Finite Group Databasebeta

← C2×#22590035 #32150295

Subgroups — C2×#22590035 #32150295

Order 18176.

1198 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985983C212yesmaximal
2#22590035C218yesmaximal, direct product factor
3C2×#17985798C214yesmaximal, complemented
4C2×#536×C71C211yesmaximal, characteristic
5C22×#11765849—22no—
6#17985983—24no—
7#17985983C2218yes—
8C2×#14556047C2214yes—
9C2×#14556045—22no—
10#17985798C22116yescomplemented
11C22×#41×C71C2211yescharacteristic
12C23×Q8×C71C411yescharacteristic
13#536×C71—24no—
14#536×C71C414yes—
15#536×C71C2214yes—
16C2×C4⋊Q8×C71C2212yes—
17C2×#124×C71C412yes—
18C2×#123×C71—22no—
19C2×C22⋊Q8×C71—22no—
20C2×#117×C71C411yescharacteristic
21C2×#11765849—24no—
22C2×#11765849—28no—
23C2×#11765849—42no—
24C2×#11765849—44no—
25C22×C71⋊C8—42no—
26#14556047—24no—
27#14556047C2318yes—
28#14556045—28no—
29C2×#41×C71—42no—
30C2×#41×C71—42no—
31C2×#41×C71C2×C412yes—
32C2×#41×C71D414yes—
33C2×#41×C71C2312yes—
34C22×Q8×C71—21no—
35C22×Q8×C71—22no—
36C22×Q8×C71—42no—
37C22×Q8×C71—42no—
38C22×Q8×C71C2×C412yes—
39C22×Q8×C71C2×C414yes—
40C22×Q8×C71C2311yescharacteristic
41C22×D4×C71C2×C411yescharacteristic
42C22×D4×C71D412yes—
43C23×C4×C71—21no—
44C23×C4×C71C2×C411yescharacteristic
45C23×C4×C71D412yes—
46C4⋊Q8×C71—24no—
47C4⋊Q8×C71C2×C414yes—
48C4⋊Q8×C71C2314yes—
49#124×C71—24no—
50#124×C71C2×C418yes—
51#123×C71—28no—
52#123×C71—28no—
53C22⋊Q8×C71—28no—
54C22⋊Q8×C71—28no—
55#117×C71—22no—
56#117×C71C2×C414yes—
57C2×C4⋊C4×C71—21no—
58C2×C4⋊C4×C71—24no—
59C2×C22⋊C4×C71—21no—
60C2×C22⋊C4×C71—24no—
61C2×C42×C71C2×C412yes—
62#11765849—28no—
63#11765849—44no—
64#11765849—48no—
65C2×C71⋊C8—44no—
66C2×C71⋊C8—48no—
67C24×C71C22⋊C412yes—
68C24×C71C22⋊C411yescharacteristic
69#41×C71—44no—
70#41×C71—44no—
71#41×C71—44no—
72#41×C71—44no—
73C2×Q8×C71—24no—
74C2×Q8×C71—22no—
75C2×Q8×C71—41no—
76C2×Q8×C71—41no—
77C2×Q8×C71—48no—
78C2×Q8×C71—48no—
79C2×Q8×C71—42no—
80C2×Q8×C71—42no—
81C2×Q8×C71—42no—
82C2×Q8×C71—42no—
83C2×Q8×C71C22×C414yes—
84C2×Q8×C71C22×C411yescharacteristic
85C2×Q8×C71C2×D412yes—
86C2×Q8×C71C2411yescharacteristic
87C2×D4×C71—41no—
88C2×D4×C71—41no—
89C2×D4×C71—42no—
90C2×D4×C71—42no—
91C2×D4×C71C22⋊C414yes—
92C2×D4×C71C22⋊C412yes—
93C2×D4×C71C22×C412yes—
94C2×D4×C71C2×D414yes—
95C22×C4×C71—22no—
96C22×C4×C71—22no—
97C22×C4×C71—22no—
98C22×C4×C71—22no—
99C22×C4×C71—24no—
100C22×C4×C71—22no—
101C22×C4×C71—22no—
102C22×C4×C71—24no—
103C22×C4×C71—42no—
104C22×C4×C71—42no—
105C22×C4×C71C22⋊C412yes—
106C22×C4×C71C22⋊C414yes—
107C22×C4×C71C22⋊C411yescharacteristic
108C22×C4×C71C22×C411yescharacteristic
109C22×C4×C71C22×C412yes—
110C22×C4×C71C2×D412yes—
111C22×C4×C71C2×D414yes—
112C4⋊C4×C71—24no—
113C4⋊C4×C71—28no—
114C4⋊C4×C71—28no—
115C22⋊C4×C71—24no—
116C22⋊C4×C71—216no—
117C42×C71—22no—
118C42×C71C22×C414yes—
119C23×C71—21no—
120C23×C71—21no—
121C23×C71—22no—
122C23×C71—22no—
123C23×C71—42no—
124C23×C71—44no—
125C23×C71C2×C22⋊C411yescharacteristic
126C23×C71C2×C22⋊C414yes—
127C23×C71C2×C22⋊C412yes—
128Q8×C71—41no—
129Q8×C71—42no—
130Q8×C71—41no—
131Q8×C71—44no—
132Q8×C71—44no—
133Q8×C71—48no—
134D4×C71—44no—
135D4×C71—42no—
136D4×C71—42no—
137D4×C71—44no—
138C2×C4×C71—21no—
139C2×C4×C71—21no—
140C2×C4×C71—22no—
141C2×C4×C71—22no—
142C2×C4×C71—24no—
143C2×C4×C71—24no—
144C2×C4×C71—24no—
145C2×C4×C71—24no—
146C2×C4×C71—24no—
147C2×C4×C71—24no—
148C2×C4×C71—24no—
149C2×C4×C71—24no—
150C2×C4×C71—44no—
151C2×C4×C71—48no—
152C2×C4×C71—42no—
153C2×C4×C71—42no—
154C2×C4×C71#9912yes—
155C2×C4×C71#9912yes—
156C2×C4×C71C2×C22⋊C411yescharacteristic
157C2×C4×C71C2×C22⋊C412yes—
158C2×C4×C71C2×C22⋊C412yes—
159C2×C4×C71C23×C411yescharacteristic
160C2×C4×C71C22×D412yes—
161C71⋊C8—48no—
162C22×C71—22no—
163C22×C71—22no—
164C22×C71—24no—
165C22×C71—42no—
166C22×C71—44no—
167C22×C71—42no—
168C22×C71—42no—
169C22×C71—44no—
170C22×C71—82no—
171C22×C71C2×#9911yescharacteristic
172C22×C71C2×#9911yescharacteristic
173C22×C71C22×C22⋊C411yescharacteristic
174C4×C71—22no—
175C4×C71—22no—
176C4×C71—21no—
177C4×C71—21no—
178C4×C71—44no—
179C4×C71—44no—
180C4×C71C2×#9914yes—
181C2×#2135—711nomaximal, Sylow
182C2×C71—21no—
183C2×C71—21no—
184C2×C71—42no—
185C2×C71—44no—
186C2×C71#213512yescomplemented
187C2×C71C22×#9911yescharacteristic
188C2×#536D7111yescharacteristic
189C2×#413—712no—
190#2135—718no—
191C2×#356—714no—
192C71C2×#213511yescharacteristic, complemented, Sylow
193C22×#41C2×D7111yescharacteristic
194C23×Q8Dic7111yescharacteristic
195C22×M16—1422no—
196#536—24no—
197#536Dic7114yes—
198#536C2×D7114yes—
199C2×C4⋊Q8C2×D7112yes—
200C2×#124Dic7112yes—
201C2×#123—22no—
202C2×C22⋊Q8—22no—
203C2×#117Dic7111yescharacteristic
204#413—718no—
205#413—1424no—
206C2×#101—714no—
207C2×#100—1422no—
208#356—7116no—
209C2×#41—42no—
210C2×#41—42no—
211C2×#41C2×Dic7112yes—
212C2×#41C22⋊D7114yes—
213C2×#41C22×D7112yes—
214C22×Q8—22no—
215C22×Q8—21no—
216C22×Q8—42no—
217C22×Q8—42no—
218C22×Q8C2×Dic7112yes—
219C22×Q8C2×Dic7114yes—
220C22×Q8C22×D7111yescharacteristic
221C22×D4C2×Dic7111yescharacteristic
222C22×D4C22⋊D7112yes—
223C23×C4—21no—
224C23×C4C2×Dic7111yescharacteristic
225C23×C4C22⋊D7112yes—
226C2×M16—2842no—
227C2×M16—2844no—
228C2×M16—1424no—
229C2×M16—1428no—
230C22×C8—2842no—
231C4⋊Q8—24no—
232C4⋊Q8C2×Dic7114yes—
233C4⋊Q8C22×D7114yes—
234#124—24no—
235#124C2×Dic7118yes—
236#123—28no—
237#123—28no—
238C22⋊Q8—28no—
239C22⋊Q8—28no—
240#117—22no—
241#117C2×Dic7114yes—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—24no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—24no—
246C2×C42C2×Dic7112yes—
247#101—718no—
248#101—1424no—
249#100—1428no—
250C24C22⋊Dic7112yes—
251C24C22⋊Dic7111yescharacteristic
252#41—44no—
253#41—44no—
254#41—44no—
255#41—44no—
256C2×Q8—24no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—48no—
261C2×Q8—48no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8C22×Dic7114yes—
267C2×Q8C22×Dic7111yescharacteristic
268C2×Q8C2×C22⋊D7112yes—
269C2×Q8C23×D7111yescharacteristic
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4C22⋊Dic7114yes—
275C2×D4C22⋊Dic7112yes—
276C2×D4C22×Dic7112yes—
277C2×D4C2×C22⋊D7114yes—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4C22⋊Dic7112yes—
289C22×C4C22⋊Dic7114yes—
290C22×C4C22⋊Dic7111yescharacteristic
291C22×C4C22×Dic7111yescharacteristic
292C22×C4C22×Dic7112yes—
293C22×C4C2×C22⋊D7112yes—
294C22×C4C2×C22⋊D7114yes—
295M16—2844no—
296M16—2848no—
297M16—1428no—
298C2×C8—2844no—
299C2×C8—2848no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—28no—
303C22⋊C4—24no—
304C22⋊C4—216no—
305C42—22no—
306C42C22×Dic7114yes—
307C23—21no—
308C23—21no—
309C23—22no—
310C23—22no—
311C23—42no—
312C23—44no—
313C23C2×C22⋊Dic7111yescharacteristic
314C23C2×C22⋊Dic7114yes—
315C23C2×C22⋊Dic7112yes—
316Q8—41no—
317Q8—42no—
318Q8—41no—
319Q8—44no—
320Q8—44no—
321Q8—48no—
322D4—42no—
323D4—44no—
324D4—42no—
325D4—44no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—48no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4#1455604312yes—
343C2×C4#1455604312yes—
344C2×C4C2×C22⋊Dic7111yescharacteristic
345C2×C4C2×C22⋊Dic7112yes—
346C2×C4C2×C22⋊Dic7112yes—
347C2×C4C23×Dic7111yescharacteristic
348C2×C4C22×C22⋊D7112yes—
349C8—2848no—
350C22—22no—
351C22—22no—
352C22—24no—
353C22—42no—
354C22—44no—
355C22—42no—
356C22—42no—
357C22—44no—
358C22—82no—
359C22C2×#1455604311yescharacteristic
360C22C2×#1455604311yescharacteristic
361C22C22×C22⋊Dic7111yescharacteristic
362C4—22no—
363C4—21no—
364C4—21no—
365C4—22no—
366C4—44no—
367C4—44no—
368C4C2×#1455604314yes—
369C2—21no—
370C2—21no—
371C2—42no—
372C2—44no—
373C2#2259003512yesdirect product factor
374C2C22×#1455604311yescharacteristic
subgroupG/H
centerC22C2×#14556043
commutatorC2×C4×C71C23×C4
FrattiniC2×Q8C23×D71
FittingC2×#536×C71C2
socleC22×C71C2×#99
prime radicalC22×#41×C71C22
cosocleC2×Q8×C71C24
hypercenterC2×#536D71
hypocenterC71C2×#2135
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. #22590035C2direct (N × H)
3. C2×#17985798C2semidirect
10. #17985798C22semidirect
186. C2×C71#2135semidirect
192. C71C2×#2135semidirect
373. C2#22590035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179859832
#225900352
C2×#179857982
C2×#536×C712
C2×#213571