Finite Group Databasebeta

← C3×#85855 #11909999

Subgroups — C3×#85855 #11909999

Order 1152.

2215 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic, complemented
2C3×#5834C211yesmaximal, characteristic, complemented
3C3×#5831C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C3×#5574C211yesmaximal, characteristic, complemented
6C3×#5572C211yesmaximal, characteristic, complemented
7C3×#5569C211yesmaximal, characteristic, complemented
8C3×#5562C213yesmaximal, complemented
9C3×#5561C213yesmaximal, complemented
10C3×#5559C213yesmaximal, complemented
11C3×#5558C213yesmaximal, complemented
12C3×#5532C213yesmaximal, complemented
13C3×#5529C213yesmaximal, complemented
14C3×#5479C213yesmaximal, complemented
15C3×#5479C213yesmaximal, complemented
16C3×#3524—31nomaximal
17#85855C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C32×C4×D4C2213yes—
24C32×C4×D4C2213yes—
25C32×#117C2213yes—
26C2×C32×C42C2213yes—
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×#940C2213yes—
30C3×#938C2213yes—
31C3×#938C2213yes—
32C3×#936C2213yes—
33C3×#930C2213yes—
34C3×#930C2213yes—
35C3×#929C2213yes—
36C3×#929C2213yes—
37C3×#929C2216yes—
38C3×C4×#67C2213yes—
39C3×C4×#67C2213yes—
40C3×C4×#67C2216yes—
41C3×#924C2213yes—
42C3×#924C2213yes—
43C3×#897C2213yes—
44C3×#895C2213yes—
45C3×#893C2213yes—
46C3×#892C2213yes—
47C3×D3×C4⋊C4C2213yes—
48C3×#890C2213yes—
49C3×#888C2213yes—
50C3×#887C2213yes—
51C3×#885C2216yes—
52C3×#884C2216yes—
53C3×#883C2216yes—
54C3×#879C2216yes—
55C3×#876C2211yescharacteristic
56C3×#876C2213yes—
57C3×#875C2213yes—
58C3×#875C2213yes—
59C3×C4×D12C2213yes—
60C3×C4×D12C2213yes—
61C3×#872C2216yes—
62C3×#872C2213yes—
63C3×#872C2213yes—
64C3×#870C2213yes—
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—31no—
74C3×#548—31no—
75C3×#548—31no—
76C3×#542—33no—
77C3×#540—33no—
78C3×#529—33no—
79C3×#529—33no—
80C3×#520—31no—
81C3×#519—31no—
82C3×C4×#41—21no—
83C3×C4×#41D311yescharacteristic, complemented
84C3×C4×#41C2×C311yescharacteristic, complemented
85#5834C2×C311yescharacteristic, complemented
86#5831C2×C311yescharacteristic, complemented
87#5576C2×C311yescharacteristic, complemented
88#5574C2×C311yescharacteristic, complemented
89#5572C2×C311yescharacteristic, complemented
90#5569C2×C311yescharacteristic, complemented
91#5562C2×C313yescomplemented
92#5561C2×C313yescomplemented
93#5559C2×C313yescomplemented
94#5558C2×C313yescomplemented
95#5532C2×C313yescomplemented
96#5529C2×C313yescomplemented
97#5479C2×C313yescomplemented
98#5479C2×C313yescomplemented
99C32×#41—24no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2313yes—
102C22×C32×C4C2313yes—
103C22×C32×C4C2313yes—
104C22×C32×C4C2313yes—
105C2×C3×#67C2313yes—
106C2×C3×#67C2313yes—
107C2×C3×#67C2316yes—
108C3×#239—24no—
109C3×D3×Q8—24no—
110C2×C3×D12C2313yes—
111C2×C3×D12C2313yes—
112C2×C3×C4×D3C2313yes—
113C2×C3×C4×D3C2313yes—
114C2×C3×C4×D3C2316yes—
115C2×C3×Dic6C2313yes—
116C2×C3×Dic6C2313yes—
117C32×C4⋊C4C2313yes—
118C32×C4⋊C4C2313yes—
119C32×C22⋊C4C2316yes—
120C32×C42C2311yescharacteristic
121C32×C42C2313yes—
122C32×C42C2313yes—
123C32×C42C2313yes—
124C3×#217C2313yes—
125C3×#217C2316yes—
126C3×#217C2313yes—
127C3×(C2×D3)⋊C4C2316yes—
128C3×(C2×D3)⋊C4C2313yes—
129C3×(C2×D3)⋊C4C2313yes—
130C3×(C2×D3)⋊C4C2311yescharacteristic
131C3×(C2×D3)⋊C4C2313yes—
132C3×(C2×D3)⋊C4C2313yes—
133C3×(C2×D3)⋊C4C2311yescharacteristic
134C3×(C2×D3)⋊C4C2313yes—
135C3×(C2×D3)⋊C4C2311yescharacteristic
136C3×C4⋊Dic3C2313yes—
137C3×C4⋊Dic3C2313yes—
138C3×C4⋊Dic3C2313yes—
139C3×C4⋊Dic3C2313yes—
140C3×Dic3⋊C4C2313yes—
141C3×Dic3⋊C4C2316yes—
142C3×Dic3⋊C4C2313yes—
143C3×Dic3⋊C4C2311yescharacteristic
144C3×Dic3⋊C4C2313yes—
145C3×Dic3⋊C4C2313yes—
146C3×Dic3⋊C4C2311yescharacteristic
147C3×Dic3⋊C4C2313yes—
148C3×Dic3⋊C4C2311yescharacteristic
149C3×C4×Dic3C2316yes—
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—31no—
158C2×#239C22×C311yescharacteristic
159C2×D3×Q8C22×C311yescharacteristic
160C3×C4⋊Q8—33no—
161C3×#127—33no—
162C3×#126—36no—
163C3×#126—31no—
164C3×#126—33no—
165C3×#125—33no—
166C3×#125—33no—
167C3×#125—33no—
168C3×#124—33no—
169C3×#124—36no—
170C3×#124—33no—
171C3×#124—33no—
172C3×#123—33no—
173C3×#123—36no—
174C3×#123—33no—
175C3×#123—36no—
176C3×C22⋊Q8—33no—
177C3×C22⋊Q8—33no—
178C3×C22⋊Q8—33no—
179C3×#121—33no—
180C3×#121—33no—
181C3×#121—33no—
182C3×#121—33no—
183C3×#121—33no—
184C3×#121—36no—
185C3×C4×Q8—21no—
186C3×C4×Q8—21no—
187C3×C4×Q8—31no—
188C3×C4×Q8—31no—
189C3×C4×Q8—33no—
190C3×C4×Q8—33no—
191C3×C4×Q8—33no—
192C3×C4×Q8C2×D311yescharacteristic
193C3×C4×Q8C2×D311yescharacteristic
194C3×C4×Q8C22×C311yescharacteristic
195C3×C4×Q8C22×C311yescharacteristic
196C3×C4×D4—23no—
197C3×C4×D4—23no—
198C3×C4×D4—36no—
199C3×C4×D4—33no—
200C3×C4×D4—33no—
201C3×C4×D4—33no—
202C3×C4×D4—33no—
203C3×C4×D4—33no—
204C3×C4×D4C2×D313yes—
205C3×C4×D4C2×D313yes—
206C3×C4×D4C22×C313yes—
207C3×C4×D4C22×C313yes—
208C3×#117—23no—
209C3×#117—33no—
210C3×#117—33no—
211C3×#117—33no—
212C3×#117—36no—
213C3×#117C2×D313yes—
214C3×#117C22×C313yes—
215C2×C3×C4⋊C4—33no—
216C2×C3×C42—23no—
217C2×C3×C42C2×D313yes—
218C2×C3×C42C22×C313yes—
219Q8×Dic3C22×C311yescharacteristic
220Q8×Dic3C22×C311yescharacteristic
221#940C22×C313yes—
222#938C22×C313yes—
223#938C22×C313yes—
224#936C22×C313yes—
225#930C22×C313yes—
226#930C22×C313yes—
227#929C22×C313yes—
228#929C22×C313yes—
229#929C22×C316yes—
230C4×#67C22×C313yes—
231C4×#67C22×C313yes—
232C4×#67C22×C316yes—
233#924C22×C313yes—
234#924C22×C313yes—
235#897C22×C313yes—
236#895C22×C313yes—
237#893C22×C313yes—
238#892C22×C313yes—
239D3×C4⋊C4C22×C313yes—
240#890C22×C313yes—
241#888C22×C313yes—
242#887C22×C313yes—
243#885C22×C316yes—
244#884C22×C316yes—
245#883C22×C316yes—
246#879C22×C316yes—
247#876C22×C311yescharacteristic
248#876C22×C313yes—
249#875C22×C313yes—
250#875C22×C313yes—
251C4×D12C22×C313yes—
252C4×D12C22×C313yes—
253#872C22×C316yes—
254#872C22×C313yes—
255#872C22×C313yes—
256#870C22×C313yes—
257#870C22×C313yes—
258C4×Dic6C22×C313yes—
259C4×Dic6C22×C313yes—
260C23×C32C2413yes—
261C22×C3×D3C2411yescharacteristic
262C22×C3×D3C2413yes—
263C32×Q8#4114yes—
264C32×D4—26no—
265C2×C32×C4—26no—
266C2×C32×C4—43no—
267C2×C32×C4—43no—
268C2×C32×C4C2413yes—
269C2×C32×C4C2411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C2×C32×C4C2413yes—
273C2×C32×C4C2413yes—
274C3×#67—46no—
275C3×#67—43no—
276C3×#67—43no—
277C2×C3×Dic3C2411yescharacteristic
278C2×C3×Dic3C2413yes—
279C2×C3×Dic3C2411yescharacteristic
280C2×C3×Dic3C2413yes—
281C2×C3×Dic3C2413yes—
282C2×C3×Dic3C2411yescharacteristic
283C3×D12—26no—
284C3×D12—43no—
285C3×C4×D3—26no—
286C3×C4×D3—26no—
287C3×C4×D3—46no—
288C3×Dic6—26no—
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#548—31no—
298#542—33no—
299#540—33no—
300#529—33no—
301#529—33no—
302#520—31no—
303#519—31no—
304C4×#41C3×D311yescharacteristic, complemented
305C3×#41—28no—
306C3×#41—24no—
307C3×#41—24no—
308C3×#41—64no—
309C2×C3×Q8—21no—
310C2×C3×Q8—33no—
311C2×C3×Q8—33no—
312C2×C3×Q8—64no—
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C23×C311yescharacteristic
315C2×C3×D4—23no—
316C2×C3×D4—33no—
317C2×C3×D4—36no—
318C2×C3×D4—33no—
319C2×C3×D4—33no—
320C2×C3×D4—33no—
321C2×C3×D4C22×D313yes—
322C2×C3×D4C23×C313yes—
323C22×C3×C4—23no—
324C22×C3×C4—23no—
325C22×C3×C4—23no—
326C22×C3×C4—33no—
327C22×C3×C4—33no—
328C22×C3×C4—36no—
329C22×C3×C4C22×D313yes—
330C22×C3×C4C22×D313yes—
331C22×C3×C4C22×D313yes—
332C22×C3×C4C23×C313yes—
333C22×C3×C4C23×C313yes—
334C22×C3×C4C23×C313yes—
335C2×#67C23×C313yes—
336C2×#67C23×C313yes—
337C2×#67C23×C316yes—
338#239—24no—
339D3×Q8—24no—
340C2×D12C23×C313yes—
341C2×D12C23×C313yes—
342C2×C4×D3C23×C313yes—
343C2×C4×D3C23×C313yes—
344C2×C4×D3C23×C316yes—
345C2×Dic6C23×C313yes—
346C2×Dic6C23×C313yes—
347C3×C4⋊C4—23no—
348C3×C4⋊C4—23no—
349C3×C4⋊C4—33no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—33no—
352C3×C4⋊C4—33no—
353C3×C4⋊C4—33no—
354C3×C4⋊C4—36no—
355C3×C4⋊C4—31no—
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⋊C4C22×D313yes—
363C3×C4⋊C4C22×D313yes—
364C3×C4⋊C4C23×C313yes—
365C3×C4⋊C4C23×C313yes—
366C3×C22⋊C4—26no—
367C3×C22⋊C4—33no—
368C3×C22⋊C4—36no—
369C3×C22⋊C4—33no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—33no—
372C3×C22⋊C4—33no—
373C3×C22⋊C4—33no—
374C3×C22⋊C4—33no—
375C3×C22⋊C4—36no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—33no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4C22×D316yes—
380C3×C22⋊C4C23×C316yes—
381C3×C42—21no—
382C3×C42—23no—
383C3×C42—23no—
384C3×C42—23no—
385C3×C42—36no—
386C3×C42—33no—
387C3×C42—33no—
388C3×C42C22×D311yescharacteristic
389C3×C42C22×D313yes—
390C3×C42C22×D313yes—
391C3×C42C22×D313yes—
392C3×C42C23×C313yes—
393C3×C42C23×C313yes—
394C3×C42C23×C313yes—
395C3×C42C23×C311yescharacteristic
396#217C23×C313yes—
397#217C23×C316yes—
398#217C23×C313yes—
399(C2×D3)⋊C4C23×C311yescharacteristic
400(C2×D3)⋊C4C23×C313yes—
401(C2×D3)⋊C4C23×C313yes—
402(C2×D3)⋊C4C23×C316yes—
403(C2×D3)⋊C4C23×C313yes—
404(C2×D3)⋊C4C23×C313yes—
405(C2×D3)⋊C4C23×C311yescharacteristic
406(C2×D3)⋊C4C23×C313yes—
407(C2×D3)⋊C4C23×C311yescharacteristic
408C4⋊Dic3C23×C313yes—
409C4⋊Dic3C23×C313yes—
410C4⋊Dic3C23×C313yes—
411C4⋊Dic3C23×C313yes—
412Dic3⋊C4C23×C311yescharacteristic
413Dic3⋊C4C23×C313yes—
414Dic3⋊C4C23×C313yes—
415Dic3⋊C4C23×C311yescharacteristic
416Dic3⋊C4C23×C313yes—
417Dic3⋊C4C23×C313yes—
418Dic3⋊C4C23×C316yes—
419Dic3⋊C4C23×C313yes—
420Dic3⋊C4C23×C311yescharacteristic
421C4×Dic3C23×C316yes—
422C4×Dic3C23×C313yes—
423C4×Dic3C23×C313yes—
424C22×C32—23no—
425C22×C32—23no—
426C22×C32—23no—
427C22×C32C2511yescharacteristic
428C2×C3×D3—21no—
429C2×C3×D3—23no—
430C2×C3×D3—23no—
431C2×C3×D3—21no—
432C2×C3×D3—23no—
433C2×C3×D3—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—23no—
438C32×C4—23no—
439C32×C4C2×#4116yes—
440C3×Dic3—23no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—23no—
444C3×Dic3—23no—
445C3×Dic3—21no—
446C2×#41—31no—
447C2×#41C2×C3×D311yescharacteristic
448C22×Q8—31no—
449C4⋊Q8—33no—
450#127—33no—
451#126—36no—
452#126—31no—
453#126—33no—
454#125—33no—
455#125—33no—
456#125—33no—
457#124—33no—
458#124—36no—
459#124—33no—
460#124—33no—
461#123—36no—
462#123—33no—
463#123—33no—
464#123—36no—
465C22⋊Q8—33no—
466C22⋊Q8—33no—
467C22⋊Q8—33no—
468#121—33no—
469#121—33no—
470#121—33no—
471#121—33no—
472#121—33no—
473#121—36no—
474C4×Q8—31no—
475C4×Q8—31no—
476C4×Q8—33no—
477C4×Q8—33no—
478C4×Q8—33no—
479C4×Q8C2×C3×D311yescharacteristic
480C4×Q8C2×C3×D311yescharacteristic
481C4×D4—33no—
482C4×D4—33no—
483C4×D4—36no—
484C4×D4—33no—
485C4×D4—33no—
486C4×D4—33no—
487C4×D4C2×C3×D313yes—
488C4×D4C2×C3×D313yes—
489#117—33no—
490#117—33no—
491#117—33no—
492#117—36no—
493#117C2×C3×D313yes—
494C2×C4⋊C4—33no—
495C2×C42C2×C3×D313yes—
496C23×C3—23no—
497C23×C3—31no—
498C23×C3—33no—
499C23×C3C23×D313yes—
500C23×C3C24×C313yes—
501C22×D3C24×C311yescharacteristic
502C22×D3C24×C313yes—
503C3×Q8—24no—
504C3×Q8—66no—
505C3×Q8—123no—
506C3×Q8#23514yes—
507C3×Q8C3×#4114yes—
508C3×D4—212no—
509C3×D4—26no—
510C3×D4—26no—
511C3×D4—66no—
512C3×D4—123no—
513C3×D4—123no—
514C3×D4—123no—
515C3×D4—126no—
516C2×C3×C4—212no—
517C2×C3×C4—26no—
518C2×C3×C4—26no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—23no—
523C2×C3×C4—23no—
524C2×C3×C4—23no—
525C2×C3×C4—31no—
526C2×C3×C4—33no—
527C2×C3×C4—31no—
528C2×C3×C4—33no—
529C2×C3×C4—33no—
530C2×C3×C4—31no—
531C2×C3×C4—43no—
532C2×C3×C4—43no—
533C2×C3×C4—43no—
534C2×C3×C4—43no—
535C2×C3×C4—46no—
536C2×C3×C4—46no—
537C2×C3×C4—66no—
538C2×C3×C4—66no—
539C2×C3×C4—126no—
540C2×C3×C4C23×D313yes—
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D313yes—
545C2×C3×C4C23×D313yes—
546C2×C3×C4C24×C313yes—
547C2×C3×C4C24×C311yescharacteristic
548C2×C3×C4C24×C311yescharacteristic
549C2×C3×C4C24×C311yescharacteristic
550C2×C3×C4C24×C313yes—
551C2×C3×C4C24×C313yes—
552#67—46no—
553#67—43no—
554#67—43no—
555C2×Dic3C24×C311yescharacteristic
556C2×Dic3C24×C313yes—
557C2×Dic3C24×C311yescharacteristic
558C2×Dic3C24×C313yes—
559C2×Dic3C24×C313yes—
560C2×Dic3C24×C311yescharacteristic
561D12—26no—
562D12—43no—
563C4×D3—26no—
564C4×D3—26no—
565C4×D3—46no—
566Dic6—26no—
567Dic6—43no—
568C2×C32—43no—
569C2×C32C22×#4111yescharacteristic
570C2×C32#58511yescharacteristic
571C2×C32#58511yescharacteristic
572C3×D3—41no—
573C3×D3—43no—
574#41—24no—
575#41—64no—
576C2×Q8—33no—
577C2×Q8—33no—
578C2×Q8—64no—
579C2×Q8C22×C3×D311yescharacteristic
580C2×D4—33no—
581C2×D4—36no—
582C2×D4—33no—
583C2×D4—33no—
584C2×D4—33no—
585C2×D4C22×C3×D313yes—
586C22×C4—33no—
587C22×C4—33no—
588C22×C4—36no—
589C22×C4C22×C3×D313yes—
590C22×C4C22×C3×D313yes—
591C22×C4C22×C3×D313yes—
592C4⋊C4—33no—
593C4⋊C4—33no—
594C4⋊C4—31no—
595C4⋊C4—33no—
596C4⋊C4—33no—
597C4⋊C4—33no—
598C4⋊C4—33no—
599C4⋊C4—36no—
600C4⋊C4—31no—
601C4⋊C4—33no—
602C4⋊C4—33no—
603C4⋊C4—31no—
604C4⋊C4—33no—
605C4⋊C4C22×C3×D313yes—
606C4⋊C4C22×C3×D313yes—
607C22⋊C4—33no—
608C22⋊C4—36no—
609C22⋊C4—33no—
610C22⋊C4—31no—
611C22⋊C4—33no—
612C22⋊C4—33no—
613C22⋊C4—33no—
614C22⋊C4—33no—
615C22⋊C4—36no—
616C22⋊C4—31no—
617C22⋊C4—33no—
618C22⋊C4—31no—
619C22⋊C4C22×C3×D316yes—
620C42—36no—
621C42—33no—
622C42—33no—
623C42C22×C3×D311yescharacteristic
624C42C22×C3×D313yes—
625C42C22×C3×D313yes—
626C42C22×C3×D313yes—
627C22×C3—26no—
628C22×C3—23no—
629C22×C3—23no—
630C22×C3—23no—
631C22×C3—23no—
632C22×C3—23no—
633C22×C3—23no—
634C22×C3—21no—
635C22×C3—43no—
636C22×C3—43no—
637C22×C3—61no—
638C22×C3—63no—
639C22×C3—63no—
640C22×C3—61no—
641C22×C3—63no—
642C22×C3—61no—
643C22×C3C24×D311yescharacteristic
644C22×C3C25×C311yescharacteristic
645C2×D3—21no—
646C2×D3—23no—
647C2×D3—23no—
648C2×D3—21no—
649C2×D3—23no—
650C2×D3—21no—
651C3×C4—22no—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—23no—
658C3×C4—23no—
659C3×C4—21no—
660C3×C4—23no—
661C3×C4—23no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—26no—
665C3×C4—43no—
666C3×C4—43no—
667C3×C4—61no—
668C3×C4—63no—
669C3×C4—63no—
670C3×C4—61no—
671C3×C4—63no—
672C3×C4—61no—
673C3×C4C2×#23516yes—
674C3×C4C2×C3×#4116yes—
675Dic3—23no—
676Dic3—21no—
677Dic3—21no—
678Dic3—23no—
679Dic3—23no—
680Dic3—21no—
681C32#352411yescharacteristic, complemented, Sylow
682C23—31no—
683C23—33no—
684C23C23×C3×D313yes—
685Q8—66no—
686Q8—123no—
687Q8C3×#23514yes—
688D4—26no—
689D4—66no—
690D4—123no—
691D4—123no—
692D4—123no—
693D4—126no—
694C2×C4—26no—
695C2×C4—31no—
696C2×C4—33no—
697C2×C4—31no—
698C2×C4—33no—
699C2×C4—33no—
700C2×C4—31no—
701C2×C4—43no—
702C2×C4—43no—
703C2×C4—66no—
704C2×C4—66no—
705C2×C4—126no—
706C2×C4C23×C3×D313yes—
707C2×C4C23×C3×D311yescharacteristic
708C2×C4C23×C3×D311yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C2×C4C23×C3×D313yes—
711C2×C4C23×C3×D313yes—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—46no—
716C2×C3—43no—
717C2×C3—43no—
718C2×C3—121no—
719C2×C3—123no—
720C2×C3C22×#23511yescharacteristic
721C2×C3#596411yescharacteristic
722C2×C3#596411yescharacteristic
723C2×C3C22×C3×#4111yescharacteristic
724C2×C3C3×#58511yescharacteristic
725C2×C3C3×#58511yescharacteristic
726D3—41no—
727D3—43no—
728C22—23no—
729C22—23no—
730C22—23no—
731C22—61no—
732C22—63no—
733C22—63no—
734C22—61no—
735C22—63no—
736C22—61no—
737C22C24×C3×D311yescharacteristic
738C4—21no—
739C4—21no—
740C4—21no—
741C4—23no—
742C4—23no—
743C4—61no—
744C4—63no—
745C4—63no—
746C4—61no—
747C4—63no—
748C4—61no—
749C4C2×C3×#23516yes—
750C3—21no—
751C3#8585511yescharacteristic, direct product factor
752C3C3×#352411yescharacteristic, complemented
753C2—43no—
754C2—121no—
755C2—123no—
756C2C22×C3×#23511yescharacteristic
757C2C3×#596411yescharacteristic
758C2C3×#596411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×C4×#41C2
socleC22×C32C25
hypercenterC3×C4×#41D3
hypocenterC3C3×#3524
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
1. C32×C4×#41C2semidirect
2. C3×#5834C2semidirect
3. C3×#5831C2semidirect
4. C3×#5576C2semidirect
5. C3×#5574C2semidirect
6. C3×#5572C2semidirect
7. C3×#5569C2semidirect
8. C3×#5562C2semidirect
9. C3×#5561C2semidirect
10. C3×#5559C2semidirect
11. C3×#5558C2semidirect
12. C3×#5532C2semidirect
13. C3×#5529C2semidirect
14. C3×#5479C2semidirect
15. C3×#5479C2semidirect
17. #85855C3direct (N × H)
83. C3×C4×#41D3semidirect
84. C3×C4×#41C2×C3semidirect
85. #5834C2×C3semidirect
86. #5831C2×C3semidirect
87. #5576C2×C3semidirect
88. #5574C2×C3semidirect
89. #5572C2×C3semidirect
90. #5569C2×C3semidirect
91. #5562C2×C3semidirect
92. #5561C2×C3semidirect
93. #5559C2×C3semidirect
94. #5558C2×C3semidirect
95. #5532C2×C3semidirect
96. #5529C2×C3semidirect
97. #5479C2×C3semidirect
98. #5479C2×C3semidirect
304. C4×#41C3×D3semidirect
681. C32#3524semidirect
751. C3#85855direct (N × H)
752. C3C3×#3524semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C3×#58342
C3×#58312
C3×#55762
C3×#55742
C3×#55722
C3×#55692
C3×#55622
C3×#55612
C3×#55592
C3×#55582
C3×#55322
C3×#55292
C3×#54792
C3×#35243
#858553