Finite Group Databasebeta

← C2×#26023009 #36713286

Subgroups — C2×#26023009 #36713286

Order 22784.

2678 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667989C211yesmaximal, characteristic
2#26023009C2116yesmaximal, direct product factor
3C2×#19151503C211yesmaximal, characteristic, complemented
4C2×#19151502C211yesmaximal, characteristic, complemented
5C2×#19151492C211yesmaximal, characteristic
6C2×#19151492C211yesmaximal, characteristic
7C2×#19151491C211yesmaximal, characteristic
8C2×#19151485C211yesmaximal, characteristic, complemented
9C2×#19151482C211yesmaximal, characteristic, complemented
10C2×#19151481C211yesmaximal, characteristic, complemented
11C2×#19151479C211yesmaximal, characteristic, complemented
12C2×#19151459C211yesmaximal, characteristic
13C2×C4×C4⋊Dic89C211yesmaximal, characteristic, complemented
14C2×#19151449C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic89C211yesmaximal, characteristic
16C2×#388×C89C211yesmaximal, characteristic
17C23×Dic178C2211yescharacteristic
18C24×Dic89C2211yescharacteristic
19C2×#15667989C4116yescomplemented
20C2×#15667989C2218yes—
21C22×C4⋊Dic89C2211yescharacteristic
22C22×C4⋊Dic89C2211yescharacteristic
23C22×#13083553C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×C22⋊Dic89C2211yescharacteristic
28C22×C22⋊Dic89C2211yescharacteristic
29C22×C22⋊Dic89C2211yescharacteristic
30C22×C4×Dic89C2211yescharacteristic
31C22×C4×Dic89C2211yescharacteristic
32C22×C4×Dic89C2211yescharacteristic
33C22×C4×Dic89C2211yescharacteristic
34C22×C4×Dic89C2211yescharacteristic
35#19151503C2218yescomplemented
36#19151502C2218yescomplemented
37#19151492C2218yes—
38#19151492C2218yes—
39#19151491C2218yes—
40#19151485C2218yescomplemented
41#19151482C2218yescomplemented
42#19151481C2218yescomplemented
43#19151479C2218yescomplemented
44#19151459C2218yes—
45C4×C4⋊Dic89C2218yescomplemented
46#19151449C2218yescomplemented
47C22⋊C4×Dic89C2218yes—
48C2×#15667919C2211yescharacteristic
49C2×#15667919C2211yescharacteristic
50C2×#15667919C2211yescharacteristic
51C2×#15667919C2211yescharacteristic
52C2×#15667919C2211yescharacteristic
53C2×#15667919C2211yescharacteristic
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C22×C4⋊C4×C89C2211yescharacteristic
61C22×C22⋊C4×C89C2211yescharacteristic
62C22×C22⋊C4×C89C2211yescharacteristic
63C22×C22⋊C4×C89C2211yescharacteristic
64C22×C42×C89C2211yescharacteristic
65#388×C89C2218yes—
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C22×Dic178—42no—
69C22×Dic178—42no—
70C22×Dic178C2×C418yes—
71C22×Dic178C2314yes—
72C23×Dic89—42no—
73C23×Dic89—42no—
74C23×Dic89C2×C418yes—
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C23×Dic89C2311yescharacteristic
81C23×Dic89C2311yescharacteristic
82C23×Dic89C2311yescharacteristic
83C23×Dic89C2314yes—
84#15667989C2×C4164yescomplemented
85C2×C4⋊Dic89—24no—
86C2×C4⋊Dic89C2×C418yes—
87C2×C4⋊Dic89C2314yes—
88C2×C4⋊Dic89C2314yes—
89C2×#13083553—24no—
90C2×#13083553—42no—
91C2×#13083553C2×C418yes—
92C2×#13083553C2×C418yes—
93C2×#13083553C2314yes—
94C2×#13083553C2314yes—
95C2×#13083553C2314yes—
96C2×#13083553C2314yes—
97C2×C22⋊Dic89—24no—
98C2×C22⋊Dic89—42no—
99C2×C22⋊Dic89C2×C418yes—
100C2×C22⋊Dic89C2314yes—
101C2×C22⋊Dic89C2314yes—
102C2×C22⋊Dic89C2314yes—
103C2×C4×Dic89—24no—
104C2×C4×Dic89—42no—
105C2×C4×Dic89—42no—
106C2×C4×Dic89—42no—
107C2×C4×Dic89—42no—
108C2×C4×Dic89C2314yes—
109C2×C4×Dic89C2314yes—
110C2×C4×Dic89C2314yes—
111C2×C4×Dic89C2314yes—
112C2×C4×Dic89C2314yes—
113#15667919C2314yes—
114#15667919C2314yes—
115#15667919C2314yes—
116#15667919C2314yes—
117#15667919C2314yes—
118#15667919C2314yes—
119#15667919C2314yes—
120#15667919C2314yes—
121#15667919C2314yes—
122#15667919C2314yes—
123#15667919C2314yes—
124#15667919C2314yes—
125C25×C89C2311yescharacteristic
126C23×C4×C89C2311yescharacteristic
127C23×C4×C89C2311yescharacteristic
128C23×C4×C89C2311yescharacteristic
129C23×C4×C89C2311yescharacteristic
130C23×C4×C89C2311yescharacteristic
131C23×C4×C89C2311yescharacteristic
132C2×C4⋊C4×C89—42no—
133C2×C4⋊C4×C89C2314yes—
134C2×C22⋊C4×C89—24no—
135C2×C22⋊C4×C89—42no—
136C2×C22⋊C4×C89C2×C418yes—
137C2×C22⋊C4×C89C2314yes—
138C2×C22⋊C4×C89C2314yes—
139C2×C22⋊C4×C89C2314yes—
140C2×C42×C89—24no—
141C2×C42×C89C2314yes—
142#95×C89C2314yes—
143#95×C89C2314yes—
144C2×Dic178—416no—
145C2×Dic178—44no—
146C2×Dic178—44no—
147C2×Dic178C22×C4116yes—
148C22×Dic89—22no—
149C22×Dic89—22no—
150C22×Dic89—22no—
151C22×Dic89—22no—
152C22×Dic89—22no—
153C22×Dic89—22no—
154C22×Dic89—22no—
155C22×Dic89—22no—
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—416no—
168C22×Dic89—44no—
169C22×Dic89—44no—
170C22×Dic89C22×C414yes—
171C22×Dic89C22×C414yes—
172C22×Dic89C22×C414yes—
173C22×Dic89C22×C414yes—
174C22×Dic89C22×C4116yes—
175C22×Dic89#4114yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C22×Dic89C2412yes—
181C22×Dic89C2412yes—
182C22×Dic89C2412yes—
183C22×Dic89C2412yes—
184C4⋊Dic89—28no—
185C4⋊Dic89C22×C4116yes—
186#13083553—28no—
187#13083553—44no—
188#13083553C22×C4116yes—
189#13083553C22×C4116yes—
190C22⋊Dic89—28no—
191C22⋊Dic89—44no—
192C22⋊Dic89C22×C4116yes—
193C4×Dic89—28no—
194C4×Dic89—44no—
195C4×Dic89—44no—
196C4×Dic89—44no—
197C4×Dic89—44no—
198C24×C89—22no—
199C24×C89—22no—
200C24×C89—22no—
201C24×C89—22no—
202C24×C89—22no—
203C24×C89—22no—
204C24×C89C22×C414yes—
205C24×C89C2412yes—
206C24×C89C2411yescharacteristic
207C22×C4×C89—22no—
208C22×C4×C89—22no—
209C22×C4×C89—22no—
210C22×C4×C89—22no—
211C22×C4×C89—22no—
212C22×C4×C89—22no—
213C22×C4×C89—22no—
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×C89C22×C414yes—
223C22×C4×C89C22×C414yes—
224C22×C4×C89#4114yes—
225C22×C4×C89C2412yes—
226C22×C4×C89C2412yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C22×C4×C89C2412yes—
230C22×C4×C89C2412yes—
231C4⋊C4×C89—44no—
232C22⋊C4×C89—28no—
233C22⋊C4×C89—44no—
234C22⋊C4×C89C22×C4116yes—
235C42×C89—28no—
236C23×C89—28no—
237C23×C89—28no—
238C23×C89—28no—
239C23×C89—22no—
240C23×C89—22no—
241C23×C89—22no—
242C23×C89—22no—
243C23×C89—22no—
244C23×C89—22no—
245C23×C89—44no—
246C23×C89—44no—
247C23×C89—44no—
248C23×C89—44no—
249C23×C89C23×C414yes—
250C23×C89C23×C412yes—
251C23×C89C2×#4112yes—
252C23×C89C2×#4112yes—
253C23×C89H(5,𝔽2)12yes—
254C23×C89H(5,𝔽2)12yes—
255C23×C892−1+412yes—
256C23×C892−1+412yes—
257C23×C89C2511yescharacteristic
258C2×C4×C89—28no—
259C2×C4×C89—28no—
260C2×C4×C89—28no—
261C2×C4×C89—22no—
262C2×C4×C89—22no—
263C2×C4×C89—22no—
264C2×C4×C89—22no—
265C2×C4×C89—22no—
266C2×C4×C89—22no—
267C2×C4×C89—22no—
268C2×C4×C89—22no—
269C2×C4×C89—22no—
270C2×C4×C89—22no—
271C2×C4×C89—22no—
272C2×C4×C89—22no—
273C2×C4×C89—22no—
274C2×C4×C89—22no—
275C2×C4×C89—22no—
276C2×C4×C89—44no—
277C2×C4×C89—44no—
278C2×C4×C89—44no—
279C2×C4×C89C23×C414yes—
280C2×C4×C89C23×C414yes—
281C2×C4×C89C2×#4114yes—
282C2×Dic89—28no—
283C2×Dic89—28no—
284C2×Dic89—28no—
285C2×Dic89—28no—
286C2×Dic89—28no—
287C2×Dic89—22no—
288C2×Dic89—22no—
289C2×Dic89—22no—
290C2×Dic89—22no—
291C2×Dic89—22no—
292C2×Dic89—22no—
293C2×Dic89—22no—
294C2×Dic89—22no—
295C2×Dic89—22no—
296C2×Dic89—22no—
297C2×Dic89—22no—
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—416no—
307C2×Dic89—44no—
308C2×Dic89—44no—
309C2×Dic89—44no—
310C2×Dic89C23×C414yes—
311C2×Dic89C23×C414yes—
312C2×Dic89C23×C414yes—
313C2×Dic89C23×C414yes—
314C2×Dic89C2×#4114yes—
315Dic178—416no—
316C22×C89—24no—
317C22×C89—24no—
318C22×C89—24no—
319C22×C89—416no—
320C22×C89—42no—
321C22×C89—42no—
322C22×C89—42no—
323C22×C89—42no—
324C22×C89C4×#4114yes—
325C22×C89#51814yes—
326C22×C89#51914yes—
327C22×C89#53914yes—
328C22×C89#53914yes—
329C22×C89#54214yes—
330C22×C89#54214yes—
331C22×C89C24×C411yescharacteristic
332C22×C89C22×#4111yescharacteristic
333C22×C89C22×#4111yescharacteristic
334C22×C89C2×H(5,𝔽2)11yescharacteristic
335C22×C89C2×H(5,𝔽2)11yescharacteristic
336C22×C89C2×2−1+411yescharacteristic
337C22×C89C2×2−1+411yescharacteristic
338C4×C89—24no—
339C4×C89—24no—
340C4×C89—24no—
341C4×C89—42no—
342C4×C89—42no—
343C4×C89—42no—
344Dic89—24no—
345Dic89—24no—
346Dic89—24no—
347Dic89—24no—
348Dic89—24no—
349Dic89—42no—
350Dic89—42no—
351Dic89—42no—
352C2×#2332—891nomaximal, Sylow
353C2×C89—44no—
354C2×C89#233218yescomplemented
355C2×C89C2×C4×#4111yescharacteristic
356C2×C89C2×#51811yescharacteristic
357C2×C89C2×#51911yescharacteristic
358C2×C89C2×#53911yescharacteristic
359C2×C89C2×#53911yescharacteristic
360C2×C89C2×#54211yescharacteristic
361C2×C89C2×#54211yescharacteristic
362C22×C22⋊Q8—891no—
363#2332—8916no—
364C2×#391—891no—
365C2×#391—891no—
366C2×#388—891no—
367C2×#388—891no—
368C2×#388—891no—
369C2×#388D8911yescharacteristic
370C2×#387—891no—
371C2×#387—891no—
372C2×#387—891no—
373C2×#387—891no—
374C2×#381—891no—
375C2×C4×C4⋊C4—891no—
376C2×C4×C4⋊C4—891no—
377C2×C4×C22⋊C4—891no—
378C89C2×#233211yescharacteristic, complemented, Sylow
379C23×Q8—891no—
380C24×C4—891no—
381C2×C22⋊Q8—8916no—
382C2×C22⋊Q8—898no—
383C22×C4⋊C4—891no—
384C22×C4⋊C4—891no—
385C22×C4⋊C4—891no—
386C22×C4⋊C4—891no—
387C22×C4⋊C4—891no—
388C22×C4⋊C4—891no—
389C22×C4⋊C4C2×D8911yescharacteristic
390C22×C22⋊C4—891no—
391C22×C22⋊C4—891no—
392C22×C22⋊C4—891no—
393C22×C22⋊C4C2×D8911yescharacteristic
394C22×C22⋊C4C2×D8911yescharacteristic
395C22×C22⋊C4C2×D8911yescharacteristic
396C22×C42—891no—
397C22×C42—891no—
398C22×C42—891no—
399C22×C42—891no—
400C22×C42—891no—
401C22×C42C2×D8911yescharacteristic
402#391—898no—
403#391—898no—
404#388—898no—
405#388—898no—
406#388—898no—
407#388C2×D8918yes—
408#387—898no—
409#387—898no—
410#387—898no—
411#387—898no—
412#381—898no—
413C4×C4⋊C4—898no—
414C4×C4⋊C4—898no—
415C4×C22⋊C4—898no—
416C2×#95—891no—
417C2×#95—891no—
418C2×#95—891no—
419C2×#95—891no—
420C2×#95—891no—
421C2×#95—891no—
422C2×#95—891no—
423C2×#95—891no—
424C2×#95—891no—
425C2×#95—891no—
426C2×#95—891no—
427C2×#95—891no—
428C2×#95C2×D8911yescharacteristic
429C2×#95C2×D8911yescharacteristic
430C25C22×D8911yescharacteristic
431C22×Q8—898no—
432C22×Q8—894no—
433C22×Q8—3562no—
434C22×Q8—3562no—
435C23×C4—898no—
436C23×C4—894no—
437C23×C4—891no—
438C23×C4—891no—
439C23×C4—891no—
440C23×C4—891no—
441C23×C4—891no—
442C23×C4—891no—
443C23×C4—891no—
444C23×C4—891no—
445C23×C4—3562no—
446C23×C4—3562no—
447C23×C4C22×D8911yescharacteristic
448C23×C4C22×D8911yescharacteristic
449C23×C4C22×D8911yescharacteristic
450C23×C4C22×D8911yescharacteristic
451C23×C4C22×D8911yescharacteristic
452C23×C4C22×D8911yescharacteristic
453C22⋊Q8—8964no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—898no—
456C2×C4⋊C4—898no—
457C2×C4⋊C4—898no—
458C2×C4⋊C4—894no—
459C2×C4⋊C4—894no—
460C2×C4⋊C4—894no—
461C2×C4⋊C4—894no—
462C2×C4⋊C4—894no—
463C2×C4⋊C4—894no—
464C2×C4⋊C4—3562no—
465C2×C4⋊C4—1784no—
466C2×C4⋊C4—1784no—
467C2×C4⋊C4C22×D8914yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—898no—
471C2×C22⋊C4—894no—
472C2×C22⋊C4—894no—
473C2×C22⋊C4—894no—
474C2×C22⋊C4—3562no—
475C2×C22⋊C4—1784no—
476C2×C22⋊C4C4×D8918yes—
477C2×C22⋊C4C22×D8914yes—
478C2×C22⋊C4C22×D8914yes—
479C2×C22⋊C4C22×D8914yes—
480C2×C42—24no—
481C2×C42—894no—
482C2×C42—894no—
483C2×C42—894no—
484C2×C42—894no—
485C2×C42—894no—
486C2×C42—3562no—
487C2×C42—3562no—
488C2×C42—3562no—
489C2×C42—3562no—
490C2×C42—1784no—
491C2×C42C22×D8914yes—
492#95—894no—
493#95—894no—
494#95—894no—
495#95—894no—
496#95—894no—
497#95—894no—
498#95—894no—
499#95—894no—
500#95—894no—
501#95—894no—
502#95—894no—
503#95—894no—
504#95C22×D8914yes—
505#95C22×D8914yes—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24C2×C4×D8914yes—
513C24C23×D8912yes—
514C24C23×D8911yescharacteristic
515C2×Q8—8916no—
516C2×Q8—3564no—
517C2×Q8—3564no—
518C2×Q8—35616no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—8916no—
535C22×C4—894no—
536C22×C4—894no—
537C22×C4—894no—
538C22×C4—894no—
539C22×C4—894no—
540C22×C4—892no—
541C22×C4—892no—
542C22×C4—892no—
543C22×C4—892no—
544C22×C4—892no—
545C22×C4—892no—
546C22×C4—892no—
547C22×C4—892no—
548C22×C4—3564no—
549C22×C4—3564no—
550C22×C4—35616no—
551C22×C4—1782no—
552C22×C4—1782no—
553C22×C4—1782no—
554C22×C4—1782no—
555C22×C4—1782no—
556C22×C4—1782no—
557C22×C4—1782no—
558C22×C4—1782no—
559C22×C4—1782no—
560C22×C4—1782no—
561C22×C4—1782no—
562C22×C4—1782no—
563C22×C4—1782no—
564C22×C4—1782no—
565C22×C4—1782no—
566C22×C4—1782no—
567C22×C4—1782no—
568C22×C4—1782no—
569C22×C4—1782no—
570C22×C4C2×C4×D8914yes—
571C22×C4C2×C4×D8914yes—
572C22×C4#1308357314yes—
573C22×C4C23×D8912yes—
574C22×C4C23×D8912yes—
575C22×C4C23×D8912yes—
576C22×C4C23×D8912yes—
577C22×C4C23×D8912yes—
578C22×C4C23×D8912yes—
579C4⋊C4—44no—
580C4⋊C4—8916no—
581C4⋊C4—8916no—
582C4⋊C4—8916no—
583C4⋊C4—3564no—
584C4⋊C4—1788no—
585C4⋊C4—1788no—
586C22⋊C4—28no—
587C22⋊C4—44no—
588C22⋊C4—8916no—
589C22⋊C4—3564no—
590C22⋊C4—1788no—
591C22⋊C4C2×C4×D89116yes—
592C42—28no—
593C42—3564no—
594C42—3564no—
595C42—3564no—
596C42—3564no—
597C42—1788no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—28no—
605C23—28no—
606C23—28no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23C22×C4×D8914yes—
612C23C22×C4×D8912yes—
613C23#41×D8912yes—
614C23C2×#1308357312yes—
615C23#1566805712yes—
616C23#1566805812yes—
617C23#1566805912yes—
618C23#1566805912yes—
619C23C24×D8911yescharacteristic
620Q8—35616no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—28no—
628C2×C4—28no—
629C2×C4—28no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—894no—
643C2×C4—894no—
644C2×C4—894no—
645C2×C4—894no—
646C2×C4—894no—
647C2×C4—3564no—
648C2×C4—3564no—
649C2×C4—3564no—
650C2×C4—35616no—
651C2×C4—1782no—
652C2×C4—1782no—
653C2×C4—1782no—
654C2×C4—1782no—
655C2×C4—1782no—
656C2×C4—1782no—
657C2×C4—1782no—
658C2×C4—1782no—
659C2×C4—1782no—
660C2×C4—1782no—
661C2×C4—1782no—
662C2×C4—1782no—
663C2×C4—1782no—
664C2×C4—1782no—
665C2×C4—1782no—
666C2×C4—1782no—
667C2×C4—1782no—
668C2×C4—1782no—
669C2×C4—1782no—
670C2×C4—1788no—
671C2×C4—1788no—
672C2×C4—1788no—
673C2×C4—1788no—
674C2×C4—1788no—
675C2×C4C22×C4×D8914yes—
676C2×C4C22×C4×D8914yes—
677C2×C4C2×#1308357314yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—416no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22C4×#1308357314yes—
687C22#1915207014yes—
688C22#1915207514yes—
689C22#1915218914yes—
690C22#1915219214yes—
691C22#1915221214yes—
692C22#1915221514yes—
693C22C23×C4×D8911yescharacteristic
694C22C2×#41×D8911yescharacteristic
695C22C22×#1308357311yescharacteristic
696C22C2×#1566805711yescharacteristic
697C22C2×#1566805811yescharacteristic
698C22C2×#1566805911yescharacteristic
699C22C2×#1566805911yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—3562no—
707C4—3562no—
708C4—3562no—
709C4—1784no—
710C4—1784no—
711C4—1784no—
712C4—1784no—
713C4—1784no—
714C2—44no—
715C2#2602300918yesdirect product factor
716C2C2×C4×#1308357311yescharacteristic
717C2C2×#1915207011yescharacteristic
718C2C2×#1915207511yescharacteristic
719C2C2×#1915218911yescharacteristic
720C2C2×#1915219211yescharacteristic
721C2C2×#1915221211yescharacteristic
722C2C2×#1915221511yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#388×C89C2
socleC24×C89C24
prime radicalC25×C89C23
cosocleC23×C89C25
hypercenterC2×#388D89
hypocenterC89C2×#2332
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #26023009C2direct (N × H)
3. C2×#19151503C2semidirect
4. C2×#19151502C2semidirect
8. C2×#19151485C2semidirect
9. C2×#19151482C2semidirect
10. C2×#19151481C2semidirect
11. C2×#19151479C2semidirect
13. C2×C4×C4⋊Dic89C2semidirect
14. C2×#19151449C2semidirect
19. C2×#15667989C4semidirect
35. #19151503C22semidirect
36. #19151502C22semidirect
40. #19151485C22semidirect
41. #19151482C22semidirect
42. #19151481C22semidirect
43. #19151479C22semidirect
45. C4×C4⋊Dic89C22semidirect
46. #19151449C22semidirect
84. #15667989C2×C4semidirect
354. C2×C89#2332semidirect
378. C89C2×#2332semidirect
715. C2#26023009direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679892
#260230092
C2×#191515032
C2×#191515022
C2×#191514922
C2×#191514912
C2×#191514852
C2×#191514822
C2×#191514812
C2×#191514792
C2×#191514592
C2×C4×C4⋊Dic892
C2×#191514492
C2×C22⋊C4×Dic892
C2×#388×C892
C2×#233289