Finite Group Databasebeta

← #23775571

Subgroups — #23775571

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099259C211yesmaximal, characteristic
2#19098931C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098896C211yesmaximal, characteristic, complemented
5#19098870C211yesmaximal, characteristic, complemented
6#19098811C211yesmaximal, characteristic, complemented
7#19098794C211yesmaximal, characteristic, complemented
8#19098765C211yesmaximal, characteristic, complemented
9#19098702C211yesmaximal, characteristic, complemented
10#19098702C211yesmaximal, characteristic, complemented
11#19098661C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098572C211yesmaximal, characteristic, complemented
14C2×#14579085C211yesmaximal, characteristic, complemented
15D4×Q8×C79C211yesmaximal, characteristic, complemented
16C2×#11929611C2211yescharacteristic
17C2×#11929611C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929608C2211yescharacteristic
20C22×C79⋊C8C2211yescharacteristic
21#14579156—21no—
22#14579153C2211yescharacteristic
23#14579143—21no—
24#14579135C2211yescharacteristic
25#14579135C2211yescharacteristic
26#14579133—21no—
27C4×D316C2211yescharacteristic
28(C22⋊D79)⋊C4—21no—
29#14579120C2211yescharacteristic
30C2×C4⋊Dic79C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579085C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579085C2211yescharacteristic
43#14579085C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C22×Q8×C79C2211yescharacteristic
49C22×Q8×C79C2211yescharacteristic
50C4⋊Q8×C79—21no—
51C4⋊Q8×C79C2211yescharacteristic
52C22⋊Q8×C79—21no—
53C22⋊Q8×C79—21no—
54C22⋊Q8×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79—21no—
58C4×D4×C79C2211yescharacteristic
59C2×D316C2311yescharacteristic
60C2×C22⋊D79—21no—
61C2×C22⋊D79—21no—
62C22×Dic79—21no—
63C2×C4×D79—21no—
64#11929611—22no—
65#11929611—41no—
66#11929611—41no—
67#11929608—41no—
68C2×C79⋊C8—41no—
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C4⋊Dic79—21no—
74C4⋊Dic79C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80(C2×D79)⋊C4—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83C4×Dic79—21no—
84C2×Q8×C79—21no—
85C2×Q8×C79—21no—
86C2×Q8×C79—22no—
87C2×Q8×C79—22no—
88C2×Q8×C79—41no—
89C2×Q8×C79—41no—
90C2×Q8×C79C2311yescharacteristic
91C2×Q8×C79C2311yescharacteristic
92C2×Q8×C79C2311yescharacteristic
93C2×D4×C79D411yescharacteristic
94C22×C4×C79—21no—
95C22×C4×C79—21no—
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C4⋊C4×C79—21no—
99C4⋊C4×C79—21no—
100C4⋊C4×C79—21no—
101C4⋊C4×C79—21no—
102C4⋊C4×C79—21no—
103C4⋊C4×C79D411yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—21no—
118Q8×C79—21no—
119Q8×C79—42no—
120Q8×C79—42no—
121Q8×C79#4112yes—
122D4×C79—22no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—42no—
132C2×C4×C79—42no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2411yescharacteristic
138C22⋊D79—42no—
139C22⋊D79—81no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—81no—
144D316—21no—
145D316—21no—
146C4×D79—81no—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79#13712yes—
157C22×C79C22×D411yescharacteristic
158C2×D79—41no—
159C2×D79—41no—
160C2×D79—41no—
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—22no—
164C4×C79—21no—
165C4×C79—21no—
166C4×C79—41no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79C2×#4111yescharacteristic
170C4×C79H(5,𝔽2)11yescharacteristic
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—22no—
175C2×C79—41no—
176C2×C79#54611yescharacteristic
177C2×C79C2×#13711yescharacteristic
178C2×C79#57711yescharacteristic
179D79—81no—
180#3320—791nomaximal, Sylow
181C79#332011yescharacteristic, complemented, Sylow
182#553—791no—
183D4×Q8D7911yescharacteristic, complemented
184#491—791no—
185#485—791no—
186#484—791no—
187#479—791no—
188#468—791no—
189#465—791no—
190#461—791no—
191#448—791no—
192#448—791no—
193#440—791no—
194#435—791no—
195#419—791no—
196C2×#103—791no—
197C22×Q8C2×D7911yescharacteristic
198C22×Q8C2×D7911yescharacteristic
199C2×SD16—791no—
200C2×SD16—791no—
201C2×SD16—791no—
202C2×M16—791no—
203C22×C8—791no—
204C4⋊Q8—21no—
205C4⋊Q8C2×D7911yescharacteristic
206#126—1581no—
207#125—791no—
208#123—1581no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D7911yescharacteristic
212C22⋊Q8C2×D7911yescharacteristic
213#121—791no—
214#121—791no—
215#121—1581no—
216C4×Q8C2×D7911yescharacteristic
217C4×D4—21no—
218C4×D4—791no—
219C4×D4—1581no—
220C4×D4C2×D7911yescharacteristic
221#117—791no—
222C2×C4⋊C4—791no—
223#107—791no—
224#107—791no—
225#106—791no—
226C4⋊C8—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#102—791no—
237C22⋊C8—791no—
238C22⋊C8—791no—
239#97—791no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C22×D7911yescharacteristic
247C2×Q8C22×D7911yescharacteristic
248C2×Q8C22×D7911yescharacteristic
249C2×D4—791no—
250C2×D4—1581no—
251C2×D4—1581no—
252C2×D4C22⋊D7911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258C22×C4C22×D7911yescharacteristic
259SD16—3161no—
260SD16—3161no—
261SD16—1582no—
262M16—3161no—
263C2×C8—3161no—
264C2×C8—791no—
265C2×C8—791no—
266C2×C8—791no—
267C2×C8—791no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4C22⋊D7911yescharacteristic
280C4⋊C4C22×D7911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4C22⋊D7911yescharacteristic
288C22⋊C4C22⋊D7911yescharacteristic
289C42—21no—
290C42—1581no—
291C42C22×D7911yescharacteristic
292C23—1581no—
293C23C2×C22⋊D7911yescharacteristic
294C23C2×C22⋊D7911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8#1192962312yes—
303D4—22no—
304D4—3162no—
305D4—6321no—
306D4—1581no—
307D4—1581no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—6321no—
319C2×C4—6321no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4C2×C22⋊D7911yescharacteristic
324C2×C4C2×C22⋊D7911yescharacteristic
325C2×C4C2×C22⋊D7911yescharacteristic
326C2×C4C2×C22⋊D7911yescharacteristic
327C2×C4C23×D7911yescharacteristic
328C8—1581no—
329C8—1581no—
330C8—1581no—
331C8—1581no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—3161no—
338C22—3161no—
339C22—3161no—
340C22#1457919212yes—
341C22C22×C22⋊D7911yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—3161no—
351C4—3161no—
352C4—3161no—
353C4C2×#1192962311yescharacteristic
354C4#1457920611yescharacteristic
355C2—22no—
356C2—41no—
357C2—6321no—
358C2#1909920711yescharacteristic
359C2C2×#1457919211yescharacteristic
360C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingD4×Q8×C79C2
socleC22×C79C22×D4
prime radical#19099259C2
hypercenterD4×Q8D79
hypocenterC79#3320
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #19098931C2semidirect
3. #19098901C2semidirect
4. #19098896C2semidirect
5. #19098870C2semidirect
6. #19098811C2semidirect
7. #19098794C2semidirect
8. #19098765C2semidirect
9. #19098702C2semidirect
10. #19098702C2semidirect
11. #19098661C2semidirect
12. #19098635C2semidirect
13. #19098572C2semidirect
14. C2×#14579085C2semidirect
15. D4×Q8×C79C2semidirect
181. C79#3320semidirect
183. D4×Q8D79semidirect