Finite Group Databasebeta

← #23767769

Subgroups — #23767769

Order 10112.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579160C211yesmaximal, characteristic, complemented
2C2×#14579139C211yesmaximal, characteristic
3#19098505C211yesmaximal, characteristic, complemented
4#19098476C211yesmaximal, characteristic
5#19098476C211yesmaximal, characteristic
6#19098468C211yesmaximal, characteristic, complemented
7#19098467C211yesmaximal, characteristic, complemented
8#19098467C211yesmaximal, characteristic, complemented
9#19098467C211yesmaximal, characteristic, complemented
10#19098455C211yesmaximal, characteristic
11#19098453C211yesmaximal, characteristic
12#19098422C211yesmaximal, characteristic
13#19098414C211yesmaximal, characteristic, complemented
14#19098410C211yesmaximal, characteristic
15#400×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C22×Dic158C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579160—24no—
21#14579139—24no—
22C2×C4⋊Dic79C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×(C2×D79)⋊C4C2211yescharacteristic
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×C4×Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
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
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C2×Dic158—22no—
55C2×Dic158—22no—
56C2×Dic158—22no—
57C2×Dic158—22no—
58C2×Dic158—22no—
59C2×Dic158—22no—
60C2×Dic158—22no—
61C2×Dic158—41no—
62C2×Dic158—41no—
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C2×C4×D79—22no—
71C2×C4×D79—22no—
72C2×C4×D79—22no—
73C4⋊Dic79—22no—
74Dic79⋊C4—22no—
75Dic79⋊C4—22no—
76Dic79⋊C4—22no—
77Dic79⋊C4D414yes—
78(C2×D79)⋊C4—22no—
79(C2×D79)⋊C4—22no—
80(C2×D79)⋊C4—22no—
81(C2×D79)⋊C4—41no—
82(C2×D79)⋊C4—41no—
83(C2×D79)⋊C4Q814yescomplemented
84C4×Dic79—22no—
85C4×Dic79—22no—
86C4×Dic79—41no—
87C4×Dic79—41no—
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C4⋊C4×C79—22no—
96C4⋊C4×C79—22no—
97C23×C79C2411yescharacteristic
98C22×D79—21no—
99C22×D79—21no—
100C22×D79—21no—
101C22×D79—21no—
102C22×D79—21no—
103C22×D79—21no—
104C22×D79C2×Q812yes—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—21no—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
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×C79C2×D412yes—
125C2×C4×C79C2×Q812yes—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79C2×D412yes—
142C2×Dic79C2×D412yes—
143C2×Dic79C2×Q812yes—
144C2×Dic79#4112yes—
145C2×Dic79#4112yes—
146C2×Dic79#4112yes—
147C4×D79—44no—
148Dic158—44no—
149Dic158—44no—
150Dic158—44no—
151C22×C79C22×D411yescharacteristic
152C22×C79C22×Q811yescharacteristic
153C22×C79C2×#4111yescharacteristic
154C22×C79C2×#4111yescharacteristic
155C22×C79C2×#4111yescharacteristic
156C22×C79H(5,𝔽2)11yescharacteristic
157C22×C792−1+411yescharacteristic
158C2×D79—22no—
159C2×D79—22no—
160C2×D79—22no—
161C2×D79—41no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C4×C79—22no—
166C4×C79—22no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79—41no—
172Dic79—22no—
173Dic79—22no—
174Dic79—22no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178Dic79#12414yes—
179C2×C79C2×#12411yescharacteristic
180C2×C79#53311yescharacteristic
181C2×C79#54211yescharacteristic
182C2×C79#54611yescharacteristic
183C2×C79D4×Q811yescharacteristic
184C2×C79#55411yescharacteristic
185C2×C79#55611yescharacteristic
186D79—42no—
187#2492—791nomaximal, Sylow
188C79#249211yescharacteristic, complemented, Sylow
189C2×C4⋊Q8—791no—
190C2×C22⋊Q8—791no—
191#400—791no—
192#400D7911yescharacteristic, complemented
193#393—791no—
194#393—791no—
195#391—791no—
196#391—791no—
197#391—791no—
198#391—791no—
199#388—791no—
200#388—791no—
201#380—791no—
202C4×C4⋊C4—791no—
203C4×C22⋊C4—791no—
204C22×Q8—791no—
205C22×Q8—791no—
206C22×Q8—791no—
207C23×C4—791no—
208C4⋊Q8—1584no—
209C22⋊Q8—1584no—
210C2×C4⋊C4—791no—
211C2×C4⋊C4—791no—
212C2×C4⋊C4—791no—
213C2×C4⋊C4—791no—
214C2×C4⋊C4—791no—
215C2×C4⋊C4C2×D7911yescharacteristic
216C2×C4⋊C4C2×D7911yescharacteristic
217C2×C22⋊C4—791no—
218C2×C22⋊C4—791no—
219C2×C22⋊C4—791no—
220C2×C22⋊C4—791no—
221C2×C22⋊C4—791no—
222C2×C22⋊C4—791no—
223C2×C42—791no—
224C2×C42—791no—
225C2×C42—791no—
226C2×C42—791no—
227#95—791no—
228#95—791no—
229#95—791no—
230#95—791no—
231#95—791no—
232#95—791no—
233#95—791no—
234#95—791no—
235#95—791no—
236#95C2×D7911yescharacteristic
237#95C2×D7911yescharacteristic
238#95C2×D7911yescharacteristic
239#95C2×D7911yescharacteristic
240#95C2×D7911yescharacteristic
241C24—791no—
242C2×Q8—3161no—
243C2×Q8—3161no—
244C2×Q8—1582no—
245C2×Q8—1582no—
246C2×Q8—1582no—
247C2×Q8—1582no—
248C2×Q8—1582no—
249C2×Q8—1582no—
250C2×Q8—1582no—
251C22×C4—791no—
252C22×C4—791no—
253C22×C4—791no—
254C22×C4—791no—
255C22×C4—791no—
256C22×C4—791no—
257C22×C4—791no—
258C22×C4—1582no—
259C22×C4—1582no—
260C22×C4—1582no—
261C22×C4C22×D7911yescharacteristic
262C22×C4C22×D7911yescharacteristic
263C22×C4C22×D7911yescharacteristic
264C22×C4C22×D7911yescharacteristic
265C22×C4C22×D7911yescharacteristic
266C22×C4C22×D7911yescharacteristic
267C22×C4C22×D7911yescharacteristic
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—794no—
271C4⋊C4—1582no—
272C4⋊C4—1582no—
273C4⋊C4—1582no—
274C4⋊C4—1582no—
275C22⋊C4—3161no—
276C22⋊C4—3161no—
277C22⋊C4—794no—
278C22⋊C4—1582no—
279C22⋊C4—1582no—
280C22⋊C4—1582no—
281C42—3161no—
282C42—3161no—
283C42—1582no—
284C42—1582no—
285C23—792no—
286C23—1581no—
287C23—1581no—
288C23—1581no—
289C23—1581no—
290C23—1581no—
291C23—1581no—
292C23C23×D7911yescharacteristic
293Q8—3164no—
294Q8—3164no—
295Q8—3164no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
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—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—3164no—
316C2×C4—792no—
317C2×C4—792no—
318C2×C4—792no—
319C2×C4—792no—
320C2×C4—792no—
321C2×C4—792no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4D4×D7912yes—
338C2×C4Q8×D7912yes—
339C22—3161no—
340C22—3161no—
341C22—3161no—
342C22—3161no—
343C22—1582no—
344C22—1582no—
345C22—1582no—
346C22C2×D4×D7911yescharacteristic
347C22C2×Q8×D7911yescharacteristic
348C22#41×D7911yescharacteristic
349C22#41×D7911yescharacteristic
350C22#41×D7911yescharacteristic
351C22#1457920711yescharacteristic
352C22#1457920811yescharacteristic
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3161no—
361C4—3161no—
362C4—3161no—
363C4—794no—
364C4—1582no—
365C4—1582no—
366C4—1582no—
367C2—3162no—
368C2#124×D7911yescharacteristic
369C2#1909911911yescharacteristic
370C2#1909917911yescharacteristic
371C2#1909920511yescharacteristic
372C2#1909922611yescharacteristic
373C2#1909926911yescharacteristic
374C2#1909928011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#400×C79C2
prime radicalC23×D79C23
hypercenter#400D79
hypocenterC79#2492
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14579160C2semidirect
3. #19098505C2semidirect
6. #19098468C2semidirect
7. #19098467C2semidirect
8. #19098467C2semidirect
9. #19098467C2semidirect
13. #19098414C2semidirect
15. #400×C79C2semidirect
83. (C2×D79)⋊C4Q8semidirect
188. C79#2492semidirect
192. #400D79semidirect