Finite Group Databasebeta

← #23774913

Subgroups — #23774913

Order 10112.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579192C211yesmaximal, characteristic, complemented
2C2×SD16×D79C211yesmaximal, characteristic, complemented
3Q8×C22⋊D79C211yesmaximal, characteristic, complemented
4#19099210C211yesmaximal, characteristic
5#19098954C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098803C211yesmaximal, characteristic, complemented
8#19098783C211yesmaximal, characteristic, complemented
9#19098767C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098720C211yesmaximal, characteristic, complemented
12#19098712C211yesmaximal, characteristic, complemented
13#19098666C211yesmaximal, characteristic, complemented
14#19098637C211yesmaximal, characteristic, complemented
15#448×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19#14579192—24no—
20C2×Dic316C2211yescharacteristic, complemented
21C2×#11929614C2211yescharacteristic, complemented
22C2×#11929614C2211yescharacteristic, complemented
23C2×#11929613C2211yescharacteristic
24C2×#11929612C2211yescharacteristic
25C2×#11929611C2211yescharacteristic
26C2×#11929611C2211yescharacteristic
27SD16×D79—24no—
28C2×#11929608C2211yescharacteristic, complemented
29C2×C8×D79C2211yescharacteristic
30#14579159—21no—
31#14579159C2211yescharacteristic, complemented
32#14579148C2211yescharacteristic
33#14579143—21no—
34#14579141C2211yescharacteristic
35#14579140—21no—
36#14579140C2211yescharacteristic, complemented
37#14579137—21no—
38#14579137C2211yescharacteristic
39#14579132—21no—
40#14579129—21no—
41Q8×Dic79C2211yescharacteristic, complemented
42#14579123C2211yescharacteristic
43C4×C22⋊D79—21no—
44C4×C22⋊D79C2211yescharacteristic
45C22⋊C4×D79—21no—
46#14579094C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579084C2211yescharacteristic, complemented
50#14579083C2211yescharacteristic
51#14579082C2211yescharacteristic
52(C2×D79)⋊C8C2211yescharacteristic
53#14579071C2211yescharacteristic, complemented
54C22×Q8×C79C2211yescharacteristic, complemented
55C2×SD16×C79C2211yescharacteristic
56C2×SD16×C79C2211yescharacteristic
57#121×C79C2211yescharacteristic
58#103×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60C22⋊C8×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62#11929624—22no—
63#11929624—41no—
64C2×Dic158—21no—
65C2×Dic158C2311yescharacteristic
66C2×Dic158C2311yescharacteristic
67Q8×D79—22no—
68Q8×D79—41no—
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79D411yescharacteristic
73D4×D79—22no—
74D4×D79—41no—
75C2×C4×D79—21no—
76C2×C4×D79—21no—
77C2×C4×D79—21no—
78C2×C4×D79C2311yescharacteristic
79Dic316—41no—
80#11929614—22no—
81#11929614—22no—
82#11929613—22no—
83#11929612—22no—
84#11929611—22no—
85#11929611D414yescomplemented
86#11929608—22no—
87C2×C79⋊C8C2311yescharacteristic
88C2×C79⋊C8C2311yescharacteristic
89C8×D79—22no—
90C4⋊Dic79—21no—
91C4⋊Dic79—21no—
92C4⋊Dic79C2311yescharacteristic
93Dic79⋊C4—21no—
94Dic79⋊C4—21no—
95Dic79⋊C4—21no—
96Dic79⋊C4—21no—
97Dic79⋊C4D411yescharacteristic
98C22⋊Dic79—21no—
99C22⋊Dic79—21no—
100C22⋊Dic79—21no—
101C22⋊Dic79D411yescharacteristic
102(C2×D79)⋊C4—21no—
103(C2×D79)⋊C4—21no—
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4D411yescharacteristic
106C4×Dic79—21no—
107C4×Dic79C2311yescharacteristic
108C2×Q8×C79—21no—
109C2×Q8×C79—22no—
110C2×Q8×C79—41no—
111C2×Q8×C79C2311yescharacteristic
112C2×Q8×C79C2311yescharacteristic
113C2×D4×C79—21no—
114C2×D4×C79C2311yescharacteristic
115C22×C4×C79—21no—
116C22×C4×C79C2311yescharacteristic
117SD16×C79—22no—
118SD16×C79—41no—
119C2×C8×C79C2311yescharacteristic
120C2×C8×C79C2311yescharacteristic
121C4⋊C4×C79C2311yescharacteristic
122C22⋊C4×C79—21no—
123C23×C79—21no—
124C23×C79C2×D411yescharacteristic
125C22×D79—21no—
126C22×D79—42no—
127C22×D79—42no—
128C22×D79—81no—
129C22×D79C2×D411yescharacteristic
130Q8×C79—21no—
131Q8×C79—21no—
132Q8×C79—21no—
133Q8×C79—42no—
134Q8×C79C2×D412yes—
135D4×C79—21no—
136D4×C79—21no—
137D4×C79—81no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—42no—
144C2×C4×C79C2×D411yescharacteristic
145C2×C4×C79C2411yescharacteristic
146C22⋊D79—22no—
147C22⋊D79—42no—
148C22⋊D79—42no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79C2×D411yescharacteristic
153C2×Dic79C2×D411yescharacteristic
154C2×Dic79C2×D411yescharacteristic
155D316—21no—
156D316C2×D412yes—
157C4×D79—21no—
158C4×D79—21no—
159C4×D79—42no—
160C4×D79—42no—
161C4×D79—81no—
162Dic158—21no—
163Dic158—21no—
164Dic158—21no—
165Dic158—21no—
166Dic158—42no—
167C8×C79—21no—
168C8×C79—21no—
169C79⋊C8—21no—
170C79⋊C8C2×D412yes—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79—21no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79C22×D411yescharacteristic
178C2×D79—21no—
179C2×D79—21no—
180C2×D79—22no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—84no—
184C2×D79#13712yescomplemented
185C4×C79—21no—
186C4×C79—22no—
187C4×C79—41no—
188C4×C79—41no—
189C4×C79C22×D411yescharacteristic
190C4×C79H(5,𝔽2)11yescharacteristic
191Dic79—21no—
192Dic79—21no—
193Dic79—21no—
194Dic79—41no—
195Dic79—41no—
196Dic79—41no—
197C2×C79—41no—
198C2×C79—81no—
199C2×C79D4211yescharacteristic
200C2×C79C2×#13711yescharacteristic
201C2×C79#57711yescharacteristic
202D79—22no—
203D79—42no—
204#3266—791nomaximal, Sylow
205C79#326611yescharacteristic, complemented, Sylow
206C2×#137—791no—
207C22×SD16—791no—
208D4×Q8—791no—
209#546—791no—
210#497—791no—
211#468—791no—
212#467—791no—
213#464—791no—
214#461—791no—
215#452—791no—
216#451—791no—
217#450—791no—
218#448D7911yescharacteristic, complemented
219#440—791no—
220#435—791no—
221C2×#41—791no—
222C22×Q8—791no—
223C22×Q8C2×D7911yescharacteristic, complemented
224C22×D4—791no—
225#137—1584no—
226C2×Q16—791no—
227C2×Q16—791no—
228C2×Q16—791no—
229C2×SD16—791no—
230C2×SD16—791no—
231C2×SD16—791no—
232C2×SD16—791no—
233C2×SD16—1584no—
234C2×SD16C2×D7911yescharacteristic
235C2×SD16C2×D7911yescharacteristic
236C2×M16—791no—
237C22×C8—791no—
238C4⋊Q8—791no—
239C4⋊Q8—1581no—
240#124—791no—
241#123—1581no—
242C22⋊Q8—791no—
243C22⋊Q8—791no—
244C22⋊Q8—791no—
245C22⋊Q8—1581no—
246C22⋊Q8—1581no—
247#121—1581no—
248#121C2×D7911yescharacteristic
249#120—1581no—
250C4×Q8—791no—
251C4×D4—791no—
252C4×D4—791no—
253C4×D4—1581no—
254C2×C22⋊C4—1581no—
255#107—791no—
256C4⋊C8—791no—
257#103—791no—
258#103—791no—
259#103C2×D7911yescharacteristic, complemented
260#103C2×D7911yescharacteristic, complemented
261#102—791no—
262#102—791no—
263C22⋊C8—791no—
264C22⋊C8C2×D7911yescharacteristic, complemented
265#97—791no—
266C24—1581no—
267#41—3161no—
268#41—1582no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—3161no—
273C2×Q8—791no—
274C2×Q8—791no—
275C2×Q8—1581no—
276C2×Q8—1582no—
277C2×Q8C22×D7911yescharacteristic
278C2×Q8C22×D7911yescharacteristic
279C2×D4—21no—
280C2×D4—3161no—
281C2×D4—791no—
282C2×D4—791no—
283C2×D4—1581no—
284C2×D4—1582no—
285C2×D4—1581no—
286C2×D4C22×D7911yescharacteristic
287C22×C4—21no—
288C22×C4—791no—
289C22×C4—1581no—
290C22×C4—1581no—
291C22×C4—1581no—
292C22×C4C22×D7911yescharacteristic
293Q16—3161no—
294Q16—1582no—
295Q16—1582no—
296SD16—22no—
297SD16—41no—
298SD16—794no—
299SD16—1582no—
300SD16—1582no—
301SD16—1582no—
302M16—1582no—
303C2×C8—791no—
304C2×C8—791no—
305C2×C8—1582no—
306C2×C8C22×D7911yescharacteristic
307C2×C8C22×D7911yescharacteristic
308C4⋊C4—791no—
309C4⋊C4—791no—
310C4⋊C4—1581no—
311C4⋊C4—1581no—
312C4⋊C4—1581no—
313C4⋊C4—1581no—
314C4⋊C4—1581no—
315C4⋊C4—1581no—
316C4⋊C4C22×D7911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—791no—
319C22⋊C4—791no—
320C22⋊C4—1581no—
321C22⋊C4—1581no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C42—791no—
327C42—1581no—
328C23—21no—
329C23—3162no—
330C23—3162no—
331C23—791no—
332C23—6321no—
333C23—1581no—
334C23D4×D7911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—3162no—
340Q8—1581no—
341Q8—1581no—
342Q8—1581no—
343Q8—1581no—
344Q8D4×D7912yes—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—3162no—
349D4—3162no—
350D4—792no—
351D4—1582no—
352D4—1581no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—3162no—
360C2×C4—3162no—
361C2×C4—791no—
362C2×C4—791no—
363C2×C4—791no—
364C2×C4—6321no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4—1581no—
368C2×C4—1581no—
369C2×C4—1581no—
370C2×C4D4×D7911yescharacteristic
371C2×C4C23×D7911yescharacteristic
372C8—21no—
373C8—21no—
374C8—792no—
375C8—1581no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—3161no—
383C22—3161no—
384C22—792no—
385C22—6324no—
386C22—1582no—
387C22—1581no—
388C22—1581no—
389C22C2×D4×D7911yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—3161no—
395C4—3161no—
396C4—3161no—
397C4—1581no—
398C4—1581no—
399C4—1581no—
400C4C2×D4×D7911yescharacteristic
401C4#1457920611yescharacteristic
402C2—41no—
403C2—81no—
404C2—3162no—
405C2—1582no—
406C2#1909919511yescharacteristic
407C2#137×D7911yescharacteristic
408C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#448×C79C2
socleC22×C79C22×D4
prime radical#19099210C2
hypercenter#448D79
hypocenterC79#3266
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#14579192C2semidirect
2. C2×SD16×D79C2semidirect
3. Q8×C22⋊D79C2semidirect
5. #19098954C2semidirect
6. #19098807C2semidirect
7. #19098803C2semidirect
8. #19098783C2semidirect
9. #19098767C2semidirect
10. #19098727C2semidirect
11. #19098720C2semidirect
12. #19098712C2semidirect
13. #19098666C2semidirect
14. #19098637C2semidirect
15. #448×C79C2semidirect
20. C2×Dic316C22semidirect
21. C2×#11929614C22semidirect
22. C2×#11929614C22semidirect
28. C2×#11929608C22semidirect
31. #14579159C22semidirect
36. #14579140C22semidirect
41. Q8×Dic79C22semidirect
46. #14579094C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579086C22semidirect
49. #14579084C22semidirect
53. #14579071C22semidirect
54. C22×Q8×C79C22semidirect
58. #103×C79C22semidirect
59. #103×C79C22semidirect
60. C22⋊C8×C79C22semidirect
85. #11929611D4semidirect
184. C2×D79#137semidirect
205. C79#3266semidirect
218. #448D79semidirect
223. C22×Q8C2×D79semidirect
259. #103C2×D79semidirect
260. #103C2×D79semidirect
264. C22⋊C8C2×D79semidirect