Finite Group Databasebeta

← #23774481

Subgroups — #23774481

Order 10112.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099173C211yesmaximal, characteristic, complemented
2#19099134C211yesmaximal, characteristic
3#19098954C211yesmaximal, characteristic, complemented
4#19098941C211yesmaximal, characteristic, complemented
5#19098930C211yesmaximal, characteristic, complemented
6#19098916C211yesmaximal, characteristic, complemented
7#19098784C211yesmaximal, characteristic, complemented
8#19098783C211yesmaximal, characteristic, complemented
9#19098772C211yesmaximal, characteristic, complemented
10#19098771C211yesmaximal, characteristic, complemented
11#19098725C211yesmaximal, characteristic
12#19098721C211yesmaximal, characteristic, complemented
13#19098718C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#452×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C2×Dic316C2211yescharacteristic
18C2×Dic316C2211yescharacteristic
19C2×#11929614C2211yescharacteristic
20C2×#11929614C2211yescharacteristic
21C2×#11929614C2211yescharacteristic
22C2×#11929612C2211yescharacteristic
23#14579159C2211yescharacteristic
24#14579159C2211yescharacteristic
25#14579159C2211yescharacteristic
26#14579154—21no—
27#14579154—21no—
28#14579152—21no—
29#14579152C2211yescharacteristic
30#14579151—21no—
31#14579148C2211yescharacteristic
32#14579148C2211yescharacteristic
33#14579142—21no—
34#14579142—21no—
35#14579140—21no—
36#14579140—21no—
37#14579140C2211yescharacteristic
38Q8×Dic79C2211yescharacteristic
39#14579126C2211yescharacteristic
40#14579120C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579084C2211yescharacteristic
47#14579084C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×Q16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158—41no—
61C2×Dic158—41no—
62C2×Dic158C2311yescharacteristic
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65C22×Dic79—21no—
66Dic316—41no—
67Dic316—41no—
68#11929614—41no—
69#11929614—41no—
70#11929614—41no—
71#11929612—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79D411yescharacteristic
77C4⋊Dic79D411yescharacteristic
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⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79D411yescharacteristic
94C22⋊Dic79D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C4×Dic79C2311yescharacteristic
99#41×C79—41no—
100#41×C79—41no—
101C2×Q8×C79C2311yescharacteristic
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C22×C4×C79—21no—
106C22×C4×C79C2311yescharacteristic
107Q16×C79—41no—
108SD16×C79—41no—
109C2×C8×C79C2311yescharacteristic
110C2×C8×C79C2311yescharacteristic
111C4⋊C4×C79—21no—
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79C2×D411yescharacteristic
116Q8×C79—21no—
117Q8×C79—21no—
118Q8×C79—21no—
119Q8×C79—21no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—42no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—42no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—42no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140Dic158—21no—
141Dic158—21no—
142Dic158—21no—
143Dic158—21no—
144Dic158—21no—
145Dic158—21no—
146Dic158—42no—
147C8×C79—21no—
148C8×C79—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79C22×D411yescharacteristic
158C4×C79—21no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79H(5,𝔽2)11yescharacteristic
163C4×C79H(5,𝔽2)11yescharacteristic
164Dic79—21no—
165Dic79—21no—
166Dic79—21no—
167Dic79—21no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172C2×C79—41no—
173C2×C79—81no—
174C2×C79#53511yescharacteristic
175C2×C79#57811yescharacteristic
176C2×C79#57811yescharacteristic
177#3223—791nomaximal, Sylow
178C79#322311yescharacteristic, complemented, Sylow
179#541—791no—
180#536—791no—
181#497—791no—
182#494—791no—
183#491—791no—
184#488—791no—
185#464—791no—
186#464—791no—
187#462—791no—
188#462—791no—
189#452—791no—
190#452D7911yescharacteristic
191#451—791no—
192#451—791no—
193#433—791no—
194C2×#41C2×D7911yescharacteristic
195C22×Q8—791no—
196C2×Q16—791no—
197C2×Q16—791no—
198C2×Q16—791no—
199C2×Q16—791no—
200C2×Q16—791no—
201C2×Q16C2×D7911yescharacteristic
202C2×SD16—791no—
203C2×SD16C2×D7911yescharacteristic
204C4⋊Q8—791no—
205C4⋊Q8—791no—
206C4⋊Q8—791no—
207#126—1581no—
208#126—1581no—
209#125—791no—
210#125—1581no—
211#125—1581no—
212#124—791no—
213#124—791no—
214#123—1581no—
215#123—1581no—
216C22⋊Q8—791no—
217C22⋊Q8—1581no—
218C22⋊Q8—1581no—
219C22⋊Q8C2×D7911yescharacteristic
220C4×Q8—791no—
221C4×Q8—791no—
222#117—791no—
223C4⋊C8—791no—
224C4⋊C8—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103C2×D7911yescharacteristic
231#102—791no—
232#102C2×D7911yescharacteristic
233C22⋊C8—791no—
234C22⋊C8C2×D7911yescharacteristic
235#97—791no—
236C4×C8—791no—
237#41—41no—
238#41—41no—
239C2×Q8—3161no—
240C2×Q8—3161no—
241C2×Q8—791no—
242C2×Q8—791no—
243C2×Q8—791no—
244C2×Q8—1581no—
245C2×Q8C22×D7911yescharacteristic
246C2×Q8C22×D7911yescharacteristic
247C2×D4—21no—
248C2×D4C22×D7911yescharacteristic
249C22×C4—21no—
250C22×C4—1581no—
251C22×C4C22×D7911yescharacteristic
252Q16—41no—
253Q16—3161no—
254Q16—3161no—
255Q16—3161no—
256Q16—3161no—
257Q16—3161no—
258SD16—41no—
259SD16—3161no—
260C2×C8—791no—
261C2×C8—791no—
262C2×C8C22×D7911yescharacteristic
263C2×C8C22×D7911yescharacteristic
264C4⋊C4—21no—
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⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4C22×D7911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—791no—
282C22⋊C4—791no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C42—791no—
289C42—791no—
290C42—1581no—
291C42—1581no—
292C23—21no—
293C23D4×D7911yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—3162no—
299Q8—1581no—
300Q8—1581no—
301Q8—1581no—
302Q8—1581no—
303Q8—1581no—
304Q8—1581no—
305D4—21no—
306D4—21no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—3162no—
315C2×C4—791no—
316C2×C4—791no—
317C2×C4—791no—
318C2×C4—791no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4D4×D7911yescharacteristic
324C2×C4C23×D7911yescharacteristic
325C8—21no—
326C8—21no—
327C8—1581no—
328C8—1581no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D7911yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—3161no—
341C4—3161no—
342C4—3161no—
343C4—3161no—
344C4—1581no—
345C4—1581no—
346C4—1581no—
347C4—1581no—
348C4#1457920611yescharacteristic
349C4#1457920611yescharacteristic
350C2—41no—
351C2—81no—
352C2#1909912811yescharacteristic
353C2#1909937711yescharacteristic
354C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#452×C79C2
socleC22×C79C22×D4
prime radicalC2×#41×C79C22
hypercenter#452D79
hypocenterC79#3223
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #19099173C2semidirect
3. #19098954C2semidirect
4. #19098941C2semidirect
5. #19098930C2semidirect
6. #19098916C2semidirect
7. #19098784C2semidirect
8. #19098783C2semidirect
9. #19098772C2semidirect
10. #19098771C2semidirect
12. #19098721C2semidirect
13. #19098718C2semidirect
14. #19098621C2semidirect
178. C79#3223semidirect