Finite Group Databasebeta

← #11857062

Subgroups — #11857062

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592368C211yesmaximal, characteristic
2C3×#4654C211yesmaximal, characteristic, complemented
3C3×#4653C211yesmaximal, characteristic, complemented
4#10591289C211yesmaximal, characteristic
5#10591266C211yesmaximal, characteristic
6#10591266C211yesmaximal, characteristic
7#10591263C211yesmaximal, characteristic, complemented
8#10591262C211yesmaximal, characteristic, complemented
9#10591259C211yesmaximal, characteristic
10#10591258C211yesmaximal, characteristic
11#10591253C211yesmaximal, characteristic, complemented
12#10591251C211yesmaximal, characteristic, complemented
13C4×Dic32C211yesmaximal, characteristic, complemented
14#10591194C211yesmaximal, characteristic
15#10591192C211yesmaximal, characteristic, complemented
16#75294—31nomaximal
17#75294—31nomaximal
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×#3722C2211yescharacteristic
32C2×#3722C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C32×#95C2211yescharacteristic
40#63658C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×#387—31no—
54C3×#387—31no—
55#4990—31no—
56#4990—31no—
57#4990—31no—
58#4990—31no—
59#4980—31no—
60#4980—31no—
61#4978—31no—
62#4978—31no—
63#4940—31no—
64#4940—31no—
65C42×Dic3—31no—
66C42×Dic3—31no—
67#4670—31no—
68#4670—31no—
69#4670—31no—
70#4670—31no—
71#4669—31no—
72#4669—31no—
73#4669—31no—
74#4669—31no—
75#4669—61no—
76#4655—31no—
77#4655—31no—
78#4654—31no—
79#4654D311yescharacteristic, complemented
80#4653—31no—
81#4653D311yescharacteristic, complemented
82#4652—31no—
83#4652—31no—
84C23×C3⋊D3C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99#3752—22no—
100#3752—22no—
101#3752—22no—
102#3750—22no—
103C4×C3⋊Dic3—22no—
104C3×C4⋊Dic3—22no—
105C3×C4⋊Dic3—22no—
106C3×Dic3⋊C4—22no—
107C3×Dic3⋊C4—22no—
108C3×C4×Dic3—22no—
109C3×C4×Dic3—22no—
110Dic3⋊Dic3—22no—
111Dic3⋊Dic3—22no—
112#3722—22no—
113#3722—22no—
114#3722—22no—
115#3722—22no—
116Dic32—22no—
117Dic32—22no—
118Dic32—22no—
119Dic32—22no—
120#2866—91noSylow
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C42—31no—
126C2×C3×C42—31no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—31no—
132C2×(C2×D3)⋊C4—31no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—61no—
142C2×(C2×D3)⋊C4—61no—
143C2×(C2×D3)⋊C4—61no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—61no—
153C2×Dic3⋊C4C2×D311yescharacteristic
154C2×Dic3⋊C4C2×D311yescharacteristic
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—61no—
166C2×C4×Dic3C2×D311yescharacteristic
167C2×C4×Dic3C2×D311yescharacteristic
168C3×#95—21no—
169C3×#95—31no—
170C3×#95—31no—
171C3×#95—31no—
172C3×#95—31no—
173C3×#95—31no—
174C3×#95—31no—
175C3×#95C2×D311yescharacteristic
176C3×#95C2×D311yescharacteristic
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—61no—
192C3⋊#95C2×D311yescharacteristic
193C3⋊#95C2×D311yescharacteristic
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32C2411yescharacteristic
199C22×C3⋊D3—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4#4112yes—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3#4112yes—
223C2×C3⋊Dic3#4112yes—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3#4112yes—
245C2×C3×Dic3#4112yes—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248#388—91no—
249#388—91no—
250#388—91no—
251#388—91no—
252#388—91no—
253#388—91no—
254#388—91no—
255#387—31no—
256#387—31no—
257#387—91no—
258#387—91no—
259#387—91no—
260#387—91no—
261#387—91no—
262C43—91no—
263C23×D3—31no—
264C23×D3—31no—
265C23×D3—61no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C3×C4⋊C4—62no—
301C3×C4⋊C4—62no—
302C3×C4⋊C4—62no—
303C3×C4⋊C4—62no—
304C3×C42—62no—
305C3×C42—62no—
306(C2×D3)⋊C4—62no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—62no—
309(C2×D3)⋊C4—62no—
310(C2×D3)⋊C4—62no—
311(C2×D3)⋊C4—62no—
312(C2×D3)⋊C4—62no—
313(C2×D3)⋊C4—62no—
314(C2×D3)⋊C4—64no—
315(C2×D3)⋊C4—62no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—62no—
318(C2×D3)⋊C4—62no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—62no—
321(C2×D3)⋊C4—122no—
322(C2×D3)⋊C4—122no—
323C4⋊Dic3—22no—
324C4⋊Dic3—22no—
325C4⋊Dic3—62no—
326C4⋊Dic3—62no—
327Dic3⋊C4—22no—
328Dic3⋊C4—22no—
329Dic3⋊C4—62no—
330Dic3⋊C4—62no—
331Dic3⋊C4—62no—
332Dic3⋊C4—62no—
333Dic3⋊C4—122no—
334C4×Dic3—22no—
335C4×Dic3—22no—
336C4×Dic3—62no—
337C4×Dic3—62no—
338C4×Dic3—62no—
339C4×Dic3—62no—
340C4×Dic3—62no—
341C4×Dic3—62no—
342C4×Dic3—62no—
343C4×Dic3—62no—
344C4×Dic3—62no—
345C4×Dic3—62no—
346C4×Dic3—122no—
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4111yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32C2×#4111yescharacteristic
353C22×C32C2×#4111yescharacteristic
354C2×C3⋊D3—41no—
355C2×C3⋊D3—41no—
356C2×C3⋊D3—41no—
357C2×C3⋊D3—41no—
358C2×C3⋊D3—41no—
359C2×C3⋊D3—41no—
360C2×C3⋊D3—41no—
361C32×C4—22no—
362C32×C4—41no—
363C32×C4—41no—
364C3⋊Dic3—22no—
365C3⋊Dic3—22no—
366C3⋊Dic3—41no—
367C3×Dic3—22no—
368C3×Dic3—22no—
369C3×Dic3—22no—
370C3×Dic3—22no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—91no—
380C2×C4⋊C4—91no—
381C2×C4⋊C4—91no—
382C2×C22⋊C4—91no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—91no—
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C42—31no—
390C2×C42—31no—
391C2×C42—91no—
392C2×C42—91no—
393C2×C42—91no—
394C2×C42—91no—
395C2×C42—91no—
396#95—31no—
397#95—31no—
398#95—31no—
399#95—31no—
400#95—31no—
401#95—31no—
402#95—91no—
403#95—91no—
404#95—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95D3211yescharacteristic
410C23×C3—21no—
411C23×C3C23×D311yescharacteristic
412C23×C3C23×D311yescharacteristic
413C22×D3—62no—
414C22×D3—61no—
415C22×D3—61no—
416C22×D3—61no—
417C22×D3—61no—
418C22×D3—61no—
419C22×D3—61no—
420C22×D3—61no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—61no—
427C22×D3—61no—
428C22×D3—121no—
429C22×D3—121no—
430C22×D3—121no—
431C22×D3—121no—
432C22×D3—121no—
433C22×D3—121no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4#23712yes—
484C2×C3×C4#23912yes—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—32no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—62no—
510C2×Dic3—62no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—62no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3#23512yes—
533C2×Dic3#23512yes—
534C2×Dic3#23712yes—
535C2×Dic3#23912yes—
536C2×C32#52911yescharacteristic
537C2×C32#52911yescharacteristic
538C2×C32#52911yescharacteristic
539C2×C32#52911yescharacteristic
540C2×C32#52911yescharacteristic
541C2×C32#52911yescharacteristic
542C2×C32#52911yescharacteristic
543C3⋊D3—81no—
544C24—91no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—91no—
554C22×C4—91no—
555C22×C4—91no—
556C22×C4C2×D3211yescharacteristic
557C22×C4C2×D3211yescharacteristic
558C22×C4C2×D3211yescharacteristic
559C4⋊C4—62no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—62no—
563C4⋊C4—182no—
564C4⋊C4—182no—
565C4⋊C4—182no—
566C22⋊C4—182no—
567C22⋊C4—182no—
568C22⋊C4—182no—
569C22⋊C4—182no—
570C22⋊C4—182no—
571C22⋊C4—182no—
572C22⋊C4—182no—
573C42—62no—
574C42—62no—
575C42—182no—
576C42—182no—
577C42—182no—
578C42—182no—
579C42—182no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3C2×#23511yescharacteristic
588C22×C3C2×#23511yescharacteristic
589C22×C3C2×#23711yescharacteristic
590C22×C3C2×#23711yescharacteristic
591C22×C3C2×#23911yescharacteristic
592C22×C3C2×#23911yescharacteristic
593C22×C3D3×#4111yescharacteristic
594C22×C3D3×#4111yescharacteristic
595C22×C3D3×#4111yescharacteristic
596C22×C3D3×#4111yescharacteristic
597C22×C3D3×#4111yescharacteristic
598C22×C3D3×#4111yescharacteristic
599C22×C3D3×#4111yescharacteristic
600C22×C3D3×#4111yescharacteristic
601C2×D3—122no—
602C2×D3—122no—
603C2×D3—122no—
604C2×D3—121no—
605C2×D3—121no—
606C2×D3—121no—
607C2×D3—121no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—121no—
615C2×D3—121no—
616C2×D3—121no—
617C2×D3—121no—
618C2×D3—241no—
619C2×D3—241no—
620C2×D3—241no—
621C2×D3—241no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—81no—
634C3×C4—81no—
635C3×C4—121no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4—121no—
639Dic3—22no—
640Dic3—22no—
641Dic3—22no—
642Dic3—22no—
643Dic3—41no—
644Dic3—41no—
645Dic3—41no—
646Dic3—41no—
647Dic3—62no—
648Dic3—62no—
649Dic3—62no—
650Dic3—62no—
651Dic3—122no—
652Dic3—122no—
653Dic3—122no—
654Dic3—121no—
655Dic3—121no—
656C32#286611yescharacteristic, complemented, Sylow
657C23—181no—
658C23—181no—
659C23—181no—
660C23—181no—
661C23—181no—
662C23—181no—
663C23—181no—
664C23C22×D3211yescharacteristic
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—32no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—92no—
698C2×C4—92no—
699C2×C4—181no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4#379612yes—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3#552811yescharacteristic
715C2×C3#552811yescharacteristic
716C2×C3#553811yescharacteristic
717C2×C3#553811yescharacteristic
718C2×C3#558011yescharacteristic
719C2×C3#558011yescharacteristic
720C2×C3#562411yescharacteristic
721C2×C3#562411yescharacteristic
722C2×C3#564911yescharacteristic
723C2×C3#564911yescharacteristic
724C2×C3#569111yescharacteristic
725C2×C3#569111yescharacteristic
726C2×C3#570611yescharacteristic
727C2×C3#570611yescharacteristic
728D3—242no—
729D3—241no—
730D3—241no—
731C22—361no—
732C22—361no—
733C22—361no—
734C22—361no—
735C22—361no—
736C22—361no—
737C22—361no—
738C22C2×#379611yescharacteristic
739C22D3×#23511yescharacteristic
740C22D3×#23511yescharacteristic
741C22D3×#23711yescharacteristic
742C22#6431211yescharacteristic
743C22#6431211yescharacteristic
744C22D3×#23911yescharacteristic
745C4—22no—
746C4—41no—
747C4—41no—
748C4—62no—
749C4—62no—
750C4—62no—
751C4—62no—
752C4—121no—
753C4—121no—
754C4—121no—
755C4—121no—
756C4—182no—
757C4—182no—
758C4—361no—
759C3—21no—
760C3#7529411yescharacteristic, complemented
761C3#7529411yescharacteristic, complemented
762C2—721no—
763C2#1059391111yescharacteristic
764C2#1059408811yescharacteristic
765C2#1059410611yescharacteristic
766C2#1059414411yescharacteristic
767C2#1059440311yescharacteristic
768C2#1059442311yescharacteristic
769C2#1059445311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2866
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#4654C2semidirect
3. C3×#4653C2semidirect
7. #10591263C2semidirect
8. #10591262C2semidirect
11. #10591253C2semidirect
12. #10591251C2semidirect
13. C4×Dic32C2semidirect
15. #10591192C2semidirect
79. #4654D3semidirect
81. #4653D3semidirect
656. C32#2866semidirect
760. C3#75294semidirect
761. C3#75294semidirect

Maximal subgroups

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

subgroupindex
#105923682
C3×#46542
C3×#46532
#105912892
#105912662
#105912632
#105912622
#105912592
#105912582
#105912532
#105912512
C4×Dic322
#105911942
#105911922
#752943