Finite Group Databasebeta

← #23766115

Subgroups — #23766115

Order 10112.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579160C211yesmaximal, characteristic
2C2×C4×Dic158C211yesmaximal, characteristic
3C2×#14579126C211yesmaximal, characteristic
4#19098467C211yesmaximal, characteristic
5#19098467C211yesmaximal, characteristic
6#19098450C211yesmaximal, characteristic
7#19098449C211yesmaximal, characteristic
8#19098448C211yesmaximal, characteristic
9#19098447C211yesmaximal, characteristic
10#19098446C211yesmaximal, characteristic
11#19098445C211yesmaximal, characteristic
12#19098444C211yesmaximal, characteristic
13#19098427C211yesmaximal, characteristic
14#19098408C211yesmaximal, characteristic
15#387×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18#14579160C418yescomplemented
19C4×Dic158—24no—
20#14579126—24no—
21C2×C4⋊Dic79C2211yescharacteristic
22C2×C4⋊Dic79C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
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
45C79⋊#95C2211yescharacteristic
46C79⋊#95C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C42×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53#95×C79C2211yescharacteristic
54C2×Dic158—22no—
55C2×Dic158—22no—
56C2×Dic158—22no—
57C2×Dic158—22no—
58C2×Dic158C2×C414yes—
59C2×Dic158C2×C414yes—
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C4⋊Dic79—22no—
69C4⋊Dic79C2×C414yes—
70Dic79⋊C4—22no—
71Dic79⋊C4—22no—
72Dic79⋊C4—22no—
73Dic79⋊C4—22no—
74Dic79⋊C4C2×C414yes—
75Dic79⋊C4C2×C414yes—
76C4×Dic79—22no—
77C4×Dic79—22no—
78C4×Dic79—22no—
79C4×Dic79—22no—
80C4×Dic79C2×C414yes—
81C4×Dic79D414yes—
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C4⋊C4×C79—22no—
90C4⋊C4×C79C2×C414yes—
91C42×C79—22no—
92C23×C79C2411yescharacteristic
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×C79C22×C412yes—
111C2×C4×C79C22×C412yes—
112C2×C4×C79C22×C412yes—
113C2×C4×C79C2×D412yes—
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×Dic79C22×C412yes—
132C2×Dic79C22×C412yes—
133C2×Dic79C22×C412yes—
134C2×Dic79C22×C412yes—
135C2×Dic79C2×D412yes—
136C2×Dic79C2×D412yes—
137C2×Dic79#4112yes—
138Dic158—28no—
139Dic158—28no—
140C22×C79C23×C411yescharacteristic
141C22×C79C22×D411yescharacteristic
142C22×C79C2×#4111yescharacteristic
143C22×C792−1+411yescharacteristic
144C22×C792−1+411yescharacteristic
145C22×C792−1+411yescharacteristic
146C22×C792−1+411yescharacteristic
147C4×C79—22no—
148C4×C79—22no—
149C4×C79—22no—
150C4×C79—22no—
151C4×C79—41no—
152C4×C79—41no—
153C4×C79—41no—
154Dic79—22no—
155Dic79—22no—
156Dic79—22no—
157Dic79—22no—
158Dic79—41no—
159Dic79—41no—
160Dic79—41no—
161Dic79C4×D414yes—
162C2×C79C2×C4×D411yescharacteristic
163C2×C79#51911yescharacteristic
164C2×C79#51911yescharacteristic
165C2×C79#53611yescharacteristic
166C2×C79#53611yescharacteristic
167C2×C79#54111yescharacteristic
168C2×C79#54111yescharacteristic
169#2327—791nomaximal, Sylow
170C79#232711yescharacteristic, complemented, Sylow
171C2×C4⋊Q8—791no—
172C2×C4×Q8—791no—
173C2×C4×Q8—791no—
174#391—791no—
175#391—791no—
176#387—791no—
177#387—791no—
178#387—791no—
179#387—791no—
180#387—791no—
181#387—791no—
182#387—791no—
183#387D7911yescharacteristic
184#382—791no—
185#376—791no—
186C22×Q8—791no—
187C22×Q8—791no—
188C4⋊Q8—798no—
189C4×Q8—1584no—
190C4×Q8—1584no—
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×C42—791no—
206C2×C42—791no—
207C2×C42C2×D7911yescharacteristic
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#95—791no—
219#95—791no—
220#95C2×D7911yescharacteristic
221#95C2×D7911yescharacteristic
222#95C2×D7911yescharacteristic
223#95C2×D7911yescharacteristic
224C2×Q8—794no—
225C2×Q8—794no—
226C2×Q8—1582no—
227C2×Q8—1582no—
228C2×Q8—1582no—
229C2×Q8—1582no—
230C22×C4—791no—
231C22×C4—791no—
232C22×C4—791no—
233C22×C4—791no—
234C22×C4—791no—
235C22×C4—791no—
236C22×C4—791no—
237C22×C4—791no—
238C22×C4C22×D7911yescharacteristic
239C22×C4C22×D7911yescharacteristic
240C22×C4C22×D7911yescharacteristic
241C22×C4C22×D7911yescharacteristic
242C22×C4C22×D7911yescharacteristic
243C22×C4C22×D7911yescharacteristic
244C22×C4C22×D7911yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—794no—
247C4⋊C4—794no—
248C4⋊C4—794no—
249C4⋊C4—1582no—
250C4⋊C4—1582no—
251C4⋊C4—1582no—
252C4⋊C4—1582no—
253C4⋊C4—1582no—
254C4⋊C4C4×D7914yes—
255C42—22no—
256C42—794no—
257C42—794no—
258C42—1582no—
259C42—1582no—
260C42—1582no—
261C42—1582no—
262C23C23×D7911yescharacteristic
263Q8—1588no—
264Q8—1588no—
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—21no—
282C2×C4—792no—
283C2×C4—792no—
284C2×C4—792no—
285C2×C4—792no—
286C2×C4—792no—
287C2×C4—792no—
288C2×C4—792no—
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×C4—1581no—
306C2×C4C2×C4×D7912yes—
307C2×C4C2×C4×D7912yes—
308C2×C4C2×C4×D7912yes—
309C2×C4D4×D7912yes—
310C22C22×C4×D7911yescharacteristic
311C22C2×D4×D7911yescharacteristic
312C22#41×D7911yescharacteristic
313C22#1457920811yescharacteristic
314C22#1457920811yescharacteristic
315C22#1457920811yescharacteristic
316C22#1457920911yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3161no—
325C4—3161no—
326C4—3161no—
327C4—794no—
328C4—1582no—
329C4—1582no—
330C4—1582no—
331C4—1582no—
332C2C4×D4×D7911yescharacteristic
333C2#1909903911yescharacteristic
334C2#1909904011yescharacteristic
335C2#1909913511yescharacteristic
336C2#1909913611yescharacteristic
337C2#1909917011yescharacteristic
338C2#1909917211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#387×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenter#387D79
hypocenterC79#2327
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
18. #14579160C4semidirect
170. C79#2327semidirect