Finite Group Databasebeta

← #23774228

Subgroups — #23774228

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#19099070C211yesmaximal, characteristic
2C22⋊Q8×D79C211yesmaximal, characteristic, complemented
3#19098905C211yesmaximal, characteristic, complemented
4#19098901C211yesmaximal, characteristic, complemented
5#19098897C211yesmaximal, characteristic, complemented
6#19098880C211yesmaximal, characteristic, complemented
7#19098820C211yesmaximal, characteristic, complemented
8#19098818C211yesmaximal, characteristic, complemented
9#19098808C211yesmaximal, characteristic, complemented
10#19098806C211yesmaximal, characteristic, complemented
11#19098725C211yesmaximal, characteristic, complemented
12#19098717C211yesmaximal, characteristic, complemented
13#19098700C211yesmaximal, characteristic, complemented
14#19098525C211yesmaximal, characteristic, complemented
15#452×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929612C2211yescharacteristic, complemented
20C2×#11929607C2211yescharacteristic
21C2×#11929607C2211yescharacteristic
22#14579142—21no—
23#14579141C2211yescharacteristic
24#14579140C2211yescharacteristic
25#14579139—21no—
26#14579138—21no—
27#14579137C2211yescharacteristic
28#14579137C2211yescharacteristic
29#14579137C2211yescharacteristic
30#14579132C2211yescharacteristic
31#14579132C2211yescharacteristic
32#14579129—21no—
33C4×C22⋊D79—21no—
34C4×C22⋊D79—21no—
35#14579120C2211yescharacteristic
36C4⋊C4×D79—21no—
37C4⋊C4×D79C2211yescharacteristic
38C22⋊C4×D79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579085C2211yescharacteristic, complemented
46#14579085C2211yescharacteristic, complemented
47#14579085C2211yescharacteristic, complemented
48#14579082C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×Q16×C79C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic, complemented
55C22⋊Q8×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79D411yescharacteristic
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62Q8×D79—41no—
63Q8×D79—41no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C22×Dic79D411yescharacteristic
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—41no—
70C2×C4×D79—41no—
71C2×C4×D79D411yescharacteristic
72C2×C4×D79D411yescharacteristic
73C2×C4×D79C2311yescharacteristic
74C2×C4×D79C2311yescharacteristic
75#11929614—41no—
76#11929612—41no—
77#11929607—41no—
78#11929607—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98C4×Dic79—21no—
99#41×C79—41no—
100#41×C79—41no—
101C2×Q8×C79C2311yescharacteristic
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C22×C4×C79—21no—
106C22×C4×C79C2311yescharacteristic
107Q16×C79—41no—
108SD16×C79—41no—
109C2×C8×C79C2311yescharacteristic
110C2×C8×C79C2311yescharacteristic
111C4⋊C4×C79—21no—
112C4⋊C4×C79C2311yescharacteristic
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—
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—42no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—42no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2411yescharacteristic
136C22⋊D79—42no—
137C22⋊D79—42no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—41no—
143C2×Dic79C2×D411yescharacteristic
144C2×Dic79C2×D411yescharacteristic
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—41no—
150C4×D79—41no—
151C4×D79—42no—
152C4×D79—42no—
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#468—791no—
205#452—791no—
206#452D7911yescharacteristic, complemented
207#451—791no—
208#448—791no—
209#407—791no—
210C2×#41C2×D7911yescharacteristic
211C22×Q8—791no—
212C23×C4—791no—
213C2×Q16—791no—
214C2×Q16C2×D7911yescharacteristic, complemented
215C2×SD16—791no—
216C2×SD16C2×D7911yescharacteristic, complemented
217C2×M16—791no—
218C2×M16—791no—
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#121—791no—
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#107—791no—
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⋊C8C2×D7911yescharacteristic
253C24—791no—
254#41—41no—
255#41—41no—
256C2×Q8—3161no—
257C2×Q8—3161no—
258C2×Q8—791no—
259C2×Q8—1581no—
260C2×Q8C22×D7911yescharacteristic
261C2×Q8C22×D7911yescharacteristic
262C2×D4—21no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22×D7911yescharacteristic
266C22×C4—21no—
267C22×C4—3161no—
268C22×C4—3161no—
269C22×C4—791no—
270C22×C4—791no—
271C22×C4—791no—
272C22×C4—791no—
273C22×C4—791no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277Q16—41no—
278Q16—3161no—
279SD16—41no—
280SD16—3161no—
281M16—3161no—
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—791no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4—1581no—
296C4⋊C4—1581no—
297C4⋊C4C22×D7911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—1581no—
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—21no—
318Q8—21no—
319Q8—3162no—
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—42no—
333C2×C4—3161no—
334C2×C4—3161no—
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#1457920611yescharacteristic
380C2—41no—
381C2—81no—
382C2—3161no—
383C2—1582no—
384C2#1909912311yescharacteristic
385C2#137×D7911yescharacteristic
386C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#452×C79C2
socleC22×C79C22×D4
prime radical#19099070C2
hypercenter#452D79
hypocenterC79#3196
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D79C2semidirect
3. #19098905C2semidirect
4. #19098901C2semidirect
5. #19098897C2semidirect
6. #19098880C2semidirect
7. #19098820C2semidirect
8. #19098818C2semidirect
9. #19098808C2semidirect
10. #19098806C2semidirect
11. #19098725C2semidirect
12. #19098717C2semidirect
13. #19098700C2semidirect
14. #19098525C2semidirect
15. #452×C79C2semidirect
18. C2×#11929614C22semidirect
19. C2×#11929612C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579093C22semidirect
42. #14579092C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
45. #14579085C22semidirect
46. #14579085C22semidirect
47. #14579085C22semidirect
48. #14579082C22semidirect
53. C2×Q16×C79C22semidirect
54. C2×SD16×C79C22semidirect
56. #103×C79C22semidirect
57. #102×C79C22semidirect
194. C79#3196semidirect
206. #452D79semidirect
214. C2×Q16C2×D79semidirect
216. C2×SD16C2×D79semidirect
246. #103C2×D79semidirect
248. #102C2×D79semidirect