Finite Group Databasebeta

← #23767173

Subgroups — #23767173

Order 10112.

460 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579160C211yesmaximal, characteristic
2C2×C4×Dic158C211yesmaximal, characteristic
3#19098504C211yesmaximal, characteristic
4#19098503C211yesmaximal, characteristic
5#19098496C211yesmaximal, characteristic
6#19098493C211yesmaximal, characteristic
7#19098467C211yesmaximal, characteristic
8#19098467C211yesmaximal, characteristic
9#19098467C211yesmaximal, characteristic
10#19098458C211yesmaximal, characteristic
11#19098450C211yesmaximal, characteristic
12#19098447C211yesmaximal, characteristic
13#19098445C211yesmaximal, characteristic
14#19098414C211yesmaximal, characteristic
15#387×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18#14579160—24no—
19C4×Dic158—24no—
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×Dic79⋊C4C2211yescharacteristic
30C2×C4×Dic79C2211yescharacteristic
31C2×C4×Dic79C2211yescharacteristic
32C2×C4×Dic79C2211yescharacteristic
33C2×C4×Dic79C2211yescharacteristic
34C79⋊#95C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C42×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C2×Dic158—22no—
54C2×Dic158—22no—
55C2×Dic158—22no—
56C2×Dic158—22no—
57C2×Dic158—22no—
58C2×Dic158D414yes—
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C4⋊Dic79—22no—
68C4⋊Dic79—22no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4—22no—
72Dic79⋊C4—22no—
73Dic79⋊C4—22no—
74Dic79⋊C4—22no—
75Dic79⋊C4—22no—
76Dic79⋊C4Q814yescomplemented
77C4×Dic79—22no—
78C4×Dic79—22no—
79C4×Dic79—22no—
80C4×Dic79—22no—
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C4⋊C4×C79—22no—
89C4⋊C4×C79—22no—
90C42×C79—22no—
91C23×C79C2411yescharacteristic
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×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79C2×D412yes—
111C2×C4×C79C2×Q812yes—
112C2×C4×C79#4112yes—
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×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79C2×D412yes—
132C2×Dic79C2×D412yes—
133C2×Dic79C2×Q812yes—
134C2×Dic79C2×Q812yes—
135C2×Dic79#4112yes—
136C2×Dic79#4112yes—
137Dic158—28no—
138Dic158—44no—
139C22×C79C22×D411yescharacteristic
140C22×C79C22×Q811yescharacteristic
141C22×C79C2×#4111yescharacteristic
142C22×C79C2×#4111yescharacteristic
143C22×C79C2×#4111yescharacteristic
144C22×C792−1+411yescharacteristic
145C22×C792−1+411yescharacteristic
146C4×C79—22no—
147C4×C79—22no—
148C4×C79—22no—
149C4×C79—41no—
150C4×C79—41no—
151C4×C79—41no—
152C4×C79—41no—
153Dic79—22no—
154Dic79—22no—
155Dic79—22no—
156Dic79—41no—
157Dic79—41no—
158Dic79—41no—
159Dic79—41no—
160Dic79#12314yes—
161C2×C79C2×#12311yescharacteristic
162C2×C79#53311yescharacteristic
163C2×C79#54111yescharacteristic
164C2×C79#54811yescharacteristic
165C2×C79D4×Q811yescharacteristic
166C2×C79#55611yescharacteristic
167C2×C79#55711yescharacteristic
168#2446—791nomaximal, Sylow
169C79#244611yescharacteristic, complemented, Sylow
170C2×C4⋊Q8—791no—
171C2×C4×Q8—791no—
172#400—791no—
173#400—791no—
174#398—791no—
175#398—791no—
176#391—791no—
177#391—791no—
178#391—791no—
179#389—791no—
180#387—791no—
181#387—791no—
182#387—791no—
183#387D7911yescharacteristic
184C4×C4⋊C4—791no—
185C22×Q8—791no—
186C22×Q8—791no—
187C4⋊Q8—1584no—
188C4×Q8—1584no—
189C2×C4⋊C4—791no—
190C2×C4⋊C4—791no—
191C2×C4⋊C4—791no—
192C2×C4⋊C4—791no—
193C2×C4⋊C4—791no—
194C2×C4⋊C4—791no—
195C2×C4⋊C4—791no—
196C2×C4⋊C4—791no—
197C2×C4⋊C4—791no—
198C2×C4⋊C4—791no—
199C2×C4⋊C4C2×D7911yescharacteristic
200C2×C4⋊C4C2×D7911yescharacteristic
201C2×C42—791no—
202C2×C42—791no—
203C2×C42—791no—
204C2×C42—791no—
205C2×C42C2×D7911yescharacteristic
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#95—791no—
216#95—791no—
217#95—791no—
218#95C2×D7911yescharacteristic
219#95C2×D7911yescharacteristic
220#95C2×D7911yescharacteristic
221#95C2×D7911yescharacteristic
222C2×Q8—794no—
223C2×Q8—1582no—
224C2×Q8—1582no—
225C2×Q8—1582no—
226C2×Q8—1582no—
227C2×Q8—1582no—
228C22×C4—791no—
229C22×C4—791no—
230C22×C4—791no—
231C22×C4—791no—
232C22×C4—791no—
233C22×C4—791no—
234C22×C4—791no—
235C22×C4—791no—
236C22×C4C22×D7911yescharacteristic
237C22×C4C22×D7911yescharacteristic
238C22×C4C22×D7911yescharacteristic
239C22×C4C22×D7911yescharacteristic
240C22×C4C22×D7911yescharacteristic
241C22×C4C22×D7911yescharacteristic
242C22×C4C22×D7911yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—794no—
246C4⋊C4—1582no—
247C4⋊C4—1582no—
248C4⋊C4—1582no—
249C4⋊C4—1582no—
250C4⋊C4—1582no—
251C4⋊C4—1582no—
252C4⋊C4—1582no—
253C4⋊C4—1582no—
254C4⋊C4—1582no—
255C42—22no—
256C42—1582no—
257C42—1582no—
258C42—1582no—
259C42—1582no—
260C23C23×D7911yescharacteristic
261Q8—3164no—
262Q8—1588no—
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—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—792no—
282C2×C4—792no—
283C2×C4—792no—
284C2×C4—792no—
285C2×C4—792no—
286C2×C4—792no—
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×C4—1581no—
300C2×C4—1581no—
301C2×C4—1581no—
302C2×C4—1581no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4D4×D7912yes—
306C2×C4Q8×D7912yes—
307C2×C4#1192962412yes—
308C22C2×D4×D7911yescharacteristic
309C22C2×Q8×D7911yescharacteristic
310C22#41×D7911yescharacteristic
311C22#41×D7911yescharacteristic
312C22C2×#1192962411yescharacteristic
313C22#1457920811yescharacteristic
314C22#1457920811yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—3161no—
323C4—3161no—
324C4—3161no—
325C4—3161no—
326C4—794no—
327C4—1582no—
328C4—1582no—
329C4—1582no—
330C2#123×D7911yescharacteristic
331C2#1909911711yescharacteristic
332C2#1909917011yescharacteristic
333C2#1909922211yescharacteristic
334C2#1909922611yescharacteristic
335C2#1909928111yescharacteristic
336C2#1909929011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#387×C79C2
hypercenter#387D79
hypocenterC79#2446
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
76. Dic79⋊C4Q8semidirect
169. C79#2446semidirect