Finite Group Databasebeta

← C3×#86724 #11909978

Subgroups — C3×#86724 #11909978

Order 1152.

2205 conjugacy classes of subgroups.

The subgroup lattice has 765 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
5C3×#5812C211yesmaximal, characteristic, complemented
6C3×#5681C213yesmaximal, complemented
7C3×#5680C213yesmaximal, complemented
8C3×#5643C213yesmaximal, complemented
9C3×#5642C213yesmaximal, complemented
10C3×#5619C213yesmaximal, complemented
11C3×#5616C213yesmaximal, complemented
12C3×C4×#239C211yesmaximal, characteristic, complemented
13C3×#5569C211yesmaximal, characteristic, complemented
14C3×#5565C213yesmaximal, complemented
15C3×#5557C213yesmaximal, complemented
16C3×#3524—31nomaximal
17#86724C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C32×#124C2213yes—
22C32×C22⋊Q8C2213yes—
23C32×#121C2213yes—
24C32×C4×Q8C2211yescharacteristic
25C32×C4×D4C2213yes—
26C3×#947C2213yes—
27C3×#946C2213yes—
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×Q8×Dic3C2213yes—
31C3×Q8×Dic3C2213yes—
32C3×Q8×Dic3C2211yescharacteristic
33C3×#940C2213yes—
34C3×#939C2216yes—
35C3×#938C2213yes—
36C3×#938C2213yes—
37C3×#936C2213yes—
38C3×D4×Dic3C2213yes—
39C3×D4×Dic3C2213yes—
40C3×#930C2213yes—
41C3×#930C2213yes—
42C3×C4×#67C2213yes—
43C3×C4×#67C2213yes—
44C3×#926C2213yes—
45C3×#926C2213yes—
46C3×#926C2213yes—
47C2×C3×C4⋊Dic3C2213yes—
48C3×#898C2216yes—
49C3×#897C2213yes—
50C3×#893C2213yes—
51C3×#892C2213yes—
52C3×#890C2213yes—
53C3×#890C2213yes—
54C3×#888C2213yes—
55C3×#886C2216yes—
56C3×#885C2216yes—
57C3×#883C2213yes—
58C3×#883C2213yes—
59C3×#883C2216yes—
60C3×#67⋊C4C2216yes—
61C3×#879C2211yescharacteristic
62C3×#879C2213yes—
63C3×#877C2216yes—
64C3×C4×D12C2213yes—
65C3×C42×D3C2213yes—
66C3×#870C2213yes—
67C3×C4×Dic6C2213yes—
68C3×#559—33no—
69C3×#557—31no—
70C3×#555—33no—
71C3×#553—33no—
72C3×#552—33no—
73C3×#550—31no—
74C3×#548—21no—
75C3×#548—31no—
76C3×#548D311yescharacteristic, complemented
77C3×#548C2×C311yescharacteristic, complemented
78C3×#542—33no—
79C3×#540—33no—
80C3×#529—33no—
81C3×#529—33no—
82C3×#520—31no—
83C3×#519—31no—
84C3×C4×#41—31no—
85#5834C2×C311yescharacteristic, complemented
86#5827C2×C311yescharacteristic, complemented
87#5817C2×C311yescharacteristic, complemented
88#5812C2×C311yescharacteristic, complemented
89#5681C2×C313yescomplemented
90#5680C2×C313yescomplemented
91#5643C2×C313yescomplemented
92#5642C2×C313yescomplemented
93#5619C2×C313yescomplemented
94#5616C2×C313yescomplemented
95C4×#239C2×C311yescharacteristic, complemented
96#5569C2×C311yescharacteristic, complemented
97#5565C2×C313yescomplemented
98#5557C2×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×#67C2316yes—
108C2×C3×#67C2313yes—
109C2×C3×#67C2313yes—
110C22×C3×Dic3C2316yes—
111C3×#239—24no—
112C2×C3×D12C2313yes—
113C2×C3×C4×D3C2313yes—
114C2×C3×C4×D3C2313yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×Dic6C2313yes—
117C32×C4⋊C4C2313yes—
118C32×C4⋊C4C2313yes—
119C32×C22⋊C4C2316yes—
120C32×C22⋊C4C2313yes—
121C32×C22⋊C4C2311yescharacteristic
122C32×C42C2313yes—
123C3×#217C2313yes—
124C3×#217C2313yes—
125C3×#217C2311yescharacteristic
126C3×#217C2311yescharacteristic
127C3×#217C2313yes—
128C3×#217C2313yes—
129C3×(C2×D3)⋊C4C2316yes—
130C3×(C2×D3)⋊C4C2313yes—
131C3×(C2×D3)⋊C4C2313yes—
132C3×(C2×D3)⋊C4C2316yes—
133C3×C4⋊Dic3C2313yes—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2313yes—
136C3×C4⋊Dic3C2313yes—
137C3×C4⋊Dic3C2313yes—
138C3×C4⋊Dic3C2313yes—
139C3×C4⋊Dic3C2313yes—
140C3×C4⋊Dic3C2313yes—
141C3×Dic3⋊C4C2313yes—
142C3×Dic3⋊C4C2316yes—
143C3×Dic3⋊C4C2313yes—
144C3×Dic3⋊C4C2311yescharacteristic
145C3×Dic3⋊C4C2311yescharacteristic
146C3×C4×Dic3C2313yes—
147C3×C4×Dic3C2316yes—
148C3×C4×Dic3C2311yescharacteristic
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2313yes—
152#3524—31noSylow
153C2×C3×#41—21no—
154C2×C3×#41—31no—
155C2×C3×#41C2×D311yescharacteristic
156C2×C3×#41C22×C311yescharacteristic
157C22×C3×Q8—21no—
158C22×C3×Q8C2×D311yescharacteristic
159C22×C3×Q8C22×C311yescharacteristic
160C2×#239C22×C311yescharacteristic
161C3×C4⋊Q8—33no—
162C3×#127—33no—
163C3×#126—36no—
164C3×#126—31no—
165C3×#126—33no—
166C3×#125—33no—
167C3×#125—33no—
168C3×#125—33no—
169C3×#124—23no—
170C3×#124—33no—
171C3×#124—33no—
172C3×#124—36no—
173C3×#124C2×D313yes—
174C3×#124C22×C313yes—
175C3×#123—33no—
176C3×#123—36no—
177C3×#123—36no—
178C3×#123—33no—
179C3×C22⋊Q8—23no—
180C3×C22⋊Q8—33no—
181C3×C22⋊Q8—33no—
182C3×C22⋊Q8C2×D313yes—
183C3×C22⋊Q8C22×C313yes—
184C3×#121—23no—
185C3×#121—33no—
186C3×#121—33no—
187C3×#121—36no—
188C3×#121—33no—
189C3×#121—33no—
190C3×#121C2×D313yes—
191C3×#121C22×C313yes—
192C3×C4×Q8—21no—
193C3×C4×Q8—33no—
194C3×C4×Q8—31no—
195C3×C4×Q8—33no—
196C3×C4×Q8—31no—
197C3×C4×Q8—31no—
198C3×C4×Q8—33no—
199C3×C4×Q8C2×D311yescharacteristic
200C3×C4×Q8C22×C311yescharacteristic
201C3×C4×D4—23no—
202C3×C4×D4—33no—
203C3×C4×D4—33no—
204C3×C4×D4—33no—
205C3×C4×D4—33no—
206C3×C4×D4—33no—
207C3×C4×D4—36no—
208C3×C4×D4—33no—
209C3×C4×D4C2×D313yes—
210C3×C4×D4C22×C313yes—
211C3×#117—33no—
212C3×#117—33no—
213C3×#117—33no—
214C3×#117—33no—
215C3×#117—36no—
216C2×C3×C4⋊C4—33no—
217C2×C3×C42—33no—
218#947C22×C313yes—
219#946C22×C313yes—
220Q8×Dic3C22×C313yes—
221Q8×Dic3C22×C313yes—
222Q8×Dic3C22×C311yescharacteristic
223Q8×Dic3C22×C311yescharacteristic
224Q8×Dic3C22×C311yescharacteristic
225#940C22×C313yes—
226#939C22×C316yes—
227#938C22×C313yes—
228#938C22×C313yes—
229#936C22×C313yes—
230D4×Dic3C22×C313yes—
231D4×Dic3C22×C313yes—
232#930C22×C313yes—
233#930C22×C313yes—
234C4×#67C22×C313yes—
235C4×#67C22×C313yes—
236#926C22×C313yes—
237#926C22×C313yes—
238#926C22×C313yes—
239C2×C4⋊Dic3C22×C313yes—
240#898C22×C316yes—
241#897C22×C313yes—
242#893C22×C313yes—
243#892C22×C313yes—
244#890C22×C313yes—
245#890C22×C313yes—
246#888C22×C313yes—
247#886C22×C316yes—
248#885C22×C316yes—
249#883C22×C316yes—
250#883C22×C313yes—
251#883C22×C313yes—
252#67⋊C4C22×C316yes—
253#879C22×C313yes—
254#879C22×C311yescharacteristic
255#877C22×C316yes—
256C4×D12C22×C313yes—
257C42×D3C22×C313yes—
258#870C22×C313yes—
259C4×Dic6C22×C313yes—
260C23×C32C2411yescharacteristic
261C23×C32C2413yes—
262C22×C3×D3C2413yes—
263C32×Q8—26no—
264C32×Q8#4114yes—
265C32×D4—26no—
266C32×D4—43no—
267C2×C32×C4—26no—
268C2×C32×C4—26no—
269C2×C32×C4C2413yes—
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2413yes—
272C2×C32×C4C2411yescharacteristic
273C2×C32×C4C2413yes—
274C3×#67—46no—
275C3×#67—43no—
276C3×#67—43no—
277C2×C3×Dic3—46no—
278C2×C3×Dic3C2411yescharacteristic
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2411yescharacteristic
281C2×C3×Dic3C2413yes—
282C2×C3×Dic3C2411yescharacteristic
283C2×C3×Dic3C2411yescharacteristic
284C2×C3×Dic3C2413yes—
285C3×D12—26no—
286C3×C4×D3—26no—
287C3×C4×D3—43no—
288C3×C4×D3—43no—
289C3×Dic6—43no—
290#559—33no—
291#557—31no—
292#555—33no—
293#553—33no—
294#552—33no—
295#550—31no—
296#548—31no—
297#548C3×D311yescharacteristic, complemented
298#542—33no—
299#540—33no—
300#529—33no—
301#529—33no—
302#520—31no—
303#519—31no—
304C4×#41—31no—
305C3×#41—24no—
306C3×#41—24no—
307C3×#41—44no—
308C3×#41—64no—
309C2×C3×Q8—24no—
310C2×C3×Q8—24no—
311C2×C3×Q8—21no—
312C2×C3×Q8—23no—
313C2×C3×Q8—33no—
314C2×C3×Q8—44no—
315C2×C3×Q8C22×D313yes—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C23×C313yes—
318C2×C3×Q8C23×C311yescharacteristic
319C2×C3×D4—23no—
320C2×C3×D4—23no—
321C2×C3×D4—33no—
322C2×C3×D4—36no—
323C2×C3×D4—33no—
324C2×C3×D4—33no—
325C2×C3×D4C22×D313yes—
326C2×C3×D4C22×D313yes—
327C2×C3×D4C23×C313yes—
328C2×C3×D4C23×C313yes—
329C22×C3×C4—23no—
330C22×C3×C4—23no—
331C22×C3×C4—36no—
332C22×C3×C4—33no—
333C22×C3×C4—33no—
334C22×C3×C4—33no—
335C22×C3×C4C22×D313yes—
336C22×C3×C4C22×D313yes—
337C22×C3×C4C23×C313yes—
338C22×C3×C4C23×C313yes—
339C2×#67C23×C316yes—
340C2×#67C23×C313yes—
341C2×#67C23×C313yes—
342C22×Dic3C23×C316yes—
343#239—24no—
344C2×D12C23×C313yes—
345C2×C4×D3C23×C313yes—
346C2×C4×D3C23×C313yes—
347C2×C4×D3C23×C313yes—
348C2×Dic6C23×C313yes—
349C3×C4⋊C4—23no—
350C3×C4⋊C4—23no—
351C3×C4⋊C4—33no—
352C3×C4⋊C4—36no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—33no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—33no—
357C3×C4⋊C4—33no—
358C3×C4⋊C4—33no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—33no—
362C3×C4⋊C4—33no—
363C3×C4⋊C4—33no—
364C3×C4⋊C4C22×D313yes—
365C3×C4⋊C4C22×D313yes—
366C3×C4⋊C4C23×C313yes—
367C3×C4⋊C4C23×C313yes—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—23no—
370C3×C22⋊C4—26no—
371C3×C22⋊C4—31no—
372C3×C22⋊C4—33no—
373C3×C22⋊C4—33no—
374C3×C22⋊C4—33no—
375C3×C22⋊C4—33no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—36no—
378C3×C22⋊C4—33no—
379C3×C22⋊C4—36no—
380C3×C22⋊C4—33no—
381C3×C22⋊C4C22×D316yes—
382C3×C22⋊C4C22×D313yes—
383C3×C22⋊C4C22×D311yescharacteristic
384C3×C22⋊C4C23×C316yes—
385C3×C22⋊C4C23×C313yes—
386C3×C22⋊C4C23×C311yescharacteristic
387C3×C42—23no—
388C3×C42—31no—
389C3×C42—33no—
390C3×C42—33no—
391C3×C42—36no—
392C3×C42—33no—
393C3×C42—33no—
394C3×C42C22×D313yes—
395C3×C42C23×C313yes—
396#217C23×C313yes—
397#217C23×C313yes—
398#217C23×C311yescharacteristic
399#217C23×C311yescharacteristic
400#217C23×C313yes—
401#217C23×C313yes—
402(C2×D3)⋊C4C23×C316yes—
403(C2×D3)⋊C4C23×C316yes—
404(C2×D3)⋊C4C23×C313yes—
405(C2×D3)⋊C4C23×C313yes—
406C4⋊Dic3C23×C313yes—
407C4⋊Dic3C23×C313yes—
408C4⋊Dic3C23×C313yes—
409C4⋊Dic3C23×C313yes—
410C4⋊Dic3C23×C313yes—
411C4⋊Dic3C23×C311yescharacteristic
412C4⋊Dic3C23×C313yes—
413C4⋊Dic3C23×C313yes—
414Dic3⋊C4C23×C311yescharacteristic
415Dic3⋊C4C23×C313yes—
416Dic3⋊C4C23×C316yes—
417Dic3⋊C4C23×C313yes—
418Dic3⋊C4C23×C311yescharacteristic
419C4×Dic3C23×C313yes—
420C4×Dic3C23×C313yes—
421C4×Dic3C23×C311yescharacteristic
422C4×Dic3C23×C313yes—
423C4×Dic3C23×C313yes—
424C4×Dic3C23×C316yes—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—23no—
428C22×C32—23no—
429C22×C32—21no—
430C22×C32—23no—
431C22×C32C2511yescharacteristic
432C2×C3×D3—23no—
433C2×C3×D3—23no—
434C2×C3×D3—23no—
435C32×C4—21no—
436C32×C4—23no—
437C32×C4—23no—
438C32×C4—21no—
439C32×C4C2×#4116yes—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—23no—
443C3×Dic3—21no—
444C3×Dic3—23no—
445C3×Dic3—23no—
446C3×Dic3—21no—
447C2×#41—31no—
448C2×#41C2×C3×D311yescharacteristic
449C22×Q8C2×C3×D311yescharacteristic
450C4⋊Q8—33no—
451#127—33no—
452#126—36no—
453#126—31no—
454#126—33no—
455#125—33no—
456#125—33no—
457#125—33no—
458#124—33no—
459#124—33no—
460#124—36no—
461#124C2×C3×D313yes—
462#123—36no—
463#123—33no—
464#123—33no—
465#123—36no—
466C22⋊Q8—33no—
467C22⋊Q8—33no—
468C22⋊Q8C2×C3×D313yes—
469#121—33no—
470#121—33no—
471#121—36no—
472#121—33no—
473#121—33no—
474#121C2×C3×D313yes—
475C4×Q8—31no—
476C4×Q8—33no—
477C4×Q8—31no—
478C4×Q8—33no—
479C4×Q8—31no—
480C4×Q8—33no—
481C4×Q8C2×C3×D311yescharacteristic
482C4×D4—33no—
483C4×D4—33no—
484C4×D4—33no—
485C4×D4—33no—
486C4×D4—33no—
487C4×D4—36no—
488C4×D4—33no—
489C4×D4C2×C3×D313yes—
490#117—33no—
491#117—33no—
492#117—33no—
493#117—33no—
494#117—36no—
495C2×C4⋊C4—33no—
496C2×C42—33no—
497C23×C3—21no—
498C23×C3—23no—
499C23×C3—33no—
500C23×C3C23×D311yescharacteristic
501C23×C3C23×D313yes—
502C23×C3C24×C311yescharacteristic
503C23×C3C24×C313yes—
504C22×D3C24×C313yes—
505C3×Q8—26no—
506C3×Q8—26no—
507C3×Q8—24no—
508C3×Q8—46no—
509C3×Q8—123no—
510C3×Q8#23714yes—
511C3×Q8C3×#4114yes—
512C3×D4—26no—
513C3×D4—26no—
514C3×D4—46no—
515C3×D4—43no—
516C3×D4—43no—
517C3×D4—46no—
518C3×D4—66no—
519C3×D4—126no—
520C3×D4—123no—
521C3×D4—123no—
522C2×C3×C4—26no—
523C2×C3×C4—26no—
524C2×C3×C4—26no—
525C2×C3×C4—26no—
526C2×C3×C4—23no—
527C2×C3×C4—21no—
528C2×C3×C4—23no—
529C2×C3×C4—23no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—33no—
534C2×C3×C4—31no—
535C2×C3×C4—33no—
536C2×C3×C4—31no—
537C2×C3×C4—33no—
538C2×C3×C4—46no—
539C2×C3×C4—46no—
540C2×C3×C4—66no—
541C2×C3×C4—123no—
542C2×C3×C4—123no—
543C2×C3×C4—126no—
544C2×C3×C4C23×D313yes—
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D313yes—
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D313yes—
549C2×C3×C4C24×C313yes—
550C2×C3×C4C24×C311yescharacteristic
551C2×C3×C4C24×C313yes—
552C2×C3×C4C24×C311yescharacteristic
553C2×C3×C4C24×C313yes—
554#67—46no—
555#67—43no—
556#67—43no—
557C2×Dic3—46no—
558C2×Dic3C24×C311yescharacteristic
559C2×Dic3C24×C313yes—
560C2×Dic3C24×C311yescharacteristic
561C2×Dic3C24×C313yes—
562C2×Dic3C24×C311yescharacteristic
563C2×Dic3C24×C311yescharacteristic
564C2×Dic3C24×C313yes—
565D12—26no—
566C4×D3—26no—
567C4×D3—43no—
568C4×D3—43no—
569Dic6—43no—
570C2×C32—41no—
571C2×C32—43no—
572C2×C32C22×#4111yescharacteristic
573C2×C32#58511yescharacteristic
574C2×C32#58511yescharacteristic
575C3×D3—43no—
576#41—24no—
577#41—64no—
578C2×Q8—24no—
579C2×Q8—33no—
580C2×Q8C22×C3×D313yes—
581C2×Q8C22×C3×D311yescharacteristic
582C2×D4—33no—
583C2×D4—36no—
584C2×D4—33no—
585C2×D4—33no—
586C2×D4C22×C3×D313yes—
587C2×D4C22×C3×D313yes—
588C22×C4—36no—
589C22×C4—33no—
590C22×C4—33no—
591C22×C4—33no—
592C22×C4C22×C3×D313yes—
593C22×C4C22×C3×D313yes—
594C4⋊C4—33no—
595C4⋊C4—33no—
596C4⋊C4—33no—
597C4⋊C4—31no—
598C4⋊C4—33no—
599C4⋊C4—33no—
600C4⋊C4—33no—
601C4⋊C4—33no—
602C4⋊C4—36no—
603C4⋊C4—31no—
604C4⋊C4—33no—
605C4⋊C4—31no—
606C4⋊C4—33no—
607C4⋊C4C22×C3×D313yes—
608C4⋊C4C22×C3×D313yes—
609C22⋊C4—31no—
610C22⋊C4—33no—
611C22⋊C4—33no—
612C22⋊C4—33no—
613C22⋊C4—33no—
614C22⋊C4—31no—
615C22⋊C4—36no—
616C22⋊C4—33no—
617C22⋊C4—36no—
618C22⋊C4—33no—
619C22⋊C4C22×C3×D316yes—
620C22⋊C4C22×C3×D313yes—
621C22⋊C4C22×C3×D311yescharacteristic
622C42—31no—
623C42—33no—
624C42—33no—
625C42—36no—
626C42—33no—
627C42—33no—
628C42C22×C3×D313yes—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—23no—
632C22×C3—21no—
633C22×C3—23no—
634C22×C3—23no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—23no—
638C22×C3—23no—
639C22×C3—21no—
640C22×C3—23no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—43no—
646C22×C3—43no—
647C22×C3—43no—
648C22×C3—63no—
649C22×C3—63no—
650C22×C3—63no—
651C22×C3C24×D311yescharacteristic
652C22×C3C25×C311yescharacteristic
653C2×D3—23no—
654C2×D3—23no—
655C2×D3—23no—
656C3×C4—21no—
657C3×C4—23no—
658C3×C4—23no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—23no—
662C3×C4—23no—
663C3×C4—21no—
664C3×C4—26no—
665C3×C4—41no—
666C3×C4—43no—
667C3×C4—43no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—63no—
672C3×C4—61no—
673C3×C4—63no—
674C3×C4—63no—
675C3×C4—61no—
676C3×C4C2×#23716yes—
677C3×C4C2×C3×#4116yes—
678Dic3—21no—
679Dic3—21no—
680Dic3—23no—
681Dic3—21no—
682Dic3—23no—
683Dic3—23no—
684Dic3—21no—
685C32#352411yescharacteristic, complemented, Sylow
686C23—33no—
687C23C23×C3×D311yescharacteristic
688C23C23×C3×D313yes—
689Q8—26no—
690Q8—123no—
691Q8C3×#23714yes—
692D4—26no—
693D4—43no—
694D4—66no—
695D4—126no—
696D4—123no—
697D4—123no—
698C2×C4—26no—
699C2×C4—26no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—33no—
703C2×C4—31no—
704C2×C4—33no—
705C2×C4—31no—
706C2×C4—33no—
707C2×C4—66no—
708C2×C4—123no—
709C2×C4—123no—
710C2×C4—126no—
711C2×C4C23×C3×D313yes—
712C2×C4C23×C3×D311yescharacteristic
713C2×C4C23×C3×D313yes—
714C2×C4C23×C3×D311yescharacteristic
715C2×C4C23×C3×D313yes—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—42no—
720C2×C3—41no—
721C2×C3—43no—
722C2×C3—41no—
723C2×C3—43no—
724C2×C3—83no—
725C2×C3—123no—
726C2×C3C22×#23711yescharacteristic
727C2×C3#596411yescharacteristic
728C2×C3#596811yescharacteristic
729C2×C3C22×C3×#4111yescharacteristic
730C2×C3C3×#58511yescharacteristic
731C2×C3C3×#58511yescharacteristic
732D3—43no—
733C22—21no—
734C22—23no—
735C22—21no—
736C22—23no—
737C22—23no—
738C22—21no—
739C22—63no—
740C22—63no—
741C22—63no—
742C22C24×C3×D311yescharacteristic
743C4—21no—
744C4—23no—
745C4—23no—
746C4—21no—
747C4—61no—
748C4—61no—
749C4—63no—
750C4—61no—
751C4—63no—
752C4—63no—
753C4—61no—
754C4C2×C3×#23716yes—
755C3—21no—
756C3#8672411yescharacteristic, direct product factor
757C3C3×#352411yescharacteristic, complemented
758C2—41no—
759C2—43no—
760C2—123no—
761C2C22×C3×#23711yescharacteristic
762C2C3×#596411yescharacteristic
763C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#548C2
socleC22×C32C25
hypercenterC3×#548D3
hypocenterC3C3×#3524
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. C3×#5812C2semidirect
6. C3×#5681C2semidirect
7. C3×#5680C2semidirect
8. C3×#5643C2semidirect
9. C3×#5642C2semidirect
10. C3×#5619C2semidirect
11. C3×#5616C2semidirect
12. C3×C4×#239C2semidirect
13. C3×#5569C2semidirect
14. C3×#5565C2semidirect
15. C3×#5557C2semidirect
17. #86724C3direct (N × H)
76. C3×#548D3semidirect
77. C3×#548C2×C3semidirect
85. #5834C2×C3semidirect
86. #5827C2×C3semidirect
87. #5817C2×C3semidirect
88. #5812C2×C3semidirect
89. #5681C2×C3semidirect
90. #5680C2×C3semidirect
91. #5643C2×C3semidirect
92. #5642C2×C3semidirect
93. #5619C2×C3semidirect
94. #5616C2×C3semidirect
95. C4×#239C2×C3semidirect
96. #5569C2×C3semidirect
97. #5565C2×C3semidirect
98. #5557C2×C3semidirect
297. #548C3×D3semidirect
685. C32#3524semidirect
756. C3#86724direct (N × H)
757. C3C3×#3524semidirect

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
C3×#58122
C3×#56812
C3×#56802
C3×#56432
C3×#56422
C3×#56192
C3×#56162
C3×C4×#2392
C3×#55692
C3×#55652
C3×#55572
C3×#35243
#867243