Finite Group Databasebeta

← #23775110

Subgroups — #23775110

Order 10112.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579181C211yesmaximal, characteristic, complemented
2C2×SD16×D79C211yesmaximal, characteristic, complemented
3#19099220C211yesmaximal, characteristic, complemented
4#19099210C211yesmaximal, characteristic, complemented
5#19098946C211yesmaximal, characteristic, complemented
6#19098791C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098783C211yesmaximal, characteristic, complemented
9#19098777C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098720C211yesmaximal, characteristic, complemented
12#19098695C211yesmaximal, characteristic, complemented
13#19098648C211yesmaximal, characteristic, complemented
14(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19#14579181—24no—
20C2×Dic316C2211yescharacteristic, complemented
21C2×#11929614C2211yescharacteristic, complemented
22C2×#11929613C2211yescharacteristic
23C2×#11929612C2211yescharacteristic
24C2×#11929612C2211yescharacteristic, complemented
25C2×#11929611C2211yescharacteristic
26SD16×D79—24no—
27C2×#11929609C2211yescharacteristic
28C22×C79⋊C8C2211yescharacteristic, complemented
29C2×C8×D79C2211yescharacteristic
30#14579148—21no—
31#14579148C2211yescharacteristic
32#14579148C2211yescharacteristic, complemented
33#14579143—21no—
34#14579141C2211yescharacteristic
35#14579140—21no—
36#14579140C2211yescharacteristic, complemented
37#14579132—21no—
38#14579132—21no—
39#14579132C2211yescharacteristic
40#14579129—21no—
41Q8×Dic79C2211yescharacteristic, complemented
42#14579123C2211yescharacteristic
43C4×C22⋊D79—21no—
44C4×C22⋊D79C2211yescharacteristic
45C22⋊C4×D79—21no—
46#14579092C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579084C2211yescharacteristic, complemented
50#14579083C2211yescharacteristic
51#14579082C2211yescharacteristic
52(C2×D79)⋊C8C2211yescharacteristic
53C8×Dic79C2211yescharacteristic, complemented
54C2×#41×C79C2211yescharacteristic, complemented
55C2×SD16×C79C2211yescharacteristic
56C2×D8×C79C2211yescharacteristic
57#121×C79C2211yescharacteristic
58#103×C79C2211yescharacteristic, complemented
59#102×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⋊D79—21no—
73C2×C22⋊D79D411yescharacteristic
74D4×D79—22no—
75D4×D79—41no—
76C2×C4×D79—21no—
77C2×C4×D79—21no—
78C2×C4×D79—21no—
79C2×C4×D79C2311yescharacteristic
80Dic316—41no—
81#11929614—22no—
82#11929613—22no—
83#11929612—22no—
84#11929612—22no—
85#11929611D414yescomplemented
86#11929609—22no—
87C2×C79⋊C8—22no—
88C2×C79⋊C8C2311yescharacteristic
89C2×C79⋊C8C2311yescharacteristic
90C8×D79—22no—
91C4⋊Dic79—21no—
92C4⋊Dic79—21no—
93C4⋊Dic79C2311yescharacteristic
94Dic79⋊C4—21no—
95Dic79⋊C4D411yescharacteristic
96C22⋊Dic79—21no—
97C22⋊Dic79—21no—
98C22⋊Dic79—21no—
99C22⋊Dic79—21no—
100C22⋊Dic79—21no—
101C22⋊Dic79—21no—
102C22⋊Dic79D411yescharacteristic
103(C2×D79)⋊C4—21no—
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4D411yescharacteristic
106C4×Dic79—21no—
107C4×Dic79C2311yescharacteristic
108#41×C79—22no—
109#41×C79—41no—
110C2×Q8×C79C2311yescharacteristic
111C2×D4×C79—21no—
112C2×D4×C79—21no—
113C2×D4×C79C2311yescharacteristic
114C2×D4×C79C2311yescharacteristic
115C22×C4×C79—21no—
116C22×C4×C79C2311yescharacteristic
117SD16×C79—22no—
118D8×C79—41no—
119C2×C8×C79C2311yescharacteristic
120C2×C8×C79C2311yescharacteristic
121C4⋊C4×C79C2311yescharacteristic
122C22⋊C4×C79—21no—
123C23×C79—21no—
124C23×C79—21no—
125C23×C79C2×D411yescharacteristic
126C22×D79—21no—
127C22×D79—42no—
128C22×D79—42no—
129C22×D79—81no—
130C22×D79C2×D411yescharacteristic
131Q8×C79—21no—
132Q8×C79C2×D412yes—
133D4×C79—21no—
134D4×C79—21no—
135D4×C79—21no—
136D4×C79—21no—
137D4×C79—42no—
138D4×C79—81no—
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—
149C22⋊D79—42no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79C2×D411yescharacteristic
154C2×Dic79C2×D411yescharacteristic
155C2×Dic79C2×D411yescharacteristic
156D316—21no—
157D316C2×D412yes—
158C4×D79—21no—
159C4×D79—21no—
160C4×D79—42no—
161C4×D79—42no—
162C4×D79—81no—
163Dic158—21no—
164Dic158—21no—
165Dic158—21no—
166Dic158—21no—
167Dic158—42no—
168C8×C79—21no—
169C8×C79—21no—
170C79⋊C8—21no—
171C79⋊C8C2×D412yes—
172C22×C79—21no—
173C22×C79—21no—
174C22×C79—21no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79C22×D411yescharacteristic
182C2×D79—21no—
183C2×D79—21no—
184C2×D79—22no—
185C2×D79—41no—
186C2×D79—41no—
187C2×D79—84no—
188C2×D79#13512yescomplemented
189C4×C79—21no—
190C4×C79—22no—
191C4×C79—41no—
192C4×C79C22×D411yescharacteristic
193C4×C79H(5,𝔽2)11yescharacteristic
194Dic79—21no—
195Dic79—21no—
196Dic79—21no—
197Dic79—41no—
198Dic79—41no—
199Dic79—41no—
200C2×C79—41no—
201C2×C79—81no—
202C2×C79—81no—
203C2×C79D4211yescharacteristic
204C2×C79C2×#13511yescharacteristic
205C2×C79#57711yescharacteristic
206D79—22no—
207D79—42no—
208#3282—791nomaximal, Sylow
209C79#328211yescharacteristic, complemented, Sylow
210C2×#135—791no—
211C22×SD16—791no—
212#548—791no—
213#546—791no—
214#495—791no—
215#465—791no—
216#465—791no—
217#464—791no—
218#463—791no—
219#452—791no—
220#451—791no—
221#449D7911yescharacteristic, complemented
222#447—791no—
223C4×SD16—791no—
224C8×D4—791no—
225C2×#41—791no—
226C2×#41C2×D7911yescharacteristic, complemented
227C22×Q8—791no—
228C22×D4—791no—
229#135—1584no—
230C2×Q16—791no—
231C2×Q16—791no—
232C2×SD16—791no—
233C2×SD16—791no—
234C2×SD16—791no—
235C2×SD16—791no—
236C2×SD16—1584no—
237C2×SD16C2×D7911yescharacteristic
238C2×D8—791no—
239C2×D8C2×D7911yescharacteristic
240C22×C8—791no—
241C22×C8—791no—
242#124—791no—
243#124—791no—
244#124—1581no—
245#123—1581no—
246C22⋊Q8—791no—
247C22⋊Q8—791no—
248C22⋊Q8—1581no—
249#121—791no—
250#121—1581no—
251#121—1581no—
252#121C2×D7911yescharacteristic
253#120—1581no—
254C4×Q8—791no—
255C4×D4—791no—
256C4×D4—791no—
257C4×D4—1581no—
258C2×C22⋊C4—1581no—
259#106—791no—
260C4⋊C8—791no—
261#103—791no—
262#103—791no—
263#103C2×D7911yescharacteristic, complemented
264#102—791no—
265#102—791no—
266#102C2×D7911yescharacteristic, complemented
267C22⋊C8—791no—
268C22⋊C8C2×D7911yescharacteristic, complemented
269C4×C8—791no—
270C24—1581no—
271#41—22no—
272#41—41no—
273#41—3161no—
274#41—1582no—
275C2×Q8—3161no—
276C2×Q8—791no—
277C2×Q8—791no—
278C2×Q8—1581no—
279C2×Q8—1582no—
280C2×Q8C22×D7911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—3161no—
284C2×D4—791no—
285C2×D4—791no—
286C2×D4—1581no—
287C2×D4—1582no—
288C2×D4—1581no—
289C2×D4—1581no—
290C2×D4C22×D7911yescharacteristic
291C2×D4C22×D7911yescharacteristic
292C22×C4—21no—
293C22×C4—791no—
294C22×C4—1581no—
295C22×C4—1581no—
296C22×C4—1581no—
297C22×C4C22×D7911yescharacteristic
298Q16—3161no—
299Q16—1582no—
300SD16—22no—
301SD16—794no—
302SD16—1582no—
303SD16—1582no—
304SD16—1582no—
305D8—41no—
306D8—1582no—
307C2×C8—791no—
308C2×C8—791no—
309C2×C8—1582no—
310C2×C8—1582no—
311C2×C8C22×D7911yescharacteristic
312C2×C8C22×D7911yescharacteristic
313C4⋊C4—791no—
314C4⋊C4—791no—
315C4⋊C4—1581no—
316C4⋊C4—1581no—
317C4⋊C4—1581no—
318C4⋊C4C22×D7911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—791no—
321C22⋊C4—791no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C22⋊C4—1581no—
327C22⋊C4—1581no—
328C22⋊C4—1581no—
329C22⋊C4—1581no—
330C42—791no—
331C42—1581no—
332C23—21no—
333C23—21no—
334C23—3162no—
335C23—3162no—
336C23—791no—
337C23—6321no—
338C23—1581no—
339C23D4×D7911yescharacteristic
340Q8—21no—
341Q8—3162no—
342Q8—1581no—
343Q8—1581no—
344Q8—1581no—
345Q8—1581no—
346Q8D4×D7912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—3162no—
354D4—3162no—
355D4—3162no—
356D4—792no—
357D4—1582no—
358D4—1581no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—3162no—
365C2×C4—3162no—
366C2×C4—791no—
367C2×C4—791no—
368C2×C4—791no—
369C2×C4—6321no—
370C2×C4—1581no—
371C2×C4—1581no—
372C2×C4—1581no—
373C2×C4—1581no—
374C2×C4—1581no—
375C2×C4D4×D7911yescharacteristic
376C2×C4C23×D7911yescharacteristic
377C8—21no—
378C8—21no—
379C8—792no—
380C8—1581no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—3161no—
391C22—3161no—
392C22—792no—
393C22—6324no—
394C22—1582no—
395C22—1581no—
396C22—1581no—
397C22C2×D4×D7911yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—3161no—
402C4—3161no—
403C4—3161no—
404C4—1581no—
405C4—1581no—
406C4—1581no—
407C4C2×D4×D7911yescharacteristic
408C4#1457920611yescharacteristic
409C2—41no—
410C2—81no—
411C2—81no—
412C2—3162no—
413C2—1582no—
414C2#1909919511yescharacteristic
415C2#135×D7911yescharacteristic
416C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3282
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14579181C2semidirect
2. C2×SD16×D79C2semidirect
3. #19099220C2semidirect
4. #19099210C2semidirect
5. #19098946C2semidirect
6. #19098791C2semidirect
7. #19098790C2semidirect
8. #19098783C2semidirect
9. #19098777C2semidirect
10. #19098727C2semidirect
11. #19098720C2semidirect
12. #19098695C2semidirect
13. #19098648C2semidirect
14. (C22⋊D79)⋊C8C2semidirect
15. #449×C79C2semidirect
20. C2×Dic316C22semidirect
21. C2×#11929614C22semidirect
24. C2×#11929612C22semidirect
28. C22×C79⋊C8C22semidirect
32. #14579148C22semidirect
36. #14579140C22semidirect
41. Q8×Dic79C22semidirect
46. #14579092C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579086C22semidirect
49. #14579084C22semidirect
53. C8×Dic79C22semidirect
54. C2×#41×C79C22semidirect
58. #103×C79C22semidirect
59. #102×C79C22semidirect
60. C22⋊C8×C79C22semidirect
85. #11929611D4semidirect
188. C2×D79#135semidirect
209. C79#3282semidirect
221. #449D79semidirect
226. C2×#41C2×D79semidirect
263. #103C2×D79semidirect
266. #102C2×D79semidirect
268. C22⋊C8C2×D79semidirect