Finite Group Databasebeta

← #23774080

Subgroups — #23774080

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#19099182C211yesmaximal, characteristic, complemented
2#19099167C211yesmaximal, characteristic, complemented
3#19098972C211yesmaximal, characteristic, complemented
4#19098917C211yesmaximal, characteristic, complemented
5#19098909C211yesmaximal, characteristic, complemented
6#19098813C211yesmaximal, characteristic, complemented
7#19098806C211yesmaximal, characteristic, complemented
8#19098796C211yesmaximal, characteristic, complemented
9#19098789C211yesmaximal, characteristic, complemented
10#19098675C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12SD16×Dic79C211yesmaximal, characteristic, complemented
13D8×Dic79C211yesmaximal, characteristic, complemented
14#19098520C211yesmaximal, characteristic, complemented
15#496×C79C211yesmaximal, characteristic, complemented
16C2×#11929607C2211yescharacteristic
17C2×C8×D79C2211yescharacteristic
18#14579161C2211yescharacteristic
19#14579154—21no—
20#14579153C2211yescharacteristic
21#14579147—21no—
22#14579145—21no—
23#14579142—21no—
24#14579142—21no—
25#14579138—21no—
26#14579137C2211yescharacteristic
27#14579133—21no—
28#14579133—21no—
29#14579132C2211yescharacteristic
30#14579132C2211yescharacteristic
31#14579132C2211yescharacteristic
32Q8×Dic79C2211yescharacteristic
33D4×Dic79C2211yescharacteristic
34D4×Dic79C2211yescharacteristic
35D4×Dic79C2211yescharacteristic
36#14579118C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579095C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579093C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579085C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579082C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579071C2211yescharacteristic
50C4×C79⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×SD16×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×D8×C79C2211yescharacteristic
55C2×D8×C79C2211yescharacteristic
56#127×C79C2211yescharacteristic
57#124×C79C2211yescharacteristic
58#97×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×C22⋊D79—21no—
61C2×C22⋊D79—21no—
62C2×C22⋊D79—21no—
63C22×Dic79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C2×C4×D79C2311yescharacteristic
67#11929607—22no—
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C8×D79—22no—
71C4⋊Dic79—21no—
72C4⋊Dic79—21no—
73C4⋊Dic79C2311yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4D411yescharacteristic
81Dic79⋊C4D411yescharacteristic
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4D411yescharacteristic
90(C2×D79)⋊C4D411yescharacteristic
91C4×Dic79—21no—
92C4×Dic79C2311yescharacteristic
93C2×Q8×C79C2311yescharacteristic
94C2×D4×C79—21no—
95C2×D4×C79—21no—
96C2×D4×C79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C2×D4×C79C2311yescharacteristic
99SD16×C79—22no—
100SD16×C79—22no—
101D8×C79—22no—
102D8×C79—22no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C22×D79C2×D411yescharacteristic
112Q8×C79—21no—
113Q8×C79—21no—
114D4×C79—21no—
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—81no—
121D4×C79—81no—
122C2×C4×C79—21no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C22⋊D79—81no—
127C22⋊D79—81no—
128C22⋊D79—81no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C2×Dic79—81no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C4×D79—21no—
140C4×D79—21no—
141Dic158—81no—
142C8×C79#4112yes—
143C8×C79#4112yes—
144C79⋊C8—21no—
145C79⋊C8—21no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79C22×D411yescharacteristic
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—21no—
159C4×C79—21no—
160C4×C79—21no—
161C4×C79—41no—
162C4×C79C2×#4111yescharacteristic
163C4×C79C2×#4111yescharacteristic
164Dic79—21no—
165Dic79—21no—
166Dic79—21no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171C2×C79—81no—
172C2×C79—81no—
173C2×C79—81no—
174C2×C79#53211yescharacteristic
175C2×C79#57611yescharacteristic
176C2×C79#57711yescharacteristic
177D79—41no—
178#3179—791nomaximal, Sylow
179C79#317911yescharacteristic, complemented, Sylow
180#542—791no—
181#540—791no—
182#501—791no—
183#496D7911yescharacteristic, complemented
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#405—791no—
195C2×SD16C2×D7911yescharacteristic
196C2×SD16C2×D7911yescharacteristic
197C2×D8C2×D7911yescharacteristic
198C2×D8C2×D7911yescharacteristic
199C2×M16—791no—
200C22×C8—791no—
201C4⋊Q8—791no—
202#127C2×D7911yescharacteristic
203#126—1581no—
204#125—791no—
205#124—1581no—
206#124C2×D7911yescharacteristic
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#117—791no—
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#97—791no—
235#97C2×D7911yescharacteristic
236C4×C8—791no—
237C4×C8—791no—
238C2×Q8—1581no—
239C2×Q8C22×D7911yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—1581no—
243C2×D4—1581no—
244C2×D4—1581no—
245C2×D4C22×D7911yescharacteristic
246C2×D4C22×D7911yescharacteristic
247C2×D4C22×D7911yescharacteristic
248C22×C4—791no—
249C22×C4—1581no—
250C22×C4—1581no—
251C22×C4—1581no—
252SD16—22no—
253SD16—22no—
254D8—22no—
255D8—22no—
256M16—1582no—
257C2×C8—791no—
258C2×C8—791no—
259C2×C8—1582no—
260C2×C8C22×D7911yescharacteristic
261C2×C8C22×D7911yescharacteristic
262C4⋊C4—791no—
263C4⋊C4—791no—
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—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—791no—
276C22⋊C4—791no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C42—791no—
285C42—1581no—
286C42C22×D7911yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—791no—
291Q8—21no—
292Q8—21no—
293Q8—6321no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—6321no—
303D4—6321no—
304D4—6321no—
305C2×C4—21no—
306C2×C4—791no—
307C2×C4—791no—
308C2×C4—791no—
309C2×C4—6321no—
310C2×C4—6321no—
311C2×C4—6321no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4D4×D7911yescharacteristic
319C2×C4D4×D7911yescharacteristic
320C2×C4C23×D7911yescharacteristic
321C8—1581no—
322C8—1581no—
323C8#1192962312yes—
324C8#1192962312yes—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1581no—
335C22—1581no—
336C22—1581no—
337C22C2×D4×D7911yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—3161no—
342C4—3161no—
343C4—3161no—
344C4—3161no—
345C4—1581no—
346C4—1581no—
347C4—1581no—
348C4C2×#1192962311yescharacteristic
349C4C2×#1192962311yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—3161no—
354C2#1909911111yescharacteristic
355C2#1909936711yescharacteristic
356C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#496×C79C2
socleC22×C79C22×D4
hypercenter#496D79
hypocenterC79#3179
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #19099182C2semidirect
2. #19099167C2semidirect
3. #19098972C2semidirect
4. #19098917C2semidirect
5. #19098909C2semidirect
6. #19098813C2semidirect
7. #19098806C2semidirect
8. #19098796C2semidirect
9. #19098789C2semidirect
10. #19098675C2semidirect
11. #19098664C2semidirect
12. SD16×Dic79C2semidirect
13. D8×Dic79C2semidirect
14. #19098520C2semidirect
15. #496×C79C2semidirect
179. C79#3179semidirect
183. #496D79semidirect