Finite Group Databasebeta

← C3×#86722 #11909722

Subgroups — C3×#86722 #11909722

Order 1152.

2353 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#548C211yesmaximal, characteristic, complemented
2C3×#5834C211yesmaximal, characteristic, complemented
3C3×#5827C211yesmaximal, characteristic, complemented
4C3×#5817C211yesmaximal, characteristic, complemented
5C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
6C3×#5682C213yesmaximal, complemented
7C3×#5681C213yesmaximal, complemented
8C3×#5643C213yesmaximal, complemented
9C3×#5635C213yesmaximal, complemented
10C3×#5611C213yesmaximal, complemented
11C3×#5596C213yesmaximal, complemented
12C3×#5574C211yesmaximal, characteristic, complemented
13C3×Q8×Dic6C211yesmaximal, characteristic, complemented
14C3×#5555C213yesmaximal, complemented
15C3×#5538C213yesmaximal, complemented
16C3×#3522—31nomaximal
17#86722C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×#237C2216yes—
22C32×#124C2213yes—
23C32×C22⋊Q8C2213yes—
24C32×#121C2213yes—
25C32×C4×Q8C2211yescharacteristic
26C32×C4×D4C2213yes—
27C3×#947C2213yes—
28C3×#946C2213yes—
29C3×Q8×Dic3C2211yescharacteristic
30C3×Q8×Dic3C2211yescharacteristic
31C3×Q8×Dic3C2213yes—
32C3×Q8×Dic3C2213yes—
33C3×Q8×Dic3C2211yescharacteristic
34C3×#940C2213yes—
35C3×#939C2213yes—
36C3×#938C2213yes—
37C3×#935C2213yes—
38C3×D4×Dic3C2213yes—
39C3×D4×Dic3C2213yes—
40C3×#930C2213yes—
41C3×#930C2213yes—
42C3×C4×#67C2213yes—
43C3×C4×#67C2213yes—
44C3×#926C2213yes—
45C2×C3×C4⋊Dic3C2213yes—
46C2×C3×C4⋊Dic3C2213yes—
47C2×C3×C4×Dic3C2213yes—
48C3×#898C2213yes—
49C3×#897C2216yes—
50C3×#893C2213yes—
51C3×D3×C4⋊C4C2213yes—
52C3×#889C2213yes—
53C3×#888C2213yes—
54C3×#888C2213yes—
55C3×#886C2213yes—
56C3×#886C2216yes—
57C3×#885C2213yes—
58C3×#885C2216yes—
59C3×#883C2216yes—
60C3×#67⋊C4C2216yes—
61C3×#879C2213yes—
62C3×#878C2211yescharacteristic
63C3×#878C2216yes—
64C3×C4×D12C2213yes—
65C3×#872C2213yes—
66C3×#869C2213yes—
67C3×C4×Dic6C2213yes—
68C3×#559—33no—
69C3×Q82—31no—
70C3×#554—33no—
71C3×#550—31no—
72C3×#548—21no—
73C3×#548—31no—
74C3×#548D311yescharacteristic, complemented
75C3×#548C2×C311yescharacteristic, complemented
76C3×#547—33no—
77C3×#547—33no—
78C3×#542—33no—
79C3×#542—33no—
80C3×#532—33no—
81C3×#529—33no—
82C3×#520—31no—
83C3×#520—31no—
84C2×C3×C4×Q8—31no—
85#5834C2×C311yescharacteristic, complemented
86#5827C2×C311yescharacteristic, complemented
87#5817C2×C311yescharacteristic, complemented
88C2×Q8×Dic3C2×C311yescharacteristic, complemented
89#5682C2×C313yescomplemented
90#5681C2×C313yescomplemented
91#5643C2×C313yescomplemented
92#5635C2×C313yescomplemented
93#5611C2×C313yescomplemented
94#5596C2×C313yescomplemented
95#5574C2×C311yescharacteristic, complemented
96Q8×Dic6C2×C311yescharacteristic, complemented
97#5555C2×C313yescomplemented
98#5538C2×C313yescomplemented
99C32×#41—24no—
100C2×C32×Q8—24no—
101C2×C32×Q8C2313yes—
102C2×C32×Q8C2311yescharacteristic
103C2×C32×D4C2313yes—
104C2×C32×D4C2313yes—
105C22×C32×C4C2313yes—
106C22×C32×C4C2313yes—
107C2×C3×#67C2313yes—
108C2×C3×#67C2313yes—
109C2×C3×#67C2316yes—
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2313yes—
112C22×C3×Dic3C2316yes—
113C3×#239—24no—
114C3×#237—412no—
115C2×C3×D12C2313yes—
116C2×C3×C4×D3C2313yes—
117C2×C3×C4×D3C2316yes—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2316yes—
120C32×C4⋊C4C2313yes—
121C32×C4⋊C4C2313yes—
122C32×C22⋊C4C2316yes—
123C32×C22⋊C4C2311yescharacteristic
124C32×C22⋊C4C2313yes—
125C32×C42C2313yes—
126C3×#217C2313yes—
127C3×#217C2311yescharacteristic
128C3×#217C2313yes—
129C3×#217C2313yes—
130C3×(C2×D3)⋊C4C2316yes—
131C3×(C2×D3)⋊C4C2313yes—
132C3×(C2×D3)⋊C4C2313yes—
133C3×(C2×D3)⋊C4C2313yes—
134C3×(C2×D3)⋊C4C2313yes—
135C3×C4⋊Dic3C2316yes—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2313yes—
138C3×C4⋊Dic3C2313yes—
139C3×C4⋊Dic3C2313yes—
140C3×C4⋊Dic3C2313yes—
141C3×C4⋊Dic3C2313yes—
142C3×Dic3⋊C4C2313yes—
143C3×Dic3⋊C4C2313yes—
144C3×Dic3⋊C4C2311yescharacteristic
145C3×Dic3⋊C4C2311yescharacteristic
146C3×Dic3⋊C4C2313yes—
147C3×Dic3⋊C4C2313yes—
148C3×C4×Dic3C2313yes—
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2313yes—
152C3×C4×Dic3C2313yes—
153#3522—31noSylow
154C2×C3×#41—21no—
155C2×C3×#41—31no—
156C2×C3×#41—36no—
157C2×C3×#41C2×D311yescharacteristic
158C2×C3×#41C22×C311yescharacteristic
159C22×C3×Q8—21no—
160C22×C3×Q8C2×D311yescharacteristic
161C22×C3×Q8C22×C311yescharacteristic
162C2×#239C22×C311yescharacteristic
163C2×#237C22×C316yes—
164C3×C4⋊Q8—33no—
165C3×C4⋊Q8—33no—
166C3×C4⋊Q8—33no—
167C3×#127—33no—
168C3×#126—33no—
169C3×#126—33no—
170C3×#125—33no—
171C3×#124—23no—
172C3×#124—33no—
173C3×#124—33no—
174C3×#124—36no—
175C3×#124C2×D313yes—
176C3×#124C22×C313yes—
177C3×#123—33no—
178C3×#123—36no—
179C3×#123—36no—
180C3×#123—33no—
181C3×C22⋊Q8—23no—
182C3×C22⋊Q8—33no—
183C3×C22⋊Q8—36no—
184C3×C22⋊Q8—31no—
185C3×C22⋊Q8—36no—
186C3×C22⋊Q8C2×D313yes—
187C3×C22⋊Q8C22×C313yes—
188C3×#121—23no—
189C3×#121—33no—
190C3×#121—33no—
191C3×#121—33no—
192C3×#121—33no—
193C3×#121C2×D313yes—
194C3×#121C22×C313yes—
195C3×C4×Q8—21no—
196C3×C4×Q8—31no—
197C3×C4×Q8—31no—
198C3×C4×Q8—33no—
199C3×C4×Q8—31no—
200C3×C4×Q8—33no—
201C3×C4×Q8—33no—
202C3×C4×Q8C2×D311yescharacteristic
203C3×C4×Q8C22×C311yescharacteristic
204C3×C4×D4—23no—
205C3×C4×D4—33no—
206C3×C4×D4—33no—
207C3×C4×D4—33no—
208C3×C4×D4—33no—
209C3×C4×D4—33no—
210C3×C4×D4—36no—
211C3×C4×D4—33no—
212C3×C4×D4C2×D313yes—
213C3×C4×D4C22×C313yes—
214C3×#117—33no—
215C3×#117—33no—
216C2×C3×C4⋊C4—33no—
217C2×C3×C4⋊C4—33no—
218C2×C3×C4⋊C4—33no—
219C2×C3×C42—33no—
220#947C22×C313yes—
221#946C22×C313yes—
222Q8×Dic3C22×C313yes—
223Q8×Dic3C22×C313yes—
224Q8×Dic3C22×C311yescharacteristic
225Q8×Dic3C22×C311yescharacteristic
226Q8×Dic3C22×C311yescharacteristic
227#940C22×C313yes—
228#939C22×C313yes—
229#938C22×C313yes—
230#935C22×C313yes—
231D4×Dic3C22×C313yes—
232D4×Dic3C22×C313yes—
233#930C22×C313yes—
234#930C22×C313yes—
235C4×#67C22×C313yes—
236C4×#67C22×C313yes—
237#926C22×C313yes—
238C2×C4⋊Dic3C22×C313yes—
239C2×C4⋊Dic3C22×C313yes—
240C2×C4×Dic3C22×C313yes—
241#898C22×C313yes—
242#897C22×C316yes—
243#893C22×C313yes—
244D3×C4⋊C4C22×C313yes—
245#889C22×C313yes—
246#888C22×C313yes—
247#888C22×C313yes—
248#886C22×C316yes—
249#886C22×C313yes—
250#885C22×C316yes—
251#885C22×C313yes—
252#883C22×C316yes—
253#67⋊C4C22×C316yes—
254#879C22×C313yes—
255#878C22×C316yes—
256#878C22×C311yescharacteristic
257C4×D12C22×C313yes—
258#872C22×C313yes—
259#869C22×C313yes—
260C4×Dic6C22×C313yes—
261C23×C32C2413yes—
262C23×C32C2411yescharacteristic
263C22×C3×D3C2413yes—
264C32×Q8—26no—
265C32×Q8#4114yescomplemented
266C32×D4—26no—
267C32×D4—26no—
268C2×C32×C4—26no—
269C2×C32×C4—26no—
270C2×C32×C4C2413yes—
271C2×C32×C4C2413yes—
272C2×C32×C4C2411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C2×C32×C4C2413yes—
275C3×#67—26no—
276C3×#67—26no—
277C3×#67—46no—
278C2×C3×Dic3—26no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—46no—
281C2×C3×Dic3C2411yescharacteristic
282C2×C3×Dic3C2411yescharacteristic
283C2×C3×Dic3C2413yes—
284C2×C3×Dic3C2413yes—
285C2×C3×Dic3C2413yes—
286C2×C3×Dic3C2411yescharacteristic
287C2×C3×Dic3C2411yescharacteristic
288C3×D12—26no—
289C3×C4×D3—26no—
290C3×C4×D3—46no—
291C3×Dic6—22no—
292C3×Dic6—46no—
293#559—33no—
294Q82—31no—
295#554—33no—
296#550—31no—
297#548—31no—
298#548C3×D311yescharacteristic, complemented
299#547—33no—
300#547—33no—
301#542—33no—
302#542—33no—
303#532—33no—
304#529—33no—
305#520—31no—
306#520—31no—
307C2×C4×Q8—31no—
308C3×#41—24no—
309C3×#41—24no—
310C3×#41—44no—
311C3×#41—64no—
312C3×#41—1212no—
313C2×C3×Q8—24no—
314C2×C3×Q8—24no—
315C2×C3×Q8—21no—
316C2×C3×Q8—23no—
317C2×C3×Q8—31no—
318C2×C3×Q8—36no—
319C2×C3×Q8—44no—
320C2×C3×Q8C22×D313yes—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C23×C313yes—
323C2×C3×Q8C23×C311yescharacteristic
324C2×C3×D4—23no—
325C2×C3×D4—23no—
326C2×C3×D4—33no—
327C2×C3×D4—33no—
328C2×C3×D4—36no—
329C2×C3×D4—33no—
330C2×C3×D4C22×D313yes—
331C2×C3×D4C22×D313yes—
332C2×C3×D4C23×C313yes—
333C2×C3×D4C23×C313yes—
334C22×C3×C4—23no—
335C22×C3×C4—23no—
336C22×C3×C4—31no—
337C22×C3×C4—33no—
338C22×C3×C4—36no—
339C22×C3×C4—33no—
340C22×C3×C4—36no—
341C22×C3×C4C22×D313yes—
342C22×C3×C4C22×D313yes—
343C22×C3×C4C23×C313yes—
344C22×C3×C4C23×C313yes—
345C2×#67C23×C313yes—
346C2×#67C23×C313yes—
347C2×#67C23×C316yes—
348C22×Dic3C23×C311yescharacteristic
349C22×Dic3C23×C313yes—
350C22×Dic3C23×C316yes—
351#239—24no—
352#237—412no—
353C2×D12C23×C313yes—
354C2×C4×D3C23×C313yes—
355C2×C4×D3C23×C316yes—
356C2×Dic6C23×C311yescharacteristic
357C2×Dic6C23×C316yes—
358C3×C4⋊C4—23no—
359C3×C4⋊C4—23no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—33no—
364C3×C4⋊C4—33no—
365C3×C4⋊C4—33no—
366C3×C4⋊C4—33no—
367C3×C4⋊C4—33no—
368C3×C4⋊C4—33no—
369C3×C4⋊C4—33no—
370C3×C4⋊C4—36no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—33no—
373C3×C4⋊C4C22×D313yes—
374C3×C4⋊C4C22×D313yes—
375C3×C4⋊C4C23×C313yes—
376C3×C4⋊C4C23×C313yes—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—23no—
379C3×C22⋊C4—26no—
380C3×C22⋊C4—33no—
381C3×C22⋊C4—33no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—33no—
384C3×C22⋊C4—33no—
385C3×C22⋊C4—33no—
386C3×C22⋊C4—33no—
387C3×C22⋊C4—36no—
388C3×C22⋊C4—33no—
389C3×C22⋊C4C22×D316yes—
390C3×C22⋊C4C22×D311yescharacteristic
391C3×C22⋊C4C22×D313yes—
392C3×C22⋊C4C23×C316yes—
393C3×C22⋊C4C23×C311yescharacteristic
394C3×C22⋊C4C23×C313yes—
395C3×C42—23no—
396C3×C42—33no—
397C3×C42—33no—
398C3×C42—33no—
399C3×C42—33no—
400C3×C42—33no—
401C3×C42C22×D313yes—
402C3×C42C23×C313yes—
403#217C23×C313yes—
404#217C23×C311yescharacteristic
405#217C23×C313yes—
406#217C23×C313yes—
407(C2×D3)⋊C4C23×C313yes—
408(C2×D3)⋊C4C23×C313yes—
409(C2×D3)⋊C4C23×C316yes—
410(C2×D3)⋊C4C23×C313yes—
411(C2×D3)⋊C4C23×C313yes—
412C4⋊Dic3C23×C313yes—
413C4⋊Dic3C23×C313yes—
414C4⋊Dic3C23×C313yes—
415C4⋊Dic3C23×C313yes—
416C4⋊Dic3C23×C316yes—
417C4⋊Dic3C23×C311yescharacteristic
418C4⋊Dic3C23×C313yes—
419Dic3⋊C4C23×C313yes—
420Dic3⋊C4C23×C313yes—
421Dic3⋊C4C23×C311yescharacteristic
422Dic3⋊C4C23×C313yes—
423Dic3⋊C4C23×C313yes—
424Dic3⋊C4C23×C311yescharacteristic
425C4×Dic3C23×C313yes—
426C4×Dic3C23×C313yes—
427C4×Dic3C23×C313yes—
428C4×Dic3C23×C313yes—
429C4×Dic3C23×C313yes—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—23no—
433C22×C32—23no—
434C22×C32—23no—
435C22×C32H(5,𝔽2)12yes—
436C22×C32C2511yescharacteristic
437C2×C3×D3—23no—
438C2×C3×D3—23no—
439C2×C3×D3—23no—
440C32×C4—21no—
441C32×C4—23no—
442C32×C4—23no—
443C32×C4—21no—
444C32×C4C2×#4116yes—
445C3×Dic3—21no—
446C3×Dic3—23no—
447C3×Dic3—23no—
448C3×Dic3—23no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic32−1+412yes—
452C2×#41—31no—
453C2×#41—36no—
454C2×#41C2×C3×D311yescharacteristic
455C22×Q8C2×C3×D311yescharacteristic
456C4⋊Q8—33no—
457C4⋊Q8—33no—
458C4⋊Q8—33no—
459#127—33no—
460#126—33no—
461#126—33no—
462#125—33no—
463#124—33no—
464#124—33no—
465#124—36no—
466#124C2×C3×D313yes—
467#123—33no—
468#123—33no—
469#123—36no—
470#123—36no—
471C22⋊Q8—33no—
472C22⋊Q8—36no—
473C22⋊Q8—31no—
474C22⋊Q8—36no—
475C22⋊Q8C2×C3×D313yes—
476#121—33no—
477#121—33no—
478#121—33no—
479#121—33no—
480#121C2×C3×D313yes—
481C4×Q8—31no—
482C4×Q8—33no—
483C4×Q8—31no—
484C4×Q8—33no—
485C4×Q8—31no—
486C4×Q8—33no—
487C4×Q8C2×C3×D311yescharacteristic
488C4×D4—33no—
489C4×D4—33no—
490C4×D4—33no—
491C4×D4—33no—
492C4×D4—33no—
493C4×D4—36no—
494C4×D4—33no—
495C4×D4C2×C3×D313yes—
496#117—33no—
497#117—33no—
498C2×C4⋊C4—33no—
499C2×C4⋊C4—33no—
500C2×C4⋊C4—33no—
501C2×C42—33no—
502C23×C3—21no—
503C23×C3—23no—
504C23×C3—33no—
505C23×C3C23×D313yes—
506C23×C3C23×D311yescharacteristic
507C23×C3C24×C313yes—
508C23×C3C24×C311yescharacteristic
509C22×D3C24×C313yes—
510C3×Q8—26no—
511C3×Q8—26no—
512C3×Q8—24no—
513C3×Q8—46no—
514C3×Q8—62no—
515C3×Q8—126no—
516C3×Q8#23714yescomplemented
517C3×Q8C3×#4114yescomplemented
518C3×D4—26no—
519C3×D4—26no—
520C3×D4—26no—
521C3×D4—26no—
522C3×D4—46no—
523C3×D4—46no—
524C3×D4—66no—
525C3×D4—66no—
526C3×D4—66no—
527C3×D4—126no—
528C2×C3×C4—26no—
529C2×C3×C4—26no—
530C2×C3×C4—26no—
531C2×C3×C4—26no—
532C2×C3×C4—23no—
533C2×C3×C4—21no—
534C2×C3×C4—23no—
535C2×C3×C4—23no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—33no—
541C2×C3×C4—33no—
542C2×C3×C4—33no—
543C2×C3×C4—31no—
544C2×C3×C4—46no—
545C2×C3×C4—46no—
546C2×C3×C4—62no—
547C2×C3×C4—66no—
548C2×C3×C4—66no—
549C2×C3×C4—126no—
550C2×C3×C4—126no—
551C2×C3×C4C23×D313yes—
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D313yes—
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D313yes—
556C2×C3×C4C24×C313yes—
557C2×C3×C4C24×C313yes—
558C2×C3×C4C24×C311yescharacteristic
559C2×C3×C4C24×C311yescharacteristic
560C2×C3×C4C24×C313yes—
561#67—26no—
562#67—26no—
563#67—46no—
564C2×Dic3—26no—
565C2×Dic3—22no—
566C2×Dic3—46no—
567C2×Dic3C24×C311yescharacteristic
568C2×Dic3C24×C311yescharacteristic
569C2×Dic3C24×C313yes—
570C2×Dic3C24×C313yes—
571C2×Dic3C24×C313yes—
572C2×Dic3C24×C311yescharacteristic
573C2×Dic3C24×C311yescharacteristic
574D12—26no—
575C4×D3—26no—
576C4×D3—46no—
577Dic6—22no—
578Dic6—46no—
579C2×C32—22no—
580C2×C32—43no—
581C2×C32C22×#4111yescharacteristic
582C2×C32C2×H(5,𝔽2)11yescharacteristic
583C2×C32C2×2−1+411yescharacteristic
584C3×D3—43no—
585#41—24no—
586#41—64no—
587#41—1212no—
588C2×Q8—24no—
589C2×Q8—31no—
590C2×Q8—36no—
591C2×Q8C22×C3×D313yes—
592C2×Q8C22×C3×D311yescharacteristic
593C2×D4—33no—
594C2×D4—33no—
595C2×D4—36no—
596C2×D4—33no—
597C2×D4C22×C3×D313yes—
598C2×D4C22×C3×D313yes—
599C22×C4—31no—
600C22×C4—33no—
601C22×C4—36no—
602C22×C4—33no—
603C22×C4—36no—
604C22×C4C22×C3×D313yes—
605C22×C4C22×C3×D313yes—
606C4⋊C4—33no—
607C4⋊C4—33no—
608C4⋊C4—33no—
609C4⋊C4—33no—
610C4⋊C4—33no—
611C4⋊C4—36no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—33no—
616C4⋊C4—33no—
617C4⋊C4—33no—
618C4⋊C4—33no—
619C4⋊C4C22×C3×D313yes—
620C4⋊C4C22×C3×D313yes—
621C22⋊C4—33no—
622C22⋊C4—33no—
623C22⋊C4—31no—
624C22⋊C4—33no—
625C22⋊C4—33no—
626C22⋊C4—33no—
627C22⋊C4—33no—
628C22⋊C4—36no—
629C22⋊C4—33no—
630C22⋊C4C22×C3×D316yes—
631C22⋊C4C22×C3×D311yescharacteristic
632C22⋊C4C22×C3×D313yes—
633C42—33no—
634C42—33no—
635C42—33no—
636C42—33no—
637C42—33no—
638C42C22×C3×D313yes—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—23no—
644C22×C3—23no—
645C22×C3—23no—
646C22×C3—23no—
647C22×C3—23no—
648C22×C3—23no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—43no—
654C22×C3—43no—
655C22×C3—43no—
656C22×C3—63no—
657C22×C3—63no—
658C22×C3—63no—
659C22×C3#100912yes—
660C22×C3C3×H(5,𝔽2)12yes—
661C22×C3C24×D311yescharacteristic
662C22×C3C25×C311yescharacteristic
663C2×D3—23no—
664C2×D3—23no—
665C2×D3—23no—
666C3×C4—21no—
667C3×C4—23no—
668C3×C4—23no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—23no—
672C3×C4—23no—
673C3×C4—21no—
674C3×C4—26no—
675C3×C4—32no—
676C3×C4—41no—
677C3×C4—43no—
678C3×C4—43no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—63no—
682C3×C4—63no—
683C3×C4—63no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4C2×#23716yes—
687C3×C4C2×C3×#4116yes—
688Dic3—21no—
689Dic3—23no—
690Dic3—23no—
691Dic3—23no—
692Dic3—21no—
693Dic3—21no—
694Dic3C3×2−1+412yes—
695C32#352211yescharacteristic, complemented, Sylow
696C23—33no—
697C23C23×C3×D313yes—
698C23C23×C3×D311yescharacteristic
699Q8—26no—
700Q8—62no—
701Q8—126no—
702Q8C3×#23714yescomplemented
703D4—26no—
704D4—26no—
705D4—66no—
706D4—66no—
707D4—66no—
708D4—126no—
709C2×C4—26no—
710C2×C4—26no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—33no—
715C2×C4—33no—
716C2×C4—33no—
717C2×C4—31no—
718C2×C4—62no—
719C2×C4—66no—
720C2×C4—66no—
721C2×C4—126no—
722C2×C4—126no—
723C2×C4C23×C3×D313yes—
724C2×C4C23×C3×D311yescharacteristic
725C2×C4C23×C3×D313yes—
726C2×C4C23×C3×D311yescharacteristic
727C2×C4C23×C3×D313yes—
728C2×C3—22no—
729C2×C3—22no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—42no—
734C2×C3—43no—
735C2×C3—43no—
736C2×C3—83no—
737C2×C3—123no—
738C2×C3C22×#23711yescharacteristic
739C2×C3C2×#100911yescharacteristic
740C2×C3D3×2−1+411yescharacteristic
741C2×C3C22×C3×#4111yescharacteristic
742C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
743C2×C3C2×C3×2−1+411yescharacteristic
744D3—43no—
745C22—21no—
746C22—21no—
747C22—23no—
748C22—23no—
749C22—23no—
750C22—63no—
751C22—63no—
752C22—63no—
753C22C3×#100912yes—
754C22C24×C3×D311yescharacteristic
755C4—21no—
756C4—23no—
757C4—23no—
758C4—21no—
759C4—32no—
760C4—61no—
761C4—63no—
762C4—63no—
763C4—63no—
764C4—61no—
765C4—61no—
766C4C2×C3×#23716yes—
767C3—21no—
768C3#8672211yescharacteristic, direct product factor
769C3C3×#352211yescharacteristic, complemented
770C2—22no—
771C2—43no—
772C2—123no—
773C2C22×C3×#23711yescharacteristic
774C2C2×C3×#100911yescharacteristic
775C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#548C2
socleC22×C32C25
hypercenterC3×#548D3
hypocenterC3C3×#3522
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#548

Complements

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

NH ≅ G/Ntype
1. C32×#548C2semidirect
2. C3×#5834C2semidirect
3. C3×#5827C2semidirect
4. C3×#5817C2semidirect
5. C2×C3×Q8×Dic3C2semidirect
6. C3×#5682C2semidirect
7. C3×#5681C2semidirect
8. C3×#5643C2semidirect
9. C3×#5635C2semidirect
10. C3×#5611C2semidirect
11. C3×#5596C2semidirect
12. C3×#5574C2semidirect
13. C3×Q8×Dic6C2semidirect
14. C3×#5555C2semidirect
15. C3×#5538C2semidirect
17. #86722C3direct (N × H)
74. C3×#548D3semidirect
75. C3×#548C2×C3semidirect
85. #5834C2×C3semidirect
86. #5827C2×C3semidirect
87. #5817C2×C3semidirect
88. C2×Q8×Dic3C2×C3semidirect
89. #5682C2×C3semidirect
90. #5681C2×C3semidirect
91. #5643C2×C3semidirect
92. #5635C2×C3semidirect
93. #5611C2×C3semidirect
94. #5596C2×C3semidirect
95. #5574C2×C3semidirect
96. Q8×Dic6C2×C3semidirect
97. #5555C2×C3semidirect
98. #5538C2×C3semidirect
265. C32×Q8#41semidirect
298. #548C3×D3semidirect
516. C3×Q8#237semidirect
517. C3×Q8C3×#41semidirect
695. C32#3522semidirect
702. Q8C3×#237semidirect
768. C3#86722direct (N × H)
769. C3C3×#3522semidirect

Maximal subgroups

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

subgroupindex
C32×#5482
C3×#58342
C3×#58272
C3×#58172
C2×C3×Q8×Dic32
C3×#56822
C3×#56812
C3×#56432
C3×#56352
C3×#56112
C3×#55962
C3×#55742
C3×Q8×Dic62
C3×#55552
C3×#55382
C3×#35223
#867223