Finite Group Databasebeta

← #23773362

Subgroups — #23773362

Order 10112.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099136C211yesmaximal, characteristic
2#19099044C211yesmaximal, characteristic
3#19098907C211yesmaximal, characteristic, complemented
4#19098905C211yesmaximal, characteristic, complemented
5#19098902C211yesmaximal, characteristic, complemented
6#19098901C211yesmaximal, characteristic, complemented
7#19098898C211yesmaximal, characteristic, complemented
8#19098897C211yesmaximal, characteristic, complemented
9#19098895C211yesmaximal, characteristic, complemented
10#19098602C211yesmaximal, characteristic, complemented
11#19098598C211yesmaximal, characteristic, complemented
12#19098570C211yesmaximal, characteristic, complemented
13#103×D79C211yesmaximal, characteristic, complemented
14#19098528C211yesmaximal, characteristic
15#483×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C2×#11929607C2211yescharacteristic
19C2×C8×D79C2211yescharacteristic
20#14579160—21no—
21#14579147—21no—
22#14579146—21no—
23#14579143—21no—
24#14579141C2211yescharacteristic
25#14579140C2211yescharacteristic
26#14579137C2211yescharacteristic
27#14579126—21no—
28#14579123—21no—
29C4×C22⋊D79—21no—
30C4×C22⋊D79—21no—
31#14579120C2211yescharacteristic
32#14579119C2211yescharacteristic
33#14579119C2211yescharacteristic
34#14579119C2211yescharacteristic
35C4⋊C4×D79C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579094C2211yescharacteristic
39#14579094C2211yescharacteristic
40#14579094C2211yescharacteristic
41#14579093C2211yescharacteristic
42#14579092C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579084C2211yescharacteristic
48#14579084C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C22⋊Q8×C79C2211yescharacteristic
53C2×C4⋊C4×C79C2211yescharacteristic
54#106×C79C2211yescharacteristic
55#106×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61C2×Dic158—21no—
62C2×Dic158D411yescharacteristic
63C2×Dic158C2311yescharacteristic
64Q8×D79—22no—
65Q8×D79—22no—
66C2×D316D411yescharacteristic
67C2×C22⋊D79D411yescharacteristic
68C2×C22⋊D79D411yescharacteristic
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79C2311yescharacteristic
73C2×C4×D79C2311yescharacteristic
74#11929607—22no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C8×D79—22no—
78C4⋊Dic79—21no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C2×Q8×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C22×C4×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79—21no—
103C4⋊C4×C79—21no—
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79C2×D411yescharacteristic
109C22×D79C2×D411yescharacteristic
110C22×D79C2×D411yescharacteristic
111Q8×C79—21no—
112Q8×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—81no—
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2411yescharacteristic
122C22⋊D79—22no—
123C22⋊D79—22no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130D316—22no—
131C4×D79—21no—
132C4×D79—21no—
133C4×D79—42no—
134C4×D79—81no—
135C4×D79—81no—
136C4×D79#4112yes—
137C4×D79#4112yes—
138Dic158—22no—
139Dic158—21no—
140Dic158—21no—
141Dic158—42no—
142C8×C79—21no—
143C8×C79—21no—
144C79⋊C8—21no—
145C79⋊C8—21no—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79C22×D411yescharacteristic
150C2×D79—21no—
151C2×D79—21no—
152C2×D79—21no—
153C2×D79—21no—
154C2×D79—21no—
155C2×D79#12312yes—
156C4×C79—21no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79C2×#4111yescharacteristic
162C4×C79C2×#4111yescharacteristic
163Dic79—21no—
164Dic79—41no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168Dic79#12312yes—
169C2×C79—41no—
170C2×C79C2×#12311yescharacteristic
171C2×C79#57711yescharacteristic
172C2×C79#57811yescharacteristic
173D79—22no—
174D79—41no—
175#3097—791nomaximal, Sylow
176C79#309711yescharacteristic, complemented, Sylow
177#536—791no—
178#520—791no—
179#485—791no—
180#485—791no—
181#485—791no—
182#485—791no—
183#484—791no—
184#484—791no—
185#483—791no—
186#483D7911yescharacteristic, complemented
187#428—791no—
188#427—791no—
189#419—791no—
190C2×#103—791no—
191#408—791no—
192C2×#41—791no—
193C22×Q8—791no—
194C2×M16—791no—
195C22×C8—791no—
196C4⋊Q8—1581no—
197#124—1581no—
198#123—1581no—
199#123—1581no—
200C22⋊Q8—791no—
201C22⋊Q8—791no—
202C22⋊Q8—791no—
203C22⋊Q8C2×D7911yescharacteristic
204C4×Q8—1581no—
205C4×D4—1581no—
206C4×D4—1581no—
207C4×D4—1581no—
208#117—791no—
209#117—791no—
210#117—791no—
211#117—791no—
212C2×C4⋊C4—791no—
213C2×C4⋊C4—791no—
214C2×C4⋊C4C2×D7911yescharacteristic
215#107—791no—
216#107—791no—
217#107—791no—
218#107—791no—
219#106—791no—
220#106—791no—
221#106C2×D7911yescharacteristic
222#106C2×D7911yescharacteristic
223#103—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#103—791no—
229#103C2×D7911yescharacteristic
230#103C2×D7911yescharacteristic
231C22⋊C8—791no—
232C22⋊C8—791no—
233C22⋊C8—791no—
234C22⋊C8C2×D7911yescharacteristic
235#41—1582no—
236#41—1582no—
237C2×Q8—791no—
238C2×Q8—791no—
239C2×Q8—1581no—
240C2×Q8—1582no—
241C2×Q8—1582no—
242C2×Q8C22×D7911yescharacteristic
243C2×D4—791no—
244C2×D4—791no—
245C2×D4—791no—
246C22×C4—21no—
247C22×C4—791no—
248C22×C4—791no—
249C22×C4—1581no—
250C22×C4—1581no—
251C22×C4—1581no—
252C22×C4C22×D7911yescharacteristic
253M16—1582no—
254C2×C8—791no—
255C2×C8—791no—
256C2×C8—1582no—
257C2×C8C22×D7911yescharacteristic
258C2×C8C22×D7911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—791no—
262C4⋊C4—791no—
263C4⋊C4—791no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4C22×D7911yescharacteristic
270C4⋊C4C22×D7911yescharacteristic
271C4⋊C4C22×D7911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C42—1581no—
281C42—1581no—
282C42—1581no—
283C42—1581no—
284C23—791no—
285C23—791no—
286C23D4×D7911yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—3162no—
290Q8—1582no—
291Q8—1581no—
292Q8—1581no—
293D4—1582no—
294D4—1582no—
295D4—1582no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—3162no—
304C2×C4—791no—
305C2×C4—792no—
306C2×C4—792no—
307C2×C4—791no—
308C2×C4—6321no—
309C2×C4—6321no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4D4×D7911yescharacteristic
317C2×C4C23×D7911yescharacteristic
318C8—21no—
319C8—21no—
320C8—1581no—
321C8—1581no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—792no—
326C22—1581no—
327C22—1581no—
328C22—1581no—
329C22—1581no—
330C22—1581no—
331C22C2×D4×D7911yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—3161no—
338C4—3161no—
339C4—3161no—
340C4—3161no—
341C4—792no—
342C4—1581no—
343C4#41×D7911yescharacteristic
344C4#41×D7911yescharacteristic
345C2—41no—
346C2—3161no—
347C2—1582no—
348C2#123×D7911yescharacteristic
349C2#1909936911yescharacteristic
350C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#483×C79C2
socleC22×C79C22×D4
prime radicalC2×#11929624C22
hypercenter#483D79
hypocenterC79#3097
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #19098907C2semidirect
4. #19098905C2semidirect
5. #19098902C2semidirect
6. #19098901C2semidirect
7. #19098898C2semidirect
8. #19098897C2semidirect
9. #19098895C2semidirect
10. #19098602C2semidirect
11. #19098598C2semidirect
12. #19098570C2semidirect
13. #103×D79C2semidirect
15. #483×C79C2semidirect
176. C79#3097semidirect
186. #483D79semidirect