Finite Group Databasebeta

← C2×#26022931 #36713167

Subgroups — C2×#26022931 #36713167

Order 22784.

3198 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667989C211yesmaximal, characteristic
2C22×C4×Dic178C211yesmaximal, characteristic, complemented
3C22×#15667968C211yesmaximal, characteristic
4#26022931C2116yesmaximal, direct product factor
5C2×#19151502C211yesmaximal, characteristic, complemented
6C2×#19151495C211yesmaximal, characteristic, complemented
7C2×#19151494C211yesmaximal, characteristic, complemented
8C2×#19151493C211yesmaximal, characteristic, complemented
9C2×#19151491C211yesmaximal, characteristic
10C2×#19151486C211yesmaximal, characteristic
11C2×#19151486C211yesmaximal, characteristic
12C2×#19151483C211yesmaximal, characteristic, complemented
13C2×#19151482C211yesmaximal, characteristic, complemented
14C2×#19151456C211yesmaximal, characteristic
15C2×#19151449C211yesmaximal, characteristic, complemented
16C2×#388×C89C211yesmaximal, characteristic
17C23×Dic178C2211yescharacteristic
18C24×Dic89C2211yescharacteristic
19C2×#15667989C4116yescomplemented
20C2×#15667989C2218yes—
21C2×C4×Dic178—28no—
22C2×C4×Dic178C2218yescomplemented
23C2×#15667968—28no—
24C2×#15667968C2218yes—
25C22×C4⋊Dic89C2211yescharacteristic
26C22×C4⋊Dic89C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083553C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×#13083553C2211yescharacteristic
32C22×#13083553C2211yescharacteristic
33C22×#13083553C2211yescharacteristic
34C22×#13083553C2211yescharacteristic
35C22×C22⋊Dic89C2211yescharacteristic
36C22×C22⋊Dic89C2211yescharacteristic
37C22×C22⋊Dic89C2211yescharacteristic
38C22×C4×Dic89C2211yescharacteristic
39C22×C4×Dic89C2211yescharacteristic
40C22×C4×Dic89C2211yescharacteristic
41C22×C4×Dic89C2211yescharacteristic
42C22×C4×Dic89C2211yescharacteristic
43#19151502C2218yescomplemented
44#19151495C2218yescomplemented
45#19151494C2218yescomplemented
46#19151493C2218yescomplemented
47#19151491C2218yes—
48#19151486C2218yes—
49#19151486C2218yes—
50#19151483C2218yescomplemented
51#19151482C2218yescomplemented
52#19151456C2218yes—
53#19151449C2218yescomplemented
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C2×#15667919C2211yescharacteristic
62C22×C4⋊C4×C89C2211yescharacteristic
63C22×C22⋊C4×C89C2211yescharacteristic
64C22×C22⋊C4×C89C2211yescharacteristic
65C22×C22⋊C4×C89C2211yescharacteristic
66C22×C42×C89C2211yescharacteristic
67#388×C89C2218yes—
68C2×#95×C89C2211yescharacteristic
69C2×#95×C89C2211yescharacteristic
70C22×Dic178—24no—
71C22×Dic178—24no—
72C22×Dic178C2×C418yes—
73C22×Dic178C2314yes—
74C23×Dic89—24no—
75C23×Dic89—24no—
76C23×Dic89C2×C418yes—
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C23×Dic89C2311yescharacteristic
81C23×Dic89C2314yes—
82C23×Dic89C2311yescharacteristic
83C23×Dic89C2311yescharacteristic
84C23×Dic89C2311yescharacteristic
85C23×Dic89C2311yescharacteristic
86#15667989C2×C4164yescomplemented
87C4×Dic178—232no—
88#15667968—232no—
89C2×C4⋊Dic89—24no—
90C2×C4⋊Dic89C2×C418yes—
91C2×C4⋊Dic89C2314yes—
92C2×C4⋊Dic89C2314yes—
93C2×#13083553—24no—
94C2×#13083553—24no—
95C2×#13083553—24no—
96C2×#13083553—24no—
97C2×#13083553—24no—
98C2×#13083553—42no—
99C2×#13083553C2×C418yes—
100C2×#13083553C2×C418yes—
101C2×#13083553C2314yes—
102C2×#13083553C2314yes—
103C2×#13083553C2314yes—
104C2×#13083553C2314yes—
105C2×#13083553C2314yes—
106C2×#13083553C2314yes—
107C2×#13083553C2314yes—
108C2×#13083553C2314yes—
109C2×C22⋊Dic89—24no—
110C2×C22⋊Dic89—42no—
111C2×C22⋊Dic89C2×C418yes—
112C2×C22⋊Dic89C2314yes—
113C2×C22⋊Dic89C2314yes—
114C2×C22⋊Dic89C2314yes—
115C2×C4×Dic89—24no—
116C2×C4×Dic89—24no—
117C2×C4×Dic89—42no—
118C2×C4×Dic89—42no—
119C2×C4×Dic89D418yes—
120C2×C4×Dic89C2314yes—
121C2×C4×Dic89C2314yes—
122C2×C4×Dic89C2314yes—
123C2×C4×Dic89C2314yes—
124C2×C4×Dic89C2314yes—
125#15667919C2314yes—
126#15667919C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131#15667919C2314yes—
132#15667919C2314yes—
133C25×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×C89C2314yes—
142C2×C22⋊C4×C89—24no—
143C2×C22⋊C4×C89—42no—
144C2×C22⋊C4×C89C2×C418yes—
145C2×C22⋊C4×C89C2314yes—
146C2×C22⋊C4×C89C2314yes—
147C2×C22⋊C4×C89C2314yes—
148C2×C42×C89—24no—
149C2×C42×C89C2314yes—
150#95×C89C2314yes—
151#95×C89C2314yes—
152C2×Dic178—232no—
153C2×Dic178—28no—
154C2×Dic178—28no—
155C2×Dic178C22×C4116yes—
156C22×Dic89—22no—
157C22×Dic89—22no—
158C22×Dic89—22no—
159C22×Dic89—22no—
160C22×Dic89—22no—
161C22×Dic89—22no—
162C22×Dic89—22no—
163C22×Dic89—22no—
164C22×Dic89—232no—
165C22×Dic89—28no—
166C22×Dic89—28no—
167C22×Dic89—22no—
168C22×Dic89—22no—
169C22×Dic89—22no—
170C22×Dic89—22no—
171C22×Dic89—22no—
172C22×Dic89—22no—
173C22×Dic89—22no—
174C22×Dic89—22no—
175C22×Dic89—22no—
176C22×Dic89C22×C4116yes—
177C22×Dic89C22×C414yes—
178C22×Dic89C22×C414yes—
179C22×Dic89C22×C414yes—
180C22×Dic89C22×C414yes—
181C22×Dic89C2×D414yes—
182C22×Dic89C2×D414yes—
183C22×Dic89#4114yes—
184C22×Dic89C2412yes—
185C22×Dic89C2412yes—
186C22×Dic89C2412yes—
187C22×Dic89C2412yes—
188C22×Dic89C2412yes—
189C22×Dic89C2412yes—
190C22×Dic89C2412yes—
191C22×Dic89C2412yes—
192C4⋊Dic89—28no—
193C4⋊Dic89C22×C4116yes—
194#13083553—28no—
195#13083553—28no—
196#13083553—28no—
197#13083553—28no—
198#13083553—28no—
199#13083553—44no—
200#13083553C22×C4116yes—
201#13083553C22×C4116yes—
202C22⋊Dic89—28no—
203C22⋊Dic89—44no—
204C22⋊Dic89C22×C4116yes—
205C4×Dic89—28no—
206C4×Dic89—28no—
207C4×Dic89—44no—
208C4×Dic89—44no—
209C4×Dic89C2×D4116yes—
210C24×C89—22no—
211C24×C89—22no—
212C24×C89—22no—
213C24×C89—22no—
214C24×C89—22no—
215C24×C89—22no—
216C24×C89C22×C414yes—
217C24×C89C2412yes—
218C24×C89C2411yescharacteristic
219C22×C4×C89—22no—
220C22×C4×C89—22no—
221C22×C4×C89—22no—
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×C89C22×C414yes—
235C22×C4×C89C22×C414yes—
236C22×C4×C89C2×D414yes—
237C22×C4×C89C2412yes—
238C22×C4×C89C2412yes—
239C22×C4×C89C2412yes—
240C22×C4×C89C2412yes—
241C22×C4×C89C2412yes—
242C22×C4×C89C2412yes—
243C4⋊C4×C89—44no—
244C22⋊C4×C89—28no—
245C22⋊C4×C89—44no—
246C22⋊C4×C89C22×C4116yes—
247C42×C89—28no—
248C23×C89—28no—
249C23×C89—28no—
250C23×C89—28no—
251C23×C89—22no—
252C23×C89—22no—
253C23×C89—22no—
254C23×C89—22no—
255C23×C89—22no—
256C23×C89—22no—
257C23×C89—44no—
258C23×C89—44no—
259C23×C89—44no—
260C23×C89—44no—
261C23×C89C23×C414yes—
262C23×C89C23×C412yes—
263C23×C89C22×D412yes—
264C23×C89C2×#4112yes—
265C23×C89H(5,𝔽2)12yes—
266C23×C892−1+412yes—
267C23×C892−1+412yes—
268C23×C892−1+412yes—
269C23×C89C2511yescharacteristic
270C2×C4×C89—28no—
271C2×C4×C89—28no—
272C2×C4×C89—28no—
273C2×C4×C89—22no—
274C2×C4×C89—22no—
275C2×C4×C89—22no—
276C2×C4×C89—22no—
277C2×C4×C89—22no—
278C2×C4×C89—22no—
279C2×C4×C89—22no—
280C2×C4×C89—22no—
281C2×C4×C89—22no—
282C2×C4×C89—22no—
283C2×C4×C89—22no—
284C2×C4×C89—22no—
285C2×C4×C89—22no—
286C2×C4×C89—22no—
287C2×C4×C89—22no—
288C2×C4×C89—44no—
289C2×C4×C89—44no—
290C2×C4×C89—44no—
291C2×C4×C89C23×C414yes—
292C2×C4×C89C23×C414yes—
293C2×C4×C89C22×D414yes—
294C2×Dic89—28no—
295C2×Dic89—28no—
296C2×Dic89—28no—
297C2×Dic89—28no—
298C2×Dic89—22no—
299C2×Dic89—22no—
300C2×Dic89—22no—
301C2×Dic89—22no—
302C2×Dic89—22no—
303C2×Dic89—22no—
304C2×Dic89—22no—
305C2×Dic89—22no—
306C2×Dic89—232no—
307C2×Dic89—22no—
308C2×Dic89—22no—
309C2×Dic89—22no—
310C2×Dic89—22no—
311C2×Dic89—22no—
312C2×Dic89—22no—
313C2×Dic89—22no—
314C2×Dic89—22no—
315C2×Dic89—22no—
316C2×Dic89—44no—
317C2×Dic89—44no—
318C2×Dic89—44no—
319C2×Dic89C4×D4116yes—
320C2×Dic89C23×C414yes—
321C2×Dic89C23×C414yes—
322C2×Dic89C23×C414yes—
323C2×Dic89C23×C414yes—
324C2×Dic89C22×D414yes—
325C2×Dic89C22×D414yes—
326C2×Dic89C2×#4114yes—
327Dic178—232no—
328C22×C89—24no—
329C22×C89—24no—
330C22×C89—24no—
331C22×C89—416no—
332C22×C89—42no—
333C22×C89—42no—
334C22×C89—42no—
335C22×C89—42no—
336C22×C89C2×C4×D414yes—
337C22×C89#51914yes—
338C22×C89#52014yes—
339C22×C89#53614yes—
340C22×C89#53714yes—
341C22×C89#54114yes—
342C22×C89#54214yes—
343C22×C89C24×C411yescharacteristic
344C22×C89C23×D411yescharacteristic
345C22×C89C22×#4111yescharacteristic
346C22×C89C2×H(5,𝔽2)11yescharacteristic
347C22×C89C2×2−1+411yescharacteristic
348C22×C89C2×2−1+411yescharacteristic
349C22×C89C2×2−1+411yescharacteristic
350C4×C89—24no—
351C4×C89—24no—
352C4×C89—24no—
353C4×C89—42no—
354C4×C89—42no—
355C4×C89—42no—
356Dic89—24no—
357Dic89—24no—
358Dic89—24no—
359Dic89—24no—
360Dic89—42no—
361Dic89—42no—
362Dic89—42no—
363Dic89C2×C4×D418yes—
364C2×#2323—891nomaximal, Sylow
365C2×C89—44no—
366C2×C89#232318yescomplemented
367C2×C89C22×C4×D411yescharacteristic
368C2×C89C2×#51911yescharacteristic
369C2×C89C2×#52011yescharacteristic
370C2×C89C2×#53611yescharacteristic
371C2×C89C2×#53711yescharacteristic
372C2×C89C2×#54111yescharacteristic
373C2×C89C2×#54211yescharacteristic
374C22×C22⋊Q8—891no—
375C22×C4×Q8—891no—
376C22×#117—891no—
377#2323—8916no—
378C2×#391—891no—
379C2×#389—891no—
380C2×#389—891no—
381C2×#389—891no—
382C2×#388—891no—
383C2×#388—891no—
384C2×#388—891no—
385C2×#388D8911yescharacteristic
386C2×#387—891no—
387C2×#387—891no—
388C2×#380—891no—
389C2×C4×C4⋊C4—891no—
390C89C2×#232311yescharacteristic, complemented, Sylow
391C23×Q8—891no—
392C24×C4—891no—
393C2×C22⋊Q8—8916no—
394C2×C22⋊Q8—898no—
395C2×C4×Q8—898no—
396C2×C4×Q8—1788no—
397C2×#117—898no—
398C2×#117—1788no—
399C22×C4⋊C4—891no—
400C22×C4⋊C4—891no—
401C22×C4⋊C4—891no—
402C22×C4⋊C4—891no—
403C22×C4⋊C4—891no—
404C22×C4⋊C4—891no—
405C22×C4⋊C4—891no—
406C22×C4⋊C4—891no—
407C22×C4⋊C4—891no—
408C22×C4⋊C4—891no—
409C22×C4⋊C4C2×D8911yescharacteristic
410C22×C22⋊C4—891no—
411C22×C22⋊C4—891no—
412C22×C22⋊C4—891no—
413C22×C22⋊C4C2×D8911yescharacteristic
414C22×C22⋊C4C2×D8911yescharacteristic
415C22×C22⋊C4C2×D8911yescharacteristic
416C22×C42—891no—
417C22×C42—891no—
418C22×C42—891no—
419C22×C42—891no—
420C22×C42—891no—
421C22×C42C2×D8911yescharacteristic
422#391—898no—
423#389—898no—
424#389—898no—
425#389—898no—
426#388—898no—
427#388—898no—
428#388—898no—
429#388C2×D8918yes—
430#387—898no—
431#387—898no—
432#380—898no—
433C4×C4⋊C4—898no—
434C2×#95—891no—
435C2×#95—891no—
436C2×#95—891no—
437C2×#95—891no—
438C2×#95—891no—
439C2×#95—891no—
440C2×#95—891no—
441C2×#95—891no—
442C2×#95C2×D8911yescharacteristic
443C2×#95C2×D8911yescharacteristic
444C25C22×D8911yescharacteristic
445C22×Q8—898no—
446C22×Q8—894no—
447C22×Q8—1784no—
448C22×Q8—1784no—
449C23×C4—891no—
450C23×C4—898no—
451C23×C4—894no—
452C23×C4—891no—
453C23×C4—891no—
454C23×C4—891no—
455C23×C4—891no—
456C23×C4—891no—
457C23×C4—891no—
458C23×C4—891no—
459C23×C4—1784no—
460C23×C4—1784no—
461C23×C4C22×D8911yescharacteristic
462C23×C4C22×D8911yescharacteristic
463C23×C4C22×D8911yescharacteristic
464C23×C4C22×D8911yescharacteristic
465C23×C4C22×D8911yescharacteristic
466C23×C4C22×D8911yescharacteristic
467C22⋊Q8—8964no—
468C4×Q8—17832no—
469#117—17832no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—898no—
472C2×C4⋊C4—898no—
473C2×C4⋊C4—898no—
474C2×C4⋊C4—894no—
475C2×C4⋊C4—894no—
476C2×C4⋊C4—894no—
477C2×C4⋊C4—894no—
478C2×C4⋊C4—894no—
479C2×C4⋊C4—894no—
480C2×C4⋊C4—894no—
481C2×C4⋊C4—894no—
482C2×C4⋊C4—894no—
483C2×C4⋊C4—894no—
484C2×C4⋊C4—3562no—
485C2×C4⋊C4—1784no—
486C2×C4⋊C4—1784no—
487C2×C4⋊C4—1784no—
488C2×C4⋊C4—1784no—
489C2×C4⋊C4—1784no—
490C2×C4⋊C4—1784no—
491C2×C4⋊C4C22×D8914yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—898no—
495C2×C22⋊C4—894no—
496C2×C22⋊C4—894no—
497C2×C22⋊C4—894no—
498C2×C22⋊C4—3562no—
499C2×C22⋊C4—1784no—
500C2×C22⋊C4C4×D8918yes—
501C2×C22⋊C4C22×D8914yes—
502C2×C22⋊C4C22×D8914yes—
503C2×C22⋊C4C22×D8914yes—
504C2×C42—24no—
505C2×C42—898no—
506C2×C42—894no—
507C2×C42—894no—
508C2×C42—894no—
509C2×C42—894no—
510C2×C42—894no—
511C2×C42—3562no—
512C2×C42—3562no—
513C2×C42—1784no—
514C2×C42—1784no—
515C2×C42C22×D8914yes—
516#95—894no—
517#95—894no—
518#95—894no—
519#95—894no—
520#95—894no—
521#95—894no—
522#95—894no—
523#95—894no—
524#95C22×D8914yes—
525#95C22×D8914yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24C2×C4×D8914yes—
533C24C23×D8912yes—
534C24C23×D8911yescharacteristic
535C2×Q8—8916no—
536C2×Q8—1788no—
537C2×Q8—1788no—
538C2×Q8—17832no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—894no—
555C22×C4—894no—
556C22×C4—894no—
557C22×C4—892no—
558C22×C4—894no—
559C22×C4—894no—
560C22×C4—894no—
561C22×C4—8916no—
562C22×C4—894no—
563C22×C4—892no—
564C22×C4—892no—
565C22×C4—892no—
566C22×C4—892no—
567C22×C4—892no—
568C22×C4—892no—
569C22×C4—892no—
570C22×C4—1788no—
571C22×C4—1788no—
572C22×C4—17832no—
573C22×C4—1782no—
574C22×C4—1782no—
575C22×C4—1782no—
576C22×C4—1782no—
577C22×C4—1782no—
578C22×C4—1782no—
579C22×C4—1782no—
580C22×C4—1782no—
581C22×C4—1782no—
582C22×C4—1782no—
583C22×C4—1782no—
584C22×C4—1782no—
585C22×C4—1782no—
586C22×C4—1782no—
587C22×C4—1782no—
588C22×C4—1782no—
589C22×C4—1782no—
590C22×C4C2×C4×D8914yes—
591C22×C4C2×C4×D8914yes—
592C22×C4D4×D8914yes—
593C22×C4C23×D8912yes—
594C22×C4C23×D8912yes—
595C22×C4C23×D8912yes—
596C22×C4C23×D8912yes—
597C22×C4C23×D8912yes—
598C22×C4C23×D8912yes—
599C4⋊C4—44no—
600C4⋊C4—8916no—
601C4⋊C4—8916no—
602C4⋊C4—8916no—
603C4⋊C4—3564no—
604C4⋊C4—1788no—
605C4⋊C4—1788no—
606C4⋊C4—1788no—
607C4⋊C4—1788no—
608C4⋊C4—1788no—
609C4⋊C4—1788no—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4—8916no—
613C22⋊C4—3564no—
614C22⋊C4—1788no—
615C22⋊C4C2×C4×D89116yes—
616C42—28no—
617C42—8916no—
618C42—3564no—
619C42—3564no—
620C42—1788no—
621C42—1788no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23C22×C4×D8914yes—
636C23C22×C4×D8912yes—
637C23C2×D4×D8912yes—
638C23#41×D8912yes—
639C23#1566805712yes—
640C23#1566805912yes—
641C23#1566805912yes—
642C23#1566805912yes—
643C23C24×D8911yescharacteristic
644Q8—17832no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—894no—
667C2×C4—894no—
668C2×C4—894no—
669C2×C4—8916no—
670C2×C4—894no—
671C2×C4—894no—
672C2×C4—894no—
673C2×C4—894no—
674C2×C4—3564no—
675C2×C4—3564no—
676C2×C4—3564no—
677C2×C4—17832no—
678C2×C4—1782no—
679C2×C4—1782no—
680C2×C4—1782no—
681C2×C4—1782no—
682C2×C4—1782no—
683C2×C4—1782no—
684C2×C4—1782no—
685C2×C4—1782no—
686C2×C4—1782no—
687C2×C4—1782no—
688C2×C4—1782no—
689C2×C4—1782no—
690C2×C4—1782no—
691C2×C4—1782no—
692C2×C4—1782no—
693C2×C4—1782no—
694C2×C4—1782no—
695C2×C4—1788no—
696C2×C4—1788no—
697C2×C4—1788no—
698C2×C4—1788no—
699C2×C4C22×C4×D8914yes—
700C2×C4C22×C4×D8914yes—
701C2×C4C2×D4×D8914yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—416no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22C4×D4×D8914yes—
711C22#1915207514yes—
712C22#1915207714yes—
713C22#1915217014yes—
714C22#1915217714yes—
715C22#1915220514yes—
716C22#1915221214yes—
717C22C23×C4×D8911yescharacteristic
718C22C22×D4×D8911yescharacteristic
719C22C2×#41×D8911yescharacteristic
720C22C2×#1566805711yescharacteristic
721C22C2×#1566805911yescharacteristic
722C22C2×#1566805911yescharacteristic
723C22C2×#1566805911yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—898no—
731C4—3562no—
732C4—3562no—
733C4—3562no—
734C4—1784no—
735C4—1784no—
736C4—1784no—
737C4—1784no—
738C2—44no—
739C2#2602293118yesdirect product factor
740C2C2×C4×D4×D8911yescharacteristic
741C2C2×#1915207511yescharacteristic
742C2C2×#1915207711yescharacteristic
743C2C2×#1915217011yescharacteristic
744C2C2×#1915217711yescharacteristic
745C2C2×#1915220511yescharacteristic
746C2C2×#1915221211yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#388×C89C2
socleC24×C89C24
prime radicalC25×C89C23
cosocleC23×C89C25
hypercenterC2×#388D89
hypocenterC89C2×#2323
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic178C2semidirect
4. #26022931C2direct (N × H)
5. C2×#19151502C2semidirect
6. C2×#19151495C2semidirect
7. C2×#19151494C2semidirect
8. C2×#19151493C2semidirect
12. C2×#19151483C2semidirect
13. C2×#19151482C2semidirect
15. C2×#19151449C2semidirect
19. C2×#15667989C4semidirect
22. C2×C4×Dic178C22semidirect
43. #19151502C22semidirect
44. #19151495C22semidirect
45. #19151494C22semidirect
46. #19151493C22semidirect
50. #19151483C22semidirect
51. #19151482C22semidirect
53. #19151449C22semidirect
86. #15667989C2×C4semidirect
366. C2×C89#2323semidirect
390. C89C2×#2323semidirect
739. C2#26022931direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679892
C22×C4×Dic1782
C22×#156679682
#260229312
C2×#191515022
C2×#191514952
C2×#191514942
C2×#191514932
C2×#191514912
C2×#191514862
C2×#191514832
C2×#191514822
C2×#191514562
C2×#191514492
C2×#388×C892
C2×#232389