Finite Group Databasebeta

← C89×#60335 #36438183

Subgroups — C89×#60335 #36438183

Order 22784.

1746 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C89×#3482C211yesmaximal, characteristic
2C89×#2994C213yesmaximal, complemented
3C89×#2993C213yesmaximal, complemented
4C89×#2990C213yesmaximal, complemented
5C89×#2988C211yesmaximal, characteristic, complemented
6C89×#2985C213yesmaximal, complemented
7C89×#2984C211yesmaximal, characteristic, complemented
8C89×#2982C211yesmaximal, characteristic, complemented
9C89×#2971C211yesmaximal, characteristic, complemented
10C89×#2969C213yesmaximal, complemented
11C89×#2966C213yesmaximal, complemented
12C89×#2965C213yesmaximal, complemented
13Q8×M16×C89C211yesmaximal, characteristic, complemented
14C89×#2962C213yesmaximal, complemented
15C2×C8×Q8×C89C211yesmaximal, characteristic, complemented
16#557×C89C411yescharacteristic
17#556×C89C413yes—
18#552×C89C413yes—
19#552×C89C413yes—
20D4×Q8×C89C411yescharacteristic
21#548×C89C411yescharacteristic
22#548×C89C411yescharacteristic
23#547×C89C413yes—
24#533×C89C2213yes—
25#529×C89C2213yes—
26#529×C89C2213yes—
27C4×#41×C89C2213yes—
28C4×#41×C89C2211yescharacteristic
29C2×C4×Q8×C89C2211yescharacteristic
30C2×C4×Q8×C89C2211yescharacteristic
31#446×C89C2213yes—
32#446×C89C2213yes—
33#446×C89C2213yes—
34#446×C89C2216yes—
35#446×C89C2213yes—
36#446×C89C2213yes—
37#446×C89C2213yes—
38C8×Q8×C89C2213yes—
39C8×Q8×C89C2211yescharacteristic
40C8×Q8×C89C2211yescharacteristic
41C8×Q8×C89C2213yes—
42C8×Q8×C89C2213yes—
43C8×Q8×C89C2211yescharacteristic
44C8×Q8×C89C2213yes—
45C8×Q8×C89C2211yescharacteristic
46#436×C89C2213yes—
47#436×C89C2213yes—
48#436×C89C2213yes—
49#436×C89C2213yes—
50#435×C89C2211yescharacteristic
51#435×C89C2213yes—
52#435×C89C2213yes—
53#435×C89C2213yes—
54#435×C89C2216yes—
55C8×D4×C89C2213yes—
56C8×D4×C89C2216yes—
57C8×D4×C89C2213yes—
58#433×C89C2216yes—
59#433×C89C2216yes—
60#432×C89C2213yes—
61#432×C89C2213yes—
62#431×C89C2213yes—
63#431×C89C2213yes—
64#431×C89C2213yes—
65#431×C89C2213yes—
66#424×C89C2216yes—
67#423×C89C2213yes—
68C2×C4⋊C8×C89C2213yes—
69C2×C4⋊C8×C89C2213yes—
70#405×C89C2216yes—
71C4×M16×C89C2213yes—
72C4×M16×C89C2213yes—
73C2×C4×C8×C89C2213yes—
74C2×#41×C89C2×C411yescharacteristic
75C2×#41×C89C2×C413yes—
76C22×Q8×C89C2×C411yescharacteristic
77C22×Q8×C89C2×C411yescharacteristic
78C2×M16×C89C2311yescharacteristic
79C2×M16×C89C2313yes—
80C2×M16×C89C2313yes—
81C2×M16×C89C2313yes—
82C22×C8×C89C2311yescharacteristic
83C22×C8×C89C2313yes—
84C22×C8×C89C2316yes—
85C4⋊Q8×C89C2×C413yes—
86C4⋊Q8×C89C2×C413yes—
87#126×C89C2×C416yes—
88#126×C89C2×C416yes—
89#125×C89C2×C413yes—
90#125×C89C2×C413yes—
91#125×C89C2×C416yes—
92#124×C89C2×C413yes—
93#124×C89C2×C413yes—
94#123×C89C2×C416yes—
95#123×C89C2×C416yes—
96C22⋊Q8×C89C2×C413yes—
97C22⋊Q8×C89C2×C413yes—
98C22⋊Q8×C89C2×C416yes—
99C22⋊Q8×C89C2×C413yes—
100C22⋊Q8×C89C2×C413yes—
101#121×C89C2×C413yes—
102#121×C89C2×C413yes—
103C4×Q8×C89C2×C411yescharacteristic
104C4×Q8×C89C2×C411yescharacteristic
105C4×Q8×C89C2×C413yes—
106C4×Q8×C89C2×C413yes—
107C4×Q8×C89C2×C411yescharacteristic
108C4×Q8×C89C2×C413yes—
109C4×Q8×C89C2311yescharacteristic
110C4×Q8×C89C2313yes—
111C4×Q8×C89C2313yes—
112C4×Q8×C89C2313yes—
113C4×D4×C89C2×C413yes—
114C4×D4×C89C2×C413yes—
115C4×D4×C89C2×C413yes—
116C4×D4×C89C2×C413yes—
117C4×D4×C89C2313yes—
118C4×D4×C89C2313yes—
119C4×D4×C89C2311yescharacteristic
120C4×D4×C89C2313yes—
121#117×C89C2×C413yes—
122#117×C89C2×C413yes—
123#117×C89C2×C413yes—
124#117×C89C2×C413yes—
125#117×C89C2316yes—
126C2×C4⋊C4×C89C2×C413yes—
127C2×C4⋊C4×C89C2×C413yes—
128C2×C42×C89C2313yes—
129C2×C42×C89C2313yes—
130C2×C42×C89C2313yes—
131C4⋊C8×C89C2313yes—
132C4⋊C8×C89C2313yes—
133C4⋊C8×C89C2313yes—
134C4⋊C8×C89C2313yes—
135C4⋊C8×C89C2316yes—
136C4⋊C8×C89C2316yes—
137C4⋊C8×C89C2313yes—
138C4⋊C8×C89C2313yes—
139C4⋊C8×C89C2311yescharacteristic
140C4⋊C8×C89C2313yes—
141C4⋊C8×C89C2313yes—
142C4⋊C8×C89C2313yes—
143C22⋊C8×C89C2311yescharacteristic
144C22⋊C8×C89C2313yes—
145C22⋊C8×C89C2311yescharacteristic
146C22⋊C8×C89C2313yes—
147C22⋊C8×C89C2313yes—
148C22⋊C8×C89C2313yes—
149C22⋊C8×C89C2316yes—
150#97×C89C2311yescharacteristic
151#97×C89C2313yes—
152#97×C89C2313yes—
153#97×C89C2313yes—
154#97×C89C2316yes—
155C4×C8×C89C2313yes—
156C4×C8×C89C2313yes—
157C4×C8×C89C2313yes—
158C4×C8×C89C2313yes—
159C4×C8×C89C2313yes—
160C4×C8×C89C2313yes—
161C4×C8×C89C2316yes—
162#41×C89—24no—
163#41×C89—46no—
164C2×Q8×C89—24no—
165C2×Q8×C89—24no—
166C2×Q8×C89C22×C413yes—
167C2×Q8×C89C22×C413yes—
168C2×Q8×C89C22×C413yes—
169C2×Q8×C89C22×C411yescharacteristic
170C2×D4×C89C22×C411yescharacteristic
171C2×D4×C89C22×C413yes—
172C2×D4×C89C22×C413yes—
173C2×D4×C89C22×C413yes—
174C22×C4×C89C22×C413yes—
175C22×C4×C89C22×C413yes—
176C22×C4×C89C22×C413yes—
177C22×C4×C89C22×C413yes—
178C22×C4×C89C22×C413yes—
179C22×C4×C89C22×C413yes—
180C22×C4×C89C2411yescharacteristic
181C22×C4×C89C2411yescharacteristic
182C22×C4×C89C2413yes—
183M16×C89—22no—
184M16×C89—26no—
185M16×C89—43no—
186M16×C89—43no—
187C2×C8×C89—22no—
188C2×C8×C89—46no—
189C2×C8×C89—43no—
190C2×C8×C89C2411yescharacteristic
191C2×C8×C89C2413yes—
192C2×C8×C89C2411yescharacteristic
193C2×C8×C89C2413yes—
194C2×C8×C89C2411yescharacteristic
195C2×C8×C89C2413yes—
196C2×C8×C89C2413yes—
197C2×C8×C89C2411yescharacteristic
198C4⋊C4×C89C22×C413yes—
199C4⋊C4×C89C22×C413yes—
200C4⋊C4×C89C22×C413yes—
201C4⋊C4×C89C22×C416yes—
202C4⋊C4×C89C22×C416yes—
203C4⋊C4×C89C22×C411yescharacteristic
204C4⋊C4×C89C22×C413yes—
205C4⋊C4×C89C22×C413yes—
206C4⋊C4×C89C22×C413yes—
207C4⋊C4×C89C22×C413yes—
208C4⋊C4×C89C22×C413yes—
209C4⋊C4×C89C22×C413yes—
210C4⋊C4×C89C22×C416yes—
211C4⋊C4×C89C22×C416yes—
212C22⋊C4×C89C22×C411yescharacteristic
213C22⋊C4×C89C22×C411yescharacteristic
214C22⋊C4×C89C22×C413yes—
215C22⋊C4×C89C22×C413yes—
216C22⋊C4×C89C22×C416yes—
217C22⋊C4×C89C22×C413yes—
218C22⋊C4×C89C22×C413yes—
219C22⋊C4×C89C22×C416yes—
220C22⋊C4×C89C22×C416yes—
221C42×C89C22×C413yes—
222C42×C89C22×C413yes—
223C42×C89C22×C413yes—
224C42×C89C22×C413yes—
225C42×C89C22×C413yes—
226C42×C89C22×C413yes—
227C42×C89C2413yes—
228C42×C89C2413yes—
229C42×C89C2413yes—
230C42×C89C2411yescharacteristic
231C23×C89C23×C413yes—
232C23×C89C23×C411yescharacteristic
233C23×C89C23×C411yescharacteristic
234Q8×C89—26no—
235Q8×C89—26no—
236Q8×C89—43no—
237Q8×C89#13114yes—
238D4×C89—26no—
239D4×C89—22no—
240D4×C89—26no—
241D4×C89—43no—
242C2×C4×C89—26no—
243C2×C4×C89—26no—
244C2×C4×C89—26no—
245C2×C4×C89—26no—
246C2×C4×C89—21no—
247C2×C4×C89—21no—
248C2×C4×C89—23no—
249C2×C4×C89—21no—
250C2×C4×C89—23no—
251C2×C4×C89—21no—
252C2×C4×C89—43no—
253C2×C4×C89—43no—
254C2×C4×C89C23×C411yescharacteristic
255C2×C4×C89C23×C411yescharacteristic
256C2×C4×C89C23×C411yescharacteristic
257C2×C4×C89C23×C413yes—
258C2×C4×C89C23×C411yescharacteristic
259C2×C4×C89C23×C413yes—
260C2×C4×C89C23×C413yes—
261C2×C4×C89C23×C413yes—
262C2×C4×C89C23×C413yes—
263C2×C4×C89C23×C413yes—
264C2×C4×C89C23×C413yes—
265C2×C4×C89C2511yescharacteristic
266C8×C89—21no—
267C8×C89—21no—
268C8×C89—23no—
269C8×C89—23no—
270C8×C89—23no—
271C8×C89—23no—
272C8×C89—21no—
273C8×C892−1+412yes—
274C22×C89—21no—
275C22×C89—21no—
276C22×C89—23no—
277C22×C89—21no—
278C22×C89—21no—
279C22×C89—23no—
280C22×C89—21no—
281C22×C89—23no—
282C22×C89#56812yes—
283C22×C89C24×C411yescharacteristic
284C4×C89—21no—
285C4×C89—23no—
286C4×C89—21no—
287C4×C89—21no—
288C4×C89—23no—
289C4×C89—23no—
290C4×C89—23no—
291C4×C89—23no—
292C4×C89—21no—
293C4×C89—23no—
294C4×C89C2×#13116yes—
295C4×C89C2×2−1+411yescharacteristic
296C4×C89#58511yescharacteristic
297#60335C8911yesmaximal, characteristic, direct product factor, Sylow
298C2×C89—22no—
299C2×C89—41no—
300C2×C89—43no—
301C2×C89C4×2−1+411yescharacteristic
302C2×C89C22×#13111yescharacteristic
303C2×C89C2×#56811yescharacteristic
304#3482C2×C8911yescharacteristic
305#2994C2×C8913yescomplemented
306#2993C2×C8913yescomplemented
307#2990C2×C8913yescomplemented
308#2988C2×C8911yescharacteristic, complemented
309#2985C2×C8913yescomplemented
310#2984C2×C8911yescharacteristic, complemented
311#2982C2×C8911yescharacteristic, complemented
312#2971C2×C8911yescharacteristic, complemented
313#2969C2×C8913yescomplemented
314#2966C2×C8913yescomplemented
315#2965C2×C8913yescomplemented
316Q8×M16C2×C8911yescharacteristic, complemented
317#2962C2×C8913yescomplemented
318C2×C8×Q8C2×C8911yescharacteristic, complemented
319C89#6033511yescharacteristic, direct product factor, Sylow
320#557C4×C8911yescharacteristic
321#556C4×C8913yes—
322#552C4×C8913yes—
323#552C4×C8913yes—
324D4×Q8C4×C8911yescharacteristic
325#548C4×C8911yescharacteristic
326#548C4×C8911yescharacteristic
327#547C4×C8913yes—
328#533C22×C8913yes—
329#529C22×C8913yes—
330#529C22×C8913yes—
331C4×#41C22×C8913yes—
332C4×#41C22×C8911yescharacteristic
333C2×C4×Q8C22×C8911yescharacteristic
334C2×C4×Q8C22×C8911yescharacteristic
335#446C22×C8913yes—
336#446C22×C8913yes—
337#446C22×C8913yes—
338#446C22×C8916yes—
339#446C22×C8913yes—
340#446C22×C8913yes—
341#446C22×C8913yes—
342C8×Q8C22×C8913yes—
343C8×Q8C22×C8911yescharacteristic
344C8×Q8C22×C8911yescharacteristic
345C8×Q8C22×C8913yes—
346C8×Q8C22×C8913yes—
347C8×Q8C22×C8911yescharacteristic
348C8×Q8C22×C8913yes—
349C8×Q8C22×C8911yescharacteristic
350#436C22×C8913yes—
351#436C22×C8913yes—
352#436C22×C8913yes—
353#436C22×C8913yes—
354#435C22×C8911yescharacteristic
355#435C22×C8913yes—
356#435C22×C8913yes—
357#435C22×C8913yes—
358#435C22×C8916yes—
359C8×D4C22×C8913yes—
360C8×D4C22×C8916yes—
361C8×D4C22×C8913yes—
362#433C22×C8916yes—
363#433C22×C8916yes—
364#432C22×C8913yes—
365#432C22×C8913yes—
366#431C22×C8913yes—
367#431C22×C8913yes—
368#431C22×C8913yes—
369#431C22×C8913yes—
370#424C22×C8916yes—
371#423C22×C8913yes—
372C2×C4⋊C8C22×C8913yes—
373C2×C4⋊C8C22×C8913yes—
374#405C22×C8916yes—
375C4×M16C22×C8913yes—
376C4×M16C22×C8913yes—
377C2×C4×C8C22×C8913yes—
378C2×#41C2×C4×C8911yescharacteristic
379C2×#41C2×C4×C8913yes—
380C22×Q8C2×C4×C8911yescharacteristic
381C22×Q8C2×C4×C8911yescharacteristic
382C2×M16C23×C8911yescharacteristic
383C2×M16C23×C8913yes—
384C2×M16C23×C8913yes—
385C2×M16C23×C8913yes—
386C22×C8C23×C8911yescharacteristic
387C22×C8C23×C8913yes—
388C22×C8C23×C8916yes—
389C4⋊Q8C2×C4×C8913yes—
390C4⋊Q8C2×C4×C8913yes—
391#126C2×C4×C8916yes—
392#126C2×C4×C8916yes—
393#125C2×C4×C8913yes—
394#125C2×C4×C8913yes—
395#125C2×C4×C8916yes—
396#124C2×C4×C8913yes—
397#124C2×C4×C8913yes—
398#123C2×C4×C8916yes—
399#123C2×C4×C8916yes—
400C22⋊Q8C2×C4×C8913yes—
401C22⋊Q8C2×C4×C8913yes—
402C22⋊Q8C2×C4×C8916yes—
403C22⋊Q8C2×C4×C8913yes—
404C22⋊Q8C2×C4×C8913yes—
405#121C2×C4×C8913yes—
406#121C2×C4×C8913yes—
407C4×Q8C2×C4×C8911yescharacteristic
408C4×Q8C2×C4×C8911yescharacteristic
409C4×Q8C2×C4×C8913yes—
410C4×Q8C2×C4×C8913yes—
411C4×Q8C2×C4×C8911yescharacteristic
412C4×Q8C2×C4×C8913yes—
413C4×Q8C23×C8911yescharacteristic
414C4×Q8C23×C8913yes—
415C4×Q8C23×C8913yes—
416C4×Q8C23×C8913yes—
417C4×D4C2×C4×C8913yes—
418C4×D4C2×C4×C8913yes—
419C4×D4C2×C4×C8913yes—
420C4×D4C2×C4×C8913yes—
421C4×D4C23×C8911yescharacteristic
422C4×D4C23×C8913yes—
423C4×D4C23×C8913yes—
424C4×D4C23×C8913yes—
425#117C2×C4×C8913yes—
426#117C2×C4×C8913yes—
427#117C2×C4×C8913yes—
428#117C2×C4×C8913yes—
429#117C23×C8916yes—
430C2×C4⋊C4C2×C4×C8913yes—
431C2×C4⋊C4C2×C4×C8913yes—
432C2×C42C23×C8913yes—
433C2×C42C23×C8913yes—
434C2×C42C23×C8913yes—
435C4⋊C8C23×C8913yes—
436C4⋊C8C23×C8913yes—
437C4⋊C8C23×C8913yes—
438C4⋊C8C23×C8913yes—
439C4⋊C8C23×C8916yes—
440C4⋊C8C23×C8916yes—
441C4⋊C8C23×C8913yes—
442C4⋊C8C23×C8913yes—
443C4⋊C8C23×C8911yescharacteristic
444C4⋊C8C23×C8913yes—
445C4⋊C8C23×C8913yes—
446C4⋊C8C23×C8913yes—
447C22⋊C8C23×C8911yescharacteristic
448C22⋊C8C23×C8913yes—
449C22⋊C8C23×C8911yescharacteristic
450C22⋊C8C23×C8913yes—
451C22⋊C8C23×C8913yes—
452C22⋊C8C23×C8913yes—
453C22⋊C8C23×C8916yes—
454#97C23×C8911yescharacteristic
455#97C23×C8913yes—
456#97C23×C8913yes—
457#97C23×C8913yes—
458#97C23×C8916yes—
459C4×C8C23×C8913yes—
460C4×C8C23×C8913yes—
461C4×C8C23×C8913yes—
462C4×C8C23×C8913yes—
463C4×C8C23×C8913yes—
464C4×C8C23×C8913yes—
465C4×C8C23×C8916yes—
466#41—24no—
467#41—46no—
468C2×Q8—24no—
469C2×Q8—24no—
470C2×Q8C22×C4×C8913yes—
471C2×Q8C22×C4×C8913yes—
472C2×Q8C22×C4×C8913yes—
473C2×Q8C22×C4×C8911yescharacteristic
474C2×D4C22×C4×C8911yescharacteristic
475C2×D4C22×C4×C8913yes—
476C2×D4C22×C4×C8913yes—
477C2×D4C22×C4×C8913yes—
478C22×C4C22×C4×C8913yes—
479C22×C4C22×C4×C8913yes—
480C22×C4C22×C4×C8913yes—
481C22×C4C22×C4×C8913yes—
482C22×C4C22×C4×C8913yes—
483C22×C4C22×C4×C8913yes—
484C22×C4C24×C8911yescharacteristic
485C22×C4C24×C8911yescharacteristic
486C22×C4C24×C8913yes—
487M16—22no—
488M16—26no—
489M16—43no—
490M16—43no—
491C2×C8—22no—
492C2×C8—46no—
493C2×C8—43no—
494C2×C8C24×C8911yescharacteristic
495C2×C8C24×C8913yes—
496C2×C8C24×C8911yescharacteristic
497C2×C8C24×C8913yes—
498C2×C8C24×C8911yescharacteristic
499C2×C8C24×C8913yes—
500C2×C8C24×C8913yes—
501C2×C8C24×C8911yescharacteristic
502C4⋊C4C22×C4×C8913yes—
503C4⋊C4C22×C4×C8913yes—
504C4⋊C4C22×C4×C8913yes—
505C4⋊C4C22×C4×C8916yes—
506C4⋊C4C22×C4×C8916yes—
507C4⋊C4C22×C4×C8911yescharacteristic
508C4⋊C4C22×C4×C8913yes—
509C4⋊C4C22×C4×C8913yes—
510C4⋊C4C22×C4×C8913yes—
511C4⋊C4C22×C4×C8913yes—
512C4⋊C4C22×C4×C8913yes—
513C4⋊C4C22×C4×C8913yes—
514C4⋊C4C22×C4×C8916yes—
515C4⋊C4C22×C4×C8916yes—
516C22⋊C4C22×C4×C8911yescharacteristic
517C22⋊C4C22×C4×C8911yescharacteristic
518C22⋊C4C22×C4×C8913yes—
519C22⋊C4C22×C4×C8913yes—
520C22⋊C4C22×C4×C8916yes—
521C22⋊C4C22×C4×C8913yes—
522C22⋊C4C22×C4×C8913yes—
523C22⋊C4C22×C4×C8916yes—
524C22⋊C4C22×C4×C8916yes—
525C42C22×C4×C8913yes—
526C42C22×C4×C8913yes—
527C42C22×C4×C8913yes—
528C42C22×C4×C8913yes—
529C42C22×C4×C8913yes—
530C42C22×C4×C8913yes—
531C42C24×C8913yes—
532C42C24×C8913yes—
533C42C24×C8913yes—
534C42C24×C8911yescharacteristic
535C23C23×C4×C8913yes—
536C23C23×C4×C8911yescharacteristic
537C23C23×C4×C8911yescharacteristic
538Q8—26no—
539Q8—26no—
540Q8—43no—
541Q8#131×C8914yes—
542D4—26no—
543D4—22no—
544D4—26no—
545D4—43no—
546C2×C4—26no—
547C2×C4—26no—
548C2×C4—26no—
549C2×C4—26no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—23no—
553C2×C4—21no—
554C2×C4—23no—
555C2×C4—21no—
556C2×C4—43no—
557C2×C4—43no—
558C2×C4C23×C4×C8911yescharacteristic
559C2×C4C23×C4×C8911yescharacteristic
560C2×C4C23×C4×C8911yescharacteristic
561C2×C4C23×C4×C8913yes—
562C2×C4C23×C4×C8911yescharacteristic
563C2×C4C23×C4×C8913yes—
564C2×C4C23×C4×C8913yes—
565C2×C4C23×C4×C8913yes—
566C2×C4C23×C4×C8913yes—
567C2×C4C23×C4×C8913yes—
568C2×C4C23×C4×C8913yes—
569C2×C4C25×C8911yescharacteristic
570C8—21no—
571C8—21no—
572C8—23no—
573C8—23no—
574C8—23no—
575C8—23no—
576C8—21no—
577C82−1+4×C8912yes—
578C22—21no—
579C22—21no—
580C22—23no—
581C22—21no—
582C22—21no—
583C22—23no—
584C22—21no—
585C22—23no—
586C22#568×C8912yes—
587C22C24×C4×C8911yescharacteristic
588C4—21no—
589C4—23no—
590C4—21no—
591C4—21no—
592C4—23no—
593C4—23no—
594C4—23no—
595C4—23no—
596C4—21no—
597C4—23no—
598C4C2×#131×C8916yes—
599C4C2×2−1+4×C8911yescharacteristic
600C4#585×C8911yescharacteristic
601C2—22no—
602C2—41no—
603C2—43no—
604C2C4×2−1+4×C8911yescharacteristic
605C2C22×#131×C8911yescharacteristic
606C2C2×#568×C8911yescharacteristic
subgroupG/H
centerC2×C4×C89C25
commutatorC22C24×C4×C89
Frattini, cosocleC2×C4C25×C89
socleC22×C89C24×C4
prime radicalC89×#3482C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C89×#2994C2semidirect
3. C89×#2993C2semidirect
4. C89×#2990C2semidirect
5. C89×#2988C2semidirect
6. C89×#2985C2semidirect
7. C89×#2984C2semidirect
8. C89×#2982C2semidirect
9. C89×#2971C2semidirect
10. C89×#2969C2semidirect
11. C89×#2966C2semidirect
12. C89×#2965C2semidirect
13. Q8×M16×C89C2semidirect
14. C89×#2962C2semidirect
15. C2×C8×Q8×C89C2semidirect
297. #60335C89direct (N × H)
305. #2994C2×C89semidirect
306. #2993C2×C89semidirect
307. #2990C2×C89semidirect
308. #2988C2×C89semidirect
309. #2985C2×C89semidirect
310. #2984C2×C89semidirect
311. #2982C2×C89semidirect
312. #2971C2×C89semidirect
313. #2969C2×C89semidirect
314. #2966C2×C89semidirect
315. #2965C2×C89semidirect
316. Q8×M16C2×C89semidirect
317. #2962C2×C89semidirect
318. C2×C8×Q8C2×C89semidirect
319. C89#60335direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#34822
C89×#29942
C89×#29932
C89×#29902
C89×#29882
C89×#29852
C89×#29842
C89×#29822
C89×#29712
C89×#29692
C89×#29662
C89×#29652
Q8×M16×C892
C89×#29622
C2×C8×Q8×C892
#6033589