Finite Group Databasebeta

← C3×#79841 #11889361

Subgroups — C3×#79841 #11889361

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5581C211yesmaximal, characteristic
2C3×Q8×D12C211yesmaximal, characteristic
3C32×#441C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic, complemented
5C3×#5186C211yesmaximal, characteristic, complemented
6C3×#5031C211yesmaximal, characteristic, complemented
7C3×#5022C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×#4862C211yesmaximal, characteristic, complemented
10C3×#4816C211yesmaximal, characteristic, complemented
11C3×#4813C211yesmaximal, characteristic, complemented
12C3×#4802C211yesmaximal, characteristic, complemented
13C3×D3×#103C211yesmaximal, characteristic, complemented
14C3×#4706C211yesmaximal, characteristic
15C3×#4703C211yesmaximal, characteristic, complemented
16C3×#3312—31nomaximal
17#79841C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#897—21no—
30C3×#897—21no—
31C3×#897C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#894—21no—
34C3×#892C2211yescharacteristic
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×#889—21no—
37C3×#876—21no—
38C3×C4×D12—21no—
39C3×C4×D12C2211yescharacteristic
40C3×#872—21no—
41C3×#870C2211yescharacteristic
42C3×#869—21no—
43C3×#869C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#97C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—31no—
63#5581C2×C311yescharacteristic
64Q8×D12C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#479—31no—
69C3×#470—31no—
70C3×#467—31no—
71C3×#462—31no—
72C3×#451—31no—
73C3×#451—31no—
74C3×#441—21no—
75C3×#441D311yescharacteristic, complemented
76C3×#441C2×C311yescharacteristic, complemented
77C3×#435—31no—
78C3×#419—31no—
79C2×C3×#103—31no—
80#5186C2×C311yescharacteristic, complemented
81#5186C2×C311yescharacteristic, complemented
82#5031C2×C311yescharacteristic, complemented
83#5022C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85#4862C2×C311yescharacteristic, complemented
86#4816C2×C311yescharacteristic, complemented
87#4813C2×C311yescharacteristic, complemented
88#4802C2×C311yescharacteristic, complemented
89D3×#103C2×C311yescharacteristic, complemented
90#4706C2×C311yescharacteristic
91#4703C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C3×D3×Q8—41no—
98C2×C3×D12D411yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C32×Q16—22no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C42—21no—
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118C3×#216—41no—
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3312—31noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C22×C311yescharacteristic
148C2×D3×Q8C22×C311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C22×C311yescharacteristic
154C2×C3×M16—31no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—31no—
157C3×C4⋊Q8—61no—
158C3×#126—61no—
159C3×#125—31no—
160C3×#125—61no—
161C3×#123—61no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—61no—
167C3×C22⋊Q8—61no—
168C3×C4×Q8—21no—
169C3×C4×Q8—21no—
170C3×C4×Q8C2×D311yescharacteristic
171C3×C4×Q8C2×D311yescharacteristic
172C3×C4×Q8C22×C311yescharacteristic
173C3×C4×Q8C22×C311yescharacteristic
174C3×C4×D4—31no—
175C3×C4×D4—61no—
176C3×#117—31no—
177C3×#117—61no—
178C2×C3×C4⋊C4—31no—
179#946C22×C311yescharacteristic
180#946C22×C311yescharacteristic
181C2×#216C22×C311yescharacteristic
182C2×#216C22×C311yescharacteristic
183C2×ΓL(1,𝔽25)C22×C311yescharacteristic
184C2×D3×C8C22×C311yescharacteristic
185#897—21no—
186#897—21no—
187#897C22×C311yescharacteristic
188#897C22×C311yescharacteristic
189#894—21no—
190#892C22×C311yescharacteristic
191D3×C4⋊C4C22×C311yescharacteristic
192#889—21no—
193#876—21no—
194C4×D12—21no—
195C4×D12C22×C311yescharacteristic
196#872—21no—
197#870C22×C311yescharacteristic
198#869—21no—
199#869C22×C311yescharacteristic
200C3×#107—31no—
201C3×#106—21no—
202C3×#106—31no—
203C3×#106C2×D311yescharacteristic
204C3×#106C22×C311yescharacteristic
205C3×C4⋊C8—31no—
206C3×#103—21no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103C2×D311yescharacteristic
217C3×#103C2×D311yescharacteristic
218C3×#103C22×C311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×C22⋊C8—31no—
221C3×C22⋊C8—31no—
222C3×#97—21no—
223C3×#97C2×D311yescharacteristic
224C3×#97C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#808C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237C4⋊(C3⋊C8)C22×C311yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—22no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6—42no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—31no—
277#491—31no—
278#485—31no—
279#483—31no—
280#479—31no—
281#470—31no—
282#467—31no—
283#462—31no—
284#451—31no—
285#451—31no—
286#441C3×D311yescharacteristic, complemented
287#435—31no—
288#419—31no—
289C2×#103—31no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8—121no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310D3×Q8—22no—
311D3×Q8—22no—
312D3×Q8—41no—
313D3×Q8—41no—
314C2×D12C3×D411yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3C23×C311yescharacteristic
319C2×C4×D3C23×C311yescharacteristic
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6C23×C311yescharacteristic
323C2×Dic6C23×C311yescharacteristic
324C3×Q16—24no—
325C3×Q16—22no—
326C3×Q16—22no—
327C3×Q16—121no—
328C3×Q16—121no—
329C3×M16—121no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—121no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C23×C311yescharacteristic
338C2×C3×C8C23×C311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—41no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—41no—
376C3×C42—41no—
377C3×C42—61no—
378C3×C42C22×D311yescharacteristic
379C3×C42C23×C311yescharacteristic
380#216—41no—
381#216—41no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4C3×D411yescharacteristic
388(C2×D3)⋊C4C3×D411yescharacteristic
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3C3×D411yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401C4×Dic3—21no—
402C2×C3⋊C8C23×C311yescharacteristic
403C2×C3⋊C8C23×C311yescharacteristic
404ΓL(1,𝔽25)—41no—
405D3×C8—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#13712yes—
413C32×C4—22no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×Q8—31no—
428C22×Q8—31no—
429C2×Q16—31no—
430C2×Q16—31no—
431C2×Q16C2×C3×D311yescharacteristic
432C2×M16—31no—
433C22×C8—31no—
434C4⋊Q8—31no—
435C4⋊Q8—61no—
436#126—61no—
437#125—31no—
438#125—61no—
439#123—61no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—61no—
445C22⋊Q8—61no—
446C4×Q8C2×C3×D311yescharacteristic
447C4×Q8C2×C3×D311yescharacteristic
448C4×D4—31no—
449C4×D4—61no—
450#117—31no—
451#117—61no—
452C2×C4⋊C4—31no—
453#107—31no—
454#106—31no—
455#106C2×C3×D311yescharacteristic
456C4⋊C8—31no—
457#103—31no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103C2×C3×D311yescharacteristic
466#103C2×C3×D311yescharacteristic
467C22⋊C8—31no—
468C22⋊C8—31no—
469#97C2×C3×D311yescharacteristic
470C23×C3—31no—
471C23×C3—31no—
472C22×D3C2×C3×D411yescharacteristic
473C22×D3C2×C3×D411yescharacteristic
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—22no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—22no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—122no—
489C3×Q8—122no—
490C3×Q8#23512yes—
491C3×Q8C3×#4112yes—
492C3×D4—62no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—122no—
519C2×C3×C4—122no—
520C2×C3×C4—122no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×C3×D411yescharacteristic
524C2×C3×C4C2×C3×D411yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C24×C311yescharacteristic
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3C2×C3×D411yescharacteristic
532C2×Dic3C2×C3×D411yescharacteristic
533D12—22no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—42no—
539C4×D3—42no—
540C4×D3—42no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—42no—
546Dic6—42no—
547C3×C8—22no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—41no—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C2×C32#54611yescharacteristic
558C2×C32C2×#13711yescharacteristic
559C2×C32#57811yescharacteristic
560C3×D3—22no—
561C3×D3—41no—
562C2×Q8—31no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×Q8—61no—
566C2×Q8—62no—
567C2×Q8—62no—
568C2×Q8—121no—
569C2×Q8—121no—
570C2×Q8C22×C3×D311yescharacteristic
571C2×Q8C22×C3×D311yescharacteristic
572C2×D4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578Q16—22no—
579Q16—121no—
580Q16—121no—
581M16—121no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—121no—
585C2×C8C22×C3×D311yescharacteristic
586C2×C8C22×C3×D311yescharacteristic
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4C22×C3×D311yescharacteristic
602C4⋊C4C22×C3×D311yescharacteristic
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C42—21no—
611C42—21no—
612C42—61no—
613C42C22×C3×D311yescharacteristic
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C22×C3×D411yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3C3×#13712yes—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4C2×#23511yescharacteristic
656C3×C4#100911yescharacteristic
657C3×C4C2×C3×#4111yescharacteristic
658C3×C4C3×H(5,𝔽2)11yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—41no—
665C32#331211yescharacteristic, complemented, Sylow
666C23—31no—
667C23—31no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674Q8—61no—
675Q8—122no—
676Q8—122no—
677Q8C3×#23512yes—
678D4—62no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4C3×D3×D411yescharacteristic
697C2×C4C3×D3×D411yescharacteristic
698C2×C4C23×C3×D311yescharacteristic
699C8—21no—
700C8—21no—
701C8—61no—
702C8—61no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—62no—
707C2×C3—121no—
708C2×C3#555011yescharacteristic
709C2×C3D3×#13711yescharacteristic
710C2×C3#577911yescharacteristic
711C2×C3C3×#54611yescharacteristic
712C2×C3C2×C3×#13711yescharacteristic
713C2×C3C3×#57811yescharacteristic
714D3—22no—
715D3—41no—
716C22—32no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—61no—
721C22—61no—
722C22C2×C3×D3×D411yescharacteristic
723C4—21no—
724C4—21no—
725C4—22no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—61no—
730C4—61no—
731C4—121no—
732C4—121no—
733C4—121no—
734C4—121no—
735C4C2×C3×#23511yescharacteristic
736C4C3×#100911yescharacteristic
737C3—21no—
738C3#7984111yescharacteristic, direct product factor
739C3C3×#331211yescharacteristic, complemented
740C2—62no—
741C2—121no—
742C2C3×#555011yescharacteristic
743C2C3×D3×#13711yescharacteristic
744C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC3×#441D3
hypocenterC3C3×#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#441

Complements

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

NH ≅ G/Ntype
3. C32×#441C2semidirect
4. C3×#5186C2semidirect
5. C3×#5186C2semidirect
6. C3×#5031C2semidirect
7. C3×#5022C2semidirect
8. C3×#4868C2semidirect
9. C3×#4862C2semidirect
10. C3×#4816C2semidirect
11. C3×#4813C2semidirect
12. C3×#4802C2semidirect
13. C3×D3×#103C2semidirect
15. C3×#4703C2semidirect
17. #79841C3direct (N × H)
75. C3×#441D3semidirect
76. C3×#441C2×C3semidirect
80. #5186C2×C3semidirect
81. #5186C2×C3semidirect
82. #5031C2×C3semidirect
83. #5022C2×C3semidirect
84. #4868C2×C3semidirect
85. #4862C2×C3semidirect
86. #4816C2×C3semidirect
87. #4813C2×C3semidirect
88. #4802C2×C3semidirect
89. D3×#103C2×C3semidirect
91. #4703C2×C3semidirect
286. #441C3×D3semidirect
665. C32#3312semidirect
738. C3#79841direct (N × H)
739. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C3×#55812
C3×Q8×D122
C32×#4412
C3×#51862
C3×#50312
C3×#50222
C3×#48682
C3×#48622
C3×#48162
C3×#48132
C3×#48022
C3×D3×#1032
C3×#47062
C3×#47032
C3×#33123
#798413