Finite Group Databasebeta

← C2×#26024920 #36723508

Subgroups — C2×#26024920 #36723508

Order 22784.

2466 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
1C22×#15668005C211yesmaximal, characteristic
2C22×#15668002C211yesmaximal, characteristic, complemented
3#26024920C2116yesmaximal, direct product factor
4C2×#19151530C211yesmaximal, characteristic, complemented
5C2×#19151529C211yesmaximal, characteristic, complemented
6C2×#19151521C211yesmaximal, characteristic
7C2×#19151494C211yesmaximal, characteristic, complemented
8C2×#19151492C211yesmaximal, characteristic
9C2×#19151491C211yesmaximal, characteristic
10C2×#19151491C211yesmaximal, characteristic
11C2×#19151486C211yesmaximal, characteristic
12C2×#19151484C211yesmaximal, characteristic, complemented
13C2×#19151463C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic89C211yesmaximal, characteristic, complemented
15C2×#19151449C211yesmaximal, characteristic, complemented
16C2×#399×C89C211yesmaximal, characteristic
17C2×#15668005—28no—
18C2×#15668005C2218yes—
19C2×#15668002—28no—
20C2×#15668002C2218yescomplemented
21C22×C4⋊Dic89C2211yescharacteristic
22C22×C4⋊Dic89C2211yescharacteristic
23C22×C4⋊Dic89C2211yescharacteristic
24C22×C4⋊Dic89C2211yescharacteristic
25C22×#13083553C2211yescharacteristic
26C22×#13083553C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083553C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×C22⋊Dic89C2211yescharacteristic
32C22×C22⋊Dic89C2211yescharacteristic
33C22×C22⋊Dic89C2211yescharacteristic
34C22×C22⋊Dic89C2211yescharacteristic
35C22×C4×Dic89C2211yescharacteristic
36C22×C4×Dic89C2211yescharacteristic
37C22×C4×Dic89C2211yescharacteristic
38C22×C4×Dic89C2211yescharacteristic
39C22×C4×Dic89C2211yescharacteristic
40#19151530C2218yescomplemented
41#19151529C2218yescomplemented
42#19151521C2218yes—
43#19151494C2218yescomplemented
44#19151492C2218yes—
45#19151491C2218yes—
46#19151491C2218yes—
47#19151486C2218yes—
48#19151484C2218yescomplemented
49#19151463C2218yescomplemented
50C4⋊C4×Dic89C2218yescomplemented
51#19151449C2218yescomplemented
52C2×#15667919C2211yescharacteristic
53C2×#15667919C2211yescharacteristic
54C2×#15667919C2211yescharacteristic
55C2×#15667919C2211yescharacteristic
56C2×#15667919C2211yescharacteristic
57C2×#15667919C2211yescharacteristic
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C22×C4⋊C4×C89C2211yescharacteristic
62C22×C4⋊C4×C89C2211yescharacteristic
63C22×C4⋊C4×C89C2211yescharacteristic
64C22×C22⋊C4×C89C2211yescharacteristic
65C22×C22⋊C4×C89C2211yescharacteristic
66C22×C22⋊C4×C89C2211yescharacteristic
67#399×C89C2218yes—
68C2×#95×C89C2211yescharacteristic
69C23×Dic89C2311yescharacteristic
70C23×Dic89C2311yescharacteristic
71C23×Dic89C2311yescharacteristic
72C23×Dic89C2311yescharacteristic
73C23×Dic89C2311yescharacteristic
74C23×Dic89C2311yescharacteristic
75C23×Dic89C2311yescharacteristic
76C23×Dic89C2311yescharacteristic
77#15668005—232no—
78#15668002—232no—
79C2×C4⋊Dic89—24no—
80C2×C4⋊Dic89—24no—
81C2×C4⋊Dic89—24no—
82C2×C4⋊Dic89—24no—
83C2×C4⋊Dic89C2314yes—
84C2×C4⋊Dic89C2314yes—
85C2×C4⋊Dic89C2314yes—
86C2×C4⋊Dic89C2314yes—
87C2×#13083553—24no—
88C2×#13083553—24no—
89C2×#13083553—24no—
90C2×#13083553—24no—
91C2×#13083553—24no—
92C2×#13083553D418yes—
93C2×#13083553C2314yes—
94C2×#13083553C2314yes—
95C2×#13083553C2314yes—
96C2×#13083553C2314yes—
97C2×#13083553C2314yes—
98C2×#13083553C2314yes—
99C2×C22⋊Dic89—24no—
100C2×C22⋊Dic89—24no—
101C2×C22⋊Dic89—24no—
102C2×C22⋊Dic89—24no—
103C2×C22⋊Dic89C2314yes—
104C2×C22⋊Dic89C2314yes—
105C2×C22⋊Dic89C2314yes—
106C2×C22⋊Dic89C2314yes—
107C2×C4×Dic89—24no—
108C2×C4×Dic89—24no—
109C2×C4×Dic89—24no—
110C2×C4×Dic89—24no—
111C2×C4×Dic89—24no—
112C2×C4×Dic89C2314yes—
113C2×C4×Dic89C2314yes—
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—
126C25×C89C2311yescharacteristic
127C23×C4×C89C2311yescharacteristic
128C23×C4×C89C2311yescharacteristic
129C23×C4×C89C2311yescharacteristic
130C23×C4×C89C2311yescharacteristic
131C23×C4×C89C2311yescharacteristic
132C23×C4×C89C2311yescharacteristic
133C2×C4⋊C4×C89—24no—
134C2×C4⋊C4×C89—24no—
135C2×C4⋊C4×C89—24no—
136C2×C4⋊C4×C89C2314yes—
137C2×C4⋊C4×C89C2314yes—
138C2×C4⋊C4×C89C2314yes—
139C2×C22⋊C4×C89—24no—
140C2×C22⋊C4×C89—24no—
141C2×C22⋊C4×C89—24no—
142C2×C22⋊C4×C89C2314yes—
143C2×C22⋊C4×C89C2314yes—
144C2×C22⋊C4×C89C2314yes—
145#95×C89C2314yes—
146C22×Dic89—22no—
147C22×Dic89—22no—
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×Dic89C2×D414yes—
167C22×Dic89C2×D414yes—
168C22×Dic89#4114yes—
169C22×Dic89#4114yes—
170C22×Dic89C2412yes—
171C22×Dic89C2412yes—
172C22×Dic89C2412yes—
173C22×Dic89C2412yes—
174C22×Dic89C2412yes—
175C22×Dic89C2412yes—
176C22×Dic89C2412yes—
177C22×Dic89C2412yes—
178C4⋊Dic89—28no—
179C4⋊Dic89—28no—
180C4⋊Dic89—28no—
181C4⋊Dic89—28no—
182#13083553—28no—
183#13083553—28no—
184#13083553—28no—
185#13083553—28no—
186#13083553—28no—
187#13083553C2×D4116yes—
188C22⋊Dic89—28no—
189C22⋊Dic89—28no—
190C22⋊Dic89—28no—
191C22⋊Dic89—28no—
192C4×Dic89—28no—
193C4×Dic89—28no—
194C4×Dic89—28no—
195C4×Dic89—28no—
196C4×Dic89—28no—
197C24×C89—22no—
198C24×C89—22no—
199C24×C89—22no—
200C24×C89—22no—
201C24×C89—22no—
202C24×C89—22no—
203C24×C89—22no—
204C24×C89C2412yes—
205C24×C89C2411yescharacteristic
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×C89C2×D414yes—
222C22×C4×C89#4114yes—
223C22×C4×C89#4114yes—
224C22×C4×C89C2412yes—
225C22×C4×C89C2412yes—
226C22×C4×C89C2412yes—
227C22×C4×C89C2412yes—
228C22×C4×C89C2412yes—
229C22×C4×C89C2412yes—
230C4⋊C4×C89—28no—
231C4⋊C4×C89—28no—
232C4⋊C4×C89—28no—
233C22⋊C4×C89—28no—
234C22⋊C4×C89—28no—
235C22⋊C4×C89—28no—
236C23×C89—22no—
237C23×C89—22no—
238C23×C89—22no—
239C23×C89—22no—
240C23×C89—22no—
241C23×C89—22no—
242C23×C89—22no—
243C23×C89—44no—
244C23×C89—44no—
245C23×C89—44no—
246C23×C89—44no—
247C23×C89—44no—
248C23×C89—44no—
249C23×C89—44no—
250C23×C89C22×D412yes—
251C23×C89C2×#4112yes—
252C23×C89C2×#4112yes—
253C23×C89C2×#4112yes—
254C23×C89C2×#4112yes—
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×C89C22×D414yes—
280C2×C4×C89C2×#4114yes—
281C2×C4×C89C2×#4114yes—
282C2×Dic89—28no—
283C2×Dic89—28no—
284C2×Dic89—28no—
285C2×Dic89—28no—
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—22no—
306C2×Dic89—44no—
307C2×Dic89—44no—
308C2×Dic89—44no—
309C2×Dic89—44no—
310C2×Dic89C22×D414yes—
311C2×Dic89C22×D414yes—
312C2×Dic89C2×#4114yes—
313C2×Dic89C2×#4114yes—
314C22×C89—42no—
315C22×C89—42no—
316C22×C89—42no—
317C22×C89—42no—
318C22×C89—42no—
319C22×C89—42no—
320C22×C89—42no—
321C22×C89—88no—
322C22×C89#52914yes—
323C22×C89#53214yes—
324C22×C89#54114yes—
325C22×C89#54714yes—
326C22×C89#54814yes—
327C22×C89#55214yes—
328C22×C89#55214yes—
329C22×C89C23×D411yescharacteristic
330C22×C89C22×#4111yescharacteristic
331C22×C89C22×#4111yescharacteristic
332C22×C89C22×#4111yescharacteristic
333C22×C89C22×#4111yescharacteristic
334C22×C89C2×2−1+411yescharacteristic
335C22×C89C2×2−1+411yescharacteristic
336C4×C89—24no—
337C4×C89—24no—
338C4×C89—24no—
339C4×C89—42no—
340C4×C89—42no—
341C4×C89—42no—
342Dic89—24no—
343Dic89—24no—
344Dic89—24no—
345Dic89—24no—
346Dic89—42no—
347Dic89—42no—
348Dic89—42no—
349Dic89—42no—
350C2×#2519—891nomaximal, Sylow
351C2×C89—82no—
352C2×C89#251918yescomplemented
353C2×C89C2×#52911yescharacteristic
354C2×C89C2×#53211yescharacteristic
355C2×C89C2×#54111yescharacteristic
356C2×C89C2×#54711yescharacteristic
357C2×C89C2×#54811yescharacteristic
358C2×C89C2×#55211yescharacteristic
359C2×C89C2×#55211yescharacteristic
360C22×#126—891no—
361C22×#125—891no—
362#2519—8916no—
363C2×#399D8911yescharacteristic
364C2×#398—891no—
365C2×#398—891no—
366C2×#396—891no—
367C2×#389—891no—
368C2×#388—891no—
369C2×#388—891no—
370C2×#388—891no—
371C2×#388—891no—
372C2×#387—891no—
373C2×#382—891no—
374C2×C4×C4⋊C4—891no—
375C2×C4×C4⋊C4—891no—
376C89C2×#251911yescharacteristic, complemented, Sylow
377C2×#126—898no—
378C2×#126—1788no—
379C2×#125—898no—
380C2×#125—1788no—
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⋊C4—891no—
389C22×C4⋊C4—891no—
390C22×C4⋊C4—891no—
391C22×C4⋊C4C2×D8911yescharacteristic
392C22×C4⋊C4C2×D8911yescharacteristic
393C22×C4⋊C4C2×D8911yescharacteristic
394C22×C22⋊C4—891no—
395C22×C22⋊C4—891no—
396C22×C22⋊C4—891no—
397C22×C22⋊C4—891no—
398C22×C22⋊C4C2×D8911yescharacteristic
399C22×C22⋊C4C2×D8911yescharacteristic
400C22×C22⋊C4C2×D8911yescharacteristic
401C22×C42—891no—
402C22×C42—891no—
403C22×C42—891no—
404C22×C42—891no—
405C22×C42—891no—
406#399C2×D8918yes—
407#398—898no—
408#398—898no—
409#396—898no—
410#389—898no—
411#388—898no—
412#388—898no—
413#388—898no—
414#388—898no—
415#387—898no—
416#382—898no—
417C4×C4⋊C4—898no—
418C4×C4⋊C4—898no—
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
429C25C22×D8911yescharacteristic
430C23×C4—891no—
431C23×C4—891no—
432C23×C4—891no—
433C23×C4—891no—
434C23×C4—891no—
435C23×C4—891no—
436C23×C4—891no—
437C23×C4—891no—
438C23×C4C22×D8911yescharacteristic
439C23×C4C22×D8911yescharacteristic
440C23×C4C22×D8911yescharacteristic
441C23×C4C22×D8911yescharacteristic
442C23×C4C22×D8911yescharacteristic
443C23×C4C22×D8911yescharacteristic
444#126—17832no—
445#125—17832no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—898no—
450C2×C4⋊C4—894no—
451C2×C4⋊C4—894no—
452C2×C4⋊C4—894no—
453C2×C4⋊C4—894no—
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—1784no—
461C2×C4⋊C4—1784no—
462C2×C4⋊C4—1784no—
463C2×C4⋊C4—1784no—
464C2×C4⋊C4—1784no—
465C2×C4⋊C4—1784no—
466C2×C4⋊C4—1784no—
467C2×C4⋊C4—1784no—
468C2×C4⋊C4—1784no—
469C2×C4⋊C4C22×D8914yes—
470C2×C4⋊C4C22×D8914yes—
471C2×C4⋊C4C22×D8914yes—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—894no—
476C2×C22⋊C4—894no—
477C2×C22⋊C4—894no—
478C2×C22⋊C4—894no—
479C2×C22⋊C4—1784no—
480C2×C22⋊C4—1784no—
481C2×C22⋊C4—1784no—
482C2×C22⋊C4—1784no—
483C2×C22⋊C4C22×D8914yes—
484C2×C22⋊C4C22×D8914yes—
485C2×C22⋊C4C22×D8914yes—
486C2×C42—894no—
487C2×C42—894no—
488C2×C42—894no—
489C2×C42—894no—
490C2×C42—894no—
491C2×C42—1784no—
492C2×C42—1784no—
493C2×C42—1784no—
494C2×C42—1784no—
495C2×C42—1784no—
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#95—894no—
505#95C22×D8914yes—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24C23×D8912yes—
514C24C23×D8911yescharacteristic
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—894no—
531C22×C4—894no—
532C22×C4—894no—
533C22×C4—894no—
534C22×C4—892no—
535C22×C4—892no—
536C22×C4—892no—
537C22×C4—892no—
538C22×C4—892no—
539C22×C4—892no—
540C22×C4—892no—
541C22×C4—892no—
542C22×C4—1782no—
543C22×C4—1782no—
544C22×C4—1782no—
545C22×C4—1782no—
546C22×C4—1782no—
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×C4D4×D8914yes—
563C22×C4#1308357314yes—
564C22×C4#1308357314yes—
565C22×C4C23×D8912yes—
566C22×C4C23×D8912yes—
567C22×C4C23×D8912yes—
568C22×C4C23×D8912yes—
569C22×C4C23×D8912yes—
570C22×C4C23×D8912yes—
571C4⋊C4—28no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—8916no—
575C4⋊C4—1788no—
576C4⋊C4—1788no—
577C4⋊C4—1788no—
578C4⋊C4—1788no—
579C4⋊C4—1788no—
580C4⋊C4—1788no—
581C4⋊C4—1788no—
582C4⋊C4—1788no—
583C4⋊C4—1788no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—1788no—
588C22⋊C4—1788no—
589C22⋊C4—1788no—
590C22⋊C4—1788no—
591C42—1788no—
592C42—1788no—
593C42—1788no—
594C42—1788no—
595C42—1788no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23C2×D4×D8912yes—
611C23#41×D8912yes—
612C23#41×D8912yes—
613C23C2×#1308357312yes—
614C23C2×#1308357312yes—
615C23#1566805912yes—
616C23#1566806012yes—
617C23C24×D8911yescharacteristic
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
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—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—894no—
640C2×C4—894no—
641C2×C4—894no—
642C2×C4—894no—
643C2×C4—3564no—
644C2×C4—3564no—
645C2×C4—3564no—
646C2×C4—3564no—
647C2×C4—1782no—
648C2×C4—1782no—
649C2×C4—1782no—
650C2×C4—1782no—
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—1788no—
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—1788no—
669C2×C4—1788no—
670C2×C4—1788no—
671C2×C4C2×D4×D8914yes—
672C2×C4C2×#1308357314yes—
673C2×C4C2×#1308357314yes—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—88no—
682C22#1915212514yes—
683C22#1915214614yes—
684C22#1915220814yes—
685C22#1915224614yes—
686C22#1915225814yes—
687C22#1915228214yes—
688C22#1915228514yes—
689C22C22×D4×D8911yescharacteristic
690C22C2×#41×D8911yescharacteristic
691C22C2×#41×D8911yescharacteristic
692C22C22×#1308357311yescharacteristic
693C22C22×#1308357311yescharacteristic
694C22C2×#1566805911yescharacteristic
695C22C2×#1566806011yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—3562no—
703C4—3562no—
704C4—3562no—
705C4—3562no—
706C4—1784no—
707C4—1784no—
708C4—1784no—
709C4—1784no—
710C2—82no—
711C2#2602492018yesdirect product factor
712C2C2×#1915212511yescharacteristic
713C2C2×#1915214611yescharacteristic
714C2C2×#1915220811yescharacteristic
715C2C2×#1915224611yescharacteristic
716C2C2×#1915225811yescharacteristic
717C2C2×#1915228211yescharacteristic
718C2C2×#1915228511yescharacteristic
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#399×C89C2
socleC24×C89C24
prime radicalC25×C89C23
hypercenterC2×#399D89
hypocenterC89C2×#2519
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. C22×#15668002C2semidirect
3. #26024920C2direct (N × H)
4. C2×#19151530C2semidirect
5. C2×#19151529C2semidirect
7. C2×#19151494C2semidirect
12. C2×#19151484C2semidirect
13. C2×#19151463C2semidirect
14. C2×C4⋊C4×Dic89C2semidirect
15. C2×#19151449C2semidirect
20. C2×#15668002C22semidirect
40. #19151530C22semidirect
41. #19151529C22semidirect
43. #19151494C22semidirect
48. #19151484C22semidirect
49. #19151463C22semidirect
50. C4⋊C4×Dic89C22semidirect
51. #19151449C22semidirect
352. C2×C89#2519semidirect
376. C89C2×#2519semidirect
711. C2#26024920direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156680052
C22×#156680022
#260249202
C2×#191515302
C2×#191515292
C2×#191515212
C2×#191514942
C2×#191514922
C2×#191514912
C2×#191514862
C2×#191514842
C2×#191514632
C2×C4⋊C4×Dic892
C2×#191514492
C2×#399×C892
C2×#251989