Finite Group Databasebeta

← #23774225

Subgroups — #23774225

Order 10112.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099073C211yesmaximal, characteristic
2C22⋊Q8×D79C211yesmaximal, characteristic, complemented
3#19098906C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098900C211yesmaximal, characteristic, complemented
6#19098880C211yesmaximal, characteristic, complemented
7#19098821C211yesmaximal, characteristic, complemented
8#19098819C211yesmaximal, characteristic, complemented
9#19098807C211yesmaximal, characteristic, complemented
10#19098726C211yesmaximal, characteristic, complemented
11#19098722C211yesmaximal, characteristic, complemented
12#19098720C211yesmaximal, characteristic, complemented
13#19098700C211yesmaximal, characteristic, complemented
14#19098526C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C2×Dic316C2211yescharacteristic, complemented
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929612C2211yescharacteristic, complemented
22C2×#11929608C2211yescharacteristic
23#14579143—21no—
24#14579141C2211yescharacteristic
25#14579141C2211yescharacteristic
26#14579140C2211yescharacteristic
27#14579140C2211yescharacteristic
28#14579139—21no—
29#14579138—21no—
30#14579137C2211yescharacteristic
31#14579132C2211yescharacteristic
32#14579129—21no—
33D4×Dic79—21no—
34(C22⋊D79)⋊C4—21no—
35#14579119C2211yescharacteristic
36C4⋊C4×D79—21no—
37C4⋊C4×D79C2211yescharacteristic
38C22⋊C4×D79—21no—
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579084C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C2×SD16×C79C2211yescharacteristic, complemented
53C2×M16×C79C2211yescharacteristic
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79D411yescharacteristic
60#11929623—41no—
61#11929623—41no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65Q8×D79—41no—
66Q8×D79—41no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C22×Dic79—21no—
70C22×Dic79D411yescharacteristic
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—41no—
74C2×C4×D79—41no—
75C2×C4×D79D411yescharacteristic
76C2×C4×D79D411yescharacteristic
77C2×C4×D79C2311yescharacteristic
78C2×C4×D79C2311yescharacteristic
79Dic316—41no—
80#11929614—41no—
81#11929612—41no—
82#11929608—41no—
83C2×C79⋊C8C2311yescharacteristic
84C2×C79⋊C8C2311yescharacteristic
85C4⋊Dic79—21no—
86C4⋊Dic79—21no—
87C4⋊Dic79C2311yescharacteristic
88C4⋊Dic79C2311yescharacteristic
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91Dic79⋊C4—21no—
92Dic79⋊C4—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95C22⋊Dic79—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100C4×Dic79—21no—
101C2×Q8×C79C2311yescharacteristic
102C2×D4×C79—21no—
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105SD16×C79—41no—
106M16×C79—41no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C4⋊C4×C79—21no—
110C4⋊C4×C79C2311yescharacteristic
111C4⋊C4×C79C2311yescharacteristic
112C22⋊C4×C79—21no—
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79C2×D411yescharacteristic
116C22×D79—22no—
117C22×D79—41no—
118C22×D79—41no—
119C22×D79C2×D411yescharacteristic
120C22×D79C2×D411yescharacteristic
121Q8×C79—21no—
122Q8×C79—21no—
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—42no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2411yescharacteristic
133C22⋊D79—42no—
134C22⋊D79—42no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—41no—
140C2×Dic79—42no—
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—41no—
148C4×D79—41no—
149C4×D79—42no—
150C4×D79—42no—
151Dic158—21no—
152Dic158—21no—
153Dic158—21no—
154Dic158—21no—
155Dic158—42no—
156C8×C79—21no—
157C8×C79—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79C22×D411yescharacteristic
167C2×D79—21no—
168C2×D79—21no—
169C2×D79—21no—
170C2×D79—21no—
171C2×D79—21no—
172C2×D79—44no—
173C2×D79#13712yes—
174C4×C79—21no—
175C4×C79—41no—
176C4×C79—41no—
177C4×C79—41no—
178C4×C79H(5,𝔽2)11yescharacteristic
179C4×C79H(5,𝔽2)11yescharacteristic
180Dic79—21no—
181Dic79—21no—
182Dic79—41no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186C2×C79—41no—
187C2×C79—81no—
188C2×C79#53411yescharacteristic
189C2×C79C2×#13711yescharacteristic
190C2×C79#57511yescharacteristic
191D79—22no—
192D79—41no—
193#3196—791nomaximal, Sylow
194C79#319611yescharacteristic, complemented, Sylow
195#525—791no—
196C2×C22⋊Q8—791no—
197#485—791no—
198#485—791no—
199#484—791no—
200#481—791no—
201#470—791no—
202#470—791no—
203#468—791no—
204#468D7911yescharacteristic, complemented
205#452—791no—
206#452—791no—
207#451—791no—
208#448—791no—
209#407—791no—
210C2×#41—791no—
211C22×Q8—791no—
212C23×C4—791no—
213C2×Q16—791no—
214C2×Q16—791no—
215C2×SD16—791no—
216C2×SD16C2×D7911yescharacteristic, complemented
217C2×M16—791no—
218C2×M16C2×D7911yescharacteristic
219#123—1581no—
220C22⋊Q8—791no—
221C22⋊Q8—791no—
222C22⋊Q8—791no—
223C22⋊Q8—791no—
224C22⋊Q8—791no—
225C22⋊Q8—1581no—
226C22⋊Q8—1581no—
227C22⋊Q8C2×D7911yescharacteristic
228#121—791no—
229#121C2×D7911yescharacteristic
230#120—1581no—
231C4×D4—1581no—
232C4×D4—1581no—
233#117—791no—
234C2×C4⋊C4—791no—
235C2×C4⋊C4—1581no—
236C2×C22⋊C4—1581no—
237#107—791no—
238#107C2×D7911yescharacteristic, complemented
239#106—791no—
240#106—791no—
241#103—791no—
242#103—791no—
243#103—791no—
244#103—791no—
245#103—791no—
246#103C2×D7911yescharacteristic, complemented
247#102—791no—
248#102C2×D7911yescharacteristic, complemented
249C22⋊C8—791no—
250C22⋊C8—791no—
251C22⋊C8—791no—
252C22⋊C8—791no—
253C24—791no—
254#41—3161no—
255#41—3161no—
256C2×Q8—3161no—
257C2×Q8—3161no—
258C2×Q8—791no—
259C2×Q8—791no—
260C2×Q8—1581no—
261C2×Q8C22×D7911yescharacteristic
262C2×D4—21no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22×D7911yescharacteristic
266C22×C4—3161no—
267C22×C4—3161no—
268C22×C4—791no—
269C22×C4—791no—
270C22×C4—791no—
271C22×C4—791no—
272C22×C4—791no—
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277Q16—3161no—
278Q16—3161no—
279SD16—41no—
280SD16—3161no—
281M16—41no—
282M16—3161no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8C22×D7911yescharacteristic
286C2×C8C22×D7911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4—1581no—
296C4⋊C4C22×D7911yescharacteristic
297C4⋊C4C22×D7911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C42—1581no—
308C23—21no—
309C23—3161no—
310C23—3161no—
311C23—791no—
312C23—791no—
313C23—1582no—
314C23D4×D7911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3162no—
318Q8—1581no—
319Q8—1581no—
320Q8—1581no—
321Q8—1581no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—3162no—
326D4—3162no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—3161no—
333C2×C4—3161no—
334C2×C4—3162no—
335C2×C4—3162no—
336C2×C4—3162no—
337C2×C4—3161no—
338C2×C4—791no—
339C2×C4—791no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4D4×D7911yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1581no—
353C8—1581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—3164no—
361C22—792no—
362C22—1581no—
363C22—1581no—
364C22—1581no—
365C22—1581no—
366C22—1581no—
367C22C2×D4×D7911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—3161no—
373C4—3161no—
374C4—3161no—
375C4—3161no—
376C4—1581no—
377C4—1581no—
378C4#1457920611yescharacteristic
379C4#1457920711yescharacteristic
380C2—41no—
381C2—81no—
382C2—3161no—
383C2—1582no—
384C2#1909912111yescharacteristic
385C2#137×D7911yescharacteristic
386C2#1909935911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
prime radical#19099073C2
hypercenter#468D79
hypocenterC79#3196
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D79C2semidirect
3. #19098906C2semidirect
4. #19098902C2semidirect
5. #19098900C2semidirect
6. #19098880C2semidirect
7. #19098821C2semidirect
8. #19098819C2semidirect
9. #19098807C2semidirect
10. #19098726C2semidirect
11. #19098722C2semidirect
12. #19098720C2semidirect
13. #19098700C2semidirect
14. #19098526C2semidirect
15. #468×C79C2semidirect
19. C2×Dic316C22semidirect
20. C2×#11929614C22semidirect
21. C2×#11929612C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. #14579092C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579085C22semidirect
45. #14579084C22semidirect
46. #14579084C22semidirect
47. #14579082C22semidirect
52. C2×SD16×C79C22semidirect
56. #107×C79C22semidirect
57. #103×C79C22semidirect
58. #102×C79C22semidirect
194. C79#3196semidirect
204. #468D79semidirect
216. C2×SD16C2×D79semidirect
238. #107C2×D79semidirect
246. #103C2×D79semidirect
248. #102C2×D79semidirect