Finite Group Databasebeta

← C2×#26019739 #36536933

Subgroups — C2×#26019739 #36536933

Order 22784.

758 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151977C211yesmaximal, characteristic, complemented
2C2×#19151878C211yesmaximal, characteristic
3C2×#19151676C211yesmaximal, characteristic
4#26019739C218yesmaximal, direct product factor
5C2×#19151348C211yesmaximal, characteristic, complemented
6C2×#19151344C211yesmaximal, characteristic, complemented
7C2×#19151343C211yesmaximal, characteristic, complemented
8C2×#474×C89C211yesmaximal, characteristic
9C22×#13083564—21no—
10C22×#13083564—21no—
11C22×#13083558—21no—
12C2×#15668012C2211yescharacteristic
13#19151977—22no—
14#19151977C2214yescomplemented
15#19151878—22no—
16#19151878C2214yes—
17#19151676—22no—
18#19151676C2214yes—
19C2×#15667945—21no—
20C2×C4⋊#10623494C2211yescharacteristic
21C2×C4⋊#10623494C2211yescharacteristic
22C2×#15667933—21no—
23C2×C22⋊#10623494—21no—
24C2×C4×#10623494C2211yescharacteristic
25#19151348C2214yescomplemented
26#19151344C2214yescomplemented
27#19151343C2214yescomplemented
28C2×C4⋊Q8×C89C2211yescharacteristic
29C2×C4×D4×C89C2211yescharacteristic
30#474×C89—22no—
31#474×C89C2214yes—
32C2×#107×C89—21no—
33C2×C4⋊C8×C89C2211yescharacteristic
34C2×#102×C89—21no—
35C22×Dic178—21no—
36C2×#13083564—24no—
37C2×#13083564—24no—
38C2×#13083564—44no—
39C2×#13083564—44no—
40C2×#13083558—24no—
41C2×#13083558—44no—
42C22×#10623494—21no—
43C22×#10623494—21no—
44C22×#10623494D411yescharacteristic
45C22×#10623494D411yescharacteristic
46#15668012—21no—
47#15668012—21no—
48#15668012—21no—
49#15668012C2312yes—
50C2×C4⋊Dic89—21no—
51C2×C4⋊Dic89—21no—
52#15667945—24no—
53C4⋊#10623494—21no—
54C4⋊#10623494—21no—
55C4⋊#10623494C2312yes—
56C4⋊#10623494C2312yes—
57#15667933—24no—
58C22⋊#10623494—24no—
59C4×#10623494D412yes—
60C4×#10623494C2312yes—
61C22×Q8×C89—21no—
62C22×D4×C89D411yescharacteristic
63C23×C4×C89—21no—
64C22×C8×C89—21no—
65C4⋊Q8×C89—21no—
66C4⋊Q8×C89—21no—
67C4⋊Q8×C89—21no—
68C4⋊Q8×C89C2312yes—
69C4×D4×C89—21no—
70C4×D4×C89—21no—
71C4×D4×C89D412yes—
72C4×D4×C89C2312yes—
73C2×C4⋊C4×C89—21no—
74C2×C4⋊C4×C89—21no—
75C2×C4⋊C4×C89D411yescharacteristic
76C2×C22⋊C4×C89—21no—
77C2×C42×C89C2311yescharacteristic
78#107×C89—24no—
79C4⋊C8×C89—21no—
80C4⋊C8×C89C2312yes—
81#102×C89—24no—
82C2×Dic178—22no—
83C2×Dic178—42no—
84C2×Dic178—42no—
85C2×Dic178—41no—
86C22×Dic89—41no—
87#13083564—48no—
88#13083564—48no—
89#13083558—48no—
90C2×#10623494—22no—
91C2×#10623494—22no—
92C2×#10623494—22no—
93C2×#10623494—42no—
94C2×#10623494—42no—
95C2×#10623494D814yes—
96C2×#10623494C2×D412yes—
97C2×#10623494C2×D412yes—
98C4⋊Dic89—22no—
99C4⋊Dic89—22no—
100C4⋊Dic89—41no—
101C4⋊Dic89—41no—
102C24×C89—21no—
103C2×Q8×C89—22no—
104C2×Q8×C89—41no—
105C2×Q8×C89—42no—
106C2×Q8×C89—42no—
107C2×D4×C89—21no—
108C2×D4×C89—22no—
109C2×D4×C89—22no—
110C2×D4×C89C2×D412yes—
111C22×C4×C89—21no—
112C22×C4×C89—22no—
113C22×C4×C89—22no—
114C22×C4×C89—42no—
115C22×C4×C89—42no—
116C22×C4×C89—41no—
117C22×C4×C89C2×D411yescharacteristic
118C22×C4×C89C2×D411yescharacteristic
119C22×C4×C89#4111yescharacteristic
120C2×C8×C89—22no—
121C2×C8×C89—42no—
122C4⋊C4×C89—21no—
123C4⋊C4×C89—22no—
124C4⋊C4×C89—22no—
125C4⋊C4×C89—41no—
126C4⋊C4×C89—41no—
127C4⋊C4×C89C2×D412yes—
128C22⋊C4×C89—22no—
129C22⋊C4×C89—22no—
130C42×C89C2×D411yescharacteristic
131C42×C89C2×D411yescharacteristic
132C42×C89#4111yescharacteristic
133C42×C89C2411yescharacteristic
134C23×C89—22no—
135C23×C89—42no—
136C23×C89—42no—
137C23×C89—42no—
138C23×C89#12111yescharacteristic
139Q8×C89—42no—
140Q8×C89—42no—
141Q8×C89—82no—
142D4×C89—22no—
143D4×C89—22no—
144D4×C89—42no—
145C2×C4×C89—22no—
146C2×C4×C89—22no—
147C2×C4×C89—42no—
148C2×C4×C89—42no—
149C2×C4×C89—42no—
150C2×C4×C89—44no—
151C2×C4×C89—42no—
152C2×C4×C89—82no—
153C2×C4×C89#12111yescharacteristic
154C2×C4×C89#12111yescharacteristic
155C2×C4×C89#12111yescharacteristic
156C2×C4×C89C2×D812yes—
157C2×C4×C89AGL(1,ℤ/8)12yes—
158C2×C4×C89#13712yes—
159C2×C4×C89#13712yes—
160C2×C4×C89C22×D411yescharacteristic
161C2×C4×C89C22×D411yescharacteristic
162C2×C4×C89C2×#4111yescharacteristic
163C2×Dic89—42no—
164C2×Dic89—82no—
165Dic178—42no—
166Dic178—42no—
167Dic178—82no—
168C8×C89—42no—
169#10623494—22no—
170#10623494—42no—
171#10623494—42no—
172#10623494C2×D814yes—
173C22×C89—42no—
174C22×C89—42no—
175C22×C89—42no—
176C22×C89—84no—
177C22×C89#45912yes—
178C22×C89#47012yes—
179C22×C89#47312yes—
180C22×C89C2×#12111yescharacteristic
181C4×C89—21no—
182C4×C89—21no—
183C4×C89—42no—
184C4×C89—82no—
185C4×C89#45912yes—
186C4×C89#47012yes—
187C4×C89C22×D811yescharacteristic
188C4×C89C2×AGL(1,ℤ/8)11yescharacteristic
189C4×C89C2×#13711yescharacteristic
190C4×C89C2×#13711yescharacteristic
191Dic89—82no—
192C2×#1689—891nomaximal, Sylow
193C2×C89—82no—
194C2×C89#168914yescomplemented
195C2×C89C2×#45911yescharacteristic
196C2×C89C2×#47011yescharacteristic
197C2×C89C2×#47311yescharacteristic
198C2×#494—891no—
199C2×#474—891no—
200C2×#474D8911yescharacteristic
201C2×#436—891no—
202#1689—898no—
203C2×#334—891no—
204C2×#332—891no—
205C2×#332—891no—
206C89C2×#168911yescharacteristic, complemented, Sylow
207C22×Q16—1781no—
208C22×Q16—1781no—
209C22×M16—1781no—
210C2×C4⋊Q8—891no—
211C2×C4⋊Q8C2×D8911yescharacteristic
212C2×C4×D4C2×D8911yescharacteristic
213#494—894no—
214#494—1782no—
215#474—22no—
216#474—894no—
217#474—1782no—
218#474C2×D8914yes—
219#436—894no—
220#436—1782no—
221C2×#107—21no—
222C2×#107—1781no—
223C2×C4⋊C8—891no—
224C2×C4⋊C8—891no—
225C2×C4⋊C8C2×D8911yescharacteristic
226C2×#102—21no—
227C2×#102—1781no—
228C2×C22⋊C8—1781no—
229C2×C4×C8—891no—
230#334—894no—
231#332—894no—
232#332—894no—
233C22×Q8—21no—
234C22×Q8—1781no—
235C22×D4C22⋊D8911yescharacteristic
236C23×C4—21no—
237C2×Q16—3564no—
238C2×Q16—3564no—
239C2×Q16—1784no—
240C2×Q16—1784no—
241C2×M16—3564no—
242C2×M16—1784no—
243C22×C8—21no—
244C22×C8—891no—
245C22×C8—891no—
246C22×C8—1781no—
247C22×C8—1781no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—892no—
252C4⋊Q8—1781no—
253C4⋊Q8—1781no—
254C4⋊Q8—1781no—
255C4⋊Q8C22×D8912yes—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C22⋊D8912yes—
259C4×D4C22×D8912yes—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—1781no—
263C2×C4⋊C4—1781no—
264C2×C4⋊C4C22⋊D8911yescharacteristic
265C2×C22⋊C4—21no—
266C2×C42C22×D8911yescharacteristic
267#107—24no—
268#107—1784no—
269C4⋊C8—21no—
270C4⋊C8—892no—
271C4⋊C8—892no—
272C4⋊C8—1781no—
273C4⋊C8—1781no—
274C4⋊C8C22×D8912yes—
275#102—24no—
276#102—1784no—
277C22⋊C8—1784no—
278C4×C8—892no—
279C4×C8—892no—
280C24—21no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—3561no—
286C2×Q8—3562no—
287C2×Q8—3562no—
288C2×Q8—1782no—
289C2×D4—21no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4C2×C22⋊D8912yes—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—41no—
299C22×C4—3561no—
300C22×C4D4×D8911yescharacteristic
301C22×C4C2×C22⋊D8911yescharacteristic
302C22×C4#1308357311yescharacteristic
303Q16—3568no—
304Q16—3568no—
305M16—3568no—
306C2×C8—22no—
307C2×C8—42no—
308C2×C8—894no—
309C2×C8—892no—
310C2×C8—892no—
311C2×C8—3562no—
312C2×C8—3562no—
313C2×C8—1782no—
314C2×C8—1782no—
315C2×C8—1782no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—3561no—
322C4⋊C4—3561no—
323C4⋊C4—1782no—
324C4⋊C4—1782no—
325C4⋊C4C2×C22⋊D8912yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C42D4×D8911yescharacteristic
329C42C2×C22⋊D8911yescharacteristic
330C42#1308357311yescharacteristic
331C42C23×D8911yescharacteristic
332C23—22no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23#1566798411yescharacteristic
337Q8—42no—
338Q8—42no—
339Q8—82no—
340Q8—3562no—
341Q8—3562no—
342Q8—7122no—
343D4—22no—
344D4—22no—
345D4—42no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—82no—
354C2×C4—3562no—
355C2×C4—7122no—
356C2×C4#1566798411yescharacteristic
357C2×C4#1566798411yescharacteristic
358C2×C4#1566798411yescharacteristic
359C2×C4D8×D8912yes—
360C2×C4#1566803612yes—
361C2×C4#1566804212yes—
362C2×C4#1566804312yes—
363C2×C4C2×D4×D8911yescharacteristic
364C2×C4C22×C22⋊D8911yescharacteristic
365C2×C4C2×#1308357311yescharacteristic
366C8—42no—
367C8—894no—
368C8—3562no—
369C8—3562no—
370C8—1782no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—84no—
375C22#1915179112yes—
376C22#1915185412yes—
377C22#1915187112yes—
378C22C2×#1566798411yescharacteristic
379C4—21no—
380C4—21no—
381C4—42no—
382C4—82no—
383C4—7122no—
384C4#1915179112yes—
385C4#1915185412yes—
386C4C2×D8×D8911yescharacteristic
387C4C2×#1566803611yescharacteristic
388C4C2×#1566804211yescharacteristic
389C4C2×#1566804311yescharacteristic
390C2—82no—
391C2#2601973914yesdirect product factor
392C2C2×#1915179111yescharacteristic
393C2C2×#1915185411yescharacteristic
394C2C2×#1915187111yescharacteristic
subgroupG/H
centerC23#15667984
commutator, cosocleC42×C89C24
FrattiniC42C23×D89
FittingC2×#474×C89C2
socleC23×C89#121
prime radicalC22×D4×C89D4
hypercenterC2×#474D89
hypocenterC89C2×#1689
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#19151977C2semidirect
4. #26019739C2direct (N × H)
5. C2×#19151348C2semidirect
6. C2×#19151344C2semidirect
7. C2×#19151343C2semidirect
14. #19151977C22semidirect
25. #19151348C22semidirect
26. #19151344C22semidirect
27. #19151343C22semidirect
194. C2×C89#1689semidirect
206. C89C2×#1689semidirect
391. C2#26019739direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191519772
C2×#191518782
C2×#191516762
#260197392
C2×#191513482
C2×#191513442
C2×#191513432
C2×#474×C892
C2×#168989