Finite Group Databasebeta

← #23775269

Subgroups — #23775269

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099271C211yesmaximal, characteristic
2Q8×C22⋊D79C211yesmaximal, characteristic
3#19098912C211yesmaximal, characteristic, complemented
4#19098899C211yesmaximal, characteristic, complemented
5#19098897C211yesmaximal, characteristic, complemented
6#19098856C211yesmaximal, characteristic, complemented
7#19098802C211yesmaximal, characteristic, complemented
8#19098801C211yesmaximal, characteristic, complemented
9#19098771C211yesmaximal, characteristic, complemented
10#19098717C211yesmaximal, characteristic, complemented
11Q16×Dic79C211yesmaximal, characteristic, complemented
12(C22⋊D79)⋊C8C211yesmaximal, characteristic
13C2×#14579085C211yesmaximal, characteristic, complemented
14#103×D79C211yesmaximal, characteristic, complemented
15#451×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C22×C79⋊C8C2211yescharacteristic
19C2×C8×D79C2211yescharacteristic
20#14579160C2211yescharacteristic
21#14579159—21no—
22#14579159C2211yescharacteristic
23#14579151—21no—
24#14579141—21no—
25#14579140—21no—
26#14579140C2211yescharacteristic
27#14579138—21no—
28#14579137—21no—
29#14579137C2211yescharacteristic
30#14579137C2211yescharacteristic
31Q8×Dic79C2211yescharacteristic
32Q8×Dic79C2211yescharacteristic
33C4×C22⋊D79—21no—
34C4×C22⋊D79C2211yescharacteristic
35(C22⋊D79)⋊C4—21no—
36C2×C4⋊Dic79C2211yescharacteristic
37C4⋊C4×D79C2211yescharacteristic
38#14579095C2211yescharacteristic
39#14579095C2211yescharacteristic
40#14579094C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579085C2211yescharacteristic
48#14579085C2211yescharacteristic
49#14579084C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C22×Q8×C79C2211yescharacteristic
53C2×Q16×C79C2211yescharacteristic
54C2×Q16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62Q8×D79—22no—
63Q8×D79—41no—
64C2×C22⋊D79D411yescharacteristic
65C22×Dic79—21no—
66C2×C4×D79—21no—
67C2×C4×D79—21no—
68C2×C4×D79C2311yescharacteristic
69#11929614—41no—
70C2×C79⋊C8—41no—
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C8×D79—41no—
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4D411yescharacteristic
88C22⋊Dic79—21no—
89C22⋊Dic79D411yescharacteristic
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4D411yescharacteristic
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96C2×Q8×C79—21no—
97C2×Q8×C79—22no—
98C2×Q8×C79—41no—
99C2×Q8×C79C2311yescharacteristic
100C2×Q8×C79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104Q16×C79—22no—
105Q16×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C23×C79C2×D411yescharacteristic
112C22×D79C2×D411yescharacteristic
113Q8×C79—21no—
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—21no—
118Q8×C79—42no—
119Q8×C79#4112yes—
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×C79C2411yescharacteristic
129C22⋊D79Q1614yescomplemented
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—81no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C4×D79—21no—
139C4×D79—21no—
140C4×D79—42no—
141C4×D79—81no—
142Dic158—21no—
143Dic158—21no—
144Dic158—42no—
145Dic158—81no—
146C8×C79—21no—
147C8×C79—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C79C2×Q1612yes—
153C22×C79C22×D411yescharacteristic
154C2×D79—21no—
155C2×D79—21no—
156C2×D79C2×Q1612yes—
157C4×C79—21no—
158C4×C79—22no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79C2×#4111yescharacteristic
163C4×C79H(5,𝔽2)11yescharacteristic
164Dic79—21no—
165Dic79—21no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79C2×Q1612yes—
171C2×C79—22no—
172C2×C79#54611yescharacteristic
173C2×C79C22×Q1611yescharacteristic
174C2×C79#57711yescharacteristic
175D79—22no—
176#3299—791nomaximal, Sylow
177C79#329911yescharacteristic, complemented, Sylow
178#554—791no—
179D4×Q8—791no—
180#487—791no—
181#484—791no—
182#484—791no—
183#477—791no—
184#467—791no—
185#467—791no—
186#462—791no—
187#451—791no—
188#451D7911yescharacteristic, complemented
189C4×Q16—791no—
190C8×D4—791no—
191C2×#103—791no—
192C2×#103—791no—
193C22×Q8—791no—
194C22×Q8C2×D7911yescharacteristic
195C2×Q16—791no—
196C2×Q16C2×D7911yescharacteristic
197C2×Q16C2×D7911yescharacteristic
198C22×C8—791no—
199C22×C8—791no—
200C4⋊Q8—791no—
201C4⋊Q8—791no—
202C4⋊Q8—1581no—
203#125—1581no—
204C22⋊Q8—791no—
205C22⋊Q8—791no—
206C22⋊Q8—791no—
207C22⋊Q8—1581no—
208C22⋊Q8—1581no—
209C22⋊Q8—1581no—
210C22⋊Q8—1581no—
211C22⋊Q8C2×D7911yescharacteristic
212C4×Q8—791no—
213C4×Q8—791no—
214C4×D4—791no—
215C4×D4—1581no—
216C4×D4—1581no—
217C2×C4⋊C4—791no—
218C2×C4⋊C4—791no—
219#107—791no—
220#107—791no—
221#107—791no—
222C4⋊C8—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103C2×D7911yescharacteristic
232#103C2×D7911yescharacteristic
233C22⋊C8—791no—
234C22⋊C8C2×D7911yescharacteristic
235C4×C8—791no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—3161no—
240C2×Q8—791no—
241C2×Q8—1581no—
242C2×Q8—1581no—
243C2×Q8—1582no—
244C2×Q8C22×D7911yescharacteristic
245C2×Q8C22×D7911yescharacteristic
246C2×Q8C22×D7911yescharacteristic
247C2×D4—791no—
248C22×C4—21no—
249C22×C4—791no—
250C22×C4—1581no—
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4C22×D7911yescharacteristic
254Q16—22no—
255Q16—41no—
256Q16—3161no—
257C2×C8—3161no—
258C2×C8—3161no—
259C2×C8—791no—
260C2×C8—791no—
261C2×C8C22×D7911yescharacteristic
262C2×C8C22×D7911yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—791no—
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4C22×D7911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—791no—
281C22⋊C4—791no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C42—791no—
286C42—1581no—
287C42—1581no—
288C23—791no—
289C23D4×D7911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—3162no—
297Q8—6321no—
298Q8—1581no—
299Q8—1581no—
300Q8#1192962312yes—
301D4—794no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—3162no—
310C2×C4—791no—
311C2×C4—791no—
312C2×C4—791no—
313C2×C4—6321no—
314C2×C4—6321no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4D4×D7911yescharacteristic
322C2×C4C23×D7911yescharacteristic
323C8—21no—
324C8—21no—
325C8—1581no—
326C8—1581no—
327C22—21no—
328C22—21no—
329C22—792no—
330C22—1581no—
331C22—1581no—
332C22Q16×D7912yes—
333C22C2×D4×D7911yescharacteristic
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—3161no—
340C4—3161no—
341C4—3161no—
342C4—3161no—
343C4—792no—
344C4—1581no—
345C4—1581no—
346C4C2×#1192962311yescharacteristic
347C4#1457920611yescharacteristic
348C2—22no—
349C2—1582no—
350C2#1909920011yescharacteristic
351C2C2×Q16×D7911yescharacteristic
352C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#451×C79C2
socleC22×C79C22×D4
prime radicalC2×C22⋊D79D4
hypercenter#451D79
hypocenterC79#3299
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #19098912C2semidirect
4. #19098899C2semidirect
5. #19098897C2semidirect
6. #19098856C2semidirect
7. #19098802C2semidirect
8. #19098801C2semidirect
9. #19098771C2semidirect
10. #19098717C2semidirect
11. Q16×Dic79C2semidirect
13. C2×#14579085C2semidirect
14. #103×D79C2semidirect
15. #451×C79C2semidirect
129. C22⋊D79Q16semidirect
177. C79#3299semidirect
188. #451D79semidirect