Finite Group Databasebeta

← C3×#81211 #11873287

Subgroups — C3×#81211 #11873287

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5698C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic
3C32×#479C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5C3×#5031C211yesmaximal, characteristic, complemented
6C3×#4888C211yesmaximal, characteristic
7C3×#4873C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic
9C3×#4853C211yesmaximal, characteristic, complemented
10C3×#4849C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic
12C3×#4809C211yesmaximal, characteristic
13C3×#4809C211yesmaximal, characteristic
14C3×#4790C211yesmaximal, characteristic, complemented
15C3×#4789C211yesmaximal, characteristic, complemented
16C3×#3127—31nomaximal
17#81211C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C3×#898—21no—
27C3×#898—21no—
28C3×#897C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×#892—21no—
31C3×#892C2211yescharacteristic
32C3×#890—21no—
33C3×#890—21no—
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#887C2211yescharacteristic
38C3×#872—21no—
39C3×#872C2211yescharacteristic
40C3×#869C2211yescharacteristic
41C3×C4×Dic6—21no—
42C3×C4×Dic6C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×C4⋊C8C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#541—31no—
62C3×#519—31no—
63#5698C2×C311yescharacteristic
64#5572C2×C311yescharacteristic
65C3×#485—31no—
66C3×#485—31no—
67C3×#479—21no—
68C3×#479—31no—
69C3×#479D311yescharacteristic, complemented
70C3×#479C2×C311yescharacteristic, complemented
71C3×#462—31no—
72C3×#462—31no—
73C3×#451—31no—
74C3×#451—31no—
75C3×#441—31no—
76C3×#441—31no—
77C3×C4×Q16—31no—
78C3×C4×Q16—31no—
79C3×#433—31no—
80#5063C2×C311yescharacteristic, complemented
81#5031C2×C311yescharacteristic, complemented
82#4888C2×C311yescharacteristic
83#4873C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic
85#4853C2×C311yescharacteristic, complemented
86#4849C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic
88#4809C2×C311yescharacteristic
89#4809C2×C311yescharacteristic
90#4790C2×C311yescharacteristic, complemented
91#4789C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C3×D3×Q8—22no—
94C3×D3×Q8—22no—
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4—21no—
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
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⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—22no—
140C3×Dic12—22no—
141#3127—31noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C2×C3×Q16—31no—
148C3×C4⋊Q8—31no—
149C3×#126—61no—
150C3×#126—61no—
151C3×#125—21no—
152C3×#125—61no—
153C3×#125—61no—
154C3×#125C2×D311yescharacteristic
155C3×#125C22×C311yescharacteristic
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—21no—
159C3×C4×Q8—31no—
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×Q8C22×C311yescharacteristic
168C3×#117—31no—
169C3×#117—31no—
170C3×#117—61no—
171C3×#117—61no—
172Q8×Dic3C22×C311yescharacteristic
173C2×#216C22×C311yescharacteristic
174C2×#216C22×C311yescharacteristic
175C2×Dic12C22×C311yescharacteristic
176C2×Dic12C22×C311yescharacteristic
177#898—21no—
178#898—21no—
179#897C22×C311yescharacteristic
180#897C22×C311yescharacteristic
181#892—21no—
182#892C22×C311yescharacteristic
183#890—21no—
184#890—21no—
185#887—21no—
186#887C22×C311yescharacteristic
187#887C22×C311yescharacteristic
188#887C22×C311yescharacteristic
189#872—21no—
190#872C22×C311yescharacteristic
191#869C22×C311yescharacteristic
192C4×Dic6—21no—
193C4×Dic6C22×C311yescharacteristic
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic
197C3×#107C22×C311yescharacteristic
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic
201C3×#106C22×C311yescharacteristic
202C3×C4⋊C8—21no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8C2×D311yescharacteristic
205C3×C4⋊C8C22×C311yescharacteristic
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×#103C2×D311yescharacteristic
215C3×#103C2×D311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#103C22×C311yescharacteristic
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222(C2×D3)⋊C8C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224#816C22×C311yescharacteristic
225#816C22×C311yescharacteristic
226#815C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C22×C3×D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8#4112yes—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×C4×D3—24no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×Dic6—24no—
256C3×Dic6—21no—
257C3×Dic6—21no—
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#479C3×D311yescharacteristic, complemented
272#462—31no—
273#462—31no—
274#451—31no—
275#451—31no—
276#441—31no—
277#441—31no—
278C4×Q16—31no—
279C4×Q16—31no—
280#433—31no—
281C2×C3×Q8—21no—
282C2×C3×Q8—31no—
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×Q8C23×C311yescharacteristic
290C22×C3×C4—31no—
291C22×C3×C4—61no—
292D3×Q8—22no—
293D3×Q8—22no—
294C2×C4×D3—21no—
295C2×C4×D3C23×C311yescharacteristic
296C2×Dic6—21no—
297C2×Dic6C23×C311yescharacteristic
298C2×Dic6C23×C311yescharacteristic
299C2×Dic6C23×C311yescharacteristic
300C3×Q16—62no—
301C3×Q16—62no—
302C3×Q16—62no—
303C3×Q16—62no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C23×C311yescharacteristic
311C2×C3×C8C23×C311yescharacteristic
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
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—41no—
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⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C23×C311yescharacteristic
340C3×C4⋊C4C23×C311yescharacteristic
341C3×C4⋊C4C23×C311yescharacteristic
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—31no—
351C3×C42—41no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C23×C311yescharacteristic
360#216—22no—
361#216—22no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4C3×D411yescharacteristic
366(C2×D3)⋊C4C3×D411yescharacteristic
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3C23×C311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4C3×D411yescharacteristic
378Dic3⋊C4C3×D411yescharacteristic
379C4×Dic3—21no—
380C4×Dic3—21no—
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3C23×C311yescharacteristic
386C2×C3⋊C8C23×C311yescharacteristic
387C2×C3⋊C8C23×C311yescharacteristic
388Dic12—22no—
389Dic12—22no—
390C22×C32C22×D411yescharacteristic
391C2×C3×D3—21no—
392C2×C3×D3—21no—
393C2×C3×D3—21no—
394C32×C4—22no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4C2×#4111yescharacteristic
401C32×C4C2×#4111yescharacteristic
402C3×Dic3—21no—
403C3×Dic3—22no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—31no—
410C2×Q16—31no—
411C2×Q16—31no—
412C2×Q16—31no—
413C2×Q16—31no—
414C4⋊Q8—31no—
415#126—61no—
416#126—61no—
417#125—61no—
418#125—61no—
419#125C2×C3×D311yescharacteristic
420C22⋊Q8—31no—
421C22⋊Q8—31no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×Q8—61no—
428C4×Q8—61no—
429C4×Q8C2×C3×D311yescharacteristic
430#117—31no—
431#117—31no—
432#117—61no—
433#117—61no—
434#107—31no—
435#107C2×C3×D311yescharacteristic
436#106—31no—
437#106C2×C3×D311yescharacteristic
438C4⋊C8—31no—
439C4⋊C8C2×C3×D311yescharacteristic
440#103—31no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103C2×C3×D311yescharacteristic
447#103C2×C3×D311yescharacteristic
448C22⋊C8—31no—
449C22⋊C8—31no—
450#97—31no—
451C4×C8—31no—
452C23×C3—31no—
453C22×D3C2×C3×D411yescharacteristic
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—22no—
457C3×Q8—32no—
458C3×Q8—41no—
459C3×Q8—64no—
460C3×Q8—61no—
461C3×Q8—61no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×Q8#23912yes—
466C3×Q8C3×#4112yes—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
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—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—64no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4D3×D411yescharacteristic
493C2×C3×C4D3×D411yescharacteristic
494C2×C3×C4C2×C3×D411yescharacteristic
495C2×C3×C4C2×C3×D411yescharacteristic
496C2×C3×C4C23×D311yescharacteristic
497C2×C3×C4C24×C311yescharacteristic
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3C2×C3×D411yescharacteristic
503C2×Dic3C2×C3×D411yescharacteristic
504C2×Dic3C2×C3×D411yescharacteristic
505C4×D3—24no—
506C4×D3—21no—
507C4×D3—21no—
508Dic6—24no—
509Dic6—21no—
510Dic6—21no—
511Dic6—21no—
512Dic6—21no—
513Dic6—21no—
514Dic6C3×#4112yes—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—41no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C2×C32#52511yescharacteristic
526C2×C32#57811yescharacteristic
527C2×C32#57811yescharacteristic
528C3×D3—41no—
529C2×Q8—31no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—61no—
533C2×Q8—62no—
534C2×Q8—62no—
535C2×Q8C22×C3×D311yescharacteristic
536C22×C4—31no—
537C22×C4—61no—
538Q16—62no—
539Q16—62no—
540Q16—62no—
541Q16—62no—
542C2×C8—31no—
543C2×C8—31no—
544C2×C8C22×C3×D311yescharacteristic
545C2×C8C22×C3×D311yescharacteristic
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4C22×C3×D311yescharacteristic
562C4⋊C4C22×C3×D311yescharacteristic
563C4⋊C4C22×C3×D311yescharacteristic
564C22⋊C4—31no—
565C22⋊C4—31no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C42—21no—
570C42—31no—
571C42—61no—
572C42—61no—
573C42—61no—
574C42—61no—
575C42—61no—
576C42—61no—
577C42C22×C3×D311yescharacteristic
578C22×C3—21no—
579C22×C3—61no—
580C22×C3—61no—
581C22×C3—61no—
582C22×C3C2×D3×D411yescharacteristic
583C22×C3C22×C3×D411yescharacteristic
584C2×D3—21no—
585C2×D3—21no—
586C2×D3—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—42no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—62no—
608C3×C4—81no—
609C3×C4—81no—
610C3×C4—81no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4C2×#23911yescharacteristic
615C3×C4D3×#4111yescharacteristic
616C3×C4C2×C3×#4111yescharacteristic
617C3×C4C2×C3×#4111yescharacteristic
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—22no—
622Dic3—41no—
623Dic3—41no—
624Dic3—41no—
625C32#312711yescharacteristic, complemented, Sylow
626C23—31no—
627Q8—21no—
628Q8—32no—
629Q8—64no—
630Q8—61no—
631Q8—61no—
632Q8—61no—
633Q8—61no—
634Q8—61no—
635Q8C3×#23912yes—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—31no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—64no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4C3×D3×D411yescharacteristic
651C2×C4C3×D3×D411yescharacteristic
652C2×C4C23×C3×D311yescharacteristic
653C8—21no—
654C8—21no—
655C8—61no—
656C8—61no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—121no—
661C2×C3#562711yescharacteristic
662C2×C3#577111yescharacteristic
663C2×C3#577911yescharacteristic
664C2×C3C3×#52511yescharacteristic
665C2×C3C3×#57811yescharacteristic
666C2×C3C3×#57811yescharacteristic
667D3—41no—
668C22—61no—
669C22—61no—
670C22—61no—
671C22C2×C3×D3×D411yescharacteristic
672C4—21no—
673C4—21no—
674C4—22no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—61no—
679C4—61no—
680C4—61no—
681C4—62no—
682C4—121no—
683C4—121no—
684C4—121no—
685C4C2×C3×#23911yescharacteristic
686C4C3×D3×#4111yescharacteristic
687C3—21no—
688C3#8121111yescharacteristic, direct product factor
689C3C3×#312711yescharacteristic, complemented
690C2—121no—
691C2C3×#562711yescharacteristic
692C2C3×#577111yescharacteristic
693C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#479D3
hypocenterC3C3×#3127
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#479

Complements

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

NH ≅ G/Ntype
3. C32×#479C2semidirect
4. C3×#5063C2semidirect
5. C3×#5031C2semidirect
7. C3×#4873C2semidirect
9. C3×#4853C2semidirect
10. C3×#4849C2semidirect
14. C3×#4790C2semidirect
15. C3×#4789C2semidirect
17. #81211C3direct (N × H)
69. C3×#479D3semidirect
70. C3×#479C2×C3semidirect
80. #5063C2×C3semidirect
81. #5031C2×C3semidirect
83. #4873C2×C3semidirect
85. #4853C2×C3semidirect
86. #4849C2×C3semidirect
90. #4790C2×C3semidirect
91. #4789C2×C3semidirect
271. #479C3×D3semidirect
625. C32#3127semidirect
688. C3#81211direct (N × H)
689. C3C3×#3127semidirect

Maximal subgroups

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

subgroupindex
C3×#56982
C3×#55722
C32×#4792
C3×#50632
C3×#50312
C3×#48882
C3×#48732
C3×#48682
C3×#48532
C3×#48492
C3×#48402
C3×#48092
C3×#47902
C3×#47892
C3×#31273
#812113