Finite Group Databasebeta

← C2×#19099314 #23777531

Subgroups — C2×#19099314 #23777531

Order 10112.

1024 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#19099314C2116yesmaximal, direct product factor
2C2×#14579160C211yesmaximal, characteristic, complemented
3C2×#14579159C211yesmaximal, characteristic, complemented
4C2×#14579156C211yesmaximal, characteristic, complemented
5C2×#14579156C211yesmaximal, characteristic, complemented
6C2×#14579154C211yesmaximal, characteristic, complemented
7C2×#14579154C211yesmaximal, characteristic, complemented
8C2×#14579152C211yesmaximal, characteristic, complemented
9C2×#14579151C211yesmaximal, characteristic, complemented
10C2×#14579147C211yesmaximal, characteristic
11C2×#14579144C211yesmaximal, characteristic
12C2×#14579143C211yesmaximal, characteristic
13C2×#14579140C211yesmaximal, characteristic, complemented
14C2×#14579139C211yesmaximal, characteristic, complemented
15C2×#14579137C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C79C211yesmaximal, characteristic, complemented
17C22×Dic158C2211yescharacteristic
18C22×Dic158C2211yescharacteristic
19C22×C22⋊D79C2211yescharacteristic
20C22×C4×D79C2211yescharacteristic
21#14579160C2218yescomplemented
22#14579159C2218yescomplemented
23#14579156C2218yescomplemented
24#14579156C2218yescomplemented
25#14579154C2218yescomplemented
26#14579154C2218yescomplemented
27#14579152C2218yescomplemented
28#14579151C2218yescomplemented
29#14579147C2218yes—
30#14579144C2218yes—
31#14579143C2218yes—
32#14579140C2218yescomplemented
33#14579139C2218yescomplemented
34#14579137C2218yescomplemented
35C2×C4⋊Dic79C2211yescharacteristic
36C2×C4⋊Dic79C2211yescharacteristic
37C2×C4⋊Dic79C2211yescharacteristic
38C2×C4⋊Dic79C2211yescharacteristic
39C2×Dic79⋊C4C2211yescharacteristic
40C2×Dic79⋊C4C2211yescharacteristic
41C2×Dic79⋊C4C2211yescharacteristic
42C2×Dic79⋊C4C2211yescharacteristic
43C2×Dic79⋊C4C2211yescharacteristic
44C2×Dic79⋊C4C2211yescharacteristic
45C2×Dic79⋊C4C2211yescharacteristic
46C2×Dic79⋊C4C2211yescharacteristic
47C2×Dic79⋊C4C2211yescharacteristic
48C2×C22⋊Dic79C2211yescharacteristic
49C2×C22⋊Dic79C2211yescharacteristic
50C2×C22⋊Dic79C2211yescharacteristic
51C2×(C2×D79)⋊C4C2211yescharacteristic
52C2×(C2×D79)⋊C4C2211yescharacteristic
53C2×(C2×D79)⋊C4C2211yescharacteristic
54C2×(C2×D79)⋊C4C2211yescharacteristic
55C2×(C2×D79)⋊C4C2211yescharacteristic
56C2×C4×Dic79C2211yescharacteristic
57C2×C4×Dic79C2211yescharacteristic
58C2×C4×Dic79C2211yescharacteristic
59C22×Q8×C79C2211yescharacteristic
60C23×C4×C79C2211yescharacteristic
61C22⋊Q8×C79C2218yescomplemented
62C2×C4⋊C4×C79C2211yescharacteristic
63C2×C4⋊C4×C79C2211yescharacteristic
64C2×C4⋊C4×C79C2211yescharacteristic
65C2×C22⋊C4×C79C2211yescharacteristic
66C2×C22⋊C4×C79C2211yescharacteristic
67C23×D79C2311yescharacteristic
68C2×Dic158—42no—
69C2×Dic158—42no—
70C2×Dic158C2314yes—
71C2×Dic158C2314yes—
72C2×C22⋊D79—42no—
73C2×C22⋊D79C2314yes—
74C22×Dic79C2311yescharacteristic
75C22×Dic79C2311yescharacteristic
76C22×Dic79C2311yescharacteristic
77C22×Dic79C2311yescharacteristic
78C22×Dic79C2311yescharacteristic
79C22×Dic79C2311yescharacteristic
80C22×Dic79C2311yescharacteristic
81C2×C4×D79—42no—
82C2×C4×D79C2314yes—
83C4⋊Dic79C2314yes—
84C4⋊Dic79C2314yes—
85C4⋊Dic79C2314yes—
86C4⋊Dic79C2314yes—
87Dic79⋊C4C2314yes—
88Dic79⋊C4C2314yes—
89Dic79⋊C4C2314yes—
90Dic79⋊C4C2314yes—
91Dic79⋊C4C2314yes—
92Dic79⋊C4C2314yes—
93Dic79⋊C4C2314yes—
94Dic79⋊C4C2314yes—
95Dic79⋊C4C2314yes—
96C22⋊Dic79C2314yes—
97C22⋊Dic79C2314yes—
98C22⋊Dic79C2314yes—
99(C2×D79)⋊C4C2314yes—
100(C2×D79)⋊C4C2314yes—
101(C2×D79)⋊C4C2314yes—
102(C2×D79)⋊C4C2314yes—
103(C2×D79)⋊C4C2314yes—
104C4×Dic79C2314yes—
105C4×Dic79C2314yes—
106C4×Dic79C2314yes—
107C24×C79C2311yescharacteristic
108C2×Q8×C79—42no—
109C2×Q8×C79C2314yes—
110C22×C4×C79—42no—
111C22×C4×C79C2311yescharacteristic
112C22×C4×C79C2311yescharacteristic
113C22×C4×C79C2311yescharacteristic
114C22×C4×C79C2311yescharacteristic
115C22×C4×C79C2311yescharacteristic
116C22×C4×C79C2311yescharacteristic
117C22×C4×C79C2314yes—
118C4⋊C4×C79C2314yes—
119C4⋊C4×C79C2314yes—
120C4⋊C4×C79C2314yes—
121C22⋊C4×C79C2314yes—
122C22⋊C4×C79C2314yes—
123C23×C79—22no—
124C23×C79—22no—
125C23×C79—22no—
126C23×C79C2412yes—
127C23×C79C2411yescharacteristic
128C22×D79—22no—
129C22×D79—22no—
130C22×D79—22no—
131C22×D79C2412yes—
132Q8×C79—44no—
133C2×C4×C79—22no—
134C2×C4×C79—22no—
135C2×C4×C79—22no—
136C2×C4×C79—22no—
137C2×C4×C79—22no—
138C2×C4×C79—22no—
139C2×C4×C79—44no—
140C2×C4×C79C2412yes—
141C2×C4×C79C2412yes—
142C2×C4×C79C2412yes—
143C2×C4×C79C2412yes—
144C2×C4×C79C2412yes—
145C2×C4×C79C2412yes—
146C22⋊D79—44no—
147C2×Dic79—22no—
148C2×Dic79—22no—
149C2×Dic79—22no—
150C2×Dic79—22no—
151C2×Dic79—22no—
152C2×Dic79—22no—
153C2×Dic79—22no—
154C2×Dic79C2412yes—
155C2×Dic79C2412yes—
156C2×Dic79C2412yes—
157C2×Dic79C2412yes—
158C2×Dic79C2412yes—
159C2×Dic79C2412yes—
160C2×Dic79C2412yes—
161C4×D79—44no—
162Dic158—44no—
163Dic158—44no—
164C22×C79—22no—
165C22×C79—22no—
166C22×C79—22no—
167C22×C79—44no—
168C22×C79H(5,𝔽2)12yes—
169C22×C792−1+412yes—
170C22×C792−1+412yes—
171C22×C79C2511yescharacteristic
172C2×D79—22no—
173C2×D79—22no—
174C2×D79—22no—
175C2×D79—44no—
176C4×C79—22no—
177C4×C79—22no—
178C4×C79—22no—
179C4×C79—22no—
180C4×C79—22no—
181C4×C79—22no—
182Dic79—22no—
183Dic79—22no—
184Dic79—22no—
185Dic79—22no—
186Dic79—22no—
187Dic79—22no—
188Dic79—22no—
189C2×C79—42no—
190C2×C79#56314yescomplemented
191C2×C79C2×H(5,𝔽2)11yescharacteristic
192C2×C79C2×2−1+411yescharacteristic
193C2×C79C2×2−1+411yescharacteristic
194D79—42no—
195C2×#563—791nomaximal, Sylow
196C79C2×#56311yescharacteristic, complemented, Sylow
197#563—7916no—
198C2×C4⋊Q8—791no—
199C2×C4⋊Q8—791no—
200C2×#126—791no—
201C2×#126—791no—
202C2×#126—791no—
203C2×#126—791no—
204C2×#125—791no—
205C2×#125—791no—
206C2×#124—791no—
207C2×#123—791no—
208C2×#123—791no—
209C2×C22⋊Q8—791no—
210C2×C22⋊Q8—791no—
211C2×C22⋊Q8—791no—
212C2×C22⋊Q8D7911yescharacteristic, complemented
213C22×Q8—791no—
214C22×Q8—791no—
215C22×Q8C2×D7911yescharacteristic
216C22×D4—791no—
217C23×C4—791no—
218C23×C4C2×D7911yescharacteristic
219C4⋊Q8—798no—
220C4⋊Q8—798no—
221#126—798no—
222#126—798no—
223#126—798no—
224#126—798no—
225#125—798no—
226#125—798no—
227#124—798no—
228#123—798no—
229#123—798no—
230C22⋊Q8—798no—
231C22⋊Q8—798no—
232C22⋊Q8—798no—
233C22⋊Q8C2×D7918yescomplemented
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C4⋊C4—791no—
237C2×C4⋊C4—791no—
238C2×C4⋊C4—791no—
239C2×C4⋊C4—791no—
240C2×C4⋊C4—791no—
241C2×C4⋊C4—791no—
242C2×C4⋊C4—791no—
243C2×C4⋊C4—791no—
244C2×C4⋊C4—791no—
245C2×C4⋊C4—791no—
246C2×C4⋊C4—791no—
247C2×C4⋊C4C2×D7911yescharacteristic
248C2×C4⋊C4C2×D7911yescharacteristic
249C2×C4⋊C4C2×D7911yescharacteristic
250C2×C22⋊C4—791no—
251C2×C22⋊C4—791no—
252C2×C22⋊C4—791no—
253C2×C22⋊C4—791no—
254C2×C22⋊C4—791no—
255C2×C22⋊C4—791no—
256C2×C22⋊C4—791no—
257C2×C22⋊C4—791no—
258C2×C22⋊C4C2×D7911yescharacteristic
259C2×C22⋊C4C2×D7911yescharacteristic
260C2×C42—791no—
261C2×C42—791no—
262C2×C42—791no—
263C24—791no—
264C24C22×D7911yescharacteristic
265C2×Q8—42no—
266C2×Q8—3162no—
267C2×Q8—3162no—
268C2×Q8—794no—
269C2×Q8—794no—
270C2×Q8C22×D7914yes—
271C2×D4—3162no—
272C2×D4—794no—
273C22×C4—42no—
274C22×C4—3162no—
275C22×C4—794no—
276C22×C4—791no—
277C22×C4—791no—
278C22×C4—791no—
279C22×C4—791no—
280C22×C4—791no—
281C22×C4—791no—
282C22×C4—791no—
283C22×C4C22×D7911yescharacteristic
284C22×C4C22×D7911yescharacteristic
285C22×C4C22×D7911yescharacteristic
286C22×C4C22×D7911yescharacteristic
287C22×C4C22×D7911yescharacteristic
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7914yes—
290C4⋊C4—794no—
291C4⋊C4—794no—
292C4⋊C4—794no—
293C4⋊C4—794no—
294C4⋊C4—794no—
295C4⋊C4—794no—
296C4⋊C4—794no—
297C4⋊C4—794no—
298C4⋊C4—794no—
299C4⋊C4—794no—
300C4⋊C4—794no—
301C4⋊C4—794no—
302C4⋊C4—794no—
303C4⋊C4C22×D7914yes—
304C4⋊C4C22×D7914yes—
305C4⋊C4C22×D7914yes—
306C22⋊C4—794no—
307C22⋊C4—794no—
308C22⋊C4—794no—
309C22⋊C4—794no—
310C22⋊C4—794no—
311C22⋊C4—794no—
312C22⋊C4—794no—
313C22⋊C4—794no—
314C22⋊C4C22×D7914yes—
315C22⋊C4C22×D7914yes—
316C42—794no—
317C42—794no—
318C42—794no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—792no—
323C23—1582no—
324C23—1582no—
325C23—1582no—
326C23C23×D7912yes—
327C23C23×D7911yescharacteristic
328Q8—44no—
329Q8—3164no—
330Q8—3164no—
331D4—3164no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—44no—
339C2×C4—3164no—
340C2×C4—792no—
341C2×C4—792no—
342C2×C4—792no—
343C2×C4—792no—
344C2×C4—792no—
345C2×C4—792no—
346C2×C4—792no—
347C2×C4—1582no—
348C2×C4—1582no—
349C2×C4—1582no—
350C2×C4—1582no—
351C2×C4—1582no—
352C2×C4—1582no—
353C2×C4—1582no—
354C2×C4C23×D7912yes—
355C2×C4C23×D7912yes—
356C2×C4C23×D7912yes—
357C2×C4C23×D7912yes—
358C2×C4C23×D7912yes—
359C2×C4C23×D7912yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—44no—
364C22—3164no—
365C22—1582no—
366C22—1582no—
367C22—1582no—
368C22#1457920612yes—
369C22#1457920812yes—
370C22#1457920912yes—
371C22C24×D7911yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—22no—
378C4—1582no—
379C4—1582no—
380C4—1582no—
381C4—1582no—
382C4—1582no—
383C4—1582no—
384C4—1582no—
385C2—42no—
386C2—3162no—
387C2#1909931414yesdirect product factor
388C2C2×#1457920611yescharacteristic
389C2C2×#1457920811yescharacteristic
390C2C2×#1457920911yescharacteristic
subgroupG/H
centerC23C23×D79
commutator, cosocleC22×C79C25
FrattiniC22C24×D79
FittingC2×C22⋊Q8×C79C2
socleC23×C79C24
prime radicalC22×C22⋊D79C22
hypercenterC2×C22⋊Q8D79
hypocenterC79C2×#563
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #19099314C2direct (N × H)
2. C2×#14579160C2semidirect
3. C2×#14579159C2semidirect
4. C2×#14579156C2semidirect
5. C2×#14579156C2semidirect
6. C2×#14579154C2semidirect
7. C2×#14579154C2semidirect
8. C2×#14579152C2semidirect
9. C2×#14579151C2semidirect
13. C2×#14579140C2semidirect
14. C2×#14579139C2semidirect
15. C2×#14579137C2semidirect
16. C2×C22⋊Q8×C79C2semidirect
21. #14579160C22semidirect
22. #14579159C22semidirect
23. #14579156C22semidirect
24. #14579156C22semidirect
25. #14579154C22semidirect
26. #14579154C22semidirect
27. #14579152C22semidirect
28. #14579151C22semidirect
32. #14579140C22semidirect
33. #14579139C22semidirect
34. #14579137C22semidirect
61. C22⋊Q8×C79C22semidirect
190. C2×C79#563semidirect
196. C79C2×#563semidirect
212. C2×C22⋊Q8D79semidirect
233. C22⋊Q8C2×D79semidirect
387. C2#19099314direct (N × H)