Finite Group Databasebeta

← #36476063

Subgroups — #36476063

Order 22784.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151491C211yesmaximal, characteristic
2C2×#19151473C211yesmaximal, characteristic
3#26018489C211yesmaximal, characteristic
4#26018489C211yesmaximal, characteristic
5#26018486C211yesmaximal, characteristic, complemented
6#26018486C211yesmaximal, characteristic, complemented
7#26018486C211yesmaximal, characteristic, complemented
8#26018484C211yesmaximal, characteristic, complemented
9#26018482C211yesmaximal, characteristic, complemented
10#26018481C211yesmaximal, characteristic, complemented
11#26018479C211yesmaximal, characteristic, complemented
12#26018477C211yesmaximal, characteristic, complemented
13#26018474C211yesmaximal, characteristic
14#26018474C211yesmaximal, characteristic
15C2×#388×C89C211yesmaximal, characteristic
16C24×Dic89C2211yescharacteristic
17C22×C4⋊Dic89C2211yescharacteristic
18C22×C4⋊Dic89C2211yescharacteristic
19C22×C4⋊Dic89C2211yescharacteristic
20C22×C22⋊Dic89C2211yescharacteristic
21C22×C22⋊Dic89C2211yescharacteristic
22C22×C22⋊Dic89C2211yescharacteristic
23C22×C4×Dic89C2211yescharacteristic
24C22×C4×Dic89C2211yescharacteristic
25C22×C4×Dic89C2211yescharacteristic
26#19151491C418yescomplemented
27#19151473C418yescomplemented
28C2×#15667919C2211yescharacteristic
29C2×#15667919C2211yescharacteristic
30C2×#15667919C2211yescharacteristic
31C2×#15667919C2211yescharacteristic
32C2×#15667919C2211yescharacteristic
33C2×#15667919C2211yescharacteristic
34C2×#15667919C2211yescharacteristic
35C2×#15667919C2211yescharacteristic
36C2×#15667919C2211yescharacteristic
37C2×#15667919C2211yescharacteristic
38C2×#15667919C2211yescharacteristic
39C2×#15667919C2211yescharacteristic
40C2×#15667919C2211yescharacteristic
41C2×#15667919C2211yescharacteristic
42C2×#15667919C2211yescharacteristic
43C2×#15667919C2211yescharacteristic
44C2×#15667919C2211yescharacteristic
45C2×#15667919C2211yescharacteristic
46C22×C4⋊C4×C89C2211yescharacteristic
47C22×C22⋊C4×C89C2211yescharacteristic
48C22×C22⋊C4×C89C2211yescharacteristic
49C22×C22⋊C4×C89C2211yescharacteristic
50C22×C42×C89C2211yescharacteristic
51#388×C89C418yescomplemented
52C2×#95×C89C2211yescharacteristic
53C2×#95×C89C2211yescharacteristic
54C23×Dic89—41no—
55C23×Dic89—41no—
56C23×Dic89—41no—
57C23×Dic89—41no—
58C23×Dic89—41no—
59C23×Dic89—41no—
60C23×Dic89C2×C414yes—
61C23×Dic89C2311yescharacteristic
62C23×Dic89C2311yescharacteristic
63C23×Dic89C2311yescharacteristic
64C23×Dic89C2311yescharacteristic
65C23×Dic89C2311yescharacteristic
66C23×Dic89C2311yescharacteristic
67C23×Dic89C2311yescharacteristic
68C23×Dic89C2311yescharacteristic
69C2×C4⋊Dic89—41no—
70C2×C4⋊Dic89—41no—
71C2×C4⋊Dic89—41no—
72C2×C4⋊Dic89—41no—
73C2×C4⋊Dic89—41no—
74C2×C4⋊Dic89—41no—
75C2×C4⋊Dic89C2×C414yes—
76C2×C4⋊Dic89C2×C414yes—
77C2×C4⋊Dic89C2×C414yescomplemented
78C2×C22⋊Dic89—41no—
79C2×C22⋊Dic89—41no—
80C2×C22⋊Dic89—41no—
81C2×C22⋊Dic89—41no—
82C2×C22⋊Dic89—41no—
83C2×C22⋊Dic89—41no—
84C2×C22⋊Dic89C2×C414yes—
85C2×C22⋊Dic89C2×C414yes—
86C2×C22⋊Dic89C2×C414yes—
87C2×C4×Dic89—41no—
88C2×C4×Dic89—41no—
89C2×C4×Dic89—41no—
90C2×C4×Dic89—41no—
91C2×C4×Dic89—41no—
92C2×C4×Dic89—41no—
93C2×C4×Dic89—41no—
94C2×C4×Dic89—41no—
95C2×C4×Dic89C2×C414yescomplemented
96#15667919—41no—
97#15667919—41no—
98#15667919—41no—
99#15667919—41no—
100#15667919—41no—
101#15667919—41no—
102#15667919—41no—
103#15667919—41no—
104#15667919—41no—
105#15667919—41no—
106#15667919—41no—
107#15667919—41no—
108#15667919—41no—
109#15667919—41no—
110#15667919C2×C414yes—
111#15667919C2×C414yes—
112#15667919C2×C414yescomplemented
113#15667919C2×C414yescomplemented
114C25×C89C2311yescharacteristic
115C23×C4×C89C2311yescharacteristic
116C23×C4×C89C2311yescharacteristic
117C23×C4×C89C2311yescharacteristic
118C23×C4×C89C2311yescharacteristic
119C23×C4×C89C2311yescharacteristic
120C23×C4×C89C2311yescharacteristic
121C2×C4⋊C4×C89—41no—
122C2×C4⋊C4×C89—41no—
123C2×C4⋊C4×C89C2×C414yescomplemented
124C2×C22⋊C4×C89—41no—
125C2×C22⋊C4×C89—41no—
126C2×C22⋊C4×C89—41no—
127C2×C22⋊C4×C89—41no—
128C2×C22⋊C4×C89C2×C414yes—
129C2×C22⋊C4×C89C2×C414yes—
130C2×C22⋊C4×C89C2×C414yes—
131C2×C22⋊C4×C89C2×C414yes—
132C2×C22⋊C4×C89C2×C414yes—
133C2×C42×C89—41no—
134C2×C42×C89—41no—
135C2×C42×C89C2×C414yescomplemented
136#95×C89C2×C414yescomplemented
137#95×C89C2×C414yescomplemented
138C22×Dic89—21no—
139C22×Dic89—21no—
140C22×Dic89—21no—
141C22×Dic89—21no—
142C22×Dic89—21no—
143C22×Dic89—21no—
144C22×Dic89—21no—
145C22×Dic89—21no—
146C22×Dic89—21no—
147C22×Dic89—21no—
148C22×Dic89—21no—
149C22×Dic89—21no—
150C22×Dic89—21no—
151C22×Dic89—21no—
152C22×Dic89—21no—
153C22×Dic89—21no—
154C22×Dic89—21no—
155C22×Dic89—21no—
156C22×Dic89—21no—
157C22×Dic89—21no—
158C22×Dic89—21no—
159C22×Dic89—21no—
160C22×Dic89—21no—
161C22×Dic89—21no—
162C22×Dic89—21no—
163C22×Dic89—21no—
164C22×Dic89—21no—
165C22×Dic89—21no—
166C22×Dic89—21no—
167C22×Dic89—21no—
168C22×Dic89—21no—
169C22×Dic89—21no—
170C22×Dic89—21no—
171C22×Dic89—21no—
172C22×Dic89—21no—
173C22×Dic89—21no—
174C22×Dic89—21no—
175C22×Dic89—21no—
176C22×Dic89—21no—
177C22×Dic89—21no—
178C22×Dic89—21no—
179C22×Dic89—21no—
180C22×Dic89—21no—
181C22×Dic89—21no—
182C22×Dic89—21no—
183C22×Dic89—21no—
184C22×Dic89—21no—
185C22×Dic89—21no—
186C22×Dic89—44no—
187C22×Dic89—44no—
188C22×Dic89—44no—
189C22×Dic89—44no—
190C22×Dic89—44no—
191C22×Dic89—44no—
192C22×Dic89—44no—
193C22×Dic89C22×C412yes—
194C22×Dic89C22×C412yes—
195C22×Dic89C22×C412yes—
196C22×Dic89C22×C412yes—
197C22×Dic89C22×C412yes—
198C22×Dic89C22×C412yes—
199C22×Dic89C22×C412yes—
200C22×Dic89C22×C412yes—
201C4⋊Dic89—44no—
202C4⋊Dic89—44no—
203C4⋊Dic89—44no—
204C22⋊Dic89—44no—
205C22⋊Dic89—44no—
206C22⋊Dic89—44no—
207C4×Dic89—44no—
208C4×Dic89—44no—
209C4×Dic89—44no—
210C24×C89—21no—
211C24×C89—21no—
212C24×C89—21no—
213C24×C89—21no—
214C24×C89—21no—
215C24×C89—21no—
216C24×C89—21no—
217C24×C89—21no—
218C24×C89—21no—
219C24×C89—21no—
220C24×C89—21no—
221C24×C89—21no—
222C24×C89C22×C412yes—
223C24×C89C22×C412yes—
224C24×C89C22×C412yes—
225C24×C89C2411yescharacteristic
226C22×C4×C89—21no—
227C22×C4×C89—21no—
228C22×C4×C89—21no—
229C22×C4×C89—21no—
230C22×C4×C89—21no—
231C22×C4×C89—21no—
232C22×C4×C89—21no—
233C22×C4×C89—21no—
234C22×C4×C89—21no—
235C22×C4×C89—21no—
236C22×C4×C89—21no—
237C22×C4×C89—21no—
238C22×C4×C89—21no—
239C22×C4×C89—21no—
240C22×C4×C89—21no—
241C22×C4×C89—21no—
242C22×C4×C89—21no—
243C22×C4×C89—21no—
244C22×C4×C89—21no—
245C22×C4×C89—21no—
246C22×C4×C89—21no—
247C22×C4×C89—21no—
248C22×C4×C89—21no—
249C22×C4×C89—21no—
250C22×C4×C89—21no—
251C22×C4×C89—21no—
252C22×C4×C89—21no—
253C22×C4×C89—21no—
254C22×C4×C89—21no—
255C22×C4×C89—21no—
256C22×C4×C89—21no—
257C22×C4×C89—21no—
258C22×C4×C89C22×C412yes—
259C22×C4×C89C22×C412yes—
260C22×C4×C89C22×C412yes—
261C22×C4×C89C22×C412yes—
262C22×C4×C89C22×C412yes—
263C22×C4×C89C22×C412yes—
264C22×C4×C89C22×C412yes—
265C22×C4×C89C22×C412yes—
266C22×C4×C89C22×C412yes—
267C22×C4×C89C22×C412yes—
268C4⋊C4×C89—44no—
269C22⋊C4×C89—44no—
270C22⋊C4×C89—44no—
271C22⋊C4×C89C42116yescomplemented
272C42×C89—44no—
273C23×C89—22no—
274C23×C89—22no—
275C23×C89—22no—
276C23×C89—22no—
277C23×C89—22no—
278C23×C89—22no—
279C23×C89—22no—
280C23×C89—22no—
281C23×C89—22no—
282C23×C89—22no—
283C23×C89—22no—
284C23×C89—22no—
285C23×C89—22no—
286C23×C89—22no—
287C23×C89—22no—
288C23×C89—22no—
289C23×C89—22no—
290C23×C89—22no—
291C23×C89—41no—
292C23×C89—41no—
293C23×C89—41no—
294C23×C89—41no—
295C23×C89—41no—
296C23×C89—41no—
297C23×C89—41no—
298C23×C89—41no—
299C23×C89—41no—
300C23×C89—41no—
301C23×C89—41no—
302C23×C89—41no—
303C23×C89—41no—
304C23×C89—41no—
305C23×C89—41no—
306C23×C89—41no—
307C23×C89C2×C4214yes—
308C23×C89C23×C411yescharacteristic
309C23×C89C23×C411yescharacteristic
310C23×C89C23×C411yescharacteristic
311C23×C89H(5,𝔽2)11yescharacteristic
312C23×C89H(5,𝔽2)11yescharacteristic
313C23×C89H(5,𝔽2)11yescharacteristic
314C23×C89H(5,𝔽2)11yescharacteristic
315C23×C89H(5,𝔽2)11yescharacteristic
316C23×C89H(5,𝔽2)11yescharacteristic
317C23×C89H(5,𝔽2)11yescharacteristic
318C23×C89H(5,𝔽2)11yescharacteristic
319C23×C892−1+411yescharacteristic
320C23×C892−1+411yescharacteristic
321C23×C892−1+411yescharacteristic
322C23×C892−1+411yescharacteristic
323C2×C4×C89—22no—
324C2×C4×C89—22no—
325C2×C4×C89—22no—
326C2×C4×C89—22no—
327C2×C4×C89—22no—
328C2×C4×C89—22no—
329C2×C4×C89—22no—
330C2×C4×C89—22no—
331C2×C4×C89—22no—
332C2×C4×C89—22no—
333C2×C4×C89—22no—
334C2×C4×C89—22no—
335C2×C4×C89—22no—
336C2×C4×C89—22no—
337C2×C4×C89—22no—
338C2×C4×C89—22no—
339C2×C4×C89—22no—
340C2×C4×C89—22no—
341C2×C4×C89—22no—
342C2×C4×C89—22no—
343C2×C4×C89—22no—
344C2×C4×C89—22no—
345C2×C4×C89—22no—
346C2×C4×C89—22no—
347C2×C4×C89—41no—
348C2×C4×C89—41no—
349C2×C4×C89—41no—
350C2×C4×C89—41no—
351C2×C4×C89—41no—
352C2×C4×C89—41no—
353C2×C4×C89—41no—
354C2×C4×C89—41no—
355C2×C4×C89—41no—
356C2×C4×C89—41no—
357C2×C4×C89—41no—
358C2×C4×C89—41no—
359C2×C4×C89—41no—
360C2×C4×C89—41no—
361C2×C4×C89—41no—
362C2×C4×C89—41no—
363C2×C4×C89C2×C4214yes—
364C2×C4×C89C2×C4214yes—
365C2×Dic89—22no—
366C2×Dic89—22no—
367C2×Dic89—22no—
368C2×Dic89—22no—
369C2×Dic89—22no—
370C2×Dic89—22no—
371C2×Dic89—22no—
372C2×Dic89—22no—
373C2×Dic89—22no—
374C2×Dic89—22no—
375C2×Dic89—22no—
376C2×Dic89—22no—
377C2×Dic89—22no—
378C2×Dic89—22no—
379C2×Dic89—22no—
380C2×Dic89—22no—
381C2×Dic89—22no—
382C2×Dic89—22no—
383C2×Dic89—22no—
384C2×Dic89—22no—
385C2×Dic89—22no—
386C2×Dic89—22no—
387C2×Dic89—22no—
388C2×Dic89—22no—
389C2×Dic89—416no—
390C2×Dic89—41no—
391C2×Dic89—41no—
392C2×Dic89—41no—
393C2×Dic89—41no—
394C2×Dic89—41no—
395C2×Dic89—41no—
396C2×Dic89—41no—
397C2×Dic89—41no—
398C2×Dic89—41no—
399C2×Dic89—41no—
400C2×Dic89—41no—
401C2×Dic89—41no—
402C2×Dic89—41no—
403C2×Dic89—41no—
404C2×Dic89—41no—
405C2×Dic89—41no—
406C2×Dic89—41no—
407C2×Dic89—41no—
408C2×Dic89—41no—
409C2×Dic89—41no—
410C2×Dic89—41no—
411C2×Dic89—41no—
412C2×Dic89—41no—
413C2×Dic89—41no—
414C2×Dic89—41no—
415C2×Dic89—41no—
416C2×Dic89—41no—
417C2×Dic89—41no—
418C2×Dic89—41no—
419C2×Dic89—41no—
420C2×Dic89—41no—
421C2×Dic89—41no—
422C22×C89—24no—
423C22×C89—24no—
424C22×C89—24no—
425C22×C89—42no—
426C22×C89—42no—
427C22×C89—42no—
428C22×C89—42no—
429C22×C89—42no—
430C22×C89—42no—
431C22×C89—42no—
432C22×C89—42no—
433C22×C89—42no—
434C22×C89—42no—
435C22×C89—42no—
436C22×C89—42no—
437C22×C89C22×C4211yescharacteristic
438C22×C89#51811yescharacteristic
439C22×C89#51811yescharacteristic
440C22×C89#51811yescharacteristic
441C22×C89#51811yescharacteristic
442C22×C89#51811yescharacteristic
443C22×C89#51811yescharacteristic
444C22×C89#51811yescharacteristic
445C22×C89#51911yescharacteristic
446C22×C89#52011yescharacteristic
447C22×C89#52011yescharacteristic
448C22×C89#52011yescharacteristic
449C22×C89#52011yescharacteristic
450C22×C89#52011yescharacteristic
451C22×C89#52011yescharacteristic
452C22×C89#52011yescharacteristic
453C22×C89#52011yescharacteristic
454C22×C89#52011yescharacteristic
455C22×C89#52011yescharacteristic
456C22×C89#56011yescharacteristic
457C22×C89#56011yescharacteristic
458C22×C89#56011yescharacteristic
459C22×C89#56011yescharacteristic
460C22×C89H(3,𝔽4)11yescharacteristic
461C22×C89#56211yescharacteristic
462C22×C89#56211yescharacteristic
463C22×C89#56211yescharacteristic
464C22×C89#56211yescharacteristic
465C22×C89#56211yescharacteristic
466C22×C89#56211yescharacteristic
467C22×C89#56311yescharacteristic
468C22×C89#56311yescharacteristic
469C22×C89#56311yescharacteristic
470C22×C89#56311yescharacteristic
471C22×C89#56311yescharacteristic
472C4×C89—24no—
473C4×C89—24no—
474C4×C89—42no—
475C4×C89—42no—
476C4×C89—42no—
477C4×C89—42no—
478Dic89—42no—
479Dic89—42no—
480Dic89—42no—
481Dic89—42no—
482Dic89—42no—
483Dic89—42no—
484Dic89—42no—
485Dic89—42no—
486#13831—891nomaximal, Sylow
487C2×C89—44no—
488C2×C89#227411yescharacteristic
489C2×C89#227511yescharacteristic
490C2×C89#227511yescharacteristic
491C2×C89#237511yescharacteristic
492C2×C89#237611yescharacteristic
493C2×C89#237611yescharacteristic
494C2×C89#237611yescharacteristic
495C2×C89#237711yescharacteristic
496C2×C89#237711yescharacteristic
497C2×C89#237811yescharacteristic
498C2×C89#237811yescharacteristic
499C2×C89#237911yescharacteristic
500C2×C89#237911yescharacteristic
501C2×C89#238311yescharacteristic
502C2×C89#238311yescharacteristic
503C2×#388—891no—
504C2×#388D8911yescharacteristic
505C2×#385—891no—
506#1437—891no—
507#1437—891no—
508#1436—891no—
509#1436—891no—
510#1436—891no—
511#1436—891no—
512C4⋊#95—891no—
513C4⋊#95—891no—
514#1434—891no—
515#1434—891no—
516C22⋊#95—891no—
517C22⋊#95—891no—
518C89#1383111yescharacteristic, complemented, Sylow
519C24×C4—891no—
520C22×C4⋊C4—891no—
521C22×C4⋊C4—891no—
522C22×C4⋊C4—891no—
523C22×C4⋊C4C2×D8911yescharacteristic
524C22×C22⋊C4—891no—
525C22×C22⋊C4—891no—
526C22×C22⋊C4—891no—
527C22×C22⋊C4C2×D8911yescharacteristic
528C22×C22⋊C4C2×D8911yescharacteristic
529C22×C22⋊C4C2×D8911yescharacteristic
530C22×C42—891no—
531C22×C42—891no—
532C22×C42—891no—
533C22×C42C2×D8911yescharacteristic
534#388—898no—
535#388Dic8918yescomplemented
536#385—898no—
537C2×#95—891no—
538C2×#95—891no—
539C2×#95—891no—
540C2×#95—891no—
541C2×#95—891no—
542C2×#95—891no—
543C2×#95—891no—
544C2×#95—891no—
545C2×#95—891no—
546C2×#95—891no—
547C2×#95—891no—
548C2×#95—891no—
549C2×#95—891no—
550C2×#95—891no—
551C2×#95—891no—
552C2×#95—891no—
553C2×#95—891no—
554C2×#95—891no—
555C2×#95C2×D8911yescharacteristic
556C2×#95C2×D8911yescharacteristic
557C25C22×D8911yescharacteristic
558C23×C4—894no—
559C23×C4—891no—
560C23×C4—891no—
561C23×C4—891no—
562C23×C4—891no—
563C23×C4—891no—
564C23×C4—891no—
565C23×C4—891no—
566C23×C4—891no—
567C23×C4—3561no—
568C23×C4—3561no—
569C23×C4—3561no—
570C23×C4—3561no—
571C23×C4—3561no—
572C23×C4—3561no—
573C23×C4C22×D8911yescharacteristic
574C23×C4C22×D8911yescharacteristic
575C23×C4C22×D8911yescharacteristic
576C23×C4C22×D8911yescharacteristic
577C23×C4C22×D8911yescharacteristic
578C23×C4C22×D8911yescharacteristic
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—894no—
582C2×C4⋊C4—894no—
583C2×C4⋊C4—894no—
584C2×C4⋊C4—3561no—
585C2×C4⋊C4—3561no—
586C2×C4⋊C4—3561no—
587C2×C4⋊C4—3561no—
588C2×C4⋊C4—3561no—
589C2×C4⋊C4—3561no—
590C2×C4⋊C4C2×Dic8914yescomplemented
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—894no—
596C2×C22⋊C4—894no—
597C2×C22⋊C4—894no—
598C2×C22⋊C4—3561no—
599C2×C22⋊C4—3561no—
600C2×C22⋊C4—3561no—
601C2×C22⋊C4—3561no—
602C2×C22⋊C4—3561no—
603C2×C22⋊C4—3561no—
604C2×C22⋊C4C4×D8914yes—
605C2×C22⋊C4C4×D8914yes—
606C2×C22⋊C4C2×Dic8914yes—
607C2×C22⋊C4C2×Dic8914yes—
608C2×C22⋊C4C2×Dic8914yes—
609C2×C42—41no—
610C2×C42—41no—
611C2×C42—894no—
612C2×C42—3561no—
613C2×C42—3561no—
614C2×C42—3561no—
615C2×C42—3561no—
616C2×C42—3561no—
617C2×C42—3561no—
618C2×C42—3561no—
619C2×C42—3561no—
620C2×C42C2×Dic8914yescomplemented
621#95—894no—
622#95—894no—
623#95—894no—
624#95—894no—
625#95—3561no—
626#95—3561no—
627#95—3561no—
628#95—3561no—
629#95—3561no—
630#95—3561no—
631#95—3561no—
632#95—3561no—
633#95—3561no—
634#95—3561no—
635#95—3561no—
636#95—3561no—
637#95—3561no—
638#95—3561no—
639#95C2×Dic8914yescomplemented
640#95C2×Dic8914yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D8912yes—
654C24C2×C4×D8912yes—
655C24C22×Dic8912yes—
656C24C23×D8911yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—892no—
690C22×C4—892no—
691C22×C4—892no—
692C22×C4—892no—
693C22×C4—892no—
694C22×C4—892no—
695C22×C4—892no—
696C22×C4—892no—
697C22×C4—3564no—
698C22×C4—3564no—
699C22×C4—3564no—
700C22×C4—3564no—
701C22×C4—3564no—
702C22×C4—3564no—
703C22×C4—3564no—
704C22×C4—1781no—
705C22×C4—1781no—
706C22×C4—1781no—
707C22×C4—1781no—
708C22×C4—1781no—
709C22×C4—1781no—
710C22×C4—1781no—
711C22×C4—1781no—
712C22×C4—1781no—
713C22×C4—1781no—
714C22×C4—1781no—
715C22×C4—1781no—
716C22×C4—1781no—
717C22×C4—1781no—
718C22×C4—1781no—
719C22×C4—1781no—
720C22×C4—1781no—
721C22×C4—1781no—
722C22×C4—1781no—
723C22×C4—1781no—
724C22×C4—1781no—
725C22×C4—1781no—
726C22×C4—1781no—
727C22×C4—1781no—
728C22×C4—1781no—
729C22×C4—1781no—
730C22×C4—1781no—
731C22×C4—1781no—
732C22×C4—1781no—
733C22×C4—1781no—
734C22×C4—1781no—
735C22×C4—1781no—
736C22×C4—1781no—
737C22×C4—1781no—
738C22×C4—1781no—
739C22×C4—1781no—
740C22×C4—1781no—
741C22×C4—1781no—
742C22×C4—1781no—
743C22×C4—1781no—
744C22×C4—1781no—
745C22×C4—1781no—
746C22×C4—1781no—
747C22×C4—1781no—
748C22×C4—1781no—
749C22×C4—1781no—
750C22×C4—1781no—
751C22×C4—1781no—
752C22×C4C2×C4×D8912yes—
753C22×C4C2×C4×D8912yes—
754C22×C4C2×C4×D8912yes—
755C22×C4C2×C4×D8912yes—
756C22×C4C22×Dic8912yes—
757C22×C4C22×Dic8912yes—
758C22×C4C22×Dic8912yes—
759C22×C4C22×Dic8912yes—
760C22×C4C22×Dic8912yes—
761C22×C4C22×Dic8912yes—
762C4⋊C4—44no—
763C4⋊C4—3564no—
764C4⋊C4—3564no—
765C4⋊C4—3564no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—3564no—
769C22⋊C4—3564no—
770C22⋊C4—3564no—
771C22⋊C4C4×Dic89116yescomplemented
772C42—44no—
773C42—3564no—
774C42—3564no—
775C42—3564no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4×Dic8914yes—
811C23C22×C4×D8911yescharacteristic
812C23C22×C4×D8911yescharacteristic
813C23C23×Dic8911yescharacteristic
814C23#1566805711yescharacteristic
815C23#1566805711yescharacteristic
816C23#1566805711yescharacteristic
817C23#1566805711yescharacteristic
818C23#1566805811yescharacteristic
819C23#1566805811yescharacteristic
820C23#1566805811yescharacteristic
821C23#1566805811yescharacteristic
822C23#1566805911yescharacteristic
823C23#1566805911yescharacteristic
824C23#1566805911yescharacteristic
825C23#1566805911yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—35616no—
867C2×C4—3561no—
868C2×C4—3561no—
869C2×C4—3561no—
870C2×C4—3561no—
871C2×C4—3561no—
872C2×C4—3561no—
873C2×C4—3561no—
874C2×C4—3561no—
875C2×C4—3561no—
876C2×C4—3561no—
877C2×C4—3561no—
878C2×C4—3561no—
879C2×C4—3561no—
880C2×C4—3561no—
881C2×C4—3561no—
882C2×C4—3561no—
883C2×C4—3561no—
884C2×C4—3561no—
885C2×C4—3561no—
886C2×C4—3561no—
887C2×C4—3561no—
888C2×C4—3561no—
889C2×C4—3561no—
890C2×C4—3561no—
891C2×C4—3561no—
892C2×C4—3561no—
893C2×C4—3561no—
894C2×C4—3561no—
895C2×C4—3561no—
896C2×C4—3561no—
897C2×C4—3561no—
898C2×C4—3561no—
899C2×C4—1782no—
900C2×C4—1782no—
901C2×C4—1782no—
902C2×C4—1782no—
903C2×C4—1782no—
904C2×C4—1782no—
905C2×C4—1782no—
906C2×C4—1782no—
907C2×C4—1782no—
908C2×C4—1782no—
909C2×C4—1782no—
910C2×C4—1782no—
911C2×C4—1782no—
912C2×C4—1782no—
913C2×C4—1782no—
914C2×C4—1782no—
915C2×C4—1782no—
916C2×C4—1782no—
917C2×C4—1782no—
918C2×C4—1782no—
919C2×C4—1782no—
920C2×C4—1782no—
921C2×C4—1782no—
922C2×C4—1782no—
923C2×C4C2×C4×Dic8914yes—
924C2×C4C2×C4×Dic8914yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4×Dic8911yescharacteristic
941C22#1915207011yescharacteristic
942C22#1915207011yescharacteristic
943C22#1915207011yescharacteristic
944C22#1915207011yescharacteristic
945C22#1915207211yescharacteristic
946C22#1915207311yescharacteristic
947C22#1915207311yescharacteristic
948C22#1915207511yescharacteristic
949C22#1915207711yescharacteristic
950C22#1915207711yescharacteristic
951C22#1915207711yescharacteristic
952C22#1915207711yescharacteristic
953C22#1915207811yescharacteristic
954C22#1915207811yescharacteristic
955C22#1915208111yescharacteristic
956C22#1915208111yescharacteristic
957C22#1915208111yescharacteristic
958C22#1915208111yescharacteristic
959C22#1915233611yescharacteristic
960C22#1915233611yescharacteristic
961C22#1915233811yescharacteristic
962C22#1915233911yescharacteristic
963C22#1915234011yescharacteristic
964C22#1915234211yescharacteristic
965C22#1915234211yescharacteristic
966C22#1915234311yescharacteristic
967C22#1915234311yescharacteristic
968C22#1915234511yescharacteristic
969C22#1915234511yescharacteristic
970C22#1915234811yescharacteristic
971C22#1915235011yescharacteristic
972C22#1915235011yescharacteristic
973C22#1915235011yescharacteristic
974C22#1915235111yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—3562no—
982C4—3562no—
983C4—3562no—
984C4—3562no—
985C4—3562no—
986C4—3562no—
987C4—3562no—
988C4—3562no—
989C2—44no—
990C2#2602260811yescharacteristic
991C2#2602261311yescharacteristic
992C2#2602261311yescharacteristic
993C2#2602339211yescharacteristic
994C2#2602339411yescharacteristic
995C2#2602339811yescharacteristic
996C2#2602340011yescharacteristic
997C2#2602340511yescharacteristic
998C2#2602340911yescharacteristic
999C2#2602341211yescharacteristic
1000C2#2602341911yescharacteristic
1001C2#2602342111yescharacteristic
1002C2#2602342611yescharacteristic
1003C2#2602343911yescharacteristic
1004C2#2602344411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D89
commutatorC22×C89C22×C42
FittingC2×#388×C89C2
socle, cosocleC24×C89C24
prime radicalC25×C89C23
hypercenterC2×#388D89
hypocenterC89#13831
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. #26018486C2semidirect
6. #26018486C2semidirect
7. #26018486C2semidirect
8. #26018484C2semidirect
9. #26018482C2semidirect
10. #26018481C2semidirect
11. #26018479C2semidirect
12. #26018477C2semidirect
26. #19151491C4semidirect
27. #19151473C4semidirect
51. #388×C89C4semidirect
77. C2×C4⋊Dic89C2×C4semidirect
95. C2×C4×Dic89C2×C4semidirect
112. #15667919C2×C4semidirect
113. #15667919C2×C4semidirect
123. C2×C4⋊C4×C89C2×C4semidirect
135. C2×C42×C89C2×C4semidirect
136. #95×C89C2×C4semidirect
137. #95×C89C2×C4semidirect
271. C22⋊C4×C89C42semidirect
518. C89#13831semidirect
535. #388Dic89semidirect
590. C2×C4⋊C4C2×Dic89semidirect
620. C2×C42C2×Dic89semidirect
639. #95C2×Dic89semidirect
640. #95C2×Dic89semidirect
771. C22⋊C4C4×Dic89semidirect

Maximal subgroups

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

subgroupindex
C2×#191514912
C2×#191514732
#260184892
#260184862
#260184842
#260184822
#260184812
#260184792
#260184772
#260184742
C2×#388×C892
#1383189