Finite Group Databasebeta

← C2×#23771580 #34494645

Subgroups — C2×#23771580 #34494645

Order 20224.

1718 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23771580C2116yesmaximal, direct product factor
2C2×C79⋊#401C212yesmaximal
3C2×#19098505C212yesmaximal
4C2×#19098503C212yesmaximal
5C2×#19098502C211yesmaximal, characteristic
6C2×#19098496C212yesmaximal
7C2×#19098483C212yesmaximal
8C2×#19098468C211yesmaximal, characteristic
9C2×#19098449C212yesmaximal
10C2×#398×C79C211yesmaximal, characteristic
11C23×Dic158C2211yescharacteristic
12C22×C4⋊Dic79C2212yes—
13C22×C4⋊Dic79C2211yescharacteristic
14C22×Dic79⋊C4C2212yes—
15C22×Dic79⋊C4C2212yes—
16C22×C4×Dic79C2211yescharacteristic
17C79⋊#401C22116yes—
18#19098505C22116yes—
19#19098503C22116yes—
20#19098502C2218yes—
21#19098496C22116yes—
22#19098483C22116yes—
23#19098468C2218yes—
24#19098449C22116yes—
25C2×C79⋊#95C2212yes—
26C2×C79⋊#95C2212yes—
27C2×C79⋊#95C2212yes—
28C2×C79⋊#95C2212yes—
29C2×C79⋊#95C2212yes—
30C2×C79⋊#95C2212yes—
31C2×C79⋊#95C2212yes—
32C2×C79⋊#95C2212yes—
33C2×C79⋊#95C2212yes—
34C2×C79⋊#95C2211yescharacteristic
35C22×C4⋊C4×C79C2212yes—
36C22×C4⋊C4×C79C2211yescharacteristic
37C22×C4⋊C4×C79C2211yescharacteristic
38#398×C79C2218yes—
39C2×#95×C79C2212yes—
40C2×#95×C79C2211yescharacteristic
41C22×Dic158—24no—
42C22×Dic158—42no—
43C22×Dic158—42no—
44C22×Dic158C2314yes—
45C23×Dic79C2312yes—
46C23×Dic79C2312yes—
47C23×Dic79C2312yes—
48C23×Dic79C2312yes—
49C2×C4⋊Dic79—44no—
50C2×C4⋊Dic79—42no—
51C2×C4⋊Dic79C2318yes—
52C2×C4⋊Dic79C2314yes—
53C2×Dic79⋊C4—44no—
54C2×Dic79⋊C4—44no—
55C2×Dic79⋊C4C2318yes—
56C2×Dic79⋊C4C2318yes—
57C2×C4×Dic79—42no—
58C2×C4×Dic79C2314yes—
59C79⋊#95C2318yes—
60C79⋊#95C2318yes—
61C79⋊#95C2318yes—
62C79⋊#95C2318yes—
63C79⋊#95C2318yes—
64C79⋊#95C2318yes—
65C79⋊#95C2318yes—
66C79⋊#95C2318yes—
67C79⋊#95C2318yes—
68C79⋊#95C2314yes—
69C23×C4×C79C2311yescharacteristic
70C23×C4×C79C2312yes—
71C23×C4×C79C2311yescharacteristic
72C23×C4×C79C2312yes—
73C23×C4×C79C2311yescharacteristic
74C2×C4⋊C4×C79—28no—
75C2×C4⋊C4×C79—42no—
76C2×C4⋊C4×C79—42no—
77C2×C4⋊C4×C79C2318yes—
78C2×C4⋊C4×C79C2314yes—
79C2×C4⋊C4×C79C2314yes—
80#95×C79C2318yes—
81#95×C79C2314yes—
82C2×Dic158—28no—
83C2×Dic158—44no—
84C2×Dic158—44no—
85C2×Dic158—416no—
86C22×Dic79—24no—
87C22×Dic79—24no—
88C22×Dic79—24no—
89C22×Dic79—24no—
90C22×Dic79—24no—
91C22×Dic79—24no—
92C22×Dic79—24no—
93C22×Dic79—24no—
94C22×Dic79—24no—
95C22×Dic79—28no—
96C22×Dic79—24no—
97C22×Dic79C2414yes—
98C22×Dic79C2414yes—
99C22×Dic79C2414yes—
100C22×Dic79C2414yes—
101C4⋊Dic79—48no—
102C4⋊Dic79—44no—
103Dic79⋊C4—48no—
104Dic79⋊C4—48no—
105C4×Dic79—44no—
106C24×C79C2411yescharacteristic
107C22×C4×C79—22no—
108C22×C4×C79—22no—
109C22×C4×C79—24no—
110C22×C4×C79—24no—
111C22×C4×C79—22no—
112C22×C4×C79—24no—
113C22×C4×C79—22no—
114C22×C4×C79—24no—
115C22×C4×C79—24no—
116C22×C4×C79—24no—
117C22×C4×C79—24no—
118C22×C4×C79—24no—
119C22×C4×C79#4114yes—
120C22×C4×C79C2414yes—
121C22×C4×C79C2412yes—
122C22×C4×C79C2412yes—
123C22×C4×C79C2414yes—
124C22×C4×C79C2412yes—
125C4⋊C4×C79—216no—
126C4⋊C4×C79—44no—
127C4⋊C4×C79—44no—
128C23×C79C2×#4112yes—
129C23×C79H(5,𝔽2)12yes—
130C23×C79H(5,𝔽2)12yes—
131C23×C792−1+414yes—
132C23×C792−1+414yes—
133C23×C79C2511yescharacteristic
134C2×C4×C79—28no—
135C2×C4×C79—22no—
136C2×C4×C79—22no—
137C2×C4×C79—24no—
138C2×C4×C79—24no—
139C2×C4×C79—24no—
140C2×C4×C79—24no—
141C2×C4×C79—22no—
142C2×C4×C79—22no—
143C2×C4×C79—24no—
144C2×C4×C79—24no—
145C2×C4×C79—24no—
146C2×C4×C79—24no—
147C2×C4×C79—48no—
148C2×C4×C79—48no—
149C2×C4×C79—44no—
150C2×C4×C79—44no—
151C2×C4×C79C2×#4114yes—
152C2×Dic79—24no—
153C2×Dic79—24no—
154C2×Dic79—24no—
155C2×Dic79—24no—
156C2×Dic79—24no—
157C2×Dic79—24no—
158C2×Dic79—24no—
159C2×Dic79—24no—
160C2×Dic79—24no—
161C2×Dic79—28no—
162C2×Dic79—24no—
163C2×Dic79—48no—
164C2×Dic79—48no—
165C2×Dic79—48no—
166C2×Dic79—48no—
167Dic158—416no—
168C22×C79#53814yes—
169C22×C79#54118yes—
170C22×C79#56314yes—
171C22×C79#56314yes—
172C22×C79#56318yes—
173C22×C79C22×#4111yescharacteristic
174C22×C79C2×H(5,𝔽2)11yescharacteristic
175C22×C79C2×H(5,𝔽2)11yescharacteristic
176C22×C79C2×2−1+412yes—
177C22×C79C2×2−1+412yes—
178C4×C79—24no—
179C4×C79—44no—
180C4×C79—44no—
181C4×C79—42no—
182C4×C79—42no—
183Dic79—44no—
184Dic79—44no—
185Dic79—44no—
186Dic79—44no—
187C2×#2833—791nomaximal, Sylow
188C2×C79#283318yescomplemented
189C2×C79C2×#53811yescharacteristic
190C2×C79C2×#54112yes—
191C2×C79C2×#56311yescharacteristic
192C2×C79C2×#56311yescharacteristic
193C2×C79C2×#56312yes—
194#2833—7916no—
195C2×#401—792no—
196C2×#400—792no—
197C2×#400—792no—
198C2×#400—791no—
199C2×#398—792no—
200C2×#398D7911yescharacteristic
201C2×#395—792no—
202C2×#391—791no—
203C2×#387—792no—
204C79C2×#283311yescharacteristic, complemented, Sylow
205C23×Q8—791no—
206C22×C4⋊C4—792no—
207C22×C4⋊C4—792no—
208C22×C4⋊C4—792no—
209C22×C4⋊C4—791no—
210C22×C4⋊C4C2×D7912yes—
211C22×C4⋊C4C2×D7911yescharacteristic
212C22×C4⋊C4C2×D7911yescharacteristic
213C22×C42—791no—
214#401—7916no—
215#400—798no—
216#400—7916no—
217#400—7916no—
218#398—7916no—
219#398C2×D7918yes—
220#395—7916no—
221#391—798no—
222#387—7916no—
223C2×#95—792no—
224C2×#95—792no—
225C2×#95—792no—
226C2×#95—792no—
227C2×#95—792no—
228C2×#95—792no—
229C2×#95—791no—
230C2×#95—792no—
231C2×#95—792no—
232C2×#95—792no—
233C2×#95C2×D7912yes—
234C2×#95C2×D7911yescharacteristic
235C22×Q8—3162no—
236C22×Q8—3162no—
237C22×Q8—794no—
238C22×Q8—1584no—
239C23×C4—792no—
240C23×C4—792no—
241C23×C4—792no—
242C23×C4—792no—
243C23×C4C22×D7912yes—
244C23×C4C22×D7911yescharacteristic
245C23×C4C22×D7911yescharacteristic
246C23×C4C22×D7912yes—
247C23×C4C22×D7911yescharacteristic
248C2×C4⋊C4—28no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—42no—
251C2×C4⋊C4—3164no—
252C2×C4⋊C4—3164no—
253C2×C4⋊C4—3162no—
254C2×C4⋊C4—3164no—
255C2×C4⋊C4—798no—
256C2×C4⋊C4—798no—
257C2×C4⋊C4—798no—
258C2×C4⋊C4—794no—
259C2×C4⋊C4C22×D7918yes—
260C2×C4⋊C4C22×D7914yes—
261C2×C4⋊C4C22×D7914yes—
262C2×C42—3162no—
263C2×C42—794no—
264#95—798no—
265#95—798no—
266#95—798no—
267#95—798no—
268#95—798no—
269#95—798no—
270#95—798no—
271#95—798no—
272#95—798no—
273#95—794no—
274#95C22×D7918yes—
275#95C22×D7914yes—
276C24C23×D7911yescharacteristic
277C2×Q8—31616no—
278C2×Q8—3164no—
279C2×Q8—3164no—
280C2×Q8—1588no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—794no—
294C22×C4—794no—
295C22×C4—794no—
296C22×C4—794no—
297C22×C4—1584no—
298C22×C4—1584no—
299C22×C4—1584no—
300C22×C4—1584no—
301C22×C4—1584no—
302C22×C4—1584no—
303C22×C4—1584no—
304C22×C4—1584no—
305C22×C4—1588no—
306C22×C4—1584no—
307C22×C4—1584no—
308C22×C4#1192962314yes—
309C22×C4C23×D7914yes—
310C22×C4C23×D7912yes—
311C22×C4C23×D7912yes—
312C22×C4C23×D7914yes—
313C22×C4C23×D7912yes—
314C4⋊C4—216no—
315C4⋊C4—44no—
316C4⋊C4—44no—
317C4⋊C4—3168no—
318C4⋊C4—3168no—
319C4⋊C4—3164no—
320C4⋊C4—3168no—
321C42—3164no—
322C23C2×#1192962312yes—
323C23#1457920612yes—
324C23#1457920712yes—
325C23#1457920814yes—
326C23#1457920914yes—
327C23C24×D7911yescharacteristic
328Q8—31616no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—48no—
343C2×C4—48no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—3168no—
347C2×C4—3168no—
348C2×C4—3168no—
349C2×C4—3168no—
350C2×C4—1584no—
351C2×C4—1584no—
352C2×C4—1584no—
353C2×C4—1584no—
354C2×C4—1584no—
355C2×C4—1584no—
356C2×C4—1584no—
357C2×C4—1588no—
358C2×C4—1584no—
359C2×C4—1584no—
360C2×C4—1584no—
361C2×C4C2×#1192962314yes—
362C22#1909915014yes—
363C22#1909917318yes—
364C22#1909931214yes—
365C22#1909931614yes—
366C22#1909931718yes—
367C22C22×#1192962311yescharacteristic
368C22C2×#1457920611yescharacteristic
369C22C2×#1457920711yescharacteristic
370C22C2×#1457920812yes—
371C22C2×#1457920912yes—
372C4—24no—
373C4—44no—
374C4—42no—
375C4—42no—
376C4—44no—
377C4—3164no—
378C4—3164no—
379C4—3164no—
380C4—3164no—
381C2#2377158018yesdirect product factor
382C2C2×#1909915011yescharacteristic
383C2C2×#1909917312yes—
384C2C2×#1909931211yescharacteristic
385C2C2×#1909931611yescharacteristic
386C2C2×#1909931712yes—
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#398×C79C2
socle, prime radicalC24×C79C24
hypercenterC2×#398D79
hypocenterC79C2×#2833
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #23771580C2direct (N × H)
188. C2×C79#2833semidirect
204. C79C2×#2833semidirect
381. C2#23771580direct (N × H)

Maximal subgroups

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

subgroupindex
#237715802
C2×C79⋊#4012
C2×#190985052
C2×#190985032
C2×#190985022
C2×#190984962
C2×#190984832
C2×#190984682
C2×#190984492
C2×#398×C792
C2×#283379