Finite Group Databasebeta

← C2×#26023198 #36713774

Subgroups — C2×#26023198 #36713774

Order 22784.

3678 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667972C211yesmaximal, characteristic
2C22×#15667969C211yesmaximal, characteristic, complemented
3C22×#15667968C211yesmaximal, characteristic, complemented
4#26023198C2116yesmaximal, direct product factor
5C2×#19151498C211yesmaximal, characteristic
6C2×#19151498C211yesmaximal, characteristic
7C2×#19151491C211yesmaximal, characteristic, complemented
8C2×#19151490C211yesmaximal, characteristic, complemented
9C2×#19151488C211yesmaximal, characteristic, complemented
10C2×#19151467C211yesmaximal, characteristic, complemented
11C2×#19151457C211yesmaximal, characteristic, complemented
12C2×#19151456C211yesmaximal, characteristic, complemented
13C2×C4×#13083553C211yesmaximal, characteristic, complemented
14C2×#19151449C211yesmaximal, characteristic, complemented
15C2×#19151449C211yesmaximal, characteristic, complemented
16C2×#388×C89C211yesmaximal, characteristic, complemented
17C23×C22⋊D89C2211yescharacteristic
18C24×Dic89C2211yescharacteristic
19C23×C4×D89C2211yescharacteristic
20C2×#15667972C4116yescomplemented
21C2×#15667972C2218yes—
22C2×#15667969—28no—
23C2×#15667969C2218yescomplemented
24C2×#15667968—28no—
25C2×#15667968C2218yescomplemented
26C22×C4⋊Dic89C2211yescharacteristic
27C22×#13083553C2211yescharacteristic
28C22×#13083553C2211yescharacteristic
29C22×#13083553C2211yescharacteristic
30C22×#13083553C2211yescharacteristic
31C22×#13083553C2211yescharacteristic
32C22×#13083553C2211yescharacteristic
33C22×#13083553C2211yescharacteristic
34C22×C22⋊Dic89C2211yescharacteristic
35C22×C22⋊Dic89C2211yescharacteristic
36C22×#13083551C2211yescharacteristic
37C22×#13083551C2211yescharacteristic
38C22×#13083551C2211yescharacteristic
39C22×#13083551C2211yescharacteristic
40C22×#13083551C2211yescharacteristic
41C22×C4×Dic89C2211yescharacteristic
42C22×C4×Dic89C2211yescharacteristic
43C22×C4×Dic89C2211yescharacteristic
44C22×C4×Dic89C2211yescharacteristic
45C22×C4×Dic89C2211yescharacteristic
46C22×C4×Dic89C2211yescharacteristic
47#19151498C2218yes—
48#19151498C2218yes—
49#19151491C2218yescomplemented
50#19151490C2218yescomplemented
51#19151488C2218yescomplemented
52#19151467C2218yescomplemented
53#19151457C2218yescomplemented
54#19151456C2218yescomplemented
55C4×#13083553C2218yescomplemented
56#19151449C2218yescomplemented
57#19151449C2218yescomplemented
58C2×#15667919C2211yescharacteristic
59C2×#15667919C2211yescharacteristic
60C2×#15667919C2211yescharacteristic
61C2×#15667919C2211yescharacteristic
62C22×C4⋊C4×C89C2211yescharacteristic
63C22×C22⋊C4×C89C2211yescharacteristic
64C22×C22⋊C4×C89C2211yescharacteristic
65C22×C22⋊C4×C89C2211yescharacteristic
66C22×C42×C89C2211yescharacteristic
67#388×C89C2218yescomplemented
68C2×#95×C89C2211yescharacteristic
69C2×#95×C89C2211yescharacteristic
70C24×D89C2311yescharacteristic
71C22×C22⋊D89—24no—
72C22×C22⋊D89—24no—
73C22×C22⋊D89C2×C418yes—
74C22×C22⋊D89C2314yes—
75C23×Dic89—24no—
76C23×Dic89—24no—
77C23×Dic89C2×C418yes—
78C23×Dic89C2311yescharacteristic
79C23×Dic89C2311yescharacteristic
80C23×Dic89C2311yescharacteristic
81C23×Dic89C2311yescharacteristic
82C23×Dic89C2314yes—
83C23×Dic89C2311yescharacteristic
84C23×Dic89C2311yescharacteristic
85C23×Dic89C2311yescharacteristic
86C22×C4×D89—24no—
87C22×C4×D89—24no—
88C22×C4×D89C2×C418yes—
89C22×C4×D89C2314yes—
90#15667972C2×C4164yescomplemented
91#15667969—232no—
92#15667968—232no—
93C2×C4⋊Dic89—42no—
94C2×C4⋊Dic89C2314yes—
95C2×#13083553—24no—
96C2×#13083553—24no—
97C2×#13083553—24no—
98C2×#13083553—24no—
99C2×#13083553—24no—
100C2×#13083553C2×C418yes—
101C2×#13083553D418yescomplemented
102C2×#13083553C2314yes—
103C2×#13083553C2314yes—
104C2×#13083553C2314yes—
105C2×#13083553C2314yes—
106C2×#13083553C2314yes—
107C2×#13083553C2314yes—
108C2×#13083553C2314yes—
109C2×C22⋊Dic89—24no—
110C2×C22⋊Dic89—42no—
111C2×C22⋊Dic89C2314yes—
112C2×C22⋊Dic89C2314yes—
113C2×#13083551—24no—
114C2×#13083551—24no—
115C2×#13083551—42no—
116C2×#13083551—42no—
117C2×#13083551C2×C418yes—
118C2×#13083551C2314yes—
119C2×#13083551C2314yes—
120C2×#13083551C2314yes—
121C2×#13083551C2314yes—
122C2×#13083551C2314yes—
123C2×C4×Dic89—24no—
124C2×C4×Dic89—24no—
125C2×C4×Dic89—24no—
126C2×C4×Dic89—24no—
127C2×C4×Dic89—24no—
128C2×C4×Dic89C2×C418yes—
129C2×C4×Dic89C2314yes—
130C2×C4×Dic89C2314yes—
131C2×C4×Dic89C2314yes—
132C2×C4×Dic89C2314yes—
133C2×C4×Dic89C2314yes—
134C2×C4×Dic89C2314yes—
135#15667919C2314yes—
136#15667919C2314yes—
137#15667919C2314yes—
138#15667919C2314yes—
139C25×C89C2311yescharacteristic
140C23×C4×C89C2311yescharacteristic
141C23×C4×C89C2311yescharacteristic
142C23×C4×C89C2311yescharacteristic
143C23×C4×C89C2311yescharacteristic
144C23×C4×C89C2311yescharacteristic
145C23×C4×C89C2311yescharacteristic
146C2×C4⋊C4×C89—42no—
147C2×C4⋊C4×C89C2314yes—
148C2×C22⋊C4×C89—24no—
149C2×C22⋊C4×C89—42no—
150C2×C22⋊C4×C89C2×C418yes—
151C2×C22⋊C4×C89C2314yes—
152C2×C22⋊C4×C89C2314yes—
153C2×C22⋊C4×C89C2314yes—
154C2×C42×C89—24no—
155C2×C42×C89C2314yes—
156#95×C89C2314yes—
157#95×C89C2314yes—
158C23×D89—22no—
159C23×D89—22no—
160C23×D89—22no—
161C23×D89—22no—
162C23×D89—22no—
163C23×D89—22no—
164C23×D89C22×C414yes—
165C23×D89C2412yes—
166C2×C22⋊D89—232no—
167C2×C22⋊D89—28no—
168C2×C22⋊D89—28no—
169C2×C22⋊D89C22×C4116yes—
170C22×Dic89—22no—
171C22×Dic89—22no—
172C22×Dic89—22no—
173C22×Dic89—22no—
174C22×Dic89—232no—
175C22×Dic89—28no—
176C22×Dic89—28no—
177C22×Dic89—22no—
178C22×Dic89—22no—
179C22×Dic89—22no—
180C22×Dic89—22no—
181C22×Dic89—22no—
182C22×Dic89—22no—
183C22×Dic89—22no—
184C22×Dic89—22no—
185C22×Dic89—22no—
186C22×Dic89C22×C4116yes—
187C22×Dic89C22×C414yes—
188C22×Dic89C22×C414yes—
189C22×Dic89C22×C414yes—
190C22×Dic89C2×D414yes—
191C22×Dic89C2×D414yes—
192C22×Dic89#4114yes—
193C22×Dic89#4114yes—
194C22×Dic89#4114yes—
195C22×Dic89C2412yes—
196C22×Dic89C2412yes—
197C22×Dic89C2412yes—
198C22×Dic89C2412yes—
199C22×Dic89C2412yes—
200C22×Dic89C2412yes—
201C22×Dic89C2412yes—
202C2×C4×D89—232no—
203C2×C4×D89—28no—
204C2×C4×D89—28no—
205C2×C4×D89C22×C4116yes—
206C4⋊Dic89—44no—
207#13083553—28no—
208#13083553—28no—
209#13083553—28no—
210#13083553—28no—
211#13083553—28no—
212#13083553C22×C4116yes—
213#13083553C2×D4116yescomplemented
214C22⋊Dic89—28no—
215C22⋊Dic89—44no—
216#13083551—28no—
217#13083551—28no—
218#13083551—44no—
219#13083551—44no—
220#13083551C22×C4116yes—
221C4×Dic89—28no—
222C4×Dic89—28no—
223C4×Dic89—28no—
224C4×Dic89—28no—
225C4×Dic89—28no—
226C4×Dic89C22×C4116yes—
227C24×C89—22no—
228C24×C89—22no—
229C24×C89—22no—
230C24×C89—22no—
231C24×C89—22no—
232C24×C89—22no—
233C24×C89C22×C414yes—
234C24×C89C2412yes—
235C24×C89C2411yescharacteristic
236C22×C4×C89—22no—
237C22×C4×C89—22no—
238C22×C4×C89—22no—
239C22×C4×C89—22no—
240C22×C4×C89—22no—
241C22×C4×C89—22no—
242C22×C4×C89—22no—
243C22×C4×C89—22no—
244C22×C4×C89—22no—
245C22×C4×C89—22no—
246C22×C4×C89—22no—
247C22×C4×C89—22no—
248C22×C4×C89—22no—
249C22×C4×C89—22no—
250C22×C4×C89—22no—
251C22×C4×C89C22×C414yes—
252C22×C4×C89C22×C414yes—
253C22×C4×C89C2×D414yes—
254C22×C4×C89C2412yes—
255C22×C4×C89C2412yes—
256C22×C4×C89C2412yes—
257C22×C4×C89C2412yes—
258C22×C4×C89C2412yes—
259C22×C4×C89C2412yes—
260C4⋊C4×C89—44no—
261C22⋊C4×C89—28no—
262C22⋊C4×C89—44no—
263C22⋊C4×C89C22×C4116yes—
264C42×C89—28no—
265C23×C89—28no—
266C23×C89—28no—
267C23×C89—28no—
268C23×C89—22no—
269C23×C89—22no—
270C23×C89—22no—
271C23×C89—22no—
272C23×C89—22no—
273C23×C89—22no—
274C23×C89—44no—
275C23×C89—44no—
276C23×C89—44no—
277C23×C89—44no—
278C23×C89C23×C414yes—
279C23×C89C23×C412yes—
280C23×C89C22×D412yes—
281C23×C89C2×#4112yes—
282C23×C89C2×#4112yes—
283C23×C89C2×#4112yes—
284C23×C89H(5,𝔽2)12yes—
285C23×C892−1+412yes—
286C23×C89C2511yescharacteristic
287C22×D89—28no—
288C22×D89—28no—
289C22×D89—28no—
290C22×D89—22no—
291C22×D89—22no—
292C22×D89—22no—
293C22×D89—22no—
294C22×D89—22no—
295C22×D89—22no—
296C22×D89—44no—
297C22×D89—44no—
298C22×D89—44no—
299C22×D89—44no—
300C22×D89C23×C414yes—
301C2×C4×C89—28no—
302C2×C4×C89—28no—
303C2×C4×C89—28no—
304C2×C4×C89—22no—
305C2×C4×C89—22no—
306C2×C4×C89—22no—
307C2×C4×C89—22no—
308C2×C4×C89—22no—
309C2×C4×C89—22no—
310C2×C4×C89—22no—
311C2×C4×C89—22no—
312C2×C4×C89—22no—
313C2×C4×C89—22no—
314C2×C4×C89—22no—
315C2×C4×C89—22no—
316C2×C4×C89—22no—
317C2×C4×C89—22no—
318C2×C4×C89—22no—
319C2×C4×C89—44no—
320C2×C4×C89—44no—
321C2×C4×C89—44no—
322C2×C4×C89C23×C414yes—
323C2×C4×C89C23×C414yes—
324C2×C4×C89C22×D414yes—
325C22⋊D89—232no—
326C2×Dic89—28no—
327C2×Dic89—28no—
328C2×Dic89—22no—
329C2×Dic89—22no—
330C2×Dic89—22no—
331C2×Dic89—22no—
332C2×Dic89—232no—
333C2×Dic89—22no—
334C2×Dic89—22no—
335C2×Dic89—22no—
336C2×Dic89—22no—
337C2×Dic89—22no—
338C2×Dic89—22no—
339C2×Dic89—22no—
340C2×Dic89—22no—
341C2×Dic89—22no—
342C2×Dic89—44no—
343C2×Dic89—44no—
344C2×Dic89—44no—
345C2×Dic89#117116yescomplemented
346C2×Dic89C4×D4116yes—
347C2×Dic89C23×C414yes—
348C2×Dic89C23×C414yes—
349C2×Dic89C23×C414yes—
350C2×Dic89C22×D414yes—
351C2×Dic89C22×D414yes—
352C2×Dic89C2×#4114yes—
353C2×Dic89C2×#4114yes—
354C2×Dic89C2×#4114yes—
355C4×D89—232no—
356C22×C89—24no—
357C22×C89—24no—
358C22×C89—24no—
359C22×C89—416no—
360C22×C89—42no—
361C22×C89—42no—
362C22×C89—42no—
363C22×C89—42no—
364C22×C89C2×#11714yes—
365C22×C89C2×C4×D414yes—
366C22×C89#52014yes—
367C22×C89#54714yes—
368C22×C89#55014yes—
369C22×C89#55514yes—
370C22×C89#55614yes—
371C22×C89C24×C411yescharacteristic
372C22×C89C23×D411yescharacteristic
373C22×C89C22×#4111yescharacteristic
374C22×C89C22×#4111yescharacteristic
375C22×C89C22×#4111yescharacteristic
376C22×C89C2×H(5,𝔽2)11yescharacteristic
377C22×C89C2×2−1+411yescharacteristic
378C2×D89—24no—
379C2×D89—24no—
380C2×D89—24no—
381C2×D89—416no—
382C2×D89—42no—
383C2×D89—42no—
384C2×D89—42no—
385C2×D89—42no—
386C4×C89—24no—
387C4×C89—24no—
388C4×C89—24no—
389C4×C89—42no—
390C4×C89—42no—
391C4×C89—42no—
392Dic89—24no—
393Dic89—24no—
394Dic89—42no—
395Dic89—42no—
396Dic89—42no—
397Dic89C2×#11718yescomplemented
398Dic89C2×C4×D418yes—
399C2×#2354—891nomaximal, Sylow
400C2×C89—44no—
401C2×C89#235418yescomplemented
402C2×C89C22×#11711yescharacteristic
403C2×C89C22×C4×D411yescharacteristic
404C2×C89C2×#52011yescharacteristic
405C2×C89C2×#54711yescharacteristic
406C2×C89C2×#55011yescharacteristic
407C2×C89C2×#55511yescharacteristic
408C2×C89C2×#55611yescharacteristic
409D89—44no—
410C22×C4×D4—891no—
411C22×#117—891no—
412C22×#117—891no—
413#2354—8916no—
414C2×#390—891no—
415C2×#390—891no—
416C2×#388—891no—
417C2×#388—891no—
418C2×#388—891no—
419C2×#388D8911yescharacteristic, complemented
420C2×#384—891no—
421C2×#380—891no—
422C2×#380—891no—
423C2×C4×C4⋊C4—891no—
424C2×C4×C4⋊C4—891no—
425C2×C4×C4⋊C4—891no—
426C89C2×#235411yescharacteristic, complemented, Sylow
427C23×D4—891no—
428C24×C4—891no—
429C24×C4—891no—
430C2×C4×D4—8916no—
431C2×C4×D4—898no—
432C2×#117—898no—
433C2×#117—898no—
434C2×#117—1788no—
435C2×#117—1788no—
436C22×C4⋊C4—891no—
437C22×C4⋊C4—891no—
438C22×C4⋊C4—891no—
439C22×C4⋊C4—891no—
440C22×C4⋊C4—891no—
441C22×C4⋊C4—891no—
442C22×C4⋊C4—891no—
443C22×C4⋊C4—891no—
444C22×C4⋊C4C2×D8911yescharacteristic
445C22×C22⋊C4—891no—
446C22×C22⋊C4—891no—
447C22×C22⋊C4—891no—
448C22×C22⋊C4—891no—
449C22×C22⋊C4—891no—
450C22×C22⋊C4—891no—
451C22×C22⋊C4—891no—
452C22×C22⋊C4C2×D8911yescharacteristic
453C22×C22⋊C4C2×D8911yescharacteristic
454C22×C22⋊C4C2×D8911yescharacteristic
455C22×C42—891no—
456C22×C42—891no—
457C22×C42—891no—
458C22×C42—891no—
459C22×C42—891no—
460C22×C42—891no—
461C22×C42C2×D8911yescharacteristic
462#390—898no—
463#390—898no—
464#388—898no—
465#388—898no—
466#388—898no—
467#388C2×D8918yescomplemented
468#384—898no—
469#380—898no—
470#380—898no—
471C4×C4⋊C4—898no—
472C4×C4⋊C4—898no—
473C4×C4⋊C4—898no—
474C2×#95—891no—
475C2×#95—891no—
476C2×#95—891no—
477C2×#95—891no—
478C2×#95C2×D8911yescharacteristic
479C2×#95C2×D8911yescharacteristic
480C25—891no—
481C25C22×D8911yescharacteristic
482C22×D4—898no—
483C22×D4—894no—
484C22×D4—1784no—
485C22×D4—1784no—
486C23×C4—891no—
487C23×C4—891no—
488C23×C4—898no—
489C23×C4—894no—
490C23×C4—891no—
491C23×C4—891no—
492C23×C4—898no—
493C23×C4—894no—
494C23×C4—891no—
495C23×C4—891no—
496C23×C4—891no—
497C23×C4—1784no—
498C23×C4—1784no—
499C23×C4—1784no—
500C23×C4—1784no—
501C23×C4C22×D8911yescharacteristic
502C23×C4C22×D8911yescharacteristic
503C23×C4C22×D8911yescharacteristic
504C23×C4C22×D8911yescharacteristic
505C23×C4C22×D8911yescharacteristic
506C23×C4C22×D8911yescharacteristic
507C4×D4—8964no—
508#117—17832no—
509#117—17832no—
510C2×C4⋊C4—42no—
511C2×C4⋊C4—898no—
512C2×C4⋊C4—898no—
513C2×C4⋊C4—894no—
514C2×C4⋊C4—894no—
515C2×C4⋊C4—894no—
516C2×C4⋊C4—894no—
517C2×C4⋊C4—894no—
518C2×C4⋊C4—894no—
519C2×C4⋊C4—894no—
520C2×C4⋊C4—894no—
521C2×C4⋊C4—3562no—
522C2×C4⋊C4—1784no—
523C2×C4⋊C4—1784no—
524C2×C4⋊C4—1784no—
525C2×C4⋊C4—1784no—
526C2×C4⋊C4—1784no—
527C2×C4⋊C4C22×D8914yes—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—898no—
531C2×C22⋊C4—894no—
532C2×C22⋊C4—894no—
533C2×C22⋊C4—894no—
534C2×C22⋊C4—894no—
535C2×C22⋊C4—894no—
536C2×C22⋊C4—894no—
537C2×C22⋊C4—894no—
538C2×C22⋊C4—3562no—
539C2×C22⋊C4—3562no—
540C2×C22⋊C4—3562no—
541C2×C22⋊C4—1784no—
542C2×C22⋊C4—1784no—
543C2×C22⋊C4—1784no—
544C2×C22⋊C4C4×D8918yes—
545C2×C22⋊C4C22×D8914yes—
546C2×C22⋊C4C22×D8914yes—
547C2×C22⋊C4C22×D8914yes—
548C2×C42—24no—
549C2×C42—898no—
550C2×C42—894no—
551C2×C42—894no—
552C2×C42—894no—
553C2×C42—894no—
554C2×C42—894no—
555C2×C42—894no—
556C2×C42—1784no—
557C2×C42—1784no—
558C2×C42—1784no—
559C2×C42—1784no—
560C2×C42—1784no—
561C2×C42C22×D8914yes—
562#95—894no—
563#95—894no—
564#95—894no—
565#95—894no—
566#95C22×D8914yes—
567#95C22×D8914yes—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—894no—
575C24—892no—
576C24—1782no—
577C24—1782no—
578C24—1782no—
579C24—1782no—
580C24—1782no—
581C24—1782no—
582C24C2×C4×D8914yes—
583C24C23×D8912yes—
584C24C23×D8911yescharacteristic
585C2×D4—8916no—
586C2×D4—1788no—
587C2×D4—1788no—
588C2×D4—17832no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—894no—
605C22×C4—894no—
606C22×C4—894no—
607C22×C4—894no—
608C22×C4—894no—
609C22×C4—894no—
610C22×C4—892no—
611C22×C4—892no—
612C22×C4—894no—
613C22×C4—8916no—
614C22×C4—894no—
615C22×C4—892no—
616C22×C4—892no—
617C22×C4—8916no—
618C22×C4—892no—
619C22×C4—892no—
620C22×C4—892no—
621C22×C4—1788no—
622C22×C4—1788no—
623C22×C4—17832no—
624C22×C4—1788no—
625C22×C4—1788no—
626C22×C4—17832no—
627C22×C4—1782no—
628C22×C4—1782no—
629C22×C4—1782no—
630C22×C4—1782no—
631C22×C4—1782no—
632C22×C4—1782no—
633C22×C4—1782no—
634C22×C4—1782no—
635C22×C4—1782no—
636C22×C4—1782no—
637C22×C4—1782no—
638C22×C4—1782no—
639C22×C4—1782no—
640C22×C4C2×C4×D8914yes—
641C22×C4C2×C4×D8914yes—
642C22×C4D4×D8914yes—
643C22×C4C23×D8912yes—
644C22×C4C23×D8912yes—
645C22×C4C23×D8912yes—
646C22×C4C23×D8912yes—
647C22×C4C23×D8912yes—
648C22×C4C23×D8912yes—
649C4⋊C4—44no—
650C4⋊C4—8916no—
651C4⋊C4—8916no—
652C4⋊C4—3564no—
653C4⋊C4—1788no—
654C4⋊C4—1788no—
655C4⋊C4—1788no—
656C4⋊C4—1788no—
657C4⋊C4—1788no—
658C22⋊C4—28no—
659C22⋊C4—44no—
660C22⋊C4—8916no—
661C22⋊C4—3564no—
662C22⋊C4—3564no—
663C22⋊C4—3564no—
664C22⋊C4—1788no—
665C22⋊C4—1788no—
666C22⋊C4—1788no—
667C22⋊C4C2×C4×D89116yes—
668C42—28no—
669C42—8916no—
670C42—1788no—
671C42—1788no—
672C42—1788no—
673C42—1788no—
674C42—1788no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—894no—
689C23—3564no—
690C23—3564no—
691C23—3564no—
692C23—3564no—
693C23—1782no—
694C23—1782no—
695C23—1782no—
696C23—1782no—
697C23—1782no—
698C23—1782no—
699C23—1788no—
700C23—1788no—
701C23—1788no—
702C23C22×C4×D8914yes—
703C23C22×C4×D8912yes—
704C23C2×D4×D8912yes—
705C23#41×D8912yes—
706C23#41×D8912yes—
707C23#41×D8912yes—
708C23#1566805712yes—
709C23#1566805912yes—
710C23C24×D8911yescharacteristic
711D4—17832no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—894no—
734C2×C4—894no—
735C2×C4—894no—
736C2×C4—894no—
737C2×C4—894no—
738C2×C4—894no—
739C2×C4—8916no—
740C2×C4—8916no—
741C2×C4—894no—
742C2×C4—894no—
743C2×C4—3564no—
744C2×C4—3564no—
745C2×C4—3564no—
746C2×C4—17832no—
747C2×C4—17832no—
748C2×C4—1782no—
749C2×C4—1782no—
750C2×C4—1782no—
751C2×C4—1782no—
752C2×C4—1782no—
753C2×C4—1782no—
754C2×C4—1782no—
755C2×C4—1782no—
756C2×C4—1782no—
757C2×C4—1782no—
758C2×C4—1782no—
759C2×C4—1782no—
760C2×C4—1782no—
761C2×C4—1788no—
762C2×C4—1788no—
763C2×C4C22×C4×D8914yes—
764C2×C4C22×C4×D8914yes—
765C2×C4C2×D4×D8914yes—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—416no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—35616no—
775C22—3562no—
776C22—3562no—
777C22—3562no—
778C22—3562no—
779C22—1784no—
780C22—1784no—
781C22—1784no—
782C22#117×D8914yes—
783C22C4×D4×D8914yes—
784C22#1915207714yes—
785C22#1915224614yes—
786C22#1915226614yes—
787C22#1915231014yes—
788C22#1915231514yes—
789C22C23×C4×D8911yescharacteristic
790C22C22×D4×D8911yescharacteristic
791C22C2×#41×D8911yescharacteristic
792C22C2×#41×D8911yescharacteristic
793C22C2×#41×D8911yescharacteristic
794C22C2×#1566805711yescharacteristic
795C22C2×#1566805911yescharacteristic
796C4—24no—
797C4—24no—
798C4—24no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—898no—
803C4—898no—
804C4—3562no—
805C4—3562no—
806C4—3562no—
807C4—1784no—
808C4—1784no—
809C2—44no—
810C2—3564no—
811C2#2602319818yesdirect product factor
812C2C2×#117×D8911yescharacteristic
813C2C2×C4×D4×D8911yescharacteristic
814C2C2×#1915207711yescharacteristic
815C2C2×#1915224611yescharacteristic
816C2C2×#1915226611yescharacteristic
817C2C2×#1915231011yescharacteristic
818C2C2×#1915231511yescharacteristic
subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×#388×C89C2
socleC24×C89C24
prime radicalC23×C22⋊D89C22
cosocleC23×C89C25
hypercenterC2×#388D89
hypocenterC89C2×#2354
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#15667969C2semidirect
3. C22×#15667968C2semidirect
4. #26023198C2direct (N × H)
7. C2×#19151491C2semidirect
8. C2×#19151490C2semidirect
9. C2×#19151488C2semidirect
10. C2×#19151467C2semidirect
11. C2×#19151457C2semidirect
12. C2×#19151456C2semidirect
13. C2×C4×#13083553C2semidirect
14. C2×#19151449C2semidirect
15. C2×#19151449C2semidirect
16. C2×#388×C89C2semidirect
20. C2×#15667972C4semidirect
23. C2×#15667969C22semidirect
25. C2×#15667968C22semidirect
49. #19151491C22semidirect
50. #19151490C22semidirect
51. #19151488C22semidirect
52. #19151467C22semidirect
53. #19151457C22semidirect
54. #19151456C22semidirect
55. C4×#13083553C22semidirect
56. #19151449C22semidirect
57. #19151449C22semidirect
67. #388×C89C22semidirect
90. #15667972C2×C4semidirect
101. C2×#13083553D4semidirect
213. #13083553C2×D4semidirect
345. C2×Dic89#117semidirect
397. Dic89C2×#117semidirect
401. C2×C89#2354semidirect
419. C2×#388D89semidirect
426. C89C2×#2354semidirect
467. #388C2×D89semidirect
811. C2#26023198direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679722
C22×#156679692
C22×#156679682
#260231982
C2×#191514982
C2×#191514912
C2×#191514902
C2×#191514882
C2×#191514672
C2×#191514572
C2×#191514562
C2×C4×#130835532
C2×#191514492
C2×#388×C892
C2×#235489