Finite Group Databasebeta

← #23775452

Subgroups — #23775452

Order 10112.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099252C211yesmaximal, characteristic
2Q8×C22⋊D79C211yesmaximal, characteristic
3#19098930C211yesmaximal, characteristic, complemented
4#19098904C211yesmaximal, characteristic, complemented
5#19098892C211yesmaximal, characteristic, complemented
6#19098868C211yesmaximal, characteristic, complemented
7#19098821C211yesmaximal, characteristic, complemented
8#19098803C211yesmaximal, characteristic, complemented
9#19098772C211yesmaximal, characteristic, complemented
10#19098720C211yesmaximal, characteristic, complemented
11#19098719C211yesmaximal, characteristic, complemented
12#19098667C211yesmaximal, characteristic, complemented
13#19098632C211yesmaximal, characteristic
14#103×D79C211yesmaximal, characteristic, complemented
15#419×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×Dic316C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929614C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic
21#14579159—21no—
22#14579159C2211yescharacteristic
23#14579154—21no—
24#14579153—21no—
25#14579152C2211yescharacteristic
26#14579143—21no—
27#14579141C2211yescharacteristic
28#14579140—21no—
29#14579140C2211yescharacteristic
30#14579140C2211yescharacteristic
31#14579137—21no—
32#14579137C2211yescharacteristic
33Q8×Dic79C2211yescharacteristic
34#14579126C2211yescharacteristic
35C4×C22⋊D79—21no—
36C4×C22⋊D79C2211yescharacteristic
37#14579118—21no—
38C4⋊C4×D79C2211yescharacteristic
39#14579094C2211yescharacteristic
40#14579093C2211yescharacteristic
41#14579092C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579084C2211yescharacteristic
48#14579084C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic
52C22×Q8×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic
54#117×C79C2211yescharacteristic
55#103×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#103×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C2×Dic158C2311yescharacteristic
62Q8×D79—22no—
63Q8×D79—41no—
64C2×C22⋊D79D411yescharacteristic
65C2×C4×D79—21no—
66C2×C4×D79—21no—
67C2×C4×D79C2311yescharacteristic
68Dic316—41no—
69#11929614—22no—
70#11929614—41no—
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C8×D79—41no—
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4D411yescharacteristic
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79D411yescharacteristic
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4D411yescharacteristic
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97C2×Q8×C79—21no—
98C2×Q8×C79—22no—
99C2×Q8×C79—41no—
100C2×Q8×C79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104M16×C79—41no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C42×C79—21no—
111C23×C79C2×D411yescharacteristic
112C22×D79C2×D411yescharacteristic
113Q8×C79—21no—
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—42no—
117Q8×C79#4112yes—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—42no—
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—22no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79C2×D411yescharacteristic
133C2×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135C4×D79—21no—
136C4×D79—21no—
137C4×D79—42no—
138C4×D79—42no—
139Dic158—21no—
140Dic158—21no—
141Dic158—21no—
142Dic158—21no—
143Dic158—42no—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79C22×D411yescharacteristic
152C2×D79—21no—
153C2×D79—21no—
154C2×D79#13712yes—
155C4×C79—21no—
156C4×C79—22no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79C2×#4111yescharacteristic
161C4×C79H(5,𝔽2)11yescharacteristic
162Dic79—21no—
163Dic79—21no—
164Dic79—21no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—41no—
170C2×C79#54611yescharacteristic
171C2×C79C2×#13711yescharacteristic
172C2×C79#57811yescharacteristic
173D79—22no—
174#3312—791nomaximal, Sylow
175C79#331211yescharacteristic, complemented, Sylow
176#552—791no—
177D4×Q8—791no—
178#491—791no—
179#485—791no—
180#483—791no—
181#479—791no—
182#470—791no—
183#467—791no—
184#462—791no—
185#451—791no—
186#451—791no—
187#441—791no—
188#435—791no—
189#419D7911yescharacteristic, complemented
190C2×#103—791no—
191C22×Q8—791no—
192C22×Q8C2×D7911yescharacteristic
193C2×Q16—791no—
194C2×Q16—791no—
195C2×Q16—791no—
196C2×M16C2×D7911yescharacteristic
197C22×C8—791no—
198C4⋊Q8—791no—
199C4⋊Q8—1581no—
200#126—1581no—
201#125—791no—
202#125—1581no—
203#123—1581no—
204C22⋊Q8—791no—
205C22⋊Q8—791no—
206C22⋊Q8—791no—
207C22⋊Q8—791no—
208C22⋊Q8—1581no—
209C22⋊Q8—1581no—
210C4×Q8—791no—
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—1581no—
214#117—1581no—
215#117C2×D7911yescharacteristic
216C2×C4⋊C4—791no—
217#107—791no—
218#106—791no—
219#106—791no—
220C4⋊C8—791no—
221#103—791no—
222#103—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#103C2×D7911yescharacteristic
228#103C2×D7911yescharacteristic
229#103C2×D7911yescharacteristic
230#103C2×D7911yescharacteristic
231C22⋊C8—791no—
232C22⋊C8—791no—
233#97—791no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—3161no—
238C2×Q8—791no—
239C2×Q8—791no—
240C2×Q8—1581no—
241C2×Q8—1582no—
242C2×Q8C22×D7911yescharacteristic
243C2×Q8C22×D7911yescharacteristic
244C2×D4—791no—
245C22×C4—21no—
246C22×C4—791no—
247C22×C4—1581no—
248C22×C4—1581no—
249C22×C4C22×D7911yescharacteristic
250Q16—3161no—
251Q16—3161no—
252Q16—1582no—
253M16—41no—
254C2×C8—3161no—
255C2×C8—791no—
256C2×C8—791no—
257C2×C8C22×D7911yescharacteristic
258C2×C8C22×D7911yescharacteristic
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4C22×D7911yescharacteristic
274C4⋊C4C22×D7911yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—791no—
277C22⋊C4—791no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C42—21no—
283C42—791no—
284C42—1581no—
285C42—1581no—
286C23—791no—
287C23D4×D7911yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8—3162no—
293Q8—1581no—
294Q8—1581no—
295Q8—1581no—
296Q8—1581no—
297Q8#1192962412yes—
298D4—1582no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—3162no—
307C2×C4—3162no—
308C2×C4—791no—
309C2×C4—791no—
310C2×C4—791no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4D4×D7911yescharacteristic
318C2×C4C23×D7911yescharacteristic
319C8—21no—
320C8—21no—
321C8—1581no—
322C8—1581no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—792no—
327C22—1581no—
328C22—1581no—
329C22C2×D4×D7911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—3161no—
336C4—3161no—
337C4—3161no—
338C4—3161no—
339C4—1581no—
340C4—1581no—
341C4—1581no—
342C4C2×#1192962411yescharacteristic
343C4#1457920611yescharacteristic
344C2—41no—
345C2—1582no—
346C2#1909920311yescharacteristic
347C2#137×D7911yescharacteristic
348C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#419×C79C2
socleC22×C79C22×D4
prime radicalC2×C22⋊D79D4
hypercenter#419D79
hypocenterC79#3312
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #19098930C2semidirect
4. #19098904C2semidirect
5. #19098892C2semidirect
6. #19098868C2semidirect
7. #19098821C2semidirect
8. #19098803C2semidirect
9. #19098772C2semidirect
10. #19098720C2semidirect
11. #19098719C2semidirect
12. #19098667C2semidirect
14. #103×D79C2semidirect
15. #419×C79C2semidirect
175. C79#3312semidirect
189. #419D79semidirect