Finite Group Databasebeta

← #23774113

Subgroups — #23774113

Order 10112.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099115C211yesmaximal, characteristic, complemented
2#19099108C211yesmaximal, characteristic
3#19098967C211yesmaximal, characteristic, complemented
4#19098934C211yesmaximal, characteristic, complemented
5#19098912C211yesmaximal, characteristic, complemented
6#19098908C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098809C211yesmaximal, characteristic, complemented
9#19098807C211yesmaximal, characteristic, complemented
10#19098666C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12#19098662C211yesmaximal, characteristic, complemented
13#19098660C211yesmaximal, characteristic, complemented
14M16×Dic79C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×#11929613C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929608C2211yescharacteristic
21#14579160C2211yescharacteristic
22#14579160C2211yescharacteristic
23#14579159C2211yescharacteristic
24#14579157C2211yescharacteristic
25#14579151—21no—
26#14579147—21no—
27#14579140C2211yescharacteristic
28#14579138—21no—
29#14579135C2211yescharacteristic
30#14579133—21no—
31Q8×Dic79C2211yescharacteristic
32#14579126—21no—
33#14579126C2211yescharacteristic
34D4×Dic79C2211yescharacteristic
35#14579123C2211yescharacteristic
36(C22⋊D79)⋊C4—21no—
37#14579117—21no—
38C2×C4×Dic79C2211yescharacteristic
39#14579095C2211yescharacteristic
40#14579094C2211yescharacteristic
41#14579094C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579085C2211yescharacteristic
44#14579084C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579071C2211yescharacteristic
49#14579071C2211yescharacteristic
50C8×Dic79C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×SD16×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—44no—
60C2×Dic158—21no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×D316C2311yescharacteristic
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C22×Dic79—21no—
68C22×Dic79D411yescharacteristic
69C22×Dic79D411yescharacteristic
70C2×C4×D79—21no—
71#11929613—22no—
72#11929612—22no—
73#11929611—22no—
74#11929608—22no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C4⋊Dic79—21no—
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90C4×Dic79—21no—
91C4×Dic79—21no—
92C4×Dic79D411yescharacteristic
93C4×Dic79D411yescharacteristic
94C4×Dic79C2311yescharacteristic
95C4×Dic79C2311yescharacteristic
96C2×Q8×C79C2311yescharacteristic
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100SD16×C79—22no—
101M16×C79—22no—
102C2×C8×C79C2311yescharacteristic
103C2×C8×C79C2311yescharacteristic
104C4⋊C4×C79—21no—
105C4⋊C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C23×C79—21no—
110C23×C79C2×D411yescharacteristic
111C22×D79—21no—
112Q8×C79—21no—
113Q8×C79—21no—
114D4×C79—21no—
115D4×C79—21no—
116D4×C79—42no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2411yescharacteristic
124C22⋊D79—42no—
125C22⋊D79—42no—
126C22⋊D79—42no—
127C2×Dic79—22no—
128C2×Dic79—22no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—42no—
133C2×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—21no—
138D316—21no—
139C4×D79—42no—
140Dic158—21no—
141Dic158—21no—
142Dic158—42no—
143Dic158—42no—
144C8×C79—21no—
145C8×C79#4112yescomplemented
146C79⋊C8—21no—
147C79⋊C8#4112yescomplemented
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79C22×D411yescharacteristic
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C4×C79—21no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79C2×#4111yescharacteristic
163C4×C79C2×#4111yescharacteristic
164Dic79—21no—
165Dic79—21no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169Dic79AGL(1,ℤ/8)12yes—
170Dic79#13712yes—
171C2×C79—41no—
172C2×C79—81no—
173C2×C79#53211yescharacteristic
174C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C79C2×#13711yescharacteristic
176D79—81no—
177#3182—791nomaximal, Sylow
178C79#318211yescharacteristic, complemented, Sylow
179#533—791no—
180#532—791no—
181#500—791no—
182#492—791no—
183#487—791no—
184#486—791no—
185#468—791no—
186#468—791no—
187#468—791no—
188#468D7911yescharacteristic, complemented
189#440—791no—
190#440—791no—
191#440—791no—
192#440—791no—
193C4×M16—791no—
194C2×#41—1581no—
195C2×SD16—791no—
196C2×SD16—791no—
197C2×SD16—791no—
198C2×SD16C2×D7911yescharacteristic
199C2×M16—791no—
200C2×M16C2×D7911yescharacteristic
201C4⋊Q8—791no—
202C4⋊Q8—791no—
203C4⋊Q8—791no—
204#127—791no—
205#125—1581no—
206#124—1581no—
207C22⋊Q8—791no—
208C22⋊Q8—1581no—
209C22⋊Q8C2×D7911yescharacteristic
210#121—791no—
211#121—1581no—
212#121C2×D7911yescharacteristic
213C4×Q8—791no—
214C4×Q8—791no—
215C4×Q8—1581no—
216C4×D4—791no—
217C4×D4—791no—
218C4×D4—1581no—
219#117—1581no—
220C2×C42—791no—
221#107—791no—
222#107—791no—
223#107—791no—
224#107C2×D7911yescharacteristic
225#103—791no—
226#103—791no—
227#103—791no—
228#103C2×D7911yescharacteristic
229#102—791no—
230#102—791no—
231#102—791no—
232#102C2×D7911yescharacteristic
233#97—791no—
234#97—791no—
235C4×C8—791no—
236C4×C8—791no—
237#41—3164no—
238C2×Q8—791no—
239C2×Q8—1581no—
240C2×Q8—1581no—
241C2×Q8C22×D7911yescharacteristic
242C2×D4—21no—
243C2×D4—791no—
244C2×D4—1581no—
245C2×D4—1581no—
246C2×D4—1581no—
247C2×D4C22×D7911yescharacteristic
248C22×C4—791no—
249C22×C4—791no—
250C22×C4—1581no—
251C22×C4—1581no—
252C22×C4C22×D7911yescharacteristic
253SD16—22no—
254SD16—1582no—
255SD16—1582no—
256SD16—1582no—
257M16—22no—
258M16—1582no—
259C2×C8—791no—
260C2×C8—791no—
261C2×C8C22×D7911yescharacteristic
262C2×C8C22×D7911yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—791no—
265C4⋊C4—791no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4C22×D7911yescharacteristic
274C4⋊C4C22×D7911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C42—791no—
282C42—791no—
283C42—791no—
284C42—791no—
285C42—1581no—
286C42—1581no—
287C23—21no—
288C23—1581no—
289C23D4×D7911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—3162no—
293Q8—3162no—
294Q8—1581no—
295Q8—1581no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—3162no—
300D4—3162no—
301D4—3162no—
302D4—1581no—
303D4—1581no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3162no—
310C2×C4—3162no—
311C2×C4—791no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1582no—
319C2×C4—1582no—
320C2×C4D4×D7911yescharacteristic
321C2×C4C23×D7911yescharacteristic
322C8—21no—
323C8—792no—
324C8—1581no—
325C8#1192962312yescomplemented
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—3161no—
333C22—3161no—
334C22—3161no—
335C22C2×D4×D7911yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—3161no—
341C4—3161no—
342C4—3161no—
343C4—792no—
344C4—792no—
345C4—1581no—
346C4—1581no—
347C4#41×D7911yescharacteristic
348C4C2×#1192962311yescharacteristic
349C2—41no—
350C2—81no—
351C2—6321no—
352C2#1909910811yescharacteristic
353C2AGL(1,ℤ/8)×D7911yescharacteristic
354C2#137×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
prime radical#19099108C2
hypercenter#468D79
hypocenterC79#3182
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #19099115C2semidirect
3. #19098967C2semidirect
4. #19098934C2semidirect
5. #19098912C2semidirect
6. #19098908C2semidirect
7. #19098811C2semidirect
8. #19098809C2semidirect
9. #19098807C2semidirect
10. #19098666C2semidirect
11. #19098664C2semidirect
12. #19098662C2semidirect
13. #19098660C2semidirect
14. M16×Dic79C2semidirect
15. #468×C79C2semidirect
145. C8×C79#41semidirect
147. C79⋊C8#41semidirect
178. C79#3182semidirect
188. #468D79semidirect
325. C8#11929623semidirect