Finite Group Databasebeta

← C3×#80192 #11878411

Subgroups — C3×#80192 #11878411

Order 1152.

830 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×#5816C211yesmaximal, characteristic
2C3×#5628C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5C3×#5189C211yesmaximal, characteristic, complemented
6C3×#5188C211yesmaximal, characteristic, complemented
7C3×#5186C211yesmaximal, characteristic, complemented
8C3×#5186C211yesmaximal, characteristic, complemented
9C3×#5045C211yesmaximal, characteristic, complemented
10C3×#4816C211yesmaximal, characteristic, complemented
11C3×#4815C211yesmaximal, characteristic, complemented
12C3×#4814C211yesmaximal, characteristic, complemented
13C3×#4813C211yesmaximal, characteristic, complemented
14C3×#4727C211yesmaximal, characteristic
15C3×#4723C211yesmaximal, characteristic, complemented
16C3×#3202—31nomaximal
17#80192C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C3×#947—21no—
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C3×#944—21no—
31C2×C3×#216C2211yescharacteristic
32C2×C3×#216C2211yescharacteristic
33C3×#929—21no—
34C3×#929—21no—
35C3×#926C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
38C2×C3×D3×C8C2211yescharacteristic
39C3×#897C2211yescharacteristic
40C3×#894—21no—
41C3×#892C2211yescharacteristic
42C3×#888—21no—
43C3×#885—21no—
44C3×#883—21no—
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×#818C2211yescharacteristic
56C3×#817C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#536—31no—
62C3×#536—31no—
63#5816C2×C311yescharacteristic
64#5628C2×C311yescharacteristic
65C3×#485—31no—
66C3×#485—31no—
67C3×#485—31no—
68C3×#485—31no—
69C3×#470—31no—
70C3×#470—31no—
71C3×#467—31no—
72C3×#467—31no—
73C3×#451—21no—
74C3×#451—31no—
75C3×#451—31no—
76C3×#451—31no—
77C3×#451D311yescharacteristic, complemented
78C3×#451C2×C311yescharacteristic, complemented
79C3×#408—31no—
80#5228C2×C311yescharacteristic, complemented
81#5189C2×C311yescharacteristic, complemented
82#5188C2×C311yescharacteristic, complemented
83#5186C2×C311yescharacteristic, complemented
84#5186C2×C311yescharacteristic, complemented
85#5045C2×C311yescharacteristic, complemented
86#4816C2×C311yescharacteristic, complemented
87#4815C2×C311yescharacteristic, complemented
88#4814C2×C311yescharacteristic, complemented
89#4813C2×C311yescharacteristic, complemented
90#4727C2×C311yescharacteristic
91#4723C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8—41no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×#67D411yescharacteristic
102C3×D3×Q8—41no—
103C3×D3×Q8—41no—
104C3×#235—41no—
105C3×#235—41no—
106C2×C3×D12D411yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6D411yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C32×Q16—41no—
114C32×Q16—41no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4—21no—
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#216—41no—
123C3×#216—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3—21no—
142C3×C4×Dic3—21no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C3×ΓL(1,𝔽25)—41no—
146C3×D3×C8—41no—
147#3202—31noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—21no—
150C22×C3×Q8—31no—
151C22×C3×Q8C2×D311yescharacteristic
152C22×C3×Q8C22×C311yescharacteristic
153C2×D3×Q8C22×C311yescharacteristic
154C2×#235C22×C311yescharacteristic
155C2×C3×Q16—21no—
156C2×C3×Q16—21no—
157C2×C3×Q16—31no—
158C2×C3×Q16—31no—
159C2×C3×Q16C2×D311yescharacteristic
160C2×C3×Q16C2×D311yescharacteristic
161C2×C3×Q16C22×C311yescharacteristic
162C2×C3×Q16C22×C311yescharacteristic
163C2×C3×M16—31no—
164C22×C3×C8—31no—
165C3×C4⋊Q8—61no—
166C3×C4⋊Q8—61no—
167C3×#124—61no—
168C3×#124—61no—
169C3×#123—61no—
170C3×#123—61no—
171C3×#123—61no—
172C3×#123—61no—
173C3×C22⋊Q8—21no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—31no—
177C3×C22⋊Q8—31no—
178C3×C22⋊Q8—31no—
179C3×C22⋊Q8—31no—
180C3×C22⋊Q8—31no—
181C3×C22⋊Q8C2×D311yescharacteristic
182C3×C22⋊Q8C22×C311yescharacteristic
183C3×#117—31no—
184C3×#117—31no—
185#947—21no—
186#946C22×C311yescharacteristic
187#946C22×C311yescharacteristic
188#946C22×C311yescharacteristic
189#946C22×C311yescharacteristic
190#946C22×C311yescharacteristic
191#944—21no—
192C2×#216C22×C311yescharacteristic
193C2×#216C22×C311yescharacteristic
194#929—21no—
195#929—21no—
196#926C22×C311yescharacteristic
197#924C22×C311yescharacteristic
198C2×ΓL(1,𝔽25)C22×C311yescharacteristic
199C2×D3×C8C22×C311yescharacteristic
200#897C22×C311yescharacteristic
201#894—21no—
202#892C22×C311yescharacteristic
203#888—21no—
204#885—21no—
205#883—21no—
206C3×#107—31no—
207C3×#107—31no—
208C3×#106—31no—
209C3×#106—31no—
210C3×#103—21no—
211C3×#103—21no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103C2×D311yescharacteristic
219C3×#103C2×D311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×#103C22×C311yescharacteristic
222C3×C22⋊C8—21no—
223C3×C22⋊C8—31no—
224C3×C22⋊C8—31no—
225C3×C22⋊C8—31no—
226C3×C22⋊C8C2×D311yescharacteristic
227C3×C22⋊C8C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229#835C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#835C22×C311yescharacteristic
232#830C22×C311yescharacteristic
233(C2×D3)⋊C8C22×C311yescharacteristic
234(C2×D3)⋊C8C22×C311yescharacteristic
235#818C22×C311yescharacteristic
236#817C22×C311yescharacteristic
237#816C22×C311yescharacteristic
238#816C22×C311yescharacteristic
239#808C22×C311yescharacteristic
240#807C22×C311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C32×Q8—21no—
250C32×Q8—42no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—42no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260C3×#67—41no—
261C3×#67—41no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—41no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—42no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—41no—
277C3×Dic6—42no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#536—31no—
283#536—31no—
284#485—31no—
285#485—31no—
286#485—31no—
287#485—31no—
288#470—31no—
289#470—31no—
290#467—31no—
291#467—31no—
292#451—31no—
293#451—31no—
294#451—31no—
295#451C3×D311yescharacteristic, complemented
296#408—31no—
297C3×#41—121no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—21no—
301C2×C3×Q8—21no—
302C2×C3×Q8—21no—
303C2×C3×Q8—21no—
304C2×C3×Q8—31no—
305C2×C3×Q8—31no—
306C2×C3×Q8—41no—
307C2×C3×Q8—41no—
308C2×C3×Q8—41no—
309C2×C3×Q8—41no—
310C2×C3×Q8—41no—
311C2×C3×Q8—42no—
312C2×C3×Q8—42no—
313C2×C3×Q8—61no—
314C2×C3×Q8—121no—
315C2×C3×Q8—121no—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C23×C311yescharacteristic
320C2×C3×Q8C23×C311yescharacteristic
321C2×C3×Q8C23×C311yescharacteristic
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—41no—
331C22×C3×C4—61no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C23×C311yescharacteristic
334C2×#67C3×D411yescharacteristic
335C2×#67C3×D411yescharacteristic
336D3×Q8—41no—
337D3×Q8—41no—
338#235—41no—
339#235—41no—
340C2×D12C3×D411yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3C23×C311yescharacteristic
343C2×C4×D3C23×C311yescharacteristic
344C2×Dic6—21no—
345C2×Dic6C3×D411yescharacteristic
346C2×Dic6C23×C311yescharacteristic
347C3×Q16—41no—
348C3×Q16—41no—
349C3×Q16—41no—
350C3×Q16—41no—
351C3×Q16—42no—
352C3×Q16—42no—
353C3×Q16—121no—
354C3×Q16—121no—
355C3×M16—121no—
356C2×C3×C8—21no—
357C2×C3×C8—21no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—121no—
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C2×C3×C8C23×C311yescharacteristic
364C2×C3×C8C23×C311yescharacteristic
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—41no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4—61no—
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C4⋊C4C23×C311yescharacteristic
381C3×C22⋊C4—21no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—41no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C42—61no—
394C3×C42—61no—
395#217—21no—
396#217—21no—
397#216—41no—
398#216—41no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406C4⋊Dic3—21no—
407C4⋊Dic3C23×C311yescharacteristic
408C4⋊Dic3C23×C311yescharacteristic
409C4⋊Dic3C23×C311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416C4×Dic3—21no—
417C4×Dic3—21no—
418C2×C3⋊C8C23×C311yescharacteristic
419C2×C3⋊C8C23×C311yescharacteristic
420ΓL(1,𝔽25)—41no—
421D3×C8—41no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4—41no—
436C32×C4—41no—
437C32×C4H(5,𝔽2)11yescharacteristic
438C32×C4H(5,𝔽2)11yescharacteristic
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C2×#41—31no—
446C22×Q8—31no—
447C22×Q8C2×C3×D311yescharacteristic
448C2×Q16—31no—
449C2×Q16—31no—
450C2×Q16C2×C3×D311yescharacteristic
451C2×Q16C2×C3×D311yescharacteristic
452C2×M16—31no—
453C22×C8—31no—
454C4⋊Q8—61no—
455C4⋊Q8—61no—
456#124—61no—
457#124—61no—
458#123—61no—
459#123—61no—
460#123—61no—
461#123—61no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—31no—
467C22⋊Q8—31no—
468C22⋊Q8—31no—
469C22⋊Q8C2×C3×D311yescharacteristic
470#117—31no—
471#117—31no—
472#107—31no—
473#107—31no—
474#106—31no—
475#106—31no—
476#103—31no—
477#103—31no—
478#103—31no—
479#103—31no—
480#103—31no—
481#103—31no—
482#103C2×C3×D311yescharacteristic
483#103C2×C3×D311yescharacteristic
484C22⋊C8—31no—
485C22⋊C8—31no—
486C22⋊C8—31no—
487C22⋊C8C2×C3×D311yescharacteristic
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3D3×D411yescharacteristic
492C23×C3C2×C3×D411yescharacteristic
493C22×D3C2×C3×D411yescharacteristic
494C22×D3C2×C3×D411yescharacteristic
495C3×Q8—22no—
496C3×Q8—22no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—41no—
512C3×Q8—41no—
513C3×Q8—42no—
514C3×Q8—42no—
515C3×Q8—44no—
516C3×Q8—61no—
517C3×Q8—61no—
518C3×Q8—121no—
519C3×Q8—122no—
520C3×D4—121no—
521C3×D4—121no—
522C3×D4—121no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—42no—
546C2×C3×C4—42no—
547C2×C3×C4—44no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—122no—
557C2×C3×C4D3×D411yescharacteristic
558C2×C3×C4C2×C3×D411yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C24×C311yescharacteristic
561#67—41no—
562#67—41no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3C2×C3×D411yescharacteristic
568C2×Dic3C2×C3×D411yescharacteristic
569D12—41no—
570C4×D3—21no—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—21no—
574C4×D3—42no—
575Dic6—21no—
576Dic6—21no—
577Dic6—41no—
578Dic6—42no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—41no—
584C3×C8—41no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C2×C32—41no—
590C2×C32#53411yescharacteristic
591C2×C32#57811yescharacteristic
592C2×C32#57811yescharacteristic
593C3×D3—41no—
594C3×D3—41no—
595#41—121no—
596#41—121no—
597C2×Q8—21no—
598C2×Q8—31no—
599C2×Q8—31no—
600C2×Q8—41no—
601C2×Q8—41no—
602C2×Q8—61no—
603C2×Q8—121no—
604C2×Q8—121no—
605C2×Q8C22×C3×D311yescharacteristic
606C2×Q8C22×C3×D311yescharacteristic
607C2×Q8C22×C3×D311yescharacteristic
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—31no—
611C22×C4—21no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4C22×C3×D311yescharacteristic
616Q16—41no—
617Q16—41no—
618Q16—121no—
619Q16—121no—
620M16—121no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—121no—
624C2×C8C22×C3×D311yescharacteristic
625C2×C8C22×C3×D311yescharacteristic
626C4⋊C4—21no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4C22×C3×D311yescharacteristic
638C22⋊C4—21no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C42—61no—
649C42—61no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C22×C3×D411yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—81no—
692C3×C4—81no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4#100411yescharacteristic
698C3×C4#100411yescharacteristic
699C3×C4C3×H(5,𝔽2)11yescharacteristic
700C3×C4C3×H(5,𝔽2)11yescharacteristic
701Dic3—21no—
702Dic3—21no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707C32#320211yescharacteristic, complemented, Sylow
708C23—31no—
709C23—31no—
710C23C3×D3×D411yescharacteristic
711Q8—21no—
712Q8—21no—
713Q8—21no—
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—42no—
718Q8—61no—
719Q8—61no—
720Q8—121no—
721Q8—122no—
722D4—121no—
723D4—121no—
724D4—121no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—42no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—122no—
743C2×C4C3×D3×D411yescharacteristic
744C2×C4C23×C3×D311yescharacteristic
745C8—21no—
746C8—21no—
747C8—61no—
748C8—61no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—41no—
754C2×C3—41no—
755C2×C3—121no—
756C2×C3—121no—
757C2×C3#558911yescharacteristic
758C2×C3#576611yescharacteristic
759C2×C3#577911yescharacteristic
760C2×C3C3×#53411yescharacteristic
761C2×C3C3×#57811yescharacteristic
762C2×C3C3×#57811yescharacteristic
763D3—41no—
764D3—41no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22C2×C3×D3×D411yescharacteristic
775C4—21no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4C3×#100411yescharacteristic
787C4C3×#100411yescharacteristic
788C3—21no—
789C3#8019211yescharacteristic, direct product factor
790C3C3×#320211yescharacteristic, complemented
791C2—41no—
792C2—121no—
793C2—121no—
794C2C3×#558911yescharacteristic
795C2C3×#576611yescharacteristic
796C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC3×#451D3
hypocenterC3C3×#3202
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
3. C32×#451C2semidirect
4. C3×#5228C2semidirect
5. C3×#5189C2semidirect
6. C3×#5188C2semidirect
7. C3×#5186C2semidirect
8. C3×#5186C2semidirect
9. C3×#5045C2semidirect
10. C3×#4816C2semidirect
11. C3×#4815C2semidirect
12. C3×#4814C2semidirect
13. C3×#4813C2semidirect
15. C3×#4723C2semidirect
17. #80192C3direct (N × H)
77. C3×#451D3semidirect
78. C3×#451C2×C3semidirect
80. #5228C2×C3semidirect
81. #5189C2×C3semidirect
82. #5188C2×C3semidirect
83. #5186C2×C3semidirect
84. #5186C2×C3semidirect
85. #5045C2×C3semidirect
86. #4816C2×C3semidirect
87. #4815C2×C3semidirect
88. #4814C2×C3semidirect
89. #4813C2×C3semidirect
91. #4723C2×C3semidirect
295. #451C3×D3semidirect
707. C32#3202semidirect
789. C3#80192direct (N × H)
790. C3C3×#3202semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C3×#56282
C32×#4512
C3×#52282
C3×#51892
C3×#51882
C3×#51862
C3×#50452
C3×#48162
C3×#48152
C3×#48142
C3×#48132
C3×#47272
C3×#47232
C3×#32023
#801923