Finite Group Databasebeta

← #23773511

Subgroups — #23773511

Order 10112.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099097C211yesmaximal, characteristic, complemented
2C4×#11929624C211yesmaximal, characteristic, complemented
3#19098905C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098871C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098786C211yesmaximal, characteristic, complemented
8#19098779C211yesmaximal, characteristic, complemented
9#19098727C211yesmaximal, characteristic, complemented
10#19098710C211yesmaximal, characteristic
11#19098676C211yesmaximal, characteristic, complemented
12#19098671C211yesmaximal, characteristic, complemented
13#19098665C211yesmaximal, characteristic, complemented
14#19098665C211yesmaximal, characteristic, complemented
15#432×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×Dic316C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×D632C2211yescharacteristic
21#14579155—21no—
22#14579153C2211yescharacteristic
23#14579149C2211yescharacteristic
24#14579144—21no—
25#14579140C2211yescharacteristic
26#14579135C2211yescharacteristic
27C4×Dic158C2211yescharacteristic
28C4×Dic158C2211yescharacteristic
29C4×Dic158C2211yescharacteristic
30C4×D316C2211yescharacteristic
31C4×D316C2211yescharacteristic
32C4×D316C2211yescharacteristic
33C4×C22⋊D79—21no—
34C4×C22⋊D79—21no—
35C4×C22⋊D79—21no—
36#14579120C2211yescharacteristic
37#14579118—21no—
38#14579118—21no—
39C42×D79—21no—
40#14579095C2211yescharacteristic
41#14579095C2211yescharacteristic
42#14579093C2211yescharacteristic
43#14579093C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579086C2211yescharacteristic
46#14579086C2211yescharacteristic
47#14579086C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic
52C2×C42×C79C2211yescharacteristic
53C4⋊C8×C79C2211yescharacteristic
54C4⋊C8×C79C2211yescharacteristic
55C22⋊C8×C79C2211yescharacteristic
56C22⋊C8×C79C2211yescharacteristic
57#97×C79C2211yescharacteristic
58#97×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61C2×Dic158C2311yescharacteristic
62C2×Dic158C2311yescharacteristic
63C2×D316C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71Dic316—22no—
72#11929613—22no—
73#11929613—22no—
74D632—22no—
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C22×C4×C79D411yescharacteristic
98C22×C4×C79D411yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C2×C8×C79C2311yescharacteristic
104C42×C79D411yescharacteristic
105C42×C79D411yescharacteristic
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79C2×D411yescharacteristic
109C22×D79—21no—
110C22×D79—21no—
111C2×C4×C79—21no—
112C2×C4×C79—21no—
113C2×C4×C79—41no—
114C2×C4×C79—41no—
115C2×C4×C79C2×D411yescharacteristic
116C2×C4×C79C2×D411yescharacteristic
117C2×C4×C79C2×D411yescharacteristic
118C2×C4×C79C2×D411yescharacteristic
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79C2411yescharacteristic
121C22⋊D79—24no—
122C22⋊D79—42no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129D316—21no—
130D316—21no—
131D316—21no—
132D316#4112yes—
133C4×D79—24no—
134C4×D79—42no—
135C4×D79—42no—
136C4×D79—42no—
137Dic158—21no—
138Dic158—21no—
139Dic158—21no—
140Dic158#4112yes—
141C8×C79—21no—
142C8×C79—21no—
143C8×C79—21no—
144C8×C79—21no—
145C22×C79—21no—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79C22×D411yescharacteristic
149C2×D79—22no—
150C2×D79—41no—
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—21no—
159C4×C79—21no—
160C4×C79C2×#4111yescharacteristic
161C4×C79C2×#4111yescharacteristic
162Dic79—22no—
163Dic79—41no—
164Dic79—41no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168C2×C79—41no—
169C2×C79#52511yescharacteristic
170C2×C79#57511yescharacteristic
171C2×C79#57511yescharacteristic
172D79—42no—
173D79—81no—
174#3111—791nomaximal, Sylow
175C79#311111yescharacteristic, complemented, Sylow
176#529—791no—
177C4×#41—791no—
178#485—791no—
179#482—791no—
180#479—791no—
181#478—791no—
182#464—791no—
183#463—791no—
184#452—791no—
185#449—791no—
186#442—791no—
187#441—791no—
188#440—791no—
189#440—791no—
190#432D7911yescharacteristic, complemented
191C2×#41—791no—
192C2×Q16—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×D8—791no—
196#126—1581no—
197#125—791no—
198#124—791no—
199#123—1581no—
200C22⋊Q8—791no—
201#121—791no—
202C4×Q8—791no—
203C4×Q8—791no—
204C4×Q8—791no—
205C4×D4—791no—
206C4×D4—791no—
207C4×D4—791no—
208C4×D4—1581no—
209C4×D4—1581no—
210C4×D4—1581no—
211#117—791no—
212#117—1581no—
213#117—1581no—
214C2×C42—1581no—
215C2×C42C2×D7911yescharacteristic
216#107—791no—
217#107—791no—
218#106—791no—
219#106—791no—
220C4⋊C8C2×D7911yescharacteristic
221C4⋊C8C2×D7911yescharacteristic
222#103—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#102—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230C22⋊C8C2×D7911yescharacteristic
231C22⋊C8C2×D7911yescharacteristic
232#97C2×D7911yescharacteristic
233#97C2×D7911yescharacteristic
234#41—1582no—
235#41—1582no—
236C2×Q8—791no—
237C2×Q8—791no—
238C2×D4—791no—
239C2×D4—791no—
240C2×D4—1581no—
241C2×D4—1581no—
242C22×C4—1581no—
243C22×C4—1581no—
244C22×C4—1581no—
245C22×C4—1581no—
246C22×C4D31611yescharacteristic
247C22×C4D31611yescharacteristic
248C22×C4C22×D7911yescharacteristic
249Q16—1582no—
250SD16—1582no—
251SD16—1582no—
252D8—1582no—
253C2×C8C22×D7911yescharacteristic
254C2×C8C22×D7911yescharacteristic
255C2×C8C22×D7911yescharacteristic
256C2×C8C22×D7911yescharacteristic
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C22⋊C4—1581no—
268C22⋊C4—1581no—
269C22⋊C4—1581no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C42—1581no—
276C42—1581no—
277C42—1581no—
278C42—1581no—
279C42D31611yescharacteristic
280C42D31611yescharacteristic
281C42C22×D7911yescharacteristic
282C42C22×D7911yescharacteristic
283C23—1581no—
284C23—1581no—
285C23C2×D31611yescharacteristic
286Q8—792no—
287Q8—1581no—
288Q8—1581no—
289Q8—1581no—
290D4—3162no—
291D4—792no—
292D4—1584no—
293D4—1581no—
294D4—1581no—
295D4—1581no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—3162no—
301C2×C4—3162no—
302C2×C4—3162no—
303C2×C4—1584no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4C2×D31611yescharacteristic
311C2×C4C2×D31611yescharacteristic
312C2×C4C2×D31611yescharacteristic
313C2×C4C2×D31611yescharacteristic
314C2×C4C2×D31611yescharacteristic
315C2×C4C23×D7911yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—3161no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22—3161no—
328C22—1582no—
329C22C22×D31611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—3161no—
336C4—3161no—
337C4—3161no—
338C4—3161no—
339C4—3161no—
340C4—1582no—
341C4#41×D7911yescharacteristic
342C4#41×D7911yescharacteristic
343C2—41no—
344C2—3162no—
345C2—6321no—
346C2#1909907511yescharacteristic
347C2#1909936311yescharacteristic
348C2#1909936311yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#432×C79C2
socleC22×C79C22×D4
prime radical#19098710C2
hypercenter#432D79
hypocenterC79#3111
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #19099097C2semidirect
2. C4×#11929624C2semidirect
3. #19098905C2semidirect
4. #19098888C2semidirect
5. #19098871C2semidirect
6. #19098864C2semidirect
7. #19098786C2semidirect
8. #19098779C2semidirect
9. #19098727C2semidirect
11. #19098676C2semidirect
12. #19098671C2semidirect
13. #19098665C2semidirect
14. #19098665C2semidirect
15. #432×C79C2semidirect
175. C79#3111semidirect
190. #432D79semidirect