Finite Group Databasebeta

← C3×#86752 #11909844

Subgroups — C3×#86752 #11909844

Order 1152.

2124 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D4×Q8C211yesmaximal, characteristic, complemented
2C3×Q8×#67C211yesmaximal, characteristic, complemented
3C3×Q8×#67C211yesmaximal, characteristic, complemented
4C3×#5812C211yesmaximal, characteristic, complemented
5C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
6C3×#5731C213yesmaximal, complemented
7C3×#5721C213yesmaximal, complemented
8C3×#5642C213yesmaximal, complemented
9C3×#5641C213yesmaximal, complemented
10C3×#5625C213yesmaximal, complemented
11C3×#5622C213yesmaximal, complemented
12C3×#5572C211yesmaximal, characteristic, complemented
13C3×#5569C211yesmaximal, characteristic, complemented
14C3×#5541C213yesmaximal, complemented
15C3×#5538C213yesmaximal
16C3×#3523—31nomaximal
17#86752C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C32×C4⋊Q8C2213yes—
22C32×C22⋊Q8C2213yes—
23C32×C22⋊Q8C2213yes—
24C32×C4×Q8C2211yescharacteristic
25C32×C4×D4C2213yes—
26C3×#946C2213yes—
27C3×#946C2213yes—
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×Q8×Dic3C2213yes—
31C3×Q8×Dic3C2213yes—
32C3×Q8×Dic3C2211yescharacteristic
33C3×Q8×Dic3C2213yes—
34C3×Q8×Dic3C2213yes—
35C3×#944C2213yes—
36C3×#944C2213yes—
37C3×#939C2211yescharacteristic
38C3×#935C2213yes—
39C3×C4×#67C2213yes—
40C3×C4×#67C2213yes—
41C3×#926C2213yes—
42C3×#926C2213yes—
43C2×C3×C4⋊Dic3C2213yes—
44C3×#924C2213yes—
45C3×#924C2213yes—
46C2×C3×C4×Dic3C2213yes—
47C3×#898C2213yes—
48C3×#898C2216yes—
49C3×#892C2213yes—
50C3×#890C2213yes—
51C3×#890C2216yes—
52C3×#889C2213yes—
53C3×#889C2216yes—
54C3×#889C2216yes—
55C3×#888C2213yes—
56C3×#887C2213yes—
57C3×#887C2216yes—
58C3×#886C2213yes—
59C3×#885C2213yes—
60C3×#879C2213yes—
61C3×#879C2216yes—
62C3×#878C2213yes—
63C3×#877C2216yes—
64C3×#872C2213yes—
65C3×#870C2213yes—
66C3×C4×Dic6C2213yes—
67C3×C4×Dic6C2213yes—
68C3×#557—33no—
69C3×#557—31no—
70C3×#556—33no—
71C3×#552—33no—
72C3×#552—33no—
73C3×D4×Q8—21no—
74C3×D4×Q8—31no—
75C3×D4×Q8—31no—
76C3×D4×Q8D311yescharacteristic, complemented
77C3×D4×Q8C2×C311yescharacteristic, complemented
78C3×#541—33no—
79C3×#541—33no—
80C3×#533—33no—
81C3×#529—33no—
82C3×#519—31no—
83C3×#519—31no—
84C2×C3×C4×Q8—31no—
85Q8×#67C2×C311yescharacteristic, complemented
86Q8×#67C2×C311yescharacteristic, complemented
87#5812C2×C311yescharacteristic, complemented
88C2×Q8×Dic3C2×C311yescharacteristic, complemented
89#5731C2×C313yescomplemented
90#5721C2×C313yescomplemented
91#5642C2×C313yescomplemented
92#5641C2×C313yescomplemented
93#5625C2×C313yescomplemented
94#5622C2×C313yescomplemented
95#5572C2×C311yescharacteristic, complemented
96#5569C2×C311yescharacteristic, complemented
97#5541C2×C313yescomplemented
98#5538C2×C313yes—
99C2×C32×Q8—24no—
100C2×C32×Q8—24no—
101C2×C32×Q8C2313yes—
102C2×C32×Q8C2313yes—
103C2×C32×Q8C2311yescharacteristic
104C2×C32×D4C2311yescharacteristic
105C22×C32×C4C2313yes—
106C22×C32×C4C2313yes—
107C2×C3×#67C2311yescharacteristic
108C2×C3×#67C2311yescharacteristic
109C22×C3×Dic3C2313yes—
110C22×C3×Dic3C2311yescharacteristic
111C3×D3×Q8—24no—
112C2×C3×C4×D3C2313yes—
113C2×C3×Dic6C2313yes—
114C2×C3×Dic6C2313yes—
115C32×C4⋊C4C2313yes—
116C32×C4⋊C4C2316yes—
117C32×C4⋊C4C2313yes—
118C32×C22⋊C4C2313yes—
119C32×C22⋊C4C2313yes—
120C32×C42C2313yes—
121C3×#217C2313yes—
122C3×#217C2313yes—
123C3×#217C2311yescharacteristic
124C3×#217C2313yes—
125C3×(C2×D3)⋊C4C2313yes—
126C3×(C2×D3)⋊C4C2313yes—
127C3×(C2×D3)⋊C4C2313yes—
128C3×(C2×D3)⋊C4C2311yescharacteristic
129C3×C4⋊Dic3C2313yes—
130C3×C4⋊Dic3C2313yes—
131C3×C4⋊Dic3C2316yes—
132C3×C4⋊Dic3C2313yes—
133C3×C4⋊Dic3C2313yes—
134C3×C4⋊Dic3C2313yes—
135C3×C4⋊Dic3C2313yes—
136C3×Dic3⋊C4C2316yes—
137C3×Dic3⋊C4C2316yes—
138C3×Dic3⋊C4C2313yes—
139C3×Dic3⋊C4C2313yes—
140C3×Dic3⋊C4C2316yes—
141C3×Dic3⋊C4C2313yes—
142C3×Dic3⋊C4C2313yes—
143C3×Dic3⋊C4C2311yescharacteristic
144C3×Dic3⋊C4C2313yes—
145C3×C4×Dic3C2316yes—
146C3×C4×Dic3C2316yes—
147C3×C4×Dic3C2313yes—
148C3×C4×Dic3C2313yes—
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2313yes—
152#3523—31noSylow
153C22×C3×Q8—21no—
154C22×C3×Q8—21no—
155C22×C3×Q8—31no—
156C22×C3×Q8C2×D311yescharacteristic
157C22×C3×Q8C2×D311yescharacteristic
158C22×C3×Q8C22×C311yescharacteristic
159C22×C3×Q8C22×C311yescharacteristic
160C2×D3×Q8C22×C311yescharacteristic
161C3×C4⋊Q8—23no—
162C3×C4⋊Q8—33no—
163C3×C4⋊Q8—33no—
164C3×C4⋊Q8—33no—
165C3×C4⋊Q8C2×D313yes—
166C3×C4⋊Q8C22×C313yes—
167C3×#126—33no—
168C3×#126—36no—
169C3×#126—33no—
170C3×#126—36no—
171C3×#125—33no—
172C3×#125—36no—
173C3×#125—36no—
174C3×#125—36no—
175C3×#125—33no—
176C3×#125—33no—
177C3×#124—33no—
178C3×#123—33no—
179C3×#123—33no—
180C3×C22⋊Q8—23no—
181C3×C22⋊Q8—23no—
182C3×C22⋊Q8—33no—
183C3×C22⋊Q8—33no—
184C3×C22⋊Q8—33no—
185C3×C22⋊Q8—33no—
186C3×C22⋊Q8—33no—
187C3×C22⋊Q8C2×D313yes—
188C3×C22⋊Q8C2×D313yes—
189C3×C22⋊Q8C22×C313yes—
190C3×C22⋊Q8C22×C313yes—
191C3×#121—31no—
192C3×C4×Q8—21no—
193C3×C4×Q8—31no—
194C3×C4×Q8—33no—
195C3×C4×Q8—31no—
196C3×C4×Q8—33no—
197C3×C4×Q8—33no—
198C3×C4×Q8—31no—
199C3×C4×Q8—33no—
200C3×C4×Q8—33no—
201C3×C4×Q8—36no—
202C3×C4×Q8—33no—
203C3×C4×Q8—33no—
204C3×C4×Q8C2×D311yescharacteristic
205C3×C4×Q8C22×C311yescharacteristic
206C3×C4×D4—23no—
207C3×C4×D4—33no—
208C3×C4×D4—33no—
209C3×C4×D4C2×D313yes—
210C3×C4×D4C22×C313yes—
211C3×#117—33no—
212C3×#117—33no—
213C3×#117—33no—
214C3×#117—36no—
215C3×#117—33no—
216C2×C3×C4⋊C4—33no—
217C2×C3×C42—33no—
218#946C22×C313yes—
219#946C22×C313yes—
220Q8×Dic3C22×C313yes—
221Q8×Dic3C22×C313yes—
222Q8×Dic3C22×C313yes—
223Q8×Dic3C22×C313yes—
224Q8×Dic3C22×C311yescharacteristic
225Q8×Dic3C22×C311yescharacteristic
226Q8×Dic3C22×C311yescharacteristic
227#944C22×C313yes—
228#944C22×C313yes—
229#939C22×C311yescharacteristic
230#935C22×C313yes—
231C4×#67C22×C313yes—
232C4×#67C22×C313yes—
233#926C22×C313yes—
234#926C22×C313yes—
235C2×C4⋊Dic3C22×C313yes—
236#924C22×C313yes—
237#924C22×C313yes—
238C2×C4×Dic3C22×C313yes—
239#898C22×C316yes—
240#898C22×C313yes—
241#892C22×C313yes—
242#890C22×C316yes—
243#890C22×C313yes—
244#889C22×C313yes—
245#889C22×C316yes—
246#889C22×C316yes—
247#888C22×C313yes—
248#887C22×C316yes—
249#887C22×C313yes—
250#886C22×C313yes—
251#885C22×C313yes—
252#879C22×C316yes—
253#879C22×C313yes—
254#878C22×C313yes—
255#877C22×C316yes—
256#872C22×C313yes—
257#870C22×C313yes—
258C4×Dic6C22×C313yes—
259C4×Dic6C22×C313yes—
260C23×C32C2411yescharacteristic
261C23×C32C2411yescharacteristic
262C22×C3×D3C2411yescharacteristic
263C32×Q8—26no—
264C32×Q8—26no—
265C32×Q8#4114yes—
266C32×D4—22no—
267C2×C32×C4—26no—
268C2×C32×C4—26no—
269C2×C32×C4C2413yes—
270C2×C32×C4C2413yes—
271C2×C32×C4C2413yes—
272C2×C32×C4C2411yescharacteristic
273C2×C32×C4C2413yes—
274C3×#67—22no—
275C3×#67—22no—
276C2×C3×Dic3—26no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3C2411yescharacteristic
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2413yes—
281C2×C3×Dic3C2411yescharacteristic
282C2×C3×Dic3C2413yes—
283C2×C3×Dic3C2413yes—
284C2×C3×Dic3C2411yescharacteristic
285C3×C4×D3—26no—
286C3×Dic6—26no—
287C3×Dic6—26no—
288#557—33no—
289#557—31no—
290#556—33no—
291#552—33no—
292#552—33no—
293D4×Q8—31no—
294D4×Q8—31no—
295D4×Q8C3×D311yescharacteristic, complemented
296#541—33no—
297#541—33no—
298#533—33no—
299#529—33no—
300#519—31no—
301#519—31no—
302C2×C4×Q8—31no—
303C2×C3×Q8—24no—
304C2×C3×Q8—24no—
305C2×C3×Q8—24no—
306C2×C3×Q8—24no—
307C2×C3×Q8—21no—
308C2×C3×Q8—23no—
309C2×C3×Q8—23no—
310C2×C3×Q8—33no—
311C2×C3×Q8—33no—
312C2×C3×Q8—44no—
313C2×C3×Q8—44no—
314C2×C3×Q8—64no—
315C2×C3×Q8C22×D313yes—
316C2×C3×Q8C22×D313yes—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C23×C313yes—
319C2×C3×Q8C23×C313yes—
320C2×C3×Q8C23×C311yescharacteristic
321C2×C3×D4—21no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C23×C311yescharacteristic
326C22×C3×C4—23no—
327C22×C3×C4—23no—
328C22×C3×C4—31no—
329C22×C3×C4—33no—
330C22×C3×C4—33no—
331C22×C3×C4C22×D313yes—
332C22×C3×C4C22×D313yes—
333C22×C3×C4C23×C313yes—
334C22×C3×C4C23×C313yes—
335C2×#67C23×C311yescharacteristic
336C2×#67C23×C311yescharacteristic
337C22×Dic3C23×C313yes—
338C22×Dic3C23×C311yescharacteristic
339D3×Q8—24no—
340C2×C4×D3C23×C313yes—
341C2×Dic6C23×C313yes—
342C2×Dic6C23×C313yes—
343C3×C4⋊C4—23no—
344C3×C4⋊C4—23no—
345C3×C4⋊C4—26no—
346C3×C4⋊C4—33no—
347C3×C4⋊C4—33no—
348C3×C4⋊C4—36no—
349C3×C4⋊C4—36no—
350C3×C4⋊C4—33no—
351C3×C4⋊C4—33no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—36no—
354C3×C4⋊C4—33no—
355C3×C4⋊C4—33no—
356C3×C4⋊C4—33no—
357C3×C4⋊C4—36no—
358C3×C4⋊C4—33no—
359C3×C4⋊C4—33no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—33no—
362C3×C4⋊C4C22×D313yes—
363C3×C4⋊C4C22×D313yes—
364C3×C4⋊C4C22×D316yes—
365C3×C4⋊C4C23×C313yes—
366C3×C4⋊C4C23×C316yes—
367C3×C4⋊C4C23×C313yes—
368C3×C22⋊C4—23no—
369C3×C22⋊C4—23no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—33no—
372C3×C22⋊C4—33no—
373C3×C22⋊C4—33no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—33no—
376C3×C22⋊C4—33no—
377C3×C22⋊C4—33no—
378C3×C22⋊C4C22×D313yes—
379C3×C22⋊C4C22×D313yes—
380C3×C22⋊C4C23×C313yes—
381C3×C22⋊C4C23×C313yes—
382C3×C42—23no—
383C3×C42—33no—
384C3×C42—33no—
385C3×C42—33no—
386C3×C42—33no—
387C3×C42—36no—
388C3×C42—36no—
389C3×C42—33no—
390C3×C42C22×D313yes—
391C3×C42C23×C313yes—
392#217C23×C313yes—
393#217C23×C313yes—
394#217C23×C311yescharacteristic
395#217C23×C313yes—
396(C2×D3)⋊C4C23×C311yescharacteristic
397(C2×D3)⋊C4C23×C313yes—
398(C2×D3)⋊C4C23×C313yes—
399(C2×D3)⋊C4C23×C313yes—
400C4⋊Dic3C23×C313yes—
401C4⋊Dic3C23×C313yes—
402C4⋊Dic3C23×C313yes—
403C4⋊Dic3C23×C313yes—
404C4⋊Dic3C23×C313yes—
405C4⋊Dic3C23×C316yes—
406C4⋊Dic3C23×C313yes—
407Dic3⋊C4C23×C311yescharacteristic
408Dic3⋊C4C23×C313yes—
409Dic3⋊C4C23×C313yes—
410Dic3⋊C4C23×C316yes—
411Dic3⋊C4C23×C313yes—
412Dic3⋊C4C23×C316yes—
413Dic3⋊C4C23×C313yes—
414Dic3⋊C4C23×C316yes—
415Dic3⋊C4C23×C313yes—
416C4×Dic3C23×C316yes—
417C4×Dic3C23×C313yes—
418C4×Dic3C23×C313yes—
419C4×Dic3C23×C313yes—
420C4×Dic3C23×C316yes—
421C4×Dic3C23×C313yes—
422C4×Dic3C23×C313yes—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C322−1+412yes—
429C22×C32C2511yescharacteristic
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C32×C4—21no—
434C32×C4—23no—
435C32×C4—23no—
436C32×C4—23no—
437C32×C4C2×#4116yes—
438C3×Dic3—23no—
439C3×Dic3—23no—
440C3×Dic3—23no—
441C3×Dic3—23no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic32−1+412yes—
445C22×Q8—31no—
446C22×Q8C2×C3×D311yescharacteristic
447C22×Q8C2×C3×D311yescharacteristic
448C4⋊Q8—33no—
449C4⋊Q8—33no—
450C4⋊Q8—33no—
451C4⋊Q8C2×C3×D313yes—
452#126—33no—
453#126—36no—
454#126—33no—
455#126—36no—
456#125—33no—
457#125—36no—
458#125—36no—
459#125—36no—
460#125—33no—
461#125—33no—
462#124—33no—
463#123—33no—
464#123—33no—
465C22⋊Q8—33no—
466C22⋊Q8—33no—
467C22⋊Q8—33no—
468C22⋊Q8—33no—
469C22⋊Q8—33no—
470C22⋊Q8C2×C3×D313yes—
471C22⋊Q8C2×C3×D313yes—
472#121—31no—
473C4×Q8—31no—
474C4×Q8—33no—
475C4×Q8—31no—
476C4×Q8—33no—
477C4×Q8—33no—
478C4×Q8—31no—
479C4×Q8—33no—
480C4×Q8—33no—
481C4×Q8—36no—
482C4×Q8—33no—
483C4×Q8—33no—
484C4×Q8C2×C3×D311yescharacteristic
485C4×D4—33no—
486C4×D4—33no—
487C4×D4C2×C3×D313yes—
488#117—33no—
489#117—33no—
490#117—33no—
491#117—36no—
492#117—33no—
493C2×C4⋊C4—33no—
494C2×C42—33no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—31no—
498C23×C3C23×D311yescharacteristic
499C23×C3C23×D311yescharacteristic
500C23×C3C24×C311yescharacteristic
501C23×C3C24×C311yescharacteristic
502C22×D3C24×C311yescharacteristic
503C3×Q8—26no—
504C3×Q8—26no—
505C3×Q8—26no—
506C3×Q8—26no—
507C3×Q8—24no—
508C3×Q8—46no—
509C3×Q8—46no—
510C3×Q8—66no—
511C3×Q8—66no—
512C3×Q8#23714yes—
513C3×Q8C3×#4114yes—
514C3×D4—24no—
515C3×D4—22no—
516C3×D4—22no—
517C3×D4—62no—
518C3×D4—62no—
519C2×C3×C4—26no—
520C2×C3×C4—26no—
521C2×C3×C4—26no—
522C2×C3×C4—26no—
523C2×C3×C4—21no—
524C2×C3×C4—23no—
525C2×C3×C4—23no—
526C2×C3×C4—23no—
527C2×C3×C4—23no—
528C2×C3×C4—31no—
529C2×C3×C4—33no—
530C2×C3×C4—31no—
531C2×C3×C4—33no—
532C2×C3×C4—31no—
533C2×C3×C4—33no—
534C2×C3×C4—33no—
535C2×C3×C4—46no—
536C2×C3×C4—46no—
537C2×C3×C4—62no—
538C2×C3×C4—66no—
539C2×C3×C4—66no—
540C2×C3×C4C23×D313yes—
541C2×C3×C4C23×D313yes—
542C2×C3×C4C23×D313yes—
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D313yes—
545C2×C3×C4C24×C313yes—
546C2×C3×C4C24×C313yes—
547C2×C3×C4C24×C313yes—
548C2×C3×C4C24×C311yescharacteristic
549C2×C3×C4C24×C313yes—
550#67—22no—
551#67—22no—
552C2×Dic3—26no—
553C2×Dic3—22no—
554C2×Dic3C24×C311yescharacteristic
555C2×Dic3C24×C313yes—
556C2×Dic3C24×C313yes—
557C2×Dic3C24×C311yescharacteristic
558C2×Dic3C24×C313yes—
559C2×Dic3C24×C313yes—
560C2×Dic3C24×C311yescharacteristic
561C4×D3—26no—
562Dic6—26no—
563Dic6—26no—
564C2×C32—22no—
565C2×C32—41no—
566C2×C32C22×#4111yescharacteristic
567C2×C32C2×2−1+411yescharacteristic
568C2×C32C2×2−1+411yescharacteristic
569C3×D3—41no—
570C2×Q8—24no—
571C2×Q8—24no—
572C2×Q8—33no—
573C2×Q8—33no—
574C2×Q8—64no—
575C2×Q8C22×C3×D313yes—
576C2×Q8C22×C3×D313yes—
577C2×Q8C22×C3×D311yescharacteristic
578C2×D4—31no—
579C2×D4—31no—
580C2×D4C22×C3×D311yescharacteristic
581C22×C4—31no—
582C22×C4—33no—
583C22×C4—33no—
584C22×C4C22×C3×D313yes—
585C22×C4C22×C3×D313yes—
586C4⋊C4—33no—
587C4⋊C4—33no—
588C4⋊C4—36no—
589C4⋊C4—33no—
590C4⋊C4—33no—
591C4⋊C4—33no—
592C4⋊C4—33no—
593C4⋊C4—33no—
594C4⋊C4—36no—
595C4⋊C4—36no—
596C4⋊C4—33no—
597C4⋊C4—33no—
598C4⋊C4—31no—
599C4⋊C4—36no—
600C4⋊C4—33no—
601C4⋊C4—33no—
602C4⋊C4C22×C3×D313yes—
603C4⋊C4C22×C3×D313yes—
604C4⋊C4C22×C3×D316yes—
605C22⋊C4—31no—
606C22⋊C4—33no—
607C22⋊C4—33no—
608C22⋊C4—33no—
609C22⋊C4—31no—
610C22⋊C4—33no—
611C22⋊C4—33no—
612C22⋊C4—33no—
613C22⋊C4C22×C3×D313yes—
614C22⋊C4C22×C3×D313yes—
615C42—33no—
616C42—33no—
617C42—33no—
618C42—33no—
619C42—36no—
620C42—36no—
621C42—33no—
622C42C22×C3×D313yes—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3#100712yes—
644C22×C3C3×2−1+412yes—
645C22×C3C24×D311yescharacteristic
646C22×C3C25×C311yescharacteristic
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C3×C4—22no—
651C3×C4—23no—
652C3×C4—23no—
653C3×C4—21no—
654C3×C4—23no—
655C3×C4—23no—
656C3×C4—23no—
657C3×C4—23no—
658C3×C4—21no—
659C3×C4—26no—
660C3×C4—32no—
661C3×C4—43no—
662C3×C4—43no—
663C3×C4—43no—
664C3×C4—63no—
665C3×C4—63no—
666C3×C4—63no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—63no—
670C3×C4C2×#23716yes—
671C3×C4C2×C3×#4116yes—
672Dic3—23no—
673Dic3—23no—
674Dic3—23no—
675Dic3—23no—
676Dic3—21no—
677Dic3—21no—
678Dic3C3×2−1+412yes—
679C32#352311yescharacteristic, complemented, Sylow
680C23—31no—
681C23C23×C3×D311yescharacteristic
682C23C23×C3×D311yescharacteristic
683Q8—26no—
684Q8—26no—
685Q8—66no—
686Q8—66no—
687Q8C3×#23714yes—
688D4—22no—
689D4—62no—
690D4—62no—
691C2×C4—26no—
692C2×C4—26no—
693C2×C4—31no—
694C2×C4—33no—
695C2×C4—31no—
696C2×C4—33no—
697C2×C4—31no—
698C2×C4—33no—
699C2×C4—33no—
700C2×C4—62no—
701C2×C4—66no—
702C2×C4—66no—
703C2×C4C23×C3×D313yes—
704C2×C4C23×C3×D313yes—
705C2×C4C23×C3×D313yes—
706C2×C4C23×C3×D311yescharacteristic
707C2×C4C23×C3×D313yes—
708C2×C3—22no—
709C2×C3—22no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—42no—
714C2×C3—42no—
715C2×C3—41no—
716C2×C3—41no—
717C2×C3—121no—
718C2×C3C22×#23711yescharacteristic
719C2×C3C2×#100711yescharacteristic
720C2×C3D3×2−1+411yescharacteristic
721C2×C3C22×C3×#4111yescharacteristic
722C2×C3C2×C3×2−1+411yescharacteristic
723C2×C3C2×C3×2−1+411yescharacteristic
724D3—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22C3×#100712yes—
734C22C24×C3×D311yescharacteristic
735C4—23no—
736C4—23no—
737C4—21no—
738C4—23no—
739C4—32no—
740C4—63no—
741C4—63no—
742C4—63no—
743C4—61no—
744C4—61no—
745C4—63no—
746C4C2×C3×#23716yes—
747C3—21no—
748C3#8675211yescharacteristic, direct product factor
749C3C3×#352311yescharacteristic, complemented
750C2—22no—
751C2—41no—
752C2—121no—
753C2C22×C3×#23711yescharacteristic
754C2C2×C3×#100711yescharacteristic
755C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×D4×Q8C2
socleC22×C32C25
prime radicalC3×#939C22
hypercenterC3×D4×Q8D3
hypocenterC3C3×#3523
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C32×D4×Q8C2semidirect
2. C3×Q8×#67C2semidirect
3. C3×Q8×#67C2semidirect
4. C3×#5812C2semidirect
5. C2×C3×Q8×Dic3C2semidirect
6. C3×#5731C2semidirect
7. C3×#5721C2semidirect
8. C3×#5642C2semidirect
9. C3×#5641C2semidirect
10. C3×#5625C2semidirect
11. C3×#5622C2semidirect
12. C3×#5572C2semidirect
13. C3×#5569C2semidirect
14. C3×#5541C2semidirect
17. #86752C3direct (N × H)
76. C3×D4×Q8D3semidirect
77. C3×D4×Q8C2×C3semidirect
85. Q8×#67C2×C3semidirect
86. Q8×#67C2×C3semidirect
87. #5812C2×C3semidirect
88. C2×Q8×Dic3C2×C3semidirect
89. #5731C2×C3semidirect
90. #5721C2×C3semidirect
91. #5642C2×C3semidirect
92. #5641C2×C3semidirect
93. #5625C2×C3semidirect
94. #5622C2×C3semidirect
95. #5572C2×C3semidirect
96. #5569C2×C3semidirect
97. #5541C2×C3semidirect
295. D4×Q8C3×D3semidirect
679. C32#3523semidirect
748. C3#86752direct (N × H)
749. C3C3×#3523semidirect

Maximal subgroups

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

subgroupindex
C32×D4×Q82
C3×Q8×#672
C3×#58122
C2×C3×Q8×Dic32
C3×#57312
C3×#57212
C3×#56422
C3×#56412
C3×#56252
C3×#56222
C3×#55722
C3×#55692
C3×#55412
C3×#55382
C3×#35233
#867523