Finite Group Databasebeta

← C3×#78853 #11888564

Subgroups — C3×#78853 #11888564

Order 1152.

867 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5824C211yesmaximal, characteristic, complemented
2C3×#5530C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5C3×#5114C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7C3×#4996C211yesmaximal, characteristic, complemented
8C3×#4818C211yesmaximal, characteristic, complemented
9C3×#4812C211yesmaximal, characteristic, complemented
10C3×#4805C211yesmaximal, characteristic, complemented
11C3×#4797C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic, complemented
13C3×#4781C211yesmaximal, characteristic, complemented
14C3×#4771C211yesmaximal, characteristic, complemented
15C3×#4763C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#78853C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#939—21no—
26C3×#935—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#929—21no—
31C3×C4×#67C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C2×C3×Dic3⋊C4—21no—
34C2×C3×#204C2211yescharacteristic
35C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
36C3×#895C2211yescharacteristic
37C3×#893C2211yescharacteristic
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#890C2211yescharacteristic
40C3×#884—21no—
41C3×#883—21no—
42C3×#876—21no—
43C3×C4×D12—21no—
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#553—31no—
62C3×#547—31no—
63#5824C2×C311yescharacteristic, complemented
64#5530C2×C311yescharacteristic, complemented
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#478—31no—
69C3×#468—31no—
70C3×#465—31no—
71C3×#461—31no—
72C3×#449—31no—
73C3×#449—31no—
74C3×#442—31no—
75C3×#435—31no—
76C3×#417—31no—
77C3×#416—21no—
78C3×#416D311yescharacteristic, complemented
79C3×#416C2×C311yescharacteristic, complemented
80#5238C2×C311yescharacteristic, complemented
81#5114C2×C311yescharacteristic, complemented
82#5111C2×C311yescharacteristic, complemented
83#4996C2×C311yescharacteristic, complemented
84#4818C2×C311yescharacteristic, complemented
85#4812C2×C311yescharacteristic, complemented
86#4805C2×C311yescharacteristic, complemented
87#4797C2×C311yescharacteristic, complemented
88#4785C2×C311yescharacteristic, complemented
89#4781C2×C311yescharacteristic, complemented
90#4771C2×C311yescharacteristic, complemented
91#4763C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C3×#237—22no—
105C3×#237—41no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C32×C8—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C42—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#215—41no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×#204—41no—
143C3×ΓL(1,𝔽25)—41no—
144#3307—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41—31no—
147C2×C3×#41C2×D311yescharacteristic
148C2×C3×#41C22×C311yescharacteristic
149C2×#237C22×C311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C2×C3×D8—31no—
153C2×C3×M16—31no—
154C22×C3×C8—21no—
155C22×C3×C8C2×D311yescharacteristic
156C22×C3×C8C22×C311yescharacteristic
157C3×C4⋊Q8—31no—
158C3×#126—61no—
159C3×#125—31no—
160C3×#123—61no—
161C3×#123—61no—
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×#121—31no—
166C3×#121—31no—
167C3×#121—61no—
168C3×#121—61no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×C4×D4—61no—
173C3×#117—21no—
174C3×#117C2×D311yescharacteristic
175C3×#117C22×C311yescharacteristic
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—61no—
178#946C22×C311yescharacteristic
179#944C22×C311yescharacteristic
180C2×#215C22×C311yescharacteristic
181#939—21no—
182#935—21no—
183D4×Dic3C22×C311yescharacteristic
184C2×#213C22×C311yescharacteristic
185#930C22×C311yescharacteristic
186#929—21no—
187C4×#67C22×C311yescharacteristic
188#924C22×C311yescharacteristic
189C2×Dic3⋊C4—21no—
190C2×#204C22×C311yescharacteristic
191C2×ΓL(1,𝔽25)C22×C311yescharacteristic
192#895C22×C311yescharacteristic
193#893C22×C311yescharacteristic
194D3×C4⋊C4C22×C311yescharacteristic
195#890C22×C311yescharacteristic
196#884—21no—
197#883—21no—
198#876—21no—
199C4×D12—21no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#103C22×C311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×#102—21no—
215C3×#102—21no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102C2×D311yescharacteristic
219C3×#102C2×D311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×#97—31no—
225#835C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227#830C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#817C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#815C22×C311yescharacteristic
233Dic3⋊C8C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—42no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—42no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—41no—
256C3×#67—42no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#547—31no—
281#491—31no—
282#485—31no—
283#483—31no—
284#478—31no—
285#468—31no—
286#465—31no—
287#461—31no—
288#449—31no—
289#449—31no—
290#442—31no—
291#435—31no—
292#417—31no—
293#416C3×D311yescharacteristic, complemented
294C3×#41—24no—
295C3×#41—22no—
296C3×#41—22no—
297C3×#41—41no—
298C3×#41—41no—
299C3×#41—42no—
300C3×#41—62no—
301C3×#41—121no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C23×C311yescharacteristic
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—41no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C23×C311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—41no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C23×C311yescharacteristic
328C2×#67—21no—
329C2×#67—21no—
330C2×#67C3×D411yescharacteristic
331C22×Dic3—21no—
332C22×Dic3—21no—
333#237—22no—
334#237—41no—
335C2×D12—21no—
336C2×D12C23×C311yescharacteristic
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3C23×C311yescharacteristic
340C2×Dic6C23×C311yescharacteristic
341C3×SD16—121no—
342C3×SD16—121no—
343C3×D8—62no—
344C3×M16—121no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—41no—
350C2×C3×C8—41no—
351C2×C3×C8—42no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C23×C311yescharacteristic
355C2×C3×C8C23×C311yescharacteristic
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C23×C311yescharacteristic
371C3×C4⋊C4C23×C311yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C42—21no—
384C3×C42—21no—
385C3×C42—31no—
386C3×C42—41no—
387#217—21no—
388#217—21no—
389#217C3×D411yescharacteristic
390#215—41no—
391#213—22no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4C3×D411yescharacteristic
397C4⋊Dic3—21no—
398C4⋊Dic3C23×C311yescharacteristic
399C4⋊Dic3C23×C311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4C3×D411yescharacteristic
407C4×Dic3C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410#204—41no—
411ΓL(1,𝔽25)—41no—
412C22×C32—21no—
413C22×C32—22no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C2×#41C2×C3×D311yescharacteristic
439C2×SD16—31no—
440C2×SD16—31no—
441C2×D8—31no—
442C2×M16—31no—
443C22×C8C2×C3×D311yescharacteristic
444C4⋊Q8—31no—
445#126—61no—
446#125—31no—
447#123—61no—
448#123—61no—
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452#121—31no—
453#121—31no—
454#121—61no—
455#121—61no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—61no—
460#117C2×C3×D311yescharacteristic
461C2×C4⋊C4—31no—
462C2×C4⋊C4—61no—
463#107—31no—
464#106—31no—
465#106—31no—
466C4⋊C8—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103C2×C3×D311yescharacteristic
472#103C2×C3×D311yescharacteristic
473#102—31no—
474#102—31no—
475#102C2×C3×D311yescharacteristic
476#102C2×C3×D311yescharacteristic
477C22⋊C8—31no—
478C22⋊C8—31no—
479#97—31no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3D3×D411yescharacteristic
487C23×C3C2×C3×D411yescharacteristic
488C22×D3—21no—
489C22×D3C2×C3×D411yescharacteristic
490C3×Q8—22no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—41no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—22no—
501C3×D4—41no—
502C3×D4—42no—
503C3×D4—42no—
504C3×D4—44no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—122no—
508C3×D4—121no—
509C3×D4—122no—
510C3×D4—241no—
511C3×D4#23512yes—
512C3×D4C3×#4112yes—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—42no—
534C2×C3×C4—42no—
535C2×C3×C4—44no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—122no—
542C2×C3×C4—122no—
543C2×C3×C4—241no—
544C2×C3×C4—241no—
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C2×C3×D411yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C24×C311yescharacteristic
549#67—41no—
550#67—42no—
551#67—81no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—42no—
556C2×Dic3—42no—
557C2×Dic3C2×C3×D411yescharacteristic
558C2×Dic3C2×C3×D411yescharacteristic
559C2×Dic3C2×C3×D411yescharacteristic
560D12—21no—
561D12—21no—
562D12—42no—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—81no—
566C4×D3—81no—
567Dic6—21no—
568Dic6—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—41no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C2×C32—41no—
580C2×C32—42no—
581C2×C32#54611yescharacteristic
582C2×C32#57511yescharacteristic
583C2×C32#57711yescharacteristic
584C3×D3—41no—
585C3×D3—81no—
586#41—22no—
587#41—41no—
588#41—62no—
589#41—121no—
590C2×Q8—31no—
591C2×Q8C22×C3×D311yescharacteristic
592C2×D4—21no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4C22×C3×D311yescharacteristic
599C22×C4—21no—
600C22×C4—31no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4C22×C3×D311yescharacteristic
606SD16—121no—
607SD16—121no—
608D8—62no—
609M16—121no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—41no—
613C2×C8C22×C3×D311yescharacteristic
614C2×C8C22×C3×D311yescharacteristic
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4C22×C3×D311yescharacteristic
626C4⋊C4C22×C3×D311yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C42—21no—
637C42—31no—
638C22×C3—22no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—22no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C22×C3×D411yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C3×C4—22no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4C2×#23511yescharacteristic
692C3×C4#100411yescharacteristic
693C3×C4C2×C3×#4111yescharacteristic
694C3×C4C3×H(5,𝔽2)11yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—21no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701C32#330711yescharacteristic, complemented, Sylow
702C23—21no—
703C23—31no—
704C23—61no—
705C23C3×D3×D411yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—61no—
709Q8—61no—
710D4—21no—
711D4—42no—
712D4—61no—
713D4—61no—
714D4—122no—
715D4—121no—
716D4—122no—
717D4—241no—
718D4C3×#23512yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—42no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4C3×D3×D411yescharacteristic
738C2×C4C23×C3×D311yescharacteristic
739C8—21no—
740C8—21no—
741C8—61no—
742C8—61no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—42no—
747C2×C3—41no—
748C2×C3—42no—
749C2×C3—41no—
750C2×C3—42no—
751C2×C3—82no—
752C2×C3—121no—
753C2×C3—241no—
754C2×C3#549011yescharacteristic
755C2×C3#576811yescharacteristic
756C2×C3#577011yescharacteristic
757C2×C3C3×#54611yescharacteristic
758C2×C3C3×#57511yescharacteristic
759C2×C3C3×#57711yescharacteristic
760D3—41no—
761D3—81no—
762C22—21no—
763C22—22no—
764C22—21no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22C2×C3×D3×D411yescharacteristic
775C4—21no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—61no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4C2×C3×#23511yescharacteristic
786C4C3×#100411yescharacteristic
787C3—21no—
788C3#7885311yescharacteristic, direct product factor
789C3C3×#330711yescharacteristic, complemented
790C2—41no—
791C2—42no—
792C2—121no—
793C2—241no—
794C2C3×#549011yescharacteristic
795C2C3×#576811yescharacteristic
796C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
hypercenterC3×#416D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
1. C3×#5824C2semidirect
2. C3×#5530C2semidirect
3. C32×#416C2semidirect
4. C3×#5238C2semidirect
5. C3×#5114C2semidirect
6. C3×#5111C2semidirect
7. C3×#4996C2semidirect
8. C3×#4818C2semidirect
9. C3×#4812C2semidirect
10. C3×#4805C2semidirect
11. C3×#4797C2semidirect
12. C3×#4785C2semidirect
13. C3×#4781C2semidirect
14. C3×#4771C2semidirect
15. C3×#4763C2semidirect
17. #78853C3direct (N × H)
63. #5824C2×C3semidirect
64. #5530C2×C3semidirect
78. C3×#416D3semidirect
79. C3×#416C2×C3semidirect
80. #5238C2×C3semidirect
81. #5114C2×C3semidirect
82. #5111C2×C3semidirect
83. #4996C2×C3semidirect
84. #4818C2×C3semidirect
85. #4812C2×C3semidirect
86. #4805C2×C3semidirect
87. #4797C2×C3semidirect
88. #4785C2×C3semidirect
89. #4781C2×C3semidirect
90. #4771C2×C3semidirect
91. #4763C2×C3semidirect
293. #416C3×D3semidirect
701. C32#3307semidirect
788. C3#78853direct (N × H)
789. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
C3×#55302
C32×#4162
C3×#52382
C3×#51142
C3×#51112
C3×#49962
C3×#48182
C3×#48122
C3×#48052
C3×#47972
C3×#47852
C3×#47812
C3×#47712
C3×#47632
C3×#33073
#788533