Finite Group Databasebeta

← #23773601

Subgroups — #23773601

Order 10112.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099168C211yesmaximal, characteristic, complemented
2#19099043C211yesmaximal, characteristic, complemented
3#19098882C211yesmaximal, characteristic, complemented
4#19098877C211yesmaximal, characteristic, complemented
5#19098871C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098764C211yesmaximal, characteristic, complemented
8#19098759C211yesmaximal, characteristic, complemented
9#19098710C211yesmaximal, characteristic, complemented
10#19098710C211yesmaximal, characteristic, complemented
11#19098676C211yesmaximal, characteristic, complemented
12#19098665C211yesmaximal, characteristic, complemented
13C4×#11929613C211yesmaximal, characteristic, complemented
14C4×D632C211yesmaximal, characteristic, complemented
15#433×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929613C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×D632C2211yescharacteristic
20C2×D632C2211yescharacteristic
21#14579158C2211yescharacteristic
22#14579153C2211yescharacteristic
23#14579146—21no—
24#14579146—21no—
25#14579135C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579134—21no—
28#14579134—21no—
29C4×Dic158C2211yescharacteristic
30C4×Dic158C2211yescharacteristic
31C4×D316C2211yescharacteristic
32C4×D316C2211yescharacteristic
33C4×D316C2211yescharacteristic
34C4×D316C2211yescharacteristic
35(C22⋊D79)⋊C4—21no—
36(C22⋊D79)⋊C4—21no—
37#14579119—21no—
38C2×C4⋊Dic79C2211yescharacteristic
39C4⋊C4×D79—21no—
40#14579095C2211yescharacteristic
41#14579095C2211yescharacteristic
42#14579093C2211yescharacteristic
43#14579093C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579086C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic
52#117×C79C2211yescharacteristic
53C4⋊C8×C79C2211yescharacteristic
54C4⋊C8×C79C2211yescharacteristic
55C22⋊C8×C79C2211yescharacteristic
56C22⋊C8×C79C2211yescharacteristic
57#97×C79C2211yescharacteristic
58C4×C8×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61C2×Dic158C2311yescharacteristic
62C2×D316—21no—
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C22×Dic79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76#11929613—22no—
77#11929613—22no—
78D632—22no—
79D632—22no—
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊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—
94(C2×D79)⋊C4—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C22×C4×C79C2311yescharacteristic
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—24no—
121C22⋊D79—81no—
122C22⋊D79—81no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—81no—
129D316—21no—
130D316—21no—
131D316—21no—
132D316—21no—
133D316—21no—
134D316—81no—
135D316—81no—
136D316#4112yes—
137C4×D79—24no—
138C4×D79—81no—
139C4×D79—81no—
140C4×D79—81no—
141C4×D79—81no—
142Dic158—21no—
143Dic158#4112yes—
144C8×C79—21no—
145C8×C79—21no—
146C8×C79—21no—
147C8×C79—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79C22×D411yescharacteristic
152C2×D79—22no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C2×D79—41no—
160C2×D79—41no—
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—21no—
164C4×C79—21no—
165C4×C79—21no—
166C4×C79C2×#4111yescharacteristic
167C4×C79C2×#4111yescharacteristic
168Dic79—22no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173C2×C79—41no—
174C2×C79#52511yescharacteristic
175C2×C79#57611yescharacteristic
176C2×C79#57711yescharacteristic
177D79—42no—
178D79—81no—
179D79—81no—
180#3119—791nomaximal, Sylow
181C79#311911yescharacteristic, complemented, Sylow
182#540—791no—
183#520—791no—
184#481—791no—
185#480—791no—
186#479—791no—
187#478—791no—
188#460—791no—
189#459—791no—
190#449—791no—
191#449—791no—
192#442—791no—
193#440—791no—
194C4×SD16—791no—
195C4×D8—791no—
196#433D7911yescharacteristic, complemented
197C2×#41—791no—
198C2×SD16—791no—
199C2×SD16—791no—
200C2×D8—791no—
201C2×D8—791no—
202#127—791no—
203#125—791no—
204#123—1581no—
205#123—1581no—
206#121—791no—
207#121—791no—
208#121—1581no—
209#121—1581no—
210C4×Q8—791no—
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—1581no—
217C4×D4—1581no—
218#117—1581no—
219#117C2×D7911yescharacteristic
220C2×C4⋊C4—791no—
221C2×C4⋊C4—1581no—
222#107—791no—
223#107—791no—
224#106—791no—
225#106—791no—
226C4⋊C8C2×D7911yescharacteristic
227C4⋊C8C2×D7911yescharacteristic
228#103—791no—
229#103—791no—
230#102—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102—791no—
236C22⋊C8C2×D7911yescharacteristic
237C22⋊C8C2×D7911yescharacteristic
238#97C2×D7911yescharacteristic
239C4×C8C2×D7911yescharacteristic
240#41—1582no—
241#41—1582no—
242C2×Q8—791no—
243C2×D4—791no—
244C2×D4—791no—
245C2×D4—791no—
246C2×D4—1581no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4—1581no—
250C2×D4—1581no—
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258SD16—1582no—
259SD16—1582no—
260D8—1582no—
261D8—1582no—
262C2×C8C22×D7911yescharacteristic
263C2×C8C22×D7911yescharacteristic
264C2×C8C22×D7911yescharacteristic
265C2×C8C22×D7911yescharacteristic
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4D31611yescharacteristic
276C4⋊C4D31611yescharacteristic
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4D31611yescharacteristic
284C22⋊C4D31611yescharacteristic
285C42—1581no—
286C42—1581no—
287C42C22×D7911yescharacteristic
288C42C22×D7911yescharacteristic
289C23—1581no—
290C23—1581no—
291C23—1581no—
292C23C2×D31611yescharacteristic
293Q8—792no—
294Q8—1581no—
295D4—792no—
296D4—6321no—
297D4—6321no—
298D4—6321no—
299D4—6321no—
300D4—1584no—
301D4—1581no—
302D4—1581no—
303D4—1581no—
304D4—1581no—
305D4—1581no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—6321no—
309C2×C4—6321no—
310C2×C4—6321no—
311C2×C4—6321no—
312C2×C4—6321no—
313C2×C4—1584no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4C2×D31611yescharacteristic
320C2×C4C2×D31611yescharacteristic
321C2×C4C2×D31611yescharacteristic
322C2×C4C2×D31611yescharacteristic
323C2×C4C2×D31611yescharacteristic
324C2×C4C23×D7911yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—3161no—
333C22—3161no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22—3161no—
338C22—3161no—
339C22—3161no—
340C22—1582no—
341C22C22×D31611yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—3161no—
348C4—3161no—
349C4—3161no—
350C4—3161no—
351C4—1582no—
352C4#41×D7911yescharacteristic
353C4#41×D7911yescharacteristic
354C2—41no—
355C2—3162no—
356C2—6321no—
357C2—6321no—
358C2#1909907511yescharacteristic
359C2#1909936811yescharacteristic
360C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#433×C79C2
socleC22×C79C22×D4
hypercenter#433D79
hypocenterC79#3119
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19099168C2semidirect
2. #19099043C2semidirect
3. #19098882C2semidirect
4. #19098877C2semidirect
5. #19098871C2semidirect
6. #19098864C2semidirect
7. #19098764C2semidirect
8. #19098759C2semidirect
9. #19098710C2semidirect
10. #19098710C2semidirect
11. #19098676C2semidirect
12. #19098665C2semidirect
13. C4×#11929613C2semidirect
14. C4×D632C2semidirect
15. #433×C79C2semidirect
181. C79#3119semidirect
196. #433D79semidirect