Finite Group Databasebeta

← #27389111

Subgroups — #27389111

Order 13568.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810684C211yesmaximal, characteristic, complemented
2C2×#16810579C211yesmaximal, characteristic, complemented
3#20275656C211yesmaximal, characteristic, complemented
4#20275652C211yesmaximal, characteristic, complemented
5#20275514C211yesmaximal, characteristic, complemented
6#20275510C211yesmaximal, characteristic, complemented
7#20275013C211yesmaximal, characteristic, complemented
8#20275013C211yesmaximal, characteristic, complemented
9#20275008C211yesmaximal, characteristic, complemented
10#20275008C211yesmaximal, characteristic, complemented
11#20274481C211yesmaximal, characteristic, complemented
12#20274481C211yesmaximal, characteristic, complemented
13#20274477C211yesmaximal, characteristic, complemented
14C4×C22⋊#88322C211yesmaximal, characteristic, complemented
15C2×C53×#529C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18#16810684—24no—
19C2×C4⋊#88322C2211yescharacteristic
20C2×C4⋊#88322C2211yescharacteristic
21C2×C22⋊#88322C2211yescharacteristic
22C2×C22⋊#88322C2211yescharacteristic
23C2×C22⋊#88322C2211yescharacteristic
24C2×C22⋊#88322C2211yescharacteristic
25C2×C22⋊#88322C2211yescharacteristic
26C2×C22⋊#88322C2211yescharacteristic
27C2×C22⋊#88322C2211yescharacteristic
28C2×C22⋊#88322C2211yescharacteristic
29C2×C22⋊#88322C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31#16810579—24no—
32C2×#13133128C2211yescharacteristic
33C2×#13133128C2211yescharacteristic
34C2×#13133128C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36C2×C4×#88322C2211yescharacteristic
37C2×C4×#88322C2211yescharacteristic
38#16810378C2211yescharacteristic
39#16810378C2211yescharacteristic
40#16810378C2211yescharacteristic
41#16810378C2211yescharacteristic
42#16810378C2211yescharacteristic
43#16810378C2211yescharacteristic
44#16810378C2211yescharacteristic
45#16810378C2211yescharacteristic
46C53×#529—24no—
47C53×#529—24no—
48C2×#126×C53C411yescharacteristic
49C2×#126×C53C411yescharacteristic
50C2×#125×C53C411yescharacteristic
51C2×#124×C53C411yescharacteristic
52C2×#123×C53C411yescharacteristic
53C2×#123×C53C411yescharacteristic
54C2×C22⋊Q8×C53C411yescharacteristic
55C2×#121×C53C411yescharacteristic
56C2×C4×Q8×C53C2211yescharacteristic
57C2×C4×D4×C53C2211yescharacteristic
58C2×C4×D4×C53C2211yescharacteristic
59C2×C4×D4×C53C2211yescharacteristic
60C2×#117×C53C2211yescharacteristic
61C2×#117×C53C2211yescharacteristic
62C22×C42×C53C2211yescharacteristic
63C2×#11719917—22no—
64C2×#11719917—22no—
65C2×#11719917—22no—
66C22×#88322—22no—
67C22×#88322—22no—
68C22×#88322—22no—
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C4⋊#88322—22no—
78C4⋊#88322—22no—
79C22⋊#88322—22no—
80C22⋊#88322—22no—
81C22⋊#88322—22no—
82C22⋊#88322—22no—
83C22⋊#88322—22no—
84C22⋊#88322—22no—
85C22⋊#88322—22no—
86C22⋊#88322—22no—
87C22⋊#88322—22no—
88C22⋊#88322—22no—
89#13133128—22no—
90#13133128—22no—
91#13133128—22no—
92C4×#88322—22no—
93C4×#88322—22no—
94C4×#88322—22no—
95C22×Q8×C53C2×C411yescharacteristic
96C22×D4×C53C2×C411yescharacteristic
97C22×D4×C53C2×C411yescharacteristic
98C22×D4×C53C2×C411yescharacteristic
99C23×C4×C53C2×C411yescharacteristic
100C23×C4×C53C2×C411yescharacteristic
101C23×C4×C53C2311yescharacteristic
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2311yescharacteristic
104#126×C53—24no—
105#126×C53—24no—
106#125×C53—24no—
107#124×C53—24no—
108#123×C53—24no—
109#123×C53—24no—
110C22⋊Q8×C53—24no—
111#121×C53—24no—
112C4×Q8×C53—22no—
113C4×Q8×C53—22no—
114C4×D4×C53—22no—
115C4×D4×C53—22no—
116C4×D4×C53—22no—
117C4×D4×C53—22no—
118C4×D4×C53—22no—
119C4×D4×C53—22no—
120#117×C53—22no—
121#117×C53—22no—
122#117×C53D414yes—
123#117×C53D414yes—
124C2×C4⋊C4×C53C2×C411yescharacteristic
125C2×C4⋊C4×C53C2×C411yescharacteristic
126C2×C4⋊C4×C53C2×C411yescharacteristic
127C2×C4⋊C4×C53C2×C411yescharacteristic
128C2×C4⋊C4×C53C2×C411yescharacteristic
129C2×C4⋊C4×C53C2×C411yescharacteristic
130C2×C4⋊C4×C53C2×C411yescharacteristic
131C2×C4⋊C4×C53C2×C411yescharacteristic
132C2×C4⋊C4×C53C2×C411yescharacteristic
133C2×C4⋊C4×C53C2×C411yescharacteristic
134C2×C22⋊C4×C53C2×C411yescharacteristic
135C2×C22⋊C4×C53C2×C411yescharacteristic
136C2×C22⋊C4×C53C2×C411yescharacteristic
137C2×C22⋊C4×C53C2×C411yescharacteristic
138C2×C22⋊C4×C53C2×C411yescharacteristic
139C2×C22⋊C4×C53C2×C411yescharacteristic
140C2×C22⋊C4×C53C2×C411yescharacteristic
141C2×C22⋊C4×C53C2×C411yescharacteristic
142C2×C22⋊C4×C53C2×C411yescharacteristic
143C2×C22⋊C4×C53C2×C411yescharacteristic
144C2×C42×C53—22no—
145C2×C42×C53—22no—
146C2×C42×C53C2×C411yescharacteristic
147C2×C42×C53C2×C411yescharacteristic
148C2×C42×C53C2311yescharacteristic
149C2×C42×C53C2311yescharacteristic
150C2×C42×C53C2311yescharacteristic
151C2×C42×C53C2311yescharacteristic
152C24×C53C22×C411yescharacteristic
153C24×C53C22×C411yescharacteristic
154C24×C53C22×C411yescharacteristic
155C2×Q8×C53—22no—
156C2×Q8×C53—22no—
157C2×Q8×C53—41no—
158C2×D4×C53—22no—
159C2×D4×C53—22no—
160C2×D4×C53—22no—
161C2×D4×C53—22no—
162C2×D4×C53—22no—
163C2×D4×C53—22no—
164C2×D4×C53—41no—
165C2×D4×C53—41no—
166C2×D4×C53—41no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—41no—
188C22×C4×C53—41no—
189C22×C4×C53C22×C411yescharacteristic
190C22×C4×C53C22×C411yescharacteristic
191C22×C4×C53C22×C411yescharacteristic
192C22×C4×C53C22×C411yescharacteristic
193C22×C4×C53C22×C411yescharacteristic
194C22×C4×C53C22×C411yescharacteristic
195C22×C4×C53C22×C411yescharacteristic
196C22×C4×C53C22×C411yescharacteristic
197C22×C4×C53C22×C411yescharacteristic
198C22×C4×C53C22×C411yescharacteristic
199C22×C4×C53C22×C411yescharacteristic
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2411yescharacteristic
203C4⋊C4×C53—22no—
204C4⋊C4×C53—22no—
205C4⋊C4×C53—22no—
206C4⋊C4×C53—22no—
207C4⋊C4×C53—22no—
208C4⋊C4×C53—22no—
209C4⋊C4×C53—22no—
210C4⋊C4×C53—22no—
211C4⋊C4×C53C22⋊C414yes—
212C4⋊C4×C53C22⋊C414yes—
213C22⋊C4×C53—22no—
214C22⋊C4×C53—22no—
215C22⋊C4×C53—22no—
216C22⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—22no—
219C22⋊C4×C53—22no—
220C22⋊C4×C53—22no—
221C22⋊C4×C53C22⋊C414yes—
222C22⋊C4×C53C22⋊C414yes—
223C42×C53—22no—
224C42×C53—22no—
225C42×C53—21no—
226C42×C53—21no—
227C42×C53—21no—
228C42×C53—21no—
229C42×C53C2×D412yes—
230C42×C53C2×D412yes—
231C42×C53C2×D412yes—
232C42×C53C2×D412yes—
233#11719917—28no—
234C2×#88322—28no—
235C2×#88322—21no—
236C2×#88322—21no—
237C2×#88322—21no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322#4112yes—
256C2×#88322#4112yes—
257C2×#88322#4112yes—
258C2×#88322#4112yes—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53C2×C22⋊C412yes—
279C23×C53#13112yes—
280C23×C53C23×C411yescharacteristic
281Q8×C53—44no—
282D4×C53—44no—
283D4×C53—44no—
284D4×C53—44no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—44no—
317C2×C4×C53—44no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53C2×C22⋊C412yes—
327C2×C4×C53C2×C22⋊C412yes—
328C2×C4×C53C2×C22⋊C412yes—
329C2×C4×C53C2×C22⋊C412yes—
330C2×C4×C53C2×C22⋊C412yes—
331C2×C4×C53#13112yes—
332C2×C4×C53C22×D411yescharacteristic
333C2×C4×C53C22×D411yescharacteristic
334C2×C4×C53C2×#4111yescharacteristic
335C2×C4×C53C2×#4111yescharacteristic
336C2×C4×C53C2×#4111yescharacteristic
337C2×C4×C53C2×#4111yescharacteristic
338#88322—22no—
339#88322—22no—
340#88322—22no—
341#88322—22no—
342#88322—41no—
343#88322—41no—
344#88322—41no—
345#88322—41no—
346#21381—531nomaximal, Sylow
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—41no—
354C22×C53—41no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—41no—
364C22×C53—41no—
365C22×C53—41no—
366C22×C53—41no—
367C22×C53—41no—
368C22×C53C22×C22⋊C411yescharacteristic
369C22×C53C4×#4111yescharacteristic
370C22×C53C4×#4111yescharacteristic
371C22×C53C2×#13111yescharacteristic
372C22×C53C2×#13111yescharacteristic
373C22×C53#56811yescharacteristic
374C22×C53#56811yescharacteristic
375C4×C53—22no—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—22no—
379C4×C53—22no—
380C4×C53—22no—
381C4×C53—41no—
382C4×C53—41no—
383C4×C53—41no—
384C4×C53—41no—
385C4×C53—41no—
386C4×C53#52511yescharacteristic
387C4×C53#52511yescharacteristic
388C4×C53#53211yescharacteristic
389C4×C53#53211yescharacteristic
390C2×#529D5311yescharacteristic
391C2×#433—531no—
392C2×#405—531no—
393#1985—531no—
394#1984—531no—
395#1955—531no—
396#1954—531no—
397#1870—531no—
398#1870—531no—
399#1869—531no—
400#1869—531no—
401#1750—531no—
402#1750—531no—
403#1749—531no—
404C4×C22⋊C8—531no—
405C2×C53—42no—
406C2×C53—42no—
407C2×C53—81no—
408C2×C53#229711yescharacteristic
409C2×C53#288011yescharacteristic
410C2×C53#288011yescharacteristic
411C2×C53#296611yescharacteristic
412C2×C53#296711yescharacteristic
413C2×C53#296811yescharacteristic
414C2×C53#296911yescharacteristic
415C22×M16—531no—
416C23×C8—531no—
417#529—24no—
418#529—24no—
419C2×#126Dic5311yescharacteristic
420C2×#126Dic5311yescharacteristic
421C2×#125Dic5311yescharacteristic
422C2×#124Dic5311yescharacteristic
423C2×#123Dic5311yescharacteristic
424C2×#123Dic5311yescharacteristic
425C2×C22⋊Q8Dic5311yescharacteristic
426C2×#121Dic5311yescharacteristic
427C2×C4×Q8C2×D5311yescharacteristic
428C2×C4×D4C2×D5311yescharacteristic
429C2×C4×D4C2×D5311yescharacteristic
430C2×C4×D4C2×D5311yescharacteristic
431C2×#117C2×D5311yescharacteristic
432C2×#117C2×D5311yescharacteristic
433C22×C42C2×D5311yescharacteristic
434#433—1064no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×C22⋊C8—531no—
438C2×C22⋊C8—531no—
439C2×C22⋊C8—531no—
440C2×C22⋊C8—531no—
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×C22⋊C8—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447#405—1064no—
448C2×#97—531no—
449C2×#97—531no—
450C2×#97—531no—
451C2×C4×C8—531no—
452C2×C4×C8—531no—
453C2×C4×C8—531no—
454#336—531no—
455#336—531no—
456#336—531no—
457#336—531no—
458#336—531no—
459#336—531no—
460#336—531no—
461#336—531no—
462C53#2138111yescharacteristic, complemented, Sylow
463C22×Q8C2×Dic5311yescharacteristic
464C22×D4C2×Dic5311yescharacteristic
465C22×D4C2×Dic5311yescharacteristic
466C22×D4C2×Dic5311yescharacteristic
467C23×C4C2×Dic5311yescharacteristic
468C23×C4C2×Dic5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470C23×C4C22×D5311yescharacteristic
471C23×C4C22×D5311yescharacteristic
472C2×M16—1062no—
473C2×M16—1062no—
474C2×M16—1062no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—531no—
480C22×C8—531no—
481C22×C8—531no—
482C22×C8—531no—
483C22×C8—1062no—
484C22×C8—1062no—
485C22×C8—1062no—
486#126—24no—
487#126—24no—
488#125—24no—
489#124—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493#121—24no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—22no—
504#117C22⋊D5314yes—
505#117C22⋊D5314yes—
506C2×C4⋊C4C2×Dic5311yescharacteristic
507C2×C4⋊C4C2×Dic5311yescharacteristic
508C2×C4⋊C4C2×Dic5311yescharacteristic
509C2×C4⋊C4C2×Dic5311yescharacteristic
510C2×C4⋊C4C2×Dic5311yescharacteristic
511C2×C4⋊C4C2×Dic5311yescharacteristic
512C2×C4⋊C4C2×Dic5311yescharacteristic
513C2×C4⋊C4C2×Dic5311yescharacteristic
514C2×C4⋊C4C2×Dic5311yescharacteristic
515C2×C4⋊C4C2×Dic5311yescharacteristic
516C2×C22⋊C4C2×Dic5311yescharacteristic
517C2×C22⋊C4C2×Dic5311yescharacteristic
518C2×C22⋊C4C2×Dic5311yescharacteristic
519C2×C22⋊C4C2×Dic5311yescharacteristic
520C2×C22⋊C4C2×Dic5311yescharacteristic
521C2×C22⋊C4C2×Dic5311yescharacteristic
522C2×C22⋊C4C2×Dic5311yescharacteristic
523C2×C22⋊C4C2×Dic5311yescharacteristic
524C2×C22⋊C4C2×Dic5311yescharacteristic
525C2×C22⋊C4C2×Dic5311yescharacteristic
526C2×C42—22no—
527C2×C42—22no—
528C2×C42C2×Dic5311yescharacteristic
529C2×C42C2×Dic5311yescharacteristic
530C2×C42C22×D5311yescharacteristic
531C2×C42C22×D5311yescharacteristic
532C2×C42C22×D5311yescharacteristic
533C2×C42C22×D5311yescharacteristic
534C4⋊C8—1062no—
535C4⋊C8—1062no—
536C22⋊C8—1062no—
537C22⋊C8—1062no—
538C22⋊C8—1062no—
539C22⋊C8—1062no—
540C22⋊C8—1062no—
541C22⋊C8—1062no—
542C22⋊C8—1062no—
543C22⋊C8—1062no—
544C22⋊C8—1062no—
545C22⋊C8—1062no—
546#97—1062no—
547#97—1062no—
548#97—1062no—
549C4×C8—1062no—
550C4×C8—1062no—
551C4×C8—1062no—
552C24C22×Dic5311yescharacteristic
553C24C22×Dic5311yescharacteristic
554C24C22×Dic5311yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×Dic5311yescharacteristic
590C22×C4C22×Dic5311yescharacteristic
591C22×C4C22×Dic5311yescharacteristic
592C22×C4C22×Dic5311yescharacteristic
593C22×C4C22×Dic5311yescharacteristic
594C22×C4C22×Dic5311yescharacteristic
595C22×C4C22×Dic5311yescharacteristic
596C22×C4C22×Dic5311yescharacteristic
597C22×C4C22×Dic5311yescharacteristic
598C22×C4C22×Dic5311yescharacteristic
599C22×C4C22×Dic5311yescharacteristic
600C22×C4C2×C22⋊D5312yes—
601C22×C4C2×C22⋊D5312yes—
602C22×C4C23×D5311yescharacteristic
603M16—1068no—
604C2×C8—532no—
605C2×C8—532no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—1068no—
609C2×C8—1061no—
610C2×C8—1061no—
611C2×C8—1061no—
612C2×C8—1061no—
613C2×C8—1061no—
614C2×C8—1061no—
615C2×C8—1061no—
616C2×C8—1061no—
617C2×C8—1061no—
618C2×C8—1061no—
619C2×C8—1061no—
620C2×C8—1061no—
621C2×C8—1061no—
622C2×C8—1061no—
623C2×C8—1061no—
624C2×C8—1061no—
625C2×C8—1061no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—1061no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4C22⋊Dic5314yes—
638C4⋊C4C22⋊Dic5314yes—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4C22⋊Dic5314yes—
648C22⋊C4C22⋊Dic5314yes—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42C2×C22⋊D5312yes—
656C42C2×C22⋊D5312yes—
657C42C2×C22⋊D5312yes—
658C42C2×C22⋊D5312yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊Dic5312yes—
679C23#1313322412yes—
680C23C23×Dic5311yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C2×C22⋊Dic5312yes—
727C2×C4C2×C22⋊Dic5312yes—
728C2×C4C2×C22⋊Dic5312yes—
729C2×C4C2×C22⋊Dic5312yes—
730C2×C4C2×C22⋊Dic5312yes—
731C2×C4#1313322412yes—
732C2×C4C22×C22⋊D5311yescharacteristic
733C2×C4C22×C22⋊D5311yescharacteristic
734C2×C4#41×D5311yescharacteristic
735C2×C4#41×D5311yescharacteristic
736C2×C4#41×D5311yescharacteristic
737C2×C4#41×D5311yescharacteristic
738C8—1062no—
739C8—1062no—
740C8—1062no—
741C8—1062no—
742C8—2121no—
743C8—2121no—
744C8—2121no—
745C8—2121no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊Dic5311yescharacteristic
768C22#41×Dic5311yescharacteristic
769C22#41×Dic5311yescharacteristic
770C22C2×#1313322411yescharacteristic
771C22C2×#1313322411yescharacteristic
772C22#1681139011yescharacteristic
773C22#1681139011yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4#1681113011yescharacteristic
786C4#1681113011yescharacteristic
787C4#1681116911yescharacteristic
788C4#1681116911yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2#2027720611yescharacteristic
793C2#2028316411yescharacteristic
794C2#2028316411yescharacteristic
795C2#2028369111yescharacteristic
796C2#2028370211yescharacteristic
797C2#2028371111yescharacteristic
798C2#2028372011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC2×C53×#529C2
prime radicalC2×#121×C53C4
cosocleC22×C4×C53C24
hypercenterC2×#529D53
hypocenterC53#21381
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#16810684C2semidirect
2. C2×#16810579C2semidirect
3. #20275656C2semidirect
4. #20275652C2semidirect
5. #20275514C2semidirect
6. #20275510C2semidirect
7. #20275013C2semidirect
8. #20275013C2semidirect
9. #20275008C2semidirect
10. #20275008C2semidirect
11. #20274481C2semidirect
12. #20274481C2semidirect
13. #20274477C2semidirect
14. C4×C22⋊#88322C2semidirect
462. C53#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#168106842
C2×#168105792
#202756562
#202756522
#202755142
#202755102
#202750132
#202750082
#202744812
#202744772
C4×C22⋊#883222
C2×C53×#5292
#2138153