Finite Group Databasebeta

← #23769713

Subgroups — #23769713

Order 10112.

544 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579161C211yesmaximal, characteristic, complemented
2C2×#14579160C211yesmaximal, characteristic, complemented
3C2×#14579141C211yesmaximal, characteristic
4C2×#14579139C211yesmaximal, characteristic
5#19098500C211yesmaximal, characteristic
6#19098495C211yesmaximal, characteristic, complemented
7#19098493C211yesmaximal, characteristic, complemented
8#19098484C211yesmaximal, characteristic, complemented
9#19098484C211yesmaximal, characteristic, complemented
10#19098476C211yesmaximal, characteristic
11#19098455C211yesmaximal, characteristic
12#19098454C211yesmaximal, characteristic
13#19098448C211yesmaximal, characteristic, complemented
14#19098437C211yesmaximal, characteristic
15#387×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C22×Dic158C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579161—24no—
21#14579160—24no—
22#14579141—24no—
23#14579139—24no—
24C2×C4⋊Dic79C2211yescharacteristic
25C2×C4⋊Dic79C2211yescharacteristic
26C2×C4⋊Dic79C2211yescharacteristic
27C2×C4⋊Dic79C2211yescharacteristic
28C2×C4⋊Dic79C2211yescharacteristic
29C2×C4⋊Dic79C2211yescharacteristic
30C2×C4⋊Dic79C2211yescharacteristic
31C2×Dic79⋊C4C2211yescharacteristic
32C2×Dic79⋊C4C2211yescharacteristic
33C2×Dic79⋊C4C2211yescharacteristic
34C2×Dic79⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×(C2×D79)⋊C4C2211yescharacteristic
37C2×(C2×D79)⋊C4C2211yescharacteristic
38C2×(C2×D79)⋊C4C2211yescharacteristic
39C2×(C2×D79)⋊C4C2211yescharacteristic
40C2×(C2×D79)⋊C4C2211yescharacteristic
41C2×C4×Dic79C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C79⋊#95C2211yescharacteristic
47C79⋊#95C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C4⋊C4×C79C2211yescharacteristic
50C2×C42×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53#95×C79C2211yescharacteristic
54#95×C79C2211yescharacteristic
55C23×D79C2311yescharacteristic
56C2×Dic158—22no—
57C2×Dic158—22no—
58C2×Dic158—22no—
59C2×Dic158—22no—
60C2×Dic158—22no—
61C2×Dic158—22no—
62C2×Dic158—41no—
63C2×Dic158—41no—
64C2×Dic158—41no—
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C22×Dic79C2311yescharacteristic
71C22×Dic79C2311yescharacteristic
72C2×C4×D79—22no—
73C2×C4×D79—22no—
74C2×C4×D79—41no—
75C4⋊Dic79—22no—
76C4⋊Dic79—22no—
77C4⋊Dic79—22no—
78C4⋊Dic79—22no—
79C4⋊Dic79—22no—
80C4⋊Dic79—41no—
81C4⋊Dic79D414yes—
82Dic79⋊C4—22no—
83Dic79⋊C4—22no—
84Dic79⋊C4—22no—
85Dic79⋊C4—22no—
86(C2×D79)⋊C4—22no—
87(C2×D79)⋊C4—22no—
88(C2×D79)⋊C4—22no—
89(C2×D79)⋊C4—22no—
90(C2×D79)⋊C4—41no—
91(C2×D79)⋊C4Q814yescomplemented
92C4×Dic79—22no—
93C22×C4×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C4⋊C4×C79—22no—
101C4⋊C4×C79D414yes—
102C42×C79—22no—
103C23×C79C2411yescharacteristic
104C22×D79—21no—
105C22×D79—21no—
106C22×D79—21no—
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79C2×Q812yes—
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×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79C2×D412yes—
128C2×C4×C79C2×D412yes—
129C2×C4×C79C2×D412yes—
130C2×C4×C79C2×D412yes—
131C2×C4×C79C2×Q812yes—
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×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79C2×D412yes—
151C2×Dic79C2×D412yes—
152C2×Dic79C2×Q812yes—
153C4×D79—44no—
154Dic158—44no—
155Dic158—44no—
156Dic158—44no—
157C22×C79C22×D411yescharacteristic
158C22×C79C22×D411yescharacteristic
159C22×C79C22×Q811yescharacteristic
160C22×C79H(5,𝔽2)11yescharacteristic
161C22×C792−1+411yescharacteristic
162C22×C792−1+411yescharacteristic
163C22×C792−1+411yescharacteristic
164C2×D79—22no—
165C2×D79—22no—
166C2×D79—22no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C4×C79—22no—
172C4×C79—22no—
173C4×C79—22no—
174C4×C79—22no—
175C4×C79—22no—
176C4×C79—41no—
177C4×C79—41no—
178Dic79—22no—
179Dic79—22no—
180Dic79—22no—
181Dic79—41no—
182Dic79—41no—
183Dic79—41no—
184Dic79—41no—
185C2×C79#53611yescharacteristic
186C2×C79#53611yescharacteristic
187C2×C79#54411yescharacteristic
188C2×C79D4211yescharacteristic
189C2×C79D4×Q811yescharacteristic
190C2×C79D4×Q811yescharacteristic
191C2×C79#56311yescharacteristic
192D79—42no—
193#2677—791nomaximal, Sylow
194C79#267711yescharacteristic, complemented, Sylow
195C2×C4⋊Q8—791no—
196C2×C4⋊Q8—791no—
197C2×C22⋊Q8—791no—
198C2×C22⋊Q8—791no—
199#399—791no—
200#398—791no—
201#398—791no—
202#395—791no—
203#395—791no—
204#393—791no—
205#388—791no—
206#388—791no—
207#387—791no—
208#387D7911yescharacteristic, complemented
209#385—791no—
210C22×Q8—791no—
211C22×Q8—791no—
212C22×Q8—791no—
213C23×C4—791no—
214C4⋊Q8—1584no—
215C4⋊Q8—1584no—
216C22⋊Q8—1584no—
217C22⋊Q8—1584no—
218C2×C4⋊C4—791no—
219C2×C4⋊C4—791no—
220C2×C4⋊C4—791no—
221C2×C4⋊C4—791no—
222C2×C4⋊C4—791no—
223C2×C4⋊C4—791no—
224C2×C4⋊C4—791no—
225C2×C4⋊C4—791no—
226C2×C4⋊C4—791no—
227C2×C4⋊C4—791no—
228C2×C4⋊C4—791no—
229C2×C4⋊C4C2×D7911yescharacteristic
230C2×C4⋊C4C2×D7911yescharacteristic
231C2×C22⋊C4—791no—
232C2×C22⋊C4—791no—
233C2×C22⋊C4—791no—
234C2×C22⋊C4—791no—
235C2×C22⋊C4—791no—
236C2×C22⋊C4—791no—
237C2×C42—791no—
238C2×C42C2×D7911yescharacteristic
239#95—791no—
240#95—791no—
241#95—791no—
242#95—791no—
243#95—791no—
244#95—791no—
245#95C2×D7911yescharacteristic
246#95C2×D7911yescharacteristic
247#95C2×D7911yescharacteristic
248#95C2×D7911yescharacteristic
249C24—791no—
250C2×Q8—3161no—
251C2×Q8—3161no—
252C2×Q8—3161no—
253C2×Q8—1582no—
254C2×Q8—1582no—
255C2×Q8—1582no—
256C2×Q8—1582no—
257C2×Q8—1582no—
258C2×Q8—1582no—
259C22×C4—3161no—
260C22×C4—791no—
261C22×C4—791no—
262C22×C4—791no—
263C22×C4—791no—
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—1582no—
268C22×C4—1582no—
269C22×C4C22×D7911yescharacteristic
270C22×C4C22×D7911yescharacteristic
271C22×C4C22×D7911yescharacteristic
272C22×C4C22×D7911yescharacteristic
273C22×C4C22×D7911yescharacteristic
274C22×C4C22×D7911yescharacteristic
275C22×C4C22×D7911yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—3161no—
278C4⋊C4—794no—
279C4⋊C4—1582no—
280C4⋊C4—1582no—
281C4⋊C4—1582no—
282C4⋊C4—1582no—
283C4⋊C4—1582no—
284C4⋊C4—1582no—
285C4⋊C4—1582no—
286C4⋊C4—1582no—
287C4⋊C4—1582no—
288C4⋊C4D31614yes—
289C22⋊C4—3161no—
290C22⋊C4—794no—
291C22⋊C4—1582no—
292C22⋊C4—1582no—
293C22⋊C4—1582no—
294C22⋊C4—1582no—
295C42—22no—
296C42—1582no—
297C23—792no—
298C23—1581no—
299C23—1581no—
300C23—1581no—
301C23—1581no—
302C23—1581no—
303C23—1581no—
304C23C23×D7911yescharacteristic
305Q8—3164no—
306Q8—3164no—
307Q8—3164no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—3164no—
325C2×C4—792no—
326C2×C4—792no—
327C2×C4—792no—
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×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4D4×D7912yes—
347C2×C4C2×D31612yes—
348C2×C4C2×D31612yes—
349C2×C4C2×D31612yes—
350C2×C4Q8×D7912yes—
351C22—3161no—
352C22—3161no—
353C22—3161no—
354C22—3161no—
355C22—1582no—
356C22—1582no—
357C22—1582no—
358C22C2×D4×D7911yescharacteristic
359C22C22×D31611yescharacteristic
360C22C2×Q8×D7911yescharacteristic
361C22#1457920711yescharacteristic
362C22#1457920811yescharacteristic
363C22#1457920811yescharacteristic
364C22#1457920811yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—3161no—
373C4—3161no—
374C4—3161no—
375C4—3161no—
376C4—1582no—
377C4—1582no—
378C4—1582no—
379C2—3162no—
380C2#1909913511yescharacteristic
381C2#1909913911yescharacteristic
382C2#1909919311yescharacteristic
383C2D4×D31611yescharacteristic
384C2#1909922611yescharacteristic
385C2Q8×D31611yescharacteristic
386C2#1909931511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#387×C79C2
prime radicalC23×D79C23
hypercenter#387D79
hypocenterC79#2677
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#14579161C2semidirect
2. C2×#14579160C2semidirect
6. #19098495C2semidirect
7. #19098493C2semidirect
8. #19098484C2semidirect
9. #19098484C2semidirect
13. #19098448C2semidirect
15. #387×C79C2semidirect
91. (C2×D79)⋊C4Q8semidirect
194. C79#2677semidirect
208. #387D79semidirect