Finite Group Databasebeta

← #23772238

Subgroups — #23772238

Order 10112.

470 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
1C2×#14579193C211yesmaximal, characteristic
2#19099045C211yesmaximal, characteristic
3#19099039C211yesmaximal, characteristic, complemented
4#19098670C211yesmaximal, characteristic, complemented
5#19098668C211yesmaximal, characteristic, complemented
6#19098662C211yesmaximal, characteristic, complemented
7#19098661C211yesmaximal, characteristic, complemented
8#19098655C211yesmaximal, characteristic, complemented
9C4×#11929613C211yesmaximal, characteristic, complemented
10#19098648C211yesmaximal, characteristic, complemented
11#19098604C211yesmaximal, characteristic, complemented
12#19098558C211yesmaximal, characteristic
13#103×D79C211yesmaximal, characteristic, complemented
14#19098517C211yesmaximal, characteristic, complemented
15C4×Q16×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18#14579193C418yescomplemented
19C2×#11929614C2211yescharacteristic
20C2×#11929613C2211yescharacteristic
21C2×#11929611C2211yescharacteristic
22C2×#11929607C2211yescharacteristic
23C2×C8×D79C2211yescharacteristic
24Q8×Dic79C2211yescharacteristic
25Q8×Dic79C2211yescharacteristic
26C4×Dic158—21no—
27C4×Dic158C2211yescharacteristic
28#14579126—21no—
29#14579126C2211yescharacteristic
30C4×D316—21no—
31C4×D316C2211yescharacteristic
32#14579123—21no—
33#14579123C2211yescharacteristic
34#14579119—21no—
35#14579119C2211yescharacteristic
36#14579118—21no—
37#14579118—21no—
38#14579118C2211yescharacteristic
39C4⋊C4×D79—21no—
40C4⋊C4×D79C2211yescharacteristic
41#14579094C2211yescharacteristic
42#14579093C2211yescharacteristic
43#14579092C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579084C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579081C2211yescharacteristic
50#14579072C2211yescharacteristic
51#14579071C2211yescharacteristic
52C8×Dic79C2211yescharacteristic
53C2×Q16×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×Q8×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#103×C79C2211yescharacteristic
59C4×C8×C79C2211yescharacteristic
60#11929625—22no—
61#11929625C2×C414yes—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64Q8×D79—22no—
65Q8×D79C2×C414yescomplemented
66C2×D316—21no—
67C2×D316C2311yescharacteristic
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74#11929614C2×C414yescomplemented
75#11929613C2×C414yescomplemented
76#11929611C2×C414yescomplemented
77#11929607C2×C414yescomplemented
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C8×D79—22no—
81C4⋊Dic79—21no—
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4D411yescharacteristic
89Dic79⋊C4D411yescharacteristic
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4D411yescharacteristic
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79—21no—
98C4×Dic79—21no—
99C4×Dic79—21no—
100C4×Dic79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C2×Q8×C79C2311yescharacteristic
103Q16×C79C2×C414yescomplemented
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C42×C79—21no—
111C42×C79—21no—
112C42×C79C2311yescharacteristic
113C22×D79—21no—
114C22×D79C2×D411yescharacteristic
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79C22×C412yes—
118Q8×C79C22×C412yes—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131C2×Dic79C2×D411yescharacteristic
132D316—24no—
133D316—21no—
134D316C22×C412yes—
135C4×D79—24no—
136C4×D79—24no—
137C4×D79—81no—
138C4×D79—81no—
139C4×D79—81no—
140C4×D79C22×C412yes—
141C4×D79#4112yes—
142Dic158—21no—
143Dic158—24no—
144Dic158C22×C412yes—
145C8×C79—21no—
146C8×C79C22×C412yes—
147C79⋊C8—21no—
148C79⋊C8C22×C412yes—
149C22×C79C22×D411yescharacteristic
150C2×D79—21no—
151C2×D79—21no—
152C2×D79—22no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79C4×D412yes—
156C4×C79—22no—
157C4×C79—22no—
158C4×C79—21no—
159C4×C79—21no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79C23×C411yescharacteristic
163C4×C79C2×#4111yescharacteristic
164Dic79—22no—
165Dic79—21no—
166Dic79—21no—
167Dic79—41no—
168Dic79—41no—
169Dic79C4×D412yes—
170C2×C79C2×C4×D411yescharacteristic
171C2×C79#57711yescharacteristic
172C2×C79#57811yescharacteristic
173D79—22no—
174D79—42no—
175#2947—791nomaximal, Sylow
176C79#294711yescharacteristic, complemented, Sylow
177C2×#137—791no—
178#520—791no—
179#519—791no—
180#441—791no—
181#441—791no—
182#440—791no—
183#440—791no—
184C4×Q16—791no—
185C4×Q16D7911yescharacteristic, complemented
186C4×SD16—791no—
187C4×SD16—791no—
188#428—791no—
189#416—791no—
190C2×#103—791no—
191#405—791no—
192C2×#41—791no—
193C22×Q8—791no—
194#137—798no—
195C2×Q16—791no—
196C2×Q16C2×D7911yescharacteristic
197C2×SD16—791no—
198C2×SD16—791no—
199C2×M16—791no—
200C22×C8—791no—
201C4×Q8—791no—
202C4×Q8—791no—
203C4×Q8—791no—
204C4×Q8—791no—
205C4×Q8—1581no—
206C4×Q8—1581no—
207C4×Q8C2×D7911yescharacteristic
208C4×Q8C2×D7911yescharacteristic
209C4×D4—791no—
210C4×D4—791no—
211C4×D4—1581no—
212C4×D4—1581no—
213#117—791no—
214#117—791no—
215#117—1581no—
216#117—1581no—
217#117—1581no—
218C2×C4⋊C4—791no—
219C2×C4⋊C4—1581no—
220#107—791no—
221#107C2×D7911yescharacteristic
222#106—791no—
223#106—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#103C2×D7911yescharacteristic
229#103C2×D7911yescharacteristic
230#102—791no—
231#102—791no—
232#97—791no—
233#97—791no—
234C4×C8—791no—
235C4×C8C2×D7911yescharacteristic
236#41—794no—
237#41—1582no—
238C2×Q8—794no—
239C2×Q8—791no—
240C2×Q8—1581no—
241C2×Q8—1582no—
242C2×Q8C22×D7911yescharacteristic
243C2×Q8C22×D7911yescharacteristic
244C2×D4—791no—
245C2×D4—1581no—
246C22×C4—791no—
247C22×C4—1581no—
248C22×C4—1581no—
249C22×C4—1581no—
250C22×C4—1581no—
251C22×C4—1581no—
252Q16—794no—
253Q16C4×D7914yescomplemented
254SD16—794no—
255SD16—794no—
256M16—794no—
257C2×C8—791no—
258C2×C8—791no—
259C2×C8—1582no—
260C2×C8C22×D7911yescharacteristic
261C2×C8C22×D7911yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—791no—
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4C22×D7911yescharacteristic
274C4⋊C4C22×D7911yescharacteristic
275C22⋊C4—791no—
276C22⋊C4—791no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C42—21no—
281C42—21no—
282C42—791no—
283C42—1581no—
284C42—1581no—
285C42—1581no—
286C42—1581no—
287C42—1581no—
288C42C22×D7911yescharacteristic
289C23—791no—
290C23—1581no—
291Q8—21no—
292Q8—21no—
293Q8—792no—
294Q8—1584no—
295Q8—1581no—
296Q8C2×C4×D7912yes—
297Q8C2×C4×D7912yes—
298D4—792no—
299D4—1584no—
300D4—1581no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—791no—
306C2×C4—792no—
307C2×C4—792no—
308C2×C4—791no—
309C2×C4—791no—
310C2×C4—6321no—
311C2×C4—6321no—
312C2×C4—6321no—
313C2×C4—1584no—
314C2×C4—1584no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4D4×D7911yescharacteristic
319C2×C4D4×D7911yescharacteristic
320C2×C4C23×D7911yescharacteristic
321C8—21no—
322C8—792no—
323C8—1581no—
324C8C2×C4×D7912yes—
325C22—3161no—
326C22—3161no—
327C22—792no—
328C22—1582no—
329C22—1581no—
330C22—1581no—
331C22C2×D4×D7911yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—3161no—
339C4—3161no—
340C4—792no—
341C4—1582no—
342C4—1581no—
343C4—1581no—
344C4C22×C4×D7911yescharacteristic
345C4#41×D7911yescharacteristic
346C2—3162no—
347C2—1582no—
348C2C4×D4×D7911yescharacteristic
349C2#1909937011yescharacteristic
350C2#1909937611yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutatorC4×C79C23×C4
FrattiniC2×C4C23×D79
FittingC4×Q16×C79C2
socleC22×C79C22×D4
prime radicalC2×#11929625C22
cosocleC2×C4×C79C24
hypercenterC4×Q16D79
hypocenterC79#2947
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. #19099039C2semidirect
4. #19098670C2semidirect
5. #19098668C2semidirect
6. #19098662C2semidirect
7. #19098661C2semidirect
8. #19098655C2semidirect
9. C4×#11929613C2semidirect
10. #19098648C2semidirect
11. #19098604C2semidirect
13. #103×D79C2semidirect
14. #19098517C2semidirect
15. C4×Q16×C79C2semidirect
18. #14579193C4semidirect
65. Q8×D79C2×C4semidirect
74. #11929614C2×C4semidirect
75. #11929613C2×C4semidirect
76. #11929611C2×C4semidirect
77. #11929607C2×C4semidirect
103. Q16×C79C2×C4semidirect
176. C79#2947semidirect
185. C4×Q16D79semidirect
253. Q16C4×D79semidirect