Finite Group Databasebeta

← #11808898

Subgroups — #11808898

Order 1152.

953 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592347C211yesmaximal, characteristic, complemented
2C3×#4675C211yesmaximal, characteristic
3C3×#4658C211yesmaximal, characteristic, complemented
4#10591368C211yesmaximal, characteristic
5#10591368C211yesmaximal, characteristic
6#10591368C211yesmaximal, characteristic
7#10591306C211yesmaximal, characteristic
8#10591301C211yesmaximal, characteristic
9#10591296C211yesmaximal, characteristic
10#10591241C211yesmaximal, characteristic, complemented
11#10591241C211yesmaximal, characteristic, complemented
12#10591241C211yesmaximal, characteristic, complemented
13#10591228C211yesmaximal, characteristic, complemented
14#10591207C211yesmaximal, characteristic, complemented
15#10591196C211yesmaximal, characteristic, complemented
16#78132—31nomaximal
17#77461—31nomaximal
18C22×D3×Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×Dic32C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C32×#95C2211yescharacteristic
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
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×#400—31no—
54C3×#397—31no—
55#4994—31no—
56#4992—31no—
57#4985—31no—
58Dic3×C4⋊C4—31no—
59Dic3×C4⋊C4—31no—
60Dic3×C4⋊C4—31no—
61#4952—31no—
62#4952—31no—
63#4948—31no—
64Dic3×C22⋊C4—31no—
65Dic3×C22⋊C4—31no—
66Dic3×C22⋊C4—31no—
67#4675D311yescharacteristic
68#4674—31no—
69#4666—31no—
70#4666—31no—
71#4666—31no—
72C3⋊#401—31no—
73C3⋊#401—31no—
74#4660—31no—
75#4660—31no—
76#4659—31no—
77#4658D311yescharacteristic, complemented
78#4649—31no—
79#4649—31no—
80#4649—31no—
81#4648—31no—
82#4648—31no—
83#4648—61no—
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
99C2×D3×Dic3—22no—
100C2×D3×Dic3—22no—
101C2×D3×Dic3—22no—
102C4×C3⋊Dic3—22no—
103C4×C3⋊Dic3—22no—
104C4×C3⋊Dic3—22no—
105C3×(C2×D3)⋊C4—22no—
106C3×(C2×D3)⋊C4—22no—
107C3×(C2×D3)⋊C4—22no—
108C3×Dic3⋊C4—22no—
109C3×Dic3⋊C4—22no—
110C3×Dic3⋊C4—22no—
111Dic3⋊Dic3—22no—
112Dic3⋊Dic3—22no—
113Dic3⋊Dic3—22no—
114(C2×D3)⋊Dic3—22no—
115(C2×D3)⋊Dic3—22no—
116(C2×D3)⋊Dic3—22no—
117Dic32—22no—
118Dic32—22no—
119Dic32—22no—
120#2401—91noSylow
121C23×Dic3—31no—
122C22×C4×D3—31no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C22⋊C4—31no—
128C2×C3×C22⋊C4—31no—
129C2×#217—31no—
130C2×#217—31no—
131C2×#217—31no—
132C2×(C2×D3)⋊C4—31no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4C2×D311yescharacteristic
136C2×(C2×D3)⋊C4C2×D311yescharacteristic
137C2×(C2×D3)⋊C4C2×D311yescharacteristic
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—31no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4C2×D311yescharacteristic
145C2×Dic3⋊C4C2×D311yescharacteristic
146C2×Dic3⋊C4C2×D311yescharacteristic
147C2×C4×Dic3—31no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—61no—
160C2×C4×Dic3—61no—
161C2×C4×Dic3—61no—
162C3×#95—21no—
163C3×#95—31no—
164C3×#95—31no—
165C3×#95—31no—
166C3×#95—31no—
167C3×#95—31no—
168C3×#95—31no—
169C3×#95C2×D311yescharacteristic
170C3×#95C2×D311yescharacteristic
171C3⋊#95—31no—
172C3⋊#95—31no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
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—61no—
190C3⋊#95—61no—
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#4112yes—
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—21no—
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—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3#4112yes—
225C2×C3⋊Dic3#4112yes—
226C2×C3⋊Dic3#4112yes—
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—21no—
245C2×C3×Dic3#4112yes—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248D3×Dic3—44no—
249#401—91no—
250#400—31no—
251#400—91no—
252#400—91no—
253#397—31no—
254#397—91no—
255#397—91no—
256#396—91no—
257C4×C4⋊C4—91no—
258C4×C4⋊C4—91no—
259C4×C4⋊C4—91no—
260C4×C22⋊C4—91no—
261C4×C22⋊C4—91no—
262C4×C22⋊C4—91no—
263#376—91no—
264C24×C3—31no—
265C23×D3C22×D311yescharacteristic
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×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—62no—
295C22×Dic3—62no—
296C22×Dic3—62no—
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C2×C4×D3—62no—
305C2×C4×D3—62no—
306C2×C4×D3—62no—
307C3×C4⋊C4—62no—
308C3×C4⋊C4—62no—
309C3×C4⋊C4—62no—
310C3×C22⋊C4—62no—
311C3×C22⋊C4—62no—
312C3×C22⋊C4—62no—
313#217—62no—
314#217—62no—
315#217—62no—
316(C2×D3)⋊C4—22no—
317(C2×D3)⋊C4—22no—
318(C2×D3)⋊C4—22no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—62no—
321(C2×D3)⋊C4—62no—
322C4⋊Dic3—62no—
323C4⋊Dic3—62no—
324C4⋊Dic3—62no—
325Dic3⋊C4—22no—
326Dic3⋊C4—22no—
327Dic3⋊C4—22no—
328Dic3⋊C4—62no—
329Dic3⋊C4—62no—
330Dic3⋊C4—62no—
331C4×Dic3—62no—
332C4×Dic3—62no—
333C4×Dic3—62no—
334C4×Dic3—62no—
335C4×Dic3—62no—
336C4×Dic3—62no—
337C4×Dic3—62no—
338C4×Dic3—62no—
339C4×Dic3—62no—
340C4×Dic3—62no—
341C4×Dic3—62no—
342C4×Dic3—62no—
343C4×Dic3—64no—
344C4×Dic3—64no—
345C4×Dic3—64no—
346C22×C32C2×#4111yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4111yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32C2×#4111yescharacteristic
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—22no—
356C2×C3×D3—41no—
357C2×C3×D3—41no—
358C2×C3×D3—41no—
359C2×C3×D3—41no—
360C32×C4—41no—
361C32×C4—41no—
362C32×C4—41no—
363C3⋊Dic3—41no—
364C3⋊Dic3—41no—
365C3⋊Dic3—41no—
366C3⋊Dic3#12614yes—
367C3×Dic3—22no—
368C3×Dic3—22no—
369C3×Dic3—22no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C23×C4—91no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—91no—
379C2×C4⋊C4—91no—
380C2×C4⋊C4—91no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—91no—
387C2×C42—91no—
388C2×C42—91no—
389C2×C42—91no—
390C2×C42—91no—
391C2×C42—91no—
392C2×C42—91no—
393#95—31no—
394#95—31no—
395#95—31no—
396#95—31no—
397#95—31no—
398#95—31no—
399#95—91no—
400#95—91no—
401#95—91no—
402#95—91no—
403#95—91no—
404#95—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95D3211yescharacteristic
409C23×C3—21no—
410C23×C3—32no—
411C23×C3—61no—
412C23×C3—61no—
413C23×C3—61no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—61no—
417C23×C3C23×D311yescharacteristic
418C23×C3C23×D311yescharacteristic
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3#23712yes—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
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—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
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×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—32no—
493C2×Dic3—32no—
494C2×Dic3—32no—
495C2×Dic3—32no—
496C2×Dic3—32no—
497C2×Dic3—32no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
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—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—124no—
529C2×Dic3#23712yes—
530C2×Dic3#23712yes—
531C2×Dic3#23912yes—
532C4×D3—124no—
533C2×C32C2×#12611yescharacteristic
534C2×C32#52911yescharacteristic
535C2×C32#52911yescharacteristic
536C2×C32#52911yescharacteristic
537C2×C32#52911yescharacteristic
538C2×C32#52911yescharacteristic
539C2×C32#52911yescharacteristic
540C3×D3—42no—
541C24—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—91no—
550C22×C4—91no—
551C22×C4—91no—
552C22×C4—91no—
553C22×C4—182no—
554C22×C4—182no—
555C22×C4—182no—
556C22×C4C2×D3211yescharacteristic
557C22×C4C2×D3211yescharacteristic
558C22×C4C2×D3211yescharacteristic
559C4⋊C4—62no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—182no—
563C4⋊C4—182no—
564C4⋊C4—182no—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4—62no—
568C22⋊C4—182no—
569C22⋊C4—182no—
570C22⋊C4—182no—
571C42—182no—
572C42—182no—
573C42—182no—
574C42—182no—
575C42—182no—
576C42—182no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—62no—
585C22×C3—62no—
586C22×C3—62no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3C2×#23711yescharacteristic
592C22×C3C2×#23711yescharacteristic
593C22×C3C2×#23711yescharacteristic
594C22×C3C2×#23911yescharacteristic
595C22×C3D3×#4111yescharacteristic
596C22×C3D3×#4111yescharacteristic
597C22×C3D3×#4111yescharacteristic
598C22×C3D3×#4111yescharacteristic
599C22×C3D3×#4111yescharacteristic
600C22×C3D3×#4111yescharacteristic
601C22×C3D3×#4111yescharacteristic
602C22×C3D3×#4111yescharacteristic
603C22×C3D3×#4111yescharacteristic
604C22×C3D3×#4111yescharacteristic
605C2×D3—22no—
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—62no—
622C3×C4—62no—
623C3×C4—62no—
624C3×C4—121no—
625C3×C4—121no—
626C3×C4—121no—
627C3×C4—121no—
628Dic3—22no—
629Dic3—22no—
630Dic3—22no—
631Dic3—34no—
632Dic3—34no—
633Dic3—41no—
634Dic3—41no—
635Dic3—41no—
636Dic3—41no—
637Dic3—64no—
638Dic3—122no—
639Dic3—122no—
640Dic3—122no—
641Dic3—121no—
642Dic3—121no—
643Dic3—121no—
644Dic3—121no—
645Dic3—121no—
646Dic3—121no—
647C32#240111yescharacteristic, complemented, Sylow
648C23—32no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23C22×D3211yescharacteristic
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
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—92no—
687C2×C4—92no—
688C2×C4—92no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4—364no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—122no—
707C2×C3#560011yescharacteristic
708C2×C3#562411yescharacteristic
709C2×C3#564911yescharacteristic
710C2×C3#564911yescharacteristic
711C2×C3#564911yescharacteristic
712C2×C3#564911yescharacteristic
713C2×C3#568011yescharacteristic
714C2×C3#568011yescharacteristic
715C2×C3#569111yescharacteristic
716C2×C3#569111yescharacteristic
717C2×C3D3×#12611yescharacteristic
718C2×C3D3×#12611yescharacteristic
719C2×C3#570611yescharacteristic
720C2×C3#570611yescharacteristic
721D3—42no—
722C22—62no—
723C22—62no—
724C22—62no—
725C22—121no—
726C22—121no—
727C22—121no—
728C22—121no—
729C22#6430611yescharacteristic
730C22#6430611yescharacteristic
731C22#6430611yescharacteristic
732C22D3×#23711yescharacteristic
733C22D3×#23711yescharacteristic
734C22D3×#23711yescharacteristic
735C22D3×#23911yescharacteristic
736C4—41no—
737C4—41no—
738C4—41no—
739C4—62no—
740C4—62no—
741C4—62no—
742C4—94no—
743C4—121no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4—361no—
748C4—361no—
749C4—361no—
750C3—21no—
751C3#7746111yescharacteristic, complemented
752C3#7813211yescharacteristic, complemented
753C2—122no—
754C2#1059402011yescharacteristic
755C2#1059411111yescharacteristic
756C2#1059411111yescharacteristic
757C2#1059411211yescharacteristic
758C2#1059444111yescharacteristic
759C2#1059444111yescharacteristic
760C2#1059444211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #10592347C2semidirect
3. C3×#4658C2semidirect
10. #10591241C2semidirect
11. #10591241C2semidirect
12. #10591241C2semidirect
13. #10591228C2semidirect
14. #10591207C2semidirect
15. #10591196C2semidirect
77. #4658D3semidirect
647. C32#2401semidirect
751. C3#77461semidirect
752. C3#78132semidirect

Maximal subgroups

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

subgroupindex
#105923472
C3×#46752
C3×#46582
#105913682
#105913062
#105913012
#105912962
#105912412
#105912282
#105912072
#105911962
#781323
#774613