Finite Group Databasebeta

← C2×#26028510 #36760849

Subgroups — C2×#26028510 #36760849

Order 22784.

2110 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26028510C2116yesmaximal, direct product factor
2C2×#19151537C211yesmaximal, characteristic, complemented
3C2×#19151536C211yesmaximal, characteristic, complemented
4C2×#19151533C211yesmaximal, characteristic
5C2×#19151532C211yesmaximal, characteristic, complemented
6C2×#19151532C211yesmaximal, characteristic, complemented
7C2×#19151528C211yesmaximal, characteristic, complemented
8C2×#19151520C211yesmaximal, characteristic
9C2×#19151520C211yesmaximal, characteristic
10C2×#19151519C211yesmaximal, characteristic, complemented
11C2×#19151518C211yesmaximal, characteristic, complemented
12C2×#19151511C211yesmaximal, characteristic
13C2×#19151460C211yesmaximal, characteristic
14C2×#19151457C211yesmaximal, characteristic
15C2×#19151455C211yesmaximal, characteristic
16C2×#398×C89C211yesmaximal, characteristic, complemented
17C23×Dic178C2211yescharacteristic
18C23×C4×D89C2211yescharacteristic
19C22×C4⋊Dic89C2211yescharacteristic
20C22×C4⋊Dic89C2211yescharacteristic
21C22×C4⋊Dic89C2211yescharacteristic
22C22×#13083553C2211yescharacteristic
23C22×#13083553C2211yescharacteristic
24C22×#13083553C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083551C2211yescharacteristic
29C22×#13083551C2211yescharacteristic
30C22×#13083551C2211yescharacteristic
31C22×#13083551C2211yescharacteristic
32C22×#13083551C2211yescharacteristic
33C22×#13083551C2211yescharacteristic
34#19151537C2218yescomplemented
35#19151536C2218yescomplemented
36#19151533C2218yes—
37#19151532C2218yescomplemented
38#19151532C2218yescomplemented
39#19151528C2218yescomplemented
40#19151520C2218yes—
41#19151520C2218yes—
42#19151519C2218yescomplemented
43#19151518C2218yescomplemented
44#19151511C2218yes—
45#19151460C2218yes—
46#19151457C2218yes—
47#19151455C2218yes—
48C2×#15667919C2211yescharacteristic
49C2×#15667919C2211yescharacteristic
50C2×#15667919C2211yescharacteristic
51C2×#15667919C2211yescharacteristic
52C2×#15667919C2211yescharacteristic
53C2×#15667919C2211yescharacteristic
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C22×C4⋊C4×C89C2211yescharacteristic
60C22×C4⋊C4×C89C2211yescharacteristic
61C22×C4⋊C4×C89C2211yescharacteristic
62C22×C4⋊C4×C89C2211yescharacteristic
63#398×C89C2218yescomplemented
64C2×#95×C89C2211yescharacteristic
65C2×#95×C89C2211yescharacteristic
66C2×#95×C89C2211yescharacteristic
67C24×D89C2311yescharacteristic
68C22×Dic178—42no—
69C22×Dic178—42no—
70C22×Dic178—42no—
71C22×Dic178C2314yes—
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77C23×Dic89C2311yescharacteristic
78C23×Dic89C2311yescharacteristic
79C22×C4×D89—42no—
80C22×C4×D89—42no—
81C22×C4×D89Q818yescomplemented
82C22×C4×D89C2314yes—
83C2×C4⋊Dic89—42no—
84C2×C4⋊Dic89—42no—
85C2×C4⋊Dic89—42no—
86C2×C4⋊Dic89C2314yes—
87C2×C4⋊Dic89C2314yes—
88C2×C4⋊Dic89C2314yes—
89C2×#13083553—42no—
90C2×#13083553—42no—
91C2×#13083553—42no—
92C2×#13083553—42no—
93C2×#13083553—42no—
94C2×#13083553—42no—
95C2×#13083553C2314yes—
96C2×#13083553C2314yes—
97C2×#13083553C2314yes—
98C2×#13083553C2314yes—
99C2×#13083553C2314yes—
100C2×#13083553C2314yes—
101C2×#13083551—42no—
102C2×#13083551—42no—
103C2×#13083551—42no—
104C2×#13083551—42no—
105C2×#13083551—42no—
106C2×#13083551—42no—
107C2×#13083551C2314yes—
108C2×#13083551C2314yes—
109C2×#13083551C2314yes—
110C2×#13083551C2314yes—
111C2×#13083551C2314yes—
112C2×#13083551C2314yes—
113#15667919C2314yes—
114#15667919C2314yes—
115#15667919C2314yes—
116#15667919C2314yes—
117#15667919C2314yes—
118#15667919C2314yes—
119#15667919C2314yes—
120#15667919C2314yes—
121#15667919C2314yes—
122#15667919C2314yes—
123#15667919C2314yes—
124C23×C4×C89C2311yescharacteristic
125C23×C4×C89C2311yescharacteristic
126C23×C4×C89C2311yescharacteristic
127C23×C4×C89C2311yescharacteristic
128C23×C4×C89C2311yescharacteristic
129C23×C4×C89C2311yescharacteristic
130C23×C4×C89C2311yescharacteristic
131C2×C4⋊C4×C89—42no—
132C2×C4⋊C4×C89—42no—
133C2×C4⋊C4×C89—42no—
134C2×C4⋊C4×C89—42no—
135C2×C4⋊C4×C89C2314yes—
136C2×C4⋊C4×C89C2314yes—
137C2×C4⋊C4×C89C2314yes—
138C2×C4⋊C4×C89C2314yes—
139#95×C89C2314yes—
140#95×C89C2314yes—
141#95×C89C2314yes—
142C23×D89—22no—
143C23×D89—22no—
144C23×D89—22no—
145C23×D89—22no—
146C23×D89—22no—
147C23×D89—22no—
148C23×D89C2×Q814yes—
149C23×D89C2412yes—
150C2×Dic178—44no—
151C2×Dic178—44no—
152C2×Dic178—44no—
153C2×Dic178—416no—
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—22no—
168C22×Dic89—22no—
169C22×Dic89—22no—
170C22×Dic89—22no—
171C22×Dic89—22no—
172C22×Dic89—22no—
173C22×Dic89—22no—
174C22×Dic89C2×Q814yes—
175C22×Dic89C2412yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C22×Dic89C2412yes—
179C22×Dic89C2412yes—
180C22×Dic89C2412yes—
181C22×Dic89C2412yes—
182C2×C4×D89—416no—
183C2×C4×D89—44no—
184C2×C4×D89—44no—
185C2×C4×D89C2×Q8116yescomplemented
186C4⋊Dic89—44no—
187C4⋊Dic89—44no—
188C4⋊Dic89—44no—
189#13083553—44no—
190#13083553—44no—
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#13083551—44no—
200#13083551—44no—
201C24×C89C2411yescharacteristic
202C22×C4×C89—22no—
203C22×C4×C89—22no—
204C22×C4×C89—22no—
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×C89C2×Q814yes—
223C22×C4×C89C2412yes—
224C22×C4×C89C2412yes—
225C22×C4×C89C2412yes—
226C22×C4×C89C2412yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C22×C4×C89C2412yes—
230C4⋊C4×C89—44no—
231C4⋊C4×C89—44no—
232C4⋊C4×C89—44no—
233C4⋊C4×C89—44no—
234C23×C89C22×Q812yes—
235C23×C89H(5,𝔽2)12yes—
236C23×C89H(5,𝔽2)12yes—
237C23×C89H(5,𝔽2)12yes—
238C23×C89H(5,𝔽2)12yes—
239C23×C892−1+412yes—
240C23×C892−1+412yes—
241C23×C89C2511yescharacteristic
242C22×D89—28no—
243C22×D89—28no—
244C22×D89—28no—
245C22×D89—22no—
246C22×D89—22no—
247C22×D89—22no—
248C22×D89—22no—
249C22×D89—22no—
250C22×D89—22no—
251C22×D89—44no—
252C22×D89—44no—
253C22×D89—44no—
254C22×D89—44no—
255C22×D89C22×Q814yes—
256C2×C4×C89—28no—
257C2×C4×C89—22no—
258C2×C4×C89—22no—
259C2×C4×C89—22no—
260C2×C4×C89—22no—
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—44no—
278C2×C4×C89—44no—
279C2×C4×C89—44no—
280C2×C4×C89—44no—
281C2×C4×C89—44no—
282C2×C4×C89—44no—
283C2×C4×C89C22×Q814yes—
284C2×Dic89—28no—
285C2×Dic89—22no—
286C2×Dic89—22no—
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—44no—
306C2×Dic89—44no—
307C2×Dic89—44no—
308C2×Dic89—44no—
309C2×Dic89—44no—
310C2×Dic89—44no—
311C2×Dic89C22×Q814yes—
312C4×D89—416no—
313Dic178—416no—
314C22×C89#54314yes—
315C22×C89#54414yes—
316C22×C89#54414yes—
317C22×C89#56014yes—
318C22×C89#56214yes—
319C22×C89#56214yes—
320C22×C89#56314yes—
321C22×C89C23×Q811yescharacteristic
322C22×C89C2×H(5,𝔽2)11yescharacteristic
323C22×C89C2×H(5,𝔽2)11yescharacteristic
324C22×C89C2×H(5,𝔽2)11yescharacteristic
325C22×C89C2×H(5,𝔽2)11yescharacteristic
326C22×C89C2×2−1+411yescharacteristic
327C22×C89C2×2−1+411yescharacteristic
328C2×D89—24no—
329C2×D89—24no—
330C2×D89—24no—
331C2×D89—416no—
332C2×D89—42no—
333C2×D89—42no—
334C2×D89—42no—
335C2×D89—42no—
336C4×C89—24no—
337C4×C89—42no—
338C4×C89—42no—
339C4×C89—42no—
340C4×C89—42no—
341C4×C89—42no—
342C4×C89—42no—
343Dic89—24no—
344Dic89—42no—
345Dic89—42no—
346Dic89—42no—
347Dic89—42no—
348Dic89—42no—
349Dic89—42no—
350C2×#2841—891nomaximal, Sylow
351C2×C89#284118yescomplemented
352C2×C89C2×#54311yescharacteristic
353C2×C89C2×#54411yescharacteristic
354C2×C89C2×#54411yescharacteristic
355C2×C89C2×#56011yescharacteristic
356C2×C89C2×#56211yescharacteristic
357C2×C89C2×#56211yescharacteristic
358C2×C89C2×#56311yescharacteristic
359D89—44no—
360#2841—8916no—
361C2×#400—891no—
362C2×#400—891no—
363C2×#399—891no—
364C2×#398—891no—
365C2×#398—891no—
366C2×#398—891no—
367C2×#398D8911yescharacteristic, complemented
368C2×#396—891no—
369C2×#396—891no—
370C2×#395—891no—
371C2×#395—891no—
372C2×#393—891no—
373C2×#381—891no—
374C2×#380—891no—
375C2×#380—891no—
376C89C2×#284111yescharacteristic, complemented, Sylow
377C23×Q8—891no—
378C24×C4—891no—
379C22×C4⋊C4—891no—
380C22×C4⋊C4—891no—
381C22×C4⋊C4—891no—
382C22×C4⋊C4—891no—
383C22×C4⋊C4—891no—
384C22×C4⋊C4—891no—
385C22×C4⋊C4—891no—
386C22×C4⋊C4—891no—
387C22×C4⋊C4—891no—
388C22×C4⋊C4C2×D8911yescharacteristic
389C22×C4⋊C4C2×D8911yescharacteristic
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—
398#400—898no—
399#400—898no—
400#399—898no—
401#398—898no—
402#398—898no—
403#398—898no—
404#398C2×D8918yescomplemented
405#396—898no—
406#396—898no—
407#395—898no—
408#395—898no—
409#393—898no—
410#381—898no—
411#380—898no—
412#380—898no—
413C2×#95—891no—
414C2×#95—891no—
415C2×#95—891no—
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×#95C2×D8911yescharacteristic
425C2×#95C2×D8911yescharacteristic
426C2×#95C2×D8911yescharacteristic
427C25—891no—
428C22×Q8—894no—
429C22×Q8—3562no—
430C22×Q8—3562no—
431C22×Q8—3562no—
432C23×C4—891no—
433C23×C4—898no—
434C23×C4—894no—
435C23×C4—891no—
436C23×C4—891no—
437C23×C4—891no—
438C23×C4—891no—
439C23×C4—891no—
440C23×C4—891no—
441C23×C4—3562no—
442C23×C4—3562no—
443C23×C4C22×D8911yescharacteristic
444C23×C4C22×D8911yescharacteristic
445C23×C4C22×D8911yescharacteristic
446C23×C4C22×D8911yescharacteristic
447C23×C4C22×D8911yescharacteristic
448C23×C4C22×D8911yescharacteristic
449C23×C4C22×D8911yescharacteristic
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—894no—
455C2×C4⋊C4—894no—
456C2×C4⋊C4—894no—
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—3562no—
464C2×C4⋊C4—3562no—
465C2×C4⋊C4—3562no—
466C2×C4⋊C4—3562no—
467C2×C4⋊C4—3562no—
468C2×C4⋊C4—3562no—
469C2×C4⋊C4—3562no—
470C2×C4⋊C4—3562no—
471C2×C4⋊C4—3562no—
472C2×C4⋊C4C22×D8914yes—
473C2×C4⋊C4C22×D8914yes—
474C2×C4⋊C4C22×D8914yes—
475C2×C4⋊C4C22×D8914yes—
476C2×C22⋊C4—894no—
477C2×C22⋊C4—894no—
478C2×C22⋊C4—894no—
479C2×C22⋊C4—894no—
480C2×C22⋊C4—894no—
481C2×C22⋊C4—894no—
482C2×C22⋊C4—3562no—
483C2×C22⋊C4—3562no—
484C2×C22⋊C4—3562no—
485C2×C22⋊C4—3562no—
486C2×C22⋊C4—3562no—
487C2×C22⋊C4—3562no—
488#95—894no—
489#95—894no—
490#95—894no—
491#95—894no—
492#95—894no—
493#95—894no—
494#95—894no—
495#95—894no—
496#95—894no—
497#95—894no—
498#95—894no—
499#95C22×D8914yes—
500#95C22×D8914yes—
501#95C22×D8914yes—
502C24—894no—
503C24—892no—
504C24—1782no—
505C24—1782no—
506C24—1782no—
507C24—1782no—
508C24—1782no—
509C24—1782no—
510C24C23×D8911yescharacteristic
511C2×Q8—3564no—
512C2×Q8—3564no—
513C2×Q8—3564no—
514C2×Q8—35616no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
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—894no—
536C22×C4—892no—
537C22×C4—8916no—
538C22×C4—892no—
539C22×C4—892no—
540C22×C4—892no—
541C22×C4—892no—
542C22×C4—892no—
543C22×C4—892no—
544C22×C4—3564no—
545C22×C4—3564no—
546C22×C4—35616no—
547C22×C4—1782no—
548C22×C4—1782no—
549C22×C4—1782no—
550C22×C4—1782no—
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×C4Q8×D8914yes—
568C22×C4C23×D8912yes—
569C22×C4C23×D8912yes—
570C22×C4C23×D8912yes—
571C22×C4C23×D8912yes—
572C22×C4C23×D8912yes—
573C22×C4C23×D8912yes—
574C22×C4C23×D8912yes—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—3564no—
580C4⋊C4—3564no—
581C4⋊C4—3564no—
582C4⋊C4—3564no—
583C4⋊C4—3564no—
584C4⋊C4—3564no—
585C4⋊C4—3564no—
586C4⋊C4—3564no—
587C4⋊C4—3564no—
588C22⋊C4—3564no—
589C22⋊C4—3564no—
590C22⋊C4—3564no—
591C22⋊C4—3564no—
592C22⋊C4—3564no—
593C22⋊C4—3564no—
594C23—894no—
595C23—3564no—
596C23—3564no—
597C23—3564no—
598C23—3564no—
599C23—1782no—
600C23—1782no—
601C23—1782no—
602C23—1782no—
603C23—1782no—
604C23—1782no—
605C23—1788no—
606C23—1788no—
607C23—1788no—
608C23C2×Q8×D8912yes—
609C23#1566805712yes—
610C23#1566805712yes—
611C23#1566805812yes—
612C23#1566805812yes—
613C23#1566805912yes—
614C23#1566806012yes—
615C23C24×D8911yescharacteristic
616Q8—35616no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
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—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—894no—
645C2×C4—35616no—
646C2×C4—3564no—
647C2×C4—3564no—
648C2×C4—3564no—
649C2×C4—3564no—
650C2×C4—3564no—
651C2×C4—3564no—
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—1782no—
671C2×C4—1782no—
672C2×C4—1788no—
673C2×C4C2×Q8×D8914yes—
674C22—3562no—
675C22—3562no—
676C22—3562no—
677C22—3562no—
678C22—35616no—
679C22—1784no—
680C22—1784no—
681C22—1784no—
682C22#1915222314yes—
683C22#1915222514yes—
684C22#1915222814yes—
685C22#1915233814yes—
686C22#1915234314yes—
687C22#1915234414yes—
688C22#1915235214yes—
689C22C22×Q8×D8911yescharacteristic
690C22C2×#1566805711yescharacteristic
691C22C2×#1566805711yescharacteristic
692C22C2×#1566805811yescharacteristic
693C22C2×#1566805811yescharacteristic
694C22C2×#1566805911yescharacteristic
695C22C2×#1566806011yescharacteristic
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3562no—
704C4—3562no—
705C4—3562no—
706C4—3562no—
707C4—3562no—
708C4—3562no—
709C4—1784no—
710C2—3564no—
711C2#2602851018yesdirect product factor
712C2C2×#1915222311yescharacteristic
713C2C2×#1915222511yescharacteristic
714C2C2×#1915222811yescharacteristic
715C2C2×#1915233811yescharacteristic
716C2C2×#1915234311yescharacteristic
717C2C2×#1915234411yescharacteristic
718C2C2×#1915235211yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#398×C89C2
socleC24×C89C24
prime radicalC24×D89C23
hypercenterC2×#398D89
hypocenterC89C2×#2841
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #26028510C2direct (N × H)
2. C2×#19151537C2semidirect
3. C2×#19151536C2semidirect
5. C2×#19151532C2semidirect
6. C2×#19151532C2semidirect
7. C2×#19151528C2semidirect
10. C2×#19151519C2semidirect
11. C2×#19151518C2semidirect
16. C2×#398×C89C2semidirect
34. #19151537C22semidirect
35. #19151536C22semidirect
37. #19151532C22semidirect
38. #19151532C22semidirect
39. #19151528C22semidirect
42. #19151519C22semidirect
43. #19151518C22semidirect
63. #398×C89C22semidirect
81. C22×C4×D89Q8semidirect
185. C2×C4×D89C2×Q8semidirect
351. C2×C89#2841semidirect
367. C2×#398D89semidirect
376. C89C2×#2841semidirect
404. #398C2×D89semidirect
711. C2#26028510direct (N × H)

Maximal subgroups

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

subgroupindex
#260285102
C2×#191515372
C2×#191515362
C2×#191515332
C2×#191515322
C2×#191515282
C2×#191515202
C2×#191515192
C2×#191515182
C2×#191515112
C2×#191514602
C2×#191514572
C2×#191514552
C2×#398×C892
C2×#284189