Finite Group Databasebeta

← C3×#83140 #11870545

Subgroups — C3×#83140 #11870545

Order 1152.

909 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#529C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C3×#5066C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5C3×#5057C211yesmaximal, characteristic, complemented
6C3×#5054C211yesmaximal, characteristic, complemented
7C3×#5047C211yesmaximal, characteristic, complemented
8C3×#5045C211yesmaximal, characteristic, complemented
9C3×#5037C211yesmaximal, characteristic
10C3×#5035C211yesmaximal, characteristic, complemented
11C3×C4×#216C211yesmaximal, characteristic, complemented
12C3×C4×#215C211yesmaximal, characteristic, complemented
13C3×C4×#214C211yesmaximal, characteristic, complemented
14C3×C4×#213C211yesmaximal, characteristic, complemented
15C3×#4925C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#83140C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C32×#126—21no—
20C32×#125C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C32×#123—21no—
23C32×C22⋊Q8C2211yescharacteristic
24C32×#121C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C32×C4×D4—21no—
27C32×C4×D4C2211yescharacteristic
28C32×#117—21no—
29C2×C32×C42C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×C4×#67—21no—
35C3×C4×#67—21no—
36C3×#926C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×#872—21no—
40C3×C42×D3—21no—
41C3×C4×Dic6C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#807C2211yescharacteristic
56C3×#807C2211yescharacteristic
57C3×C4⋊(C3⋊C8)C2211yescharacteristic
58C3×C4⋊(C3⋊C8)C2211yescharacteristic
59C3×C4×C3⋊C8C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#529—21no—
62C3×#529D311yescharacteristic, complemented
63C3×#529C2×C311yescharacteristic, complemented
64C3×C4×#41—31no—
65C4×#235C2×C311yescharacteristic, complemented
66C3×#485—31no—
67C3×#482—31no—
68C3×#479—31no—
69C3×#478—31no—
70C3×#464—31no—
71C3×#463—31no—
72C3×#452—31no—
73C3×#449—31no—
74C3×C4×Q16—31no—
75C3×C4×SD16—31no—
76C3×C4×SD16—31no—
77C3×C4×D8—31no—
78C3×#431—31no—
79#5066C2×C311yescharacteristic, complemented
80#5063C2×C311yescharacteristic, complemented
81#5057C2×C311yescharacteristic, complemented
82#5054C2×C311yescharacteristic, complemented
83#5047C2×C311yescharacteristic, complemented
84#5045C2×C311yescharacteristic, complemented
85#5037C2×C311yescharacteristic
86#5035C2×C311yescharacteristic, complemented
87C4×#216C2×C311yescharacteristic, complemented
88C4×#215C2×C311yescharacteristic, complemented
89C4×#214C2×C311yescharacteristic, complemented
90C4×#213C2×C311yescharacteristic, complemented
91#4925C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C22×C32×C4D411yescharacteristic
97C22×C32×C4D411yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—21no—
100C3×#235—22no—
101C3×#235—22no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×Dic6C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C42—21no—
119C32×C42D411yescharacteristic
120C32×C42D411yescharacteristic
121C32×C42C2311yescharacteristic
122C32×C42C2311yescharacteristic
123C3×#217—21no—
124C3×#216—22no—
125C3×#215—22no—
126C3×#214—22no—
127C3×#213—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#235C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—31no—
148C3×#126—22no—
149C3×#126—21no—
150C3×#126—21no—
151C3×#125—21no—
152C3×#125C2×D311yescharacteristic
153C3×#125C22×C311yescharacteristic
154C3×#124—21no—
155C3×#124C2×D311yescharacteristic
156C3×#124C22×C311yescharacteristic
157C3×#123—22no—
158C3×#123—21no—
159C3×#123—21no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8C2×D311yescharacteristic
162C3×C22⋊Q8C22×C311yescharacteristic
163C3×#121—21no—
164C3×#121C2×D311yescharacteristic
165C3×#121C22×C311yescharacteristic
166C3×C4×Q8—21no—
167C3×C4×Q8—31no—
168C3×C4×Q8—31no—
169C3×C4×Q8C2×D311yescharacteristic
170C3×C4×Q8C22×C311yescharacteristic
171C3×C4×D4—22no—
172C3×C4×D4—21no—
173C3×C4×D4—21no—
174C3×C4×D4—21no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178C3×C4×D4—61no—
179C3×C4×D4C2×D311yescharacteristic
180C3×C4×D4C22×C311yescharacteristic
181C3×#117—22no—
182C3×#117—21no—
183C3×#117—21no—
184C3×#117—31no—
185C3×#117—61no—
186C2×C3×C42—21no—
187C2×C3×C42—61no—
188C2×C3×C42C2×D311yescharacteristic
189C2×C3×C42C22×C311yescharacteristic
190C2×#216C22×C311yescharacteristic
191C2×#215C22×C311yescharacteristic
192C2×#214C22×C311yescharacteristic
193C2×#213C22×C311yescharacteristic
194C4×#67—21no—
195C4×#67—21no—
196#926C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C4×D12C22×C311yescharacteristic
199#872—21no—
200C42×D3—21no—
201C4×Dic6C22×C311yescharacteristic
202C4×Dic6C22×C311yescharacteristic
203C3×#107—31no—
204C3×#107—31no—
205C3×#106—31no—
206C3×#106—31no—
207C3×C4⋊C8—31no—
208C3×C4⋊C8—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8—31no—
219C3×C4×C8—31no—
220C3×C4×C8—31no—
221#835C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#832C22×C311yescharacteristic
225#830C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#808C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C4⋊(C3⋊C8)C22×C311yescharacteristic
236C4⋊(C3⋊C8)C22×C311yescharacteristic
237C4×C3⋊C8C22×C311yescharacteristic
238C4×C3⋊C8C22×C311yescharacteristic
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4—42no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—22no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—41no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—24no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6#4112yes—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#529C3×D311yescharacteristic, complemented
277C4×#41—31no—
278#485—31no—
279#482—31no—
280#479—31no—
281#478—31no—
282#464—31no—
283#463—31no—
284#452—31no—
285#449—31no—
286C4×Q16—31no—
287C4×SD16—31no—
288C4×SD16—31no—
289C4×D8—31no—
290#431—31no—
291C3×#41—62no—
292C3×#41—62no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C23×C311yescharacteristic
297C2×C3×D4—22no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C23×C311yescharacteristic
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4#6711yescharacteristic
315C22×C3×C4#6711yescharacteristic
316C22×C3×C4C3×D411yescharacteristic
317C22×C3×C4C3×D411yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C2×#67—21no—
321#235—22no—
322#235—22no—
323C2×D12C23×C311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×Dic6C23×C311yescharacteristic
328C3×Q16—62no—
329C3×SD16—62no—
330C3×SD16—62no—
331C3×D8—62no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—22no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C23×C311yescharacteristic
357C3×C4⋊C4C23×C311yescharacteristic
358C3×C22⋊C4—22no—
359C3×C22⋊C4—22no—
360C3×C22⋊C4—22no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—22no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C42—22no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42—61no—
386C3×C42#6711yescharacteristic
387C3×C42#6711yescharacteristic
388C3×C42C3×D411yescharacteristic
389C3×C42C3×D411yescharacteristic
390C3×C42C22×D311yescharacteristic
391C3×C42C22×D311yescharacteristic
392C3×C42C23×C311yescharacteristic
393C3×C42C23×C311yescharacteristic
394#217—21no—
395#216—22no—
396#215—22no—
397#214—22no—
398#213—22no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401C4⋊Dic3C23×C311yescharacteristic
402C4⋊Dic3C23×C311yescharacteristic
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405C4×Dic3—21no—
406C4×Dic3—21no—
407C4×Dic3—21no—
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410C2×C3⋊C8C23×C311yescharacteristic
411C2×C3⋊C8C23×C311yescharacteristic
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3×D3—22no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4#13512yes—
430C32×C4C2×#4111yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3×Dic3—22no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C2×Q16—31no—
437C2×SD16—31no—
438C2×SD16—31no—
439C2×D8—31no—
440#126—21no—
441#125C2×C3×D311yescharacteristic
442#124C2×C3×D311yescharacteristic
443#123—21no—
444C22⋊Q8C2×C3×D311yescharacteristic
445#121C2×C3×D311yescharacteristic
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8C2×C3×D311yescharacteristic
449C4×D4—21no—
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—61no—
453C4×D4—61no—
454C4×D4C2×C3×D311yescharacteristic
455#117—21no—
456#117—31no—
457#117—61no—
458C2×C42—61no—
459C2×C42C2×C3×D311yescharacteristic
460#107—31no—
461#107—31no—
462#106—31no—
463#106—31no—
464C4⋊C8—31no—
465C4⋊C8—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103—31no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102—31no—
474C22⋊C8—31no—
475C22⋊C8—31no—
476C4×C8—31no—
477C4×C8—31no—
478C23×C3—22no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—61no—
483C23×C3C2×#6711yescharacteristic
484C23×C3C2×C3×D411yescharacteristic
485C22×D3—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—32no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—32no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—44no—
502C3×D4—42no—
503C3×D4—42no—
504C3×D4—64no—
505C3×D4—61no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—42no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—44no—
533C2×C3×C4—42no—
534C2×C3×C4—42no—
535C2×C3×C4—42no—
536C2×C3×C4—64no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—122no—
541C2×C3×C4—122no—
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C2×#6711yescharacteristic
545C2×C3×C4C2×#6711yescharacteristic
546C2×C3×C4C2×#6711yescharacteristic
547C2×C3×C4C2×C3×D411yescharacteristic
548C2×C3×C4C2×C3×D411yescharacteristic
549C2×C3×C4C2×C3×D411yescharacteristic
550C2×C3×C4C2×C3×D411yescharacteristic
551C2×C3×C4C2×C3×D411yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C24×C311yescharacteristic
554#67—24no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558D12—21no—
559D12C3×#4112yes—
560C4×D3—24no—
561C4×D3—42no—
562C4×D3—42no—
563Dic6—21no—
564Dic6C3×#4112yes—
565C3×C8—61no—
566C3×C8—61no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32—81no—
575C2×C32#52511yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32#57511yescharacteristic
578C3×D3—42no—
579#41—62no—
580#41—62no—
581C2×Q8—31no—
582C2×Q8C22×C3×D311yescharacteristic
583C2×D4—21no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4C22×C3×D311yescharacteristic
587C22×C4—21no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4C3×#6711yescharacteristic
592C22×C4C3×#6711yescharacteristic
593C22×C4C22×C3×D311yescharacteristic
594Q16—62no—
595SD16—62no—
596SD16—62no—
597D8—62no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—31no—
601C2×C8—31no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4C22×C3×D311yescharacteristic
611C4⋊C4C22×C3×D311yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C42—21no—
621C42—61no—
622C42—61no—
623C42—61no—
624C42C3×#6711yescharacteristic
625C42C3×#6711yescharacteristic
626C42C22×C3×D311yescharacteristic
627C42C22×C3×D311yescharacteristic
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—62no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C22×#6711yescharacteristic
651C22×C3C22×C3×D411yescharacteristic
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—22no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4—42no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—62no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4#95012yes—
683C3×C4C3×#13512yes—
684C3×C4D3×#4111yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4C2×C3×#4111yescharacteristic
687C3×C4C2×C3×#4111yescharacteristic
688Dic3—22no—
689Dic3—41no—
690Dic3—41no—
691C32#310211yescharacteristic, complemented, Sylow
692C23—21no—
693C23—61no—
694C23C2×C3×#6711yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—32no—
698Q8—61no—
699D4—21no—
700D4—21no—
701D4—32no—
702D4—42no—
703D4—64no—
704D4—61no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—64no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4C2×C3×#6711yescharacteristic
720C2×C4C2×C3×#6711yescharacteristic
721C2×C4C2×C3×#6711yescharacteristic
722C2×C4C2×C3×#6711yescharacteristic
723C2×C4C2×C3×#6711yescharacteristic
724C2×C4C23×C3×D311yescharacteristic
725C8—61no—
726C8—61no—
727C8—61no—
728C8—61no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—41no—
734C2×C3—41no—
735C2×C3—82no—
736C2×C3—81no—
737C2×C3—81no—
738C2×C3—122no—
739C2×C3C2×#95011yescharacteristic
740C2×C3#582211yescharacteristic
741C2×C3#582811yescharacteristic
742C2×C3C3×#52511yescharacteristic
743C2×C3C2×C3×#13511yescharacteristic
744C2×C3C3×#57511yescharacteristic
745D3—42no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—62no—
753C22—121no—
754C22—121no—
755C22C22×C3×#6711yescharacteristic
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—62no—
764C4—121no—
765C4—121no—
766C4C3×#95012yes—
767C4C3×D3×#4111yescharacteristic
768C4C3×D3×#4111yescharacteristic
769C3—21no—
770C3#8314011yescharacteristic, direct product factor
771C3C3×#310211yescharacteristic, complemented
772C2—41no—
773C2—81no—
774C2—122no—
775C2C2×C3×#95011yescharacteristic
776C2C3×#582211yescharacteristic
777C2C3×#582811yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#529C2
socleC22×C32C22×D4
prime radicalC3×#5037C2
hypercenterC3×#529D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#529

Complements

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

NH ≅ G/Ntype
1. C32×#529C2semidirect
2. C3×C4×#235C2semidirect
3. C3×#5066C2semidirect
4. C3×#5063C2semidirect
5. C3×#5057C2semidirect
6. C3×#5054C2semidirect
7. C3×#5047C2semidirect
8. C3×#5045C2semidirect
10. C3×#5035C2semidirect
11. C3×C4×#216C2semidirect
12. C3×C4×#215C2semidirect
13. C3×C4×#214C2semidirect
14. C3×C4×#213C2semidirect
15. C3×#4925C2semidirect
17. #83140C3direct (N × H)
62. C3×#529D3semidirect
63. C3×#529C2×C3semidirect
65. C4×#235C2×C3semidirect
79. #5066C2×C3semidirect
80. #5063C2×C3semidirect
81. #5057C2×C3semidirect
82. #5054C2×C3semidirect
83. #5047C2×C3semidirect
84. #5045C2×C3semidirect
86. #5035C2×C3semidirect
87. C4×#216C2×C3semidirect
88. C4×#215C2×C3semidirect
89. C4×#214C2×C3semidirect
90. C4×#213C2×C3semidirect
91. #4925C2×C3semidirect
276. #529C3×D3semidirect
691. C32#3102semidirect
770. C3#83140direct (N × H)
771. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
C3×C4×#2352
C3×#50662
C3×#50632
C3×#50572
C3×#50542
C3×#50472
C3×#50452
C3×#50372
C3×#50352
C3×C4×#2162
C3×C4×#2152
C3×C4×#2142
C3×C4×#2132
C3×#49252
C3×#31023
#831403