Finite Group Databasebeta

← #23772383

Subgroups — #23772383

Order 10112.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099091C211yesmaximal, characteristic
2#19098692C211yesmaximal, characteristic, complemented
3#19098690C211yesmaximal, characteristic, complemented
4#19098640C211yesmaximal, characteristic, complemented
5#19098638C211yesmaximal, characteristic, complemented
6#19098637C211yesmaximal, characteristic, complemented
7#19098633C211yesmaximal, characteristic, complemented
8#19098631C211yesmaximal, characteristic, complemented
9#19098631C211yesmaximal, characteristic, complemented
10#19098622C211yesmaximal, characteristic, complemented
11#19098618C211yesmaximal, characteristic, complemented
12#19098520C211yesmaximal, characteristic, complemented
13#19098519C211yesmaximal, characteristic, complemented
14C4×#11929607C211yesmaximal, characteristic, complemented
15#433×C79C211yesmaximal, characteristic, complemented
16C2×#11929608C2211yescharacteristic
17C2×#11929607C2211yescharacteristic
18C2×#11929607C2211yescharacteristic
19C2×#11929607C2211yescharacteristic
20C22×C79⋊C8C2211yescharacteristic
21C2×C8×D79C2211yescharacteristic
22#14579156C411yescharacteristic
23#14579154C411yescharacteristic
24#14579151C411yescharacteristic
25#14579147C411yescharacteristic
26#14579146C411yescharacteristic
27#14579143C411yescharacteristic
28#14579139C411yescharacteristic
29#14579134C411yescharacteristic
30C4×Dic158C2211yescharacteristic
31C4×D316C2211yescharacteristic
32C4×C22⋊D79C2211yescharacteristic
33C4×C22⋊D79C2211yescharacteristic
34#14579118C2211yescharacteristic
35C42×D79C2211yescharacteristic
36Dic79⋊C8C2211yescharacteristic
37Dic79⋊C8C2211yescharacteristic
38Dic79⋊C8C2211yescharacteristic
39Dic79⋊C8C2211yescharacteristic
40(C2×D79)⋊C8C2211yescharacteristic
41(C2×D79)⋊C8C2211yescharacteristic
42(C2×D79)⋊C8C2211yescharacteristic
43(C2×D79)⋊C8C2211yescharacteristic
44#14579072C2211yescharacteristic
45#14579072C2211yescharacteristic
46#14579071C2211yescharacteristic
47#14579071C2211yescharacteristic
48#14579071C2211yescharacteristic
49C4×C79⋊C8C2211yescharacteristic
50C4×C79⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52#117×C79C2211yescharacteristic
53C4⋊C8×C79C2211yescharacteristic
54C4⋊C8×C79C2211yescharacteristic
55C22⋊C8×C79C2211yescharacteristic
56C22⋊C8×C79C2211yescharacteristic
57#97×C79C2211yescharacteristic
58C4×C8×C79C2211yescharacteristic
59C2×Dic158C2×C411yescharacteristic
60C2×D316C2×C411yescharacteristic
61C2×C22⋊D79C2×C411yescharacteristic
62C2×C22⋊D79C2×C411yescharacteristic
63C2×C4×D79C2×C411yescharacteristic
64C2×C4×D79C2×C411yescharacteristic
65C2×C4×D79C2311yescharacteristic
66C2×C4×D79C2311yescharacteristic
67#11929608—22no—
68#11929607—22no—
69#11929607—22no—
70#11929607—22no—
71C2×C79⋊C8—22no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C8×D79—22no—
77C4⋊Dic79C2×C411yescharacteristic
78C4⋊Dic79C2×C411yescharacteristic
79Dic79⋊C4C2×C411yescharacteristic
80Dic79⋊C4C2×C411yescharacteristic
81Dic79⋊C4C2×C411yescharacteristic
82Dic79⋊C4C2×C411yescharacteristic
83Dic79⋊C4C2×C411yescharacteristic
84Dic79⋊C4C2×C411yescharacteristic
85C22⋊Dic79C2×C411yescharacteristic
86C22⋊Dic79C2×C411yescharacteristic
87(C2×D79)⋊C4C2×C411yescharacteristic
88(C2×D79)⋊C4C2×C411yescharacteristic
89(C2×D79)⋊C4C2×C411yescharacteristic
90(C2×D79)⋊C4C2×C411yescharacteristic
91(C2×D79)⋊C4C2×C411yescharacteristic
92(C2×D79)⋊C4C2×C411yescharacteristic
93C4×Dic79C2×C411yescharacteristic
94C4×Dic79C2×C411yescharacteristic
95C4×Dic79C2311yescharacteristic
96C4×Dic79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C2×C8×C79C2311yescharacteristic
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79C2×C411yescharacteristic
103C4⋊C4×C79C2×C411yescharacteristic
104C22⋊C4×C79C2×C411yescharacteristic
105C22⋊C4×C79C2×C411yescharacteristic
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79C22×C411yescharacteristic
109C22×D79C22×C411yescharacteristic
110C22×D79C22×C411yescharacteristic
111C2×C4×C79—21no—
112C2×C4×C79—21no—
113C2×C4×C79C22×C411yescharacteristic
114C2×C4×C79C22×C411yescharacteristic
115C2×C4×C79C22×C411yescharacteristic
116C2×C4×C79C22×C411yescharacteristic
117C2×C4×C79C22×C411yescharacteristic
118C2×C4×C79C2411yescharacteristic
119C22⋊D79—41no—
120C22⋊D79—41no—
121C2×Dic79C22×C411yescharacteristic
122C2×Dic79C22×C411yescharacteristic
123C2×Dic79C22×C411yescharacteristic
124C2×Dic79C22×C411yescharacteristic
125C2×Dic79C22×C411yescharacteristic
126C2×Dic79C22×C411yescharacteristic
127D316—41no—
128C4×D79—21no—
129C4×D79—21no—
130C4×D79—21no—
131C4×D79—21no—
132C4×D79—41no—
133C4×D79—41no—
134Dic158—41no—
135C8×C79—21no—
136C8×C79—21no—
137C8×C79—21no—
138C8×C79—21no—
139C79⋊C8—21no—
140C79⋊C8—21no—
141C79⋊C8#4112yes—
142C79⋊C8#4112yes—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79—21no—
146C22×C79C23×C411yescharacteristic
147C2×D79—21no—
148C2×D79—21no—
149C2×D79—21no—
150C2×D79—21no—
151C2×D79—21no—
152C2×D79—21no—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79C2×#4111yescharacteristic
159C4×C79C2×#4111yescharacteristic
160Dic79—21no—
161Dic79—21no—
162Dic79—21no—
163Dic79—21no—
164Dic79—21no—
165Dic79—21no—
166C2×C79—41no—
167C2×C79C4×#4111yescharacteristic
168C2×C79#56811yescharacteristic
169C2×C79#56811yescharacteristic
170D79—41no—
171D79—41no—
172#2967—791nomaximal, Sylow
173C79#296711yescharacteristic, complemented, Sylow
174#529—791no—
175#446—791no—
176#446—791no—
177#436—791no—
178#436—791no—
179#435—791no—
180#435—791no—
181#435—791no—
182#435—791no—
183#433—791no—
184#433D7911yescharacteristic, complemented
185#432—791no—
186#405—791no—
187#405—791no—
188C4×M16—791no—
189C2×M16—791no—
190C2×M16—791no—
191C2×M16—791no—
192C2×M16—791no—
193C22×C8—791no—
194C22×C8—791no—
195#126—791no—
196#126—791no—
197#125—791no—
198#124—791no—
199#123—791no—
200#123—791no—
201C22⋊Q8—791no—
202#121—791no—
203C4×Q8—791no—
204C4×D4—791no—
205C4×D4—791no—
206C4×D4—791no—
207#117—791no—
208#117C2×D7911yescharacteristic
209C2×C42—791no—
210C4⋊C8—791no—
211C4⋊C8—791no—
212C4⋊C8—791no—
213C4⋊C8—791no—
214C4⋊C8C2×D7911yescharacteristic
215C4⋊C8C2×D7911yescharacteristic
216C22⋊C8—791no—
217C22⋊C8—791no—
218C22⋊C8—791no—
219C22⋊C8—791no—
220C22⋊C8C2×D7911yescharacteristic
221C22⋊C8C2×D7911yescharacteristic
222#97—791no—
223#97—791no—
224#97—791no—
225#97—791no—
226#97—791no—
227#97C2×D7911yescharacteristic
228C4×C8—791no—
229C4×C8—791no—
230C4×C8—791no—
231C4×C8C2×D7911yescharacteristic
232C2×Q8—791no—
233C2×D4—791no—
234C2×D4—791no—
235C2×D4—791no—
236C22×C4—791no—
237C22×C4—791no—
238C22×C4—791no—
239C22×C4—791no—
240C22×C4C22×D7911yescharacteristic
241M16—1582no—
242M16—1582no—
243M16—1582no—
244M16—1582no—
245C2×C8—791no—
246C2×C8—791no—
247C2×C8—791no—
248C2×C8—791no—
249C2×C8—1582no—
250C2×C8—1582no—
251C2×C8C22×D7911yescharacteristic
252C2×C8C22×D7911yescharacteristic
253C2×C8C22×D7911yescharacteristic
254C2×C8C22×D7911yescharacteristic
255C4⋊C4—791no—
256C4⋊C4—791no—
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—791no—
263C4⋊C4C4×D7911yescharacteristic
264C4⋊C4C4×D7911yescharacteristic
265C22⋊C4—791no—
266C22⋊C4—791no—
267C22⋊C4—791no—
268C22⋊C4—791no—
269C22⋊C4—791no—
270C22⋊C4—791no—
271C22⋊C4—791no—
272C22⋊C4—791no—
273C22⋊C4C4×D7911yescharacteristic
274C22⋊C4C4×D7911yescharacteristic
275C42—791no—
276C42—791no—
277C42—791no—
278C42—791no—
279C42C22×D7911yescharacteristic
280C42C22×D7911yescharacteristic
281C23—791no—
282C23—791no—
283C23C2×C4×D7911yescharacteristic
284Q8—3161no—
285D4—3161no—
286D4—3161no—
287D4—3161no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—3161no—
291C2×C4—3161no—
292C2×C4—791no—
293C2×C4—791no—
294C2×C4—791no—
295C2×C4—791no—
296C2×C4—791no—
297C2×C4—791no—
298C2×C4—1581no—
299C2×C4—1581no—
300C2×C4—1581no—
301C2×C4—1581no—
302C2×C4C2×C4×D7911yescharacteristic
303C2×C4C2×C4×D7911yescharacteristic
304C2×C4C2×C4×D7911yescharacteristic
305C2×C4C2×C4×D7911yescharacteristic
306C2×C4C2×C4×D7911yescharacteristic
307C2×C4C23×D7911yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C8—792no—
313C8—792no—
314C8—1581no—
315C8—1581no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—1581no—
320C22—1581no—
321C22—1581no—
322C22—1581no—
323C22—1581no—
324C22—1581no—
325C22C22×C4×D7911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—1581no—
332C4—1581no—
333C4—1581no—
334C4—1581no—
335C4—1581no—
336C4—1581no—
337C4#41×D7911yescharacteristic
338C4#41×D7911yescharacteristic
339C2—41no—
340C2—3161no—
341C2—3161no—
342C2#1909903111yescharacteristic
343C2#1909932811yescharacteristic
344C2#1909932811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D79
commutator, socleC22×C79C23×C4
Fitting#433×C79C2
prime radical#14579134C4
cosocleC2×C4×C79C24
hypercenter#433D79
hypocenterC79#2967
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #19098692C2semidirect
3. #19098690C2semidirect
4. #19098640C2semidirect
5. #19098638C2semidirect
6. #19098637C2semidirect
7. #19098633C2semidirect
8. #19098631C2semidirect
9. #19098631C2semidirect
10. #19098622C2semidirect
11. #19098618C2semidirect
12. #19098520C2semidirect
13. #19098519C2semidirect
14. C4×#11929607C2semidirect
15. #433×C79C2semidirect
173. C79#2967semidirect
184. #433D79semidirect