Finite Group Databasebeta

← C3×#85898 #11909975

Subgroups — C3×#85898 #11909975

Order 1152.

2207 conjugacy classes of subgroups.

The subgroup lattice has 759 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#520C211yesmaximal, characteristic, complemented
2C3×#5834C211yesmaximal, characteristic, complemented
3C3×#5831C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C3×C4×#239C211yesmaximal, characteristic, complemented
6C3×#5572C211yesmaximal, characteristic, complemented
7C3×#5570C211yesmaximal, characteristic, complemented
8C3×#5563C213yesmaximal, complemented
9C3×#5562C213yesmaximal, complemented
10C3×#5559C213yesmaximal, complemented
11C3×#5557C213yesmaximal, complemented
12C3×#5534C213yesmaximal, complemented
13C3×#5528C213yesmaximal, complemented
14C3×#5514C213yesmaximal, complemented
15C3×#5513C213yesmaximal, complemented
16C3×#3524—31nomaximal
17#85898C311yesmaximal, 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×C4⋊C4C2213yes—
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×#940C2213yes—
30C3×#938C2213yes—
31C3×#938C2213yes—
32C3×#936C2213yes—
33C3×#930C2213yes—
34C3×#930C2216yes—
35C3×#929C2216yes—
36C3×C4×#67C2213yes—
37C3×C4×#67C2213yes—
38C3×C4×#67C2216yes—
39C3×#926C2216yes—
40C3×#924C2213yes—
41C3×#898C2216yes—
42C3×#898C2211yescharacteristic
43C3×#897C2213yes—
44C3×#896C2213yes—
45C3×#895C2213yes—
46C3×#894C2213yes—
47C3×#893C2213yes—
48C3×#892C2213yes—
49C3×#892C2213yes—
50C3×#890C2213yes—
51C3×#890C2213yes—
52C3×#889C2213yes—
53C3×#887C2213yes—
54C3×#885C2213yes—
55C3×#885C2216yes—
56C3×#884C2213yes—
57C3×#883C2213yes—
58C3×#883C2216yes—
59C3×#879C2213yes—
60C3×#875C2213yes—
61C3×C4×D12C2213yes—
62C3×C4×D12C2213yes—
63C3×#872C2213yes—
64C3×C42×D3C2213yes—
65C3×#869C2213yes—
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—21no—
81C3×#520D311yescharacteristic, complemented
82C3×#520C2×C311yescharacteristic, complemented
83C3×#519—31no—
84C3×C4×#41—31no—
85#5834C2×C311yescharacteristic, complemented
86#5831C2×C311yescharacteristic, complemented
87#5576C2×C311yescharacteristic, complemented
88C4×#239C2×C311yescharacteristic, complemented
89#5572C2×C311yescharacteristic, complemented
90#5570C2×C311yescharacteristic, complemented
91#5563C2×C313yescomplemented
92#5562C2×C313yescomplemented
93#5559C2×C313yescomplemented
94#5557C2×C313yescomplemented
95#5534C2×C313yescomplemented
96#5528C2×C313yescomplemented
97#5514C2×C313yescomplemented
98#5513C2×C313yescomplemented
99C32×#41—24no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2313yes—
102C22×C32×C4C2313yes—
103C22×C32×C4C2316yes—
104C2×C3×#67C2313yes—
105C2×C3×#67C2316yes—
106C2×C3×#67C2313yes—
107C3×#239—24no—
108C3×D3×Q8—24no—
109C2×C3×D12C2313yes—
110C2×C3×D12C2313yes—
111C2×C3×C4×D3C2313yes—
112C2×C3×C4×D3C2313yes—
113C2×C3×C4×D3C2313yes—
114C2×C3×C4×D3C2313yes—
115C2×C3×Dic6C2313yes—
116C2×C3×Dic6C2313yes—
117C32×C4⋊C4C2313yes—
118C32×C4⋊C4C2313yes—
119C32×C4⋊C4C2313yes—
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4C2313yes—
122C32×C22⋊C4C2313yes—
123C32×C42C2313yes—
124C32×C42C2313yes—
125C3×#217C2313yes—
126C3×#217C2313yes—
127C3×#217C2316yes—
128C3×(C2×D3)⋊C4C2313yes—
129C3×(C2×D3)⋊C4C2316yes—
130C3×(C2×D3)⋊C4C2311yescharacteristic
131C3×(C2×D3)⋊C4C2311yescharacteristic
132C3×(C2×D3)⋊C4C2313yes—
133C3×(C2×D3)⋊C4C2316yes—
134C3×(C2×D3)⋊C4C2311yescharacteristic
135C3×(C2×D3)⋊C4C2313yes—
136C3×C4⋊Dic3C2313yes—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2316yes—
139C3×C4⋊Dic3C2313yes—
140C3×C4⋊Dic3C2313yes—
141C3×Dic3⋊C4C2313yes—
142C3×Dic3⋊C4C2313yes—
143C3×Dic3⋊C4C2313yes—
144C3×Dic3⋊C4C2313yes—
145C3×Dic3⋊C4C2311yescharacteristic
146C3×Dic3⋊C4C2313yes—
147C3×C4×Dic3C2311yescharacteristic
148C3×C4×Dic3C2316yes—
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—31no—
158C2×#239C22×C311yescharacteristic
159C2×D3×Q8C22×C311yescharacteristic
160C3×C4⋊Q8—33no—
161C3×#127—33no—
162C3×#126—31no—
163C3×#126—36no—
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—36no—
173C3×#123—33no—
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—36no—
182C3×#121—33no—
183C3×#121—33no—
184C3×#121—33no—
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—36no—
210C3×#117—33no—
211C3×#117—33no—
212C3×#117—33no—
213C3×#117C2×D313yes—
214C3×#117C22×C313yes—
215C2×C3×C4⋊C4—23no—
216C2×C3×C4⋊C4C2×D313yes—
217C2×C3×C4⋊C4C22×C313yes—
218C2×C3×C42—33no—
219Q8×Dic3C22×C311yescharacteristic
220Q8×Dic3C22×C311yescharacteristic
221#940C22×C313yes—
222#938C22×C313yes—
223#938C22×C313yes—
224#936C22×C313yes—
225#930C22×C313yes—
226#930C22×C316yes—
227#929C22×C316yes—
228C4×#67C22×C313yes—
229C4×#67C22×C313yes—
230C4×#67C22×C316yes—
231#926C22×C316yes—
232#924C22×C313yes—
233#898C22×C316yes—
234#898C22×C311yescharacteristic
235#897C22×C313yes—
236#896C22×C313yes—
237#895C22×C313yes—
238#894C22×C313yes—
239#893C22×C313yes—
240#892C22×C313yes—
241#892C22×C313yes—
242#890C22×C313yes—
243#890C22×C313yes—
244#889C22×C313yes—
245#887C22×C313yes—
246#885C22×C313yes—
247#885C22×C316yes—
248#884C22×C313yes—
249#883C22×C313yes—
250#883C22×C316yes—
251#879C22×C313yes—
252#875C22×C313yes—
253C4×D12C22×C313yes—
254C4×D12C22×C313yes—
255#872C22×C313yes—
256C42×D3C22×C313yes—
257#869C22×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—46no—
267C2×C32×C4C2413yes—
268C2×C32×C4C2411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C32×C4C2413yes—
271C2×C32×C4C2411yescharacteristic
272C2×C32×C4C2413yes—
273C3×#67—43no—
274C3×#67—46no—
275C3×#67—43no—
276C2×C3×Dic3C2411yescharacteristic
277C2×C3×Dic3C2411yescharacteristic
278C2×C3×Dic3C2411yescharacteristic
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2413yes—
281C2×C3×Dic3C2413yes—
282C3×D12—26no—
283C3×D12—43no—
284C3×C4×D3—26no—
285C3×C4×D3—26no—
286C3×C4×D3—43no—
287C3×C4×D3—43no—
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#520C3×D311yescharacteristic, complemented
303#519—31no—
304C4×#41—31no—
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—26no—
325C22×C3×C4—33no—
326C22×C3×C4—33no—
327C22×C3×C4—33no—
328C22×C3×C4—33no—
329C22×C3×C4C22×D313yes—
330C22×C3×C4C22×D316yes—
331C22×C3×C4C23×C313yes—
332C22×C3×C4C23×C316yes—
333C2×#67C23×C313yes—
334C2×#67C23×C316yes—
335C2×#67C23×C313yes—
336#239—24no—
337D3×Q8—24no—
338C2×D12C23×C313yes—
339C2×D12C23×C313yes—
340C2×C4×D3C23×C313yes—
341C2×C4×D3C23×C313yes—
342C2×C4×D3C23×C313yes—
343C2×C4×D3C23×C313yes—
344C2×Dic6C23×C313yes—
345C2×Dic6C23×C313yes—
346C3×C4⋊C4—23no—
347C3×C4⋊C4—23no—
348C3×C4⋊C4—23no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—33no—
351C3×C4⋊C4—33no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—33no—
354C3×C4⋊C4—33no—
355C3×C4⋊C4—33no—
356C3×C4⋊C4—33no—
357C3×C4⋊C4—33no—
358C3×C4⋊C4—33no—
359C3×C4⋊C4—36no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4C22×D313yes—
362C3×C4⋊C4C22×D313yes—
363C3×C4⋊C4C22×D313yes—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C23×C313yes—
366C3×C4⋊C4C23×C313yes—
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—31no—
375C3×C22⋊C4—33no—
376C3×C22⋊C4—36no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—33no—
380C3×C22⋊C4—36no—
381C3×C22⋊C4—33no—
382C3×C22⋊C4C22×D313yes—
383C3×C22⋊C4C22×D313yes—
384C3×C22⋊C4C23×C313yes—
385C3×C22⋊C4C23×C313yes—
386C3×C42—23no—
387C3×C42—23no—
388C3×C42—31no—
389C3×C42—33no—
390C3×C42—33no—
391C3×C42—36no—
392C3×C42—33no—
393C3×C42C22×D313yes—
394C3×C42C22×D313yes—
395C3×C42C23×C313yes—
396C3×C42C23×C313yes—
397#217C23×C313yes—
398#217C23×C313yes—
399#217C23×C316yes—
400(C2×D3)⋊C4C23×C311yescharacteristic
401(C2×D3)⋊C4C23×C313yes—
402(C2×D3)⋊C4C23×C311yescharacteristic
403(C2×D3)⋊C4C23×C313yes—
404(C2×D3)⋊C4C23×C316yes—
405(C2×D3)⋊C4C23×C316yes—
406(C2×D3)⋊C4C23×C311yescharacteristic
407(C2×D3)⋊C4C23×C313yes—
408C4⋊Dic3C23×C311yescharacteristic
409C4⋊Dic3C23×C313yes—
410C4⋊Dic3C23×C313yes—
411C4⋊Dic3C23×C316yes—
412C4⋊Dic3C23×C313yes—
413Dic3⋊C4C23×C313yes—
414Dic3⋊C4C23×C313yes—
415Dic3⋊C4C23×C313yes—
416Dic3⋊C4C23×C313yes—
417Dic3⋊C4C23×C311yescharacteristic
418Dic3⋊C4C23×C313yes—
419C4×Dic3C23×C313yes—
420C4×Dic3C23×C313yes—
421C4×Dic3C23×C316yes—
422C4×Dic3C23×C311yescharacteristic
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—23no—
432C2×C3×D3—21no—
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—23no—
443C3×Dic3—23no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C2×#41—31no—
447C2×#41C2×C3×D311yescharacteristic
448C22×Q8—31no—
449C4⋊Q8—33no—
450#127—33no—
451#126—31no—
452#126—36no—
453#126—33no—
454#125—33no—
455#125—33no—
456#125—33no—
457#124—33no—
458#124—33no—
459#124—36no—
460#124—33no—
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—36no—
471#121—33no—
472#121—33no—
473#121—33no—
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—36no—
490#117—33no—
491#117—33no—
492#117—33no—
493#117C2×C3×D313yes—
494C2×C4⋊C4C2×C3×D313yes—
495C2×C42—33no—
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—23no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—23no—
524C2×C3×C4—23no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—33no—
528C2×C3×C4—31no—
529C2×C3×C4—33no—
530C2×C3×C4—33no—
531C2×C3×C4—46no—
532C2×C3×C4—46no—
533C2×C3×C4—66no—
534C2×C3×C4—66no—
535C2×C3×C4—86no—
536C2×C3×C4—123no—
537C2×C3×C4—123no—
538C2×C3×C4C23×D313yes—
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C23×D313yes—
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D313yes—
544C2×C3×C4C24×C313yes—
545C2×C3×C4C24×C311yescharacteristic
546C2×C3×C4C24×C311yescharacteristic
547C2×C3×C4C24×C313yes—
548C2×C3×C4C24×C311yescharacteristic
549C2×C3×C4C24×C313yes—
550#67—43no—
551#67—46no—
552#67—43no—
553C2×Dic3C24×C311yescharacteristic
554C2×Dic3C24×C311yescharacteristic
555C2×Dic3C24×C311yescharacteristic
556C2×Dic3C24×C313yes—
557C2×Dic3C24×C313yes—
558C2×Dic3C24×C313yes—
559D12—26no—
560D12—43no—
561C4×D3—26no—
562C4×D3—26no—
563C4×D3—43no—
564C4×D3—43no—
565Dic6—26no—
566Dic6—43no—
567C2×C32—43no—
568C2×C32C22×#4111yescharacteristic
569C2×C32#58511yescharacteristic
570C2×C32#58511yescharacteristic
571C3×D3—41no—
572C3×D3—43no—
573#41—24no—
574#41—64no—
575C2×Q8—33no—
576C2×Q8—33no—
577C2×Q8—64no—
578C2×Q8C22×C3×D311yescharacteristic
579C2×D4—33no—
580C2×D4—36no—
581C2×D4—33no—
582C2×D4—33no—
583C2×D4—33no—
584C2×D4C22×C3×D313yes—
585C22×C4—33no—
586C22×C4—33no—
587C22×C4—33no—
588C22×C4—33no—
589C22×C4C22×C3×D313yes—
590C22×C4C22×C3×D316yes—
591C4⋊C4—33no—
592C4⋊C4—33no—
593C4⋊C4—33no—
594C4⋊C4—33no—
595C4⋊C4—33no—
596C4⋊C4—36no—
597C4⋊C4—31no—
598C4⋊C4—33no—
599C4⋊C4—33no—
600C4⋊C4—31no—
601C4⋊C4—33no—
602C4⋊C4C22×C3×D313yes—
603C4⋊C4C22×C3×D313yes—
604C4⋊C4C22×C3×D313yes—
605C4⋊C4C22×C3×D311yescharacteristic
606C22⋊C4—33no—
607C22⋊C4—36no—
608C22⋊C4—33no—
609C22⋊C4—31no—
610C22⋊C4—33no—
611C22⋊C4—36no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—33no—
615C22⋊C4—36no—
616C22⋊C4—33no—
617C22⋊C4C22×C3×D313yes—
618C22⋊C4C22×C3×D313yes—
619C42—31no—
620C42—33no—
621C42—33no—
622C42—36no—
623C42—33no—
624C42C22×C3×D313yes—
625C42C22×C3×D313yes—
626C22×C3—26no—
627C22×C3—23no—
628C22×C3—23no—
629C22×C3—23no—
630C22×C3—23no—
631C22×C3—23no—
632C22×C3—23no—
633C22×C3—21no—
634C22×C3—43no—
635C22×C3—43no—
636C22×C3—61no—
637C22×C3—63no—
638C22×C3—63no—
639C22×C3—61no—
640C22×C3—63no—
641C22×C3—61no—
642C22×C3C24×D311yescharacteristic
643C22×C3C25×C311yescharacteristic
644C2×D3—21no—
645C2×D3—23no—
646C2×D3—23no—
647C2×D3—23no—
648C2×D3—21no—
649C2×D3—21no—
650C3×C4—22no—
651C3×C4—21no—
652C3×C4—23no—
653C3×C4—23no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—23no—
660C3×C4—23no—
661C3×C4—26no—
662C3×C4—43no—
663C3×C4—43no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—63no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—63no—
671C3×C4—63no—
672C3×C4C2×#23516yes—
673C3×C4C2×C3×#4116yes—
674Dic3—23no—
675Dic3—21no—
676Dic3—23no—
677Dic3—23no—
678Dic3—21no—
679Dic3—21no—
680C32#352411yescharacteristic, complemented, Sylow
681C23—31no—
682C23—33no—
683C23C23×C3×D313yes—
684Q8—66no—
685Q8—123no—
686Q8C3×#23514yes—
687D4—26no—
688D4—66no—
689D4—123no—
690D4—123no—
691D4—123no—
692D4—126no—
693C2×C4—26no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—33no—
697C2×C4—31no—
698C2×C4—33no—
699C2×C4—33no—
700C2×C4—46no—
701C2×C4—66no—
702C2×C4—66no—
703C2×C4—123no—
704C2×C4—123no—
705C2×C4C23×C3×D313yes—
706C2×C4C23×C3×D311yescharacteristic
707C2×C4C23×C3×D311yescharacteristic
708C2×C4C23×C3×D313yes—
709C2×C4C23×C3×D311yescharacteristic
710C2×C4C23×C3×D313yes—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—46no—
715C2×C3—43no—
716C2×C3—43no—
717C2×C3—121no—
718C2×C3—123no—
719C2×C3C22×#23511yescharacteristic
720C2×C3#596611yescharacteristic
721C2×C3#596811yescharacteristic
722C2×C3C22×C3×#4111yescharacteristic
723C2×C3C3×#58511yescharacteristic
724C2×C3C3×#58511yescharacteristic
725D3—41no—
726D3—43no—
727C22—23no—
728C22—23no—
729C22—23no—
730C22—61no—
731C22—63no—
732C22—63no—
733C22—61no—
734C22—63no—
735C22—61no—
736C22C24×C3×D311yescharacteristic
737C4—21no—
738C4—23no—
739C4—23no—
740C4—21no—
741C4—21no—
742C4—61no—
743C4—63no—
744C4—61no—
745C4—61no—
746C4—63no—
747C4—63no—
748C4C2×C3×#23516yes—
749C3—21no—
750C3#8589811yescharacteristic, direct product factor
751C3C3×#352411yescharacteristic, complemented
752C2—43no—
753C2—121no—
754C2—123no—
755C2C22×C3×#23511yescharacteristic
756C2C3×#596611yescharacteristic
757C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#520C2
socleC22×C32C25
hypercenterC3×#520D3
hypocenterC3C3×#3524
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#520

Complements

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

NH ≅ G/Ntype
1. C32×#520C2semidirect
2. C3×#5834C2semidirect
3. C3×#5831C2semidirect
4. C3×#5576C2semidirect
5. C3×C4×#239C2semidirect
6. C3×#5572C2semidirect
7. C3×#5570C2semidirect
8. C3×#5563C2semidirect
9. C3×#5562C2semidirect
10. C3×#5559C2semidirect
11. C3×#5557C2semidirect
12. C3×#5534C2semidirect
13. C3×#5528C2semidirect
14. C3×#5514C2semidirect
15. C3×#5513C2semidirect
17. #85898C3direct (N × H)
81. C3×#520D3semidirect
82. C3×#520C2×C3semidirect
85. #5834C2×C3semidirect
86. #5831C2×C3semidirect
87. #5576C2×C3semidirect
88. C4×#239C2×C3semidirect
89. #5572C2×C3semidirect
90. #5570C2×C3semidirect
91. #5563C2×C3semidirect
92. #5562C2×C3semidirect
93. #5559C2×C3semidirect
94. #5557C2×C3semidirect
95. #5534C2×C3semidirect
96. #5528C2×C3semidirect
97. #5514C2×C3semidirect
98. #5513C2×C3semidirect
302. #520C3×D3semidirect
680. C32#3524semidirect
750. C3#85898direct (N × H)
751. C3C3×#3524semidirect

Maximal subgroups

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

subgroupindex
C32×#5202
C3×#58342
C3×#58312
C3×#55762
C3×C4×#2392
C3×#55722
C3×#55702
C3×#55632
C3×#55622
C3×#55592
C3×#55572
C3×#55342
C3×#55282
C3×#55142
C3×#55132
C3×#35243
#858983