Finite Group Databasebeta

← C2×#17989274 #22623440

Subgroups — C2×#17989274 #22623440

Order 9344.

1124 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
1#17989274C2116yesmaximal, direct product factor
2C2×#14556584C211yesmaximal, characteristic, complemented
3C2×#14556584C211yesmaximal, characteristic, complemented
4C2×#14556582C211yesmaximal, characteristic, complemented
5C2×#14556581C211yesmaximal, characteristic, complemented
6C2×#14556581C211yesmaximal, characteristic, complemented
7C2×#14556572C211yesmaximal, characteristic
8C2×#14556568C211yesmaximal, characteristic, complemented
9C2×#14556568C211yesmaximal, characteristic, complemented
10C2×#14556556C211yesmaximal, characteristic, complemented
11C2×D4×Dic73C211yesmaximal, characteristic
12C2×#14556550C211yesmaximal, characteristic, complemented
13C2×#14556547C211yesmaximal, characteristic, complemented
14C2×#14556547C211yesmaximal, characteristic, complemented
15C22×#11924007C211yesmaximal, characteristic, complemented
16C2×#123×C73C211yesmaximal, characteristic
17C22×Dic146C2211yescharacteristic
18C23×Dic73C2211yescharacteristic
19C23×Dic73C2211yescharacteristic
20C23×Dic73C2211yescharacteristic
21#14556584C2218yescomplemented
22#14556584C2218yescomplemented
23#14556582C2218yescomplemented
24#14556581C2218yescomplemented
25#14556581C2218yescomplemented
26#14556572C2218yes—
27#14556568C2218yescomplemented
28#14556568C2218yescomplemented
29#14556556C2218yescomplemented
30D4×Dic73C2218yes—
31#14556550C2218yescomplemented
32#14556547C2218yescomplemented
33#14556547C2218yescomplemented
34C2×C4⋊Dic73C2211yescharacteristic
35C2×C4⋊Dic73C2211yescharacteristic
36C2×C4⋊Dic73C2211yescharacteristic
37C2×C4⋊Dic73C2211yescharacteristic
38C2×#11924007C2211yescharacteristic
39C2×#11924007C2211yescharacteristic
40C2×#11924007C2211yescharacteristic
41C2×#11924007C2211yescharacteristic
42C2×#11924007C2211yescharacteristic
43C2×#11924007C2211yescharacteristic
44C2×#11924007C2211yescharacteristic
45C2×#11924007C2211yescharacteristic
46C2×#11924007C2211yescharacteristic
47C2×#11924007C2211yescharacteristic
48C2×#11924007C2218yescomplemented
49C2×C22⋊Dic73C2211yescharacteristic
50C2×C22⋊Dic73C2211yescharacteristic
51C2×C22⋊Dic73C2211yescharacteristic
52C2×C22⋊Dic73C2211yescharacteristic
53C2×C22⋊Dic73C2211yescharacteristic
54C2×C4×Dic73C2211yescharacteristic
55C2×C4×Dic73C2211yescharacteristic
56C2×C4×Dic73C2211yescharacteristic
57C2×C4×Dic73C2211yescharacteristic
58C2×C4×Dic73C2211yescharacteristic
59C22×D4×C73C2211yescharacteristic
60C23×C4×C73C2211yescharacteristic
61#123×C73C2218yes—
62C2×C4⋊C4×C73C2211yescharacteristic
63C2×C4⋊C4×C73C2211yescharacteristic
64C2×C22⋊C4×C73C2211yescharacteristic
65C2×C22⋊C4×C73C2211yescharacteristic
66C2×C22⋊C4×C73C2211yescharacteristic
67C2×Dic146—24no—
68C2×Dic146C2314yes—
69C22×Dic73—24no—
70C22×Dic73—24no—
71C22×Dic73—24no—
72C22×Dic73C2311yescharacteristic
73C22×Dic73C2311yescharacteristic
74C22×Dic73C2311yescharacteristic
75C22×Dic73C2311yescharacteristic
76C22×Dic73C2311yescharacteristic
77C22×Dic73C2311yescharacteristic
78C22×Dic73C2311yescharacteristic
79C22×Dic73C2314yes—
80C22×Dic73C2314yes—
81C22×Dic73C2314yes—
82C22×Dic73C2311yescharacteristic
83C4⋊Dic73C2314yes—
84C4⋊Dic73C2314yes—
85C4⋊Dic73C2314yes—
86C4⋊Dic73C2314yes—
87#11924007C2314yes—
88#11924007C2314yes—
89#11924007C2314yes—
90#11924007C2314yes—
91#11924007C2314yes—
92#11924007C2314yes—
93#11924007C2314yes—
94#11924007C2314yes—
95#11924007C2314yes—
96#11924007C2314yes—
97C22⋊Dic73C2314yes—
98C22⋊Dic73C2314yes—
99C22⋊Dic73C2314yes—
100C22⋊Dic73C2314yes—
101C22⋊Dic73C2314yes—
102C4×Dic73C2314yes—
103C4×Dic73C2314yes—
104C4×Dic73C2314yes—
105C4×Dic73C2314yes—
106C4×Dic73C2314yes—
107C24×C73C2311yescharacteristic
108C24×C73C2311yescharacteristic
109C2×D4×C73—24no—
110C2×D4×C73C2314yes—
111C22×C4×C73—24no—
112C22×C4×C73C2311yescharacteristic
113C22×C4×C73C2311yescharacteristic
114C22×C4×C73C2311yescharacteristic
115C22×C4×C73C2311yescharacteristic
116C22×C4×C73C2311yescharacteristic
117C22×C4×C73C2314yes—
118C4⋊C4×C73C2314yes—
119C4⋊C4×C73C2314yes—
120C22⋊C4×C73C2314yes—
121C22⋊C4×C73C2314yes—
122C22⋊C4×C73C2314yes—
123C23×C73—22no—
124C23×C73—22no—
125C23×C73—22no—
126C23×C73—22no—
127C23×C73—22no—
128C23×C73#4114yes—
129C23×C73C2412yes—
130C23×C73C2412yes—
131C23×C73C2411yescharacteristic
132D4×C73—28no—
133C2×C4×C73—28no—
134C2×C4×C73—22no—
135C2×C4×C73—22no—
136C2×C4×C73—22no—
137C2×C4×C73—22no—
138C2×C4×C73—22no—
139C2×C4×C73C2412yes—
140C2×C4×C73C2412yes—
141C2×C4×C73C2412yes—
142C2×C4×C73C2412yes—
143C2×C4×C73C2412yes—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—28no—
147C2×Dic73—22no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73—22no—
151C2×Dic73—22no—
152C2×Dic73—28no—
153C2×Dic73—28no—
154C2×Dic73#4114yes—
155C2×Dic73C2412yes—
156C2×Dic73C2412yes—
157C2×Dic73C2412yes—
158C2×Dic73C2412yes—
159C2×Dic73C2412yes—
160C2×Dic73C2412yes—
161C2×Dic73C2412yes—
162C2×Dic73C2412yes—
163Dic146—28no—
164C22×C73—28no—
165C22×C73—22no—
166C22×C73—22no—
167C22×C73—22no—
168C22×C73—22no—
169C22×C73—22no—
170C22×C73—44no—
171C22×C73C2×#4112yes—
172C22×C73C2×#4114yes—
173C22×C73C2×#4112yes—
174C22×C732−1+412yes—
175C22×C73C2511yescharacteristic
176C4×C73—22no—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—22no—
180C4×C73—22no—
181Dic73—22no—
182Dic73—22no—
183Dic73—22no—
184Dic73—22no—
185Dic73—22no—
186Dic73—22no—
187Dic73—22no—
188Dic73C2×#4114yes—
189C2×C73—24no—
190C2×C73—42no—
191C2×C73#55214yescomplemented
192C2×C73C22×#4111yescharacteristic
193C2×C73C22×#4111yescharacteristic
194C2×C73C2×2−1+411yescharacteristic
195C2×#552—731nomaximal, Sylow
196C73C2×#55211yescharacteristic, complemented, Sylow
197#552—7316no—
198C2×#126—731no—
199C2×#126—731no—
200C2×#125—731no—
201C2×#125—731no—
202C2×#125—731no—
203C2×#123—731no—
204C2×#123D7311yescharacteristic
205C2×C22⋊Q8—731no—
206C2×C22⋊Q8—731no—
207C2×C4×Q8—731no—
208C2×C4×D4—731no—
209C2×#117—731no—
210C2×#117—731no—
211C2×#117—731no—
212C22×C4⋊C4—731no—
213C22×Q8—731no—
214C22×D4C2×D7311yescharacteristic
215C23×C4—731no—
216C23×C4—731no—
217C23×C4—731no—
218C23×C4C2×D7311yescharacteristic
219#126—738no—
220#126—738no—
221#125—738no—
222#125—738no—
223#125—738no—
224#123—738no—
225#123C2×D7318yes—
226C22⋊Q8—738no—
227C22⋊Q8—738no—
228C4×Q8—738no—
229C4×D4—738no—
230#117—738no—
231#117—738no—
232#117—738no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—731no—
236C2×C4⋊C4—731no—
237C2×C4⋊C4—738no—
238C2×C4⋊C4—731no—
239C2×C4⋊C4—731no—
240C2×C4⋊C4—731no—
241C2×C4⋊C4—731no—
242C2×C4⋊C4—731no—
243C2×C4⋊C4—731no—
244C2×C4⋊C4—731no—
245C2×C4⋊C4—731no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—731no—
248C2×C4⋊C4C2×D7311yescharacteristic
249C2×C4⋊C4C2×D7311yescharacteristic
250C2×C22⋊C4—731no—
251C2×C22⋊C4—731no—
252C2×C22⋊C4—731no—
253C2×C22⋊C4—731no—
254C2×C22⋊C4—731no—
255C2×C22⋊C4C2×D7311yescharacteristic
256C2×C22⋊C4C2×D7311yescharacteristic
257C2×C22⋊C4C2×D7311yescharacteristic
258C2×C42—731no—
259C2×C42—731no—
260C2×C42—731no—
261C2×C42—731no—
262C2×C42—731no—
263C24C22×D7311yescharacteristic
264C24C22×D7311yescharacteristic
265C2×Q8—734no—
266C2×Q8—1464no—
267C2×D4—24no—
268C2×D4C22×D7314yes—
269C22×C4—24no—
270C22×C4—731no—
271C22×C4—734no—
272C22×C4—734no—
273C22×C4—734no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—1464no—
282C22×C4—1464no—
283C22×C4—1464no—
284C22×C4C22×D7314yes—
285C22×C4C22×D7311yescharacteristic
286C22×C4C22×D7311yescharacteristic
287C22×C4C22×D7311yescharacteristic
288C22×C4C22×D7311yescharacteristic
289C22×C4C22×D7311yescharacteristic
290C4⋊C4—734no—
291C4⋊C4—734no—
292C4⋊C4—734no—
293C4⋊C4—734no—
294C4⋊C4—734no—
295C4⋊C4—734no—
296C4⋊C4—734no—
297C4⋊C4—734no—
298C4⋊C4—734no—
299C4⋊C4—734no—
300C4⋊C4—734no—
301C4⋊C4—734no—
302C4⋊C4—734no—
303C4⋊C4—734no—
304C4⋊C4C22×D7314yes—
305C4⋊C4C22×D7314yes—
306C22⋊C4—734no—
307C22⋊C4—734no—
308C22⋊C4—734no—
309C22⋊C4—734no—
310C22⋊C4—734no—
311C22⋊C4C22×D7314yes—
312C22⋊C4C22×D7314yes—
313C22⋊C4C22×D7314yes—
314C42—734no—
315C42—734no—
316C42—734no—
317C42—734no—
318C42—734no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23#1192402714yes—
325C23C23×D7312yes—
326C23C23×D7312yes—
327C23C23×D7311yescharacteristic
328Q8—1468no—
329D4—28no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—734no—
337C2×C4—732no—
338C2×C4—732no—
339C2×C4—732no—
340C2×C4—732no—
341C2×C4—732no—
342C2×C4—732no—
343C2×C4—732no—
344C2×C4—732no—
345C2×C4—1468no—
346C2×C4—1468no—
347C2×C4—1462no—
348C2×C4—1462no—
349C2×C4—1462no—
350C2×C4—1468no—
351C2×C4—1462no—
352C2×C4—1462no—
353C2×C4—1462no—
354C2×C4—1462no—
355C2×C4C23×D7312yes—
356C2×C4C23×D7312yes—
357C2×C4C23×D7312yes—
358C2×C4C23×D7312yes—
359C2×C4C23×D7312yes—
360C22—22no—
361C22—22no—
362C22—28no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—44no—
367C22#41×D7312yes—
368C22C2×#1192402714yes—
369C22C2×#1192402712yes—
370C22#1455663812yes—
371C22C24×D7311yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—734no—
378C4—1462no—
379C4—1462no—
380C4—1462no—
381C4—1462no—
382C4—1462no—
383C4—1462no—
384C4—1462no—
385C2—24no—
386C2—42no—
387C2#1798927414yesdirect product factor
388C2C2×#41×D7311yescharacteristic
389C2C22×#1192402711yescharacteristic
390C2C2×#1455663811yescharacteristic
subgroupG/H
centerC23C23×D73
commutatorC22×C73C25
FrattiniC22C24×D73
FittingC2×#123×C73C2
socleC23×C73C24
hypercenterC2×#123D73
hypocenterC73C2×#552
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #17989274C2direct (N × H)
2. C2×#14556584C2semidirect
3. C2×#14556584C2semidirect
4. C2×#14556582C2semidirect
5. C2×#14556581C2semidirect
6. C2×#14556581C2semidirect
8. C2×#14556568C2semidirect
9. C2×#14556568C2semidirect
10. C2×#14556556C2semidirect
12. C2×#14556550C2semidirect
13. C2×#14556547C2semidirect
14. C2×#14556547C2semidirect
15. C22×#11924007C2semidirect
21. #14556584C22semidirect
22. #14556584C22semidirect
23. #14556582C22semidirect
24. #14556581C22semidirect
25. #14556581C22semidirect
27. #14556568C22semidirect
28. #14556568C22semidirect
29. #14556556C22semidirect
31. #14556550C22semidirect
32. #14556547C22semidirect
33. #14556547C22semidirect
48. C2×#11924007C22semidirect
191. C2×C73#552semidirect
196. C73C2×#552semidirect
387. C2#17989274direct (N × H)