Finite Group Databasebeta

← C2×#23769230 #34455336

Subgroups — C2×#23769230 #34455336

Order 20224.

2614 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579153C211yesmaximal, characteristic, complemented
2#23769230C2116yesmaximal, direct product factor
3C2×#19098496C214yesmaximal, complemented
4C2×#19098486C214yesmaximal
5C2×#19098461C212yesmaximal, complemented
6C2×#19098433C211yesmaximal, characteristic, complemented
7C2×#19098423C212yesmaximal
8C22×#117×C79C211yesmaximal, characteristic
9C2×#14579153—28no—
10C2×#14579153C2218yescomplemented
11C22×C4⋊Dic79C2212yes—
12C22×C4⋊Dic79C2212yes—
13C22×C4⋊Dic79C2214yes—
14C22×Dic79⋊C4C2214yes—
15C22×Dic79⋊C4C2214yes—
16C22×C22⋊Dic79C2214yes—
17#19098496C22132yescomplemented
18#19098486C22132yes—
19#19098461C22116yescomplemented
20#19098433C2218yescomplemented
21#19098423C22116yes—
22C2×C79⋊#95C2214yes—
23C2×C79⋊#95C2214yes—
24C24×C4×C79C2211yescharacteristic
25C2×#117×C79—28no—
26C2×#117×C79C2218yes—
27C22×C4⋊C4×C79C2212yes—
28C22×C22⋊C4×C79C2212yes—
29C22×C42×C79C2211yescharacteristic
30C22×C42×C79C2211yescharacteristic
31C23×Dic79C2314yes—
32C23×Dic79C2314yes—
33#14579153—232no—
34C2×C4⋊Dic79—28no—
35C2×C4⋊Dic79—28no—
36C2×C4⋊Dic79—48no—
37C2×C4⋊Dic79C2318yes—
38C2×C4⋊Dic79C2318yes—
39C2×C4⋊Dic79C23116yes—
40C2×Dic79⋊C4—216no—
41C2×Dic79⋊C4—48no—
42C2×Dic79⋊C4C23116yes—
43C2×Dic79⋊C4C23116yes—
44C2×C22⋊Dic79—48no—
45C2×C22⋊Dic79C23116yes—
46C79⋊#95C23116yes—
47C79⋊#95C23116yes—
48C25×C79C2311yescharacteristic
49C23×C4×C79—24no—
50C23×C4×C79—24no—
51C23×C4×C79Q818yes—
52C23×C4×C79C2312yes—
53C23×C4×C79C2312yes—
54C23×C4×C79C2311yescharacteristic
55C23×C4×C79C2314yes—
56C23×C4×C79C2311yescharacteristic
57#117×C79—232no—
58C2×C4⋊C4×C79—28no—
59C2×C4⋊C4×C79C2318yes—
60C2×C22⋊C4×C79—28no—
61C2×C22⋊C4×C79C2318yes—
62C2×C42×C79—24no—
63C2×C42×C79D418yes—
64C2×C42×C79C2314yes—
65C2×C42×C79C2314yes—
66C22×Dic79—28no—
67C22×Dic79—28no—
68C22×Dic79—28no—
69C22×Dic79—28no—
70C22×Dic79—28no—
71C22×Dic79—28no—
72C22×Dic79C2418yes—
73C22×Dic79C2418yes—
74C4⋊Dic79—216no—
75C4⋊Dic79—216no—
76C4⋊Dic79—416no—
77Dic79⋊C4—232no—
78Dic79⋊C4—416no—
79C22⋊Dic79—416no—
80C24×C79—22no—
81C24×C79—22no—
82C24×C79—24no—
83C24×C79—24no—
84C24×C79C2×Q814yes—
85C24×C79C2412yes—
86C24×C79C2411yescharacteristic
87C22×C4×C79—22no—
88C22×C4×C79—22no—
89C22×C4×C79—24no—
90C22×C4×C79—24no—
91C22×C4×C79—232no—
92C22×C4×C79—28no—
93C22×C4×C79—28no—
94C22×C4×C79—24no—
95C22×C4×C79—24no—
96C22×C4×C79—24no—
97C22×C4×C79C2×D418yes—
98C22×C4×C79C2×D414yes—
99C22×C4×C79C2×Q814yes—
100C22×C4×C79C2×Q8116yes—
101C22×C4×C79C2×Q814yes—
102C22×C4×C79#4114yes—
103C22×C4×C79C2414yes—
104C22×C4×C79C2414yes—
105C22×C4×C79C2412yes—
106C22×C4×C79C2412yes—
107C4⋊C4×C79—216no—
108C22⋊C4×C79—216no—
109C42×C79—28no—
110C42×C79C2×D4116yes—
111C23×C79—28no—
112C23×C79—216no—
113C23×C79—22no—
114C23×C79—22no—
115C23×C79—24no—
116C23×C79—24no—
117C23×C79—48no—
118C23×C79—44no—
119C23×C79—44no—
120C23×C79C22×D412yes—
121C23×C79C22×Q814yes—
122C23×C79C22×Q812yes—
123C23×C79C2×#4112yes—
124C23×C79H(5,𝔽2)14yes—
125C23×C792−1+414yes—
126C23×C79C2511yescharacteristic
127C2×C4×C79—28no—
128C2×C4×C79—216no—
129C2×C4×C79—22no—
130C2×C4×C79—22no—
131C2×C4×C79—24no—
132C2×C4×C79—24no—
133C2×C4×C79—232no—
134C2×C4×C79—24no—
135C2×C4×C79—24no—
136C2×C4×C79—24no—
137C2×C4×C79—48no—
138C2×C4×C79C22⋊Q8116yes—
139C2×C4×C79C22×D418yes—
140C2×C4×C79C22×D414yes—
141C2×C4×C79C22×Q814yes—
142C2×C4×C79C22×Q814yes—
143C2×C4×C79C2×#4114yes—
144C2×Dic79—28no—
145C2×Dic79—28no—
146C2×Dic79—28no—
147C2×Dic79—28no—
148C2×Dic79—28no—
149C2×Dic79—28no—
150C2×Dic79—416no—
151C2×Dic79—416no—
152C22×C79—24no—
153C22×C79—28no—
154C22×C79—416no—
155C22×C79—44no—
156C22×C79—42no—
157C22×C79—42no—
158C22×C79C2×C22⋊Q814yes—
159C22×C79#53718yes—
160C22×C79#54014yes—
161C22×C79#54114yes—
162C22×C79#54418yes—
163C22×C79C23×D411yescharacteristic
164C22×C79C23×Q811yescharacteristic
165C22×C79C22×#4111yescharacteristic
166C22×C79C2×H(5,𝔽2)12yes—
167C22×C79C2×2−1+412yes—
168C4×C79—24no—
169C4×C79—28no—
170C4×C79—44no—
171C4×C79C2×C22⋊Q818yes—
172Dic79—48no—
173Dic79—48no—
174C2×#2629—791nomaximal, Sylow
175C2×C79—44no—
176C2×C79#262918yescomplemented
177C2×C79C22×C22⋊Q811yescharacteristic
178C2×C79C2×#53712yes—
179C2×C79C2×#54011yescharacteristic
180C2×C79C2×#54111yescharacteristic
181C2×C79C2×#54412yes—
182C22×#125—791no—
183C22×#117D7911yescharacteristic
184#2629—7916no—
185C2×#398—794no—
186C2×#396—794no—
187C2×#389—792no—
188C2×#384—791no—
189C2×#380—792no—
190C79C2×#262911yescharacteristic, complemented, Sylow
191C24×C4C2×D7911yescharacteristic
192C2×#125—798no—
193C2×#125—1588no—
194C2×#117—28no—
195C2×#117C2×D7918yes—
196C22×C4⋊C4—794no—
197C22×C4⋊C4—794no—
198C22×C4⋊C4—794no—
199C22×C4⋊C4—792no—
200C22×C4⋊C4—792no—
201C22×C4⋊C4C2×D7912yes—
202C22×C22⋊C4—794no—
203C22×C22⋊C4C2×D7912yes—
204C22×C42C2×D7911yescharacteristic
205C22×C42C2×D7911yescharacteristic
206#398—7932no—
207#396—7932no—
208#389—7916no—
209#384—798no—
210#380—7916no—
211C2×#95—794no—
212C2×#95—794no—
213C25C22×D7911yescharacteristic
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—794no—
217C23×C4—794no—
218C23×C4Dic15818yes—
219C23×C4C22×D7912yes—
220C23×C4C22×D7912yes—
221C23×C4C22×D7914yes—
222C23×C4C22×D7911yescharacteristic
223C23×C4C22×D7911yescharacteristic
224#125—15832no—
225#117—232no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—3168no—
228C2×C4⋊C4—3168no—
229C2×C4⋊C4—7916no—
230C2×C4⋊C4—7916no—
231C2×C4⋊C4—798no—
232C2×C4⋊C4—7916no—
233C2×C4⋊C4—798no—
234C2×C4⋊C4—15816no—
235C2×C4⋊C4—1588no—
236C2×C4⋊C4—1588no—
237C2×C4⋊C4C22×D7918yes—
238C2×C22⋊C4—28no—
239C2×C22⋊C4—3168no—
240C2×C22⋊C4—7916no—
241C2×C22⋊C4C22×D7918yes—
242C2×C42—24no—
243C2×C42C22⋊D7918yes—
244C2×C42C22×D7914yes—
245C2×C42C22×D7914yes—
246#95—7916no—
247#95—7916no—
248C24—22no—
249C24—24no—
250C24—24no—
251C24—22no—
252C24C2×Dic15814yes—
253C24C23×D7912yes—
254C24C23×D7911yescharacteristic
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—28no—
260C22×C4—232no—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—798no—
266C22×C4—798no—
267C22×C4—1588no—
268C22×C4—1588no—
269C22×C4—1588no—
270C22×C4—1588no—
271C22×C4—1588no—
272C22×C4—1588no—
273C22×C4C2×C22⋊D7918yes—
274C22×C4C2×C22⋊D7914yes—
275C22×C4C2×Dic15814yes—
276C22×C4C2×Dic158116yes—
277C22×C4C2×Dic15814yes—
278C22×C4#1192962414yes—
279C22×C4C23×D7914yes—
280C22×C4C23×D7912yes—
281C22×C4C23×D7914yes—
282C22×C4C23×D7912yes—
283C4⋊C4—216no—
284C4⋊C4—31616no—
285C4⋊C4—31616no—
286C4⋊C4—15816no—
287C4⋊C4—15832no—
288C4⋊C4—15816no—
289C22⋊C4—216no—
290C22⋊C4—31616no—
291C42—28no—
292C42C2×C22⋊D79116yes—
293C23—24no—
294C23—24no—
295C23—216no—
296C23—28no—
297C23—22no—
298C23—22no—
299C23—48no—
300C23—44no—
301C23—44no—
302C23C22×C22⋊D7912yes—
303C23C22×Dic15814yes—
304C23C22×Dic15812yes—
305C23C2×#1192962412yes—
306C23#1457920714yes—
307C23#1457920814yes—
308C23C24×D7911yescharacteristic
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—216no—
312C2×C4—28no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—232no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—48no—
320C2×C4—31616no—
321C2×C4—31616no—
322C2×C4—1588no—
323C2×C4—1588no—
324C2×C4—1588no—
325C2×C4—1588no—
326C2×C4—1588no—
327C2×C4—1588no—
328C2×C4#14579140116yes—
329C2×C4C22×C22⋊D7918yes—
330C2×C4C22×C22⋊D7914yes—
331C2×C4C22×Dic15814yes—
332C2×C4C22×Dic15814yes—
333C2×C4C2×#1192962414yes—
334C22—28no—
335C22—24no—
336C22—42no—
337C22—416no—
338C22—44no—
339C22—42no—
340C22C2×#1457914014yes—
341C22#1909914118yes—
342C22#1909916814yes—
343C22#1909917514yes—
344C22#1909919118yes—
345C22C23×C22⋊D7911yescharacteristic
346C22C23×Dic15811yescharacteristic
347C22C22×#1192962411yescharacteristic
348C22C2×#1457920712yes—
349C22C2×#1457920812yes—
350C4—24no—
351C4—28no—
352C4—44no—
353C4—3168no—
354C4—3168no—
355C4C2×#1457914018yes—
356C2—44no—
357C2#2376923018yesdirect product factor
358C2C22×#1457914011yescharacteristic
359C2C2×#1909914112yes—
360C2C2×#1909916811yescharacteristic
361C2C2×#1909917511yescharacteristic
362C2C2×#1909919112yes—
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC22×#117×C79C2
socleC24×C79C24
prime radicalC25×C79C23
hypercenterC22×#117D79
hypocenterC79C2×#2629
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#14579153C2semidirect
2. #23769230C2direct (N × H)
3. C2×#19098496C2semidirect
5. C2×#19098461C2semidirect
6. C2×#19098433C2semidirect
10. C2×#14579153C22semidirect
17. #19098496C22semidirect
19. #19098461C22semidirect
20. #19098433C22semidirect
176. C2×C79#2629semidirect
190. C79C2×#2629semidirect
357. C2#23769230direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791532
#237692302
C2×#190984962
C2×#190984862
C2×#190984612
C2×#190984332
C2×#190984232
C22×#117×C792
C2×#262979