Finite Group Databasebeta

← #28312838

Subgroups — #28312838

Order 13568.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811574C211yesmaximal, characteristic
2C2×#16811572C211yesmaximal, characteristic
3C2×C4⋊C4×#6157C211yesmaximal, characteristic
4C2×C4×C4⋊#6157C211yesmaximal, characteristic
5#20289895C211yesmaximal, characteristic
6#20289895C211yesmaximal, characteristic
7#20289895C211yesmaximal, characteristic
8#20289895C211yesmaximal, characteristic
9#20289895C211yesmaximal, characteristic
10#20289894C211yesmaximal, characteristic
11C4×(C2×#6157)⋊C4C211yesmaximal, characteristic
12#95×#6157C211yesmaximal, characteristic
13#95×#6157C211yesmaximal, characteristic
14#95×#6157C211yesmaximal, characteristic
15#387×D53C211yesmaximal, characteristic
16C22×C4⋊#6157C2211yescharacteristic
17C22×C4⋊#6157C2211yescharacteristic
18C22×C4⋊#6157C2211yescharacteristic
19C22×C4⋊#6157C2211yescharacteristic
20C22×C4×#6157C2211yescharacteristic
21C22×C4×#6157C2211yescharacteristic
22C22×C4×#6157C2211yescharacteristic
23C22×C4×#6157C2211yescharacteristic
24C22×C4×#6157C2211yescharacteristic
25C22×C4×#6157C2211yescharacteristic
26C22×C4×#6157C2211yescharacteristic
27C22×C4×#6157C2211yescharacteristic
28#16811574C418yescomplemented
29#16811572C418yescomplemented
30C4⋊C4×#6157—24no—
31C4×C4⋊#6157—24no—
32C2×(C2×#6157)⋊C4C2211yescharacteristic
33C2×(C2×#6157)⋊C4C2211yescharacteristic
34C2×(C2×#6157)⋊C4C2211yescharacteristic
35C2×(C2×#6157)⋊C4C2211yescharacteristic
36C2×(C2×#6157)⋊C4C2211yescharacteristic
37C2×(C2×#6157)⋊C4C2211yescharacteristic
38C2×(C2×#6157)⋊C4C2211yescharacteristic
39C2×(C2×#6157)⋊C4C2211yescharacteristic
40C2×(C2×#6157)⋊C4C2211yescharacteristic
41C2×(C2×#6157)⋊C4C2211yescharacteristic
42C2×(C2×#6157)⋊C4C2211yescharacteristic
43C2×(C2×#6157)⋊C4C2211yescharacteristic
44C2×(C2×#6157)⋊C4C2211yescharacteristic
45C2×(C2×#6157)⋊C4C2211yescharacteristic
46C2×(C2×#6157)⋊C4C2211yescharacteristic
47C2×(C2×#6157)⋊C4C2211yescharacteristic
48C2×C4⋊C4×D53C2211yescharacteristic
49C2×C4⋊C4×D53C2211yescharacteristic
50C2×C42×D53C2211yescharacteristic
51#16810510C411yescharacteristic, complemented
52#16810509C411yescharacteristic, complemented
53#16810508C411yescharacteristic, complemented
54#16810507C411yescharacteristic, complemented
55#16810506C411yescharacteristic, complemented
56#16810505C411yescharacteristic, complemented
57#16810504C411yescharacteristic, complemented
58#95×D53C2211yescharacteristic
59#95×D53C2211yescharacteristic
60#95×D53C2211yescharacteristic
61#95×D53C2211yescharacteristic
62C53×#387C411yescharacteristic, complemented
63C23×#6157C2311yescharacteristic
64C23×#6157C2311yescharacteristic
65C23×#6157C2311yescharacteristic
66C23×#6157C2311yescharacteristic
67C23×#6157C2311yescharacteristic
68C23×#6157C2311yescharacteristic
69C23×#6157C2311yescharacteristic
70C23×#6157C2311yescharacteristic
71C2×C4⋊#6157—22no—
72C2×C4⋊#6157—22no—
73C2×C4⋊#6157—22no—
74C2×C4⋊#6157—22no—
75C2×C4⋊#6157—22no—
76C2×C4⋊#6157—22no—
77C2×C4⋊#6157—41no—
78C2×C4⋊#6157—41no—
79C2×C4⋊#6157C2×C414yes—
80C2×C4⋊#6157C2×C414yes—
81C2×C4⋊#6157C2×C414yes—
82C2×C4⋊#6157C2×C414yes—
83C2×C4×#6157—22no—
84C2×C4×#6157—22no—
85C2×C4×#6157—22no—
86C2×C4×#6157—22no—
87C2×C4×#6157—22no—
88C2×C4×#6157—22no—
89C2×C4×#6157—22no—
90C2×C4×#6157—22no—
91C2×C4×#6157—22no—
92C2×C4×#6157—22no—
93C2×C4×#6157—22no—
94C2×C4×#6157—22no—
95C2×C4×#6157—22no—
96C2×C4×#6157—22no—
97C2×C4×#6157—41no—
98C2×C4×#6157—41no—
99C2×C4×#6157—41no—
100C2×C4×#6157—41no—
101C2×C4×#6157—41no—
102C2×C4×#6157—41no—
103C2×C4×#6157—41no—
104C2×C4×#6157—41no—
105C2×C4×#6157C2×C414yes—
106C2×C4×#6157C2×C414yes—
107(C2×#6157)⋊C4—22no—
108(C2×#6157)⋊C4—22no—
109(C2×#6157)⋊C4—22no—
110(C2×#6157)⋊C4—22no—
111(C2×#6157)⋊C4—22no—
112(C2×#6157)⋊C4—22no—
113(C2×#6157)⋊C4—41no—
114(C2×#6157)⋊C4—41no—
115(C2×#6157)⋊C4C2×C414yes—
116(C2×#6157)⋊C4C2×C414yes—
117(C2×#6157)⋊C4C2×C414yes—
118(C2×#6157)⋊C4C2×C414yes—
119(C2×#6157)⋊C4C2×C414yes—
120(C2×#6157)⋊C4C2×C414yes—
121(C2×#6157)⋊C4D414yes—
122(C2×#6157)⋊C4Q814yes—
123C22×C4×D53C2311yescharacteristic
124C22×C4×D53C2311yescharacteristic
125C22×C4×D53C2311yescharacteristic
126C22×C4×D53C2311yescharacteristic
127C22×C4×D53C2311yescharacteristic
128C22×C4×D53C2311yescharacteristic
129C22×C4×D53C2311yescharacteristic
130C2×C4⋊Dic53C2×C411yescharacteristic
131C2×C4⋊Dic53C2×C411yescharacteristic
132C2×#11719919C2×C411yescharacteristic
133C2×#11719919C2×C411yescharacteristic
134C2×#11719919C2×C411yescharacteristic
135C2×#11719919C2×C411yescharacteristic
136C4⋊C4×D53—22no—
137C4⋊C4×D53—22no—
138C4⋊C4×D53C2×C414yes—
139C4⋊C4×D53C2×C414yes—
140C2×C4×Dic53C2×C411yescharacteristic
141C2×C4×Dic53C2×C411yescharacteristic
142C2×C4×Dic53C2×C411yescharacteristic
143C42×D53—22no—
144C42×D53—22no—
145#13133124C2×C411yescharacteristic
146#13133124C2×C411yescharacteristic
147#13133124C2×C411yescharacteristic
148#13133124C2×C411yescharacteristic
149#13133124C2×C411yescharacteristic
150#13133124C2×C411yescharacteristic
151#13133124C2×C411yescharacteristic
152#13133124C2×C411yescharacteristic
153#13133124C2×C411yescharacteristic
154#13133124C2×C411yescharacteristic
155#13133124C2×C411yescharacteristic
156#13133124C2×C411yescharacteristic
157C2×C4⋊C4×C53C2×C411yescharacteristic
158C2×C4⋊C4×C53C2×C411yescharacteristic
159C2×C42×C53C2×C411yescharacteristic
160#95×C53C2×C411yescharacteristic
161#95×C53C2×C411yescharacteristic
162#95×C53C2×C411yescharacteristic
163#95×C53C2×C411yescharacteristic
164C23×D53C2411yescharacteristic
165C22×#6157—21no—
166C22×#6157—21no—
167C22×#6157—21no—
168C22×#6157—21no—
169C22×#6157—21no—
170C22×#6157—21no—
171C22×#6157—21no—
172C22×#6157—21no—
173C22×#6157—21no—
174C22×#6157—21no—
175C22×#6157—21no—
176C22×#6157—21no—
177C22×#6157—21no—
178C22×#6157—21no—
179C22×#6157—21no—
180C22×#6157—21no—
181C22×#6157—21no—
182C22×#6157—21no—
183C22×#6157—21no—
184C22×#6157—21no—
185C22×#6157—21no—
186C22×#6157—21no—
187C22×#6157—21no—
188C22×#6157—21no—
189C22×#6157—21no—
190C22×#6157—21no—
191C22×#6157—21no—
192C22×#6157—21no—
193C22×#6157—21no—
194C22×#6157—21no—
195C22×#6157—21no—
196C22×#6157—21no—
197C22×#6157—21no—
198C22×#6157—21no—
199C22×#6157—21no—
200C22×#6157—21no—
201C22×#6157—21no—
202C22×#6157—21no—
203C22×#6157—21no—
204C22×#6157—21no—
205C22×#6157C22×C412yes—
206C22×#6157C22×C412yes—
207C22×#6157C22×C412yes—
208C22×#6157C22×C412yes—
209C22×#6157C22×C412yes—
210C22×#6157C22×C412yes—
211C22×#6157C22×C412yes—
212C22×#6157C22×C412yes—
213C22×#6157C2×D412yes—
214C22×#6157C2×D412yes—
215C22×#6157C2×Q812yes—
216C22×#6157C2×Q812yes—
217C22×#6157#4112yes—
218C22×#6157#4112yes—
219C22×#6157#4112yes—
220C22×#6157#4112yes—
221C22×C4×C53C22×C411yescharacteristic
222C22×C4×C53C22×C411yescharacteristic
223C22×C4×C53C22×C411yescharacteristic
224C22×C4×C53C22×C411yescharacteristic
225C22×C4×C53C22×C411yescharacteristic
226C22×C4×C53C22×C411yescharacteristic
227C22×C4×C53C22×C411yescharacteristic
228C22×Dic53C22×C411yescharacteristic
229C22×Dic53C22×C411yescharacteristic
230C22×Dic53C22×C411yescharacteristic
231C22×Dic53C22×C411yescharacteristic
232C22×Dic53C22×C411yescharacteristic
233C22×Dic53C22×C411yescharacteristic
234C22×Dic53C22×C411yescharacteristic
235C2×C4×D53—21no—
236C2×C4×D53—21no—
237C2×C4×D53—21no—
238C2×C4×D53—21no—
239C2×C4×D53—21no—
240C2×C4×D53—21no—
241C2×C4×D53—21no—
242C2×C4×D53—21no—
243C2×C4×D53—21no—
244C2×C4×D53—21no—
245C2×C4×D53—21no—
246C2×C4×D53—21no—
247C2×C4×D53—21no—
248C2×C4×D53—21no—
249C2×C4×D53—21no—
250C2×C4×D53—21no—
251C2×C4×D53—21no—
252C2×C4×D53—21no—
253C2×C4×D53—21no—
254C2×C4×D53—21no—
255C2×C4×D53—21no—
256C2×C4×D53—21no—
257C2×C4×D53—21no—
258C2×C4×D53—21no—
259C2×C4×D53—21no—
260C2×C4×D53—21no—
261C2×C4×D53—21no—
262C2×C4×D53—21no—
263C2×C4×D53—21no—
264C2×C4×D53—21no—
265C2×C4×D53—21no—
266C2×C4×D53—21no—
267C2×C4×D53C22×C412yes—
268C2×C4×D53C22×C412yes—
269C2×C4×D53C22×C412yes—
270C2×C4×D53C22×C412yes—
271C2×C4×D53C22×C412yes—
272C2×C4×D53C22×C412yes—
273C2×C4×D53C2×D412yes—
274C2×C4×D53C2×Q812yes—
275C2×C4×D53#4112yes—
276C2×C4×D53#4112yes—
277C4⋊#6157—28no—
278C4⋊#6157—28no—
279C4⋊#6157—28no—
280C4⋊#6157—44no—
281C4×#6157—28no—
282C4×#6157—44no—
283C4×#6157—44no—
284C4×#6157—44no—
285C4×#6157—44no—
286C4×#6157—44no—
287C4×#6157—44no—
288C4×#6157—44no—
289C4⋊C4×C53—22no—
290C4⋊C4×C53C4214yescomplemented
291C42×C53—22no—
292C4⋊Dic53—22no—
293C4⋊Dic53C4214yescomplemented
294#11719919—22no—
295#11719919—22no—
296#11719919C4214yescomplemented
297#11719919C4214yescomplemented
298C4×Dic53—22no—
299C4×Dic53—22no—
300C4×Dic53—22no—
301C23×C53C23×C411yescharacteristic
302C22×D53C23×C411yescharacteristic
303C22×D53C23×C411yescharacteristic
304C22×D53C22×D411yescharacteristic
305C22×D53C22×Q811yescharacteristic
306C22×D53C2×#4111yescharacteristic
307C22×D53C2×#4111yescharacteristic
308C22×D53C2×#4111yescharacteristic
309C22×D53C2×#4111yescharacteristic
310C22×D53C2×#4111yescharacteristic
311C22×D53C2×#4111yescharacteristic
312C22×D53H(5,𝔽2)11yescharacteristic
313C22×D53H(5,𝔽2)11yescharacteristic
314C22×D532−1+411yescharacteristic
315C22×D532−1+411yescharacteristic
316C2×#6157—22no—
317C2×#6157—22no—
318C2×#6157—22no—
319C2×#6157—22no—
320C2×#6157—22no—
321C2×#6157—22no—
322C2×#6157—22no—
323C2×#6157—22no—
324C2×#6157—22no—
325C2×#6157—22no—
326C2×#6157—22no—
327C2×#6157—22no—
328C2×#6157—22no—
329C2×#6157—22no—
330C2×#6157—22no—
331C2×#6157—22no—
332C2×#6157—22no—
333C2×#6157—22no—
334C2×#6157—22no—
335C2×#6157—22no—
336C2×#6157—22no—
337C2×#6157—22no—
338C2×#6157—22no—
339C2×#6157—22no—
340C2×#6157—22no—
341C2×#6157—22no—
342C2×#6157—22no—
343C2×#6157—22no—
344C2×#6157—22no—
345C2×#6157—22no—
346C2×#6157—22no—
347C2×#6157—22no—
348C2×#6157—22no—
349C2×#6157—22no—
350C2×#6157—22no—
351C2×#6157—22no—
352C2×#6157—41no—
353C2×#6157—41no—
354C2×#6157—41no—
355C2×#6157—41no—
356C2×#6157—41no—
357C2×#6157—41no—
358C2×#6157—41no—
359C2×#6157—41no—
360C2×#6157—41no—
361C2×#6157—41no—
362C2×#6157—41no—
363C2×#6157—41no—
364C2×#6157—41no—
365C2×#6157—41no—
366C2×#6157—41no—
367C2×#6157—41no—
368C2×#6157C4×D414yes—
369C2×#6157C4×D414yes—
370C2×#6157C4×Q814yes—
371C2×#6157C4×Q814yes—
372C2×C4×C53—21no—
373C2×C4×C53—21no—
374C2×C4×C53—21no—
375C2×C4×C53—21no—
376C2×C4×C53—21no—
377C2×C4×C53—21no—
378C2×C4×C53—21no—
379C2×C4×C53—21no—
380C2×C4×C53—21no—
381C2×C4×C53—21no—
382C2×C4×C53—21no—
383C2×C4×C53—21no—
384C2×C4×C53—21no—
385C2×C4×C53—21no—
386C2×C4×C53—21no—
387C2×C4×C53—21no—
388C2×C4×C53C2×C4212yes—
389C2×C4×C53C2×C4212yes—
390C2×C4×C53C2×C4212yes—
391C2×C4×C53C4×D412yes—
392C2×C4×C53C4×Q812yes—
393C2×Dic53—21no—
394C2×Dic53—21no—
395C2×Dic53—21no—
396C2×Dic53—21no—
397C2×Dic53—21no—
398C2×Dic53—21no—
399C2×Dic53—21no—
400C2×Dic53—21no—
401C2×Dic53—21no—
402C2×Dic53—21no—
403C2×Dic53—21no—
404C2×Dic53—21no—
405C2×Dic53—21no—
406C2×Dic53—21no—
407C2×Dic53—21no—
408C2×Dic53—21no—
409C2×Dic53C2×C4212yes—
410C2×Dic53C2×C4212yes—
411C2×Dic53C2×C4212yes—
412C2×Dic53C4×D412yes—
413C2×Dic53C4×Q812yes—
414C4×D53—22no—
415C4×D53—22no—
416C4×D53—22no—
417C4×D53—22no—
418C4×D53—22no—
419C4×D53—22no—
420C4×D53—22no—
421C4×D53—22no—
422C4×D53—22no—
423C4×D53—22no—
424C4×D53—22no—
425C4×D53—22no—
426C4×D53—22no—
427C4×D53—22no—
428C4×D53—22no—
429C4×D53—22no—
430C4×D53—22no—
431C4×D53—22no—
432C4×D53—22no—
433C4×D53—22no—
434C4×D53—41no—
435C4×D53—41no—
436C4×D53—41no—
437C4×D53—41no—
438C4×D53—41no—
439C4×D53—41no—
440C4×D53—41no—
441C4×D53—41no—
442#13825—531nomaximal, Sylow
443C22×C53C22×C4211yescharacteristic
444C22×C53C2×C4×D411yescharacteristic
445C22×C53C2×C4×Q811yescharacteristic
446C22×C53C4×#4111yescharacteristic
447C22×C53C4×#4111yescharacteristic
448C22×C53#52011yescharacteristic
449C22×C53#52011yescharacteristic
450C2×D53C2×C4×D411yescharacteristic
451C2×D53C2×C4×D411yescharacteristic
452C2×D53C2×C4×Q811yescharacteristic
453C2×D53C2×C4×Q811yescharacteristic
454C2×D53C4×#4111yescharacteristic
455C2×D53C4×#4111yescharacteristic
456C2×D53C4×#4111yescharacteristic
457C2×D53C4×#4111yescharacteristic
458C2×D53#51811yescharacteristic
459C2×D53#51911yescharacteristic
460C2×D53#52011yescharacteristic
461C2×D53#52011yescharacteristic
462C2×D53#54611yescharacteristic
463C2×D53#54611yescharacteristic
464C2×D53#54711yescharacteristic
465C2×D53D4×Q811yescharacteristic
466C2×D53#55111yescharacteristic
467C2×D53#55111yescharacteristic
468C2×D53#55211yescharacteristic
469C2×D53#55211yescharacteristic
470C2×D53#55211yescharacteristic
471C2×D53#55211yescharacteristic
472C2×D53#55311yescharacteristic
473C2×D53#55311yescharacteristic
474C2×D53#55411yescharacteristic
475C2×D53#55411yescharacteristic
476C2×D53#55611yescharacteristic
477C2×D53#55711yescharacteristic
478#6157—24no—
479#6157—24no—
480#6157—24no—
481#6157—24no—
482#6157—42no—
483#6157—42no—
484#6157—42no—
485#6157—42no—
486C4×C53—22no—
487C4×C53—22no—
488C4×C53—22no—
489C4×C53—22no—
490C4×C53—22no—
491C4×C53—41no—
492C4×C53—41no—
493Dic53—22no—
494Dic53—22no—
495Dic53—22no—
496Dic53—22no—
497Dic53—22no—
498Dic53—41no—
499Dic53—41no—
500C2×#389—531no—
501C2×#387—531no—
502C2×#387—531no—
503C2×C4×C4⋊C4—531no—
504C2×C4×C4⋊C4—531no—
505#1436—531no—
506#1436—531no—
507#1436—531no—
508#1436—531no—
509#1436—531no—
510#1436—531no—
511C4×#95—531no—
512C4×#95—531no—
513C4×#95—531no—
514C4×#95—531no—
515C2×C53C42×D411yescharacteristic
516C2×C53C42×Q811yescharacteristic
517C2×C53#227411yescharacteristic
518C2×C53#235911yescharacteristic
519C2×C53#236011yescharacteristic
520C2×C53#237011yescharacteristic
521C2×C53#237311yescharacteristic
522D53#235911yescharacteristic
523D53#236011yescharacteristic
524D53#236411yescharacteristic
525D53#236511yescharacteristic
526D53#236811yescharacteristic
527D53#237011yescharacteristic
528D53#237111yescharacteristic
529D53#237311yescharacteristic
530C22×C4⋊C4—531no—
531C22×C4⋊C4—531no—
532C22×C4⋊C4—531no—
533C22×C4⋊C4—531no—
534C22×C4⋊C4—531no—
535C22×C4⋊C4—531no—
536C22×C42—531no—
537C22×C42—531no—
538C22×C42—531no—
539C22×C42—531no—
540C22×C42—531no—
541C22×C42—531no—
542C22×C42—531no—
543C22×C42—531no—
544C22×C42—531no—
545#389—538no—
546#387—538no—
547#387—531no—
548#387—531no—
549#387—531no—
550#387—531no—
551#387—531no—
552#387—531no—
553#387—531no—
554#387#615711yescharacteristic, complemented
555C4×C4⋊C4—1064no—
556C4×C4⋊C4—1064no—
557C2×#95—531no—
558C2×#95—531no—
559C2×#95—531no—
560C2×#95—531no—
561C2×#95—531no—
562C2×#95—531no—
563C2×#95—531no—
564C2×#95—531no—
565C2×#95—531no—
566C2×#95—531no—
567C2×#95—531no—
568C2×#95—531no—
569C2×#95—531no—
570C2×#95—531no—
571C2×#95—531no—
572C2×#95—531no—
573C2×#95—531no—
574C2×#95—531no—
575C2×#95—531no—
576C2×#95—531no—
577C53#1382511yescharacteristic, complemented, Sylow
578C23×C4—531no—
579C23×C4—531no—
580C23×C4—531no—
581C23×C4—531no—
582C23×C4—531no—
583C23×C4—531no—
584C23×C4—531no—
585C23×C4—531no—
586C23×C4—531no—
587C23×C4—531no—
588C23×C4—531no—
589C23×C4—531no—
590C23×C4—531no—
591C23×C4—531no—
592C23×C4—531no—
593C2×C4⋊C4—531no—
594C2×C4⋊C4—531no—
595C2×C4⋊C4—531no—
596C2×C4⋊C4—534no—
597C2×C4⋊C4—534no—
598C2×C4⋊C4—534no—
599C2×C4⋊C4—534no—
600C2×C4⋊C4—534no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—531no—
603C2×C4⋊C4—531no—
604C2×C4⋊C4—534no—
605C2×C4⋊C4—1062no—
606C2×C4⋊C4—1062no—
607C2×C4⋊C4—1062no—
608C2×C4⋊C4—1062no—
609C2×C4⋊C4—1062no—
610C2×C4⋊C4—1062no—
611C2×C4⋊C4—1062no—
612C2×C4⋊C4—1062no—
613C2×C4⋊C4—2121no—
614C2×C4⋊C4—2121no—
615C2×C4⋊C4C2×#615711yescharacteristic
616C2×C4⋊C4C2×#615711yescharacteristic
617C2×C42—534no—
618C2×C42—531no—
619C2×C42—531no—
620C2×C42—531no—
621C2×C42—534no—
622C2×C42—1062no—
623C2×C42—1062no—
624C2×C42—1062no—
625C2×C42—1062no—
626C2×C42—1062no—
627C2×C42—1062no—
628C2×C42—1062no—
629C2×C42—1062no—
630C2×C42—1062no—
631C2×C42—1062no—
632C2×C42—1062no—
633C2×C42—1062no—
634C2×C42—1062no—
635C2×C42—1062no—
636C2×C42—1062no—
637C2×C42—1062no—
638C2×C42—2121no—
639C2×C42—2121no—
640C2×C42—2121no—
641C2×C42—2121no—
642C2×C42—2121no—
643C2×C42—2121no—
644C2×C42—2121no—
645C2×C42—2121no—
646C2×C42C2×#615711yescharacteristic
647#95—534no—
648#95—534no—
649#95—534no—
650#95—534no—
651#95—534no—
652#95—534no—
653#95—534no—
654#95—534no—
655#95—531no—
656#95—531no—
657#95—531no—
658#95—531no—
659#95—531no—
660#95—531no—
661#95—531no—
662#95—531no—
663#95—531no—
664#95—531no—
665#95—531no—
666#95—531no—
667#95—1062no—
668#95—1062no—
669#95—1062no—
670#95—1062no—
671#95—1062no—
672#95—1062no—
673#95—2121no—
674#95—2121no—
675#95C2×#615711yescharacteristic
676#95C2×#615711yescharacteristic
677#95C2×#615711yescharacteristic
678#95C2×#615711yescharacteristic
679C24—531no—
680C22×C4—532no—
681C22×C4—532no—
682C22×C4—532no—
683C22×C4—532no—
684C22×C4—532no—
685C22×C4—532no—
686C22×C4—532no—
687C22×C4—532no—
688C22×C4—532no—
689C22×C4—532no—
690C22×C4—532no—
691C22×C4—532no—
692C22×C4—531no—
693C22×C4—531no—
694C22×C4—531no—
695C22×C4—531no—
696C22×C4—531no—
697C22×C4—532no—
698C22×C4—532no—
699C22×C4—532no—
700C22×C4—532no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—532no—
706C22×C4—532no—
707C22×C4—532no—
708C22×C4—532no—
709C22×C4—532no—
710C22×C4—532no—
711C22×C4—531no—
712C22×C4—531no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4—1061no—
776C22×C4—1061no—
777C22×C4—1061no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—1061no—
782C22×C4—1061no—
783C22×C4—1061no—
784C22×C4—1061no—
785C22×C4C22×#615711yescharacteristic
786C22×C4C22×#615711yescharacteristic
787C22×C4C22×#615711yescharacteristic
788C22×C4C22×#615711yescharacteristic
789C22×C4C22×#615711yescharacteristic
790C22×C4C22×#615711yescharacteristic
791C22×C4C22×#615711yescharacteristic
792C4⋊C4—22no—
793C4⋊C4—534no—
794C4⋊C4—534no—
795C4⋊C4—534no—
796C4⋊C4—1062no—
797C4⋊C4—1062no—
798C4⋊C4—1068no—
799C4⋊C4—1068no—
800C4⋊C4—1068no—
801C4⋊C4—1062no—
802C4⋊C4—2124no—
803C4⋊C4C4×#615714yescomplemented
804C42—22no—
805C42—1062no—
806C42—1062no—
807C42—1068no—
808C42—1062no—
809C42—2124no—
810C42—2124no—
811C42—2124no—
812C42—2124no—
813C42—2124no—
814C42—2124no—
815C42—2124no—
816C23—531no—
817C23—531no—
818C23—531no—
819C23—531no—
820C23—531no—
821C23—531no—
822C23—531no—
823C23—531no—
824C23—531no—
825C23—531no—
826C23—531no—
827C23—531no—
828C23—531no—
829C23—531no—
830C23C23×#615711yescharacteristic
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—534no—
848C2×C4—534no—
849C2×C4—534no—
850C2×C4—534no—
851C2×C4—532no—
852C2×C4—532no—
853C2×C4—532no—
854C2×C4—532no—
855C2×C4—532no—
856C2×C4—1062no—
857C2×C4—1062no—
858C2×C4—1062no—
859C2×C4—1062no—
860C2×C4—1062no—
861C2×C4—1062no—
862C2×C4—1062no—
863C2×C4—1062no—
864C2×C4—1062no—
865C2×C4—1062no—
866C2×C4—1062no—
867C2×C4—1062no—
868C2×C4—1062no—
869C2×C4—1062no—
870C2×C4—1062no—
871C2×C4—1062no—
872C2×C4—1062no—
873C2×C4—1062no—
874C2×C4—1062no—
875C2×C4—1062no—
876C2×C4—1062no—
877C2×C4—1062no—
878C2×C4—1062no—
879C2×C4—1062no—
880C2×C4—1062no—
881C2×C4—1062no—
882C2×C4—1062no—
883C2×C4—1062no—
884C2×C4—1062no—
885C2×C4—1062no—
886C2×C4—1062no—
887C2×C4—1062no—
888C2×C4—1062no—
889C2×C4—1062no—
890C2×C4—1062no—
891C2×C4—1062no—
892C2×C4—1062no—
893C2×C4—1062no—
894C2×C4—1062no—
895C2×C4—1062no—
896C2×C4—1062no—
897C2×C4—1062no—
898C2×C4—1062no—
899C2×C4—1062no—
900C2×C4—1061no—
901C2×C4—1061no—
902C2×C4—1061no—
903C2×C4—1061no—
904C2×C4—1061no—
905C2×C4—1061no—
906C2×C4—1061no—
907C2×C4—1061no—
908C2×C4—1061no—
909C2×C4—1061no—
910C2×C4—1062no—
911C2×C4—1062no—
912C2×C4—1062no—
913C2×C4—1062no—
914C2×C4—1062no—
915C2×C4—1062no—
916C2×C4—1062no—
917C2×C4—1062no—
918C2×C4—1062no—
919C2×C4—1062no—
920C2×C4—1062no—
921C2×C4—1062no—
922C2×C4—1061no—
923C2×C4—1061no—
924C2×C4—1061no—
925C2×C4—1061no—
926C2×C4—1061no—
927C2×C4—1061no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—2121no—
940C2×C4—2121no—
941C2×C4—2121no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4—2121no—
945C2×C4—2121no—
946C2×C4—2121no—
947C2×C4—2121no—
948C2×C4—2121no—
949C2×C4—2121no—
950C2×C4—2121no—
951C2×C4—2121no—
952C2×C4C2×C4×#615712yes—
953C2×C4C2×C4×#615712yes—
954C2×C4C2×C4×#615712yes—
955C2×C4D4×#615712yes—
956C2×C4Q8×#615712yes—
957C22—531no—
958C22—531no—
959C22—531no—
960C22—531no—
961C22—531no—
962C22—531no—
963C22—531no—
964C22—531no—
965C22—531no—
966C22—531no—
967C22—531no—
968C22—531no—
969C22—531no—
970C22—531no—
971C22—531no—
972C22—531no—
973C22—531no—
974C22—531no—
975C22—531no—
976C22—531no—
977C22—531no—
978C22—531no—
979C22—531no—
980C22—531no—
981C22—531no—
982C22—531no—
983C22—531no—
984C22—531no—
985C22C22×C4×#615711yescharacteristic
986C22C2×D4×#615711yescharacteristic
987C22C2×Q8×#615711yescharacteristic
988C22#41×#615711yescharacteristic
989C22#41×#615711yescharacteristic
990C22#1681169211yescharacteristic
991C22#1681169211yescharacteristic
992C4—22no—
993C4—22no—
994C4—22no—
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—1064no—
1000C4—1064no—
1001C4—1064no—
1002C4—1064no—
1003C4—1062no—
1004C4—1062no—
1005C4—1062no—
1006C4—1062no—
1007C4—1062no—
1008C4—2122no—
1009C4—2122no—
1010C4—2122no—
1011C4—2122no—
1012C4—2121no—
1013C4—2121no—
1014C2—531no—
1015C2—531no—
1016C2—531no—
1017C2—531no—
1018C2—531no—
1019C2—531no—
1020C2—531no—
1021C2—531no—
1022C2C4×D4×#615711yescharacteristic
1023C2C4×Q8×#615711yescharacteristic
1024C2#2029115211yescharacteristic
1025C2#2029123811yescharacteristic
1026C2#2029123911yescharacteristic
1027C2#2029124911yescharacteristic
1028C2#2029125211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutatorC22×C53C22×C42
FittingC53×#387C4
socleC23×C53C23×C4
prime radical, cosocleC23×D53C24
hypercenter#387#6157
hypocenterC53#13825
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
28. #16811574C4semidirect
29. #16811572C4semidirect
51. #16810510C4semidirect
52. #16810509C4semidirect
53. #16810508C4semidirect
54. #16810507C4semidirect
55. #16810506C4semidirect
56. #16810505C4semidirect
57. #16810504C4semidirect
62. C53×#387C4semidirect
290. C4⋊C4×C53C42semidirect
293. C4⋊Dic53C42semidirect
296. #11719919C42semidirect
297. #11719919C42semidirect
554. #387#6157semidirect
577. C53#13825semidirect
803. C4⋊C4C4×#6157semidirect

Maximal subgroups

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

subgroupindex
C2×#168115742
C2×#168115722
C2×C4⋊C4×#61572
C2×C4×C4⋊#61572
#202898952
#202898942
C4×(C2×#6157)⋊C42
#95×#61572
#387×D532
#1382553