Finite Group Databasebeta

← #23769864

Subgroups — #23769864

Order 10112.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579152C211yesmaximal, characteristic, complemented
2C2×#14579139C211yesmaximal, characteristic
3#19098503C211yesmaximal, characteristic, complemented
4#19098503C211yesmaximal, characteristic, complemented
5#19098493C211yesmaximal, characteristic, complemented
6#19098490C211yesmaximal, characteristic
7#19098490C211yesmaximal, characteristic
8#19098484C211yesmaximal, characteristic, complemented
9#19098469C211yesmaximal, characteristic, complemented
10#19098455C211yesmaximal, characteristic
11#19098454C211yesmaximal, characteristic
12#19098448C211yesmaximal, characteristic, complemented
13#19098437C211yesmaximal, characteristic
14#19098420C211yesmaximal, characteristic
15#387×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18#14579152—24no—
19#14579139—24no—
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×C4⋊Dic79C2211yescharacteristic
23C2×C4⋊Dic79C2211yescharacteristic
24C2×C4⋊Dic79C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C42×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C2×Dic158—22no—
55C2×Dic158—22no—
56C2×Dic158—41no—
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C2×C4×D79—22no—
65C2×C4×D79—22no—
66C2×C4×D79—41no—
67C4⋊Dic79—22no—
68C4⋊Dic79—22no—
69C4⋊Dic79—22no—
70C4⋊Dic79—22no—
71C4⋊Dic79—41no—
72Dic79⋊C4—22no—
73Dic79⋊C4—22no—
74Dic79⋊C4—22no—
75Dic79⋊C4—22no—
76(C2×D79)⋊C4—22no—
77(C2×D79)⋊C4—22no—
78(C2×D79)⋊C4—22no—
79(C2×D79)⋊C4—22no—
80(C2×D79)⋊C4—22no—
81(C2×D79)⋊C4—41no—
82C4×Dic79—22no—
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C4⋊C4×C79—41no—
91C4⋊C4×C79D414yes—
92C42×C79—41no—
93C23×C79C2411yescharacteristic
94C22×D79—21no—
95C22×D79—21no—
96C22×D79—21no—
97C22×D79—21no—
98C22×D79—21no—
99C22×D79—21no—
100C22×D79#4112yes—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
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×C79C2×D412yes—
120C2×C4×C79C2×D412yes—
121C2×C4×C79C2×D412yes—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
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#4112yes—
143C4×D79—44no—
144Dic158—44no—
145C22×C79C22×D411yescharacteristic
146C22×C79C2×#4111yescharacteristic
147C22×C79C2×#4111yescharacteristic
148C22×C79H(5,𝔽2)11yescharacteristic
149C22×C792−1+411yescharacteristic
150C22×C792−1+411yescharacteristic
151C22×C792−1+411yescharacteristic
152C2×D79—22no—
153C2×D79—22no—
154C2×D79—22no—
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C4×C79—22no—
160C4×C79—22no—
161C4×C79—22no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166Dic79—22no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173C2×C79#53611yescharacteristic
174C2×C79#53911yescharacteristic
175C2×C79#54111yescharacteristic
176C2×C79#54611yescharacteristic
177C2×C79#54811yescharacteristic
178C2×C79#55211yescharacteristic
179C2×C79#56311yescharacteristic
180D79—42no—
181#2690—791nomaximal, Sylow
182C79#269011yescharacteristic, complemented, Sylow
183C2×#125—791no—
184C2×C22⋊Q8—791no—
185#400—791no—
186#400—791no—
187#398—791no—
188#397—791no—
189#397—791no—
190#395—791no—
191#391—791no—
192#388—791no—
193#388—791no—
194#387—791no—
195#387D7911yescharacteristic, complemented
196#385—791no—
197#380—791no—
198C22×Q8—791no—
199C23×C4—791no—
200#125—1584no—
201C22⋊Q8—1584no—
202C2×C4⋊C4—791no—
203C2×C4⋊C4—791no—
204C2×C4⋊C4—791no—
205C2×C4⋊C4—791no—
206C2×C4⋊C4—791no—
207C2×C4⋊C4—791no—
208C2×C4⋊C4—791no—
209C2×C4⋊C4—791no—
210C2×C4⋊C4—791no—
211C2×C4⋊C4C2×D7911yescharacteristic
212C2×C4⋊C4C2×D7911yescharacteristic
213C2×C22⋊C4—791no—
214C2×C22⋊C4—791no—
215C2×C22⋊C4—791no—
216C2×C22⋊C4—791no—
217C2×C22⋊C4—791no—
218C2×C22⋊C4—791no—
219C2×C42—791no—
220C2×C42C2×D7911yescharacteristic
221#95—791no—
222#95—791no—
223#95—791no—
224#95—791no—
225#95—791no—
226#95—791no—
227#95—791no—
228#95—791no—
229#95—791no—
230#95—791no—
231#95C2×D7911yescharacteristic
232#95C2×D7911yescharacteristic
233#95C2×D7911yescharacteristic
234#95C2×D7911yescharacteristic
235C24—791no—
236C2×Q8—3161no—
237C2×Q8—1582no—
238C2×Q8—1582no—
239C22×C4—3161no—
240C22×C4—791no—
241C22×C4—791no—
242C22×C4—791no—
243C22×C4—791no—
244C22×C4—791no—
245C22×C4—791no—
246C22×C4—791no—
247C22×C4—1582no—
248C22×C4—1582no—
249C22×C4C22×D7911yescharacteristic
250C22×C4C22×D7911yescharacteristic
251C22×C4C22×D7911yescharacteristic
252C22×C4C22×D7911yescharacteristic
253C22×C4C22×D7911yescharacteristic
254C22×C4C22×D7911yescharacteristic
255C22×C4C22×D7911yescharacteristic
256C4⋊C4—41no—
257C4⋊C4—3161no—
258C4⋊C4—1582no—
259C4⋊C4—1582no—
260C4⋊C4—1582no—
261C4⋊C4—1582no—
262C4⋊C4—1582no—
263C4⋊C4—1582no—
264C4⋊C4—1582no—
265C4⋊C4—1582no—
266C4⋊C4D31614yes—
267C22⋊C4—3161no—
268C22⋊C4—1582no—
269C22⋊C4—1582no—
270C22⋊C4—1582no—
271C22⋊C4—1582no—
272C22⋊C4—1582no—
273C42—41no—
274C42—1582no—
275C23—792no—
276C23—1581no—
277C23—1581no—
278C23—1581no—
279C23—1581no—
280C23—1581no—
281C23—1581no—
282C23C23×D7911yescharacteristic
283Q8—3164no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—3164no—
303C2×C4—792no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4C2×D31612yes—
325C2×C4C2×D31612yes—
326C2×C4C2×D31612yes—
327C22—3161no—
328C22—3161no—
329C22—3161no—
330C22—3161no—
331C22—1582no—
332C22—1582no—
333C22—1582no—
334C22C22×D31611yescharacteristic
335C22#41×D7911yescharacteristic
336C22#41×D7911yescharacteristic
337C22#1457920611yescharacteristic
338C22#1457920811yescharacteristic
339C22#1457920811yescharacteristic
340C22#1457920911yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3161no—
349C4—3161no—
350C4—3161no—
351C4—3161no—
352C4—3161no—
353C4—3161no—
354C4—1582no—
355C2—3162no—
356C2#1909913911yescharacteristic
357C2#1909915611yescharacteristic
358C2#1909917211yescharacteristic
359C2#1909920811yescharacteristic
360C2#1909922511yescharacteristic
361C2#1909924911yescharacteristic
362C2#1909931411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#387×C79C2
prime radicalC23×D79C23
hypercenter#387D79
hypocenterC79#2690
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#14579152C2semidirect
3. #19098503C2semidirect
4. #19098503C2semidirect
5. #19098493C2semidirect
8. #19098484C2semidirect
9. #19098469C2semidirect
12. #19098448C2semidirect
15. #387×C79C2semidirect
182. C79#2690semidirect
195. #387D79semidirect