Finite Group Databasebeta

← C2×#26019673 #36536711

Subgroups — C2×#26019673 #36536711

Order 22784.

758 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151948C211yesmaximal, characteristic, complemented
2C2×#19151803C211yesmaximal, characteristic
3C2×D4×#10623494C211yesmaximal, characteristic
4#26019673C218yesmaximal, direct product factor
5C2×#19151348C211yesmaximal, characteristic, complemented
6C2×#19151345C211yesmaximal, characteristic, complemented
7C2×#19151344C211yesmaximal, characteristic, complemented
8C2×#474×C89C211yesmaximal, characteristic
9C22×#13083562—21no—
10C23×#10623494—21no—
11C2×#15668012C2211yescharacteristic
12#19151948—22no—
13#19151948C2214yescomplemented
14#19151803—22no—
15#19151803C2214yes—
16D4×#10623494—22no—
17D4×#10623494C2214yes—
18C2×C4⋊#10623494C2211yescharacteristic
19C2×C4⋊#10623494C2211yescharacteristic
20C2×#15667936—21no—
21C2×#15667936—21no—
22C2×#15667935—21no—
23C2×C22⋊#10623494—21no—
24C2×C4×#10623494C2211yescharacteristic
25#19151348C2214yescomplemented
26#19151345C2214yescomplemented
27#19151344C2214yescomplemented
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×#13083562—24no—
37C2×#13083562—44no—
38C22×#10623494—24no—
39C22×#10623494—21no—
40C22×#10623494—21no—
41C22×#10623494—44no—
42C22×#10623494D411yescharacteristic
43C22×#10623494D411yescharacteristic
44#15668012—21no—
45#15668012—21no—
46#15668012—21no—
47#15668012C2312yes—
48C2×C4⋊Dic89—21no—
49C2×C4⋊Dic89—21no—
50C4⋊#10623494—21no—
51C4⋊#10623494—21no—
52C4⋊#10623494C2312yes—
53C4⋊#10623494C2312yes—
54#15667936—24no—
55#15667936—24no—
56#15667935—24no—
57C22⋊#10623494—24no—
58C4×#10623494D412yes—
59C4×#10623494C2312yes—
60C22×Q8×C89—21no—
61C22×D4×C89D411yescharacteristic
62C23×C4×C89—21no—
63C22×C8×C89—21no—
64C4⋊Q8×C89—21no—
65C4⋊Q8×C89—21no—
66C4⋊Q8×C89—21no—
67C4⋊Q8×C89C2312yes—
68C4×D4×C89—21no—
69C4×D4×C89—21no—
70C4×D4×C89D412yes—
71C4×D4×C89C2312yes—
72C2×C4⋊C4×C89—21no—
73C2×C4⋊C4×C89—21no—
74C2×C4⋊C4×C89D411yescharacteristic
75C2×C22⋊C4×C89—21no—
76C2×C42×C89C2311yescharacteristic
77#107×C89—24no—
78C4⋊C8×C89—21no—
79C4⋊C8×C89C2312yes—
80#102×C89—24no—
81C2×Dic178—22no—
82C2×Dic178—42no—
83C2×Dic178—42no—
84C2×Dic178—41no—
85C22×Dic89—41no—
86#13083562—48no—
87C2×#10623494—22no—
88C2×#10623494—22no—
89C2×#10623494—22no—
90C2×#10623494—22no—
91C2×#10623494—48no—
92C2×#10623494—42no—
93C2×#10623494—42no—
94C2×#10623494C2×D412yes—
95C2×#10623494C2×D412yes—
96C4⋊Dic89—22no—
97C4⋊Dic89—22no—
98C4⋊Dic89—41no—
99C4⋊Dic89—41no—
100C24×C89—21no—
101C2×Q8×C89—22no—
102C2×Q8×C89—41no—
103C2×Q8×C89—42no—
104C2×Q8×C89—42no—
105C2×D4×C89—21no—
106C2×D4×C89—22no—
107C2×D4×C89SD1614yes—
108C2×D4×C89C2×D412yes—
109C22×C4×C89—21no—
110C22×C4×C89—22no—
111C22×C4×C89—22no—
112C22×C4×C89—42no—
113C22×C4×C89—42no—
114C22×C4×C89—41no—
115C22×C4×C89C2×D411yescharacteristic
116C22×C4×C89C2×D411yescharacteristic
117C22×C4×C89#4111yescharacteristic
118C2×C8×C89—22no—
119C2×C8×C89—42no—
120C4⋊C4×C89—21no—
121C4⋊C4×C89—22no—
122C4⋊C4×C89—22no—
123C4⋊C4×C89—41no—
124C4⋊C4×C89—41no—
125C4⋊C4×C89C2×D412yes—
126C22⋊C4×C89—22no—
127C22⋊C4×C89—22no—
128C42×C89C2×D411yescharacteristic
129C42×C89C2×D411yescharacteristic
130C42×C89#4111yescharacteristic
131C42×C89C2411yescharacteristic
132C23×C89—22no—
133C23×C89—24no—
134C23×C89—42no—
135C23×C89—42no—
136C23×C89#12111yescharacteristic
137Q8×C89—42no—
138Q8×C89—42no—
139Q8×C89—82no—
140D4×C89—22no—
141D4×C89—24no—
142D4×C89C2×SD1614yes—
143C2×C4×C89—22no—
144C2×C4×C89—22no—
145C2×C4×C89—42no—
146C2×C4×C89—42no—
147C2×C4×C89—42no—
148C2×C4×C89—44no—
149C2×C4×C89—42no—
150C2×C4×C89—82no—
151C2×C4×C89#12111yescharacteristic
152C2×C4×C89#12111yescharacteristic
153C2×C4×C89#12111yescharacteristic
154C2×C4×C89C2×SD1612yes—
155C2×C4×C89#13512yes—
156C2×C4×C89#13512yes—
157C2×C4×C89AGL(1,ℤ/8)12yes—
158C2×C4×C89C22×D411yescharacteristic
159C2×C4×C89C22×D411yescharacteristic
160C2×C4×C89C2×#4111yescharacteristic
161C2×Dic89—42no—
162C2×Dic89—82no—
163Dic178—42no—
164Dic178—42no—
165Dic178—82no—
166C8×C89—42no—
167#10623494—22no—
168#10623494—22no—
169#10623494—42no—
170#10623494—42no—
171C22×C89—24no—
172C22×C89—48no—
173C22×C89—42no—
174C22×C89—42no—
175C22×C89#46312yes—
176C22×C89#46512yes—
177C22×C89#47312yes—
178C22×C89C2×#12111yescharacteristic
179C4×C89—21no—
180C4×C89—21no—
181C4×C89—42no—
182C4×C89—82no—
183C4×C89#46312yes—
184C4×C89#46512yes—
185C4×C89C22×SD1611yescharacteristic
186C4×C89C2×#13511yescharacteristic
187C4×C89C2×#13511yescharacteristic
188C4×C89C2×AGL(1,ℤ/8)11yescharacteristic
189Dic89—82no—
190C2×#1679—891nomaximal, Sylow
191C2×C89—44no—
192C2×C89#167914yescomplemented
193C2×C89C2×#46311yescharacteristic
194C2×C89C2×#46511yescharacteristic
195C2×C89C2×#47311yescharacteristic
196C2×#487—891no—
197C2×#474D8911yescharacteristic
198C2×#461—891no—
199C2×C8×D4—891no—
200#1679—898no—
201C2×#334—891no—
202C2×#332—891no—
203C2×#332—891no—
204C89C2×#167911yescharacteristic, complemented, Sylow
205C22×SD16—1781no—
206C23×C8—1781no—
207C2×C4⋊Q8—891no—
208C2×C4⋊Q8C2×D8911yescharacteristic
209C2×C4×D4C2×D8911yescharacteristic
210#487—894no—
211#487—1782no—
212#474—22no—
213#474C2×D8914yes—
214#461—894no—
215#461—1782no—
216C8×D4—894no—
217C8×D4—1782no—
218C2×#107—21no—
219C2×C4⋊C8—891no—
220C2×C4⋊C8—891no—
221C2×C4⋊C8C2×D8911yescharacteristic
222C2×#103—1781no—
223C2×#103—1781no—
224C2×#103—1781no—
225C2×#102—21no—
226C2×C22⋊C8—1781no—
227C2×C4×C8—891no—
228#334—894no—
229#332—894no—
230#332—894no—
231C22×Q8—21no—
232C22×Q8—1781no—
233C22×D4C22⋊D8911yescharacteristic
234C23×C4—21no—
235C2×SD16—3564no—
236C2×SD16—1784no—
237C22×C8—21no—
238C22×C8—891no—
239C22×C8—891no—
240C22×C8—3564no—
241C22×C8—1784no—
242C22×C8—1781no—
243C22×C8—1781no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—892no—
248C4⋊Q8—1781no—
249C4⋊Q8—1781no—
250C4⋊Q8—1781no—
251C4⋊Q8C22×D8912yes—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4C22⋊D8912yes—
255C4×D4C22×D8912yes—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—1781no—
259C2×C4⋊C4—1781no—
260C2×C4⋊C4C22⋊D8911yescharacteristic
261C2×C22⋊C4—21no—
262C2×C42C22×D8911yescharacteristic
263#107—24no—
264C4⋊C8—21no—
265C4⋊C8—892no—
266C4⋊C8—892no—
267C4⋊C8—1781no—
268C4⋊C8—1781no—
269C4⋊C8C22×D8912yes—
270#103—1784no—
271#103—1784no—
272#103—1784no—
273#102—24no—
274C22⋊C8—1784no—
275C4×C8—892no—
276C4×C8—892no—
277C24—21no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—3561no—
283C2×Q8—3562no—
284C2×Q8—3562no—
285C2×Q8—1782no—
286C2×D4—21no—
287C2×D4—22no—
288C2×D4#1308356114yes—
289C2×D4C2×C22⋊D8912yes—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4—3561no—
297C22×C4D4×D8911yescharacteristic
298C22×C4C2×C22⋊D8911yescharacteristic
299C22×C4#1308357311yescharacteristic
300SD16—3568no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—892no—
304C2×C8—892no—
305C2×C8—3562no—
306C2×C8—3562no—
307C2×C8—3568no—
308C2×C8—1782no—
309C2×C8—1782no—
310C2×C8—1782no—
311C2×C8—1782no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—3561no—
318C4⋊C4—3561no—
319C4⋊C4—1782no—
320C4⋊C4—1782no—
321C4⋊C4C2×C22⋊D8912yes—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C42D4×D8911yescharacteristic
325C42C2×C22⋊D8911yescharacteristic
326C42#1308357311yescharacteristic
327C42C23×D8911yescharacteristic
328C23—24no—
329C23—22no—
330C23—42no—
331C23—42no—
332C23#1566798411yescharacteristic
333Q8—42no—
334Q8—42no—
335Q8—82no—
336Q8—3562no—
337Q8—3562no—
338Q8—7122no—
339D4—24no—
340D4—22no—
341D4C2×#1308356114yes—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—3562no—
351C2×C4—7122no—
352C2×C4#1566798411yescharacteristic
353C2×C4#1566798411yescharacteristic
354C2×C4#1566798411yescharacteristic
355C2×C4C2×#1308356112yes—
356C2×C4#1566803112yes—
357C2×C4#1566803212yes—
358C2×C4#1566803612yes—
359C2×C4C2×D4×D8911yescharacteristic
360C2×C4C22×C22⋊D8911yescharacteristic
361C2×C4C2×#1308357311yescharacteristic
362C8—42no—
363C8—3562no—
364C8—3562no—
365C8—1782no—
366C8—1782no—
367C22—24no—
368C22—48no—
369C22—42no—
370C22—42no—
371C22#1915181112yes—
372C22#1915182912yes—
373C22#1915187112yes—
374C22C2×#1566798411yescharacteristic
375C4—21no—
376C4—21no—
377C4—42no—
378C4—82no—
379C4—7122no—
380C4#1915181112yes—
381C4#1915182912yes—
382C4C22×#1308356111yescharacteristic
383C4C2×#1566803111yescharacteristic
384C4C2×#1566803211yescharacteristic
385C4C2×#1566803611yescharacteristic
386C2—44no—
387C2#2601967314yesdirect product factor
388C2C2×#1915181111yescharacteristic
389C2C2×#1915182911yescharacteristic
390C2C2×#1915187111yescharacteristic
subgroupG/H
centerC23#15667984
commutator, cosocleC42×C89C24
FrattiniC42C23×D89
FittingC2×#474×C89C2
socleC23×C89#121
prime radicalC22×D4×C89D4
hypercenterC2×#474D89
hypocenterC89C2×#1679
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×#19151948C2semidirect
4. #26019673C2direct (N × H)
5. C2×#19151348C2semidirect
6. C2×#19151345C2semidirect
7. C2×#19151344C2semidirect
13. #19151948C22semidirect
25. #19151348C22semidirect
26. #19151345C22semidirect
27. #19151344C22semidirect
192. C2×C89#1679semidirect
204. C89C2×#1679semidirect
387. C2#26019673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191519482
C2×#191518032
C2×D4×#106234942
#260196732
C2×#191513482
C2×#191513452
C2×#191513442
C2×#474×C892
C2×#167989