Finite Group Databasebeta

← C3×#79836 #11873278

Subgroups — C3×#79836 #11873278

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5583C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic
3C32×#441C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic
5C3×#5182C211yesmaximal, characteristic, complemented
6C3×C4×#216C211yesmaximal, characteristic, complemented
7C3×C4×#216C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic
9C3×#4857C211yesmaximal, characteristic, complemented
10C3×#4815C211yesmaximal, characteristic
11C3×#4809C211yesmaximal, characteristic
12C3×#4799C211yesmaximal, characteristic, complemented
13C3×#4795C211yesmaximal, characteristic, complemented
14C3×#4716C211yesmaximal, characteristic, complemented
15C3×#4709C211yesmaximal, characteristic
16C3×#3127—31nomaximal
17#79836C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic
28C3×#898—21no—
29C3×#897C2211yescharacteristic
30C3×#892—21no—
31C3×#892C2211yescharacteristic
32C3×#890C2211yescharacteristic
33C3×#889—21no—
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#876—21no—
37C3×#872—21no—
38C3×#872C2211yescharacteristic
39C3×#870—21no—
40C3×C4×Dic6—21no—
41C3×C4×Dic6C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#541—31no—
62C3×#519—31no—
63#5583C2×C311yescharacteristic
64#5572C2×C311yescharacteristic
65C3×#485—31no—
66C3×#485—31no—
67C3×#479—31no—
68C3×#479—31no—
69C3×#462—31no—
70C3×#462—31no—
71C3×#451—31no—
72C3×#451—31no—
73C3×#441—21no—
74C3×#441—31no—
75C3×#441D311yescharacteristic, complemented
76C3×#441C2×C311yescharacteristic, complemented
77C3×C4×Q16—31no—
78C3×C4×Q16—31no—
79C3×#433—31no—
80#5186C2×C311yescharacteristic
81#5182C2×C311yescharacteristic, complemented
82C4×#216C2×C311yescharacteristic, complemented
83C4×#216C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic
85#4857C2×C311yescharacteristic, complemented
86#4815C2×C311yescharacteristic
87#4809C2×C311yescharacteristic
88#4799C2×C311yescharacteristic, complemented
89#4795C2×C311yescharacteristic, complemented
90#4716C2×C311yescharacteristic, complemented
91#4709C2×C311yescharacteristic
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×Q16—22no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C42—21no—
109C32×C42—21no—
110C32×C42C2311yescharacteristic
111C3×#216—22no—
112C3×#216—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4D411yescharacteristic
117C3×(C2×D3)⋊C4D411yescharacteristic
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×Dic12—22no—
141#3127—31noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C22×C311yescharacteristic
144C2×C3×Q16—21no—
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C2×C3×Q16—31no—
148C2×C3×Q16C2×D311yescharacteristic
149C2×C3×Q16C22×C311yescharacteristic
150C3×C4⋊Q8—31no—
151C3×#126—61no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#125—61no—
155C3×#125—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—21no—
159C3×C4×Q8—21no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—61no—
165C3×C4×Q8—61no—
166C3×C4×Q8C2×D311yescharacteristic
167C3×C4×Q8C2×D311yescharacteristic
168C3×C4×Q8C22×C311yescharacteristic
169C3×C4×Q8C22×C311yescharacteristic
170C3×#117—31no—
171C3×#117—31no—
172C3×#117—61no—
173C3×#117—61no—
174#946C22×C311yescharacteristic
175Q8×Dic3C22×C311yescharacteristic
176#944C22×C311yescharacteristic
177C2×#216C22×C311yescharacteristic
178C2×#216C22×C311yescharacteristic
179C2×Dic12C22×C311yescharacteristic
180#898—21no—
181#897C22×C311yescharacteristic
182#892—21no—
183#892C22×C311yescharacteristic
184#890C22×C311yescharacteristic
185#889—21no—
186#887—21no—
187#887C22×C311yescharacteristic
188#876—21no—
189#872—21no—
190#872C22×C311yescharacteristic
191#870—21no—
192C4×Dic6—21no—
193C4×Dic6C22×C311yescharacteristic
194C4×Dic6C22×C311yescharacteristic
195C3×#107—31no—
196C3×#107—31no—
197C3×#106—21no—
198C3×#106—31no—
199C3×#106C2×D311yescharacteristic
200C3×#106C22×C311yescharacteristic
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103C2×D311yescharacteristic
212C3×#103C2×D311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×#97—21no—
218C3×#97C2×D311yescharacteristic
219C3×#97C22×C311yescharacteristic
220C3×C4×C8—31no—
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225#817C22×C311yescharacteristic
226#816C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#807C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4×C3⋊C8C22×C311yescharacteristic
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C32×Q8#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×C4×D3—24no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×Dic6—24no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262C32×C8—21no—
263C32×C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—31no—
267#519—31no—
268#485—31no—
269#485—31no—
270#479—31no—
271#479—31no—
272#462—31no—
273#462—31no—
274#451—31no—
275#451—31no—
276#441—31no—
277#441C3×D311yescharacteristic, complemented
278C4×Q16—31no—
279C4×Q16—31no—
280#433—31no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8—62no—
287C2×C3×Q8—62no—
288C2×C3×Q8C22×D311yescharacteristic
289C2×C3×Q8C22×D311yescharacteristic
290C2×C3×Q8C23×C311yescharacteristic
291C2×C3×Q8C23×C311yescharacteristic
292C22×C3×C4—31no—
293C22×C3×C4—61no—
294D3×Q8—22no—
295D3×Q8—22no—
296C2×C4×D3—21no—
297C2×C4×D3C23×C311yescharacteristic
298C2×Dic6—21no—
299C2×Dic6C23×C311yescharacteristic
300C2×Dic6C23×C311yescharacteristic
301C3×Q16—24no—
302C3×Q16—22no—
303C3×Q16—22no—
304C3×Q16—62no—
305C3×Q16—62no—
306C3×Q16—62no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8C22×D311yescharacteristic
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C23×C311yescharacteristic
314C2×C3×C8C23×C311yescharacteristic
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—41no—
326C3×C4⋊C4—41no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C23×C311yescharacteristic
340C3×C4⋊C4C23×C311yescharacteristic
341C3×C22⋊C4—31no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—31no—
352C3×C42—41no—
353C3×C42—41no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42—61no—
359C3×C42C22×D311yescharacteristic
360C3×C42C23×C311yescharacteristic
361#216—22no—
362#216—22no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4C3×D411yescharacteristic
367(C2×D3)⋊C4C3×D411yescharacteristic
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3C23×C311yescharacteristic
372C4⋊Dic3C23×C311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4C3×D411yescharacteristic
381Dic3⋊C4C3×D411yescharacteristic
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3C23×C311yescharacteristic
388C2×C3⋊C8C23×C311yescharacteristic
389C2×C3⋊C8C23×C311yescharacteristic
390Dic12—22no—
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C32×C4—22no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C2×#4111yescharacteristic
402C32×C4C2×#4111yescharacteristic
403C3×Dic3—21no—
404C3×Dic3—22no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C22×Q8—31no—
411C2×Q16—31no—
412C2×Q16—31no—
413C2×Q16—31no—
414C2×Q16C2×C3×D311yescharacteristic
415C4⋊Q8—31no—
416#126—61no—
417#126—61no—
418#125—31no—
419#125—61no—
420#125—61no—
421C22⋊Q8—31no—
422C22⋊Q8—31no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8—61no—
428C4×Q8—61no—
429C4×Q8C2×C3×D311yescharacteristic
430C4×Q8C2×C3×D311yescharacteristic
431#117—31no—
432#117—31no—
433#117—61no—
434#117—61no—
435#107—31no—
436#107—31no—
437#106—31no—
438#106C2×C3×D311yescharacteristic
439C4⋊C8—31no—
440C4⋊C8—31no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103—31no—
447#103C2×C3×D311yescharacteristic
448#103C2×C3×D311yescharacteristic
449C22⋊C8—31no—
450C22⋊C8—31no—
451#97C2×C3×D311yescharacteristic
452C4×C8—31no—
453C23×C3—31no—
454C22×D3C2×C3×D411yescharacteristic
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—22no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—22no—
463C3×Q8—32no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—64no—
467C3×Q8—61no—
468C3×Q8—61no—
469C3×Q8—61no—
470C3×Q8#23512yes—
471C3×Q8C3×#4112yes—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—64no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4C2×C3×D411yescharacteristic
500C2×C3×C4C2×C3×D411yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502C2×C3×C4C24×C311yescharacteristic
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3C2×C3×D411yescharacteristic
508C2×Dic3C2×C3×D411yescharacteristic
509C2×Dic3C2×C3×D411yescharacteristic
510C4×D3—24no—
511C4×D3—21no—
512C4×D3—21no—
513Dic6—24no—
514Dic6—21no—
515Dic6—21no—
516Dic6—21no—
517Dic6C3×#4112yes—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C3×D3—41no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—61no—
535C2×Q8—62no—
536C2×Q8—62no—
537C2×Q8C22×C3×D311yescharacteristic
538C2×Q8C22×C3×D311yescharacteristic
539C22×C4—31no—
540C22×C4—61no—
541Q16—22no—
542Q16—62no—
543Q16—62no—
544Q16—62no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8C22×C3×D311yescharacteristic
548C2×C8C22×C3×D311yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4C22×C3×D311yescharacteristic
566C4⋊C4C22×C3×D311yescharacteristic
567C22⋊C4—31no—
568C22⋊C4—31no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C42—21no—
573C42—21no—
574C42—31no—
575C42—61no—
576C42—61no—
577C42—61no—
578C42—61no—
579C42—61no—
580C42C22×C3×D311yescharacteristic
581C22×C3—21no—
582C22×C3—61no—
583C22×C3—61no—
584C22×C3—61no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C22×C3×D411yescharacteristic
587C2×D3—21no—
588C2×D3—21no—
589C2×D3—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—42no—
601C3×C4—42no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—62no—
612C3×C4—81no—
613C3×C4—81no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4C2×#23511yescharacteristic
618C3×C4D3×#4111yescharacteristic
619C3×C4C2×C3×#4111yescharacteristic
620C3×C4C2×C3×#4111yescharacteristic
621Dic3—21no—
622Dic3—21no—
623Dic3—21no—
624Dic3—22no—
625Dic3—41no—
626Dic3—41no—
627Dic3—41no—
628C32#312711yescharacteristic, complemented, Sylow
629C23—31no—
630Q8—21no—
631Q8—21no—
632Q8—21no—
633Q8—32no—
634Q8—64no—
635Q8—61no—
636Q8—61no—
637Q8—61no—
638Q8C3×#23512yes—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—64no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4C3×D3×D411yescharacteristic
654C2×C4C3×D3×D411yescharacteristic
655C2×C4C23×C3×D311yescharacteristic
656C8—21no—
657C8—21no—
658C8—61no—
659C8—61no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—121no—
664C2×C3#554711yescharacteristic
665C2×C3#577911yescharacteristic
666C2×C3#577911yescharacteristic
667C2×C3C3×#52511yescharacteristic
668C2×C3C3×#57811yescharacteristic
669C2×C3C3×#57811yescharacteristic
670D3—41no—
671C22—61no—
672C22—61no—
673C22—61no—
674C22C2×C3×D3×D411yescharacteristic
675C4—21no—
676C4—21no—
677C4—22no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—61no—
682C4—61no—
683C4—61no—
684C4—62no—
685C4—121no—
686C4—121no—
687C4—121no—
688C4C2×C3×#23511yescharacteristic
689C4C3×D3×#4111yescharacteristic
690C3—21no—
691C3#7983611yescharacteristic, direct product factor
692C3C3×#312711yescharacteristic, complemented
693C2—121no—
694C2C3×#554711yescharacteristic
695C2C3×#577911yescharacteristic
696C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#441D3
hypocenterC3C3×#3127
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
5. C3×#5182C2semidirect
6. C3×C4×#216C2semidirect
7. C3×C4×#216C2semidirect
9. C3×#4857C2semidirect
12. C3×#4799C2semidirect
13. C3×#4795C2semidirect
14. C3×#4716C2semidirect
17. #79836C3direct (N × H)
75. C3×#441D3semidirect
76. C3×#441C2×C3semidirect
81. #5182C2×C3semidirect
82. C4×#216C2×C3semidirect
83. C4×#216C2×C3semidirect
85. #4857C2×C3semidirect
88. #4799C2×C3semidirect
89. #4795C2×C3semidirect
90. #4716C2×C3semidirect
277. #441C3×D3semidirect
628. C32#3127semidirect
691. C3#79836direct (N × H)
692. C3C3×#3127semidirect

Maximal subgroups

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

subgroupindex
C3×#55832
C3×#55722
C32×#4412
C3×#51862
C3×#51822
C3×C4×#2162
C3×#48682
C3×#48572
C3×#48152
C3×#48092
C3×#47992
C3×#47952
C3×#47162
C3×#47092
C3×#31273
#798363