Finite Group Databasebeta

← C2×#17989194 #22623294

Subgroups — C2×#17989194 #22623294

Order 9344.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989194C2116yesmaximal, direct product factor
2C2×#14556590C211yesmaximal, characteristic, complemented
3C2×#14556584C211yesmaximal, characteristic
4C2×#14556584C211yesmaximal, characteristic
5C2×#14556584C211yesmaximal, characteristic
6C2×#14556583C211yesmaximal, characteristic, complemented
7C2×#14556582C211yesmaximal, characteristic, complemented
8C2×#14556581C211yesmaximal, characteristic, complemented
9C2×#14556581C211yesmaximal, characteristic, complemented
10C2×#14556581C211yesmaximal, characteristic, complemented
11C2×#14556568C211yesmaximal, characteristic
12C2×#14556568C211yesmaximal, characteristic
13C2×C4×Dic146C211yesmaximal, characteristic, complemented
14C2×#14556556C211yesmaximal, characteristic, complemented
15C2×#14556547C211yesmaximal, characteristic
16C2×#126×C73C211yesmaximal, characteristic
17C22×Dic146C2211yescharacteristic
18C22×Dic146C2211yescharacteristic
19C23×Dic73C2211yescharacteristic
20#14556590C2218yescomplemented
21#14556584C2218yes—
22#14556584C2218yes—
23#14556584C2218yes—
24#14556583C2218yescomplemented
25#14556582C2218yescomplemented
26#14556581C2218yescomplemented
27#14556581C2218yescomplemented
28#14556581C2218yescomplemented
29#14556568C2218yes—
30#14556568C2218yes—
31C4×Dic146C2218yescomplemented
32#14556556C2218yescomplemented
33#14556547C2218yes—
34C2×C4⋊Dic73C2211yescharacteristic
35C2×C4⋊Dic73C2211yescharacteristic
36C2×C4⋊Dic73C2211yescharacteristic
37C2×C4⋊Dic73C2211yescharacteristic
38C2×C4⋊Dic73C2211yescharacteristic
39C2×#11924007C2211yescharacteristic
40C2×#11924007C2211yescharacteristic
41C2×#11924007C2211yescharacteristic
42C2×#11924007C2211yescharacteristic
43C2×#11924007C2211yescharacteristic
44C2×#11924007C2211yescharacteristic
45C2×#11924007C2211yescharacteristic
46C2×#11924007C2211yescharacteristic
47C2×#11924007C2211yescharacteristic
48C2×#11924007C2211yescharacteristic
49C2×#11924007C2211yescharacteristic
50C2×#11924007C2211yescharacteristic
51C2×C22⋊Dic73C2211yescharacteristic
52C2×C22⋊Dic73C2211yescharacteristic
53C2×C22⋊Dic73C2211yescharacteristic
54C2×C4×Dic73C2211yescharacteristic
55C2×C4×Dic73C2211yescharacteristic
56C2×C4×Dic73C2211yescharacteristic
57C2×C4×Dic73C2211yescharacteristic
58C2×C4×Dic73C2211yescharacteristic
59#126×C73C2218yes—
60C2×C4⋊C4×C73C2211yescharacteristic
61C2×C4⋊C4×C73C2211yescharacteristic
62C2×C4⋊C4×C73C2211yescharacteristic
63C2×C22⋊C4×C73C2211yescharacteristic
64C2×C22⋊C4×C73C2211yescharacteristic
65C2×C22⋊C4×C73C2211yescharacteristic
66C2×C42×C73C2211yescharacteristic
67C2×Dic146—24no—
68C2×Dic146—24no—
69C2×Dic146C2314yes—
70C2×Dic146C2314yes—
71C22×Dic73—24no—
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C22×Dic73C2311yescharacteristic
79C22×Dic73C2314yes—
80C22×Dic73C2311yescharacteristic
81C4⋊Dic73C2314yes—
82C4⋊Dic73C2314yes—
83C4⋊Dic73C2314yes—
84C4⋊Dic73C2314yes—
85C4⋊Dic73C2314yes—
86#11924007C2314yes—
87#11924007C2314yes—
88#11924007C2314yes—
89#11924007C2314yes—
90#11924007C2314yes—
91#11924007C2314yes—
92#11924007C2314yes—
93#11924007C2314yes—
94#11924007C2314yes—
95#11924007C2314yes—
96#11924007C2314yes—
97#11924007C2314yes—
98C22⋊Dic73C2314yes—
99C22⋊Dic73C2314yes—
100C22⋊Dic73C2314yes—
101C4×Dic73C2314yes—
102C4×Dic73C2314yes—
103C4×Dic73C2314yes—
104C4×Dic73C2314yes—
105C4×Dic73C2314yes—
106C24×C73C2311yescharacteristic
107C22×C4×C73C2311yescharacteristic
108C22×C4×C73C2311yescharacteristic
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111C22×C4×C73C2311yescharacteristic
112C22×C4×C73C2311yescharacteristic
113C4⋊C4×C73C2314yes—
114C4⋊C4×C73C2314yes—
115C4⋊C4×C73C2314yes—
116C22⋊C4×C73C2314yes—
117C22⋊C4×C73C2314yes—
118C22⋊C4×C73C2314yes—
119C42×C73C2314yes—
120C23×C73—22no—
121C23×C73—22no—
122C23×C73—22no—
123C23×C73C2412yes—
124C23×C73C2411yescharacteristic
125C2×C4×C73—22no—
126C2×C4×C73—22no—
127C2×C4×C73—22no—
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73—22no—
131C2×C4×C73C2412yes—
132C2×C4×C73C2412yes—
133C2×C4×C73C2412yes—
134C2×C4×C73C2412yes—
135C2×C4×C73C2412yes—
136C2×C4×C73C2412yes—
137C2×Dic73—22no—
138C2×Dic73—22no—
139C2×Dic73—22no—
140C2×Dic73—22no—
141C2×Dic73—22no—
142C2×Dic73—22no—
143C2×Dic73—22no—
144C2×Dic73—28no—
145C2×Dic73#4114yes—
146C2×Dic73C2412yes—
147C2×Dic73C2412yes—
148C2×Dic73C2412yes—
149C2×Dic73C2412yes—
150C2×Dic73C2412yes—
151C2×Dic73C2412yes—
152C2×Dic73C2412yes—
153C2×Dic73C2412yes—
154Dic146—28no—
155Dic146—28no—
156C22×C73—22no—
157C22×C73—22no—
158C22×C73—22no—
159C22×C73—44no—
160C22×C73C2×#4112yes—
161C22×C732−1+412yes—
162C22×C732−1+412yes—
163C22×C73C2511yescharacteristic
164C4×C73—22no—
165C4×C73—22no—
166C4×C73—22no—
167C4×C73—22no—
168C4×C73—22no—
169C4×C73—22no—
170Dic73—22no—
171Dic73—22no—
172Dic73—22no—
173Dic73—22no—
174Dic73—22no—
175Dic73—22no—
176Dic73—22no—
177Dic73C2×#4114yes—
178C2×C73—42no—
179C2×C73#54114yescomplemented
180C2×C73C22×#4111yescharacteristic
181C2×C73C2×2−1+411yescharacteristic
182C2×C73C2×2−1+411yescharacteristic
183C2×#541—731nomaximal, Sylow
184C73C2×#54111yescharacteristic, complemented, Sylow
185#541—7316no—
186C2×C4⋊Q8—731no—
187C2×#126—731no—
188C2×#126—731no—
189C2×#126—731no—
190C2×#126D7311yescharacteristic
191C2×#125—731no—
192C2×#125—731no—
193C2×#125—731no—
194C2×#125—731no—
195C2×#125—731no—
196C2×C22⋊Q8—731no—
197C2×C22⋊Q8—731no—
198C2×C4×Q8—731no—
199C2×C4×Q8—731no—
200C2×#117—731no—
201C22×Q8—731no—
202C22×Q8—731no—
203C23×C4—731no—
204C4⋊Q8—738no—
205#126—738no—
206#126—738no—
207#126—738no—
208#126C2×D7318yes—
209#125—738no—
210#125—738no—
211#125—738no—
212#125—738no—
213#125—738no—
214C22⋊Q8—738no—
215C22⋊Q8—738no—
216C4×Q8—738no—
217C4×Q8—738no—
218#117—738no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—731no—
221C2×C4⋊C4—731no—
222C2×C4⋊C4—731no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—731no—
225C2×C4⋊C4—731no—
226C2×C4⋊C4—731no—
227C2×C4⋊C4—731no—
228C2×C4⋊C4—731no—
229C2×C4⋊C4—731no—
230C2×C4⋊C4—731no—
231C2×C4⋊C4—731no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4C2×D7311yescharacteristic
237C2×C4⋊C4C2×D7311yescharacteristic
238C2×C4⋊C4C2×D7311yescharacteristic
239C2×C22⋊C4—731no—
240C2×C22⋊C4—731no—
241C2×C22⋊C4—731no—
242C2×C22⋊C4C2×D7311yescharacteristic
243C2×C22⋊C4C2×D7311yescharacteristic
244C2×C22⋊C4C2×D7311yescharacteristic
245C2×C42—731no—
246C2×C42—731no—
247C2×C42—731no—
248C2×C42—731no—
249C2×C42—731no—
250C2×C42C2×D7311yescharacteristic
251C24C22×D7311yescharacteristic
252C2×Q8—734no—
253C2×Q8—734no—
254C2×Q8—1464no—
255C2×Q8—1464no—
256C22×C4—731no—
257C22×C4—734no—
258C22×C4—731no—
259C22×C4—731no—
260C22×C4—731no—
261C22×C4—731no—
262C22×C4—731no—
263C22×C4—731no—
264C22×C4—731no—
265C22×C4—1464no—
266C22×C4C22×D7311yescharacteristic
267C22×C4C22×D7311yescharacteristic
268C22×C4C22×D7311yescharacteristic
269C22×C4C22×D7311yescharacteristic
270C22×C4C22×D7311yescharacteristic
271C22×C4C22×D7311yescharacteristic
272C4⋊C4—734no—
273C4⋊C4—734no—
274C4⋊C4—734no—
275C4⋊C4—734no—
276C4⋊C4—734no—
277C4⋊C4—734no—
278C4⋊C4—734no—
279C4⋊C4—734no—
280C4⋊C4—734no—
281C4⋊C4—734no—
282C4⋊C4—734no—
283C4⋊C4—734no—
284C4⋊C4—734no—
285C4⋊C4—734no—
286C4⋊C4—734no—
287C4⋊C4—734no—
288C4⋊C4—734no—
289C4⋊C4C22×D7314yes—
290C4⋊C4C22×D7314yes—
291C4⋊C4C22×D7314yes—
292C22⋊C4—734no—
293C22⋊C4—734no—
294C22⋊C4—734no—
295C22⋊C4C22×D7314yes—
296C22⋊C4C22×D7314yes—
297C22⋊C4C22×D7314yes—
298C42—734no—
299C42—734no—
300C42—734no—
301C42—734no—
302C42—734no—
303C42C22×D7314yes—
304C23—22no—
305C23—22no—
306C23—22no—
307C23C23×D7312yes—
308C23C23×D7311yescharacteristic
309Q8—1468no—
310Q8—1468no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—734no—
318C2×C4—732no—
319C2×C4—732no—
320C2×C4—732no—
321C2×C4—732no—
322C2×C4—732no—
323C2×C4—732no—
324C2×C4—732no—
325C2×C4—732no—
326C2×C4—1468no—
327C2×C4—1462no—
328C2×C4—1462no—
329C2×C4—1462no—
330C2×C4—1462no—
331C2×C4—1462no—
332C2×C4—1462no—
333C2×C4—1462no—
334C2×C4C23×D7312yes—
335C2×C4C23×D7312yes—
336C2×C4C23×D7312yes—
337C2×C4C23×D7312yes—
338C2×C4C23×D7312yes—
339C2×C4C23×D7312yes—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—44no—
344C22#41×D7312yes—
345C22#1455663812yes—
346C22#1455663812yes—
347C22C24×D7311yescharacteristic
348C4—22no—
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—734no—
355C4—1462no—
356C4—1462no—
357C4—1462no—
358C4—1462no—
359C4—1462no—
360C4—1462no—
361C4—1462no—
362C2—42no—
363C2#1798919414yesdirect product factor
364C2C2×#41×D7311yescharacteristic
365C2C2×#1455663811yescharacteristic
366C2C2×#1455663811yescharacteristic
subgroupG/H
centerC23C23×D73
commutatorC22×C73C25
FrattiniC22C24×D73
FittingC2×#126×C73C2
socleC23×C73C24
hypercenterC2×#126D73
hypocenterC73C2×#541
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #17989194C2direct (N × H)
2. C2×#14556590C2semidirect
6. C2×#14556583C2semidirect
7. C2×#14556582C2semidirect
8. C2×#14556581C2semidirect
9. C2×#14556581C2semidirect
10. C2×#14556581C2semidirect
13. C2×C4×Dic146C2semidirect
14. C2×#14556556C2semidirect
20. #14556590C22semidirect
24. #14556583C22semidirect
25. #14556582C22semidirect
26. #14556581C22semidirect
27. #14556581C22semidirect
28. #14556581C22semidirect
31. C4×Dic146C22semidirect
32. #14556556C22semidirect
179. C2×C73#541semidirect
184. C73C2×#541semidirect
363. C2#17989194direct (N × H)