Finite Group Databasebeta

← C3×#79653 #11870705

Subgroups — C3×#79653 #11870705

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
2C3×#5548C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5170C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6C3×C4×#215C211yesmaximal, characteristic, complemented
7C3×C4×#214C211yesmaximal, characteristic, complemented
8C3×#4863C211yesmaximal, characteristic, complemented
9C3×#4854C211yesmaximal, characteristic, complemented
10C3×#4806C211yesmaximal, characteristic, complemented
11C3×#4791C211yesmaximal, characteristic, complemented
12C3×#4777C211yesmaximal, characteristic, complemented
13C3×#4762C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×#4685C211yesmaximal, characteristic, complemented
16C3×#3103—31nomaximal
17#79653C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235—21no—
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#940C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C3×C4×#67—21no—
29C2×C3×#204C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×D3×C4⋊C4—21no—
32C3×D3×C4⋊C4C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#885—21no—
37C3×#884—21no—
38C3×C4×D12C2211yescharacteristic
39C3×C42×D3—21no—
40C3×C42×D3C2211yescharacteristic
41C3×C4×Dic6—21no—
42C3×C4×Dic6C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#532—31no—
62C2×C3×C4×Q8—31no—
63C4×D3×Q8C2×C311yescharacteristic, complemented
64#5548C2×C311yescharacteristic
65C3×#481—31no—
66C3×#481—31no—
67C3×#475—31no—
68C3×#475—31no—
69C3×#460—31no—
70C3×#460—31no—
71C3×#448—31no—
72C3×#448—31no—
73C3×C4×SD16—21no—
74C3×C4×SD16—31no—
75C3×C4×SD16—31no—
76C3×C4×SD16—31no—
77C3×C4×SD16D311yescharacteristic, complemented
78C3×C4×SD16C2×C311yescharacteristic, complemented
79C3×#431—31no—
80#5170C2×C311yescharacteristic, complemented
81#5163C2×C311yescharacteristic, complemented
82C4×#215C2×C311yescharacteristic, complemented
83C4×#214C2×C311yescharacteristic, complemented
84#4863C2×C311yescharacteristic, complemented
85#4854C2×C311yescharacteristic, complemented
86#4806C2×C311yescharacteristic, complemented
87#4791C2×C311yescharacteristic, complemented
88#4777C2×C311yescharacteristic, complemented
89#4762C2×C311yescharacteristic, complemented
90C4×#204C2×C311yescharacteristic, complemented
91#4685C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C3×#235—44no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C32×SD16—22no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42—21no—
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#215—22no—
123C3×#214—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142#3103—31noSylow
143C2×C3×#41—61no—
144C22×C3×Q8—31no—
145C2×D3×Q8C22×C311yescharacteristic
146C2×#235—21no—
147C2×C3×SD16—21no—
148C2×C3×SD16—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16C2×D311yescharacteristic
152C2×C3×SD16C22×C311yescharacteristic
153C3×C4⋊Q8—31no—
154C3×#127—31no—
155C3×#124—61no—
156C3×#121—31no—
157C3×#121—31no—
158C3×#121—61no—
159C3×C4×Q8—21no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—61no—
164C3×C4×Q8—61no—
165C3×C4×Q8C2×D311yescharacteristic
166C3×C4×Q8C22×C311yescharacteristic
167C3×C4×D4—21no—
168C3×C4×D4—31no—
169C3×C4×D4—61no—
170C3×C4×D4C2×D311yescharacteristic
171C3×C4×D4C22×C311yescharacteristic
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—61no—
174C2×C3×C42—31no—
175C2×C3×C42—61no—
176Q8×Dic3C22×C311yescharacteristic
177C2×#215C22×C311yescharacteristic
178#940C22×C311yescharacteristic
179#938C22×C311yescharacteristic
180C2×#214C22×C311yescharacteristic
181C4×#67—21no—
182C2×#204C22×C311yescharacteristic
183#895C22×C311yescharacteristic
184D3×C4⋊C4—21no—
185D3×C4⋊C4C22×C311yescharacteristic
186#888C22×C311yescharacteristic
187#887—21no—
188#887C22×C311yescharacteristic
189#885—21no—
190#884—21no—
191C4×D12C22×C311yescharacteristic
192C42×D3—21no—
193C42×D3C22×C311yescharacteristic
194C4×Dic6—21no—
195C4×Dic6C22×C311yescharacteristic
196C3×#106—21no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic
201C3×#106C22×C311yescharacteristic
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic
209C3×#103C22×C311yescharacteristic
210C3×#102—21no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C22×C311yescharacteristic
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C4×C8—21no—
219C3×C4×C8—31no—
220C3×C4×C8C2×D311yescharacteristic
221C3×C4×C8C22×C311yescharacteristic
222#835C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227#817C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#809C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#808C22×C311yescharacteristic
235C4×C3⋊C8C22×C311yescharacteristic
236C23×C32—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8#4112yescomplemented
241C32×D4—21no—
242C32×D4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—42no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—42no—
251C3×#67—42no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—42no—
262C3×C4×D3—24no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—41no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C3×C4×D3SD1614yescomplemented
269C3×Dic6—24no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C3×Dic6#4112yescomplemented
273C32×C8—21no—
274C32×C8—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#532—31no—
278C2×C4×Q8—31no—
279#481—31no—
280#481—31no—
281#475—31no—
282#475—31no—
283#460—31no—
284#460—31no—
285#448—31no—
286#448—31no—
287C4×SD16—31no—
288C4×SD16—31no—
289C4×SD16—31no—
290C4×SD16C3×D311yescharacteristic, complemented
291#431—31no—
292C3×#41—124no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—62no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C23×C311yescharacteristic
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—21no—
321D3×Q8—22no—
322D3×Q8—22no—
323#235—44no—
324C2×D12—21no—
325C2×D12C23×C311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3C3×D411yescharacteristic
330C2×C4×D3C3×D411yescharacteristic
331C2×C4×D3C23×C311yescharacteristic
332C2×Dic6—21no—
333C2×Dic6—21no—
334C2×Dic6C23×C311yescharacteristic
335C3×SD16—24no—
336C3×SD16—22no—
337C3×SD16—22no—
338C3×SD16—62no—
339C3×SD16—62no—
340C3×SD16—62no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C4⋊C4C23×C311yescharacteristic
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—31no—
375C3×C42—31no—
376C3×C42—31no—
377C3×C42—41no—
378C3×C42—61no—
379C3×C42—61no—
380C3×C42—61no—
381C3×C42C22×D311yescharacteristic
382C3×C42C23×C311yescharacteristic
383#217—21no—
384#215—22no—
385#214—22no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3C23×C311yescharacteristic
390C4⋊Dic3C23×C311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395C4×Dic3—21no—
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3C3×D411yescharacteristic
399C4×Dic3C3×D411yescharacteristic
400C4×Dic3C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403#204—22no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3C2×SD1612yes—
414C32×C4—22no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×SD1612yes—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3×Dic3—21no—
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3C2×SD1612yes—
427C2×#41—61no—
428C22×Q8—31no—
429C2×SD16—31no—
430C2×SD16—31no—
431C2×SD16—31no—
432C2×SD16C2×C3×D311yescharacteristic
433C4⋊Q8—31no—
434#127—31no—
435#124—61no—
436#121—31no—
437#121—31no—
438#121—61no—
439C4×Q8—31no—
440C4×Q8—31no—
441C4×Q8—31no—
442C4×Q8—61no—
443C4×Q8—61no—
444C4×Q8C2×C3×D311yescharacteristic
445C4×D4—31no—
446C4×D4—61no—
447C4×D4C2×C3×D311yescharacteristic
448C2×C4⋊C4—31no—
449C2×C4⋊C4—61no—
450C2×C42—31no—
451C2×C42—61no—
452#106—31no—
453#106—31no—
454#106—31no—
455#106C2×C3×D311yescharacteristic
456C4⋊C8—31no—
457C4⋊C8—31no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103C2×C3×D311yescharacteristic
462#102—31no—
463#102—31no—
464#102—31no—
465#102C2×C3×D311yescharacteristic
466C22⋊C8—31no—
467C22⋊C8—31no—
468C4×C8—31no—
469C4×C8C2×C3×D311yescharacteristic
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—41no—
474C23×C3—61no—
475C22×D3—21no—
476C22×D3C2×C3×D411yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—32no—
481C3×Q8—41no—
482C3×Q8—64no—
483C3×Q8—61no—
484C3×Q8—122no—
485C3×Q8#23512yescomplemented
486C3×Q8C3×#4112yescomplemented
487C3×D4—22no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—41no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—122no—
496C3×D4—122no—
497C3×D4—122no—
498C3×D4—122no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—34no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4—64no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—82no—
524C2×C3×C4—121no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×C3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C24×C311yescharacteristic
533#67—42no—
534#67—42no—
535#67—42no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3C2×C3×D411yescharacteristic
540C2×Dic3C2×C3×D411yescharacteristic
541C2×Dic3C2×C3×D411yescharacteristic
542D12—21no—
543D12—21no—
544D12—42no—
545C4×D3—24no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—41no—
549C4×D3—42no—
550C4×D3—42no—
551C4×D3C3×SD1614yescomplemented
552Dic6—24no—
553Dic6—21no—
554Dic6—42no—
555Dic6C3×#4112yescomplemented
556C3×C8—22no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C2×C32—81no—
567C2×C32#52511yescharacteristic
568C2×C32C22×SD1611yescharacteristic
569C2×C32#57511yescharacteristic
570C3×D3—22no—
571C3×D3—81no—
572#41—124no—
573C2×Q8—31no—
574C2×Q8—61no—
575C2×Q8—61no—
576C2×Q8—62no—
577C2×Q8—62no—
578C2×Q8C22×C3×D311yescharacteristic
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4C22×C3×D311yescharacteristic
585C22×C4—21no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592SD16—22no—
593SD16—62no—
594SD16—62no—
595SD16—62no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8C22×C3×D311yescharacteristic
599C2×C8C22×C3×D311yescharacteristic
600C4⋊C4—21no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4C22×C3×D311yescharacteristic
609C4⋊C4C22×C3×D311yescharacteristic
610C22⋊C4—21no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C42—21no—
615C42—31no—
616C42—31no—
617C42—31no—
618C42—61no—
619C42—61no—
620C42—61no—
621C42C22×C3×D311yescharacteristic
622C22×C3—21no—
623C22×C3—32no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C22×C3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3C2×C3×SD1612yes—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—62no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4D3×SD1612yes—
668C3×C4C2×C3×SD1612yes—
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4C2×C3×#4111yescharacteristic
672C3×C4C2×C3×#4111yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—22no—
676Dic3—41no—
677Dic3—41no—
678Dic3C2×C3×SD1612yes—
679C32#310311yescharacteristic, complemented, Sylow
680C23—21no—
681C23—31no—
682C23—61no—
683Q8—21no—
684Q8—32no—
685Q8—64no—
686Q8—61no—
687Q8—122no—
688Q8C3×#23512yescomplemented
689D4—21no—
690D4—21no—
691D4—61no—
692D4—61no—
693D4—122no—
694D4—122no—
695D4—122no—
696D4—122no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—34no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—42no—
705C2×C4—64no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—121no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4C3×D3×D411yescharacteristic
715C2×C4C3×D3×D411yescharacteristic
716C2×C4C23×C3×D311yescharacteristic
717C8—21no—
718C8—21no—
719C8—61no—
720C8—61no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—62no—
725C2×C3—82no—
726C2×C3—81no—
727C2×C3—81no—
728C2×C3—241no—
729C2×C3#554711yescharacteristic
730C2×C3C2×D3×SD1611yescharacteristic
731C2×C3#576811yescharacteristic
732C2×C3C3×#52511yescharacteristic
733C2×C3C22×C3×SD1611yescharacteristic
734C2×C3C3×#57511yescharacteristic
735D3—22no—
736D3—81no—
737C22—32no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—61no—
742C22—61no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22C2×C3×D3×D411yescharacteristic
747C4—21no—
748C4—22no—
749C4—32no—
750C4—41no—
751C4—41no—
752C4—61no—
753C4—61no—
754C4—62no—
755C4—121no—
756C4—121no—
757C4C3×D3×SD1612yes—
758C4C2×C3×#23511yescharacteristic
759C4C3×D3×#4111yescharacteristic
760C3—21no—
761C3#7965311yescharacteristic, direct product factor
762C3C3×#310311yescharacteristic, complemented
763C2—62no—
764C2—81no—
765C2—241no—
766C2C3×#554711yescharacteristic
767C2C2×C3×D3×SD1611yescharacteristic
768C2C3×#576811yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5548C2
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3103
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×C4×D3×Q8C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5170C2semidirect
5. C3×#5163C2semidirect
6. C3×C4×#215C2semidirect
7. C3×C4×#214C2semidirect
8. C3×#4863C2semidirect
9. C3×#4854C2semidirect
10. C3×#4806C2semidirect
11. C3×#4791C2semidirect
12. C3×#4777C2semidirect
13. C3×#4762C2semidirect
14. C3×C4×#204C2semidirect
15. C3×#4685C2semidirect
17. #79653C3direct (N × H)
63. C4×D3×Q8C2×C3semidirect
77. C3×C4×SD16D3semidirect
78. C3×C4×SD16C2×C3semidirect
80. #5170C2×C3semidirect
81. #5163C2×C3semidirect
82. C4×#215C2×C3semidirect
83. C4×#214C2×C3semidirect
84. #4863C2×C3semidirect
85. #4854C2×C3semidirect
86. #4806C2×C3semidirect
87. #4791C2×C3semidirect
88. #4777C2×C3semidirect
89. #4762C2×C3semidirect
90. C4×#204C2×C3semidirect
91. #4685C2×C3semidirect
240. C32×Q8#41semidirect
268. C3×C4×D3SD16semidirect
272. C3×Dic6#41semidirect
290. C4×SD16C3×D3semidirect
485. C3×Q8#235semidirect
486. C3×Q8C3×#41semidirect
551. C4×D3C3×SD16semidirect
555. Dic6C3×#41semidirect
679. C32#3103semidirect
688. Q8C3×#235semidirect
761. C3#79653direct (N × H)
762. C3C3×#3103semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
C3×#55482
C32×C4×SD162
C3×#51702
C3×#51632
C3×C4×#2152
C3×C4×#2142
C3×#48632
C3×#48542
C3×#48062
C3×#47912
C3×#47772
C3×#47622
C3×C4×#2042
C3×#46852
C3×#31033
#796533