Finite Group Databasebeta

← #23775445

Subgroups — #23775445

Order 10112.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic158C211yesmaximal, characteristic
2#19098933C211yesmaximal, characteristic, complemented
3#19098904C211yesmaximal, characteristic, complemented
4#19098893C211yesmaximal, characteristic, complemented
5#19098867C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098802C211yesmaximal, characteristic, complemented
8#19098773C211yesmaximal, characteristic, complemented
9#19098718C211yesmaximal, characteristic, complemented
10#19098718C211yesmaximal, characteristic, complemented
11#19098668C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic
13#19098571C211yesmaximal, characteristic, complemented
14C2×#14579084C211yesmaximal, characteristic, complemented
15#552×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929614C2211yescharacteristic
20C2×#11929614C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic
23#14579161C2211yescharacteristic
24#14579160—21no—
25#14579140C2211yescharacteristic
26#14579140C2211yescharacteristic
27#14579138—21no—
28#14579138—21no—
29C4×Dic158C2211yescharacteristic
30D4×Dic79—21no—
31#14579094C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579084C2211yescharacteristic
37#14579084C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579084C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579084C2211yescharacteristic
43#14579084C2211yescharacteristic
44#14579084C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48#126×C79—21no—
49#125×C79—21no—
50#125×C79C2211yescharacteristic
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53C22⋊Q8×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56#117×C79—21no—
57#117×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59C2×Dic158—22no—
60C2×Dic158—22no—
61C2×Dic158—21no—
62C2×Dic158—21no—
63C2×Dic158—41no—
64C2×Dic158—41no—
65C2×Dic158C2311yescharacteristic
66C2×Dic158C2311yescharacteristic
67C2×Dic158C2311yescharacteristic
68C22×Dic79—21no—
69C22×Dic79—21no—
70#11929614—22no—
71#11929614—41no—
72#11929614—41no—
73#11929608—41no—
74C2×C79⋊C8—41no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C4⋊Dic79—21no—
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C4×Dic79—21no—
88C2×Q8×C79C2311yescharacteristic
89C2×D4×C79D411yescharacteristic
90C22×C4×C79—21no—
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79D411yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79D411yescharacteristic
107C22⋊C4×C79D411yescharacteristic
108C42×C79—21no—
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113Q8×C79—21no—
114Q8×C79—21no—
115D4×C79—22no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—42no—
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—42no—
135C2×Dic79—42no—
136Dic158—21no—
137Dic158—21no—
138Dic158—21no—
139Dic158—21no—
140Dic158—21no—
141Dic158—42no—
142Dic158—42no—
143Dic158#4112yes—
144C79⋊C8—21no—
145C79⋊C8—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79#13712yes—
154C22×C79C22×D411yescharacteristic
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—21no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79C2×#4111yescharacteristic
164C4×C79H(5,𝔽2)11yescharacteristic
165Dic79—22no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—22no—
170C2×C79—41no—
171C2×C79#54611yescharacteristic
172C2×C79C2×#13711yescharacteristic
173C2×C79#57811yescharacteristic
174#3312—791nomaximal, Sylow
175C79#331211yescharacteristic, complemented, Sylow
176#552D7911yescharacteristic
177D4×Q8—791no—
178#491—791no—
179#485—791no—
180#483—791no—
181#479—791no—
182#470—791no—
183#467—791no—
184#462—791no—
185#451—791no—
186#451—791no—
187#441—791no—
188#435—791no—
189#419—791no—
190C2×#103—791no—
191C22×Q8—791no—
192C22×Q8—791no—
193C2×Q16—791no—
194C2×Q16—791no—
195C2×Q16—791no—
196C2×M16—791no—
197C22×C8—791no—
198C4⋊Q8—791no—
199C4⋊Q8—1581no—
200#126—21no—
201#125—21no—
202#125C2×D7911yescharacteristic
203#123—21no—
204C22⋊Q8—791no—
205C22⋊Q8—791no—
206C22⋊Q8—1581no—
207C22⋊Q8—1581no—
208C22⋊Q8C2×D7911yescharacteristic
209C22⋊Q8C2×D7911yescharacteristic
210C4×Q8—791no—
211C4×Q8C2×D7911yescharacteristic
212C4×D4—1581no—
213C4×D4C2×D7911yescharacteristic
214#117—21no—
215#117C2×D7911yescharacteristic
216C2×C4⋊C4C2×D7911yescharacteristic
217#107—791no—
218#106—791no—
219#106—791no—
220C4⋊C8—791no—
221#103—791no—
222#103—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231C22⋊C8—791no—
232C22⋊C8—791no—
233#97—791no—
234C2×Q8—3161no—
235C2×Q8—3161no—
236C2×Q8—791no—
237C2×Q8—791no—
238C2×Q8—791no—
239C2×Q8—1582no—
240C2×Q8—1582no—
241C2×Q8—1581no—
242C2×Q8—1581no—
243C2×Q8C22×D7911yescharacteristic
244C2×D4C22⋊D7911yescharacteristic
245C22×C4—21no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4C22×D7911yescharacteristic
249C22×C4C22×D7911yescharacteristic
250Q16—3161no—
251Q16—3161no—
252Q16—1582no—
253M16—3161no—
254C2×C8—3161no—
255C2×C8—791no—
256C2×C8—791no—
257C2×C8—791no—
258C2×C8—791no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—791no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4C22⋊D7911yescharacteristic
272C4⋊C4C22×D7911yescharacteristic
273C4⋊C4C22×D7911yescharacteristic
274C4⋊C4C22×D7911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4C22⋊D7911yescharacteristic
281C22⋊C4C22⋊D7911yescharacteristic
282C42—21no—
283C42—21no—
284C42—1581no—
285C42C22×D7911yescharacteristic
286C23C2×C22⋊D7911yescharacteristic
287C23C2×C22⋊D7911yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—3162no—
291Q8—3162no—
292Q8—792no—
293Q8—1581no—
294Q8—1581no—
295Q8—1581no—
296Q8—1581no—
297Q8—1581no—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—3162no—
309C2×C4—3162no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4C2×C22⋊D7911yescharacteristic
315C2×C4C2×C22⋊D7911yescharacteristic
316C2×C4C2×C22⋊D7911yescharacteristic
317C2×C4C2×C22⋊D7911yescharacteristic
318C2×C4C23×D7911yescharacteristic
319C8—1581no—
320C8—1581no—
321C8—1581no—
322C8—1581no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1457919112yes—
329C22C22×C22⋊D7911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—3161no—
339C4—3161no—
340C4—3161no—
341C4—1582no—
342C4#41×D7911yescharacteristic
343C4#1457920711yescharacteristic
344C2—22no—
345C2—41no—
346C2#1909920111yescharacteristic
347C2C2×#1457919111yescharacteristic
348C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#552×C79C2
socleC22×C79C22×D4
prime radicalC2×D4×C79D4
hypercenter#552D79
hypocenterC79#3312
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #19098933C2semidirect
3. #19098904C2semidirect
4. #19098893C2semidirect
5. #19098867C2semidirect
6. #19098819C2semidirect
7. #19098802C2semidirect
8. #19098773C2semidirect
9. #19098718C2semidirect
10. #19098718C2semidirect
11. #19098668C2semidirect
13. #19098571C2semidirect
14. C2×#14579084C2semidirect
175. C79#3312semidirect