Finite Group Databasebeta

← C3×#80819 #11888561

Subgroups — C3×#80819 #11888561

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5631C211yesmaximal, characteristic, complemented
2C3×#5618C211yesmaximal, characteristic, complemented
3C32×#468C211yesmaximal, characteristic, complemented
4C3×#5172C211yesmaximal, characteristic, complemented
5C3×#5162C211yesmaximal, characteristic, complemented
6C3×#5133C211yesmaximal, characteristic, complemented
7C3×#5127C211yesmaximal, characteristic, complemented
8C3×#5043C211yesmaximal, characteristic, complemented
9C3×#5037C211yesmaximal, characteristic, complemented
10C3×#4891C211yesmaximal, characteristic, complemented
11C3×#4888C211yesmaximal, characteristic, complemented
12C3×#4804C211yesmaximal, characteristic, complemented
13C3×#4797C211yesmaximal, characteristic, complemented
14C3×#4785C211yesmaximal, characteristic, complemented
15C3×#4778C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#80819C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×C32×M16C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C32×#121C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C3×#939—21no—
26C3×#938C2211yescharacteristic
27C3×D4×Dic3—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic
34C3×#897C2211yescharacteristic
35C3×#894—21no—
36C3×#893C2211yescharacteristic
37C3×#892C2211yescharacteristic
38C3×D3×C4⋊C4—21no—
39C3×#890C2211yescharacteristic
40C3×#886—21no—
41C3×#884—21no—
42C3×#883—21no—
43C3×#879—21no—
44C32×#107C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#830C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#553—31no—
62C3×#547—31no—
63#5631C2×C311yescharacteristic, complemented
64#5618C2×C311yescharacteristic, complemented
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#478—31no—
69C3×#468—21no—
70C3×#468D311yescharacteristic, complemented
71C3×#468C2×C311yescharacteristic, complemented
72C3×#465—31no—
73C3×#461—31no—
74C3×#449—31no—
75C3×#449—31no—
76C3×#442—31no—
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5172C2×C311yescharacteristic, complemented
81#5162C2×C311yescharacteristic, complemented
82#5133C2×C311yescharacteristic, complemented
83#5127C2×C311yescharacteristic, complemented
84#5043C2×C311yescharacteristic, complemented
85#5037C2×C311yescharacteristic, complemented
86#4891C2×C311yescharacteristic, complemented
87#4888C2×C311yescharacteristic, complemented
88#4804C2×C311yescharacteristic, complemented
89#4797C2×C311yescharacteristic, complemented
90#4785C2×C311yescharacteristic, complemented
91#4778C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239—41no—
103C3×#235—22no—
104C3×#235—41no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C32×SD16—41no—
113C32×M16—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120C32×C22⋊C4—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×#214—41no—
125C3×#213—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3307—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C22×C311yescharacteristic
148C2×#235C22×C311yescharacteristic
149C2×C3×SD16—21no—
150C2×C3×SD16—31no—
151C2×C3×SD16C2×D311yescharacteristic
152C2×C3×SD16C22×C311yescharacteristic
153C2×C3×D8—31no—
154C2×C3×M16—21no—
155C2×C3×M16C2×D311yescharacteristic
156C2×C3×M16C22×C311yescharacteristic
157C22×C3×C8—31no—
158C3×C4⋊Q8—31no—
159C3×#126—61no—
160C3×#125—31no—
161C3×#123—61no—
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8C2×D311yescharacteristic
167C3×C22⋊Q8C22×C311yescharacteristic
168C3×#121—21no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#121—61no—
172C3×#121C2×D311yescharacteristic
173C3×#121C22×C311yescharacteristic
174C3×C4×D4—31no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178C3×#117—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—61no—
181#944C22×C311yescharacteristic
182#939—21no—
183#938C22×C311yescharacteristic
184D4×Dic3—21no—
185D4×Dic3C22×C311yescharacteristic
186C2×#214C22×C311yescharacteristic
187C2×#213C22×C311yescharacteristic
188C4×#67C22×C311yescharacteristic
189C2×C4⋊Dic3C22×C311yescharacteristic
190C2×D3×C8C22×C311yescharacteristic
191#897C22×C311yescharacteristic
192#894—21no—
193#893C22×C311yescharacteristic
194#892C22×C311yescharacteristic
195D3×C4⋊C4—21no—
196#890C22×C311yescharacteristic
197#886—21no—
198#884—21no—
199#883—21no—
200#879—21no—
201C3×#107—21no—
202C3×#107C2×D311yescharacteristic
203C3×#107C22×C311yescharacteristic
204C3×#106—31no—
205C3×#106—31no—
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103C2×D311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#102—21no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102C2×D311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×#97—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#815C22×C311yescharacteristic
233Dic3⋊C8C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#808C22×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—21no—
246C32×D4—42no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—41no—
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—42no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3—42no—
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#468C3×D311yescharacteristic, complemented
286#465—31no—
287#461—31no—
288#449—31no—
289#449—31no—
290#442—31no—
291#435—31no—
292#417—31no—
293#416—31no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C23×C311yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C2×#67—21no—
323C2×#67—21no—
324C2×#67C3×D411yescharacteristic
325C22×Dic3—21no—
326C22×Dic3—21no—
327#239—22no—
328#239—41no—
329#235—22no—
330#235—41no—
331C2×D12—21no—
332C2×D12C23×C311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3C23×C311yescharacteristic
337C2×Dic6C23×C311yescharacteristic
338C3×SD16—41no—
339C3×SD16—41no—
340C3×SD16—42no—
341C3×SD16—121no—
342C3×D8—62no—
343C3×M16—41no—
344C3×M16—41no—
345C3×M16—42no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C23×C311yescharacteristic
354C2×C3×C8C23×C311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—41no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C23×C311yescharacteristic
372C3×C4⋊C4C23×C311yescharacteristic
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—41no—
380C3×C22⋊C4—41no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C42—31no—
387C3×C42—61no—
388#217—21no—
389#217—21no—
390#217C3×D411yescharacteristic
391#214—41no—
392#213—22no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4C3×D411yescharacteristic
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3—21no—
400C4⋊Dic3C23×C311yescharacteristic
401C4⋊Dic3C23×C311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4C3×D411yescharacteristic
406C4×Dic3—21no—
407C4×Dic3C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410D3×C8—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—22no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C2×#41—31no—
438C2×SD16—31no—
439C2×SD16C2×C3×D311yescharacteristic
440C2×D8—31no—
441C2×M16C2×C3×D311yescharacteristic
442C22×C8—31no—
443C4⋊Q8—31no—
444#126—61no—
445#125—31no—
446#123—61no—
447#123—61no—
448#123—61no—
449C22⋊Q8—31no—
450C22⋊Q8C2×C3×D311yescharacteristic
451#121—31no—
452#121—61no—
453#121—61no—
454#121C2×C3×D311yescharacteristic
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—61no—
459#117—31no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—61no—
462#107C2×C3×D311yescharacteristic
463#106—31no—
464#106—31no—
465C4⋊C8—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103C2×C3×D311yescharacteristic
472#102—31no—
473#102—31no—
474#102—31no—
475#102C2×C3×D311yescharacteristic
476C22⋊C8—31no—
477C22⋊C8—31no—
478#97—31no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×C3×D411yescharacteristic
487C22×D3—21no—
488C22×D3C2×C3×D411yescharacteristic
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—32no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—42no—
505C3×D4—42no—
506C3×D4—61no—
507C3×D4—82no—
508C3×D4—122no—
509C3×D4—121no—
510C3×D4—122no—
511C3×D4—241no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
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—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—122no—
538C2×C3×C4—122no—
539C2×C3×C4—122no—
540C2×C3×C4—241no—
541C2×C3×C4—241no—
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×C3×D411yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C24×C311yescharacteristic
546#67—41no—
547#67—42no—
548#67—81no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—81no—
553C2×Dic3—81no—
554C2×Dic3C2×C3×D411yescharacteristic
555C2×Dic3C2×C3×D411yescharacteristic
556C2×Dic3C2×C3×D411yescharacteristic
557D12—21no—
558D12—42no—
559D12C3×#4112yes—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—42no—
563C4×D3—42no—
564C4×D3—42no—
565Dic6—21no—
566Dic6—21no—
567C3×C8—22no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—41no—
578C2×C32—81no—
579C2×C32#54611yescharacteristic
580C2×C32#57511yescharacteristic
581C2×C32#57711yescharacteristic
582C3×D3—41no—
583C3×D3—42no—
584#41—62no—
585#41—62no—
586#41—121no—
587#41—121no—
588C2×Q8—31no—
589C2×Q8C22×C3×D311yescharacteristic
590C2×D4—21no—
591C2×D4—31no—
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4C22×C3×D311yescharacteristic
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4C22×C3×D311yescharacteristic
604SD16—41no—
605SD16—121no—
606D8—62no—
607M16—41no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—121no—
611C2×C8C22×C3×D311yescharacteristic
612C2×C8C22×C3×D311yescharacteristic
613C4⋊C4—21no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4C22×C3×D311yescharacteristic
624C4⋊C4C22×C3×D311yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—31no—
628C22⋊C4—31no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C42—31no—
635C42—61no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—62no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C22×C3×D411yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4#100411yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4C2×C3×#4111yescharacteristic
692C3×C4C3×H(5,𝔽2)11yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699C32#330711yescharacteristic, complemented, Sylow
700C23—21no—
701C23—31no—
702C23—61no—
703C23C3×D3×D411yescharacteristic
704Q8—21no—
705Q8—21no—
706Q8—61no—
707Q8—61no—
708D4—21no—
709D4—21no—
710D4—32no—
711D4—42no—
712D4—61no—
713D4—122no—
714D4—121no—
715D4—122no—
716D4—241no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4C3×D3×D411yescharacteristic
736C2×C4C23×C3×D311yescharacteristic
737C8—21no—
738C8—21no—
739C8—61no—
740C8—61no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—81no—
749C2×C3—121no—
750C2×C3—122no—
751C2×C3—161no—
752C2×C3#561011yescharacteristic
753C2×C3#577311yescharacteristic
754C2×C3#577811yescharacteristic
755C2×C3C3×#54611yescharacteristic
756C2×C3C3×#57511yescharacteristic
757C2×C3C3×#57711yescharacteristic
758D3—41no—
759D3—42no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22C2×C3×D3×D411yescharacteristic
773C4—21no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—61no—
778C4—61no—
779C4—61no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4C3×#100411yescharacteristic
784C4C3×D3×#4111yescharacteristic
785C3—21no—
786C3#8081911yescharacteristic, direct product factor
787C3C3×#330711yescharacteristic, complemented
788C2—41no—
789C2—81no—
790C2—121no—
791C2—122no—
792C2C3×#561011yescharacteristic
793C2C3×#577311yescharacteristic
794C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#468C2
socleC22×C32C22×D4
hypercenterC3×#468D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#468

Complements

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

NH ≅ G/Ntype
1. C3×#5631C2semidirect
2. C3×#5618C2semidirect
3. C32×#468C2semidirect
4. C3×#5172C2semidirect
5. C3×#5162C2semidirect
6. C3×#5133C2semidirect
7. C3×#5127C2semidirect
8. C3×#5043C2semidirect
9. C3×#5037C2semidirect
10. C3×#4891C2semidirect
11. C3×#4888C2semidirect
12. C3×#4804C2semidirect
13. C3×#4797C2semidirect
14. C3×#4785C2semidirect
15. C3×#4778C2semidirect
17. #80819C3direct (N × H)
63. #5631C2×C3semidirect
64. #5618C2×C3semidirect
70. C3×#468D3semidirect
71. C3×#468C2×C3semidirect
80. #5172C2×C3semidirect
81. #5162C2×C3semidirect
82. #5133C2×C3semidirect
83. #5127C2×C3semidirect
84. #5043C2×C3semidirect
85. #5037C2×C3semidirect
86. #4891C2×C3semidirect
87. #4888C2×C3semidirect
88. #4804C2×C3semidirect
89. #4797C2×C3semidirect
90. #4785C2×C3semidirect
91. #4778C2×C3semidirect
285. #468C3×D3semidirect
699. C32#3307semidirect
786. C3#80819direct (N × H)
787. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C3×#56312
C3×#56182
C32×#4682
C3×#51722
C3×#51622
C3×#51332
C3×#51272
C3×#50432
C3×#50372
C3×#48912
C3×#48882
C3×#48042
C3×#47972
C3×#47852
C3×#47782
C3×#33073
#808193