Finite Group Databasebeta

← #23774811

Subgroups — #23774811

Order 10112.

358 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#19099168C211yesmaximal, characteristic, complemented
2#19098870C211yesmaximal, characteristic, complemented
3#19098863C211yesmaximal, characteristic, complemented
4#19098850C211yesmaximal, characteristic, complemented
5#19098840C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098797C211yesmaximal, characteristic, complemented
9#19098794C211yesmaximal, characteristic, complemented
10#19098775C211yesmaximal, characteristic, complemented
11#19098775C211yesmaximal, characteristic, complemented
12#19098763C211yesmaximal, characteristic, complemented
13#19098758C211yesmaximal, characteristic, complemented
14#19098590C211yesmaximal, characteristic, complemented
15#542×C79C211yesmaximal, characteristic, complemented
16C2×#11929611C2211yescharacteristic
17C2×#11929611C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929608C2211yescharacteristic
21C22×C79⋊C8C2211yescharacteristic
22#14579158C2211yescharacteristic
23#14579153C2211yescharacteristic
24#14579146—21no—
25#14579146—21no—
26#14579135C2211yescharacteristic
27#14579135C2211yescharacteristic
28#14579134—21no—
29#14579134—21no—
30C4×D316C2211yescharacteristic
31C4×D316C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579094C2211yescharacteristic
34#14579092C2211yescharacteristic
35#14579092C2211yescharacteristic
36C4⋊(C79⋊C8)C2211yescharacteristic
37C4⋊(C79⋊C8)C2211yescharacteristic
38C4⋊(C79⋊C8)C2211yescharacteristic
39C4⋊(C79⋊C8)C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579081C2211yescharacteristic
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic
48C4⋊Q8×C79C2211yescharacteristic
49#126×C79—21no—
50#124×C79—21no—
51#124×C79C2211yescharacteristic
52#123×C79—21no—
53C22⋊Q8×C79—21no—
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79C2211yescharacteristic
58#117×C79C2211yescharacteristic
59C2×D316—21no—
60C2×D316—21no—
61C2×D316C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C4×D79—21no—
66C2×C4×D79—21no—
67#11929611—41no—
68#11929611—41no—
69#11929609—41no—
70#11929609—41no—
71#11929608—41no—
72C2×C79⋊C8—41no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84(C2×D79)⋊C4—21no—
85C2×Q8×C79—21no—
86C2×Q8×C79C2311yescharacteristic
87C2×D4×C79—21no—
88C2×D4×C79C2311yescharacteristic
89C22×C4×C79—21no—
90C22×C4×C79C2311yescharacteristic
91C4⋊C4×C79—21no—
92C4⋊C4×C79—21no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79D411yescharacteristic
95C4⋊C4×C79D411yescharacteristic
96C4⋊C4×C79C2311yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C22⋊C4×C79—21no—
99C22⋊C4×C79—21no—
100C22⋊C4×C79—21no—
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C22⋊C4×C79D411yescharacteristic
104C22⋊C4×C79D411yescharacteristic
105C42×C79—21no—
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111C22×D79—21no—
112Q8×C79—21no—
113Q8×C79—21no—
114Q8×C79—81no—
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—81no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—81no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—81no—
131C22⋊D79—81no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134D316—21no—
135D316—21no—
136D316—21no—
137D316—21no—
138D316—81no—
139D316—81no—
140C4×D79—81no—
141C4×D79—81no—
142C79⋊C8—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C79⋊C8—21no—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79C22×D411yescharacteristic
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×C79—41no—
165C4×C79—41no—
166C4×C79—41no—
167C4×C79H(5,𝔽2)11yescharacteristic
168C4×C792−1+411yescharacteristic
169Dic79—41no—
170Dic79—41no—
171C2×C79—41no—
172C2×C79—81no—
173C2×C79#53711yescharacteristic
174C2×C79#57611yescharacteristic
175C2×C79#57711yescharacteristic
176D79—81no—
177D79—81no—
178#3257—791nomaximal, Sylow
179C79#325711yescharacteristic, complemented, Sylow
180#542D7911yescharacteristic, complemented
181#540—791no—
182#479—791no—
183#478—791no—
184#476—791no—
185#474—791no—
186#469—791no—
187#468—791no—
188#466—791no—
189#465—791no—
190#463—791no—
191#463—791no—
192#460—791no—
193#459—791no—
194#424—791no—
195C2×SD16—791no—
196C2×SD16—791no—
197C2×D8—791no—
198C2×D8—791no—
199C2×M16—791no—
200C22×C8—791no—
201C4⋊Q8C2×D7911yescharacteristic
202#127—791no—
203#126—21no—
204#125—791no—
205#124—21no—
206#124C2×D7911yescharacteristic
207#123—21no—
208#123—1581no—
209#123—1581no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D7911yescharacteristic
212#121—791no—
213#121—791no—
214#121—1581no—
215#121—1581no—
216#121C2×D7911yescharacteristic
217C4×Q8C2×D7911yescharacteristic
218C4×D4—791no—
219C4×D4—791no—
220C4×D4C2×D7911yescharacteristic
221#117C2×D7911yescharacteristic
222#107—791no—
223#107—791no—
224#106—791no—
225#106—791no—
226C4⋊C8—791no—
227C4⋊C8—791no—
228C4⋊C8—791no—
229C4⋊C8—791no—
230#103—791no—
231#103—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102—791no—
236#102—791no—
237#102—791no—
238C2×Q8—21no—
239C2×Q8C22×D7911yescharacteristic
240C2×D4—21no—
241C2×D4—791no—
242C2×D4—791no—
243C2×D4—1581no—
244C2×D4—1581no—
245C2×D4—1581no—
246C2×D4—1581no—
247C2×D4C22×D7911yescharacteristic
248C22×C4—21no—
249C22×C4—1581no—
250C22×C4—1581no—
251C22×C4C22×D7911yescharacteristic
252SD16—3161no—
253SD16—3161no—
254D8—3161no—
255D8—3161no—
256M16—3161no—
257C2×C8—3161no—
258C2×C8—791no—
259C2×C8—791no—
260C2×C8—791no—
261C2×C8—791no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4C22⋊D7911yescharacteristic
270C4⋊C4C22⋊D7911yescharacteristic
271C4⋊C4C22×D7911yescharacteristic
272C4⋊C4C22×D7911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4C22⋊D7911yescharacteristic
283C22⋊C4C22⋊D7911yescharacteristic
284C42—21no—
285C42C22×D7911yescharacteristic
286C42C22×D7911yescharacteristic
287C23—21no—
288C23—1581no—
289C23—1581no—
290C23C2×C22⋊D7911yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—6321no—
298D4—6321no—
299D4—6321no—
300D4—6321no—
301D4—1581no—
302D4—1581no—
303D4—1581no—
304D4—1581no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—6321no—
312C2×C4—6321no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4C2×C22⋊D7911yescharacteristic
316C2×C4C2×C22⋊D7911yescharacteristic
317C2×C4C2×C22⋊D7911yescharacteristic
318C2×C4C2×C22⋊D7911yescharacteristic
319C2×C4C2×C22⋊D7911yescharacteristic
320C2×C4C23×D7911yescharacteristic
321C8—1581no—
322C8—1581no—
323C8—1581no—
324C8—1581no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—3161no—
332C22—3161no—
333C22—3161no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22C22×C22⋊D7911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3161no—
347C4—3161no—
348C4#1457920711yescharacteristic
349C4#1457920811yescharacteristic
350C2—41no—
351C2—81no—
352C2—6321no—
353C2—6321no—
354C2#1909914111yescharacteristic
355C2#1909936611yescharacteristic
356C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#542×C79C2
socleC22×C79C22×D4
hypercenter#542D79
hypocenterC79#3257
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #19099168C2semidirect
2. #19098870C2semidirect
3. #19098863C2semidirect
4. #19098850C2semidirect
5. #19098840C2semidirect
6. #19098814C2semidirect
7. #19098811C2semidirect
8. #19098797C2semidirect
9. #19098794C2semidirect
10. #19098775C2semidirect
11. #19098775C2semidirect
12. #19098763C2semidirect
13. #19098758C2semidirect
14. #19098590C2semidirect
15. #542×C79C2semidirect
179. C79#3257semidirect
180. #542D79semidirect