacteristic
133C3×#627—21no—
134C3×#627—21no—
135C3×#627D411yescharacteristic
136C3×#626—21no—
137C3×#626—21no—
138C3×#626—21no—
139C3×#626D411yescharacteristic
140C3×#626D411yescharacteristic
141C3×#625—21no—
142C3×#625D411yescharacteristic
143C3×#624—21no—
144C3×#624—21no—
145C3×#624—21no—
146C3×D3×Dic3—21no—
147C3×D3×Dic3—21no—
148C3×D3×Dic3—21no—
149C33×C8C2311yescharacteristic
150C3×C3⋊(C3⋊C8)C2311yescharacteristic
151C32×C3⋊C8C2311yescharacteristic
152C32×C3⋊C8C2311yescharacteristic
153C3×#578—91no—
154#5779—31no—
155#5766—31no—
156C32×#41—31no—
157C2×C32×Q8—31no—
158C2×C32×Q8—31no—
159C2×C32×Q8—31no—
160#3832C22×C311yescharacteristic
161Q8×C3⋊D3C22×C311yescharacteristic
162C3×#239—21no—
163C3×#239—31no—
164C3×#239—31no—
165C3×#239—31no—
166C3×#239—31no—
167C3×#239—31no—
168C3×#239—61no—
169C3×#239—61no—
170C3×#239—61no—
171C3×#239—61no—
172C3×#239C2×D311yescharacteristic
173C3×#239C22×C311yescharacteristic
174C3×D3×Q8—21no—
175C3×D3×Q8—21no—
176C3×D3×Q8—21no—
177C3×D3×Q8—31no—
178C3×D3×Q8—31no—
179C3×D3×Q8—31no—
180C3×D3×Q8—31no—
181C3×D3×Q8—31no—
182C3×D3×Q8—61no—
183C3×D3×Q8—61no—
184C3×D3×Q8—61no—
185C3×D3×Q8—61no—
186C3×D3×Q8C2×D311yescharacteristic
187C3×D3×Q8C2×D311yescharacteristic
188C3×D3×Q8C2×D311yescharacteristic
189C3×D3×Q8C22×C311yescharacteristic
190C3×D3×Q8C22×C311yescharacteristic
191C3×D3×Q8C22×C311yescharacteristic
192C3×#237—31no—
193C3×#237—31no—
194C3×#237—61no—
195C3×#237—61no—
196C3×#235—31no—
197C3×#235—31no—
198C3×#235—31no—
199C3×#235—31no—
200C3×#235—31no—
201C3×#235—61no—
202C3×#235—61no—
203C3×#235—61no—
204C3×#235—61no—
205C3×#235—61no—
206C3×#235—61no—
207C3×#235—61no—
208C2×C3×Dic6—31no—
209C2×C3×Dic6—61no—
210#3799—21no—
211#3799—21no—
212#3799C22×C311yescharacteristic
213#3799C22×C311yescharacteristic
214#3798—21no—
215#3798—21no—
216#3798C22×C311yescharacteristic
217#3797—21no—
218#3797C22×C311yescharacteristic
219#3796—21no—
220#3796C22×C311yescharacteristic
221#3795—21no—
222#3795C22×C311yescharacteristic
223D3×Dic6—21no—
224D3×Dic6C22×C311yescharacteristic
225C32×Q16—21no—
226C32×Q16—21no—
227C32×Q16—21no—
228C32×Q16—31no—
229C32×Q16—31no—
230C32×Q16—31no—
231C32×Q16—31no—
232C32×Q16—41no—
233C32×Q16C2×D311yescharacteristic
234C32×Q16C2×D311yescharacteristic
235C32×Q16C22×C311yescharacteristic
236C32×SD16—31no—
237C32×SD16—31no—
238C32×M16—31no—
239C2×C32×C8—31no—
240#3756C22×C311yescharacteristic
241#3755C22×C311yescharacteristic
242#3744C22×C311yescharacteristic
243#3743C22×C311yescharacteristic
244C3×#216—21no—
245C3×#216—21no—
246C3×#216—21no—
247C3×#216—31no—
248C3×#216—31no—
249C3×#216—31no—
250C3×#216—31no—
251C3×#216—31no—
252C3×#216—31no—
253C3×#216—61no—
254C3×#216C2×D311yescharacteristic
255C3×#216C2×D311yescharacteristic
256C3×#216C2×D311yescharacteristic
257C3×#216C22×C311yescharacteristic
258C3×#216C22×C311yescharacteristic
259C3×#216C22×C311yescharacteristic
260C3×#215—21no—
261C3×#215—31no—
262C3×#215—31no—
263C3×#215—31no—
264C3×#215—31no—
265C3×#215—61no—
266C3×#215C2×D311yescharacteristic
267C3×#215C22×C311yescharacteristic
268C3×#214—31no—
269C3×#213—31no—
270C3×#208—31no—
271C2×C3×C3⋊C8—31no—
272C3×Dic12—21no—
273C3×Dic12—31no—
274C3×Dic12—31no—
275C3×Dic12C2×D311yescharacteristic
276C3×Dic12C22×C311yescharacteristic
277C3×D24—31no—
278C3×#204—21no—
279C3×#204—31no—
280C3×#204—31no—
281C3×#204—31no—
282C3×#204—61no—
283C3×#204C2×D311yescharacteristic
284C3×#204C22×C311yescharacteristic
285C3×ΓL(1,𝔽25)—21no—
286C3×ΓL(1,𝔽25)—31no—
287C3×ΓL(1,𝔽25)—31no—
288C3×ΓL(1,𝔽25)—31no—
289C3×ΓL(1,𝔽25)—61no—
290C3×ΓL(1,𝔽25)C2×D311yescharacteristic
291C3×ΓL(1,𝔽25)C22×C311yescharacteristic
292C3×D3×C8—21no—
293C3×D3×C8—31no—
294C3×D3×C8—31no—
295C3×D3×C8—31no—
296C3×D3×C8C2×D311yescharacteristic
297C3×D3×C8C22×C311yescharacteristic
298#3719C22×C311yescharacteristic
299#3719C22×C311yescharacteristic
300#3718C22×C311yescharacteristic
301#3717C22×C311yescharacteristic
302#3715C22×C311yescharacteristic
303#3714C22×C311yescharacteristic
304#3711C22×C311yescharacteristic
305#3710C22×C311yescharacteristic
306D3×C3⋊C8C22×C311yescharacteristic
307C2×C3×C3⋊D3—21no—
308C2×C3×C3⋊D3C2×D411yescharacteristic
309C2×C32×D3—21no—
310C2×C32×D3C2×D411yescharacteristic
311C2×C32×D3C2×D411yescharacteristic
312C33×C4—21no—
313C33×C4—21no—
314C33×C4C2411yescharacteristic
315C3×C3⋊Dic3—21no—
316C3×C3⋊Dic3C2×D411yescharacteristic
317C32×Dic3—21no—
318C32×Dic3—21no—
319C32×Dic3—21no—
320C32×Dic3C2×D411yescharacteristic
321C32×Dic3C2×D411yescharacteristic
322C3×2−1+4—91no—
323C3×2−1+4—91no—
324#1010—31no—
325#1007—31no—
326#1007—31no—
327#1007—31no—
328C3×#137—31no—
329C3×#137—31no—
330C3×#137—61no—
331C3×#137—91no—
332C3×#137—91no—
333C3×#137—91no—
334C3×#137—91no—
335C3×#137—91no—
336C3×#135—91no—
337C3×#135—91no—
338C3×#135—91no—
339C2×C3×Q16—31no—
340C2×C3×Q16—31no—
341C2×C3×Q16—61no—
342C2×C3×Q16—91no—
343C2×C3×Q16—91no—
344C3×#131—91no—
345#950—31no—
346C2×#216—31no—
347#942—31no—
348#942—31no—
349#919—31no—
350#919—31no—
351#918—31no—
352#918—31no—
353#918—31no—
354#918—31no—
355#918—31no—
356#918—61no—
357#918C3×D311yescharacteristic, complemented
358D3×Q16—31no—
359D3×Q16—31no—
360D3×Q16—31no—
361D3×Q16C3×D311yescharacteristic, complemented
362#916—31no—
363#916—31no—
364#915—31no—
365#915—31no—
366#909—31no—
367#907—31no—
368#904—31no—
369#901—31no—
370C32×Q8—21no—
371C32×Q8—21no—
372C32×Q8—21no—
373C32×Q8—21no—
374C32×Q8—21no—
375C32×Q8—21no—
376C32×Q8—31no—
377C32×Q8—31no—
378C32×Q8—31no—
379C32×Q8—41no—
380C32×Q8—41no—
381C32×Q8—61no—
382C32×Q8—61no—
383C32×Q8—61no—
384C32×Q8C22×D311yescharacteristic
385C32×Q8C22×D311yescharacteristic
386C32×Q8C22×D311yescharacteristic
387C32×Q8C22×D311yescharacteristic
388C32×Q8C23×C311yescharacteristic
389C32×Q8C23×C311yescharacteristic
390C32×D4—31no—
391C32×D4—61no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—61no—
395C2×C32×C4—61no—
396C2×C32×C4—61no—
397C2×C32×C4—61no—
398C4⋊(C3⋊D3)—21no—
399C4⋊(C3⋊D3)C23×C311yescharacteristic
400C4×C3⋊D3—21no—
401C4×C3⋊D3—21no—
402C4×C3⋊D3C23×C311yescharacteristic
403#634—21no—
404#634C23×C311yescharacteristic
405C3×#67—31no—
406C3×#67—31no—
407C3×#67—31no—
408C3×#67—31no—
409C3×#67—61no—
410C3×#67—61no—
411C3×#67—61no—
412C3×#67—61no—
413C3×#67—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C3×D12—21no—
418C3×D12—21no—
419C3×D12—21no—
420C3×D12—31no—
421C3×D12—31no—
422C3×D12—31no—
423C3×D12—31no—
424C3×D12—41no—
425C3×D12—61no—
426C3×D12—61no—
427C3×D12—61no—
428C3×D12—61no—
429C3×D12—61no—
430C3×D12—61no—
431C3×D12—121no—
432C3×D12C22×D311yescharacteristic
433C3×D12C23×C311yescharacteristic
434C3×C4×D3—21no—
435C3×C4×D3—21no—
436C3×C4×D3—21no—
437C3×C4×D3—21no—
438C3×C4×D3—21no—
439C3×C4×D3—21no—
440C3×C4×D3—21no—
441C3×C4×D3—21no—
442C3×C4×D3—21no—
443C3×C4×D3—21no—
444C3×C4×D3—31no—
445C3×C4×D3—31no—
446C3×C4×D3—41no—
447C3×C4×D3—41no—
448C3×C4×D3—41no—
449C3×C4×D3—41no—
450C3×C4×D3—61no—
451C3×C4×D3—61no—
452C3×C4×D3—61no—
453C3×C4×D3—61no—
454C3×C4×D3—61no—
455C3×C4×D3—61no—
456C3×C4×D3—61no—
457C3×C4×D3—61no—
458C3×C4×D3—61no—
459C3×C4×D3—61no—
460C3×C4×D3—61no—
461C3×C4×D3—61no—
462C3×C4×D3—61no—
463C3×C4×D3—61no—
464C3×C4×D3—121no—
465C3×C4×D3—121no—
466C3×C4×D3C22×D311yescharacteristic
467C3×C4×D3C22×D311yescharacteristic
468C3×C4×D3C23×C311yescharacteristic
469C3×C4×D3C23×C311yescharacteristic
470C3×Dic6—21no—
471C3×Dic6—21no—
472C3×Dic6—21no—
473C3×Dic6—21no—
474C3×Dic6—21no—
475C3×Dic6—21no—
476C3×Dic6—21no—
477C3×Dic6—21no—
478C3×Dic6—21no—
479C3×Dic6—31no—
480C3×Dic6—31no—
481C3×Dic6—31no—
482C3×Dic6—31no—
483C3×Dic6—41no—
484C3×Dic6—41no—
485C3×Dic6—41no—
486C3×Dic6—61no—
487C3×Dic6—61no—
488C3×Dic6—61no—
489C3×Dic6—61no—
490C3×Dic6—61no—
491C3×Dic6—61no—
492C3×Dic6—61no—
493C3×Dic6—121no—
494C3×Dic6C22×D311yescharacteristic
495C3×Dic6C22×D311yescharacteristic
496C3×Dic6C22×D311yescharacteristic
497C3×Dic6C23×C311yescharacteristic
498C3×Dic6C23×C311yescharacteristic
499C3×Dic6C23×C311yescharacteristic
500#627—21no—
501#627—21no—
502#627C3×D411yescharacteristic
503#626—21no—
504#626—21no—
505#626—21no—
506#626C3×D411yescharacteristic
507#626C3×D411yescharacteristic
508#625—21no—
509#625C3×D411yescharacteristic
510#624—21no—
511#624—21no—
512#624—21no—
513D3×Dic3—21no—
514D3×Dic3—21no—
515D3×Dic3—21no—
516C32×C8—21no—
517C32×C8—21no—
518C32×C8—21no—
519C32×C8—31no—
520C32×C8—31no—
521C32×C8—41no—
522C32×C8C22×D311yescharacteristic
523C32×C8C22×D311yescharacteristic
524C32×C8C23×C311yescharacteristic
525C3⋊(C3⋊C8)C23×C311yescharacteristic
526C3×C3⋊C8—21no—
527C3×C3⋊C8—21no—
528C3×C3⋊C8—31no—
529C3×C3⋊C8—31no—
530C3×C3⋊C8—61no—
531C3×C3⋊C8C22×D311yescharacteristic
532C3×C3⋊C8C22×D311yescharacteristic
533C3×C3⋊C8C23×C311yescharacteristic
534C3×C3⋊C8C23×C311yescharacteristic
535#578—91noSylow
536C2×C33C22×D411yescharacteristic
537C3×C3⋊D3—21no—
538C3×C3⋊D3—41no—
539C32×D3—21no—
540C32×D3—21no—
541C32×D3—41no—
542C3×#41—31no—
543C3×#41—31no—
544C3×#41—61no—
545C3×#41—91no—
546C3×#41—91no—
547C3×#41—91no—
548C3×#41—91no—
549C3×#41—91no—
550C3×#41—91no—
551C3×#41—181no—
552C3×#41—181no—
553C3×#41—181no—
554C3×#41—181no—
555C3×#41—181no—
556C3×#41—181no—
557C2×C3×Q8—31no—
558C2×C3×Q8—31no—
559C2×C3×Q8—31no—
560C2×C3×Q8—31no—
561C2×C3×Q8—31no—
562C2×C3×Q8—31no—
563C2×C3×Q8—61no—
564C2×C3×Q8—61no—
565C2×C3×Q8—61no—
566C2×C3×Q8—91no—
567C2×C3×Q8—91no—
568C2×C3×Q8—91no—
569C2×C3×Q8—181no—
570C2×C3×Q8—181no—
571#239—31no—
572#239—31no—
573#239—31no—
574#239—31no—
575#239—31no—
576#239—61no—
577#239—61no—
578#239—61no—
579#239—61no—
580#239C2×C3×D311yescharacteristic
581D3×Q8—31no—
582D3×Q8—31no—
583D3×Q8—31no—
584D3×Q8—31no—
585D3×Q8—31no—
586D3×Q8—61no—
587D3×Q8—61no—
588D3×Q8—61no—
589D3×Q8—61no—
590D3×Q8C2×C3×D311yescharacteristic
591D3×Q8C2×C3×D311yescharacteristic
592D3×Q8C2×C3×D311yescharacteristic
593#237—31no—
594#237—31no—
595#237—61no—
596#237—61no—
597#235—31no—
598#235—31no—
599#235—31no—
600#235—31no—
601#235—31no—
602#235—61no—
603#235—61no—
604#235—61no—
605#235—61no—
606#235—61no—
607#235—61no—
608#235—61no—
609C2×Dic6—31no—
610C2×Dic6—61no—
611C3×Q16—21no—
612C3×Q16—21no—
613C3×Q16—21no—
614C3×Q16—31no—
615C3×Q16—31no—
616C3×Q16—31no—
617C3×Q16—31no—
618C3×Q16—31no—
619C3×Q16—31no—
620C3×Q16—31no—
621C3×Q16—31no—
622C3×Q16—41no—
623C3×Q16—61no—
624C3×Q16—61no—
625C3×Q16—61no—
626C3×Q16—61no—
627C3×Q16—91no—
628C3×Q16—91no—
629C3×Q16—91no—
630C3×Q16—91no—
631C3×Q16D3211yescharacteristic
632C3×Q16C2×C3×D311yescharacteristic
633C3×Q16C2×C3×D311yescharacteristic
634C3×SD16—31no—
635C3×SD16—31no—
636C3×SD16—31no—
637C3×SD16—31no—
638C3×SD16—61no—
639C3×SD16—61no—
640C3×SD16—91no—
641C3×SD16—91no—
642C3×SD16—91no—
643C3×SD16—91no—
644C3×D8—91no—
645C3×M16—31no—
646C3×M16—31no—
647C3×M16—61no—
648C3×M16—91no—
649C3×M16—91no—
650C2×C3×C8—31no—
651C2×C3×C8—31no—
652C2×C3×C8—61no—
653C2×C3×C8—91no—
654C2×C3×C8—91no—
655#216—31no—
656#216—31no—
657#216—31no—
658#216—31no—
659#216—31no—
660#216—31no—
661#216—61no—
662#216C2×C3×D311yescharacteristic
663#216C2×C3×D311yescharacteristic
664#216C2×C3×D311yescharacteristic
665#215—31no—
666#215—31no—
667#215—31no—
668#215—31no—
669#215—61no—
670#215C2×C3×D311yescharacteristic
671#214—31no—
672#213—31no—
673#208—31no—
674C2×C3⋊C8—31no—
675Dic12—31no—
676Dic12—31no—
677Dic12C2×C3×D311yescharacteristic
678D24—31no—
679#204—31no—
680#204—31no—
681#204—31no—
682#204—61no—
683#204C2×C3×D311yescharacteristic
684ΓL(1,𝔽25)—31no—
685ΓL(1,𝔽25)—31no—
686ΓL(1,𝔽25)—31no—
687ΓL(1,𝔽25)—61no—
688ΓL(1,𝔽25)C2×C3×D311yescharacteristic
689D3×C8—31no—
690D3×C8—31no—
691D3×C8—31no—
692D3×C8C2×C3×D311yescharacteristic
693C22×C32—31no—
694C22×C32—31no—
695C22×C32—61no—
696C2×C3⋊D3—21no—
697C2×C3⋊D3C2×C3×D411yescharacteristic
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—21no—
701C2×C3×D3—21no—
702C2×C3×D3—31no—
703C2×C3×D3—31no—
704C2×C3×D3—41no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—121no—
709C2×C3×D3D3×D411yescharacteristic
710C2×C3×D3D3×D411yescharacteristic
711C2×C3×D3C2×C3×D411yescharacteristic
712C2×C3×D3C2×C3×D411yescharacteristic
713C32×C4—21no—
714C32×C4—21no—
715C32×C4—21no—
716C32×C4—21no—
717C32×C4—21no—
718C32×C4—21no—
719C32×C4—21no—
720C32×C4—21no—
721C32×C4—21no—
722C32×C4—31no—
723C32×C4—31no—
724C32×C4—41no—
725C32×C4—41no—
726C32×C4—41no—
727C32×C4—41no—
728C32×C4—41no—
729C32×C4—41no—
730C32×C4—41no—
731C32×C4—61no—
732C32×C4—61no—
733C32×C4—61no—
734C32×C4—81no—
735C32×C4—81no—
736C32×C4C23×D311yescharacteristic
737C32×C4C23×D311yescharacteristic
738C32×C4C24×C311yescharacteristic
739C3⋊Dic3—21no—
740C3⋊Dic3C2×C3×D411yescharacteristic
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—21no—
745C3×Dic3—21no—
746C3×Dic3—21no—
747C3×Dic3—21no—
748C3×Dic3—21no—
749C3×Dic3—31no—
750C3×Dic3—31no—
751C3×Dic3—41no—
752C3×Dic3—41no—
753C3×Dic3—41no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—61no—
757C3×Dic3—121no—
758C3×Dic3D3×D411yescharacteristic
759C3×Dic3D3×D411yescharacteristic
760C3×Dic3C2×C3×D411yescharacteristic
761C3×Dic3C2×C3×D411yescharacteristic
7622−1+4—91no—
7632−1+4—91no—
764#137—31no—
765#137—91no—
766#137—91no—
767#137—91no—
768#137—91no—
769#137—91no—
770#135—91no—
771#135—91no—
772#135—91no—
773C2×Q16—31no—
774C2×Q16—91no—
775C2×Q16—91no—
776#131—91no—
777C33#57811yescharacteristic, complemented, Sylow
778C3×Q8—21no—
779C3×Q8—21no—
780C3×Q8—21no—
781C3×Q8—21no—
782C3×Q8—21no—
783C3×Q8—21no—
784C3×Q8—31no—
785C3×Q8—31no—
786C3×Q8—31no—
787C3×Q8—31no—
788C3×Q8—31no—
789C3×Q8—31no—
790C3×Q8—41no—
791C3×Q8—41no—
792C3×Q8—61no—
793C3×Q8—61no—
794C3×Q8—61no—
795C3×Q8—61no—
796C3×Q8—61no—
797C3×Q8—61no—
798C3×Q8—61no—
799C3×Q8—61no—
800C3×Q8—61no—
801C3×Q8—91no—
802C3×Q8—91no—
803C3×Q8—121no—
804C3×Q8—121no—
805C3×Q8—121no—
806C3×Q8—181no—
807C3×Q8—181no—
808C3×Q8—181no—
809C3×Q8C2×D3211yescharacteristic
810C3×Q8C2×D3211yescharacteristic
811C3×Q8C22×C3×D311yescharacteristic
812C3×Q8C22×C3×D311yescharacteristic
813C3×Q8C22×C3×D311yescharacteristic
814C3×Q8C22×C3×D311yescharacteristic
815C3×D4—31no—
816C3×D4—31no—
817C3×D4—61no—
818C3×D4—61no—
819C3×D4—61no—
820C3×D4—91no—
821C3×D4—91no—
822C3×D4—91no—
823C3×D4—91no—
824C3×D4—121no—
825C3×D4—181no—
826C3×D4—181no—
827C3×D4—181no—
828C3×D4—181no—
829C3×D4—181no—
830C2×C3×C4—31no—
831C2×C3×C4—31no—
832C2×C3×C4—31no—
833C2×C3×C4—31no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—61no—
837C2×C3×C4—61no—
838C2×C3×C4—61no—
839C2×C3×C4—61no—
840C2×C3×C4—61no—
841C2×C3×C4—61no—
842C2×C3×C4—61no—
843C2×C3×C4—61no—
844C2×C3×C4—91no—
845C2×C3×C4—121no—
846C2×C3×C4—121no—
847C2×C3×C4—121no—
848C2×C3×C4—121no—
849C2×C3×C4—181no—
850C2×C3×C4—181no—
851C2×C3×C4—181no—
852C2×C3×C4—181no—
853C2×C3×C4—181no—
854C2×C3×C4—181no—
855C2×C3×C4—181no—
856C2×C3×C4—181no—
857#67—31no—
858#67—31no—
859#67—31no—
860#67—31no—
861#67—61no—
862#67—61no—
863#67—61no—
864#67—61no—
865#67—61no—
866C2×Dic3—61no—
867C2×Dic3—61no—
868C2×Dic3—61no—
869D12—21no—
870D12—31no—
871D12—31no—
872D12—31no—
873D12—31no—
874D12—61no—
875D12—61no—
876D12—61no—
877D12—61no—
878D12—61no—
879D12—61no—
880D12—121no—
881D12C22×C3×D311yescharacteristic
882C4×D3—21no—
883C4×D3—21no—
884C4×D3—21no—
885C4×D3—21no—
886C4×D3—31no—
887C4×D3—31no—
888C4×D3—61no—
889C4×D3—61no—
890C4×D3—61no—
891C4×D3—61no—
892C4×D3—61no—
893C4×D3—61no—
894C4×D3—61no—
895C4×D3—61no—
896C4×D3—61no—
897C4×D3—61no—
898C4×D3—61no—
899C4×D3—61no—
900C4×D3—61no—
901C4×D3—61no—
902C4×D3—121no—
903C4×D3—121no—
904C4×D3C22×C3×D311yescharacteristic
905C4×D3C22×C3×D311yescharacteristic
906Dic6—21no—
907Dic6—21no—
908Dic6—21no—
909Dic6—31no—
910Dic6—31no—
911Dic6—31no—
912Dic6—31no—
913Dic6—61no—
914Dic6—61no—
915Dic6—61no—
916Dic6—61no—
917Dic6—61no—
918Dic6—61no—
919Dic6—61no—
920Dic6—121no—
921Dic6C22×C3×D311yescharacteristic
922Dic6C22×C3×D311yescharacteristic
923Dic6C22×C3×D311yescharacteristic
924C3×C8—21no—
925C3×C8—21no—
926C3×C8—21no—
927C3×C8—31no—
928C3×C8—31no—
929C3×C8—31no—
930C3×C8—31no—
931C3×C8—41no—
932C3×C8—61no—
933C3×C8—61no—
934C3×C8—91no—
935C3×C8C2×D3211yescharacteristic
936C3×C8C22×C3×D311yescharacteristic
937C3×C8C22×C3×D311yescharacteristic
938C3⋊C8—31no—
939C3⋊C8—31no—
940C3⋊C8—61no—
941C3⋊C8C22×C3×D311yescharacteristic
942C3⋊C8C22×C3×D311yescharacteristic
943C2×C32—21no—
944C2×C32—21no—
945C2×C32—21no—
946C2×C32—41no—
947C2×C32—61no—
948C2×C32—61no—
949C2×C32—121no—
950C2×C32C2×D3×D411yescharacteristic
951C2×C32C2×D3×D411yescharacteristic
952C2×C32C22×C3×D411yescharacteristic
953C3⋊D3—21no—
954C3⋊D3—41no—
955C3×D3—22no—
956C3×D3—21no—
957C3×D3—21no—
958C3×D3—21no—
959C3×D3—21no—
960C3×D3—41no—
961C3×D3—41no—
962C3×D3—41no—
963C3×D3—61no—
964C3×D3—61no—
965C3×D3—81no—
966C3×D3—121no—
967C3×D3—121no—
968C3×D3—121no—
969C3×D3—241no—
970#41—31no—
971#41—91no—
972#41—91no—
973#41—91no—
974#41—91no—
975#41—91no—
976#41—91no—
977#41—181no—
978#41—181no—
979#41—181no—
980#41—181no—
981#41—181no—
982#41—181no—
983C2×Q8—31no—
984C2×Q8—31no—
985C2×Q8—31no—
986C2×Q8—91no—
987C2×Q8—91no—
988C2×Q8—91no—
989C2×Q8—181no—
990C2×Q8—181no—
991Q16—31no—
992Q16—31no—
993Q16—31no—
994Q16—31no—
995Q16—91no—
996Q16—91no—
997Q16—91no—
998Q16—91no—
999Q16C3×D3211yescharacteristic
1000SD16—31no—
1001SD16—31no—
1002SD16—91no—
1003SD16—91no—
1004SD16—91no—
1005SD16—91no—
1006D8—91no—
1007M16—31no—
1008M16—91no—
1009M16—91no—
1010C2×C8—31no—
1011C2×C8—91no—
1012C2×C8—91no—
1013C22×C3—31no—
1014C22×C3—31no—
1015C22×C3—31no—
1016C22×C3—31no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—61no—
1020C22×C3—61no—
1021C22×C3—91no—
1022C22×C3—121no—
1023C22×C3—181no—
1024C2×D3—21no—
1025C2×D3—31no—
1026C2×D3—31no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—121no—
1031C2×D3C3×D3×D411yescharacteristic
1032C2×D3C3×D3×D411yescharacteristic
1033C3×C4—21no—
1034C3×C4—21no—
1035C3×C4—21no—
1036C3×C4—21no—
1037C3×C4—21no—
1038C3×C4—21no—
1039C3×C4—21no—
1040C3×C4—21no—
1041C3×C4—21no—
1042C3×C4—31no—
1043C3×C4—31no—
1044C3×C4—31no—
1045C3×C4—31no—
1046C3×C4—41no—
1047C3×C4—41no—
1048C3×C4—41no—
1049C3×C4—41no—
1050C3×C4—41no—
1051C3×C4—41no—
1052C3×C4—41no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—61no—
1058C3×C4—61no—
1059C3×C4—61no—
1060C3×C4—61no—
1061C3×C4—81no—
1062C3×C4—81no—
1063C3×C4—91no—
1064C3×C4—121no—
1065C3×C4—121no—
1066C3×C4—121no—
1067C3×C4—181no—
1068C3×C4C22×D3211yescharacteristic
1069C3×C4C23×C3×D311yescharacteristic
1070C3×C4C23×C3×D311yescharacteristic
1071Dic3—21no—
1072Dic3—21no—
1073Dic3—21no—
1074Dic3—31no—
1075Dic3—31no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—61no—
1079Dic3—121no—
1080Dic3C3×D3×D411yescharacteristic
1081Dic3C3×D3×D411yescharacteristic
1082C32—21no—
1083C32—21no—
1084C32—21no—
1085C32—41no—
1086C32#576611yescharacteristic, complemented
1087C32#577911yescharacteristic, complemented
1088C32C3×#57811yescharacteristic, complemented
1089Q8—31no—
1090Q8—31no—
1091Q8—31no—
1092Q8—61no—
1093Q8—61no—
1094Q8—61no—
1095Q8—91no—
1096Q8—91no—
1097Q8—181no—
1098Q8—181no—
1099Q8—181no—
1100Q8C2×C3×D3211yescharacteristic
1101Q8C2×C3×D3211yescharacteristic
1102D4—31no—
1103D4—61no—
1104D4—91no—
1105D4—91no—
1106D4—91no—
1107D4—91no—
1108D4—181no—
1109D4—181no—
1110D4—181no—
1111D4—181no—
1112D4—181no—
1113C2×C4—31no—
1114C2×C4—31no—
1115C2×C4—61no—
1116C2×C4—61no—
1117C2×C4—61no—
1118C2×C4—61no—
1119C2×C4—91no—
1120C2×C4—181no—
1121C2×C4—181no—
1122C2×C4—181no—
1123C2×C4—181no—
1124C2×C4—181no—
1125C2×C4—181no—
1126C2×C4—181no—
1127C2×C4—181no—
1128C8—31no—
1129C8—31no—
1130C8—91no—
1131C8C2×C3×D3211yescharacteristic
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—41no—
1136C2×C3—62no—
1137C2×C3—61no—
1138C2×C3—61no—
1139C2×C3—61no—
1140C2×C3—61no—
1141C2×C3—121no—
1142C2×C3—121no—
1143C2×C3—121no—
1144C2×C3—181no—
1145C2×C3—241no—
1146C2×C3—361no—
1147C2×C3D32×D411yescharacteristic
1148C2×C3C2×C3×D3×D411yescharacteristic
1149C2×C3C2×C3×D3×D411yescharacteristic
1150D3—21no—
1151D3—21no—
1152D3—41no—
1153D3—61no—
1154D3—61no—
1155D3—121no—
1156D3—121no—
1157D3—121no—
1158D3—241no—
1159C22—31no—
1160C22—31no—
1161C22—61no—
1162C22—91no—
1163C22—181no—
1164C4—21no—
1165C4—21no—
1166C4—31no—
1167C4—31no—
1168C4—61no—
1169C4—61no—
1170C4—61no—
1171C4—91no—
1172C4—181no—
1173C4C22×C3×D3211yescharacteristic
1174C3—21no—
1175C3—21no—
1176C3—21no—
1177C3—41no—
1178C3#1059476611yescharacteristic, direct product factor
1179C3C3×#576611yescharacteristic, complemented
1180C3C3×#577911yescharacteristic, complemented
1181C2—61no—
1182C2—61no—
1183C2—121no—
1184C2—181no—
1185C2—361no—
1186C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×Q16C22
socleC2×C33C22×D4
hypercenterC3×Q16D32
hypocenterC32C3×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×Q16

Complements

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

NH ≅ G/Ntype
1. C3×#64316C2semidirect
2. C3×#64315C2semidirect
3. C3×#64127C2semidirect
4. C32×#918C2semidirect
5. C32×D3×Q16C2semidirect
6. C3×#63950C2semidirect
7. C3×#63949C2semidirect
8. C3×#63948C2semidirect
9. C3×#63946C2semidirect
10. C3×#63944C2semidirect
11. C3×D3×#216C2semidirect
12. C3×#63811C2semidirect
13. C3×#63806C2semidirect
14. C3×#63804C2semidirect
15. C3×#63801C2semidirect
18. #10594766C3direct (N × H)
66. #64316C2×C3semidirect
67. #64315C2×C3semidirect
70. #64127C2×C3semidirect
84. C3×#918D3semidirect
85. C3×#918C2×C3semidirect
90. C3×D3×Q16D3semidirect
91. C3×D3×Q16C2×C3semidirect
100. #63950C2×C3semidirect
101. #63949C2×C3semidirect
102. #63948C2×C3semidirect
103. #63946C2×C3semidirect
104. #63944C2×C3semidirect
105. D3×#216C2×C3semidirect
106. #63811C2×C3semidirect
107. #63806C2×C3semidirect
108. #63804C2×C3semidirect
109. #63801C2×C3semidirect
357. #918C3×D3semidirect
361. D3×Q16C3×D3semidirect
777. C33#578semidirect
1086. C32#5766semidirect
1087. C32#5779semidirect
1088. C32C3×#578semidirect
1178. C3#10594766direct (N × H)
1179. C3C3×#5766semidirect
1180. C3C3×#5779semidirect

Maximal subgroups

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

subgroupindex
C3×#643162
C3×#643152
C3×#641272
C32×#9182
C32×D3×Q162
C3×#639502
C3×#639492
C3×#639482
C3×#639462
C3×#639442
C3×D3×#2162
C3×#638112
C3×#638062
C3×#638042
C3×#638012
C3×#57793
C3×#57663
#105947663