Finite Group Databasebeta

← C3×#85879 #11910005

Subgroups — C3×#85879 #11910005

Order 1152.

2193 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#519C211yesmaximal, characteristic, complemented
2C3×#5817C211yesmaximal, characteristic, complemented
3C3×#5817C211yesmaximal, characteristic, complemented
4C3×#5585C213yesmaximal, complemented
5C3×#5582C213yesmaximal, complemented
6C3×#5581C213yesmaximal, complemented
7C3×#5580C213yesmaximal, complemented
8C3×#5577C211yesmaximal, characteristic, complemented
9C3×#5574C211yesmaximal, characteristic, complemented
10C3×C4×#239C211yesmaximal, characteristic, complemented
11C3×#5569C211yesmaximal, characteristic, complemented
12C3×#5535C213yesmaximal, complemented
13C3×#5532C213yesmaximal, complemented
14C3×#5530C213yesmaximal, complemented
15C3×#5528C213yesmaximal, complemented
16C3×#3524—31nomaximal
17#85879C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic
23C32×C4×Q8C2213yes—
24C32×C4×Q8C2213yes—
25C32×#117C2213yes—
26C32×#117C2213yes—
27C3×#947C2213yes—
28C3×#947C2213yes—
29C3×#946C2213yes—
30C3×#946C2213yes—
31C3×Q8×Dic3C2211yescharacteristic
32C3×Q8×Dic3C2211yescharacteristic
33C3×#930C2213yes—
34C3×#930C2213yes—
35C3×C4×#67C2213yes—
36C3×C4×#67C2213yes—
37C3×#898C2213yes—
38C3×#896C2213yes—
39C3×#895C2213yes—
40C3×#895C2213yes—
41C3×#894C2213yes—
42C3×#894C2216yes—
43C3×#894C2216yes—
44C3×#893C2213yes—
45C3×#893C2213yes—
46C3×#892C2213yes—
47C3×D3×C4⋊C4C2213yes—
48C3×#890C2213yes—
49C3×#889C2213yes—
50C3×#888C2213yes—
51C3×#885C2213yes—
52C3×#884C2213yes—
53C3×#884C2216yes—
54C3×#883C2213yes—
55C3×#879C2211yescharacteristic
56C3×#876C2216yes—
57C3×#875C2216yes—
58C3×#874C2213yes—
59C3×C4×D12C2213yes—
60C3×C4×D12C2216yes—
61C3×C4×D12C2213yes—
62C3×C4×D12C2213yes—
63C3×#872C2213yes—
64C3×#872C2216yes—
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—31no—
75C3×#548—31no—
76C3×#542—33no—
77C3×#540—33no—
78C3×#529—33no—
79C3×#529—33no—
80C3×#520—31no—
81C3×#519—21no—
82C3×#519D311yescharacteristic, complemented
83C3×#519C2×C311yescharacteristic, complemented
84C3×C4×#41—31no—
85#5817C2×C311yescharacteristic, complemented
86#5817C2×C311yescharacteristic, complemented
87#5585C2×C313yescomplemented
88#5582C2×C313yescomplemented
89#5581C2×C313yescomplemented
90#5580C2×C313yescomplemented
91#5577C2×C311yescharacteristic, complemented
92#5574C2×C311yescharacteristic, complemented
93C4×#239C2×C311yescharacteristic, complemented
94#5569C2×C311yescharacteristic, complemented
95#5535C2×C313yescomplemented
96#5532C2×C313yescomplemented
97#5530C2×C313yescomplemented
98#5528C2×C313yescomplemented
99C2×C32×Q8—24no—
100C2×C32×Q8C2313yes—
101C2×C32×Q8C2311yescharacteristic
102C22×C32×C4C2313yes—
103C2×C3×#67C2313yes—
104C2×C3×#67C2313yes—
105C3×#239—24no—
106C3×#239—24no—
107C2×C3×D12C2313yes—
108C2×C3×D12C2313yes—
109C2×C3×D12C2313yes—
110C2×C3×D12C2316yes—
111C2×C3×C4×D3C2313yes—
112C2×C3×C4×D3C2313yes—
113C2×C3×C4×D3C2313yes—
114C2×C3×C4×D3C2316yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×Dic6C2313yes—
117C32×C4⋊C4C2313yes—
118C32×C4⋊C4C2313yes—
119C32×C4⋊C4C2313yes—
120C32×C4⋊C4C2313yes—
121C32×C22⋊C4C2311yescharacteristic
122C32×C22⋊C4C2313yes—
123C32×C42C2313yes—
124C32×C42C2313yes—
125C32×C42C2316yes—
126C3×#217C2311yescharacteristic
127C3×#217C2311yescharacteristic
128C3×(C2×D3)⋊C4C2313yes—
129C3×(C2×D3)⋊C4C2316yes—
130C3×(C2×D3)⋊C4C2313yes—
131C3×(C2×D3)⋊C4C2313yes—
132C3×(C2×D3)⋊C4C2313yes—
133C3×(C2×D3)⋊C4C2316yes—
134C3×(C2×D3)⋊C4C2316yes—
135C3×(C2×D3)⋊C4C2313yes—
136C3×(C2×D3)⋊C4C2313yes—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2313yes—
139C3×C4⋊Dic3C2313yes—
140C3×C4⋊Dic3C2313yes—
141C3×Dic3⋊C4C2311yescharacteristic
142C3×Dic3⋊C4C2311yescharacteristic
143C3×Dic3⋊C4C2313yes—
144C3×Dic3⋊C4C2316yes—
145C3×Dic3⋊C4C2313yes—
146C3×Dic3⋊C4C2313yes—
147C3×Dic3⋊C4C2313yes—
148C3×C4×Dic3C2311yescharacteristic
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2313yes—
152#3524—31noSylow
153C2×C3×#41—31no—
154C2×C3×#41—31no—
155C22×C3×Q8—21no—
156C22×C3×Q8C2×D311yescharacteristic
157C22×C3×Q8C22×C311yescharacteristic
158C2×#239C22×C311yescharacteristic
159C2×#239C22×C311yescharacteristic
160C3×C4⋊Q8—33no—
161C3×#127—33no—
162C3×#126—33no—
163C3×#126—31no—
164C3×#126—36no—
165C3×#125—33no—
166C3×#125—33no—
167C3×#125—33no—
168C3×#124—33no—
169C3×#124—33no—
170C3×#124—33no—
171C3×#124—36no—
172C3×#123—33no—
173C3×#123—36no—
174C3×#123—36no—
175C3×#123—33no—
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—23no—
187C3×C4×Q8—21no—
188C3×C4×Q8—23no—
189C3×C4×Q8—31no—
190C3×C4×Q8—31no—
191C3×C4×Q8—33no—
192C3×C4×Q8C2×D313yes—
193C3×C4×Q8C2×D311yescharacteristic
194C3×C4×Q8C2×D313yes—
195C3×C4×Q8C2×D311yescharacteristic
196C3×C4×Q8C22×C311yescharacteristic
197C3×C4×Q8C22×C311yescharacteristic
198C3×C4×Q8C22×C313yes—
199C3×C4×Q8C22×C313yes—
200C3×C4×D4—33no—
201C3×C4×D4—33no—
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×#117—23no—
209C3×#117—23no—
210C3×#117—33no—
211C3×#117—33no—
212C3×#117—36no—
213C3×#117C2×D313yes—
214C3×#117C2×D313yes—
215C3×#117C22×C313yes—
216C3×#117C22×C313yes—
217C2×C3×C4⋊C4—33no—
218C2×C3×C42—33no—
219#947C22×C313yes—
220#947C22×C313yes—
221#946C22×C313yes—
222#946C22×C313yes—
223Q8×Dic3C22×C311yescharacteristic
224Q8×Dic3C22×C311yescharacteristic
225#930C22×C313yes—
226#930C22×C313yes—
227C4×#67C22×C313yes—
228C4×#67C22×C313yes—
229#898C22×C313yes—
230#896C22×C313yes—
231#895C22×C313yes—
232#895C22×C313yes—
233#894C22×C313yes—
234#894C22×C316yes—
235#894C22×C316yes—
236#893C22×C313yes—
237#893C22×C313yes—
238#892C22×C313yes—
239D3×C4⋊C4C22×C313yes—
240#890C22×C313yes—
241#889C22×C313yes—
242#888C22×C313yes—
243#885C22×C313yes—
244#884C22×C313yes—
245#884C22×C316yes—
246#883C22×C313yes—
247#879C22×C311yescharacteristic
248#876C22×C316yes—
249#875C22×C316yes—
250#874C22×C313yes—
251C4×D12C22×C313yes—
252C4×D12C22×C316yes—
253C4×D12C22×C313yes—
254C4×D12C22×C313yes—
255#872C22×C313yes—
256#872C22×C316yes—
257C42×D3C22×C313yes—
258#870C22×C313yes—
259C4×Dic6C22×C313yes—
260C23×C32C2411yescharacteristic
261C22×C3×D3C2413yes—
262C22×C3×D3C2413yes—
263C32×Q8—26no—
264C32×Q8#4114yes—
265C2×C32×C4—26no—
266C2×C32×C4C2411yescharacteristic
267C2×C32×C4C2413yes—
268C2×C32×C4C2411yescharacteristic
269C2×C32×C4C2413yes—
270C2×C32×C4C2413yes—
271C2×C32×C4C2413yes—
272C3×#67—43no—
273C3×#67—43no—
274C2×C3×Dic3C2411yescharacteristic
275C2×C3×Dic3C2411yescharacteristic
276C2×C3×Dic3C2411yescharacteristic
277C2×C3×Dic3C2413yes—
278C2×C3×Dic3C2413yes—
279C2×C3×Dic3C2411yescharacteristic
280C3×D12—26no—
281C3×D12—26no—
282C3×D12—46no—
283C3×D12—43no—
284C3×C4×D3—26no—
285C3×C4×D3—26no—
286C3×C4×D3—43no—
287C3×C4×D3—43no—
288C3×C4×D3—46no—
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#519C3×D311yescharacteristic, complemented
304C4×#41—31no—
305C3×#41—64no—
306C3×#41—64no—
307C2×C3×Q8—28no—
308C2×C3×Q8—24no—
309C2×C3×Q8—24no—
310C2×C3×Q8—23no—
311C2×C3×Q8—21no—
312C2×C3×Q8—33no—
313C2×C3×Q8C22×D313yes—
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×Q8C23×C313yes—
316C2×C3×Q8C23×C311yescharacteristic
317C2×C3×D4—33no—
318C2×C3×D4—33no—
319C2×C3×D4—33no—
320C2×C3×D4—33no—
321C2×C3×D4—36no—
322C2×C3×D4—33no—
323C22×C3×C4—23no—
324C22×C3×C4—33no—
325C22×C3×C4—33no—
326C22×C3×C4—33no—
327C22×C3×C4—33no—
328C22×C3×C4—36no—
329C22×C3×C4C22×D313yes—
330C22×C3×C4C23×C313yes—
331C2×#67C23×C313yes—
332C2×#67C23×C313yes—
333#239—24no—
334#239—24no—
335C2×D12C23×C313yes—
336C2×D12C23×C313yes—
337C2×D12C23×C313yes—
338C2×D12C23×C316yes—
339C2×C4×D3C23×C313yes—
340C2×C4×D3C23×C313yes—
341C2×C4×D3C23×C313yes—
342C2×C4×D3C23×C313yes—
343C2×C4×D3C23×C316yes—
344C2×Dic6C23×C313yes—
345C3×C4⋊C4—23no—
346C3×C4⋊C4—23no—
347C3×C4⋊C4—23no—
348C3×C4⋊C4—23no—
349C3×C4⋊C4—33no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—33no—
352C3×C4⋊C4—36no—
353C3×C4⋊C4—33no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—33no—
356C3×C4⋊C4—33no—
357C3×C4⋊C4—33no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—33no—
360C3×C4⋊C4C22×D313yes—
361C3×C4⋊C4C22×D313yes—
362C3×C4⋊C4C22×D313yes—
363C3×C4⋊C4C22×D313yes—
364C3×C4⋊C4C23×C313yes—
365C3×C4⋊C4C23×C313yes—
366C3×C4⋊C4C23×C313yes—
367C3×C4⋊C4C23×C313yes—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—23no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—31no—
372C3×C22⋊C4—33no—
373C3×C22⋊C4—33no—
374C3×C22⋊C4—36no—
375C3×C22⋊C4—33no—
376C3×C22⋊C4—36no—
377C3×C22⋊C4—33no—
378C3×C22⋊C4—33no—
379C3×C22⋊C4—36no—
380C3×C22⋊C4—33no—
381C3×C22⋊C4C22×D311yescharacteristic
382C3×C22⋊C4C22×D313yes—
383C3×C22⋊C4C23×C311yescharacteristic
384C3×C22⋊C4C23×C313yes—
385C3×C42—23no—
386C3×C42—26no—
387C3×C42—23no—
388C3×C42—31no—
389C3×C42—33no—
390C3×C42—33no—
391C3×C42—33no—
392C3×C42C22×D313yes—
393C3×C42C22×D316yes—
394C3×C42C22×D313yes—
395C3×C42C23×C313yes—
396C3×C42C23×C313yes—
397C3×C42C23×C316yes—
398#217C23×C311yescharacteristic
399#217C23×C311yescharacteristic
400(C2×D3)⋊C4C23×C313yes—
401(C2×D3)⋊C4C23×C313yes—
402(C2×D3)⋊C4C23×C313yes—
403(C2×D3)⋊C4C23×C316yes—
404(C2×D3)⋊C4C23×C313yes—
405(C2×D3)⋊C4C23×C316yes—
406(C2×D3)⋊C4C23×C313yes—
407(C2×D3)⋊C4C23×C316yes—
408(C2×D3)⋊C4C23×C313yes—
409C4⋊Dic3C23×C313yes—
410C4⋊Dic3C23×C313yes—
411C4⋊Dic3C23×C313yes—
412C4⋊Dic3C23×C311yescharacteristic
413Dic3⋊C4C23×C311yescharacteristic
414Dic3⋊C4C23×C313yes—
415Dic3⋊C4C23×C316yes—
416Dic3⋊C4C23×C311yescharacteristic
417Dic3⋊C4C23×C313yes—
418Dic3⋊C4C23×C313yes—
419Dic3⋊C4C23×C313yes—
420C4×Dic3C23×C313yes—
421C4×Dic3C23×C313yes—
422C4×Dic3C23×C311yescharacteristic
423C4×Dic3C23×C313yes—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32C2511yescharacteristic
428C2×C3×D3—23no—
429C2×C3×D3—23no—
430C2×C3×D3—23no—
431C2×C3×D3—23no—
432C2×C3×D3—23no—
433C2×C3×D3—23no—
434C32×C4—23no—
435C32×C4—23no—
436C32×C4—21no—
437C32×C4—23no—
438C32×C4—21no—
439C32×C4C2×#4116yes—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—23no—
444C3×Dic3—21no—
445C3×Dic3—23no—
446C2×#41—31no—
447C2×#41—31no—
448C22×Q8C2×C3×D311yescharacteristic
449C4⋊Q8—33no—
450#127—33no—
451#126—33no—
452#126—31no—
453#126—36no—
454#125—33no—
455#125—33no—
456#125—33no—
457#124—33no—
458#124—33no—
459#124—33no—
460#124—36no—
461#123—36no—
462#123—33no—
463#123—36no—
464#123—33no—
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×Q8C2×C3×D311yescharacteristic
478C4×Q8C2×C3×D313yes—
479C4×Q8C2×C3×D311yescharacteristic
480C4×Q8C2×C3×D313yes—
481C4×D4—33no—
482C4×D4—33no—
483C4×D4—33no—
484C4×D4—33no—
485C4×D4—33no—
486C4×D4—33no—
487C4×D4—33no—
488C4×D4—36no—
489#117—33no—
490#117—33no—
491#117—36no—
492#117C2×C3×D313yes—
493#117C2×C3×D313yes—
494C2×C4⋊C4—33no—
495C2×C42—33no—
496C23×C3—21no—
497C23×C3—33no—
498C23×C3—33no—
499C23×C3C23×D311yescharacteristic
500C23×C3C24×C311yescharacteristic
501C22×D3C24×C313yes—
502C22×D3C24×C313yes—
503C3×Q8—212no—
504C3×Q8—26no—
505C3×Q8—26no—
506C3×Q8—24no—
507C3×Q8—123no—
508C3×Q8#23514yes—
509C3×Q8C3×#4114yes—
510C3×D4—66no—
511C3×D4—66no—
512C3×D4—123no—
513C3×D4—126no—
514C3×D4—123no—
515C3×D4—123no—
516C2×C3×C4—212no—
517C2×C3×C4—26no—
518C2×C3×C4—26no—
519C2×C3×C4—23no—
520C2×C3×C4—23no—
521C2×C3×C4—21no—
522C2×C3×C4—23no—
523C2×C3×C4—23no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—33no—
529C2×C3×C4—33no—
530C2×C3×C4—31no—
531C2×C3×C4—66no—
532C2×C3×C4—66no—
533C2×C3×C4—123no—
534C2×C3×C4—126no—
535C2×C3×C4—123no—
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D313yes—
538C2×C3×C4C23×D313yes—
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D313yes—
541C2×C3×C4C23×D313yes—
542C2×C3×C4C24×C311yescharacteristic
543C2×C3×C4C24×C313yes—
544C2×C3×C4C24×C311yescharacteristic
545C2×C3×C4C24×C313yes—
546C2×C3×C4C24×C313yes—
547C2×C3×C4C24×C313yes—
548#67—43no—
549#67—43no—
550C2×Dic3C24×C311yescharacteristic
551C2×Dic3C24×C311yescharacteristic
552C2×Dic3C24×C311yescharacteristic
553C2×Dic3C24×C313yes—
554C2×Dic3C24×C313yes—
555C2×Dic3C24×C311yescharacteristic
556D12—26no—
557D12—26no—
558D12—46no—
559D12—43no—
560C4×D3—26no—
561C4×D3—26no—
562C4×D3—43no—
563C4×D3—43no—
564C4×D3—46no—
565Dic6—43no—
566C2×C32—41no—
567C2×C32C22×#4111yescharacteristic
568C2×C32#58511yescharacteristic
569C2×C32#58511yescharacteristic
570C3×D3—43no—
571C3×D3—43no—
572#41—64no—
573#41—64no—
574C2×Q8—24no—
575C2×Q8—33no—
576C2×Q8C22×C3×D313yes—
577C2×Q8C22×C3×D311yescharacteristic
578C2×D4—33no—
579C2×D4—33no—
580C2×D4—33no—
581C2×D4—33no—
582C2×D4—36no—
583C2×D4—33no—
584C22×C4—33no—
585C22×C4—33no—
586C22×C4—33no—
587C22×C4—33no—
588C22×C4—36no—
589C22×C4C22×C3×D313yes—
590C4⋊C4—33no—
591C4⋊C4—33no—
592C4⋊C4—31no—
593C4⋊C4—33no—
594C4⋊C4—33no—
595C4⋊C4—36no—
596C4⋊C4—31no—
597C4⋊C4—33no—
598C4⋊C4—33no—
599C4⋊C4—31no—
600C4⋊C4—33no—
601C4⋊C4C22×C3×D313yes—
602C4⋊C4C22×C3×D313yes—
603C4⋊C4C22×C3×D313yes—
604C4⋊C4C22×C3×D313yes—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—33no—
608C22⋊C4—33no—
609C22⋊C4—36no—
610C22⋊C4—33no—
611C22⋊C4—36no—
612C22⋊C4—33no—
613C22⋊C4—33no—
614C22⋊C4—36no—
615C22⋊C4—33no—
616C22⋊C4C22×C3×D311yescharacteristic
617C22⋊C4C22×C3×D313yes—
618C42—31no—
619C42—33no—
620C42—33no—
621C42—33no—
622C42C22×C3×D313yes—
623C42C22×C3×D316yes—
624C42C22×C3×D313yes—
625C22×C3—22no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—63no—
636C22×C3—63no—
637C22×C3—63no—
638C22×C3—63no—
639C22×C3—63no—
640C22×C3—63no—
641C22×C3C24×D311yescharacteristic
642C22×C3C25×C311yescharacteristic
643C2×D3—23no—
644C2×D3—23no—
645C2×D3—23no—
646C2×D3—23no—
647C2×D3—23no—
648C2×D3—23no—
649C3×C4—26no—
650C3×C4—23no—
651C3×C4—23no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—23no—
655C3×C4—23no—
656C3×C4—23no—
657C3×C4—21no—
658C3×C4—23no—
659C3×C4—21no—
660C3×C4—26no—
661C3×C4—43no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—43no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—63no—
669C3×C4—63no—
670C3×C4—61no—
671C3×C4C2×#23516yes—
672C3×C4C2×C3×#4116yes—
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—23no—
677Dic3—21no—
678Dic3—23no—
679C32#352411yescharacteristic, complemented, Sylow
680C23—33no—
681C23—33no—
682C23C23×C3×D311yescharacteristic
683Q8—26no—
684Q8—123no—
685Q8C3×#23514yes—
686D4—66no—
687D4—66no—
688D4—123no—
689D4—126no—
690D4—123no—
691D4—123no—
692C2×C4—26no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—33no—
697C2×C4—33no—
698C2×C4—31no—
699C2×C4—66no—
700C2×C4—66no—
701C2×C4—123no—
702C2×C4—126no—
703C2×C4—123no—
704C2×C4C23×C3×D311yescharacteristic
705C2×C4C23×C3×D313yes—
706C2×C4C23×C3×D313yes—
707C2×C4C23×C3×D311yescharacteristic
708C2×C4C23×C3×D313yes—
709C2×C4C23×C3×D313yes—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—42no—
714C2×C3—41no—
715C2×C3—41no—
716C2×C3—123no—
717C2×C3—123no—
718C2×C3C22×#23511yescharacteristic
719C2×C3#596811yescharacteristic
720C2×C3#596811yescharacteristic
721C2×C3C22×C3×#4111yescharacteristic
722C2×C3C3×#58511yescharacteristic
723C2×C3C3×#58511yescharacteristic
724D3—43no—
725D3—43no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—63no—
730C22—63no—
731C22—63no—
732C22—63no—
733C22—63no—
734C22—63no—
735C22C24×C3×D311yescharacteristic
736C4—23no—
737C4—23no—
738C4—21no—
739C4—21no—
740C4—23no—
741C4—61no—
742C4—61no—
743C4—61no—
744C4—63no—
745C4—63no—
746C4—61no—
747C4C2×C3×#23516yes—
748C3—21no—
749C3#8587911yescharacteristic, direct product factor
750C3C3×#352411yescharacteristic, complemented
751C2—41no—
752C2—123no—
753C2—123no—
754C2C22×C3×#23511yescharacteristic
755C2C3×#596811yescharacteristic
756C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#519C2
socleC22×C32C25
hypercenterC3×#519D3
hypocenterC3C3×#3524
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#519

Complements

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

NH ≅ G/Ntype
1. C32×#519C2semidirect
2. C3×#5817C2semidirect
3. C3×#5817C2semidirect
4. C3×#5585C2semidirect
5. C3×#5582C2semidirect
6. C3×#5581C2semidirect
7. C3×#5580C2semidirect
8. C3×#5577C2semidirect
9. C3×#5574C2semidirect
10. C3×C4×#239C2semidirect
11. C3×#5569C2semidirect
12. C3×#5535C2semidirect
13. C3×#5532C2semidirect
14. C3×#5530C2semidirect
15. C3×#5528C2semidirect
17. #85879C3direct (N × H)
82. C3×#519D3semidirect
83. C3×#519C2×C3semidirect
85. #5817C2×C3semidirect
86. #5817C2×C3semidirect
87. #5585C2×C3semidirect
88. #5582C2×C3semidirect
89. #5581C2×C3semidirect
90. #5580C2×C3semidirect
91. #5577C2×C3semidirect
92. #5574C2×C3semidirect
93. C4×#239C2×C3semidirect
94. #5569C2×C3semidirect
95. #5535C2×C3semidirect
96. #5532C2×C3semidirect
97. #5530C2×C3semidirect
98. #5528C2×C3semidirect
303. #519C3×D3semidirect
679. C32#3524semidirect
749. C3#85879direct (N × H)
750. C3C3×#3524semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
C3×#58172
C3×#55852
C3×#55822
C3×#55812
C3×#55802
C3×#55772
C3×#55742
C3×C4×#2392
C3×#55692
C3×#55352
C3×#55322
C3×#55302
C3×#55282
C3×#35243
#858793