Finite Group Databasebeta

← C3×#10590392 #13157409

Subgroups — C3×#10590392 #13157409

Order 1728.

810 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#235C211yesmaximal, characteristic
2C32×#872C211yesmaximal, characteristic, complemented
3C3×D3×#208C211yesmaximal, characteristic, complemented
4C3×#63632C211yesmaximal, characteristic, complemented
5C32×#805C211yesmaximal, characteristic, complemented
6C3×#63570C211yesmaximal, characteristic, complemented
7C3×#63569C211yesmaximal, characteristic, complemented
8C3×#5005—31nomaximal
9C3×#4821—31nomaximal
10#10590392C311yesmaximal, characteristic, direct product factor
11C3×#3828C2211yescharacteristic
12C32×#235C2211yescharacteristic
13C2×C32×C4×D3C2211yescharacteristic
14C3×D3×#67—21no—
15C3×#3804—21no—
16C3×D3×D12C411yescharacteristic, complemented
17C3×C4×D32—21no—
18C3×#3799C411yescharacteristic, complemented
19C3×#3798—21no—
20C3×#3795C411yescharacteristic, complemented
21C3×D3×Dic6C411yescharacteristic, complemented
22C33×C42C2211yescharacteristic, complemented
23C3×#3748C2211yescharacteristic, complemented
24C32×(C2×D3)⋊C4—21no—
25C32×Dic3⋊C4—21no—
26C32×C4×Dic3C2211yescharacteristic, complemented
27C32×#208C2211yescharacteristic, complemented
28C3×#3711—21no—
29C3×D3×C3⋊C8—21no—
30C3×D3×#41—31no—
31C2×C3×#235—31no—
32D3×#235C2×C311yescharacteristic
33C32×#117—31no—
34C2×C3×#208—31no—
35C3×D3×M16—31no—
36C3×#872—21no—
37C3×#872D311yescharacteristic, complemented
38C3×#872C2×C311yescharacteristic, complemented
39D3×#208C2×C311yescharacteristic, complemented
40C32×#104—31no—
41#63632C2×C311yescharacteristic, complemented
42C3×#837—31no—
43C3×#825—31no—
44C3×#805—21no—
45C3×#805—31no—
46C3×#805—31no—
47C3×#805—31no—
48C3×#805—31no—
49C3×#805—61no—
50C3×#805D311yescharacteristic, complemented
51C3×#805C2×C311yescharacteristic, complemented
52#63570C2×C311yescharacteristic, complemented
53#63569C2×C311yescharacteristic, complemented
54C22×C32×D3D411yescharacteristic
55C2×C3×D32—21no—
56C2×C33×C4—21no—
57C2×C33×C4C2311yescharacteristic
58C3×#638—21no—
59C3×C4⋊(C3⋊D3)C2×C411yescharacteristic
60C3×C4×C3⋊D3—21no—
61C3×#634C2×C411yescharacteristic
62C32×#67—21no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3D411yescharacteristic
65C32×D12C2×C411yescharacteristic
66C32×C4×D3—21no—
67C32×C4×D3C2×C411yescharacteristic
68C32×C4×D3C2×C411yescharacteristic
69C32×C4×D3D411yescharacteristic
70C32×C4×D3D411yescharacteristic
71C32×Dic6C2×C411yescharacteristic
72C3×#627—21no—
73C3×#626—21no—
74C3×#626—21no—
75C3×#625—21no—
76C3×#624—21no—
77C3×D3×Dic3—21no—
78C3×D3×Dic3—21no—
79C3×C3⋊(C3⋊C8)—21no—
80C32×C3⋊C8—21no—
81C3×#421—91no—
82#5005—31no—
83#4821—31no—
84C32×#41—31no—
85C22×C32×C4—31no—
86#3828C22×C311yescharacteristic
87C2×C3×#67—61no—
88C3×#239—31no—
89C3×D3×Q8—31no—
90C3×#237—31no—
91C3×#237—61no—
92C3×D3×D4—31no—
93C3×D3×D4—61no—
94C3×#235—21no—
95C3×#235—31no—
96C3×#235—31no—
97C3×#235—31no—
98C3×#235—31no—
99C3×#235—61no—
100C3×#235—61no—
101C3×#235—61no—
102C3×#235—61no—
103C3×#235C2×D311yescharacteristic
104C3×#235C22×C311yescharacteristic
105C2×C3×D12—31no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—61no—
108C2×C3×C4×D3—61no—
109C2×C3×C4×D3C2×D311yescharacteristic
110C2×C3×C4×D3C22×C311yescharacteristic
111C2×C3×Dic6—31no—
112D3×#67—21no—
113#3804—21no—
114D3×D12C3×C411yescharacteristic, complemented
115C4×D32—21no—
116#3799C3×C411yescharacteristic, complemented
117#3798—21no—
118#3795C3×C411yescharacteristic, complemented
119D3×Dic6C3×C411yescharacteristic, complemented
120C32×M16—31no—
121C32×C4⋊C4—61no—
122C32×C22⋊C4—61no—
123C32×C42—21no—
124C32×C42—21no—
125C32×C42—21no—
126C32×C42—31no—
127C32×C42—41no—
128C32×C42C2×D311yescharacteristic, complemented
129C32×C42C2×D311yescharacteristic, complemented
130C32×C42C22×C311yescharacteristic, complemented
131#3748C22×C311yescharacteristic, complemented
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2×D311yescharacteristic, complemented
140C3×C4×Dic3C22×C311yescharacteristic, complemented
141C3×#208—21no—
142C3×#208—31no—
143C3×#208—31no—
144C3×#208—61no—
145C3×#208—61no—
146C3×#208C2×D311yescharacteristic, complemented
147C3×#208C22×C311yescharacteristic, complemented
148C2×C3×C3⋊C8—61no—
149C3×ΓL(1,𝔽25)—61no—
150C3×D3×C8—61no—
151#3711—21no—
152D3×C3⋊C8—21no—
153C22×C33C2×D411yescharacteristic
154C2×C3×C3⋊D3—21no—
155C2×C32×D3—21no—
156C2×C32×D3—41no—
157C2×C32×D3C22⋊C411yescharacteristic
158C2×C32×D3C22⋊C411yescharacteristic
159C3×D32—42no—
160C33×C4—41no—
161C33×C4C22×C411yescharacteristic
162C33×C4C2×D411yescharacteristic
163C3×C3⋊Dic3—21no—
164C32×Dic3—21no—
165C32×Dic3—41no—
166C32×Dic3C22⋊C411yescharacteristic
167C32×Dic3C22⋊C411yescharacteristic
168C2×C3×#41—91no—
169D3×#41—31no—
170C2×#235—31no—
171C2×C3×M16—91no—
172C3×#117—31no—
173C3×#117—31no—
174C3×#117—61no—
175C2×#208—31no—
176D3×M16—31no—
177#872C3×D311yescharacteristic, complemented
178C3×#104—31no—
179C3×#104—31no—
180C3×#104—61no—
181C3×#104—91no—
182C3×#104—91no—
183C3×#104—91no—
184#837—31no—
185#825—31no—
186#805—31no—
187#805—31no—
188#805—31no—
189#805—31no—
190#805—61no—
191#805C3×D311yescharacteristic, complemented
192C23×C32—31no—
193C22×C3×D3—21no—
194C22×C3×D3—61no—
195C22×C3×D3—61no—
196C22×C3×D3#6711yescharacteristic
197C22×C3×D3C3×D411yescharacteristic
198C2×D32—21no—
199C32×Q8—31no—
200C32×D4—31no—
201C32×D4—61no—
202C2×C32×C4—21no—
203C2×C32×C4—22no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—31no—
210C2×C32×C4—31no—
211C2×C32×C4—31no—
212C2×C32×C4—31no—
213C2×C32×C4—31no—
214C2×C32×C4—41no—
215C2×C32×C4—41no—
216C2×C32×C4—41no—
217C2×C32×C4—42no—
218C2×C32×C4—61no—
219C2×C32×C4—61no—
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C23×C311yescharacteristic
223#638—21no—
224C4⋊(C3⋊D3)C2×C3×C411yescharacteristic
225C4×C3⋊D3—21no—
226#634C2×C3×C411yescharacteristic
227C3×#67—21no—
228C3×#67—21no—
229C3×#67—41no—
230C3×#67—61no—
231C3×#67—61no—
232C3×#67—61no—
233C3×#67—61no—
234C3×#67—61no—
235C3×#67—61no—
236C3×#67—121no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—61no—
243C2×C3×Dic3#6711yescharacteristic
244C2×C3×Dic3C3×D411yescharacteristic
245C3×D12—21no—
246C3×D12—31no—
247C3×D12—31no—
248C3×D12—61no—
249C3×D12—61no—
250C3×D12—61no—
251C3×D12C4×D311yescharacteristic
252C3×D12C2×C3×C411yescharacteristic
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—41no—
260C3×C4×D3—61no—
261C3×C4×D3—61no—
262C3×C4×D3—61no—
263C3×C4×D3—61no—
264C3×C4×D3—61no—
265C3×C4×D3—61no—
266C3×C4×D3—121no—
267C3×C4×D3C4×D311yescharacteristic
268C3×C4×D3C4×D311yescharacteristic
269C3×C4×D3D1211yescharacteristic
270C3×C4×D3D1211yescharacteristic
271C3×C4×D3C2×C3×C411yescharacteristic
272C3×C4×D3C2×C3×C411yescharacteristic
273C3×C4×D3C3×D411yescharacteristic
274C3×C4×D3C3×D411yescharacteristic
275C3×Dic6—21no—
276C3×Dic6—31no—
277C3×Dic6—31no—
278C3×Dic6—61no—
279C3×Dic6—61no—
280C3×Dic6—61no—
281C3×Dic6C4×D311yescharacteristic
282C3×Dic6C2×C3×C411yescharacteristic
283#627—21no—
284#626—21no—
285#626—21no—
286#625—21no—
287#624—21no—
288D3×Dic3—21no—
289D3×Dic3—21no—
290C32×C8—61no—
291C3⋊(C3⋊C8)—21no—
292C3×C3⋊C8—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—41no—
295C3×C3⋊C8—61no—
296C3×C3⋊C8—61no—
297C3×C3⋊C8—121no—
298#421—91noSylow
299C2×C33—21no—
300C2×C33C2×C22⋊C411yescharacteristic
301C3×C3⋊D3—41no—
302C32×D3—21no—
303C32×D3—21no—
304C32×D3—41no—
305C3×#41—31no—
306C3×#41—31no—
307C3×#41—61no—
308C3×#41—91no—
309C3×#41—91no—
310C3×#41—91no—
311C3×#41—181no—
312C3×#41—181no—
313C2×C3×Q8—91no—
314C2×C3×D4—91no—
315C2×C3×D4—181no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—181no—
320C2×#67—61no—
321#239—31no—
322D3×Q8—31no—
323#237—31no—
324#237—61no—
325D3×D4—31no—
326D3×D4—61no—
327#235—31no—
328#235—31no—
329#235—31no—
330#235—31no—
331#235—61no—
332#235—61no—
333#235—61no—
334#235—61no—
335#235C2×C3×D311yescharacteristic
336C2×D12—31no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3C2×C3×D311yescharacteristic
340C2×Dic6—31no—
341C3×M16—31no—
342C3×M16—31no—
343C3×M16—61no—
344C3×M16—91no—
345C3×M16—181no—
346C2×C3×C8—181no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—62no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—62no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—31no—
357C3×C42—31no—
358C3×C42—41no—
359C3×C42—61no—
360C3×C42D3211yescharacteristic, complemented
361C3×C42C2×C3×D311yescharacteristic, complemented
362C3×C42C2×C3×D311yescharacteristic, complemented
363(C2×D3)⋊C4—21no—
364Dic3⋊C4—21no—
365C4×Dic3C2×C3×D311yescharacteristic, complemented
366#208—31no—
367#208—31no—
368#208—61no—
369#208—61no—
370#208C2×C3×D311yescharacteristic, complemented
371C2×C3⋊C8—61no—
372ΓL(1,𝔽25)—61no—
373D3×C8—61no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—31no—
378C22×C32—31no—
379C22×C32—41no—
380C22×C32—61no—
381C22×C32—121no—
382C22×C32D3×D411yescharacteristic
383C22×C32C2×#6711yescharacteristic
384C22×C32C2×C3×D411yescharacteristic
385C2×C3⋊D3—21no—
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3—21no—
389C2×C3×D3—21no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—42no—
394C2×C3×D3—61no—
395C2×C3×D3—61no—
396C2×C3×D3—121no—
397C2×C3×D3—122no—
398C2×C3×D3—122no—
399C2×C3×D3(C2×D3)⋊C411yescharacteristic
400C2×C3×D3(C2×D3)⋊C411yescharacteristic
401C2×C3×D3C3×C22⋊C411yescharacteristic
402C2×C3×D3C3×C22⋊C411yescharacteristic
403D32—42no—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—31no—
411C32×C4—31no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4—42no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—42no—
419C32×C4—42no—
420C32×C4—44no—
421C32×C4—61no—
422C32×C4—121no—
423C32×C4C2×C4×D311yescharacteristic
424C32×C4C2×C4×D311yescharacteristic
425C32×C4C2×D1211yescharacteristic
426C32×C4D3×D411yescharacteristic
427C32×C4C22×C3×C411yescharacteristic
428C32×C4C2×C3×D411yescharacteristic
429C3⋊Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—42no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—61no—
439C3×Dic3—61no—
440C3×Dic3—121no—
441C3×Dic3(C2×D3)⋊C411yescharacteristic
442C3×Dic3(C2×D3)⋊C411yescharacteristic
443C3×Dic3C3×C22⋊C411yescharacteristic
444C3×Dic3C3×C22⋊C411yescharacteristic
445C2×#41—91no—
446C2×M16—91no—
447#117—31no—
448#104—31no—
449#104—91no—
450#104—91no—
451#104—91no—
452C33#42111yescharacteristic, complemented, Sylow
453C23×C3—31no—
454C23×C3—31no—
455C23×C3—61no—
456C23×C3—181no—
457C22×D3—61no—
458C22×D3—61no—
459C22×D3C3×#6711yescharacteristic
460C3×Q8—31no—
461C3×Q8—31no—
462C3×Q8—61no—
463C3×Q8—91no—
464C3×Q8—181no—
465C3×D4—31no—
466C3×D4—31no—
467C3×D4—61no—
468C3×D4—61no—
469C3×D4—61no—
470C3×D4—91no—
471C3×D4—121no—
472C3×D4—181no—
473C3×D4—181no—
474C3×D4—181no—
475C3×D4—181no—
476C2×C3×C4—22no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—42no—
496C2×C3×C4—41no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—62no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—121no—
508C2×C3×C4—181no—
509C2×C3×C4—181no—
510C2×C3×C4—181no—
511C2×C3×C4—181no—
512C2×C3×C4C2×D3211yescharacteristic
513C2×C3×C4C22×C3×D311yescharacteristic
514C2×C3×C4C22×C3×D311yescharacteristic
515#67—21no—
516#67—61no—
517#67—61no—
518#67—61no—
519#67—61no—
520#67—61no—
521#67—61no—
522#67—121no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3C3×#6711yescharacteristic
527D12—31no—
528D12—31no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12C3×C4×D311yescharacteristic
533C4×D3—21no—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—121no—
541C4×D3C3×C4×D311yescharacteristic
542C4×D3C3×C4×D311yescharacteristic
543C4×D3C3×D1211yescharacteristic
544C4×D3C3×D1211yescharacteristic
545Dic6—31no—
546Dic6—31no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6C3×C4×D311yescharacteristic
551C3×C8—61no—
552C3×C8—61no—
553C3×C8—121no—
554C3×C8—181no—
555C3⋊C8—21no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—121no—
559C2×C32—21no—
560C2×C32—22no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—41no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32—42no—
570C2×C32—61no—
571C2×C32—61no—
572C2×C32—121no—
573C2×C32D3×C22⋊C411yescharacteristic
574C2×C32C2×(C2×D3)⋊C411yescharacteristic
575C2×C32C2×C3×C22⋊C411yescharacteristic
576C3⋊D3—41no—
577C3×D3—21no—
578C3×D3—21no—
579C3×D3—21no—
580C3×D3—21no—
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—41no—
584C3×D3—41no—
585C3×D3—81no—
586C3×D3—121no—
587C3×D3—121no—
588C3×D3—241no—
589#41—31no—
590#41—91no—
591#41—91no—
592#41—91no—
593#41—181no—
594#41—181no—
595C2×Q8—91no—
596C2×D4—91no—
597C2×D4—181no—
598C22×C4—31no—
599C22×C4—181no—
600M16—31no—
601M16—91no—
602M16—181no—
603C2×C8—181no—
604C4⋊C4—61no—
605C22⋊C4—61no—
606C42—31no—
607C42C3×D3211yescharacteristic, complemented
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—31no—
612C22×C3—31no—
613C22×C3—31no—
614C22×C3—31no—
615C22×C3—41no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—122no—
624C22×C3—181no—
625C22×C3—362no—
626C22×C3D3×#6711yescharacteristic
627C22×C3C3×D3×D411yescharacteristic
628C22×C3C2×C3×#6711yescharacteristic
629C2×D3—21no—
630C2×D3—41no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—121no—
634C2×D3—122no—
635C2×D3—122no—
636C2×D3C3×(C2×D3)⋊C411yescharacteristic
637C2×D3C3×(C2×D3)⋊C411yescharacteristic
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—31no—
645C3×C4—31no—
646C3×C4—31no—
647C3×C4—31no—
648C3×C4—42no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—44no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—121no—
662C3×C4—122no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—181no—
666C3×C4C4×D3211yescharacteristic
667C3×C4D3×D1211yescharacteristic
668C3×C4C2×C3×C4×D311yescharacteristic
669C3×C4C2×C3×C4×D311yescharacteristic
670C3×C4C2×C3×D1211yescharacteristic
671C3×C4C3×D3×D411yescharacteristic
672Dic3—21no—
673Dic3—41no—
674Dic3—61no—
675Dic3—61no—
676Dic3—121no—
677Dic3C3×(C2×D3)⋊C411yescharacteristic
678Dic3C3×(C2×D3)⋊C411yescharacteristic
679C32—21no—
680C32—21no—
681C32—21no—
682C32—41no—
683C32#482111yescharacteristic, complemented
684C32#500511yescharacteristic, complemented
685C32C3×#42111yescharacteristic, complemented
686C23—31no—
687C23—181no—
688Q8—31no—
689Q8—91no—
690Q8—181no—
691D4—31no—
692D4—61no—
693D4—91no—
694D4—181no—
695D4—181no—
696D4—181no—
697D4—181no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4C2×C3×D3211yescharacteristic
711C8—61no—
712C8—181no—
713C2×C3—22no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—41no—
721C2×C3—41no—
722C2×C3—42no—
723C2×C3—41no—
724C2×C3—61no—
725C2×C3—61no—
726C2×C3—61no—
727C2×C3—61no—
728C2×C3—121no—
729C2×C3—121no—
730C2×C3—121no—
731C2×C3—121no—
732C2×C3—241no—
733C2×C3—361no—
734C2×C3D3×(C2×D3)⋊C411yescharacteristic
735C2×C3C3×D3×C22⋊C411yescharacteristic
736C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
737D3—21no—
738D3—21no—
739D3—41no—
740D3—121no—
741D3—121no—
742D3—241no—
743C22—31no—
744C22—31no—
745C22—61no—
746C22—121no—
747C22—181no—
748C22—362no—
749C22C3×D3×#6711yescharacteristic
750C4—31no—
751C4—31no—
752C4—41no—
753C4—61no—
754C4—121no—
755C4—181no—
756C4C3×C4×D3211yescharacteristic
757C4C3×D3×D1211yescharacteristic
758C3—21no—
759C3—21no—
760C3—21no—
761C3—41no—
762C3#1059039211yescharacteristic, direct product factor
763C3C3×#482111yescharacteristic, complemented
764C3C3×#500511yescharacteristic, complemented
765C2—21no—
766C2—61no—
767C2—61no—
768C2—121no—
769C2—361no—
770C2C3×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC3×C4D3×D12
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC33×C42C22
socleC2×C33C2×C22⋊C4
prime radicalC3×D3×#235C2
cosocleC2×C32×C4C23×C3
hypercenterC3×C42D32
hypocenterC32C3×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
2. C32×#872C2semidirect
3. C3×D3×#208C2semidirect
4. C3×#63632C2semidirect
5. C32×#805C2semidirect
6. C3×#63570C2semidirect
7. C3×#63569C2semidirect
10. #10590392C3direct (N × H)
16. C3×D3×D12C4semidirect
18. C3×#3799C4semidirect
20. C3×#3795C4semidirect
21. C3×D3×Dic6C4semidirect
22. C33×C42C22semidirect
23. C3×#3748C22semidirect
26. C32×C4×Dic3C22semidirect
27. C32×#208C22semidirect
37. C3×#872D3semidirect
38. C3×#872C2×C3semidirect
39. D3×#208C2×C3semidirect
41. #63632C2×C3semidirect
50. C3×#805D3semidirect
51. C3×#805C2×C3semidirect
52. #63570C2×C3semidirect
53. #63569C2×C3semidirect
114. D3×D12C3×C4semidirect
116. #3799C3×C4semidirect
118. #3795C3×C4semidirect
119. D3×Dic6C3×C4semidirect
128. C32×C42C2×D3semidirect
129. C32×C42C2×D3semidirect
130. C32×C42C22×C3semidirect
131. #3748C22×C3semidirect
139. C3×C4×Dic3C2×D3semidirect
140. C3×C4×Dic3C22×C3semidirect
146. C3×#208C2×D3semidirect
147. C3×#208C22×C3semidirect
177. #872C3×D3semidirect
191. #805C3×D3semidirect
360. C3×C42D32semidirect
361. C3×C42C2×C3×D3semidirect
362. C3×C42C2×C3×D3semidirect
365. C4×Dic3C2×C3×D3semidirect
370. #208C2×C3×D3semidirect
452. C33#421semidirect
607. C42C3×D32semidirect
683. C32#4821semidirect
684. C32#5005semidirect
685. C32C3×#421semidirect
762. C3#10590392direct (N × H)
763. C3C3×#4821semidirect
764. C3C3×#5005semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#2352
C32×#8722
C3×D3×#2082
C3×#636322
C32×#8052
C3×#635702
C3×#635692
C3×#50053
C3×#48213
#105903923