Finite Group Databasebeta

← C2×#26023126 #36713670

Subgroups — C2×#26023126 #36713670

Order 22784.

3094 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D89C211yesmaximal, characteristic
2#26023126C2116yesmaximal, direct product factor
3C2×#19151495C211yesmaximal, characteristic, complemented
4C2×#19151493C211yesmaximal, characteristic, complemented
5C2×#19151484C211yesmaximal, characteristic, complemented
6C2×#19151483C211yesmaximal, characteristic, complemented
7C2×#19151481C211yesmaximal, characteristic, complemented
8C2×#19151457C211yesmaximal, characteristic
9C2×#19151457C211yesmaximal, characteristic
10C2×#19151455C211yesmaximal, characteristic
11C2×C4×#13083553C211yesmaximal, characteristic, complemented
12C2×#19151449C211yesmaximal, characteristic, complemented
13C2×C4×#13083551C211yesmaximal, characteristic
14C2×#19151445C211yesmaximal, characteristic
15C2×#19151445C211yesmaximal, characteristic
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×C4×D89C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C22×C4⋊Dic89C2211yescharacteristic
21C22×C4⋊Dic89C2211yescharacteristic
22C22×#13083553C2211yescharacteristic
23C22×#13083553C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C2×C4⋊C4×D89C4116yescomplemented
29C2×C4⋊C4×D89C2218yes—
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×#13083551C2211yescharacteristic
33C22×#13083551C2211yescharacteristic
34C22×C4×Dic89C2211yescharacteristic
35C22×C4×Dic89C2211yescharacteristic
36C22×C4×Dic89C2211yescharacteristic
37C22×C4×Dic89C2211yescharacteristic
38C22×C4×Dic89C2211yescharacteristic
39#19151495C2218yescomplemented
40#19151493C2218yescomplemented
41#19151484C2218yescomplemented
42#19151483C2218yescomplemented
43#19151481C2218yescomplemented
44#19151457C2218yes—
45#19151457C2218yes—
46#19151455C2218yes—
47C4×#13083553C2218yescomplemented
48#19151449C2218yescomplemented
49C4×#13083551C2218yes—
50#19151445C2218yes—
51#19151445C2218yes—
52C2×#15667919C2211yescharacteristic
53C2×#15667919C2211yescharacteristic
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
69C23×Dic89C2311yescharacteristic
70C23×Dic89C2311yescharacteristic
71C23×Dic89C2311yescharacteristic
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C22×C4×D89—24no—
77C22×C4×D89—24no—
78C22×C4×D89—42no—
79C22×C4×D89—42no—
80C22×C4×D89—42no—
81C22×C4×D89—42no—
82C22×C4×D89C2×C418yes—
83C22×C4×D89C2×C418yes—
84C22×C4×D89C2×C418yes—
85C22×C4×D89C2314yes—
86C22×C4×D89C2314yes—
87C22×C4×D89C2314yes—
88C2×C4⋊Dic89—42no—
89C2×C4⋊Dic89C2×C418yes—
90C2×C4⋊Dic89C2314yes—
91C2×C4⋊Dic89C2314yes—
92C2×#13083553—24no—
93C2×#13083553—24no—
94C2×#13083553—42no—
95C2×#13083553—42no—
96C2×#13083553C2×C418yes—
97C2×#13083553C2×C418yes—
98C2×#13083553C2314yes—
99C2×#13083553C2314yes—
100C2×#13083553C2314yes—
101C2×#13083553C2314yes—
102C2×#13083553C2314yes—
103C2×#13083553C2314yes—
104C4⋊C4×D89C2×C4164yescomplemented
105C2×#13083551—24no—
106C2×#13083551—24no—
107C2×#13083551—24no—
108C2×#13083551Q818yes—
109C2×#13083551C2314yes—
110C2×#13083551C2314yes—
111C2×#13083551C2314yes—
112C2×#13083551C2314yes—
113C2×C4×Dic89—24no—
114C2×C4×Dic89—24no—
115C2×C4×Dic89—42no—
116C2×C4×Dic89—42no—
117C2×C4×Dic89—42no—
118C2×C4×Dic89C2314yes—
119C2×C4×Dic89C2314yes—
120C2×C4×Dic89C2314yes—
121C2×C4×Dic89C2314yes—
122C2×C4×Dic89C2314yes—
123#15667919C2314yes—
124#15667919C2314yes—
125#15667919C2314yes—
126#15667919C2314yes—
127#15667919C2314yes—
128#15667919C2314yes—
129#15667919C2314yes—
130#15667919C2314yes—
131C23×C4×C89C2311yescharacteristic
132C23×C4×C89C2311yescharacteristic
133C23×C4×C89C2311yescharacteristic
134C23×C4×C89C2311yescharacteristic
135C23×C4×C89C2311yescharacteristic
136C23×C4×C89C2311yescharacteristic
137C23×C4×C89C2311yescharacteristic
138C2×C4⋊C4×C89—42no—
139C2×C4⋊C4×C89C2×C418yes—
140C2×C4⋊C4×C89C2314yes—
141C2×C4⋊C4×C89C2314yes—
142C2×C42×C89—42no—
143C2×C42×C89C2314yes—
144#95×C89C2314yes—
145#95×C89C2314yes—
146#95×C89C2314yes—
147#95×C89C2314yes—
148C23×D89—22no—
149C23×D89—22no—
150C23×D89—22no—
151C23×D89—22no—
152C23×D89C22×C414yes—
153C23×D89C2×Q814yes—
154C23×D89#4114yes—
155C23×D89C2412yes—
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—22no—
165C22×Dic89—22no—
166C22×Dic89—22no—
167C22×Dic89—22no—
168C22×Dic89—22no—
169C22×Dic89—22no—
170C22×Dic89—22no—
171C22×Dic89C22×C414yes—
172C22×Dic89C22×C414yes—
173C22×Dic89C22×C414yes—
174C22×Dic89C2×Q814yes—
175C22×Dic89#4114yes—
176C22×Dic89#4114yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C22×Dic89C2412yes—
181C22×Dic89C2412yes—
182C22×Dic89C2412yes—
183C22×Dic89C2412yes—
184C2×C4×D89—232no—
185C2×C4×D89—28no—
186C2×C4×D89—28no—
187C2×C4×D89—416no—
188C2×C4×D89—416no—
189C2×C4×D89—44no—
190C2×C4×D89—44no—
191C2×C4×D89—44no—
192C2×C4×D89—44no—
193C2×C4×D89C22×C4116yes—
194C2×C4×D89C22×C4116yes—
195C2×C4×D89C22×C4116yes—
196C4⋊Dic89—44no—
197C4⋊Dic89C22×C4116yes—
198#13083553—28no—
199#13083553—28no—
200#13083553—44no—
201#13083553—44no—
202#13083553C22×C4116yes—
203#13083553C22×C4116yes—
204#13083551—28no—
205#13083551—28no—
206#13083551—28no—
207#13083551C2×Q8116yes—
208C4×Dic89—28no—
209C4×Dic89—28no—
210C4×Dic89—44no—
211C4×Dic89—44no—
212C4×Dic89—44no—
213C24×C89C2411yescharacteristic
214C22×C4×C89—22no—
215C22×C4×C89—22no—
216C22×C4×C89—22no—
217C22×C4×C89—22no—
218C22×C4×C89—22no—
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×C89C22×C414yes—
232C22×C4×C89C22×C414yes—
233C22×C4×C89C22×C414yes—
234C22×C4×C89C2×Q814yes—
235C22×C4×C89C2412yes—
236C22×C4×C89C2412yes—
237C22×C4×C89C2412yes—
238C22×C4×C89C2412yes—
239C22×C4×C89C2412yes—
240C22×C4×C89C2412yes—
241C22×C4×C89C2412yes—
242C4⋊C4×C89—44no—
243C4⋊C4×C89C22×C4116yes—
244C42×C89—44no—
245C23×C89C23×C412yes—
246C23×C89C22×Q812yes—
247C23×C89C2×#4112yes—
248C23×C89C2×#4112yes—
249C23×C89C2×#4112yes—
250C23×C89H(5,𝔽2)12yes—
251C23×C89H(5,𝔽2)12yes—
252C23×C89C2511yescharacteristic
253C22×D89—28no—
254C22×D89—28no—
255C22×D89—28no—
256C22×D89—28no—
257C22×D89—28no—
258C22×D89—28no—
259C22×D89—22no—
260C22×D89—22no—
261C22×D89—22no—
262C22×D89—22no—
263C22×D89C4×Q8116yes—
264C22×D89C23×C414yes—
265C22×D89C22×Q814yes—
266C22×D89C2×#4114yes—
267C2×C4×C89—28no—
268C2×C4×C89—28no—
269C2×C4×C89—28no—
270C2×C4×C89—28no—
271C2×C4×C89—22no—
272C2×C4×C89—22no—
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×C89C23×C414yes—
294C2×C4×C89C22×Q814yes—
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—22no—
307C2×Dic89—22no—
308C2×Dic89—22no—
309C2×Dic89—22no—
310C2×Dic89—22no—
311C2×Dic89—22no—
312C2×Dic89—22no—
313C2×Dic89—44no—
314C2×Dic89—44no—
315C2×Dic89—44no—
316C2×Dic89#117116yes—
317C2×Dic89C23×C414yes—
318C2×Dic89C23×C414yes—
319C2×Dic89C23×C414yes—
320C2×Dic89C22×Q814yes—
321C2×Dic89C2×#4114yes—
322C2×Dic89C2×#4114yes—
323C4×D89—232no—
324C4×D89—416no—
325C4×D89—416no—
326C22×C89C2×#11714yes—
327C22×C89C2×C4×Q814yes—
328C22×C89#51814yes—
329C22×C89#55314yes—
330C22×C89#55314yes—
331C22×C89#55414yes—
332C22×C89#55414yes—
333C22×C89C24×C411yescharacteristic
334C22×C89C23×Q811yescharacteristic
335C22×C89C22×#4111yescharacteristic
336C22×C89C22×#4111yescharacteristic
337C22×C89C22×#4111yescharacteristic
338C22×C89C2×H(5,𝔽2)11yescharacteristic
339C22×C89C2×H(5,𝔽2)11yescharacteristic
340C2×D89—232no—
341C2×D89—24no—
342C2×D89—24no—
343C2×D89—24no—
344C2×D89—24no—
345C2×D89—24no—
346C2×D89—24no—
347C2×D89C2×C4×Q818yes—
348C4×C89—24no—
349C4×C89—24no—
350C4×C89—24no—
351C4×C89—24no—
352C4×C89—42no—
353C4×C89—42no—
354C4×C89—42no—
355Dic89—24no—
356Dic89—24no—
357Dic89—24no—
358Dic89—42no—
359Dic89—42no—
360Dic89—42no—
361Dic89C2×#11718yes—
362C2×#2345—891nomaximal, Sylow
363C2×C89#234518yescomplemented
364C2×C89C22×#11711yescharacteristic
365C2×C89C22×C4×Q811yescharacteristic
366C2×C89C2×#51811yescharacteristic
367C2×C89C2×#55311yescharacteristic
368C2×C89C2×#55311yescharacteristic
369C2×C89C2×#55411yescharacteristic
370C2×C89C2×#55411yescharacteristic
371D89—28no—
372C23×C4⋊C4—891no—
373#2345—8916no—
374C2×#389—891no—
375C2×#389—891no—
376C2×#387—891no—
377C2×#387—891no—
378C2×#387—891no—
379C2×#387D8911yescharacteristic, complemented
380C2×#380—891no—
381C2×#380—891no—
382C2×#380—891no—
383C2×C4×C4⋊C4—891no—
384C2×C4×C4⋊C4—891no—
385C2×C4×C22⋊C4—891no—
386C2×C4×C22⋊C4—891no—
387C2×C4×C22⋊C4—891no—
388C89C2×#234511yescharacteristic, complemented, Sylow
389C24×C4—891no—
390C24×C4—891no—
391C24×C4—891no—
392C22×C4⋊C4—891no—
393C22×C4⋊C4—891no—
394C22×C4⋊C4—891no—
395C22×C4⋊C4—8916no—
396C22×C4⋊C4—898no—
397C22×C4⋊C4—891no—
398C22×C4⋊C4—891no—
399C22×C4⋊C4—891no—
400C22×C4⋊C4—891no—
401C22×C4⋊C4—891no—
402C22×C4⋊C4C2×D8911yescharacteristic
403C22×C4⋊C4C2×D8911yescharacteristic
404C22×C22⋊C4—891no—
405C22×C22⋊C4—891no—
406C22×C22⋊C4—891no—
407C22×C22⋊C4—891no—
408C22×C42—891no—
409C22×C42—891no—
410C22×C42—891no—
411C22×C42—891no—
412C22×C42—891no—
413C22×C42C2×D8911yescharacteristic
414#389—898no—
415#389—898no—
416#387—898no—
417#387—898no—
418#387—898no—
419#387C2×D8918yescomplemented
420#380—898no—
421#380—898no—
422#380—898no—
423C4×C4⋊C4—898no—
424C4×C4⋊C4—898no—
425C4×C22⋊C4—898no—
426C4×C22⋊C4—898no—
427C4×C22⋊C4—898no—
428C2×#95—891no—
429C2×#95—891no—
430C2×#95—891no—
431C2×#95—891no—
432C2×#95—891no—
433C2×#95—891no—
434C2×#95—891no—
435C2×#95—891no—
436C2×#95C2×D8911yescharacteristic
437C2×#95C2×D8911yescharacteristic
438C2×#95C2×D8911yescharacteristic
439C2×#95C2×D8911yescharacteristic
440C25—891no—
441C23×C4—891no—
442C23×C4—891no—
443C23×C4—891no—
444C23×C4—891no—
445C23×C4—898no—
446C23×C4—898no—
447C23×C4—894no—
448C23×C4—894no—
449C23×C4—898no—
450C23×C4—894no—
451C23×C4—891no—
452C23×C4—891no—
453C23×C4—891no—
454C23×C4—3562no—
455C23×C4—3562no—
456C23×C4—3562no—
457C23×C4—3562no—
458C23×C4—1784no—
459C23×C4—1784no—
460C23×C4C22×D8911yescharacteristic
461C23×C4C22×D8911yescharacteristic
462C23×C4C22×D8911yescharacteristic
463C23×C4C22×D8911yescharacteristic
464C23×C4C22×D8911yescharacteristic
465C23×C4C22×D8911yescharacteristic
466C23×C4C22×D8911yescharacteristic
467C2×C4⋊C4—42no—
468C2×C4⋊C4—898no—
469C2×C4⋊C4—898no—
470C2×C4⋊C4—898no—
471C2×C4⋊C4—894no—
472C2×C4⋊C4—894no—
473C2×C4⋊C4—894no—
474C2×C4⋊C4—8964no—
475C2×C4⋊C4—894no—
476C2×C4⋊C4—894no—
477C2×C4⋊C4—894no—
478C2×C4⋊C4—894no—
479C2×C4⋊C4—894no—
480C2×C4⋊C4—3562no—
481C2×C4⋊C4—3562no—
482C2×C4⋊C4—3562no—
483C2×C4⋊C4—1784no—
484C2×C4⋊C4—1784no—
485C2×C4⋊C4C4×D8918yes—
486C2×C4⋊C4C22×D8914yes—
487C2×C4⋊C4C22×D8914yes—
488C2×C22⋊C4—898no—
489C2×C22⋊C4—894no—
490C2×C22⋊C4—894no—
491C2×C22⋊C4—894no—
492C2×C22⋊C4—894no—
493C2×C22⋊C4—1784no—
494C2×C22⋊C4—1784no—
495C2×C22⋊C4—1784no—
496C2×C42—42no—
497C2×C42—894no—
498C2×C42—894no—
499C2×C42—894no—
500C2×C42—894no—
501C2×C42—894no—
502C2×C42—3562no—
503C2×C42—3562no—
504C2×C42—3562no—
505C2×C42—1784no—
506C2×C42—1784no—
507C2×C42C22×D8914yes—
508#95—894no—
509#95—894no—
510#95—894no—
511#95—894no—
512#95—894no—
513#95—894no—
514#95—894no—
515#95—894no—
516#95C22×D8914yes—
517#95C22×D8914yes—
518#95C22×D8914yes—
519#95C22×D8914yes—
520C24—894no—
521C24—894no—
522C24—894no—
523C24—892no—
524C24—1782no—
525C24—1782no—
526C24—1782no—
527C24—1782no—
528C24C23×D8911yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—894no—
547C22×C4—894no—
548C22×C4—894no—
549C22×C4—892no—
550C22×C4—894no—
551C22×C4—894no—
552C22×C4—894no—
553C22×C4—892no—
554C22×C4—892no—
555C22×C4—892no—
556C22×C4—8916no—
557C22×C4—8916no—
558C22×C4—8916no—
559C22×C4—892no—
560C22×C4—892no—
561C22×C4—892no—
562C22×C4—3564no—
563C22×C4—3564no—
564C22×C4—3564no—
565C22×C4—3564no—
566C22×C4—35616no—
567C22×C4—35616no—
568C22×C4—1788no—
569C22×C4—1788no—
570C22×C4—17832no—
571C22×C4—1782no—
572C22×C4—1782no—
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×C4C2×C4×D8914yes—
587C22×C4C2×C4×D8914yes—
588C22×C4C2×C4×D8914yes—
589C22×C4Q8×D8914yes—
590C22×C4C23×D8912yes—
591C22×C4C23×D8912yes—
592C22×C4C23×D8912yes—
593C22×C4C23×D8912yes—
594C22×C4C23×D8912yes—
595C22×C4C23×D8912yes—
596C22×C4C23×D8912yes—
597C4⋊C4—44no—
598C4⋊C4—8916no—
599C4⋊C4—8916no—
600C4⋊C4—8916no—
601C4⋊C4—3564no—
602C4⋊C4—3564no—
603C4⋊C4—3564no—
604C4⋊C4—1788no—
605C4⋊C4—1788no—
606C4⋊C4C2×C4×D89116yes—
607C22⋊C4—8916no—
608C22⋊C4—1788no—
609C22⋊C4—1788no—
610C22⋊C4—1788no—
611C42—44no—
612C42—3564no—
613C42—3564no—
614C42—3564no—
615C42—1788no—
616C42—1788no—
617C23—894no—
618C23—894no—
619C23—894no—
620C23—8916no—
621C23—1782no—
622C23—1782no—
623C23—1782no—
624C23—1782no—
625C23—1788no—
626C23—1788no—
627C23—1788no—
628C23—1788no—
629C23—1788no—
630C23—1788no—
631C23C22×C4×D8912yes—
632C23C2×Q8×D8912yes—
633C23#41×D8912yes—
634C23#41×D8912yes—
635C23#41×D8912yes—
636C23#1566805712yes—
637C23#1566805812yes—
638C23C24×D8911yescharacteristic
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—894no—
664C2×C4—894no—
665C2×C4—894no—
666C2×C4—8916no—
667C2×C4—894no—
668C2×C4—894no—
669C2×C4—894no—
670C2×C4—35616no—
671C2×C4—35616no—
672C2×C4—3564no—
673C2×C4—3564no—
674C2×C4—3564no—
675C2×C4—17832no—
676C2×C4—1782no—
677C2×C4—1782no—
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—1788no—
692C2×C4—1788no—
693C2×C4—1788no—
694C2×C4C22×C4×D8914yes—
695C2×C4C22×C4×D8914yes—
696C2×C4C22×C4×D8914yes—
697C2×C4C2×Q8×D8914yes—
698C22—898no—
699C22—1784no—
700C22—1784no—
701C22—1784no—
702C22—1784no—
703C22—1784no—
704C22—1784no—
705C22—17832no—
706C22#117×D8914yes—
707C22C4×Q8×D8914yes—
708C22#1915207014yes—
709C22#1915229314yes—
710C22#1915229914yes—
711C22#1915230214yes—
712C22#1915230414yes—
713C22C23×C4×D8911yescharacteristic
714C22C22×Q8×D8911yescharacteristic
715C22C2×#41×D8911yescharacteristic
716C22C2×#41×D8911yescharacteristic
717C22C2×#41×D8911yescharacteristic
718C22C2×#1566805711yescharacteristic
719C22C2×#1566805811yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—898no—
728C4—3562no—
729C4—3562no—
730C4—3562no—
731C4—1784no—
732C4—1784no—
733C4—1784no—
734C2—1788no—
735C2#2602312618yesdirect product factor
736C2C2×#117×D8911yescharacteristic
737C2C2×C4×Q8×D8911yescharacteristic
738C2C2×#1915207011yescharacteristic
739C2C2×#1915229311yescharacteristic
740C2C2×#1915229911yescharacteristic
741C2C2×#1915230211yescharacteristic
742C2C2×#1915230411yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC24×D89C23
cosocleC23×C89C25
hypercenterC2×#387D89
hypocenterC89C2×#2345
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #26023126C2direct (N × H)
3. C2×#19151495C2semidirect
4. C2×#19151493C2semidirect
5. C2×#19151484C2semidirect
6. C2×#19151483C2semidirect
7. C2×#19151481C2semidirect
11. C2×C4×#13083553C2semidirect
12. C2×#19151449C2semidirect
16. C2×#387×C89C2semidirect
28. C2×C4⋊C4×D89C4semidirect
39. #19151495C22semidirect
40. #19151493C22semidirect
41. #19151484C22semidirect
42. #19151483C22semidirect
43. #19151481C22semidirect
47. C4×#13083553C22semidirect
48. #19151449C22semidirect
63. #387×C89C22semidirect
104. C4⋊C4×D89C2×C4semidirect
363. C2×C89#2345semidirect
379. C2×#387D89semidirect
388. C89C2×#2345semidirect
419. #387C2×D89semidirect
735. C2#26023126direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D892
#260231262
C2×#191514952
C2×#191514932
C2×#191514842
C2×#191514832
C2×#191514812
C2×#191514572
C2×#191514552
C2×C4×#130835532
C2×#191514492
C2×C4×#130835512
C2×#191514452
C2×#387×C892
C2×#234589