Finite Group Databasebeta

← C2×#26018237 #36464569

Subgroups — C2×#26018237 #36464569

Order 22784.

496 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151380C211yesmaximal, characteristic, complemented
2C2×#19151355C211yesmaximal, characteristic, complemented
3#26018237C214yesmaximal, direct product factor
4C2×#469×C89C211yesmaximal, characteristic
5C2×#15667971—21no—
6C2×#15667952—21no—
7#19151380—21no—
8#19151380C2212yescomplemented
9#19151355—21no—
10#19151355C2212yescomplemented
11C22×D8×C89C411yescharacteristic, complemented
12C22×M16×C89C2211yescharacteristic
13C2×#121×C89—21no—
14#469×C89—21no—
15#469×C89—21no—
16#469×C89C412yescomplemented
17#469×C89C2212yes—
18C2×#106×C89C411yescharacteristic, complemented
19C2×#102×C89—21no—
20#15667971—22no—
21#15667971—22no—
22#15667971—41no—
23#15667971—41no—
24C2×C4⋊Dic89—41no—
25C2×C22⋊Dic89—41no—
26C2×C4×Dic89—22no—
27#15667952—22no—
28#15667952—41no—
29C2×#13083549—41no—
30C22×D4×C89—21no—
31C22×D4×C89—41no—
32C23×C4×C89D411yescharacteristic
33C2×D8×C89—21no—
34C2×D8×C89—41no—
35C2×D8×C89—41no—
36C2×D8×C89C2×C412yescomplemented
37C2×M16×C89—41no—
38C2×M16×C89—41no—
39C2×M16×C89C2×C411yescharacteristic
40C2×M16×C89D411yescharacteristic
41C2×M16×C89D411yescharacteristic
42C2×M16×C89C2311yescharacteristic
43C22×C8×C89C2×C411yescharacteristic
44C22×C8×C89D411yescharacteristic
45#121×C89—22no—
46#121×C89—22no—
47#121×C89—41no—
48#121×C89—41no—
49C2×C4⋊C4×C89—21no—
50C2×C22⋊C4×C89—41no—
51#106×C89—21no—
52#106×C89C2×C412yescomplemented
53#102×C89—22no—
54#102×C89—22no—
55C22×Dic89—42no—
56C4⋊Dic89—42no—
57C4⋊Dic89—42no—
58C22⋊Dic89—42no—
59C22⋊Dic89—42no—
60C4×Dic89—24no—
61C4×Dic89—42no—
62#13083549—42no—
63C24×C89—41no—
64C24×C89D811yescharacteristic
65C2×D4×C89—22no—
66C2×D4×C89—42no—
67C2×D4×C89—42no—
68C2×D4×C89—41no—
69C2×D4×C89—41no—
70C2×D4×C89—41no—
71C2×D4×C89—41no—
72C2×D4×C89—41no—
73C2×D4×C89—84no—
74C22×C4×C89—21no—
75C22×C4×C89—21no—
76C22×C4×C89—21no—
77C22×C4×C89—21no—
78C22×C4×C89—41no—
79C22×C4×C89C22⋊C411yescharacteristic
80C22×C4×C89C22⋊C411yescharacteristic
81C22×C4×C89D811yescharacteristic
82C22×C4×C89SD1611yescharacteristic
83C22×C4×C89SD1611yescharacteristic
84C22×C4×C89C2×D411yescharacteristic
85D8×C89—42no—
86D8×C89—42no—
87M16×C89—41no—
88M16×C89—41no—
89M16×C89—41no—
90M16×C89—41no—
91C2×C8×C89—21no—
92C2×C8×C89—21no—
93C2×C8×C89—21no—
94C2×C8×C89—21no—
95C2×C8×C89C22⋊C411yescharacteristic
96C2×C8×C89C22⋊C411yescharacteristic
97C2×C8×C89C22×C411yescharacteristic
98C2×C8×C89C2×D411yescharacteristic
99C4⋊C4×C89—22no—
100C4⋊C4×C89—41no—
101C22⋊C4×C89—42no—
102C22⋊C4×C89—42no—
103C23×C89—21no—
104C23×C89—21no—
105C23×C89—42no—
106C23×C89—42no—
107C23×C89—82no—
108C23×C89—82no—
109C23×C89—81no—
110C23×C89—81no—
111C23×C89#10211yescharacteristic
112C23×C89#10211yescharacteristic
113C23×C89C2×D811yescharacteristic
114D4×C89—42no—
115D4×C89—42no—
116D4×C89—84no—
117D4×C89—84no—
118D4×C89—81no—
119D4×C89—81no—
120C2×C4×C89—21no—
121C2×C4×C89—21no—
122C2×C4×C89—21no—
123C2×C4×C89—21no—
124C2×C4×C89—21no—
125C2×C4×C89—21no—
126C2×C4×C89—21no—
127C2×C4×C89—21no—
128C2×C4×C89—21no—
129C2×C4×C89—21no—
130C2×C4×C89—42no—
131C2×C4×C89—82no—
132C2×C4×C89#9911yescharacteristic
133C2×C4×C89#9911yescharacteristic
134C2×C4×C89#10211yescharacteristic
135C2×C4×C89#10211yescharacteristic
136C2×C4×C89#10411yescharacteristic
137C2×C4×C89#10411yescharacteristic
138C2×C4×C89C2×C22⋊C411yescharacteristic
139C2×C4×C89C2×SD1611yescharacteristic
140C2×Dic89—44no—
141C2×Dic89—84no—
142C8×C89—21no—
143C8×C89—21no—
144C8×C89—21no—
145C8×C89—21no—
146C22×C89—22no—
147C22×C89—21no—
148C22×C89—21no—
149C22×C89—41no—
150C22×C89—41no—
151C22×C89—42no—
152C22×C89—81no—
153C22×C89—82no—
154C22×C89—82no—
155C22×C89—82no—
156C22×C89—162no—
157C22×C89—162no—
158C22×C89#32711yescharacteristic
159C22×C89#32711yescharacteristic
160C22×C89C2×#10211yescharacteristic
161C4×C89—21no—
162C4×C89—21no—
163C4×C89—82no—
164C4×C89#32711yescharacteristic
165C4×C89#32711yescharacteristic
166C4×C89C2×#9911yescharacteristic
167C4×C89C2×#10411yescharacteristic
168Dic89—84no—
169C2×#1339—891nomaximal, Sylow
170C2×C89—21no—
171C2×C89—21no—
172C2×C89—41no—
173C2×C89—41no—
174C2×C89—162no—
175C2×C89#133912yescomplemented
176C2×C89C2×#32711yescharacteristic
177C2×#469D8911yescharacteristic
178C2×#349—891no—
179C2×H(3,ℤ/4)—891no—
180#1339—894no—
181C89C2×#133911yescharacteristic, complemented, Sylow
182C22×D8Dic8911yescharacteristic, complemented
183C22×M16C2×D8911yescharacteristic
184C2×#121—21no—
185C2×#117—1781no—
186C2×M32—1781no—
187#469—21no—
188#469—21no—
189#469Dic8912yescomplemented
190#469C2×D8912yes—
191C2×#106Dic8911yescharacteristic, complemented
192C2×#102—21no—
193#349—892no—
194#349—1781no—
195H(3,ℤ/4)—892no—
196H(3,ℤ/4)—1781no—
197C22×D4—21no—
198C22×D4—41no—
199C23×C4C22⋊D8911yescharacteristic
200C2×D8—21no—
201C2×D8—41no—
202C2×D8—41no—
203C2×D8C2×Dic8912yescomplemented
204C2×M16—41no—
205C2×M16—41no—
206C2×M16C2×Dic8911yescharacteristic
207C2×M16C22⋊D8911yescharacteristic
208C2×M16C22⋊D8911yescharacteristic
209C2×M16C22×D8911yescharacteristic
210C22×C8C2×Dic8911yescharacteristic
211C22×C8C22⋊D8911yescharacteristic
212#121—22no—
213#121—22no—
214#121—41no—
215#121—41no—
216#117—3561no—
217#117—3561no—
218#117—1782no—
219#117—1782no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—3561no—
222C2×C22⋊C4—41no—
223C2×C22⋊C4—3561no—
224C2×C42—1782no—
225M32—3561no—
226M32—1782no—
227C2×C16—3561no—
228#106—21no—
229#106C2×Dic8912yescomplemented
230#102—22no—
231#102—22no—
232C24—41no—
233C24#1308355911yescharacteristic
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—84no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—3562no—
249C22×C4C22⋊Dic8911yescharacteristic
250C22×C4C22⋊Dic8911yescharacteristic
251C22×C4#1308355911yescharacteristic
252C22×C4#1308356211yescharacteristic
253C22×C4#1308356211yescharacteristic
254C22×C4C2×C22⋊D8911yescharacteristic
255D8—42no—
256D8—42no—
257M16—41no—
258M16—41no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8C22⋊Dic8911yescharacteristic
266C2×C8C22⋊Dic8911yescharacteristic
267C2×C8C22×Dic8911yescharacteristic
268C2×C8C2×C22⋊D8911yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—3562no—
272C4⋊C4—3562no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—3562no—
276C22⋊C4—3562no—
277C42—3562no—
278C42—1784no—
279C16—3562no—
280C23—21no—
281C23—21no—
282C23—42no—
283C23—42no—
284C23—82no—
285C23—82no—
286C23—81no—
287C23—81no—
288C23#1566793311yescharacteristic
289C23#1566793311yescharacteristic
290C23C2×#1308355911yescharacteristic
291D4—42no—
292D4—42no—
293D4—84no—
294D4—84no—
295D4—81no—
296D4—81no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—82no—
309C2×C4—3564no—
310C2×C4—7124no—
311C2×C4#1566792711yescharacteristic
312C2×C4#1566792711yescharacteristic
313C2×C4#1566793311yescharacteristic
314C2×C4#1566793311yescharacteristic
315C2×C4#1566793911yescharacteristic
316C2×C4#1566793911yescharacteristic
317C2×C4C2×C22⋊Dic8911yescharacteristic
318C2×C4C2×#1308356211yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—42no—
329C22—81no—
330C22—82no—
331C22—82no—
332C22—82no—
333C22—162no—
334C22—162no—
335C22#1915133211yescharacteristic
336C22#1915133211yescharacteristic
337C22C2×#1566793311yescharacteristic
338C4—21no—
339C4—21no—
340C4—82no—
341C4—7124no—
342C4#1915133211yescharacteristic
343C4#1915133211yescharacteristic
344C4C2×#1566792711yescharacteristic
345C4C2×#1566793911yescharacteristic
346C2—21no—
347C2—21no—
348C2—41no—
349C2—41no—
350C2—162no—
351C2#2601823712yesdirect product factor
352C2C2×#1915133211yescharacteristic
subgroupG/H
centerC22#19151332
commutatorC2×C8×C89C22×C4
FrattiniC2×M16C22×D89
Fitting, prime radicalC2×#469×C89C2
socleC22×C89#327
cosocleC2×M16×C89C23
hypercenterC2×#469D89
hypocenterC89C2×#1339
LCSG ▷ C2×C8×C89 ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#19151380C2semidirect
2. C2×#19151355C2semidirect
3. #26018237C2direct (N × H)
8. #19151380C22semidirect
10. #19151355C22semidirect
11. C22×D8×C89C4semidirect
16. #469×C89C4semidirect
18. C2×#106×C89C4semidirect
36. C2×D8×C89C2×C4semidirect
52. #106×C89C2×C4semidirect
175. C2×C89#1339semidirect
181. C89C2×#1339semidirect
182. C22×D8Dic89semidirect
189. #469Dic89semidirect
191. C2×#106Dic89semidirect
203. C2×D8C2×Dic89semidirect
229. #106C2×Dic89semidirect
351. C2#26018237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191513802
C2×#191513552
#260182372
C2×#469×C892
C2×#133989