Finite Group Databasebeta

← C3×#86711 #11903851

Subgroups — C3×#86711 #11903851

Order 1152.

2369 conjugacy classes of subgroups.

The subgroup lattice has 781 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×Dic3×#41C211yesmaximal, characteristic, complemented
4C3×#5817C211yesmaximal, characteristic, complemented
5C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
6C3×#5681C213yesmaximal, complemented
7C3×#5680C213yesmaximal, complemented
8C3×#5641C213yesmaximal, complemented
9C3×#5624C213yesmaximal, complemented
10C3×#5618C213yesmaximal, complemented
11C3×#5596C213yesmaximal, complemented
12C3×C4×#239C211yesmaximal, characteristic, complemented
13C3×#5569C211yesmaximal, characteristic, complemented
14C3×#5565C213yesmaximal, complemented
15C3×C4×#237C213yesmaximal, complemented
16C3×#3480—31nomaximal
17#86711C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×#237C2213yes—
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×#939C2216yes—
36C3×#938C2213yes—
37C3×D4×Dic3C2213yes—
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×#898C2216yes—
49C3×#893C2213yes—
50C3×#892C2213yes—
51C3×#892C2213yes—
52C3×#890C2213yes—
53C3×#888C2213yes—
54C3×#887C2213yes—
55C3×#886C2216yes—
56C3×#885C2216yes—
57C3×#883C2216yes—
58C3×#67⋊C4C2213yes—
59C3×#67⋊C4C2213yes—
60C3×#67⋊C4C2216yes—
61C3×#879C2216yes—
62C3×#877C2211yescharacteristic
63C3×#877C2213yes—
64C3×C4×D12C2213yes—
65C3×C42×D3C2213yes—
66C3×#870C2213yes—
67C3×C4×Dic6C2213yes—
68C3×#559—33no—
69C3×#557—31no—
70C3×#556—33no—
71C3×#553—33no—
72C3×#553—33no—
73C3×#550—31no—
74C3×#548—21no—
75C3×#548—31no—
76C3×#548D311yescharacteristic, complemented
77C3×#548C2×C311yescharacteristic, complemented
78C3×#532—33no—
79C3×#529—33no—
80C3×#529—33no—
81C3×C4×#41—31no—
82C3×C4×#41—31no—
83C3×C4×#41—33no—
84C2×C3×C4×Q8—31no—
85#5834C2×C311yescharacteristic, complemented
86Dic3×#41C2×C311yescharacteristic, complemented
87#5817C2×C311yescharacteristic, complemented
88C2×Q8×Dic3C2×C311yescharacteristic, complemented
89#5681C2×C313yescomplemented
90#5680C2×C313yescomplemented
91#5641C2×C313yescomplemented
92#5624C2×C313yescomplemented
93#5618C2×C313yescomplemented
94#5596C2×C313yescomplemented
95C4×#239C2×C311yescharacteristic, complemented
96#5569C2×C311yescharacteristic, complemented
97#5565C2×C313yescomplemented
98C4×#237C2×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×Dic3C2313yes—
111C22×C3×Dic3C2313yes—
112C22×C3×Dic3C2313yes—
113C22×C3×Dic3C2311yescharacteristic
114C3×#239—24no—
115C3×#237—212no—
116C2×C3×D12C2313yes—
117C2×C3×C4×D3C2313yes—
118C2×C3×C4×D3C2313yes—
119C2×C3×C4×D3C2313yes—
120C2×C3×Dic6C2313yes—
121C32×C4⋊C4C2313yes—
122C32×C4⋊C4C2313yes—
123C32×C22⋊C4C2311yescharacteristic
124C32×C22⋊C4C2313yes—
125C32×C22⋊C4C2316yes—
126C32×C42C2313yes—
127C3×#217C2313yes—
128C3×#217C2311yescharacteristic
129C3×#217C2316yes—
130C3×(C2×D3)⋊C4C2316yes—
131C3×(C2×D3)⋊C4C2313yes—
132C3×(C2×D3)⋊C4C2313yes—
133C3×(C2×D3)⋊C4C2316yes—
134C3×C4⋊Dic3C2316yes—
135C3×C4⋊Dic3C2313yes—
136C3×C4⋊Dic3C2313yes—
137C3×C4⋊Dic3C2313yes—
138C3×C4⋊Dic3C2313yes—
139C3×Dic3⋊C4C2313yes—
140C3×Dic3⋊C4C2311yescharacteristic
141C3×Dic3⋊C4C2313yes—
142C3×Dic3⋊C4C2311yescharacteristic
143C3×Dic3⋊C4C2316yes—
144C3×C4×Dic3C2311yescharacteristic
145C3×C4×Dic3C2313yes—
146C3×C4×Dic3C2311yescharacteristic
147C3×C4×Dic3C2313yes—
148C3×C4×Dic3C2313yes—
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2313yes—
152C3×C4×Dic3C2313yes—
153#3480—31noSylow
154C2×C3×#41—21no—
155C2×C3×#41—31no—
156C2×C3×#41—33no—
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×C313yes—
164C3×C4⋊Q8—33no—
165C3×#127—33no—
166C3×#126—36no—
167C3×#126—36no—
168C3×#125—33no—
169C3×#125—33no—
170C3×#124—23no—
171C3×#124—33no—
172C3×#124—36no—
173C3×#124C2×D313yes—
174C3×#124C22×C313yes—
175C3×#123—36no—
176C3×#123—36no—
177C3×C22⋊Q8—23no—
178C3×C22⋊Q8—33no—
179C3×C22⋊Q8C2×D313yes—
180C3×C22⋊Q8C22×C313yes—
181C3×#121—23no—
182C3×#121—33no—
183C3×#121—36no—
184C3×#121—33no—
185C3×#121—33no—
186C3×#121C2×D313yes—
187C3×#121C22×C313yes—
188C3×C4×Q8—21no—
189C3×C4×Q8—33no—
190C3×C4×Q8—31no—
191C3×C4×Q8—33no—
192C3×C4×Q8—31no—
193C3×C4×Q8—31no—
194C3×C4×Q8—33no—
195C3×C4×Q8—33no—
196C3×C4×Q8C2×D311yescharacteristic
197C3×C4×Q8C22×C311yescharacteristic
198C3×C4×D4—23no—
199C3×C4×D4—33no—
200C3×C4×D4—33no—
201C3×C4×D4—33no—
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—31no—
215C3×#117—33no—
216C2×C3×C4⋊C4—33no—
217C2×C3×C42—33no—
218C2×C3×C42—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×C316yes—
229#938C22×C313yes—
230D4×Dic3C22×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×C316yes—
242#893C22×C313yes—
243#892C22×C313yes—
244#892C22×C313yes—
245#890C22×C313yes—
246#888C22×C313yes—
247#887C22×C313yes—
248#886C22×C316yes—
249#885C22×C316yes—
250#883C22×C316yes—
251#67⋊C4C22×C316yes—
252#67⋊C4C22×C313yes—
253#67⋊C4C22×C313yes—
254#879C22×C316yes—
255#877C22×C313yes—
256#877C22×C311yescharacteristic
257C4×D12C22×C313yes—
258C42×D3C22×C313yes—
259#870C22×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×C4C2411yescharacteristic
271C2×C32×C4C2413yes—
272C2×C32×C4C2411yescharacteristic
273C2×C32×C4C2413yes—
274C2×C32×C4C2413yes—
275C3×#67—26no—
276C3×#67—26no—
277C3×#67—46no—
278C2×C3×Dic3—26no—
279C2×C3×Dic3—43no—
280C2×C3×Dic3—43no—
281C2×C3×Dic3#4114yescomplemented
282C2×C3×Dic3C2411yescharacteristic
283C2×C3×Dic3C2411yescharacteristic
284C2×C3×Dic3C2413yes—
285C2×C3×Dic3C2413yes—
286C2×C3×Dic3C2413yes—
287C2×C3×Dic3C2411yescharacteristic
288C2×C3×Dic3C2411yescharacteristic
289C3×D12—26no—
290C3×C4×D3—26no—
291C3×C4×D3—26no—
292C3×C4×D3—43no—
293C3×Dic6—26no—
294#559—33no—
295#557—31no—
296#556—33no—
297#553—33no—
298#553—33no—
299#550—31no—
300#548—31no—
301#548C3×D311yescharacteristic, complemented
302#532—33no—
303#529—33no—
304#529—33no—
305C4×#41—31no—
306C4×#41—31no—
307C4×#41—33no—
308C2×C4×Q8—31no—
309C3×#41—24no—
310C3×#41—24no—
311C3×#41—44no—
312C3×#41—612no—
313C3×#41—64no—
314C2×C3×Q8—24no—
315C2×C3×Q8—24no—
316C2×C3×Q8—21no—
317C2×C3×Q8—23no—
318C2×C3×Q8—33no—
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—33no—
339C22×C3×C4—33no—
340C22×C3×C4—33no—
341C22×C3×C4—33no—
342C22×C3×C4—33no—
343C22×C3×C4C22×D313yes—
344C22×C3×C4C22×D313yes—
345C22×C3×C4C23×C313yes—
346C22×C3×C4C23×C313yes—
347C2×#67C23×C313yes—
348C2×#67C23×C313yes—
349C2×#67C23×C316yes—
350C22×Dic3C23×C313yes—
351C22×Dic3C23×C313yes—
352C22×Dic3C23×C313yes—
353C22×Dic3C23×C311yescharacteristic
354#239—24no—
355#237—212no—
356C2×D12C23×C313yes—
357C2×C4×D3C23×C313yes—
358C2×C4×D3C23×C313yes—
359C2×C4×D3C23×C313yes—
360C2×Dic6C23×C313yes—
361C3×C4⋊C4—23no—
362C3×C4⋊C4—23no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—33no—
366C3×C4⋊C4—33no—
367C3×C4⋊C4—36no—
368C3×C4⋊C4—33no—
369C3×C4⋊C4—33no—
370C3×C4⋊C4—36no—
371C3×C4⋊C4—33no—
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—31no—
381C3×C22⋊C4—33no—
382C3×C22⋊C4—36no—
383C3×C22⋊C4—33no—
384C3×C22⋊C4—36no—
385C3×C22⋊C4—33no—
386C3×C22⋊C4—36no—
387C3×C22⋊C4C22×D311yescharacteristic
388C3×C22⋊C4C22×D313yes—
389C3×C22⋊C4C22×D316yes—
390C3×C22⋊C4C23×C311yescharacteristic
391C3×C22⋊C4C23×C313yes—
392C3×C22⋊C4C23×C316yes—
393C3×C42—23no—
394C3×C42—31no—
395C3×C42—31no—
396C3×C42—33no—
397C3×C42—33no—
398C3×C42—33no—
399C3×C42—33no—
400C3×C42—33no—
401C3×C42—33no—
402C3×C42—33no—
403C3×C42C22×D313yes—
404C3×C42C23×C313yes—
405#217C23×C313yes—
406#217C23×C311yescharacteristic
407#217C23×C316yes—
408(C2×D3)⋊C4C23×C316yes—
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—
417Dic3⋊C4C23×C311yescharacteristic
418Dic3⋊C4C23×C313yes—
419Dic3⋊C4C23×C316yes—
420Dic3⋊C4C23×C313yes—
421Dic3⋊C4C23×C311yescharacteristic
422C4×Dic3C23×C313yes—
423C4×Dic3C23×C313yes—
424C4×Dic3C23×C311yescharacteristic
425C4×Dic3C23×C313yes—
426C4×Dic3C23×C313yes—
427C4×Dic3C23×C313yes—
428C4×Dic3C23×C311yescharacteristic
429C4×Dic3C23×C313yes—
430C4×Dic3C23×C313yes—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—23no—
434C22×C32—23no—
435C22×C32—23no—
436C22×C32C2×#4112yes—
437C22×C32C2511yescharacteristic
438C2×C3×D3—23no—
439C2×C3×D3—23no—
440C2×C3×D3—23no—
441C32×C4—23no—
442C32×C4—21no—
443C32×C4—23no—
444C32×C4—21no—
445C32×C4C2×#4116yes—
446C3×Dic3—23no—
447C3×Dic3—21no—
448C3×Dic3—23no—
449C3×Dic3—21no—
450C3×Dic3—23no—
451C3×Dic3C2×#4112yes—
452C3×Dic3C2×#4112yes—
453C2×#41—31no—
454C2×#41—33no—
455C2×#41C2×C3×D311yescharacteristic
456C22×Q8C2×C3×D311yescharacteristic
457C4⋊Q8—33no—
458#127—33no—
459#126—36no—
460#126—36no—
461#125—33no—
462#125—33no—
463#124—33no—
464#124—36no—
465#124C2×C3×D313yes—
466#123—36no—
467#123—36no—
468C22⋊Q8—33no—
469C22⋊Q8C2×C3×D313yes—
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×Q8—33no—
482C4×Q8C2×C3×D311yescharacteristic
483C4×D4—33no—
484C4×D4—33no—
485C4×D4—33no—
486C4×D4—33no—
487C4×D4—33no—
488C4×D4—33no—
489C4×D4—33no—
490C4×D4—33no—
491C4×D4—36no—
492C4×D4—33no—
493C4×D4C2×C3×D313yes—
494#117—33no—
495#117—33no—
496#117—33no—
497#117—31no—
498#117—33no—
499C2×C4⋊C4—33no—
500C2×C42—33no—
501C2×C42—33no—
502C2×C42—33no—
503C23×C3—21no—
504C23×C3—23no—
505C23×C3—33no—
506C23×C3C23×D313yes—
507C23×C3C23×D311yescharacteristic
508C23×C3C24×C313yes—
509C23×C3C24×C311yescharacteristic
510C22×D3C24×C313yes—
511C3×Q8—26no—
512C3×Q8—26no—
513C3×Q8—24no—
514C3×Q8—46no—
515C3×Q8—66no—
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—34no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—33no—
543C2×C3×C4—33no—
544C2×C3×C4—33no—
545C2×C3×C4—46no—
546C2×C3×C4—46no—
547C2×C3×C4—66no—
548C2×C3×C4—66no—
549C2×C3×C4—66no—
550C2×C3×C4—123no—
551C2×C3×C4—123no—
552C2×C3×C4—123no—
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D313yes—
555C2×C3×C4C23×D311yescharacteristic
556C2×C3×C4C23×D313yes—
557C2×C3×C4C23×D313yes—
558C2×C3×C4C24×C311yescharacteristic
559C2×C3×C4C24×C313yes—
560C2×C3×C4C24×C311yescharacteristic
561C2×C3×C4C24×C313yes—
562C2×C3×C4C24×C313yes—
563#67—26no—
564#67—26no—
565#67—46no—
566C2×Dic3—26no—
567C2×Dic3—43no—
568C2×Dic3—43no—
569C2×Dic3C3×#4114yescomplemented
570C2×Dic3C24×C311yescharacteristic
571C2×Dic3C24×C311yescharacteristic
572C2×Dic3C24×C313yes—
573C2×Dic3C24×C313yes—
574C2×Dic3C24×C313yes—
575C2×Dic3C24×C311yescharacteristic
576C2×Dic3C24×C311yescharacteristic
577D12—26no—
578C4×D3—26no—
579C4×D3—26no—
580C4×D3—43no—
581Dic6—26no—
582C2×C32—22no—
583C2×C32—43no—
584C2×C32C22×#4111yescharacteristic
585C2×C32C22×#4111yescharacteristic
586C2×C32#58511yescharacteristic
587C3×D3—43no—
588#41—24no—
589#41—612no—
590#41—64no—
591C2×Q8—24no—
592C2×Q8—33no—
593C2×Q8C22×C3×D313yes—
594C2×Q8C22×C3×D311yescharacteristic
595C2×D4—33no—
596C2×D4—33no—
597C2×D4—36no—
598C2×D4—33no—
599C2×D4C22×C3×D313yes—
600C2×D4C22×C3×D313yes—
601C22×C4—31no—
602C22×C4—33no—
603C22×C4—33no—
604C22×C4—33no—
605C22×C4—33no—
606C22×C4—33no—
607C22×C4—33no—
608C22×C4C22×C3×D313yes—
609C22×C4C22×C3×D313yes—
610C4⋊C4—33no—
611C4⋊C4—33no—
612C4⋊C4—36no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—33no—
616C4⋊C4—33no—
617C4⋊C4—33no—
618C4⋊C4—33no—
619C4⋊C4—36no—
620C4⋊C4C22×C3×D313yes—
621C4⋊C4C22×C3×D313yes—
622C22⋊C4—31no—
623C22⋊C4—33no—
624C22⋊C4—36no—
625C22⋊C4—33no—
626C22⋊C4—36no—
627C22⋊C4—33no—
628C22⋊C4—36no—
629C22⋊C4C22×C3×D311yescharacteristic
630C22⋊C4C22×C3×D313yes—
631C22⋊C4C22×C3×D316yes—
632C42—31no—
633C42—31no—
634C42—33no—
635C42—33no—
636C42—33no—
637C42—33no—
638C42—33no—
639C42—33no—
640C42—33no—
641C42C22×C3×D313yes—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—23no—
647C22×C3—23no—
648C22×C3—23no—
649C22×C3—23no—
650C22×C3—23no—
651C22×C3—23no—
652C22×C3—22no—
653C22×C3—21no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—43no—
657C22×C3—43no—
658C22×C3—43no—
659C22×C3—63no—
660C22×C3—63no—
661C22×C3—63no—
662C22×C3D3×#4112yes—
663C22×C3C2×C3×#4112yes—
664C22×C3C24×D311yescharacteristic
665C22×C3C25×C311yescharacteristic
666C2×D3—23no—
667C2×D3—23no—
668C2×D3—23no—
669C3×C4—21no—
670C3×C4—23no—
671C3×C4—23no—
672C3×C4—21no—
673C3×C4—23no—
674C3×C4—21no—
675C3×C4—23no—
676C3×C4—21no—
677C3×C4—26no—
678C3×C4—32no—
679C3×C4—32no—
680C3×C4—41no—
681C3×C4—43no—
682C3×C4—43no—
683C3×C4—41no—
684C3×C4—61no—
685C3×C4—63no—
686C3×C4—63no—
687C3×C4—61no—
688C3×C4—63no—
689C3×C4C2×#23716yes—
690C3×C4C2×C3×#4116yes—
691Dic3—23no—
692Dic3—21no—
693Dic3—23no—
694Dic3—21no—
695Dic3—23no—
696Dic3C2×C3×#4112yes—
697Dic3C2×C3×#4112yes—
698C32#348011yescharacteristic, complemented, Sylow
699C23—33no—
700C23C23×C3×D313yes—
701C23C23×C3×D311yescharacteristic
702Q8—26no—
703Q8—66no—
704Q8C3×#23714yescomplemented
705D4—26no—
706D4—26no—
707D4—66no—
708D4—66no—
709D4—66no—
710D4—126no—
711C2×C4—26no—
712C2×C4—26no—
713C2×C4—34no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—33no—
719C2×C4—33no—
720C2×C4—33no—
721C2×C4—66no—
722C2×C4—66no—
723C2×C4—66no—
724C2×C4—123no—
725C2×C4—123no—
726C2×C4—123no—
727C2×C4C23×C3×D311yescharacteristic
728C2×C4C23×C3×D313yes—
729C2×C4C23×C3×D311yescharacteristic
730C2×C4C23×C3×D313yes—
731C2×C4C23×C3×D313yes—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—43no—
739C2×C3—43no—
740C2×C3—83no—
741C2×C3—123no—
742C2×C3C22×#23711yescharacteristic
743C2×C3C2×D3×#4111yescharacteristic
744C2×C3#596811yescharacteristic
745C2×C3C22×C3×#4111yescharacteristic
746C2×C3C22×C3×#4111yescharacteristic
747C2×C3C3×#58511yescharacteristic
748D3—43no—
749C22—21no—
750C22—21no—
751C22—23no—
752C22—23no—
753C22—23no—
754C22—63no—
755C22—63no—
756C22—63no—
757C22C3×D3×#4112yes—
758C22C24×C3×D311yescharacteristic
759C4—21no—
760C4—23no—
761C4—23no—
762C4—21no—
763C4—32no—
764C4—32no—
765C4—61no—
766C4—63no—
767C4—63no—
768C4—61no—
769C4—63no—
770C4C2×C3×#23716yes—
771C3—21no—
772C3#8671111yescharacteristic, direct product factor
773C3C3×#348011yescharacteristic, complemented
774C2—22no—
775C2—43no—
776C2—123no—
777C2C22×C3×#23711yescharacteristic
778C2C2×C3×D3×#4111yescharacteristic
779C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#548C2
socleC22×C32C25
hypercenterC3×#548D3
hypocenterC3C3×#3480
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×Dic3×#41C2semidirect
4. C3×#5817C2semidirect
5. C2×C3×Q8×Dic3C2semidirect
6. C3×#5681C2semidirect
7. C3×#5680C2semidirect
8. C3×#5641C2semidirect
9. C3×#5624C2semidirect
10. C3×#5618C2semidirect
11. C3×#5596C2semidirect
12. C3×C4×#239C2semidirect
13. C3×#5569C2semidirect
14. C3×#5565C2semidirect
15. C3×C4×#237C2semidirect
17. #86711C3direct (N × H)
76. C3×#548D3semidirect
77. C3×#548C2×C3semidirect
85. #5834C2×C3semidirect
86. Dic3×#41C2×C3semidirect
87. #5817C2×C3semidirect
88. C2×Q8×Dic3C2×C3semidirect
89. #5681C2×C3semidirect
90. #5680C2×C3semidirect
91. #5641C2×C3semidirect
92. #5624C2×C3semidirect
93. #5618C2×C3semidirect
94. #5596C2×C3semidirect
95. C4×#239C2×C3semidirect
96. #5569C2×C3semidirect
97. #5565C2×C3semidirect
98. C4×#237C2×C3semidirect
265. C32×Q8#41semidirect
281. C2×C3×Dic3#41semidirect
301. #548C3×D3semidirect
516. C3×Q8#237semidirect
517. C3×Q8C3×#41semidirect
569. C2×Dic3C3×#41semidirect
698. C32#3480semidirect
704. Q8C3×#237semidirect
772. C3#86711direct (N × H)
773. C3C3×#3480semidirect

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×Dic3×#412
C3×#58172
C2×C3×Q8×Dic32
C3×#56812
C3×#56802
C3×#56412
C3×#56242
C3×#56182
C3×#55962
C3×C4×#2392
C3×#55692
C3×#55652
C3×C4×#2372
C3×#34803
#867113