Finite Group Databasebeta

← #23774083

Subgroups — #23774083

Order 10112.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099184C211yesmaximal, characteristic, complemented
2#19099168C211yesmaximal, characteristic, complemented
3#19098972C211yesmaximal, characteristic, complemented
4#19098952C211yesmaximal, characteristic, complemented
5#19098918C211yesmaximal, characteristic, complemented
6#19098910C211yesmaximal, characteristic, complemented
7#19098816C211yesmaximal, characteristic, complemented
8#19098809C211yesmaximal, characteristic, complemented
9#19098799C211yesmaximal, characteristic, complemented
10#19098792C211yesmaximal, characteristic, complemented
11#19098676C211yesmaximal, characteristic, complemented
12#19098665C211yesmaximal, characteristic, complemented
13C4×#11929613C211yesmaximal, characteristic, complemented
14C4×D632C211yesmaximal, characteristic, complemented
15#405×C79C211yesmaximal, characteristic, complemented
16C2×#11929613C2211yescharacteristic
17C2×#11929613C2211yescharacteristic
18C2×D632C2211yescharacteristic
19C2×D632C2211yescharacteristic
20#14579161C2211yescharacteristic
21#14579158C2211yescharacteristic
22#14579156—21no—
23#14579153C2211yescharacteristic
24#14579149C2211yescharacteristic
25#14579147—21no—
26#14579146—21no—
27#14579146—21no—
28#14579143—21no—
29#14579140C2211yescharacteristic
30#14579139—21no—
31#14579135C2211yescharacteristic
32#14579135C2211yescharacteristic
33#14579135C2211yescharacteristic
34#14579134—21no—
35#14579134—21no—
36C4×Dic158C2211yescharacteristic
37C4×D316C2211yescharacteristic
38C4×D316C2211yescharacteristic
39C4×D316C2211yescharacteristic
40#14579095C2211yescharacteristic
41#14579095C2211yescharacteristic
42#14579093C2211yescharacteristic
43#14579093C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579086C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic
52C2×M16×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54#117×C79C2211yescharacteristic
55#97×C79C2211yescharacteristic
56#97×C79C2211yescharacteristic
57C4×C8×C79C2211yescharacteristic
58C4×C8×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C2×D316—21no—
62C2×D316—21no—
63C2×D316C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72#11929613—22no—
73#11929613—22no—
74D632—22no—
75D632—22no—
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85C22⋊Dic79—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—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—
93(C2×D79)⋊C4—21no—
94C4×Dic79—21no—
95C22×C4×C79C2311yescharacteristic
96M16×C79—22no—
97C2×C8×C79—22no—
98C2×C8×C79C2311yescharacteristic
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79D411yescharacteristic
103C4⋊C4×C79D411yescharacteristic
104C22⋊C4×C79D411yescharacteristic
105C22⋊C4×C79D411yescharacteristic
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79C2×D411yescharacteristic
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—21no—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79C2×D411yescharacteristic
115C2×C4×C79C2×D411yescharacteristic
116C2×C4×C79C2×D411yescharacteristic
117C2×C4×C79C2×D411yescharacteristic
118C2×C4×C79C2×D411yescharacteristic
119C2×C4×C79C2411yescharacteristic
120C22⋊D79—81no—
121C22⋊D79—81no—
122C22⋊D79—81no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128D316—21no—
129D316—21no—
130D316—21no—
131D316—21no—
132D316—21no—
133D316—21no—
134D316—81no—
135D316—81no—
136C4×D79—81no—
137C4×D79—81no—
138C4×D79—81no—
139Dic158—21no—
140Dic158—21no—
141Dic158—81no—
142C8×C79—21no—
143C8×C79—21no—
144C8×C79#4112yes—
145C8×C79#4112yes—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79C22×D411yescharacteristic
150C2×D79—41no—
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C4×C79—21no—
160C4×C79—21no—
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—21no—
164C4×C79C2×#4111yescharacteristic
165C4×C79C2×#4111yescharacteristic
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171C2×C79—41no—
172C2×C79#53211yescharacteristic
173C2×C79#57611yescharacteristic
174C2×C79#57711yescharacteristic
175D79—81no—
176D79—81no—
177D79—81no—
178#3179—791nomaximal, Sylow
179C79#317911yescharacteristic, complemented, Sylow
180#542—791no—
181#540—791no—
182#501—791no—
183#496—791no—
184#488—791no—
185#486—791no—
186#469—791no—
187#468—791no—
188#466—791no—
189#465—791no—
190#442—791no—
191#440—791no—
192C4×SD16—791no—
193C4×D8—791no—
194#405D7911yescharacteristic, complemented
195C2×SD16—791no—
196C2×SD16—791no—
197C2×D8—791no—
198C2×D8—791no—
199C2×M16C2×D7911yescharacteristic
200C22×C8C2×D7911yescharacteristic
201C4⋊Q8—791no—
202#127—791no—
203#126—1581no—
204#125—791no—
205#124—791no—
206#124—1581no—
207#123—1581no—
208#123—1581no—
209#123—1581no—
210C22⋊Q8—791no—
211C22⋊Q8—1581no—
212#121—791no—
213#121—791no—
214#121—791no—
215#121—1581no—
216#121—1581no—
217C4×Q8—791no—
218C4×D4—791no—
219C4×D4—791no—
220C4×D4—791no—
221#117C2×D7911yescharacteristic
222#107—791no—
223#107—791no—
224#106—791no—
225#106—791no—
226#103—791no—
227#103—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#97C2×D7911yescharacteristic
235#97C2×D7911yescharacteristic
236C4×C8C2×D7911yescharacteristic
237C4×C8C2×D7911yescharacteristic
238C2×Q8—791no—
239C2×Q8—1581no—
240C2×D4—791no—
241C2×D4—791no—
242C2×D4—791no—
243C2×D4—1581no—
244C2×D4—1581no—
245C2×D4—1581no—
246C2×D4—1581no—
247C2×D4—1581no—
248C22×C4—1581no—
249C22×C4—1581no—
250C22×C4—1581no—
251C22×C4C22×D7911yescharacteristic
252SD16—1582no—
253SD16—1582no—
254D8—1582no—
255D8—1582no—
256M16—22no—
257C2×C8—22no—
258C2×C8C22×D7911yescharacteristic
259C2×C8C22×D7911yescharacteristic
260C2×C8C22×D7911yescharacteristic
261C2×C8C22×D7911yescharacteristic
262C4⋊C4—791no—
263C4⋊C4—791no—
264C4⋊C4—791no—
265C4⋊C4—791no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4D31611yescharacteristic
272C4⋊C4D31611yescharacteristic
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4D31611yescharacteristic
283C22⋊C4D31611yescharacteristic
284C42—1581no—
285C42C22×D7911yescharacteristic
286C42C22×D7911yescharacteristic
287C23—1581no—
288C23—1581no—
289C23—1581no—
290C23C2×D31611yescharacteristic
291Q8—6321no—
292Q8—1581no—
293Q8—1581no—
294D4—6321no—
295D4—6321no—
296D4—6321no—
297D4—6321no—
298D4—6321no—
299D4—1581no—
300D4—1581no—
301D4—1581no—
302D4—1581no—
303D4—1581no—
304D4—1581no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—6321no—
308C2×C4—6321no—
309C2×C4—6321no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4C2×D31611yescharacteristic
316C2×C4C2×D31611yescharacteristic
317C2×C4C2×D31611yescharacteristic
318C2×C4C2×D31611yescharacteristic
319C2×C4C2×D31611yescharacteristic
320C2×C4C23×D7911yescharacteristic
321C8—21no—
322C8—21no—
323C8#1192962412yes—
324C8#1192962412yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—3161no—
329C22—3161no—
330C22—3161no—
331C22—3161no—
332C22—3161no—
333C22—3161no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22C22×D31611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—3161no—
344C4—3161no—
345C4—3161no—
346C4—3161no—
347C4—3161no—
348C4C2×#1192962411yescharacteristic
349C4C2×#1192962411yescharacteristic
350C2—41no—
351C2—6321no—
352C2—6321no—
353C2—6321no—
354C2#1909911311yescharacteristic
355C2#1909936811yescharacteristic
356C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#405×C79C2
socleC22×C79C22×D4
hypercenter#405D79
hypocenterC79#3179
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #19099184C2semidirect
2. #19099168C2semidirect
3. #19098972C2semidirect
4. #19098952C2semidirect
5. #19098918C2semidirect
6. #19098910C2semidirect
7. #19098816C2semidirect
8. #19098809C2semidirect
9. #19098799C2semidirect
10. #19098792C2semidirect
11. #19098676C2semidirect
12. #19098665C2semidirect
13. C4×#11929613C2semidirect
14. C4×D632C2semidirect
15. #405×C79C2semidirect
179. C79#3179semidirect
194. #405D79semidirect