Finite Group Databasebeta

← C3×#79500 #11888582

Subgroups — C3×#79500 #11888582

Order 1152.

850 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×#5565C211yesmaximal, characteristic, complemented
2C3×#5551C211yesmaximal, characteristic, complemented
3C32×#435C211yesmaximal, characteristic, complemented
4C3×#5134C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic, complemented
6C3×#5114C211yesmaximal, characteristic, complemented
7C3×#5113C211yesmaximal, characteristic, complemented
8C3×#4847C211yesmaximal, characteristic, complemented
9C3×#4841C211yesmaximal, characteristic, complemented
10C3×#4734C211yesmaximal, characteristic, complemented
11C3×#4734C211yesmaximal, characteristic, complemented
12C3×#4723C211yesmaximal, characteristic, complemented
13C3×#4721C211yesmaximal, characteristic, complemented
14C3×#4711C211yesmaximal, characteristic, complemented
15C3×#4703C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#79500C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C32×M16C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×#939—21no—
24C3×#938—21no—
25C3×#930C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C2×C3×D24C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic
33C2×C3×#204C2211yescharacteristic
34C3×#898—21no—
35C3×D3×C4⋊C4—21no—
36C3×#883—21no—
37C3×#883—21no—
38C3×#883—21no—
39C3×#67⋊C4—21no—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×#870C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C32×#97C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#816C2211yescharacteristic
60C3×#816C2211yescharacteristic
61C3×#553—31no—
62C3×#547—31no—
63#5565C2×C311yescharacteristic, complemented
64#5551C2×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—21no—
76C3×#435D311yescharacteristic, complemented
77C3×#435C2×C311yescharacteristic, complemented
78C3×#417—31no—
79C3×#416—31no—
80#5134C2×C311yescharacteristic, complemented
81#5133C2×C311yescharacteristic, complemented
82#5114C2×C311yescharacteristic, complemented
83#5113C2×C311yescharacteristic, complemented
84#4847C2×C311yescharacteristic, complemented
85#4841C2×C311yescharacteristic, complemented
86#4734C2×C311yescharacteristic, complemented
87#4734C2×C311yescharacteristic, complemented
88#4723C2×C311yescharacteristic, complemented
89#4721C2×C311yescharacteristic, complemented
90#4711C2×C311yescharacteristic, complemented
91#4703C2×C311yescharacteristic, complemented
92C2×C32×D4D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×#235—22no—
101C3×#235—22no—
102C3×#235—41no—
103C3×#235—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C32×M16—41no—
113C2×C32×C8—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4D411yescharacteristic
119C32×C22⋊C4D411yescharacteristic
120C32×C22⋊C4D411yescharacteristic
121C32×C42C2311yescharacteristic
122C3×#217—21no—
123C3×#217—21no—
124C3×#217—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141C3×D24—22no—
142C3×#204—41no—
143C3×#204—41no—
144#3307—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#235C22×C311yescharacteristic
148C2×#235C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C2×C3×M16—21no—
153C2×C3×M16C2×D311yescharacteristic
154C2×C3×M16C22×C311yescharacteristic
155C22×C3×C8—21no—
156C22×C3×C8C2×D311yescharacteristic
157C22×C3×C8C22×C311yescharacteristic
158C3×C4⋊Q8—31no—
159C3×#126—61no—
160C3×#125—31no—
161C3×#123—61no—
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×#121—31no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#121—61no—
170C3×C4×D4—21no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×C4×D4—61no—
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—61no—
179#939—21no—
180#938—21no—
181#930C22×C311yescharacteristic
182#930C22×C311yescharacteristic
183#926C22×C311yescharacteristic
184C2×C4⋊Dic3C22×C311yescharacteristic
185#924C22×C311yescharacteristic
186#924C22×C311yescharacteristic
187C2×D24C22×C311yescharacteristic
188C2×#204C22×C311yescharacteristic
189C2×#204C22×C311yescharacteristic
190#898—21no—
191D3×C4⋊C4—21no—
192#883—21no—
193#883—21no—
194#883—21no—
195#67⋊C4—21no—
196C4×D12C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198#870C22×C311yescharacteristic
199#869C22×C311yescharacteristic
200C3×#107—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—21no—
204C3×C4⋊C8C2×D311yescharacteristic
205C3×C4⋊C8C22×C311yescharacteristic
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—21no—
217C3×C22⋊C8—21no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C2×D311yescharacteristic
220C3×C22⋊C8C22×C311yescharacteristic
221C3×C22⋊C8C22×C311yescharacteristic
222C3×#97—21no—
223C3×#97C2×D311yescharacteristic
224C3×#97C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229#818C22×C311yescharacteristic
230#817C22×C311yescharacteristic
231#817C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235#816C22×C311yescharacteristic
236#816C22×C311yescharacteristic
237#816C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C32×D4—41no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—42no—
253C3×#67—42no—
254C3×#67—42no—
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×C4×D3—81no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C32×C8—21no—
278C32×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#435C3×D311yescharacteristic, complemented
292#417—31no—
293#416—31no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4D1211yescharacteristic
308C2×C3×D4C3×D411yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—21no—
323C2×#67—21no—
324C22×Dic3—21no—
325#235—22no—
326#235—22no—
327#235—41no—
328#235—41no—
329C2×D12C23×C311yescharacteristic
330C2×D12C23×C311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×Dic6C23×C311yescharacteristic
336C2×Dic6C23×C311yescharacteristic
337C3×SD16—121no—
338C3×SD16—121no—
339C3×D8—62no—
340C3×M16—41no—
341C3×M16—41no—
342C3×M16—42no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—41no—
348C2×C3×C8—41no—
349C2×C3×C8—42no—
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C23×C311yescharacteristic
355C2×C3×C8C23×C311yescharacteristic
356C2×C3×C8C23×C311yescharacteristic
357C2×C3×C8C23×C311yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
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⋊C4—61no—
370C3×C4⋊C4D1211yescharacteristic
371C3×C4⋊C4C3×D411yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4D1211yescharacteristic
382C3×C22⋊C4D1211yescharacteristic
383C3×C22⋊C4C3×D411yescharacteristic
384C3×C22⋊C4C3×D411yescharacteristic
385C3×C42—21no—
386C3×C42—61no—
387C3×C42C22×D311yescharacteristic
388C3×C42C23×C311yescharacteristic
389#217—21no—
390#217—21no—
391#217—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3C23×C311yescharacteristic
400C4⋊Dic3C23×C311yescharacteristic
401C4⋊Dic3C23×C311yescharacteristic
402C4⋊Dic3C23×C311yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—21no—
407C4×Dic3—21no—
408D24—22no—
409#204—41no—
410#204—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C2×#41—31no—
438C2×SD16—31no—
439C2×SD16—31no—
440C2×D8—31no—
441C2×M16C2×C3×D311yescharacteristic
442C22×C8C2×C3×D311yescharacteristic
443C4⋊Q8—31no—
444#126—61no—
445#125—31no—
446#123—61no—
447#123—61no—
448#123—61no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451#121—31no—
452#121—31no—
453#121—61no—
454#121—61no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—61no—
458C4×D4C2×C3×D311yescharacteristic
459#117—31no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—61no—
462#107—31no—
463#106—31no—
464#106—31no—
465C4⋊C8C2×C3×D311yescharacteristic
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476C22⋊C8C2×C3×D311yescharacteristic
477C22⋊C8C2×C3×D311yescharacteristic
478#97C2×C3×D311yescharacteristic
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3C2×D1211yescharacteristic
484C23×C3C2×D1211yescharacteristic
485C23×C3C2×C3×D411yescharacteristic
486C23×C3C2×C3×D411yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—42no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—122no—
501C3×D4—122no—
502C3×D4—122no—
503C3×D4—241no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—122no—
530C2×C3×C4—241no—
531C2×C3×C4—241no—
532C2×C3×C4C2×D1211yescharacteristic
533C2×C3×C4C2×D1211yescharacteristic
534C2×C3×C4C2×D1211yescharacteristic
535C2×C3×C4C2×D1211yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C24×C311yescharacteristic
542#67—42no—
543#67—42no—
544#67—42no—
545#67—81no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—81no—
553D12—21no—
554D12—21no—
555D12—21no—
556D12C3×#4112yes—
557C4×D3—42no—
558C4×D3—42no—
559C4×D3—42no—
560C4×D3—81no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—41no—
575C3×C8—41no—
576C3×C8—41no—
577C2×C32—41no—
578C2×C32—41no—
579C2×C32#54611yescharacteristic
580C2×C32#57511yescharacteristic
581C2×C32#57711yescharacteristic
582C3×D3—42no—
583C3×D3—81no—
584#41—62no—
585#41—62no—
586#41—121no—
587#41—121no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4C3×D1211yescharacteristic
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4C22×C3×D311yescharacteristic
603C22×C4C22×C3×D311yescharacteristic
604SD16—121no—
605SD16—121no—
606D8—62no—
607M16—41no—
608C2×C8—41no—
609C2×C8C22×C3×D311yescharacteristic
610C2×C8C22×C3×D311yescharacteristic
611C2×C8C22×C3×D311yescharacteristic
612C2×C8C22×C3×D311yescharacteristic
613C4⋊C4—31no—
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⋊C4—61no—
624C4⋊C4C3×D1211yescharacteristic
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4C3×D1211yescharacteristic
633C22⋊C4C3×D1211yescharacteristic
634C42—61no—
635C42C22×C3×D311yescharacteristic
636C22×C3—22no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—62no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C22×D1211yescharacteristic
662C22×C3C22×C3×D411yescharacteristic
663C2×D3—22no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
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—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699C32#330711yescharacteristic, complemented, Sylow
700C23—61no—
701C23—61no—
702C23C2×C3×D1211yescharacteristic
703C23C2×C3×D1211yescharacteristic
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—61no—
708D4—32no—
709D4—41no—
710D4—61no—
711D4—61no—
712D4—61no—
713D4—122no—
714D4—122no—
715D4—122no—
716D4—241no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—241no—
731C2×C4—241no—
732C2×C4C2×C3×D1211yescharacteristic
733C2×C4C2×C3×D1211yescharacteristic
734C2×C4C2×C3×D1211yescharacteristic
735C2×C4C2×C3×D1211yescharacteristic
736C2×C4C23×C3×D311yescharacteristic
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—42no—
745C2×C3—41no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—41no—
749C2×C3—81no—
750C2×C3—122no—
751C2×C3—241no—
752C2×C3#555411yescharacteristic
753C2×C3#574811yescharacteristic
754C2×C3#575111yescharacteristic
755C2×C3C3×#54611yescharacteristic
756C2×C3C3×#57511yescharacteristic
757C2×C3C3×#57711yescharacteristic
758D3—42no—
759D3—81no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—62no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22C22×C3×D1211yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4C3×#100411yescharacteristic
784C4C3×D3×#4111yescharacteristic
785C3—21no—
786C3#7950011yescharacteristic, direct product factor
787C3C3×#330711yescharacteristic, complemented
788C2—41no—
789C2—41no—
790C2—122no—
791C2—241no—
792C2C3×#555411yescharacteristic
793C2C3×#574811yescharacteristic
794C2C3×#575111yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#435C2
socleC22×C32C22×D4
hypercenterC3×#435D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#435

Complements

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

NH ≅ G/Ntype
1. C3×#5565C2semidirect
2. C3×#5551C2semidirect
3. C32×#435C2semidirect
4. C3×#5134C2semidirect
5. C3×#5133C2semidirect
6. C3×#5114C2semidirect
7. C3×#5113C2semidirect
8. C3×#4847C2semidirect
9. C3×#4841C2semidirect
10. C3×#4734C2semidirect
11. C3×#4734C2semidirect
12. C3×#4723C2semidirect
13. C3×#4721C2semidirect
14. C3×#4711C2semidirect
15. C3×#4703C2semidirect
17. #79500C3direct (N × H)
63. #5565C2×C3semidirect
64. #5551C2×C3semidirect
76. C3×#435D3semidirect
77. C3×#435C2×C3semidirect
80. #5134C2×C3semidirect
81. #5133C2×C3semidirect
82. #5114C2×C3semidirect
83. #5113C2×C3semidirect
84. #4847C2×C3semidirect
85. #4841C2×C3semidirect
86. #4734C2×C3semidirect
87. #4734C2×C3semidirect
88. #4723C2×C3semidirect
89. #4721C2×C3semidirect
90. #4711C2×C3semidirect
91. #4703C2×C3semidirect
291. #435C3×D3semidirect
699. C32#3307semidirect
786. C3#79500direct (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×#55652
C3×#55512
C32×#4352
C3×#51342
C3×#51332
C3×#51142
C3×#51132
C3×#48472
C3×#48412
C3×#47342
C3×#47232
C3×#47212
C3×#47112
C3×#47032
C3×#33073
#795003