Finite Group Databasebeta

← C2×#26023399 #36717014

Subgroups — C2×#26023399 #36717014

Order 22784.

2870 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667997C211yesmaximal, characteristic
2#26023399C2116yesmaximal, direct product factor
3C2×#19151500C211yesmaximal, characteristic
4C2×#19151497C211yesmaximal, characteristic, complemented
5C2×#19151495C211yesmaximal, characteristic, complemented
6C2×#19151490C211yesmaximal, characteristic, complemented
7C2×#19151488C211yesmaximal, characteristic, complemented
8C2×#19151487C211yesmaximal, characteristic, complemented
9C2×#19151487C211yesmaximal, characteristic, complemented
10C2×#19151482C211yesmaximal, characteristic, complemented
11C2×#19151476C211yesmaximal, characteristic
12C2×#19151472C211yesmaximal, characteristic, complemented
13C2×#19151472C211yesmaximal, characteristic, complemented
14C2×#19151457C211yesmaximal, characteristic, complemented
15C2×#19151455C211yesmaximal, characteristic, complemented
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×D356C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C2×#15667997C4116yescomplemented
21C2×#15667997C2218yes—
22C22×C4⋊Dic89C2211yescharacteristic
23C22×C4⋊Dic89C2211yescharacteristic
24C22×C4⋊Dic89C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×#13083551C2211yescharacteristic
33C22×#13083551C2211yescharacteristic
34C22×#13083551C2211yescharacteristic
35C22×#13083551C2211yescharacteristic
36C22×#13083551C2211yescharacteristic
37C22×#13083551C2211yescharacteristic
38C22×#13083551C2211yescharacteristic
39C22×C4×Dic89C2211yescharacteristic
40C22×C4×Dic89C2211yescharacteristic
41#19151500C2218yes—
42#19151497C2218yescomplemented
43#19151495C2218yescomplemented
44#19151490C2218yescomplemented
45#19151488C2218yescomplemented
46#19151487C2218yescomplemented
47#19151487C2218yescomplemented
48#19151482C2218yescomplemented
49#19151476C2218yes—
50#19151472C2218yescomplemented
51#19151472C2218yescomplemented
52#19151457C2218yescomplemented
53#19151455C2218yescomplemented
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C22×C4⋊C4×C89C2211yescharacteristic
61C22×C4⋊C4×C89C2211yescharacteristic
62C22×C42×C89C2211yescharacteristic
63#387×C89C2218yescomplemented
64C2×#95×C89C2211yescharacteristic
65C2×#95×C89C2211yescharacteristic
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C24×D89C2311yescharacteristic
69C24×D89C2311yescharacteristic
70C22×D356—42no—
71C22×D356—42no—
72C22×D356C2×C418yes—
73C22×D356C2314yes—
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C22×C4×D89—42no—
81C22×C4×D89—42no—
82C22×C4×D89—42no—
83C22×C4×D89—42no—
84C22×C4×D89—42no—
85C22×C4×D89C2×C418yescomplemented
86C22×C4×D89C2314yes—
87C22×C4×D89C2314yes—
88#15667997C2×C4164yescomplemented
89C2×C4⋊Dic89—42no—
90C2×C4⋊Dic89—42no—
91C2×C4⋊Dic89—42no—
92C2×C4⋊Dic89C2314yes—
93C2×C4⋊Dic89C2314yes—
94C2×C4⋊Dic89C2314yes—
95C2×#13083553—42no—
96C2×#13083553—42no—
97C2×#13083553—42no—
98C2×#13083553C2×C418yescomplemented
99C2×#13083553C2314yes—
100C2×#13083553C2314yes—
101C2×#13083553C2314yes—
102C2×#13083553C2314yes—
103C2×#13083551—42no—
104C2×#13083551—42no—
105C2×#13083551—42no—
106C2×#13083551—42no—
107C2×#13083551—42no—
108C2×#13083551—42no—
109C2×#13083551—42no—
110C2×#13083551C2×C418yes—
111C2×#13083551C2×C418yes—
112C2×#13083551C2×C418yescomplemented
113C2×#13083551C2314yes—
114C2×#13083551C2314yes—
115C2×#13083551C2314yes—
116C2×#13083551C2314yes—
117C2×#13083551C2314yes—
118C2×#13083551C2314yes—
119C2×#13083551C2314yes—
120C2×#13083551C2314yes—
121C2×#13083551C2314yes—
122C2×#13083551C2314yes—
123C2×C4×Dic89—42no—
124C2×C4×Dic89—42no—
125C2×C4×Dic89C2314yes—
126C2×C4×Dic89C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131#15667919C2314yes—
132#15667919C2314yes—
133C23×C4×C89C2311yescharacteristic
134C23×C4×C89C2311yescharacteristic
135C23×C4×C89C2311yescharacteristic
136C23×C4×C89C2311yescharacteristic
137C23×C4×C89C2311yescharacteristic
138C23×C4×C89C2311yescharacteristic
139C23×C4×C89C2311yescharacteristic
140C2×C4⋊C4×C89—42no—
141C2×C4⋊C4×C89C2×C418yescomplemented
142C2×C4⋊C4×C89C2314yes—
143C2×C4⋊C4×C89C2314yes—
144C2×C42×C89—42no—
145C2×C42×C89C2314yes—
146#95×C89C2314yes—
147#95×C89C2314yes—
148#95×C89C2314yes—
149#95×C89C2314yes—
150C23×D89—22no—
151C23×D89—22no—
152C23×D89—22no—
153C23×D89—22no—
154C23×D89—22no—
155C23×D89—22no—
156C23×D89—22no—
157C23×D89—22no—
158C23×D89—22no—
159C23×D89—22no—
160C23×D89—22no—
161C23×D89—22no—
162C23×D89C22×C414yes—
163C23×D89C22×C414yes—
164C23×D89C2412yes—
165C23×D89C2412yes—
166C2×D356—416no—
167C2×D356—44no—
168C2×D356—44no—
169C2×D356C22×C4116yes—
170C22×Dic89—22no—
171C22×Dic89—22no—
172C22×Dic89—22no—
173C22×Dic89—22no—
174C22×Dic89—22no—
175C22×Dic89—22no—
176C22×Dic89—22no—
177C22×Dic89—22no—
178C22×Dic89—22no—
179C22×Dic89—22no—
180C22×Dic89—22no—
181C22×Dic89—22no—
182C22×Dic89—22no—
183C22×Dic89—22no—
184C22×Dic89—22no—
185C22×Dic89—22no—
186C22×Dic89C22×C414yes—
187C22×Dic89C22×C414yes—
188C22×Dic89C2412yes—
189C22×Dic89C2412yes—
190C22×Dic89C2412yes—
191C22×Dic89C2412yes—
192C22×Dic89C2412yes—
193C22×Dic89C2412yes—
194C2×C4×D89—416no—
195C2×C4×D89—44no—
196C2×C4×D89—44no—
197C2×C4×D89—44no—
198C2×C4×D89—44no—
199C2×C4×D89—44no—
200C2×C4×D89—416no—
201C2×C4×D89C22×C4116yescomplemented
202C4⋊Dic89—44no—
203C4⋊Dic89—44no—
204C4⋊Dic89—44no—
205#13083553—44no—
206#13083553—44no—
207#13083553—44no—
208#13083553C22×C4116yescomplemented
209#13083551—44no—
210#13083551—44no—
211#13083551—44no—
212#13083551—44no—
213#13083551—44no—
214#13083551—44no—
215#13083551—44no—
216#13083551C22×C4116yes—
217#13083551C22×C4116yes—
218#13083551C22×C4116yescomplemented
219C4×Dic89—44no—
220C4×Dic89—44no—
221C24×C89C2411yescharacteristic
222C22×C4×C89—22no—
223C22×C4×C89—22no—
224C22×C4×C89—22no—
225C22×C4×C89—22no—
226C22×C4×C89—22no—
227C22×C4×C89—22no—
228C22×C4×C89—22no—
229C22×C4×C89—22no—
230C22×C4×C89—22no—
231C22×C4×C89—22no—
232C22×C4×C89—22no—
233C22×C4×C89—22no—
234C22×C4×C89—22no—
235C22×C4×C89—22no—
236C22×C4×C89—22no—
237C22×C4×C89—22no—
238C22×C4×C89—22no—
239C22×C4×C89—22no—
240C22×C4×C89C22×C414yes—
241C22×C4×C89C22×C414yes—
242C22×C4×C89C22×C414yes—
243C22×C4×C89C2412yes—
244C22×C4×C89C2412yes—
245C22×C4×C89C2412yes—
246C22×C4×C89C2412yes—
247C22×C4×C89C2412yes—
248C22×C4×C89C2412yes—
249C22×C4×C89C2412yes—
250C4⋊C4×C89—44no—
251C4⋊C4×C89C22×C4116yescomplemented
252C42×C89—44no—
253C23×C89C23×C412yes—
254C23×C89H(5,𝔽2)12yes—
255C23×C89H(5,𝔽2)12yes—
256C23×C89H(5,𝔽2)12yes—
257C23×C89H(5,𝔽2)12yes—
258C23×C892−1+412yes—
259C23×C892−1+412yes—
260C23×C89C2511yescharacteristic
261C22×D89—28no—
262C22×D89—28no—
263C22×D89—28no—
264C22×D89—28no—
265C22×D89—28no—
266C22×D89—28no—
267C22×D89—22no—
268C22×D89—22no—
269C22×D89—22no—
270C22×D89—22no—
271C22×D89—22no—
272C22×D89—22no—
273C22×D89—22no—
274C22×D89—22no—
275C22×D89—22no—
276C22×D89—22no—
277C22×D89—22no—
278C22×D89—22no—
279C22×D89—44no—
280C22×D89—44no—
281C22×D89—44no—
282C22×D89—44no—
283C22×D89—44no—
284C22×D89—44no—
285C22×D89—44no—
286C22×D89—44no—
287C22×D89C23×C414yes—
288C22×D89C23×C414yes—
289C2×C4×C89—28no—
290C2×C4×C89—28no—
291C2×C4×C89—28no—
292C2×C4×C89—22no—
293C2×C4×C89—22no—
294C2×C4×C89—22no—
295C2×C4×C89—22no—
296C2×C4×C89—22no—
297C2×C4×C89—22no—
298C2×C4×C89—22no—
299C2×C4×C89—22no—
300C2×C4×C89—22no—
301C2×C4×C89—22no—
302C2×C4×C89—22no—
303C2×C4×C89—22no—
304C2×C4×C89—22no—
305C2×C4×C89—22no—
306C2×C4×C89—22no—
307C2×C4×C89—22no—
308C2×C4×C89—22no—
309C2×C4×C89—22no—
310C2×C4×C89—44no—
311C2×C4×C89—44no—
312C2×C4×C89—44no—
313C2×C4×C89—44no—
314C2×C4×C89C23×C414yes—
315C2×C4×C89C23×C414yes—
316C2×C4×C89C23×C414yes—
317C2×Dic89—28no—
318C2×Dic89—28no—
319C2×Dic89—22no—
320C2×Dic89—22no—
321C2×Dic89—22no—
322C2×Dic89—22no—
323C2×Dic89—22no—
324C2×Dic89—22no—
325C2×Dic89—22no—
326C2×Dic89—22no—
327C2×Dic89—22no—
328C2×Dic89—22no—
329C2×Dic89—22no—
330C2×Dic89—22no—
331C2×Dic89—22no—
332C2×Dic89—22no—
333C2×Dic89—22no—
334C2×Dic89—22no—
335C2×Dic89—44no—
336C2×Dic89—44no—
337C2×Dic89—44no—
338C2×Dic89—44no—
339C2×Dic89C23×C414yes—
340C2×Dic89C23×C414yes—
341D356—416no—
342C4×D89—416no—
343C4×D89—416no—
344C22×C89#51814yes—
345C22×C89#52014yes—
346C22×C89#52014yes—
347C22×C89#56014yes—
348C22×C89#56214yes—
349C22×C89#56214yes—
350C22×C89#56314yes—
351C22×C89C24×C411yescharacteristic
352C22×C89C2×H(5,𝔽2)11yescharacteristic
353C22×C89C2×H(5,𝔽2)11yescharacteristic
354C22×C89C2×H(5,𝔽2)11yescharacteristic
355C22×C89C2×H(5,𝔽2)11yescharacteristic
356C22×C89C2×2−1+411yescharacteristic
357C22×C89C2×2−1+411yescharacteristic
358C2×D89—24no—
359C2×D89—24no—
360C2×D89—24no—
361C2×D89—24no—
362C2×D89—24no—
363C2×D89—24no—
364C2×D89—416no—
365C2×D89—416no—
366C2×D89—42no—
367C2×D89—42no—
368C2×D89—42no—
369C2×D89—42no—
370C2×D89—42no—
371C2×D89—42no—
372C2×D89—42no—
373C2×D89—42no—
374C4×C89—24no—
375C4×C89—24no—
376C4×C89—24no—
377C4×C89—42no—
378C4×C89—42no—
379C4×C89—42no—
380C4×C89—42no—
381Dic89—24no—
382Dic89—24no—
383Dic89—42no—
384Dic89—42no—
385Dic89—42no—
386Dic89—42no—
387C2×#2376—891nomaximal, Sylow
388C2×C89#237618yescomplemented
389C2×C89C2×#51811yescharacteristic
390C2×C89C2×#52011yescharacteristic
391C2×C89C2×#52011yescharacteristic
392C2×C89C2×#56011yescharacteristic
393C2×C89C2×#56211yescharacteristic
394C2×C89C2×#56211yescharacteristic
395C2×C89C2×#56311yescharacteristic
396D89—44no—
397D89—44no—
398C22×#123—891no—
399#2376—8916no—
400C2×#390—891no—
401C2×#389—891no—
402C2×#389—891no—
403C2×#388—891no—
404C2×#388—891no—
405C2×#388—891no—
406C2×#388—891no—
407C2×#387—891no—
408C2×#387D8911yescharacteristic, complemented
409C2×#386—891no—
410C2×#385—891no—
411C2×#385—891no—
412C2×#380—891no—
413C2×#380—891no—
414C89C2×#237611yescharacteristic, complemented, Sylow
415C23×D4—891no—
416C24×C4—891no—
417C24×C4—891no—
418C2×#123—8916no—
419C2×#123—898no—
420C22×C4⋊C4—891no—
421C22×C4⋊C4—891no—
422C22×C4⋊C4—891no—
423C22×C4⋊C4—891no—
424C22×C4⋊C4—891no—
425C22×C4⋊C4—891no—
426C22×C4⋊C4—891no—
427C22×C4⋊C4C2×D8911yescharacteristic
428C22×C4⋊C4C2×D8911yescharacteristic
429C22×C22⋊C4—891no—
430C22×C22⋊C4—891no—
431C22×C22⋊C4—891no—
432C22×C22⋊C4—891no—
433C22×C22⋊C4—891no—
434C22×C22⋊C4—891no—
435C22×C22⋊C4—891no—
436C22×C22⋊C4—891no—
437C22×C22⋊C4—891no—
438C22×C22⋊C4—891no—
439C22×C42—891no—
440C22×C42—891no—
441C22×C42C2×D8911yescharacteristic
442#390—898no—
443#389—898no—
444#389—898no—
445#388—898no—
446#388—898no—
447#388—898no—
448#388—898no—
449#387—898no—
450#387C2×D8918yescomplemented
451#386—898no—
452#385—898no—
453#385—898no—
454#380—898no—
455#380—898no—
456C2×#95—891no—
457C2×#95—891no—
458C2×#95—891no—
459C2×#95—891no—
460C2×#95—891no—
461C2×#95—891no—
462C2×#95C2×D8911yescharacteristic
463C2×#95C2×D8911yescharacteristic
464C2×#95C2×D8911yescharacteristic
465C2×#95C2×D8911yescharacteristic
466C25—891no—
467C25—891no—
468C22×D4—898no—
469C22×D4—894no—
470C22×D4—3562no—
471C22×D4—3562no—
472C23×C4—891no—
473C23×C4—891no—
474C23×C4—898no—
475C23×C4—894no—
476C23×C4—891no—
477C23×C4—891no—
478C23×C4—891no—
479C23×C4—891no—
480C23×C4—894no—
481C23×C4—3562no—
482C23×C4—3562no—
483C23×C4—3562no—
484C23×C4—3562no—
485C23×C4—3562no—
486C23×C4C22×D8911yescharacteristic
487C23×C4C22×D8911yescharacteristic
488C23×C4C22×D8911yescharacteristic
489C23×C4C22×D8911yescharacteristic
490C23×C4C22×D8911yescharacteristic
491C23×C4C22×D8911yescharacteristic
492C23×C4C22×D8911yescharacteristic
493#123—8964no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—898no—
496C2×C4⋊C4—894no—
497C2×C4⋊C4—894no—
498C2×C4⋊C4—894no—
499C2×C4⋊C4—894no—
500C2×C4⋊C4—894no—
501C2×C4⋊C4—894no—
502C2×C4⋊C4—894no—
503C2×C4⋊C4—3562no—
504C2×C4⋊C4—3562no—
505C2×C4⋊C4—3562no—
506C2×C4⋊C4—3562no—
507C2×C4⋊C4—3562no—
508C2×C4⋊C4—3562no—
509C2×C4⋊C4C4×D8918yescomplemented
510C2×C4⋊C4C22×D8914yes—
511C2×C4⋊C4C22×D8914yes—
512C2×C22⋊C4—898no—
513C2×C22⋊C4—898no—
514C2×C22⋊C4—898no—
515C2×C22⋊C4—894no—
516C2×C22⋊C4—894no—
517C2×C22⋊C4—894no—
518C2×C22⋊C4—894no—
519C2×C22⋊C4—894no—
520C2×C22⋊C4—894no—
521C2×C22⋊C4—894no—
522C2×C22⋊C4—894no—
523C2×C22⋊C4—894no—
524C2×C22⋊C4—894no—
525C2×C22⋊C4—3562no—
526C2×C22⋊C4—3562no—
527C2×C22⋊C4—3562no—
528C2×C22⋊C4—3562no—
529C2×C22⋊C4—3562no—
530C2×C22⋊C4—3562no—
531C2×C22⋊C4—3562no—
532C2×C42—42no—
533C2×C42—894no—
534C2×C42—894no—
535C2×C42—3562no—
536C2×C42—3562no—
537C2×C42C22×D8914yes—
538#95—894no—
539#95—894no—
540#95—894no—
541#95—894no—
542#95—894no—
543#95—894no—
544#95C22×D8914yes—
545#95C22×D8914yes—
546#95C22×D8914yes—
547#95C22×D8914yes—
548C24—894no—
549C24—894no—
550C24—892no—
551C24—892no—
552C24—1782no—
553C24—1782no—
554C24—1782no—
555C24—1782no—
556C24—1782no—
557C24—1782no—
558C24—1782no—
559C24—1782no—
560C24—1782no—
561C24—1782no—
562C24—1782no—
563C24—1782no—
564C24C23×D8911yescharacteristic
565C2×D4—8916no—
566C2×D4—3564no—
567C2×D4—3564no—
568C2×D4—35616no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—894no—
588C22×C4—894no—
589C22×C4—892no—
590C22×C4—892no—
591C22×C4—8916no—
592C22×C4—892no—
593C22×C4—892no—
594C22×C4—892no—
595C22×C4—892no—
596C22×C4—3564no—
597C22×C4—3564no—
598C22×C4—35616no—
599C22×C4—3564no—
600C22×C4—3564no—
601C22×C4—3564no—
602C22×C4—35616no—
603C22×C4—1782no—
604C22×C4—1782no—
605C22×C4—1782no—
606C22×C4—1782no—
607C22×C4—1782no—
608C22×C4—1782no—
609C22×C4—1782no—
610C22×C4—1782no—
611C22×C4—1782no—
612C22×C4—1782no—
613C22×C4—1782no—
614C22×C4—1782no—
615C22×C4—1782no—
616C22×C4—1782no—
617C22×C4—1782no—
618C22×C4—1782no—
619C22×C4C2×C4×D8914yes—
620C22×C4C2×C4×D8914yes—
621C22×C4C2×C4×D8914yes—
622C22×C4C23×D8912yes—
623C22×C4C23×D8912yes—
624C22×C4C23×D8912yes—
625C22×C4C23×D8912yes—
626C22×C4C23×D8912yes—
627C22×C4C23×D8912yes—
628C22×C4C23×D8912yes—
629C4⋊C4—44no—
630C4⋊C4—8916no—
631C4⋊C4—3564no—
632C4⋊C4—3564no—
633C4⋊C4—3564no—
634C4⋊C4—3564no—
635C4⋊C4—3564no—
636C4⋊C4—3564no—
637C4⋊C4C2×C4×D89116yescomplemented
638C22⋊C4—8916no—
639C22⋊C4—8916no—
640C22⋊C4—8916no—
641C22⋊C4—3564no—
642C22⋊C4—3564no—
643C22⋊C4—3564no—
644C22⋊C4—3564no—
645C22⋊C4—3564no—
646C22⋊C4—3564no—
647C22⋊C4—3564no—
648C42—44no—
649C42—3564no—
650C42—3564no—
651C23—894no—
652C23—894no—
653C23—3564no—
654C23—3564no—
655C23—3564no—
656C23—3564no—
657C23—3564no—
658C23—3564no—
659C23—3564no—
660C23—3564no—
661C23—1782no—
662C23—1782no—
663C23—1782no—
664C23—1782no—
665C23—1782no—
666C23—1782no—
667C23—1782no—
668C23—1782no—
669C23—1782no—
670C23—1782no—
671C23—1782no—
672C23—1782no—
673C23—1788no—
674C23—1788no—
675C23—1788no—
676C23—1788no—
677C23—1788no—
678C23—1788no—
679C23C22×C4×D8912yes—
680C23#1566805712yes—
681C23#1566805812yes—
682C23#1566805812yes—
683C23#1566805812yes—
684C23#1566805912yes—
685C23#1566806012yes—
686C23C24×D8911yescharacteristic
687D4—35616no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—894no—
714C2×C4—894no—
715C2×C4—35616no—
716C2×C4—35616no—
717C2×C4—3564no—
718C2×C4—3564no—
719C2×C4—3564no—
720C2×C4—3564no—
721C2×C4—1782no—
722C2×C4—1782no—
723C2×C4—1782no—
724C2×C4—1782no—
725C2×C4—1782no—
726C2×C4—1782no—
727C2×C4—1782no—
728C2×C4—1782no—
729C2×C4—1782no—
730C2×C4—1782no—
731C2×C4—1782no—
732C2×C4—1782no—
733C2×C4—1782no—
734C2×C4—1782no—
735C2×C4—1782no—
736C2×C4—1782no—
737C2×C4—1788no—
738C2×C4—1788no—
739C2×C4C22×C4×D8914yes—
740C2×C4C22×C4×D8914yes—
741C2×C4C22×C4×D8914yes—
742C22—3562no—
743C22—3562no—
744C22—3562no—
745C22—3562no—
746C22—3562no—
747C22—3562no—
748C22—3562no—
749C22—3562no—
750C22—35616no—
751C22—35616no—
752C22—1784no—
753C22—1784no—
754C22—1784no—
755C22—1784no—
756C22—1784no—
757C22—1784no—
758C22#1915207014yes—
759C22#1915207814yes—
760C22#1915208014yes—
761C22#1915233914yes—
762C22#1915234414yes—
763C22#1915234514yes—
764C22#1915235214yes—
765C22C23×C4×D8911yescharacteristic
766C22C2×#1566805711yescharacteristic
767C22C2×#1566805811yescharacteristic
768C22C2×#1566805811yescharacteristic
769C22C2×#1566805811yescharacteristic
770C22C2×#1566805911yescharacteristic
771C22C2×#1566806011yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—3562no—
780C4—3562no—
781C4—3562no—
782C4—3562no—
783C4—1784no—
784C4—1784no—
785C2—3564no—
786C2—3564no—
787C2#2602339918yesdirect product factor
788C2C2×#1915207011yescharacteristic
789C2C2×#1915207811yescharacteristic
790C2C2×#1915208011yescharacteristic
791C2C2×#1915233911yescharacteristic
792C2C2×#1915234411yescharacteristic
793C2C2×#1915234511yescharacteristic
794C2C2×#1915235211yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC23×D356C22
cosocleC23×C89C25
hypercenterC2×#387D89
hypocenterC89C2×#2376
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #26023399C2direct (N × H)
4. C2×#19151497C2semidirect
5. C2×#19151495C2semidirect
6. C2×#19151490C2semidirect
7. C2×#19151488C2semidirect
8. C2×#19151487C2semidirect
9. C2×#19151487C2semidirect
10. C2×#19151482C2semidirect
12. C2×#19151472C2semidirect
13. C2×#19151472C2semidirect
14. C2×#19151457C2semidirect
15. C2×#19151455C2semidirect
16. C2×#387×C89C2semidirect
20. C2×#15667997C4semidirect
42. #19151497C22semidirect
43. #19151495C22semidirect
44. #19151490C22semidirect
45. #19151488C22semidirect
46. #19151487C22semidirect
47. #19151487C22semidirect
48. #19151482C22semidirect
50. #19151472C22semidirect
51. #19151472C22semidirect
52. #19151457C22semidirect
53. #19151455C22semidirect
63. #387×C89C22semidirect
85. C22×C4×D89C2×C4semidirect
88. #15667997C2×C4semidirect
98. C2×#13083553C2×C4semidirect
112. C2×#13083551C2×C4semidirect
141. C2×C4⋊C4×C89C2×C4semidirect
201. C2×C4×D89C22×C4semidirect
208. #13083553C22×C4semidirect
218. #13083551C22×C4semidirect
251. C4⋊C4×C89C22×C4semidirect
388. C2×C89#2376semidirect
408. C2×#387D89semidirect
414. C89C2×#2376semidirect
450. #387C2×D89semidirect
509. C2×C4⋊C4C4×D89semidirect
637. C4⋊C4C2×C4×D89semidirect
787. C2#26023399direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679972
#260233992
C2×#191515002
C2×#191514972
C2×#191514952
C2×#191514902
C2×#191514882
C2×#191514872
C2×#191514822
C2×#191514762
C2×#191514722
C2×#191514572
C2×#191514552
C2×#387×C892
C2×#237689