Finite Group Databasebeta

← #23765873

Subgroups — #23765873

Order 10112.

500 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579126C211yesmaximal, characteristic
2#19098467C211yesmaximal, characteristic
3#19098467C211yesmaximal, characteristic
4#19098460C211yesmaximal, characteristic
5#19098458C211yesmaximal, characteristic
6#19098449C211yesmaximal, characteristic
7#19098447C211yesmaximal, characteristic
8#19098445C211yesmaximal, characteristic
9C4⋊C4×Dic79C211yesmaximal, characteristic
10#19098414C211yesmaximal, characteristic
11#19098414C211yesmaximal, characteristic
12#19098408C211yesmaximal, characteristic
13#19098408C211yesmaximal, characteristic
14C42×Dic79C211yesmaximal, characteristic
15#387×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17#14579126C418yescomplemented
18C2×C4⋊Dic79C2211yescharacteristic
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×C4×Dic79C2211yescharacteristic
26C2×C4×Dic79C2211yescharacteristic
27C2×C4×Dic79C2211yescharacteristic
28C2×C4×Dic79C2211yescharacteristic
29C2×C4×Dic79C2211yescharacteristic
30C2×C4×Dic79C2211yescharacteristic
31C2×C4×Dic79C2211yescharacteristic
32C2×C4×Dic79C2211yescharacteristic
33C2×C4×Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C2×C4⋊C4×C79C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C42×C79C2211yescharacteristic
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52C2×Dic158—22no—
53C2×Dic158—22no—
54C2×Dic158C2×C414yes—
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C4⋊Dic79—22no—
64Dic79⋊C4—22no—
65Dic79⋊C4—22no—
66Dic79⋊C4—22no—
67Dic79⋊C4—22no—
68Dic79⋊C4C2×C414yes—
69Dic79⋊C4C2×C414yes—
70C4×Dic79—22no—
71C4×Dic79—22no—
72C4×Dic79—22no—
73C4×Dic79—22no—
74C4×Dic79—22no—
75C4×Dic79—22no—
76C4×Dic79C2×C414yes—
77C4×Dic79C2×C414yes—
78C4×Dic79C2×C414yes—
79C4×Dic79Q814yescomplemented
80C22×C4×C79C2311yescharacteristic
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C4⋊C4×C79—22no—
88C4⋊C4×C79C2×C414yes—
89C42×C79—22no—
90C23×C79C2411yescharacteristic
91C2×C4×C79—21no—
92C2×C4×C79—21no—
93C2×C4×C79—21no—
94C2×C4×C79—21no—
95C2×C4×C79—21no—
96C2×C4×C79—21no—
97C2×C4×C79—21no—
98C2×C4×C79—21no—
99C2×C4×C79—21no—
100C2×C4×C79—21no—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79C22×C412yes—
108C2×C4×C79C22×C412yes—
109C2×C4×C79C22×C412yes—
110C2×C4×C79C2×Q812yes—
111C2×C4×C79#4112yes—
112C2×Dic79—21no—
113C2×Dic79—21no—
114C2×Dic79—21no—
115C2×Dic79—21no—
116C2×Dic79—21no—
117C2×Dic79—21no—
118C2×Dic79—21no—
119C2×Dic79—21no—
120C2×Dic79—21no—
121C2×Dic79—21no—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79C22×C412yes—
127C2×Dic79C22×C412yes—
128C2×Dic79C22×C412yes—
129C2×Dic79C22×C412yes—
130C2×Dic79C2×Q812yes—
131C2×Dic79C2×Q812yes—
132C2×Dic79#4112yes—
133C2×Dic79#4112yes—
134C2×Dic79#4112yes—
135C2×Dic79#4112yes—
136Dic158—28no—
137C22×C79C23×C411yescharacteristic
138C22×C79C22×Q811yescharacteristic
139C22×C79C2×#4111yescharacteristic
140C22×C79C2×#4111yescharacteristic
141C22×C79C2×#4111yescharacteristic
142C22×C79C2×#4111yescharacteristic
143C22×C79C2×#4111yescharacteristic
144C4×C79—22no—
145C4×C79—22no—
146C4×C79—22no—
147C4×C79—22no—
148C4×C79—22no—
149C4×C79—41no—
150C4×C79—41no—
151Dic79—22no—
152Dic79—22no—
153Dic79—22no—
154Dic79—22no—
155Dic79—41no—
156Dic79—41no—
157Dic79#11714yes—
158Dic79C4×Q814yes—
159C2×C79C2×#11711yescharacteristic
160C2×C79C2×C4×Q811yescharacteristic
161C2×C79C4×#4111yescharacteristic
162C2×C79#52911yescharacteristic
163C2×C79#52911yescharacteristic
164C2×C79#53311yescharacteristic
165C2×C79#53311yescharacteristic
166#2295—791nomaximal, Sylow
167C79#229511yescharacteristic, complemented, Sylow
168C2×C4×Q8—791no—
169#391—791no—
170#391—791no—
171#389—791no—
172#389—791no—
173#387—791no—
174#387—791no—
175#387—791no—
176#387D7911yescharacteristic
177C4×C4⋊C4—791no—
178C4×C4⋊C4—791no—
179C4×C4⋊C4—791no—
180#376—791no—
181#376—791no—
182C43—791no—
183C22×Q8—791no—
184C4×Q8—798no—
185C2×C4⋊C4—791no—
186C2×C4⋊C4—791no—
187C2×C4⋊C4—791no—
188C2×C4⋊C4—791no—
189C2×C4⋊C4—791no—
190C2×C4⋊C4—791no—
191C2×C4⋊C4—791no—
192C2×C4⋊C4C2×D7911yescharacteristic
193C2×C4⋊C4C2×D7911yescharacteristic
194C2×C42—791no—
195C2×C42—791no—
196C2×C42—791no—
197C2×C42—791no—
198C2×C42—791no—
199C2×C42—791no—
200C2×C42—791no—
201C2×C42—791no—
202C2×C42—791no—
203C2×C42—791no—
204C2×C42C2×D7911yescharacteristic
205#95—791no—
206#95—791no—
207#95—791no—
208#95—791no—
209#95—791no—
210#95—791no—
211#95—791no—
212#95—791no—
213#95—791no—
214#95—791no—
215#95C2×D7911yescharacteristic
216#95C2×D7911yescharacteristic
217#95C2×D7911yescharacteristic
218#95C2×D7911yescharacteristic
219C2×Q8—794no—
220C2×Q8—1582no—
221C2×Q8—1582no—
222C22×C4—791no—
223C22×C4—791no—
224C22×C4—791no—
225C22×C4—791no—
226C22×C4—791no—
227C22×C4—791no—
228C22×C4—791no—
229C22×C4—791no—
230C22×C4C22×D7911yescharacteristic
231C22×C4C22×D7911yescharacteristic
232C22×C4C22×D7911yescharacteristic
233C22×C4C22×D7911yescharacteristic
234C22×C4C22×D7911yescharacteristic
235C22×C4C22×D7911yescharacteristic
236C22×C4C22×D7911yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—794no—
239C4⋊C4—794no—
240C4⋊C4—1582no—
241C4⋊C4—1582no—
242C4⋊C4—1582no—
243C4⋊C4—1582no—
244C4⋊C4—1582no—
245C4⋊C4C4×D7914yes—
246C42—22no—
247C42—794no—
248C42—794no—
249C42—794no—
250C42—794no—
251C42—1582no—
252C42—1582no—
253C42—1582no—
254C42—1582no—
255C42—1582no—
256C42—1582no—
257C23C23×D7911yescharacteristic
258Q8—1588no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—792no—
276C2×C4—792no—
277C2×C4—792no—
278C2×C4—792no—
279C2×C4—792no—
280C2×C4—792no—
281C2×C4—792no—
282C2×C4—792no—
283C2×C4—792no—
284C2×C4—792no—
285C2×C4—1581no—
286C2×C4—1581no—
287C2×C4—1581no—
288C2×C4—1581no—
289C2×C4—1581no—
290C2×C4—1581no—
291C2×C4—1581no—
292C2×C4—1581no—
293C2×C4—1581no—
294C2×C4—1581no—
295C2×C4—1581no—
296C2×C4—1581no—
297C2×C4—1581no—
298C2×C4—1581no—
299C2×C4C2×C4×D7912yes—
300C2×C4C2×C4×D7912yes—
301C2×C4C2×C4×D7912yes—
302C2×C4Q8×D7912yes—
303C2×C4#1192962312yes—
304C22C22×C4×D7911yescharacteristic
305C22C2×Q8×D7911yescharacteristic
306C22#41×D7911yescharacteristic
307C22#41×D7911yescharacteristic
308C22#41×D7911yescharacteristic
309C22#41×D7911yescharacteristic
310C22C2×#1192962311yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—3161no—
319C4—3161no—
320C4—794no—
321C4—794no—
322C4—1582no—
323C4—1582no—
324C4—1582no—
325C4—1582no—
326C2#117×D7911yescharacteristic
327C2C4×Q8×D7911yescharacteristic
328C2C4×#1192962311yescharacteristic
329C2#1909909011yescharacteristic
330C2#1909909611yescharacteristic
331C2#1909911511yescharacteristic
332C2#1909911911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#387×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenter#387D79
hypocenterC79#2295
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
17. #14579126C4semidirect
79. C4×Dic79Q8semidirect
167. C79#2295semidirect