Finite Group Databasebeta

← #23775089

Subgroups — #23775089

Order 10112.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11929611C211yesmaximal, characteristic, complemented
2C2×SD16×D79C211yesmaximal, characteristic, complemented
3Q8×C22⋊D79C211yesmaximal, characteristic, complemented
4#19099197C211yesmaximal, characteristic
5#19098934C211yesmaximal, characteristic, complemented
6#19098795C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098767C211yesmaximal, characteristic, complemented
9#19098761C211yesmaximal, characteristic, complemented
10#19098716C211yesmaximal, characteristic, complemented
11#19098712C211yesmaximal, characteristic, complemented
12#19098703C211yesmaximal, characteristic, complemented
13#19098648C211yesmaximal, characteristic, complemented
14(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
15#448×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic, complemented
17C22×D316C2211yescharacteristic
18C2×D4×D79—21no—
19C2×D4×D79C2211yescharacteristic
20C2×#11929613C2211yescharacteristic
21C2×#11929613C2211yescharacteristic, complemented
22C2×#11929612C2211yescharacteristic, complemented
23C2×#11929611—24no—
24C2×#11929611C2211yescharacteristic
25C2×#11929611C2211yescharacteristic
26C2×#11929611C2211yescharacteristic, complemented
27C2×#11929611C2211yescharacteristic, complemented
28SD16×D79—24no—
29C22×C79⋊C8C2211yescharacteristic, complemented
30C2×C8×D79C2211yescharacteristic, complemented
31#14579159—21no—
32#14579159C2211yescharacteristic, complemented
33#14579157C2211yescharacteristic
34#14579140—21no—
35#14579140C2211yescharacteristic, complemented
36#14579137—21no—
37#14579137C2211yescharacteristic, complemented
38#14579136C2211yescharacteristic
39#14579134—21no—
40#14579131—21no—
41#14579129—21no—
42Q8×Dic79C2211yescharacteristic, complemented
43#14579123C2211yescharacteristic
44C4×C22⋊D79—21no—
45C4×C22⋊D79C2211yescharacteristic
46#14579092C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579084C2211yescharacteristic, complemented
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic, complemented
51#14579082C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53C8×Dic79C2211yescharacteristic, complemented
54C22×Q8×C79C2211yescharacteristic, complemented
55C2×SD16×C79C2211yescharacteristic, complemented
56C2×SD16×C79C2211yescharacteristic, complemented
57#121×C79C2211yescharacteristic
58#103×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60C22⋊C8×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C23×D79—21no—
63C2×Dic158—21no—
64C2×Dic158C2311yescharacteristic
65Q8×D79—22no—
66Q8×D79—41no—
67C2×D316—21no—
68C2×D316—22no—
69C2×D316—21no—
70C2×D316—41no—
71C2×D316C2311yescharacteristic
72C2×D316C2311yescharacteristic
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C2×C22⋊D79D411yescharacteristic
77D4×D79—22no—
78D4×D79—41no—
79D4×D79—44no—
80C2×C4×D79—21no—
81C2×C4×D79—21no—
82C2×C4×D79C2311yescharacteristic
83#11929613—22no—
84#11929613—41no—
85#11929612—22no—
86#11929611—22no—
87#11929611—22no—
88#11929611—22no—
89#11929611D414yescomplemented
90C2×C79⋊C8—22no—
91C2×C79⋊C8C2311yescharacteristic
92C2×C79⋊C8C2311yescharacteristic
93C8×D79—22no—
94C4⋊Dic79—21no—
95C4⋊Dic79C2311yescharacteristic
96Dic79⋊C4—21no—
97Dic79⋊C4—21no—
98Dic79⋊C4—21no—
99Dic79⋊C4—21no—
100Dic79⋊C4D411yescharacteristic
101C22⋊Dic79—21no—
102C22⋊Dic79D411yescharacteristic
103(C2×D79)⋊C4—21no—
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4D411yescharacteristic
107C4×Dic79—21no—
108C4×Dic79C2311yescharacteristic
109C2×Q8×C79—21no—
110C2×Q8×C79—22no—
111C2×Q8×C79—41no—
112C2×Q8×C79C2311yescharacteristic
113C2×Q8×C79C2311yescharacteristic
114C2×D4×C79—21no—
115C2×D4×C79C2311yescharacteristic
116C22×C4×C79—21no—
117C22×C4×C79C2311yescharacteristic
118SD16×C79—22no—
119SD16×C79—41no—
120C2×C8×C79C2311yescharacteristic
121C2×C8×C79C2311yescharacteristic
122C4⋊C4×C79C2311yescharacteristic
123C22⋊C4×C79—21no—
124C23×C79—21no—
125C23×C79C2×D411yescharacteristic
126C22×D79—21no—
127C22×D79—21no—
128C22×D79—42no—
129C22×D79—42no—
130C22×D79—42no—
131C22×D79—42no—
132C22×D79—81no—
133C22×D79—81no—
134C22×D79C2×D411yescharacteristic
135Q8×C79—21no—
136Q8×C79—21no—
137Q8×C79—21no—
138Q8×C79—42no—
139Q8×C79C2×D412yescomplemented
140D4×C79—21no—
141D4×C79—21no—
142D4×C79—42no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—21no—
146C2×C4×C79—21no—
147C2×C4×C79—21no—
148C2×C4×C79—42no—
149C2×C4×C79C2×D411yescharacteristic
150C2×C4×C79C2411yescharacteristic
151C22⋊D79—42no—
152C22⋊D79—42no—
153C22⋊D79—81no—
154C22⋊D79SD1614yescomplemented
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79C2×D411yescharacteristic
158C2×Dic79C2×D411yescharacteristic
159C2×Dic79C2×D411yescharacteristic
160D316—21no—
161D316—21no—
162D316—21no—
163D316—42no—
164D316—42no—
165D316C2×D412yes—
166C4×D79—21no—
167C4×D79—21no—
168C4×D79—42no—
169C4×D79—42no—
170Dic158—21no—
171Dic158—21no—
172Dic158—42no—
173C8×C79—21no—
174C8×C79—21no—
175C79⋊C8—21no—
176C79⋊C8C2×D412yescomplemented
177C22×C79—21no—
178C22×C79—21no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79C2×SD1612yescomplemented
183C22×C79C22×D411yescharacteristic
184C2×D79—21no—
185C2×D79—21no—
186C2×D79—22no—
187C2×D79—41no—
188C2×D79—41no—
189C2×D79—41no—
190C2×D79—41no—
191C2×D79—41no—
192C2×D79—84no—
193C2×D79—84no—
194C2×D79C2×SD1612yescomplemented
195C4×C79—21no—
196C4×C79—22no—
197C4×C79—41no—
198C4×C79—41no—
199C4×C79C22×D411yescharacteristic
200C4×C79H(5,𝔽2)11yescharacteristic
201Dic79—21no—
202Dic79—21no—
203Dic79—41no—
204Dic79—41no—
205Dic79C2×SD1612yescomplemented
206C2×C79—22no—
207C2×C79—81no—
208C2×C79D4211yescharacteristic
209C2×C79C22×SD1611yescharacteristic
210C2×C79#57711yescharacteristic
211D79—22no—
212D79—42no—
213D79—81no—
214D4×SD16—791nomaximal, Sylow
215C79D4×SD1611yescharacteristic, complemented, Sylow
216C22×SD16—791no—
217C22×SD16—791no—
218D4×Q8—791no—
219D42—791no—
220#492—791no—
221#465—791no—
222#465—791no—
223#461—791no—
224#460—791no—
225#450—791no—
226#450—791no—
227#448—791no—
228#448D7911yescharacteristic, complemented
229C4×SD16—791no—
230C8×D4—791no—
231C22×Q8—791no—
232C22×Q8C2×D7911yescharacteristic, complemented
233C22×D4—791no—
234C22×D4—791no—
235C22×D4—1581no—
236C2×SD16—791no—
237C2×SD16—791no—
238C2×SD16—791no—
239C2×SD16—791no—
240C2×SD16—791no—
241C2×SD16—791no—
242C2×SD16—791no—
243C2×SD16—1584no—
244C2×SD16—1584no—
245C2×SD16C2×D7911yescharacteristic, complemented
246C2×SD16C2×D7911yescharacteristic, complemented
247C22×C8—791no—
248C22×C8—791no—
249C4⋊Q8—791no—
250C4⋊Q8—1581no—
251#127—791no—
252C22⋊Q8—791no—
253C22⋊Q8—791no—
254C22⋊Q8—1581no—
255C22⋊Q8—1581no—
256#121—791no—
257#121—1581no—
258#121C2×D7911yescharacteristic
259#120—1581no—
260#120—1581no—
261C4×Q8—791no—
262C4×D4—791no—
263C4×D4—791no—
264C4×D4—1581no—
265#106—791no—
266C4⋊C8—791no—
267#103—791no—
268#103C2×D7911yescharacteristic, complemented
269#103C2×D7911yescharacteristic, complemented
270#102—791no—
271#102—791no—
272#102—791no—
273C22⋊C8—791no—
274C22⋊C8C2×D7911yescharacteristic, complemented
275C4×C8—791no—
276C24—1581no—
277C24—1581no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—3161no—
282C2×Q8—791no—
283C2×Q8—1581no—
284C2×Q8—1582no—
285C2×Q8C22×D7911yescharacteristic
286C2×Q8C22×D7911yescharacteristic
287C2×D4—21no—
288C2×D4—3161no—
289C2×D4—3164no—
290C2×D4—3161no—
291C2×D4—791no—
292C2×D4—791no—
293C2×D4—791no—
294C2×D4—1581no—
295C2×D4—1582no—
296C2×D4—1581no—
297C2×D4—1581no—
298C2×D4—1581no—
299C2×D4—1582no—
300C2×D4—1581no—
301C2×D4C22×D7911yescharacteristic
302C22×C4—21no—
303C22×C4—791no—
304C22×C4—1581no—
305C22×C4—1581no—
306C22×C4C22×D7911yescharacteristic
307SD16—22no—
308SD16—41no—
309SD16—3161no—
310SD16—794no—
311SD16—1582no—
312SD16—1582no—
313SD16—1582no—
314SD16—1582no—
315SD16—1582no—
316C2×C8—791no—
317C2×C8—791no—
318C2×C8—1582no—
319C2×C8—1582no—
320C2×C8C22×D7911yescharacteristic
321C2×C8C22×D7911yescharacteristic
322C4⋊C4—791no—
323C4⋊C4—791no—
324C4⋊C4—1581no—
325C4⋊C4—1581no—
326C4⋊C4—1581no—
327C4⋊C4—1581no—
328C4⋊C4—1581no—
329C4⋊C4C22×D7911yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—791no—
332C22⋊C4—791no—
333C22⋊C4—1581no—
334C22⋊C4—1581no—
335C22⋊C4—1581no—
336C22⋊C4—1581no—
337C42—791no—
338C42—1581no—
339C23—21no—
340C23—3162no—
341C23—3162no—
342C23—3162no—
343C23—3162no—
344C23—791no—
345C23—6321no—
346C23—6321no—
347C23—1581no—
348C23—1581no—
349C23D4×D7911yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—3162no—
355Q8—1581no—
356Q8—1581no—
357Q8D4×D7912yescomplemented
358D4—21no—
359D4—21no—
360D4—42no—
361D4—3162no—
362D4—3162no—
363D4—3162no—
364D4—3162no—
365D4—794no—
366D4—792no—
367D4—6321no—
368D4—1581no—
369D4—1581no—
370D4—1581no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—3162no—
378C2×C4—3162no—
379C2×C4—791no—
380C2×C4—791no—
381C2×C4—791no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4—1581no—
386C2×C4D4×D7911yescharacteristic
387C2×C4C23×D7911yescharacteristic
388C8—21no—
389C8—21no—
390C8—792no—
391C8—1581no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—3161no—
398C22—3161no—
399C22—3161no—
400C22—3161no—
401C22—3161no—
402C22—792no—
403C22—6324no—
404C22—6324no—
405C22—1582no—
406C22—1581no—
407C22—1581no—
408C22SD16×D7912yescomplemented
409C22C2×D4×D7911yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—3161no—
415C4—3161no—
416C4—792no—
417C4—1581no—
418C4—1581no—
419C4C2×D4×D7911yescharacteristic
420C4#1457920611yescharacteristic
421C2—22no—
422C2—81no—
423C2—3162no—
424C2—6321no—
425C2—1582no—
426C2#1909919511yescharacteristic
427C2C2×SD16×D7911yescharacteristic
428C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#448×C79C2
socleC22×C79C22×D4
prime radical#19099197C2
hypercenter#448D79
hypocenterC79D4×SD16
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. C22×#11929611C2semidirect
2. C2×SD16×D79C2semidirect
3. Q8×C22⋊D79C2semidirect
5. #19098934C2semidirect
6. #19098795C2semidirect
7. #19098790C2semidirect
8. #19098767C2semidirect
9. #19098761C2semidirect
10. #19098716C2semidirect
11. #19098712C2semidirect
12. #19098703C2semidirect
13. #19098648C2semidirect
14. (C22⋊D79)⋊C8C2semidirect
15. #448×C79C2semidirect
16. C2×Q8×D79C22semidirect
21. C2×#11929613C22semidirect
22. C2×#11929612C22semidirect
26. C2×#11929611C22semidirect
27. C2×#11929611C22semidirect
29. C22×C79⋊C8C22semidirect
30. C2×C8×D79C22semidirect
32. #14579159C22semidirect
35. #14579140C22semidirect
37. #14579137C22semidirect
42. Q8×Dic79C22semidirect
46. #14579092C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579084C22semidirect
50. #14579083C22semidirect
51. #14579082C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. C8×Dic79C22semidirect
54. C22×Q8×C79C22semidirect
55. C2×SD16×C79C22semidirect
56. C2×SD16×C79C22semidirect
58. #103×C79C22semidirect
59. #103×C79C22semidirect
60. C22⋊C8×C79C22semidirect
89. #11929611D4semidirect
139. Q8×C79C2×D4semidirect
154. C22⋊D79SD16semidirect
176. C79⋊C8C2×D4semidirect
182. C22×C79C2×SD16semidirect
194. C2×D79C2×SD16semidirect
205. Dic79C2×SD16semidirect
215. C79D4×SD16semidirect
228. #448D79semidirect
232. C22×Q8C2×D79semidirect
245. C2×SD16C2×D79semidirect
246. C2×SD16C2×D79semidirect
268. #103C2×D79semidirect
269. #103C2×D79semidirect
274. C22⋊C8C2×D79semidirect
357. Q8D4×D79semidirect
408. C22SD16×D79semidirect