Finite Group Databasebeta

← C2×#26023416 #36717033

Subgroups — C2×#26023416 #36717033

Order 22784.

2566 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×#15667992C211yesmaximal, characteristic
2#26023416C2116yesmaximal, direct product factor
3C2×#19151502C211yesmaximal, characteristic, complemented
4C2×#19151502C211yesmaximal, characteristic, complemented
5C2×#19151496C211yesmaximal, characteristic, complemented
6C2×#19151494C211yesmaximal, characteristic, complemented
7C2×#19151490C211yesmaximal, characteristic
8C2×#19151489C211yesmaximal, characteristic
9C2×#19151488C211yesmaximal, characteristic
10C2×#19151487C211yesmaximal, characteristic
11C2×#19151484C211yesmaximal, characteristic, complemented
12C2×#19151483C211yesmaximal, characteristic, complemented
13C2×#19151481C211yesmaximal, characteristic, complemented
14C2×#19151460C211yesmaximal, characteristic
15C2×#19151457C211yesmaximal, characteristic
16C2×#387×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C2×#15667992C4116yescomplemented
20C2×#15667992C2218yes—
21C22×C4⋊Dic89C2211yescharacteristic
22C22×C4⋊Dic89C2211yescharacteristic
23C22×C4⋊Dic89C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083551C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×#13083551C2211yescharacteristic
33C22×#13083551C2211yescharacteristic
34C22×C4×Dic89C2211yescharacteristic
35C22×C4×Dic89C2211yescharacteristic
36C22×C4×Dic89C2211yescharacteristic
37#19151502C2218yescomplemented
38#19151502C2218yescomplemented
39#19151496C2218yescomplemented
40#19151494C2218yescomplemented
41#19151490C2218yes—
42#19151489C2218yes—
43#19151488C2218yes—
44#19151487C2218yes—
45#19151484C2218yescomplemented
46#19151483C2218yescomplemented
47#19151481C2218yescomplemented
48#19151460C2218yes—
49#19151457C2218yes—
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×C4⋊C4×C89C2211yescharacteristic
62C22×C42×C89C2211yescharacteristic
63#387×C89C2218yescomplemented
64C2×#95×C89C2211yescharacteristic
65C2×#95×C89C2211yescharacteristic
66C2×#95×C89C2211yescharacteristic
67C2×#95×C89C2211yescharacteristic
68C24×D89C2311yescharacteristic
69C22×Dic178—42no—
70C22×Dic178—42no—
71C22×Dic178C2×C418yes—
72C22×Dic178C2314yes—
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C22×C4×D89—42no—
81C22×C4×D89—42no—
82C22×C4×D89C2×C418yes—
83C22×C4×D89C2314yes—
84#15667992C2×C4164yescomplemented
85C2×C4⋊Dic89—42no—
86C2×C4⋊Dic89C2×C418yes—
87C2×C4⋊Dic89C2×C418yes—
88C2×C4⋊Dic89C2314yes—
89C2×C4⋊Dic89C2314yes—
90C2×C4⋊Dic89C2314yes—
91C2×#13083553—42no—
92C2×#13083553—42no—
93C2×#13083553—42no—
94C2×#13083553—42no—
95C2×#13083553C2314yes—
96C2×#13083553C2314yes—
97C2×#13083553C2314yes—
98C2×#13083553C2314yes—
99C2×#13083551—42no—
100C2×#13083551—42no—
101C2×#13083551—42no—
102C2×#13083551—42no—
103C2×#13083551C2×C418yes—
104C2×#13083551C2×C418yes—
105C2×#13083551C2314yes—
106C2×#13083551C2314yes—
107C2×#13083551C2314yes—
108C2×#13083551C2314yes—
109C2×#13083551C2314yes—
110C2×#13083551C2314yes—
111C2×C4×Dic89—42no—
112C2×C4×Dic89—42no—
113C2×C4×Dic89—42no—
114C2×C4×Dic89C2314yes—
115C2×C4×Dic89C2314yes—
116C2×C4×Dic89C2314yes—
117#15667919C2314yes—
118#15667919C2314yes—
119#15667919C2314yes—
120#15667919C2314yes—
121#15667919C2314yes—
122#15667919C2314yes—
123#15667919C2314yes—
124#15667919C2314yes—
125#15667919C2314yes—
126#15667919C2314yes—
127C23×C4×C89C2311yescharacteristic
128C23×C4×C89C2311yescharacteristic
129C23×C4×C89C2311yescharacteristic
130C23×C4×C89C2311yescharacteristic
131C23×C4×C89C2311yescharacteristic
132C23×C4×C89C2311yescharacteristic
133C23×C4×C89C2311yescharacteristic
134C2×C4⋊C4×C89—42no—
135C2×C4⋊C4×C89C2×C418yes—
136C2×C4⋊C4×C89C2314yes—
137C2×C4⋊C4×C89C2314yes—
138C2×C42×C89—42no—
139C2×C42×C89C2314yes—
140#95×C89C2314yes—
141#95×C89C2314yes—
142#95×C89C2314yes—
143#95×C89C2314yes—
144C23×D89—22no—
145C23×D89—22no—
146C23×D89—22no—
147C23×D89—22no—
148C23×D89—22no—
149C23×D89—22no—
150C23×D89C22×C414yes—
151C23×D89C2412yes—
152C2×Dic178—416no—
153C2×Dic178—44no—
154C2×Dic178—44no—
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—22no—
165C22×Dic89—22no—
166C22×Dic89—22no—
167C22×Dic89—22no—
168C22×Dic89—22no—
169C22×Dic89—22no—
170C22×Dic89—22no—
171C22×Dic89—22no—
172C22×Dic89—22no—
173C22×Dic89—22no—
174C22×Dic89C22×C414yes—
175C22×Dic89C22×C414yes—
176C22×Dic89C22×C414yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C22×Dic89C2412yes—
181C22×Dic89C2412yes—
182C22×Dic89C2412yes—
183C22×Dic89C2412yes—
184C2×C4×D89—416no—
185C2×C4×D89—44no—
186C2×C4×D89—44no—
187C2×C4×D89C22×C4116yes—
188C4⋊Dic89—44no—
189C4⋊Dic89C22×C4116yes—
190C4⋊Dic89C22×C4116yes—
191#13083553—44no—
192#13083553—44no—
193#13083553—44no—
194#13083553—44no—
195#13083551—44no—
196#13083551—44no—
197#13083551—44no—
198#13083551—44no—
199#13083551C22×C4116yes—
200#13083551C22×C4116yes—
201C4×Dic89—44no—
202C4×Dic89—44no—
203C4×Dic89—44no—
204C24×C89C2411yescharacteristic
205C22×C4×C89—22no—
206C22×C4×C89—22no—
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×C89—22no—
223C22×C4×C89C22×C414yes—
224C22×C4×C89C22×C414yes—
225C22×C4×C89C22×C414yes—
226C22×C4×C89C2412yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C22×C4×C89C2412yes—
230C22×C4×C89C2412yes—
231C22×C4×C89C2412yes—
232C22×C4×C89C2412yes—
233C4⋊C4×C89—44no—
234C4⋊C4×C89C22×C4116yes—
235C42×C89—44no—
236C23×C89C23×C412yes—
237C23×C89H(5,𝔽2)12yes—
238C23×C89H(5,𝔽2)12yes—
239C23×C89H(5,𝔽2)12yes—
240C23×C892−1+412yes—
241C23×C892−1+412yes—
242C23×C892−1+412yes—
243C23×C89C2511yescharacteristic
244C22×D89—28no—
245C22×D89—28no—
246C22×D89—28no—
247C22×D89—22no—
248C22×D89—22no—
249C22×D89—22no—
250C22×D89—22no—
251C22×D89—22no—
252C22×D89—22no—
253C22×D89—44no—
254C22×D89—44no—
255C22×D89—44no—
256C22×D89—44no—
257C22×D89C23×C414yes—
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—22no—
277C2×C4×C89—22no—
278C2×C4×C89—22no—
279C2×C4×C89—44no—
280C2×C4×C89—44no—
281C2×C4×C89—44no—
282C2×C4×C89—44no—
283C2×C4×C89C23×C414yes—
284C2×C4×C89C23×C414yes—
285C2×C4×C89C23×C414yes—
286C2×Dic89—28no—
287C2×Dic89—28no—
288C2×Dic89—28no—
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—22no—
307C2×Dic89—44no—
308C2×Dic89—44no—
309C2×Dic89—44no—
310C2×Dic89—44no—
311C2×Dic89C23×C414yes—
312C2×Dic89C23×C414yes—
313C2×Dic89C23×C414yes—
314C4×D89—416no—
315Dic178—416no—
316C22×C89#51814yes—
317C22×C89#51914yes—
318C22×C89#52014yes—
319C22×C89#56214yes—
320C22×C89#56214yes—
321C22×C89#56314yes—
322C22×C89#56314yes—
323C22×C89C24×C411yescharacteristic
324C22×C89C2×H(5,𝔽2)11yescharacteristic
325C22×C89C2×H(5,𝔽2)11yescharacteristic
326C22×C89C2×H(5,𝔽2)11yescharacteristic
327C22×C89C2×2−1+411yescharacteristic
328C22×C89C2×2−1+411yescharacteristic
329C22×C89C2×2−1+411yescharacteristic
330C2×D89—24no—
331C2×D89—24no—
332C2×D89—24no—
333C2×D89—416no—
334C2×D89—42no—
335C2×D89—42no—
336C2×D89—42no—
337C2×D89—42no—
338C4×C89—24no—
339C4×C89—24no—
340C4×C89—24no—
341C4×C89—42no—
342C4×C89—42no—
343C4×C89—42no—
344C4×C89—42no—
345Dic89—24no—
346Dic89—24no—
347Dic89—24no—
348Dic89—42no—
349Dic89—42no—
350Dic89—42no—
351Dic89—42no—
352C2×#2378—891nomaximal, Sylow
353C2×C89#237818yescomplemented
354C2×C89C2×#51811yescharacteristic
355C2×C89C2×#51911yescharacteristic
356C2×C89C2×#52011yescharacteristic
357C2×C89C2×#56211yescharacteristic
358C2×C89C2×#56211yescharacteristic
359C2×C89C2×#56311yescharacteristic
360C2×C89C2×#56311yescharacteristic
361D89—44no—
362C22×C22⋊Q8—891no—
363#2378—8916no—
364C2×#391—891no—
365C2×#391—891no—
366C2×#389—891no—
367C2×#389—891no—
368C2×#388—891no—
369C2×#388—891no—
370C2×#388—891no—
371C2×#388—891no—
372C2×#387—891no—
373C2×#387—891no—
374C2×#387—891no—
375C2×#387D8911yescharacteristic, complemented
376C2×#381—891no—
377C2×#380—891no—
378C89C2×#237811yescharacteristic, 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⋊C4—891no—
390C22×C4⋊C4C2×D8911yescharacteristic
391C22×C4⋊C4C2×D8911yescharacteristic
392C22×C22⋊C4—891no—
393C22×C22⋊C4—891no—
394C22×C22⋊C4—891no—
395C22×C22⋊C4—891no—
396C22×C22⋊C4—891no—
397C22×C22⋊C4—891no—
398C22×C42—891no—
399C22×C42—891no—
400C22×C42—891no—
401C22×C42C2×D8911yescharacteristic
402#391—898no—
403#391—898no—
404#389—898no—
405#389—898no—
406#388—898no—
407#388—898no—
408#388—898no—
409#388—898no—
410#387—898no—
411#387—898no—
412#387—898no—
413#387C2×D8918yescomplemented
414#381—898no—
415#380—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×#95C2×D8911yescharacteristic
427C2×#95C2×D8911yescharacteristic
428C2×#95C2×D8911yescharacteristic
429C2×#95C2×D8911yescharacteristic
430C25—891no—
431C22×Q8—898no—
432C22×Q8—894no—
433C22×Q8—3562no—
434C22×Q8—3562no—
435C23×C4—891no—
436C23×C4—891no—
437C23×C4—891no—
438C23×C4—898no—
439C23×C4—894no—
440C23×C4—891no—
441C23×C4—891no—
442C23×C4—891no—
443C23×C4—891no—
444C23×C4—3562no—
445C23×C4—3562no—
446C23×C4C22×D8911yescharacteristic
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—894no—
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—3562no—
466C2×C4⋊C4—3562no—
467C2×C4⋊C4—3562no—
468C2×C4⋊C4—3562no—
469C2×C4⋊C4C4×D8918yes—
470C2×C4⋊C4C22×D8914yes—
471C2×C4⋊C4C22×D8914yes—
472C2×C22⋊C4—898no—
473C2×C22⋊C4—898no—
474C2×C22⋊C4—894no—
475C2×C22⋊C4—894no—
476C2×C22⋊C4—894no—
477C2×C22⋊C4—894no—
478C2×C22⋊C4—894no—
479C2×C22⋊C4—894no—
480C2×C22⋊C4—3562no—
481C2×C22⋊C4—3562no—
482C2×C22⋊C4—3562no—
483C2×C22⋊C4—3562no—
484C2×C42—42no—
485C2×C42—894no—
486C2×C42—894no—
487C2×C42—894no—
488C2×C42—3562no—
489C2×C42—3562no—
490C2×C42—3562no—
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#95C22×D8914yes—
503#95C22×D8914yes—
504#95C22×D8914yes—
505#95C22×D8914yes—
506C24—894no—
507C24—892no—
508C24—1782no—
509C24—1782no—
510C24—1782no—
511C24—1782no—
512C24—1782no—
513C24—1782no—
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—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—894no—
538C22×C4—894no—
539C22×C4—894no—
540C22×C4—892no—
541C22×C4—892no—
542C22×C4—892no—
543C22×C4—8916no—
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×C4C2×C4×D8914yes—
570C22×C4C2×C4×D8914yes—
571C22×C4C2×C4×D8914yes—
572C22×C4C23×D8912yes—
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—3564no—
583C4⋊C4—3564no—
584C4⋊C4—3564no—
585C4⋊C4—3564no—
586C4⋊C4—3564no—
587C4⋊C4C2×C4×D89116yes—
588C22⋊C4—8916no—
589C22⋊C4—8916no—
590C22⋊C4—3564no—
591C22⋊C4—3564no—
592C22⋊C4—3564no—
593C22⋊C4—3564no—
594C42—44no—
595C42—3564no—
596C42—3564no—
597C42—3564no—
598C23—894no—
599C23—3564no—
600C23—3564no—
601C23—3564no—
602C23—3564no—
603C23—1782no—
604C23—1782no—
605C23—1782no—
606C23—1782no—
607C23—1782no—
608C23—1782no—
609C23—1788no—
610C23—1788no—
611C23—1788no—
612C23C22×C4×D8912yes—
613C23#1566805712yes—
614C23#1566805812yes—
615C23#1566805812yes—
616C23#1566805912yes—
617C23#1566805912yes—
618C23#1566806012yes—
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—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—894no—
647C2×C4—894no—
648C2×C4—894no—
649C2×C4—35616no—
650C2×C4—3564no—
651C2×C4—3564no—
652C2×C4—3564no—
653C2×C4—3564no—
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—1782no—
671C2×C4—1782no—
672C2×C4—1788no—
673C2×C4—1788no—
674C2×C4—1788no—
675C2×C4C22×C4×D8914yes—
676C2×C4C22×C4×D8914yes—
677C2×C4C22×C4×D8914yes—
678C22—3562no—
679C22—3562no—
680C22—3562no—
681C22—3562no—
682C22—35616no—
683C22—1784no—
684C22—1784no—
685C22—1784no—
686C22#1915207214yes—
687C22#1915207414yes—
688C22#1915207714yes—
689C22#1915234414yes—
690C22#1915234514yes—
691C22#1915235014yes—
692C22#1915235214yes—
693C22C23×C4×D8911yescharacteristic
694C22C2×#1566805711yescharacteristic
695C22C2×#1566805811yescharacteristic
696C22C2×#1566805811yescharacteristic
697C22C2×#1566805911yescharacteristic
698C22C2×#1566805911yescharacteristic
699C22C2×#1566806011yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—3562no—
708C4—3562no—
709C4—3562no—
710C4—3562no—
711C4—1784no—
712C4—1784no—
713C4—1784no—
714C2—3564no—
715C2#2602341618yesdirect product factor
716C2C2×#1915207211yescharacteristic
717C2C2×#1915207411yescharacteristic
718C2C2×#1915207711yescharacteristic
719C2C2×#1915234411yescharacteristic
720C2C2×#1915234511yescharacteristic
721C2C2×#1915235011yescharacteristic
722C2C2×#1915235211yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#387×C89C2
socleC24×C89C24
prime radicalC24×D89C23
cosocleC23×C89C25
hypercenterC2×#387D89
hypocenterC89C2×#2378
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #26023416C2direct (N × H)
3. C2×#19151502C2semidirect
4. C2×#19151502C2semidirect
5. C2×#19151496C2semidirect
6. C2×#19151494C2semidirect
11. C2×#19151484C2semidirect
12. C2×#19151483C2semidirect
13. C2×#19151481C2semidirect
16. C2×#387×C89C2semidirect
19. C2×#15667992C4semidirect
37. #19151502C22semidirect
38. #19151502C22semidirect
39. #19151496C22semidirect
40. #19151494C22semidirect
45. #19151484C22semidirect
46. #19151483C22semidirect
47. #19151481C22semidirect
63. #387×C89C22semidirect
84. #15667992C2×C4semidirect
353. C2×C89#2378semidirect
375. C2×#387D89semidirect
378. C89C2×#2378semidirect
413. #387C2×D89semidirect
715. C2#26023416direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679922
#260234162
C2×#191515022
C2×#191514962
C2×#191514942
C2×#191514902
C2×#191514892
C2×#191514882
C2×#191514872
C2×#191514842
C2×#191514832
C2×#191514812
C2×#191514602
C2×#191514572
C2×#387×C892
C2×#237889