Finite Group Databasebeta

← C2×#26021873 #36707118

Subgroups — C2×#26021873 #36707118

Order 22784.

1154 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15667952C212yesmaximal, complemented
2#26021873C218yesmaximal, direct product factor
3C2×#19151380C214yesmaximal, complemented
4C22×#131×C89C211yesmaximal, characteristic
5C2×#15667952—22no—
6C2×#15667952—24no—
7C2×#15667952C2214yes—
8C2×#15667952C2218yescomplemented
9C22×#13083549—22no—
10#19151380C22116yescomplemented
11C22×#41×C89C411yescharacteristic
12C2×#131×C89—22no—
13C2×#131×C89—22no—
14C2×#131×C89—24no—
15C2×#131×C89C414yes—
16C2×#131×C89C2214yes—
17C22×M16×C89C411yescharacteristic
18C22×M16×C89C2212yes—
19C23×C8×C89C412yes—
20C23×C8×C89C2211yescharacteristic
21#15667952—24no—
22#15667952—28no—
23#15667952C2318yes—
24C2×#13083549—24no—
25C2×#13083549—28no—
26C2×#41×C89—22no—
27C2×#41×C89—22no—
28C2×#41×C89—22no—
29C2×#41×C89—22no—
30C2×#41×C89C814yes—
31C2×#41×C89C2×C414yes—
32C22×Q8×C89C811yescharacteristic
33C22×D4×C89C812yes—
34C22×D4×C89C811yescharacteristic
35C23×C4×C89C2×C412yes—
36C23×C4×C89C2×C411yescharacteristic
37#131×C89—28no—
38#131×C89—28no—
39#131×C89—28no—
40#131×C89—28no—
41C2×M16×C89—22no—
42C2×M16×C89—22no—
43C2×M16×C89—24no—
44C2×M16×C89—24no—
45C2×M16×C89C2×C414yes—
46C2×M16×C89C2×C414yes—
47C2×M16×C89C2314yes—
48C22×C8×C89—24no—
49C22×C8×C89—22no—
50C22×C8×C89—22no—
51C22×C8×C89C2×C412yes—
52C22×C8×C89C2×C418yes—
53C22×C8×C89C2×C411yescharacteristic
54C22×C8×C89C2×C412yes—
55C22×C8×C89D412yes—
56C22×C8×C89D412yes—
57C22×C8×C89D414yes—
58C22×C8×C89C2311yescharacteristic
59C22×C8×C89C2312yes—
60#13083549—28no—
61C24×C89C2×C812yes—
62C24×C89C2×C811yescharacteristic
63#41×C89—28no—
64#41×C89—28no—
65#41×C89—28no—
66#41×C89—28no—
67C2×Q8×C89—22no—
68C2×Q8×C89—22no—
69C2×Q8×C89C2×C814yes—
70C2×D4×C89—24no—
71C2×D4×C89—24no—
72C2×D4×C89—22no—
73C2×D4×C89—22no—
74C2×D4×C89C2×C818yes—
75C2×D4×C89C2×C814yes—
76C22×C4×C89—22no—
77C22×C4×C89—22no—
78C22×C4×C89—22no—
79C22×C4×C89—22no—
80C22×C4×C89C22⋊C412yes—
81C22×C4×C89C22⋊C412yes—
82C22×C4×C89C2×C812yes—
83C22×C4×C89C2×C814yes—
84C22×C4×C89C2×C811yescharacteristic
85C22×C4×C89C2×C812yes—
86C22×C4×C89M1612yes—
87C22×C4×C89M1612yes—
88C22×C4×C89C22×C414yes—
89C22×C4×C89C22×C411yescharacteristic
90C22×C4×C89C22×C412yes—
91M16×C89—28no—
92M16×C89—28no—
93M16×C89—28no—
94C2×C8×C89—22no—
95C2×C8×C89—22no—
96C2×C8×C89—28no—
97C2×C8×C89—28no—
98C2×C8×C89C22⋊C411yescharacteristic
99C2×C8×C89C22⋊C412yes—
100C2×C8×C89C22⋊C414yes—
101C2×C8×C89C22⋊C414yes—
102C2×C8×C89C22⋊C411yescharacteristic
103C2×C8×C89C22×C414yes—
104C2×C8×C89C22×C412yes—
105C2×C8×C89C22×C411yescharacteristic
106C2×C8×C89C2×D412yes—
107C2×C8×C89C2×D412yes—
108C2×C8×C89C2×D414yes—
109C2×C8×C89C2×D414yes—
110C2×C8×C89C2411yescharacteristic
111C23×C89—22no—
112C23×C89—22no—
113C23×C89—42no—
114C23×C89—44no—
115C23×C89C22⋊C812yes—
116C23×C89C22⋊C812yes—
117C23×C89C22×C811yescharacteristic
118C23×C89C22×C814yes—
119C23×C89C22×C812yes—
120Q8×C89—28no—
121D4×C89—216no—
122D4×C89—28no—
123C2×C4×C89—22no—
124C2×C4×C89—22no—
125C2×C4×C89—24no—
126C2×C4×C89—24no—
127C2×C4×C89—24no—
128C2×C4×C89—24no—
129C2×C4×C89C22⋊C812yes—
130C2×C4×C89C22⋊C812yes—
131C2×C4×C89C22⋊C814yes—
132C2×C4×C89C22⋊C814yes—
133C2×C4×C89C2×C22⋊C411yescharacteristic
134C2×C4×C89C2×C22⋊C411yescharacteristic
135C2×C4×C89C2×C22⋊C414yes—
136C2×C4×C89C22×C814yes—
137C2×C4×C89C22×C811yescharacteristic
138C2×C4×C89C22×C812yes—
139C2×C4×C89C2×M1611yescharacteristic
140C2×C4×C89C2×M1611yescharacteristic
141C2×C4×C89C2×M1614yes—
142C2×C4×C89C23×C411yescharacteristic
143C8×C89—24no—
144C8×C89C2×C22⋊C412yes—
145C8×C89C2×C22⋊C412yes—
146C8×C89C2×C22⋊C412yes—
147C8×C89C22×D412yes—
148C22×C89—22no—
149C22×C89—24no—
150C22×C89—24no—
151C22×C89—42no—
152C22×C89—42no—
153C22×C89—44no—
154C22×C89—44no—
155C22×C89—44no—
156C22×C89C2×C22⋊C811yescharacteristic
157C22×C89C2×C22⋊C814yes—
158C22×C89C2×C22⋊C811yescharacteristic
159C22×C89C23×C811yescharacteristic
160C4×C89—24no—
161C4×C89C2×C22⋊C811yescharacteristic
162C4×C89C2×C22⋊C811yescharacteristic
163C4×C89C2×C22⋊C814yes—
164C4×C89C22×C22⋊C411yescharacteristic
165C4×C89C22×M1611yescharacteristic
166C2×#2115—891nomaximal, Sylow
167C2×C89—21no—
168C2×C89—21no—
169C2×C89—24no—
170C2×C89—44no—
171C2×C89#211512yescomplemented
172C2×C89C22×C22⋊C811yescharacteristic
173C22×#131D8911yescharacteristic
174C22×M32—892no—
175#2115—898no—
176C2×#349—894no—
177C89C2×#211511yescharacteristic, complemented, Sylow
178C22×#41Dic8911yescharacteristic
179C2×#131—22no—
180C2×#131—24no—
181C2×#131—22no—
182C2×#131Dic8914yes—
183C2×#131C2×D8914yes—
184C22×M16Dic8911yescharacteristic
185C22×M16C2×D8912yes—
186C23×C8Dic8912yes—
187C23×C8C2×D8911yescharacteristic
188C2×M32—894no—
189C2×M32—898no—
190C2×M32—1782no—
191C2×M32—1784no—
192C22×C16—1782no—
193#349—8916no—
194C2×#41—22no—
195C2×#41—22no—
196C2×#41—22no—
197C2×#41—22no—
198C2×#41#1062349414yes—
199C2×#41C2×Dic8914yes—
200C22×Q8#1062349411yescharacteristic
201C22×D4#1062349412yes—
202C22×D4#1062349411yescharacteristic
203C23×C4C2×Dic8912yes—
204C23×C4C2×Dic8911yescharacteristic
205#131—28no—
206#131—28no—
207#131—28no—
208#131—28no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—24no—
212C2×M16—24no—
213C2×M16C2×Dic8914yes—
214C2×M16C2×Dic8914yes—
215C2×M16C22×D8914yes—
216C22×C8—24no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8C2×Dic8912yes—
220C22×C8C2×Dic8918yes—
221C22×C8C2×Dic8912yes—
222C22×C8C2×Dic8911yescharacteristic
223C22×C8C22⋊D8912yes—
224C22×C8C22⋊D8914yes—
225C22×C8C22⋊D8912yes—
226C22×C8C22×D8911yescharacteristic
227C22×C8C22×D8912yes—
228M32—898no—
229M32—1784no—
230M32—1788no—
231C2×C16—1784no—
232C2×C16—1788no—
233C24C2×#1062349412yes—
234C24C2×#1062349411yescharacteristic
235#41—28no—
236#41—28no—
237#41—28no—
238#41—28no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8C2×#1062349414yes—
242C2×D4—24no—
243C2×D4—24no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4C2×#1062349418yes—
247C2×D4C2×#1062349414yes—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4C22⋊Dic8912yes—
253C22×C4C22⋊Dic8912yes—
254C22×C4C2×#1062349412yes—
255C22×C4C2×#1062349414yes—
256C22×C4C2×#1062349411yescharacteristic
257C22×C4C2×#1062349412yes—
258C22×C4#1308355812yes—
259C22×C4#1308355812yes—
260C22×C4C22×Dic8914yes—
261C22×C4C22×Dic8911yescharacteristic
262C22×C4C22×Dic8912yes—
263M16—28no—
264M16—28no—
265M16—28no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—28no—
269C2×C8—28no—
270C2×C8C22⋊Dic8911yescharacteristic
271C2×C8C22⋊Dic8912yes—
272C2×C8C22⋊Dic8914yes—
273C2×C8C22⋊Dic8914yes—
274C2×C8C22⋊Dic8911yescharacteristic
275C2×C8C22×Dic8914yes—
276C2×C8C22×Dic8912yes—
277C2×C8C22×Dic8911yescharacteristic
278C2×C8C2×C22⋊D8912yes—
279C2×C8C2×C22⋊D8914yes—
280C2×C8C2×C22⋊D8912yes—
281C2×C8C2×C22⋊D8914yes—
282C2×C8C23×D8911yescharacteristic
283C16—1788no—
284C23—22no—
285C23—22no—
286C23—42no—
287C23—44no—
288C23C22⋊#1062349412yes—
289C23C22⋊#1062349412yes—
290C23C22×#1062349411yescharacteristic
291C23C22×#1062349414yes—
292C23C22×#1062349412yes—
293Q8—28no—
294D4—216no—
295D4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4C22⋊#1062349412yes—
303C2×C4C22⋊#1062349412yes—
304C2×C4C22⋊#1062349414yes—
305C2×C4C22⋊#1062349414yes—
306C2×C4C2×C22⋊Dic8911yescharacteristic
307C2×C4C2×C22⋊Dic8911yescharacteristic
308C2×C4C2×C22⋊Dic8914yes—
309C2×C4C22×#1062349414yes—
310C2×C4C22×#1062349411yescharacteristic
311C2×C4C22×#1062349412yes—
312C2×C4C2×#1308355811yescharacteristic
313C2×C4C2×#1308355811yescharacteristic
314C2×C4C2×#1308355814yes—
315C2×C4C23×Dic8911yescharacteristic
316C8—24no—
317C8C2×C22⋊Dic8912yes—
318C8C2×C22⋊Dic8912yes—
319C8C2×C22⋊Dic8912yes—
320C8C22×C22⋊D8912yes—
321C22—22no—
322C22—24no—
323C22—24no—
324C22—42no—
325C22—42no—
326C22—44no—
327C22—44no—
328C22—44no—
329C22C2×C22⋊#1062349411yescharacteristic
330C22C2×C22⋊#1062349414yes—
331C22C2×C22⋊#1062349411yescharacteristic
332C22C23×#1062349411yescharacteristic
333C4—24no—
334C4C2×C22⋊#1062349411yescharacteristic
335C4C2×C22⋊#1062349411yescharacteristic
336C4C2×C22⋊#1062349414yes—
337C4C22×C22⋊Dic8911yescharacteristic
338C4C22×#1308355811yescharacteristic
339C2—21no—
340C2—21no—
341C2—24no—
342C2—44no—
343C2#2602187312yesdirect product factor
344C2C22×C22⋊#1062349411yescharacteristic
subgroupG/H
centerC2×C8C22⋊Dic89
commutatorC22×C89C23×C8
FrattiniC2×C8C23×D89
FittingC22×#131×C89C2
socleC22×C89C2×C22⋊C8
prime radicalC22×#41×C89C4
cosocleC2×C8×C89C24
hypercenterC22×#131D89
hypocenterC89C2×#2115
LCSG ▷ C22×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
1. C22×#15667952C2semidirect
2. #26021873C2direct (N × H)
3. C2×#19151380C2semidirect
8. C2×#15667952C22semidirect
10. #19151380C22semidirect
171. C2×C89#2115semidirect
177. C89C2×#2115semidirect
343. C2#26021873direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156679522
#260218732
C2×#191513802
C22×#131×C892
C2×#211589