Finite Group Databasebeta

← C3×#87026 #11910008

Subgroups — C3×#87026 #11910008

Order 1152.

2160 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2C3×#5734C213yesmaximal, complemented
3C3×#5733C213yesmaximal, complemented
4C3×#5697C213yesmaximal, complemented
5C3×#5695C213yesmaximal, complemented
6C3×#5694C213yesmaximal, complemented
7C3×#5691C213yesmaximal, complemented
8C3×#5585C213yesmaximal, complemented
9C3×#5580C213yesmaximal, complemented
10C3×#5577C211yesmaximal, characteristic, complemented
11C3×#5576C211yesmaximal, characteristic, complemented
12C3×#5576C211yesmaximal, characteristic, complemented
13C3×#5574C211yesmaximal, characteristic, complemented
14C3×C4×#239C211yesmaximal, characteristic, complemented
15C3×#5572C211yesmaximal, characteristic, complemented
16C3×#3524—31nomaximal
17#87026C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C32×C4⋊Q8C2213yes—
22C32×#125C2213yes—
23C32×#125C2213yes—
24C32×C4×Q8C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C32×C4×Q8C2211yescharacteristic
27C32×C4×Q8C2213yes—
28C3×#947C2213yes—
29C3×#947C2216yes—
30C3×#946C2213yes—
31C3×Q8×Dic3C2211yescharacteristic
32C3×#898C2211yescharacteristic
33C3×#898C2213yes—
34C3×#898C2216yes—
35C3×#897C2213yes—
36C3×#897C2213yes—
37C3×#895C2213yes—
38C3×#895C2213yes—
39C3×#895C2213yes—
40C3×#895C2213yes—
41C3×#895C2213yes—
42C3×#895C2216yes—
43C3×#894C2213yes—
44C3×#894C2213yes—
45C3×#894C2216yes—
46C3×#894C2216yes—
47C3×#893C2213yes—
48C3×#893C2213yes—
49C3×#893C2216yes—
50C3×#892C2213yes—
51C3×#892C2213yes—
52C3×#892C2216yes—
53C3×D3×C4⋊C4C2213yes—
54C3×#890C2213yes—
55C3×#887C2213yes—
56C3×#875C2213yes—
57C3×#875C2213yes—
58C3×#874C2213yes—
59C3×C4×D12C2213yes—
60C3×C4×D12C2213yes—
61C3×C4×D12C2213yes—
62C3×C4×D12C2213yes—
63C3×C4×D12C2213yes—
64C3×#872C2213yes—
65C3×#872C2213yes—
66C3×C42×D3C2213yes—
67C3×C4×Dic6C2213yes—
68C3×#559—33no—
69C3×#557—21no—
70C3×#557D311yescharacteristic, complemented
71C3×#557C2×C311yescharacteristic, complemented
72C3×#555—33no—
73C3×#553—33no—
74C3×#552—33no—
75C3×#550—31no—
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#5734C2×C313yescomplemented
86#5733C2×C313yescomplemented
87#5697C2×C313yescomplemented
88#5695C2×C313yescomplemented
89#5694C2×C313yescomplemented
90#5691C2×C313yescomplemented
91#5585C2×C313yescomplemented
92#5580C2×C313yescomplemented
93#5577C2×C311yescharacteristic, complemented
94#5576C2×C311yescharacteristic, complemented
95#5576C2×C311yescharacteristic, complemented
96#5574C2×C311yescharacteristic, complemented
97C4×#239C2×C311yescharacteristic, complemented
98#5572C2×C311yescharacteristic, complemented
99C2×C32×Q8C2313yes—
100C2×C32×Q8C2311yescharacteristic
101C3×#239—24no—
102C3×#239—24no—
103C3×D3×Q8—24no—
104C2×C3×D12C2313yes—
105C2×C3×D12C2313yes—
106C2×C3×D12C2316yes—
107C2×C3×D12C2313yes—
108C2×C3×D12C2313yes—
109C2×C3×D12C2313yes—
110C2×C3×C4×D3C2313yes—
111C2×C3×C4×D3C2313yes—
112C2×C3×C4×D3C2313yes—
113C2×C3×C4×D3C2316yes—
114C2×C3×C4×D3C2313yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×Dic6C2313yes—
117C32×C4⋊C4C2313yes—
118C32×C4⋊C4C2313yes—
119C32×C4⋊C4C2313yes—
120C32×C4⋊C4C2313yes—
121C32×C4⋊C4C2316yes—
122C32×C4⋊C4C2313yes—
123C32×C4⋊C4C2311yescharacteristic
124C32×C42C2313yes—
125C32×C42C2313yes—
126C32×C42C2313yes—
127C3×(C2×D3)⋊C4C2313yes—
128C3×(C2×D3)⋊C4C2313yes—
129C3×(C2×D3)⋊C4C2316yes—
130C3×(C2×D3)⋊C4C2316yes—
131C3×(C2×D3)⋊C4C2313yes—
132C3×(C2×D3)⋊C4C2313yes—
133C3×(C2×D3)⋊C4C2316yes—
134C3×(C2×D3)⋊C4C2311yescharacteristic
135C3×(C2×D3)⋊C4C2313yes—
136C3×(C2×D3)⋊C4C2313yes—
137C3×(C2×D3)⋊C4C2313yes—
138C3×(C2×D3)⋊C4C2311yescharacteristic
139C3×(C2×D3)⋊C4C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2313yes—
142C3×C4⋊Dic3C2313yes—
143C3×C4⋊Dic3C2313yes—
144C3×Dic3⋊C4C2313yes—
145C3×Dic3⋊C4C2313yes—
146C3×Dic3⋊C4C2313yes—
147C3×Dic3⋊C4C2311yescharacteristic
148C3×C4×Dic3C2316yes—
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2311yescharacteristic
152#3524—31noSylow
153C2×C3×#41—31no—
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C2×#239C22×C311yescharacteristic
157C2×#239C22×C311yescharacteristic
158C2×D3×Q8C22×C311yescharacteristic
159C3×C4⋊Q8—23no—
160C3×C4⋊Q8C2×D313yes—
161C3×C4⋊Q8C22×C313yes—
162C3×#127—33no—
163C3×#126—31no—
164C3×#126—33no—
165C3×#126—36no—
166C3×#125—23no—
167C3×#125—23no—
168C3×#125—33no—
169C3×#125C2×D313yes—
170C3×#125C2×D313yes—
171C3×#125C22×C313yes—
172C3×#125C22×C313yes—
173C3×#124—36no—
174C3×#124—33no—
175C3×#124—33no—
176C3×#124—33no—
177C3×#123—33no—
178C3×#123—36no—
179C3×#123—36no—
180C3×#123—33no—
181C3×C22⋊Q8—33no—
182C3×C22⋊Q8—33no—
183C3×C22⋊Q8—33no—
184C3×#121—33no—
185C3×#121—33no—
186C3×#121—33no—
187C3×#121—33no—
188C3×#121—36no—
189C3×#121—33no—
190C3×C4×Q8—21no—
191C3×C4×Q8—21no—
192C3×C4×Q8—21no—
193C3×C4×Q8—23no—
194C3×C4×Q8—31no—
195C3×C4×Q8—33no—
196C3×C4×Q8—33no—
197C3×C4×Q8C2×D313yes—
198C3×C4×Q8C2×D311yescharacteristic
199C3×C4×Q8C2×D311yescharacteristic
200C3×C4×Q8C2×D311yescharacteristic
201C3×C4×Q8C22×C311yescharacteristic
202C3×C4×Q8C22×C311yescharacteristic
203C3×C4×Q8C22×C311yescharacteristic
204C3×C4×Q8C22×C313yes—
205C3×C4×D4—36no—
206C3×C4×D4—33no—
207C3×C4×D4—33no—
208C3×C4×D4—33no—
209C3×C4×D4—33no—
210C3×C4×D4—33no—
211C3×C4×D4—33no—
212C3×C4×D4—33no—
213C3×#117—33no—
214C3×#117—33no—
215C3×#117—36no—
216C3×#117—33no—
217C3×#117—33no—
218C2×C3×C4⋊C4—33no—
219C2×C3×C42—33no—
220#947C22×C316yes—
221#947C22×C313yes—
222#946C22×C313yes—
223Q8×Dic3C22×C311yescharacteristic
224#898C22×C313yes—
225#898C22×C316yes—
226#898C22×C311yescharacteristic
227#897C22×C313yes—
228#897C22×C313yes—
229#895C22×C313yes—
230#895C22×C316yes—
231#895C22×C313yes—
232#895C22×C313yes—
233#895C22×C313yes—
234#895C22×C313yes—
235#894C22×C316yes—
236#894C22×C316yes—
237#894C22×C313yes—
238#894C22×C313yes—
239#893C22×C316yes—
240#893C22×C313yes—
241#893C22×C313yes—
242#892C22×C316yes—
243#892C22×C313yes—
244#892C22×C313yes—
245D3×C4⋊C4C22×C313yes—
246#890C22×C313yes—
247#887C22×C313yes—
248#875C22×C313yes—
249#875C22×C313yes—
250#874C22×C313yes—
251C4×D12C22×C313yes—
252C4×D12C22×C313yes—
253C4×D12C22×C313yes—
254C4×D12C22×C313yes—
255C4×D12C22×C313yes—
256#872C22×C313yes—
257#872C22×C313yes—
258C42×D3C22×C313yes—
259C4×Dic6C22×C313yes—
260C22×C3×D3C2411yescharacteristic
261C22×C3×D3C2413yes—
262C22×C3×D3C2413yes—
263C32×Q8—43no—
264C32×Q8#4114yes—
265C2×C32×C4C2413yes—
266C2×C32×C4C2413yes—
267C2×C32×C4C2411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C2×C32×C4C2413yes—
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2413yes—
272C2×C3×Dic3C2411yescharacteristic
273C2×C3×Dic3C2413yes—
274C2×C3×Dic3C2411yescharacteristic
275C2×C3×Dic3C2413yes—
276C2×C3×Dic3C2411yescharacteristic
277C3×D12—26no—
278C3×D12—26no—
279C3×D12—43no—
280C3×D12—43no—
281C3×D12—43no—
282C3×D12—46no—
283C3×C4×D3—26no—
284C3×C4×D3—26no—
285C3×C4×D3—26no—
286C3×C4×D3—43no—
287C3×C4×D3—46no—
288C3×C4×D3—43no—
289C3×Dic6—26no—
290#559—33no—
291#557C3×D311yescharacteristic, complemented
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×#41—31no—
305C3×#41—64no—
306C3×#41—64no—
307C2×C3×Q8—21no—
308C2×C3×Q8—23no—
309C2×C3×Q8—33no—
310C2×C3×Q8—64no—
311C2×C3×Q8C22×D313yes—
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×Q8C23×C313yes—
314C2×C3×Q8C23×C311yescharacteristic
315C2×C3×D4—33no—
316C2×C3×D4—33no—
317C2×C3×D4—33no—
318C2×C3×D4—33no—
319C2×C3×D4—36no—
320C2×C3×D4—33no—
321C22×C3×C4—33no—
322C22×C3×C4—33no—
323C22×C3×C4—33no—
324C22×C3×C4—33no—
325C22×C3×C4—33no—
326C22×C3×C4—36no—
327#239—24no—
328#239—24no—
329D3×Q8—24no—
330C2×D12C23×C313yes—
331C2×D12C23×C313yes—
332C2×D12C23×C313yes—
333C2×D12C23×C313yes—
334C2×D12C23×C313yes—
335C2×D12C23×C316yes—
336C2×C4×D3C23×C313yes—
337C2×C4×D3C23×C313yes—
338C2×C4×D3C23×C313yes—
339C2×C4×D3C23×C313yes—
340C2×C4×D3C23×C313yes—
341C2×C4×D3C23×C316yes—
342C2×Dic6C23×C313yes—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—23no—
345C3×C4⋊C4—23no—
346C3×C4⋊C4—23no—
347C3×C4⋊C4—23no—
348C3×C4⋊C4—23no—
349C3×C4⋊C4—26no—
350C3×C4⋊C4—33no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—33no—
353C3×C4⋊C4—33no—
354C3×C4⋊C4—33no—
355C3×C4⋊C4—33no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—33no—
358C3×C4⋊C4C22×D313yes—
359C3×C4⋊C4C22×D313yes—
360C3×C4⋊C4C22×D313yes—
361C3×C4⋊C4C22×D316yes—
362C3×C4⋊C4C22×D313yes—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D313yes—
365C3×C4⋊C4C23×C313yes—
366C3×C4⋊C4C23×C313yes—
367C3×C4⋊C4C23×C313yes—
368C3×C4⋊C4C23×C313yes—
369C3×C4⋊C4C23×C316yes—
370C3×C4⋊C4C23×C313yes—
371C3×C4⋊C4C23×C311yescharacteristic
372C3×C22⋊C4—31no—
373C3×C22⋊C4—33no—
374C3×C22⋊C4—33no—
375C3×C22⋊C4—33no—
376C3×C22⋊C4—36no—
377C3×C22⋊C4—33no—
378C3×C22⋊C4—36no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—33no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—33no—
383C3×C22⋊C4—36no—
384C3×C22⋊C4—33no—
385C3×C42—23no—
386C3×C42—23no—
387C3×C42—23no—
388C3×C42—31no—
389C3×C42—33no—
390C3×C42—33no—
391C3×C42—36no—
392C3×C42C22×D313yes—
393C3×C42C22×D313yes—
394C3×C42C22×D313yes—
395C3×C42C23×C313yes—
396C3×C42C23×C313yes—
397C3×C42C23×C313yes—
398(C2×D3)⋊C4C23×C311yescharacteristic
399(C2×D3)⋊C4C23×C313yes—
400(C2×D3)⋊C4C23×C313yes—
401(C2×D3)⋊C4C23×C313yes—
402(C2×D3)⋊C4C23×C311yescharacteristic
403(C2×D3)⋊C4C23×C311yescharacteristic
404(C2×D3)⋊C4C23×C313yes—
405(C2×D3)⋊C4C23×C313yes—
406(C2×D3)⋊C4C23×C313yes—
407(C2×D3)⋊C4C23×C316yes—
408(C2×D3)⋊C4C23×C313yes—
409(C2×D3)⋊C4C23×C316yes—
410(C2×D3)⋊C4C23×C316yes—
411C4⋊Dic3C23×C313yes—
412C4⋊Dic3C23×C311yescharacteristic
413C4⋊Dic3C23×C313yes—
414C4⋊Dic3C23×C313yes—
415Dic3⋊C4C23×C313yes—
416Dic3⋊C4C23×C311yescharacteristic
417Dic3⋊C4C23×C313yes—
418Dic3⋊C4C23×C313yes—
419C4×Dic3C23×C316yes—
420C4×Dic3C23×C311yescharacteristic
421C4×Dic3C23×C313yes—
422C4×Dic3C23×C313yes—
423C22×C32C2511yescharacteristic
424C2×C3×D3—21no—
425C2×C3×D3—23no—
426C2×C3×D3—23no—
427C2×C3×D3—23no—
428C2×C3×D3—23no—
429C2×C3×D3—23no—
430C2×C3×D3—21no—
431C2×C3×D3—23no—
432C2×C3×D3—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—23no—
436C32×C4—23no—
437C32×C4—21no—
438C32×C4—23no—
439C32×C4C2×#4116yes—
440C3×Dic3—23no—
441C3×Dic3—21no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—23no—
445C2×#41—31no—
446C2×#41—31no—
447C22×Q8—31no—
448C4⋊Q8C2×C3×D313yes—
449#127—33no—
450#126—31no—
451#126—33no—
452#126—36no—
453#125—33no—
454#125C2×C3×D313yes—
455#125C2×C3×D313yes—
456#124—33no—
457#124—36no—
458#124—33no—
459#124—33no—
460#123—36no—
461#123—33no—
462#123—33no—
463#123—36no—
464C22⋊Q8—33no—
465C22⋊Q8—33no—
466C22⋊Q8—33no—
467#121—33no—
468#121—33no—
469#121—33no—
470#121—33no—
471#121—36no—
472#121—33no—
473C4×Q8—31no—
474C4×Q8—33no—
475C4×Q8—33no—
476C4×Q8C2×C3×D311yescharacteristic
477C4×Q8C2×C3×D311yescharacteristic
478C4×Q8C2×C3×D311yescharacteristic
479C4×Q8C2×C3×D313yes—
480C4×D4—33no—
481C4×D4—33no—
482C4×D4—36no—
483C4×D4—33no—
484C4×D4—33no—
485C4×D4—33no—
486C4×D4—33no—
487C4×D4—33no—
488#117—33no—
489#117—33no—
490#117—36no—
491#117—33no—
492#117—33no—
493C2×C4⋊C4—33no—
494C2×C42—33no—
495C23×C3—31no—
496C23×C3—33no—
497C23×C3—33no—
498C22×D3C24×C311yescharacteristic
499C22×D3C24×C313yes—
500C22×D3C24×C313yes—
501C3×Q8—24no—
502C3×Q8—43no—
503C3×Q8—43no—
504C3×Q8—46no—
505C3×Q8—66no—
506C3×Q8#23914yes—
507C3×Q8C3×#4114yes—
508C3×D4—66no—
509C3×D4—66no—
510C3×D4—123no—
511C3×D4—126no—
512C3×D4—123no—
513C3×D4—123no—
514C2×C3×C4—23no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—23no—
519C2×C3×C4—23no—
520C2×C3×C4—23no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—33no—
524C2×C3×C4—33no—
525C2×C3×C4—31no—
526C2×C3×C4—66no—
527C2×C3×C4—66no—
528C2×C3×C4—66no—
529C2×C3×C4—123no—
530C2×C3×C4—123no—
531C2×C3×C4—126no—
532C2×C3×C4C23×D313yes—
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D313yes—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D313yes—
538C2×C3×C4C23×D313yes—
539C2×C3×C4C24×C313yes—
540C2×C3×C4C24×C313yes—
541C2×C3×C4C24×C311yescharacteristic
542C2×C3×C4C24×C311yescharacteristic
543C2×C3×C4C24×C313yes—
544C2×C3×C4C24×C311yescharacteristic
545C2×C3×C4C24×C313yes—
546C2×Dic3C24×C311yescharacteristic
547C2×Dic3C24×C313yes—
548C2×Dic3C24×C311yescharacteristic
549C2×Dic3C24×C313yes—
550C2×Dic3C24×C311yescharacteristic
551D12—26no—
552D12—26no—
553D12—43no—
554D12—43no—
555D12—43no—
556D12—46no—
557C4×D3—26no—
558C4×D3—26no—
559C4×D3—26no—
560C4×D3—43no—
561C4×D3—46no—
562C4×D3—43no—
563Dic6—26no—
564C2×C32C22×#4111yescharacteristic
565C2×C32#58511yescharacteristic
566C2×C32#58511yescharacteristic
567C3×D3—41no—
568C3×D3—43no—
569C3×D3—43no—
570#41—64no—
571#41—64no—
572C2×Q8—33no—
573C2×Q8—64no—
574C2×Q8C22×C3×D313yes—
575C2×Q8C22×C3×D311yescharacteristic
576C2×D4—33no—
577C2×D4—33no—
578C2×D4—33no—
579C2×D4—33no—
580C2×D4—36no—
581C2×D4—33no—
582C22×C4—33no—
583C22×C4—33no—
584C22×C4—33no—
585C22×C4—33no—
586C22×C4—33no—
587C22×C4—36no—
588C4⋊C4—33no—
589C4⋊C4—33no—
590C4⋊C4—31no—
591C4⋊C4—33no—
592C4⋊C4—33no—
593C4⋊C4—33no—
594C4⋊C4—31no—
595C4⋊C4—33no—
596C4⋊C4C22×C3×D313yes—
597C4⋊C4C22×C3×D313yes—
598C4⋊C4C22×C3×D313yes—
599C4⋊C4C22×C3×D316yes—
600C4⋊C4C22×C3×D313yes—
601C4⋊C4C22×C3×D311yescharacteristic
602C4⋊C4C22×C3×D313yes—
603C22⋊C4—31no—
604C22⋊C4—33no—
605C22⋊C4—33no—
606C22⋊C4—33no—
607C22⋊C4—36no—
608C22⋊C4—33no—
609C22⋊C4—36no—
610C22⋊C4—31no—
611C22⋊C4—33no—
612C22⋊C4—31no—
613C22⋊C4—33no—
614C22⋊C4—36no—
615C22⋊C4—33no—
616C42—31no—
617C42—33no—
618C42—33no—
619C42—36no—
620C42C22×C3×D313yes—
621C42C22×C3×D313yes—
622C42C22×C3×D313yes—
623C22×C3—21no—
624C22×C3—61no—
625C22×C3—63no—
626C22×C3—63no—
627C22×C3—63no—
628C22×C3—61no—
629C22×C3—63no—
630C22×C3—63no—
631C22×C3—63no—
632C22×C3—61no—
633C22×C3C24×D311yescharacteristic
634C22×C3C25×C311yescharacteristic
635C2×D3—21no—
636C2×D3—23no—
637C2×D3—23no—
638C2×D3—23no—
639C2×D3—23no—
640C2×D3—23no—
641C2×D3—21no—
642C2×D3—23no—
643C2×D3—21no—
644C3×C4—22no—
645C3×C4—23no—
646C3×C4—23no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—23no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—23no—
653C3×C4—23no—
654C3×C4—21no—
655C3×C4—23no—
656C3×C4—21no—
657C3×C4—26no—
658C3×C4—43no—
659C3×C4—43no—
660C3×C4—41no—
661C3×C4—43no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—63no—
666C3×C4—61no—
667C3×C4—63no—
668C3×C4C2×#23916yes—
669C3×C4C2×C3×#4116yes—
670Dic3—23no—
671Dic3—21no—
672Dic3—21no—
673Dic3—21no—
674Dic3—23no—
675C32#352411yescharacteristic, complemented, Sylow
676C23—31no—
677C23—33no—
678C23—33no—
679Q8—43no—
680Q8—66no—
681Q8C3×#23914yes—
682D4—66no—
683D4—66no—
684D4—123no—
685D4—126no—
686D4—123no—
687D4—123no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—33no—
691C2×C4—33no—
692C2×C4—31no—
693C2×C4—66no—
694C2×C4—66no—
695C2×C4—66no—
696C2×C4—123no—
697C2×C4—123no—
698C2×C4—126no—
699C2×C4C23×C3×D313yes—
700C2×C4C23×C3×D311yescharacteristic
701C2×C4C23×C3×D313yes—
702C2×C4C23×C3×D311yescharacteristic
703C2×C4C23×C3×D311yescharacteristic
704C2×C4C23×C3×D313yes—
705C2×C4C23×C3×D313yes—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—121no—
710C2×C3—123no—
711C2×C3—123no—
712C2×C3C22×#23911yescharacteristic
713C2×C3#596411yescharacteristic
714C2×C3#596811yescharacteristic
715C2×C3C22×C3×#4111yescharacteristic
716C2×C3C3×#58511yescharacteristic
717C2×C3C3×#58511yescharacteristic
718D3—41no—
719D3—43no—
720D3—43no—
721C22—61no—
722C22—63no—
723C22—63no—
724C22—63no—
725C22—61no—
726C22—63no—
727C22—63no—
728C22—63no—
729C22—61no—
730C22C24×C3×D311yescharacteristic
731C4—23no—
732C4—23no—
733C4—21no—
734C4—21no—
735C4—23no—
736C4—21no—
737C4—61no—
738C4—61no—
739C4—63no—
740C4—61no—
741C4—63no—
742C4C2×C3×#23916yes—
743C3—21no—
744C3#8702611yescharacteristic, direct product factor
745C3C3×#352411yescharacteristic, complemented
746C2—121no—
747C2—123no—
748C2—123no—
749C2C22×C3×#23911yescharacteristic
750C2C3×#596411yescharacteristic
751C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#557C2
socleC22×C32C25
hypercenterC3×#557D3
hypocenterC3C3×#3524
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
2. C3×#5734C2semidirect
3. C3×#5733C2semidirect
4. C3×#5697C2semidirect
5. C3×#5695C2semidirect
6. C3×#5694C2semidirect
7. C3×#5691C2semidirect
8. C3×#5585C2semidirect
9. C3×#5580C2semidirect
10. C3×#5577C2semidirect
11. C3×#5576C2semidirect
12. C3×#5576C2semidirect
13. C3×#5574C2semidirect
14. C3×C4×#239C2semidirect
15. C3×#5572C2semidirect
17. #87026C3direct (N × H)
70. C3×#557D3semidirect
71. C3×#557C2×C3semidirect
85. #5734C2×C3semidirect
86. #5733C2×C3semidirect
87. #5697C2×C3semidirect
88. #5695C2×C3semidirect
89. #5694C2×C3semidirect
90. #5691C2×C3semidirect
91. #5585C2×C3semidirect
92. #5580C2×C3semidirect
93. #5577C2×C3semidirect
94. #5576C2×C3semidirect
95. #5576C2×C3semidirect
96. #5574C2×C3semidirect
97. C4×#239C2×C3semidirect
98. #5572C2×C3semidirect
291. #557C3×D3semidirect
675. C32#3524semidirect
744. C3#87026direct (N × H)
745. C3C3×#3524semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
C3×#57342
C3×#57332
C3×#56972
C3×#56952
C3×#56942
C3×#56912
C3×#55852
C3×#55802
C3×#55772
C3×#55762
C3×#55742
C3×C4×#2392
C3×#55722
C3×#35243
#870263