Finite Group Databasebeta

← C3×#86777 #11909966

Subgroups — C3×#86777 #11909966

Order 1152.

2216 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#550C211yesmaximal, characteristic, complemented
2C3×#5831C211yesmaximal, characteristic, complemented
3C3×#5831C211yesmaximal, characteristic, complemented
4C3×#5827C211yesmaximal, characteristic, complemented
5C3×Dic3×#41C211yesmaximal, characteristic, complemented
6C3×#5719C213yesmaximal, complemented
7C3×#5713C213yesmaximal, complemented
8C3×#5618C213yesmaximal, complemented
9C3×#5616C213yesmaximal, complemented
10C3×#5603C213yesmaximal, complemented
11C3×#5600C213yesmaximal, complemented
12C3×#5572C211yesmaximal, characteristic, complemented
13C3×#5569C211yesmaximal, characteristic, complemented
14C3×#5541C213yesmaximal, complemented
15C3×#5538C213yesmaximal, complemented
16C3×#3524—31nomaximal
17#86777C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×#41C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C32×#127C2213yes—
22C32×#121C2213yes—
23C32×#121C2213yes—
24C32×C4×Q8C2211yescharacteristic
25C32×C4×D4C2213yes—
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×#939C2213yes—
30C3×#939C2216yes—
31C3×#938C2213yes—
32C3×#938C2213yes—
33C3×#936C2213yes—
34C3×#936C2213yes—
35C3×#936C2216yes—
36C3×#935C2213yes—
37C3×#935C2216yes—
38C3×#935C2216yes—
39C3×D4×Dic3C2213yes—
40C3×D4×Dic3C2213yes—
41C3×D4×Dic3C2213yes—
42C3×D4×Dic3C2213yes—
43C3×D4×Dic3C2216yes—
44C3×C4×#67C2213yes—
45C3×C4×#67C2213yes—
46C3×#926C2213yes—
47C3×#926C2213yes—
48C2×C3×C4⋊Dic3C2213yes—
49C3×#924C2213yes—
50C3×#924C2213yes—
51C2×C3×C4×Dic3C2213yes—
52C3×#898C2211yescharacteristic
53C3×#892C2213yes—
54C3×#890C2213yes—
55C3×#889C2213yes—
56C3×#888C2213yes—
57C3×#887C2213yes—
58C3×#886C2213yes—
59C3×#885C2213yes—
60C3×#879C2213yes—
61C3×#879C2216yes—
62C3×#878C2213yes—
63C3×#877C2216yes—
64C3×#872C2213yes—
65C3×#870C2213yes—
66C3×C4×Dic6C2213yes—
67C3×C4×Dic6C2213yes—
68C3×#559—33no—
69C3×#557—31no—
70C3×#555—33no—
71C3×#553—33no—
72C3×#552—33no—
73C3×#550—21no—
74C3×#550D311yescharacteristic, complemented
75C3×#550C2×C311yescharacteristic, complemented
76C3×#548—31no—
77C3×#548—31no—
78C3×#542—33no—
79C3×#540—33no—
80C3×#529—33no—
81C3×#529—33no—
82C3×#520—31no—
83C3×#519—31no—
84C3×C4×#41—31no—
85#5831C2×C311yescharacteristic, complemented
86#5831C2×C311yescharacteristic, complemented
87#5827C2×C311yescharacteristic, complemented
88Dic3×#41C2×C311yescharacteristic, complemented
89#5719C2×C313yescomplemented
90#5713C2×C313yescomplemented
91#5618C2×C313yescomplemented
92#5616C2×C313yescomplemented
93#5603C2×C313yescomplemented
94#5600C2×C313yescomplemented
95#5572C2×C311yescharacteristic, complemented
96#5569C2×C311yescharacteristic, complemented
97#5541C2×C313yescomplemented
98#5538C2×C313yescomplemented
99C32×#41—24no—
100C32×#41—24no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4C2313yes—
103C2×C32×D4C2313yes—
104C2×C32×D4C2316yes—
105C2×C32×D4C2313yes—
106C22×C32×C4C2313yes—
107C22×C32×C4C2313yes—
108C2×C3×#67C2313yes—
109C2×C3×#67C2313yes—
110C22×C3×Dic3C2316yes—
111C22×C3×Dic3C2313yes—
112C22×C3×Dic3C2313yes—
113C3×D3×Q8—24no—
114C2×C3×C4×D3C2313yes—
115C2×C3×Dic6C2313yes—
116C2×C3×Dic6C2313yes—
117C32×C4⋊C4C2313yes—
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4C2313yes—
120C32×C22⋊C4C2313yes—
121C32×C42C2313yes—
122C3×#217C2316yes—
123C3×#217C2313yes—
124C3×#217C2316yes—
125C3×#217C2313yes—
126C3×#217C2316yes—
127C3×#217C2313yes—
128C3×#217C2313yes—
129C3×(C2×D3)⋊C4C2311yescharacteristic
130C3×(C2×D3)⋊C4C2313yes—
131C3×(C2×D3)⋊C4C2311yescharacteristic
132C3×(C2×D3)⋊C4C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2313yes—
135C3×C4⋊Dic3C2313yes—
136C3×C4⋊Dic3C2313yes—
137C3×C4⋊Dic3C2313yes—
138C3×C4⋊Dic3C2313yes—
139C3×Dic3⋊C4C2313yes—
140C3×Dic3⋊C4C2316yes—
141C3×Dic3⋊C4C2313yes—
142C3×Dic3⋊C4C2313yes—
143C3×Dic3⋊C4C2313yes—
144C3×Dic3⋊C4C2313yes—
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—21no—
155C2×C3×#41C2×D311yescharacteristic
156C2×C3×#41C2×D311yescharacteristic
157C2×C3×#41C22×C311yescharacteristic
158C2×C3×#41C22×C311yescharacteristic
159C22×C3×Q8—31no—
160C2×D3×Q8C22×C311yescharacteristic
161C3×C4⋊Q8—33no—
162C3×#127—23no—
163C3×#127C2×D313yes—
164C3×#127C22×C313yes—
165C3×#126—31no—
166C3×#126—33no—
167C3×#126—36no—
168C3×#125—33no—
169C3×#125—33no—
170C3×#125—33no—
171C3×#124—33no—
172C3×#124—33no—
173C3×#124—36no—
174C3×#124—33no—
175C3×#123—33no—
176C3×#123—36no—
177C3×#123—36no—
178C3×#123—33no—
179C3×C22⋊Q8—33no—
180C3×C22⋊Q8—33no—
181C3×C22⋊Q8—33no—
182C3×#121—23no—
183C3×#121—23no—
184C3×#121—33no—
185C3×#121—33no—
186C3×#121—33no—
187C3×#121—36no—
188C3×#121C2×D313yes—
189C3×#121C2×D313yes—
190C3×#121C22×C313yes—
191C3×#121C22×C313yes—
192C3×C4×Q8—21no—
193C3×C4×Q8—31no—
194C3×C4×Q8—31no—
195C3×C4×Q8—31no—
196C3×C4×Q8—33no—
197C3×C4×Q8—33no—
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—36no—
205C3×C4×D4—33no—
206C3×C4×D4—33no—
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—
218Q8×Dic3C22×C311yescharacteristic
219Q8×Dic3C22×C311yescharacteristic
220Q8×Dic3C22×C311yescharacteristic
221#939C22×C313yes—
222#939C22×C316yes—
223#938C22×C313yes—
224#938C22×C313yes—
225#936C22×C313yes—
226#936C22×C313yes—
227#936C22×C316yes—
228#935C22×C313yes—
229#935C22×C316yes—
230#935C22×C316yes—
231D4×Dic3C22×C313yes—
232D4×Dic3C22×C313yes—
233D4×Dic3C22×C316yes—
234D4×Dic3C22×C313yes—
235D4×Dic3C22×C313yes—
236C4×#67C22×C313yes—
237C4×#67C22×C313yes—
238#926C22×C313yes—
239#926C22×C313yes—
240C2×C4⋊Dic3C22×C313yes—
241#924C22×C313yes—
242#924C22×C313yes—
243C2×C4×Dic3C22×C313yes—
244#898C22×C311yescharacteristic
245#892C22×C313yes—
246#890C22×C313yes—
247#889C22×C313yes—
248#888C22×C313yes—
249#887C22×C313yes—
250#886C22×C313yes—
251#885C22×C313yes—
252#879C22×C313yes—
253#879C22×C316yes—
254#878C22×C313yes—
255#877C22×C316yes—
256#872C22×C313yes—
257#870C22×C313yes—
258C4×Dic6C22×C313yes—
259C4×Dic6C22×C313yes—
260C23×C32C2413yes—
261C23×C32C2413yes—
262C22×C3×D3C2411yescharacteristic
263C32×Q8#4114yes—
264C32×D4—26no—
265C32×D4—26no—
266C32×D4—43no—
267C32×D4—46no—
268C2×C32×C4—26no—
269C2×C32×C4—26no—
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2413yes—
272C2×C32×C4C2411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C2×C32×C4C2413yes—
275C3×#67—43no—
276C3×#67—43no—
277C2×C3×Dic3—43no—
278C2×C3×Dic3—43no—
279C2×C3×Dic3—46no—
280C2×C3×Dic3C2411yescharacteristic
281C2×C3×Dic3C2413yes—
282C2×C3×Dic3C2411yescharacteristic
283C2×C3×Dic3C2411yescharacteristic
284C2×C3×Dic3C2413yes—
285C2×C3×Dic3C2413yes—
286C2×C3×Dic3C2413yes—
287C3×C4×D3—26no—
288C3×Dic6—26no—
289C3×Dic6—43no—
290#559—33no—
291#557—31no—
292#555—33no—
293#553—33no—
294#552—33no—
295#550C3×D311yescharacteristic, complemented
296#548—31no—
297#548—31no—
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—24no—
308C3×#41—24no—
309C3×#41—44no—
310C3×#41—44no—
311C2×C3×Q8—21no—
312C2×C3×Q8—33no—
313C2×C3×Q8—33no—
314C2×C3×Q8—64no—
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×Q8C23×C311yescharacteristic
317C2×C3×D4—23no—
318C2×C3×D4—23no—
319C2×C3×D4—23no—
320C2×C3×D4—26no—
321C2×C3×D4—33no—
322C2×C3×D4—33no—
323C2×C3×D4C22×D313yes—
324C2×C3×D4C22×D313yes—
325C2×C3×D4C22×D316yes—
326C2×C3×D4C22×D313yes—
327C2×C3×D4C23×C313yes—
328C2×C3×D4C23×C313yes—
329C2×C3×D4C23×C316yes—
330C2×C3×D4C23×C313yes—
331C22×C3×C4—23no—
332C22×C3×C4—23no—
333C22×C3×C4—33no—
334C22×C3×C4—33no—
335C22×C3×C4—36no—
336C22×C3×C4—33no—
337C22×C3×C4C22×D313yes—
338C22×C3×C4C22×D313yes—
339C22×C3×C4C23×C313yes—
340C22×C3×C4C23×C313yes—
341C2×#67C23×C313yes—
342C2×#67C23×C313yes—
343C22×Dic3C23×C316yes—
344C22×Dic3C23×C313yes—
345C22×Dic3C23×C313yes—
346D3×Q8—24no—
347C2×C4×D3C23×C313yes—
348C2×Dic6C23×C313yes—
349C2×Dic6C23×C313yes—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—23no—
352C3×C4⋊C4—33no—
353C3×C4⋊C4—33no—
354C3×C4⋊C4—33no—
355C3×C4⋊C4—36no—
356C3×C4⋊C4—33no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—33no—
359C3×C4⋊C4—33no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—33no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—33no—
364C3×C4⋊C4—33no—
365C3×C4⋊C4C22×D313yes—
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C23×C313yes—
368C3×C4⋊C4C23×C311yescharacteristic
369C3×C22⋊C4—23no—
370C3×C22⋊C4—23no—
371C3×C22⋊C4—33no—
372C3×C22⋊C4—36no—
373C3×C22⋊C4—33no—
374C3×C22⋊C4—36no—
375C3×C22⋊C4—33no—
376C3×C22⋊C4—36no—
377C3×C22⋊C4—33no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—33no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4C22×D313yes—
383C3×C22⋊C4C22×D313yes—
384C3×C22⋊C4C23×C313yes—
385C3×C22⋊C4C23×C313yes—
386C3×C42—23no—
387C3×C42—31no—
388C3×C42—33no—
389C3×C42—33no—
390C3×C42—33no—
391C3×C42—36no—
392C3×C42—33no—
393C3×C42C22×D313yes—
394C3×C42C23×C313yes—
395#217C23×C316yes—
396#217C23×C313yes—
397#217C23×C316yes—
398#217C23×C313yes—
399#217C23×C316yes—
400#217C23×C313yes—
401#217C23×C313yes—
402(C2×D3)⋊C4C23×C311yescharacteristic
403(C2×D3)⋊C4C23×C313yes—
404(C2×D3)⋊C4C23×C311yescharacteristic
405(C2×D3)⋊C4C23×C311yescharacteristic
406C4⋊Dic3C23×C313yes—
407C4⋊Dic3C23×C313yes—
408C4⋊Dic3C23×C313yes—
409C4⋊Dic3C23×C313yes—
410C4⋊Dic3C23×C311yescharacteristic
411C4⋊Dic3C23×C313yes—
412Dic3⋊C4C23×C311yescharacteristic
413Dic3⋊C4C23×C313yes—
414Dic3⋊C4C23×C313yes—
415Dic3⋊C4C23×C316yes—
416Dic3⋊C4C23×C313yes—
417Dic3⋊C4C23×C313yes—
418Dic3⋊C4C23×C313yes—
419C4×Dic3C23×C316yes—
420C4×Dic3C23×C313yes—
421C4×Dic3C23×C313yes—
422C4×Dic3C23×C313yes—
423C4×Dic3C23×C313yes—
424C4×Dic3C23×C311yescharacteristic
425C22×C32—23no—
426C22×C32—23no—
427C22×C32—23no—
428C22×C32—23no—
429C22×C32—23no—
430C22×C32—23no—
431C22×C32C2511yescharacteristic
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—23no—
439C32×C4C2×#4116yes—
440C3×Dic3—23no—
441C3×Dic3—21no—
442C3×Dic3—23no—
443C3×Dic3—21no—
444C3×Dic3—23no—
445C3×Dic3—21no—
446C3×Dic3—23no—
447C2×#41C2×C3×D311yescharacteristic
448C2×#41C2×C3×D311yescharacteristic
449C22×Q8—31no—
450C4⋊Q8—33no—
451#127C2×C3×D313yes—
452#126—31no—
453#126—33no—
454#126—36no—
455#125—33no—
456#125—33no—
457#125—33no—
458#124—33no—
459#124—33no—
460#124—36no—
461#124—33no—
462#123—36no—
463#123—33no—
464#123—36no—
465#123—33no—
466C22⋊Q8—33no—
467C22⋊Q8—33no—
468C22⋊Q8—33no—
469#121—33no—
470#121—33no—
471#121—33no—
472#121—36no—
473#121C2×C3×D313yes—
474#121C2×C3×D313yes—
475C4×Q8—31no—
476C4×Q8—31no—
477C4×Q8—31no—
478C4×Q8—33no—
479C4×Q8—33no—
480C4×Q8—33no—
481C4×Q8C2×C3×D311yescharacteristic
482C4×D4—33no—
483C4×D4—33no—
484C4×D4—33no—
485C4×D4—33no—
486C4×D4—36no—
487C4×D4—33no—
488C4×D4—33no—
489C4×D4C2×C3×D313yes—
490#117—33no—
491#117—33no—
492#117—33no—
493#117—36no—
494#117—33no—
495C2×C4⋊C4—33no—
496C2×C42—33no—
497C23×C3—23no—
498C23×C3—23no—
499C23×C3—31no—
500C23×C3C23×D313yes—
501C23×C3C23×D313yes—
502C23×C3C24×C313yes—
503C23×C3C24×C313yes—
504C22×D3C24×C311yescharacteristic
505C3×Q8—24no—
506C3×Q8—66no—
507C3×Q8—123no—
508C3×Q8#23714yes—
509C3×Q8C3×#4114yes—
510C3×D4—26no—
511C3×D4—26no—
512C3×D4—26no—
513C3×D4—26no—
514C3×D4—46no—
515C3×D4—46no—
516C3×D4—43no—
517C3×D4—46no—
518C3×D4—43no—
519C3×D4—46no—
520C3×D4—46no—
521C3×D4—86no—
522C3×D4—123no—
523C3×D4—123no—
524C2×C3×C4—26no—
525C2×C3×C4—26no—
526C2×C3×C4—26no—
527C2×C3×C4—26no—
528C2×C3×C4—21no—
529C2×C3×C4—23no—
530C2×C3×C4—23no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—33no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—33no—
538C2×C3×C4—33no—
539C2×C3×C4—33no—
540C2×C3×C4—46no—
541C2×C3×C4—46no—
542C2×C3×C4—66no—
543C2×C3×C4—123no—
544C2×C3×C4—126no—
545C2×C3×C4—123no—
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D313yes—
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D313yes—
551C2×C3×C4C24×C311yescharacteristic
552C2×C3×C4C24×C313yes—
553C2×C3×C4C24×C311yescharacteristic
554C2×C3×C4C24×C311yescharacteristic
555C2×C3×C4C24×C313yes—
556#67—43no—
557#67—43no—
558C2×Dic3—43no—
559C2×Dic3—43no—
560C2×Dic3—46no—
561C2×Dic3C24×C311yescharacteristic
562C2×Dic3C24×C313yes—
563C2×Dic3C24×C311yescharacteristic
564C2×Dic3C24×C311yescharacteristic
565C2×Dic3C24×C313yes—
566C2×Dic3C24×C313yes—
567C2×Dic3C24×C313yes—
568C4×D3—26no—
569Dic6—26no—
570Dic6—43no—
571C2×C32—43no—
572C2×C32—43no—
573C2×C32C22×#4111yescharacteristic
574C2×C32#58511yescharacteristic
575C2×C32#58511yescharacteristic
576C3×D3—41no—
577#41—24no—
578#41—24no—
579C2×Q8—33no—
580C2×Q8—33no—
581C2×Q8—64no—
582C2×Q8C22×C3×D311yescharacteristic
583C2×D4—33no—
584C2×D4—33no—
585C2×D4C22×C3×D313yes—
586C2×D4C22×C3×D313yes—
587C2×D4C22×C3×D316yes—
588C2×D4C22×C3×D313yes—
589C22×C4—33no—
590C22×C4—33no—
591C22×C4—36no—
592C22×C4—33no—
593C22×C4C22×C3×D313yes—
594C22×C4C22×C3×D313yes—
595C4⋊C4—33no—
596C4⋊C4—33no—
597C4⋊C4—33no—
598C4⋊C4—31no—
599C4⋊C4—33no—
600C4⋊C4—33no—
601C4⋊C4—33no—
602C4⋊C4—33no—
603C4⋊C4—36no—
604C4⋊C4—33no—
605C4⋊C4—33no—
606C4⋊C4—31no—
607C4⋊C4—33no—
608C4⋊C4C22×C3×D313yes—
609C4⋊C4C22×C3×D311yescharacteristic
610C22⋊C4—33no—
611C22⋊C4—36no—
612C22⋊C4—33no—
613C22⋊C4—36no—
614C22⋊C4—33no—
615C22⋊C4—36no—
616C22⋊C4—33no—
617C22⋊C4—31no—
618C22⋊C4—33no—
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4C22×C3×D313yes—
622C22⋊C4C22×C3×D313yes—
623C42—31no—
624C42—33no—
625C42—33no—
626C42—33no—
627C42—36no—
628C42—33no—
629C42C22×C3×D313yes—
630C22×C3—23no—
631C22×C3—23no—
632C22×C3—23no—
633C22×C3—23no—
634C22×C3—23no—
635C22×C3—23no—
636C22×C3—23no—
637C22×C3—23no—
638C22×C3—23no—
639C22×C3—23no—
640C22×C3—23no—
641C22×C3—23no—
642C22×C3—21no—
643C22×C3—43no—
644C22×C3—43no—
645C22×C3—43no—
646C22×C3—43no—
647C22×C3—43no—
648C22×C3—43no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3C24×D311yescharacteristic
653C22×C3C25×C311yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C3×C4—22no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—23no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—23no—
665C3×C4—21no—
666C3×C4—26no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—43no—
670C3×C4—63no—
671C3×C4—61no—
672C3×C4—63no—
673C3×C4—63no—
674C3×C4—61no—
675C3×C4—63no—
676C3×C4—61no—
677C3×C4C2×#23716yes—
678C3×C4C2×C3×#4116yes—
679Dic3—23no—
680Dic3—21no—
681Dic3—23no—
682Dic3—21no—
683Dic3—23no—
684Dic3—21no—
685Dic3—23no—
686C32#352411yescharacteristic, complemented, Sylow
687C23—31no—
688C23C23×C3×D313yes—
689C23C23×C3×D313yes—
690Q8—66no—
691Q8—123no—
692Q8C3×#23714yes—
693D4—26no—
694D4—26no—
695D4—43no—
696D4—46no—
697D4—123no—
698D4—123no—
699C2×C4—26no—
700C2×C4—26no—
701C2×C4—31no—
702C2×C4—33no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—33no—
706C2×C4—33no—
707C2×C4—33no—
708C2×C4—66no—
709C2×C4—123no—
710C2×C4—126no—
711C2×C4—123no—
712C2×C4C23×C3×D311yescharacteristic
713C2×C4C23×C3×D313yes—
714C2×C4C23×C3×D311yescharacteristic
715C2×C4C23×C3×D311yescharacteristic
716C2×C4C23×C3×D313yes—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—43no—
721C2×C3—43no—
722C2×C3—43no—
723C2×C3—43no—
724C2×C3—83no—
725C2×C3—83no—
726C2×C3—121no—
727C2×C3C22×#23711yescharacteristic
728C2×C3#596411yescharacteristic
729C2×C3#596611yescharacteristic
730C2×C3C22×C3×#4111yescharacteristic
731C2×C3C3×#58511yescharacteristic
732C2×C3C3×#58511yescharacteristic
733D3—41no—
734C22—23no—
735C22—23no—
736C22—23no—
737C22—23no—
738C22—23no—
739C22—23no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22C24×C3×D311yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—23no—
748C4—63no—
749C4—61no—
750C4—63no—
751C4—63no—
752C4—61no—
753C4—63no—
754C4—61no—
755C4C2×C3×#23716yes—
756C3—21no—
757C3#8677711yescharacteristic, direct product factor
758C3C3×#352411yescharacteristic, complemented
759C2—43no—
760C2—43no—
761C2—121no—
762C2C22×C3×#23711yescharacteristic
763C2C3×#596411yescharacteristic
764C2C3×#596611yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#550C2
socleC22×C32C25
hypercenterC3×#550D3
hypocenterC3C3×#3524
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#550

Complements

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

NH ≅ G/Ntype
1. C32×#550C2semidirect
2. C3×#5831C2semidirect
3. C3×#5831C2semidirect
4. C3×#5827C2semidirect
5. C3×Dic3×#41C2semidirect
6. C3×#5719C2semidirect
7. C3×#5713C2semidirect
8. C3×#5618C2semidirect
9. C3×#5616C2semidirect
10. C3×#5603C2semidirect
11. C3×#5600C2semidirect
12. C3×#5572C2semidirect
13. C3×#5569C2semidirect
14. C3×#5541C2semidirect
15. C3×#5538C2semidirect
17. #86777C3direct (N × H)
74. C3×#550D3semidirect
75. C3×#550C2×C3semidirect
85. #5831C2×C3semidirect
86. #5831C2×C3semidirect
87. #5827C2×C3semidirect
88. Dic3×#41C2×C3semidirect
89. #5719C2×C3semidirect
90. #5713C2×C3semidirect
91. #5618C2×C3semidirect
92. #5616C2×C3semidirect
93. #5603C2×C3semidirect
94. #5600C2×C3semidirect
95. #5572C2×C3semidirect
96. #5569C2×C3semidirect
97. #5541C2×C3semidirect
98. #5538C2×C3semidirect
295. #550C3×D3semidirect
686. C32#3524semidirect
757. C3#86777direct (N × H)
758. C3C3×#3524semidirect

Maximal subgroups

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

subgroupindex
C32×#5502
C3×#58312
C3×#58272
C3×Dic3×#412
C3×#57192
C3×#57132
C3×#56182
C3×#56162
C3×#56032
C3×#56002
C3×#55722
C3×#55692
C3×#55412
C3×#55382
C3×#35243
#867773