Finite Group Databasebeta

← #23775520

Subgroups — #23775520

Order 10112.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099234C211yesmaximal, characteristic
2#19098929C211yesmaximal, characteristic, complemented
3#19098887C211yesmaximal, characteristic, complemented
4#19098881C211yesmaximal, characteristic, complemented
5#19098867C211yesmaximal, characteristic, complemented
6#19098811C211yesmaximal, characteristic, complemented
7#19098794C211yesmaximal, characteristic, complemented
8#19098763C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098723C211yesmaximal, characteristic, complemented
11#19098668C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098562C211yesmaximal, characteristic, complemented
14#19098557C211yesmaximal, characteristic, complemented
15#552×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929624C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic
23#14579158C2211yescharacteristic
24#14579157—21no—
25#14579135C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579134—21no—
28#14579134—21no—
29C4×Dic158C2211yescharacteristic
30#14579123—21no—
31#14579094C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579084C2211yescharacteristic
37#14579084C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579081C2211yescharacteristic
40#14579081C2211yescharacteristic
41#14579081C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48#126×C79—21no—
49#125×C79—21no—
50#125×C79C2211yescharacteristic
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53C22⋊Q8×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56#117×C79—21no—
57#117×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61#11929624—41no—
62#11929624—41no—
63C2×Dic158C2311yescharacteristic
64C2×D316—21no—
65C2×D316—21no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74#11929614—22no—
75#11929611—41no—
76#11929611—41no—
77#11929608—41no—
78C2×C79⋊C8—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87C4×Dic79—21no—
88C2×Q8×C79C2311yescharacteristic
89C2×D4×C79D411yescharacteristic
90C22×C4×C79—21no—
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79D411yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79D411yescharacteristic
107C22⋊C4×C79D411yescharacteristic
108C42×C79—21no—
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117D4×C79—41no—
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—42no—
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2411yescharacteristic
132C22⋊D79—42no—
133C22⋊D79—42no—
134C22⋊D79—81no—
135C22⋊D79—81no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138D316—21no—
139D316—21no—
140D316—21no—
141D316—21no—
142D316—42no—
143D316—81no—
144C4×D79—42no—
145C4×D79—42no—
146Dic158—21no—
147Dic158#4112yes—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79C22×D411yescharacteristic
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C4×C79—21no—
166C4×C79—21no—
167C4×C79—21no—
168C4×C79—21no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79—41no—
173C4×C79C2×#4111yescharacteristic
174C4×C79H(5,𝔽2)11yescharacteristic
175Dic79—22no—
176Dic79—41no—
177C2×C79—41no—
178C2×C79—41no—
179C2×C79#54611yescharacteristic
180C2×C79#57511yescharacteristic
181C2×C79#57711yescharacteristic
182D79—81no—
183D79—81no—
184#3317—791nomaximal, Sylow
185C79#331711yescharacteristic, complemented, Sylow
186#552D7911yescharacteristic, complemented
187#550—791no—
188#490—791no—
189#482—791no—
190#481—791no—
191#479—791no—
192#468—791no—
193#465—791no—
194#460—791no—
195#452—791no—
196#452—791no—
197#441—791no—
198#435—791no—
199#417—791no—
200#416—791no—
201C2×#41—791no—
202C2×#41—791no—
203C2×Q16—791no—
204C2×SD16—791no—
205C2×SD16—791no—
206C2×M16—791no—
207C22×C8—791no—
208#127—791no—
209#127—1581no—
210#126—21no—
211#125—21no—
212#125C2×D7911yescharacteristic
213#123—21no—
214C22⋊Q8C2×D7911yescharacteristic
215C22⋊Q8C2×D7911yescharacteristic
216#121—791no—
217#121—791no—
218#121—1581no—
219#121—1581no—
220C4×Q8—791no—
221C4×Q8C2×D7911yescharacteristic
222C4×D4—1581no—
223C4×D4C2×D7911yescharacteristic
224#117—21no—
225#117C2×D7911yescharacteristic
226C2×C4⋊C4C2×D7911yescharacteristic
227#107—791no—
228#106—791no—
229#106—791no—
230C4⋊C8—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#102—791no—
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241C22⋊C8—791no—
242C22⋊C8—791no—
243#97—791no—
244#41—3161no—
245#41—3161no—
246#41—1582no—
247#41—1582no—
248C2×Q8—791no—
249C2×Q8C22×D7911yescharacteristic
250C2×D4—791no—
251C2×D4—791no—
252C2×D4—1581no—
253C2×D4—1581no—
254C2×D4—1581no—
255C2×D4—1581no—
256C2×D4—1581no—
257C2×D4—1581no—
258C2×D4C22⋊D7911yescharacteristic
259C22×C4—21no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263C22×C4C22×D7911yescharacteristic
264Q16—1582no—
265SD16—3161no—
266SD16—3161no—
267M16—3161no—
268C2×C8—3161no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8—791no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—791no—
280C4⋊C4—1581no—
281C4⋊C4C22⋊D7911yescharacteristic
282C4⋊C4C22×D7911yescharacteristic
283C4⋊C4C22×D7911yescharacteristic
284C4⋊C4C22×D7911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4C22⋊D7911yescharacteristic
291C22⋊C4C22⋊D7911yescharacteristic
292C42—21no—
293C42—21no—
294C42—1581no—
295C42C22×D7911yescharacteristic
296C23—1581no—
297C23—1581no—
298C23C2×C22⋊D7911yescharacteristic
299C23C2×C22⋊D7911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—792no—
303Q8—1581no—
304D4—41no—
305D4—3162no—
306D4—3162no—
307D4—3162no—
308D4—6321no—
309D4—6321no—
310D4—6321no—
311D4—1581no—
312D4—1581no—
313D4—1581no—
314D4—1581no—
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—42no—
324C2×C4—3162no—
325C2×C4—3162no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4C2×C22⋊D7911yescharacteristic
329C2×C4C2×C22⋊D7911yescharacteristic
330C2×C4C2×C22⋊D7911yescharacteristic
331C2×C4C2×C22⋊D7911yescharacteristic
332C2×C4C23×D7911yescharacteristic
333C8—1581no—
334C8—1581no—
335C8—1581no—
336C8—1581no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—3161no—
344C22—3161no—
345C22—3161no—
346C22—3161no—
347C22—3161no—
348C22—3161no—
349C22C22×C22⋊D7911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—3161no—
359C4—1582no—
360C4#41×D7911yescharacteristic
361C4#1457920711yescharacteristic
362C2—41no—
363C2—41no—
364C2—6321no—
365C2—6321no—
366C2#1909920111yescharacteristic
367C2#1909936111yescharacteristic
368C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#552×C79C2
socleC22×C79C22×D4
prime radical#19099234C2
hypercenter#552D79
hypocenterC79#3317
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #19098929C2semidirect
3. #19098887C2semidirect
4. #19098881C2semidirect
5. #19098867C2semidirect
6. #19098811C2semidirect
7. #19098794C2semidirect
8. #19098763C2semidirect
9. #19098723C2semidirect
10. #19098723C2semidirect
11. #19098668C2semidirect
12. #19098635C2semidirect
13. #19098562C2semidirect
14. #19098557C2semidirect
15. #552×C79C2semidirect
185. C79#3317semidirect
186. #552D79semidirect