Finite Group Databasebeta

← #23773390

Subgroups — #23773390

Order 10112.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099142C211yesmaximal, characteristic
2#19099044C211yesmaximal, characteristic, complemented
3#19098907C211yesmaximal, characteristic, complemented
4#19098905C211yesmaximal, characteristic, complemented
5#19098895C211yesmaximal, characteristic, complemented
6#19098893C211yesmaximal, characteristic, complemented
7#19098885C211yesmaximal, characteristic, complemented
8#19098884C211yesmaximal, characteristic, complemented
9#19098880C211yesmaximal, characteristic, complemented
10#19098602C211yesmaximal, characteristic, complemented
11#106×D79C211yesmaximal, characteristic, complemented
12#19098561C211yesmaximal, characteristic, complemented
13#19098556C211yesmaximal, characteristic, complemented
14#19098528C211yesmaximal, characteristic, complemented
15#481×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929623C2211yescharacteristic
18C2×#11929607C2211yescharacteristic
19C2×C8×D79C2211yescharacteristic
20#14579141C2211yescharacteristic
21#14579140C2211yescharacteristic
22#14579138—21no—
23#14579134—21no—
24#14579133—21no—
25#14579132—21no—
26#14579132C2211yescharacteristic
27#14579126—21no—
28#14579123—21no—
29C4×C22⋊D79—21no—
30C4×C22⋊D79—21no—
31#14579120C2211yescharacteristic
32#14579119C2211yescharacteristic
33#14579119C2211yescharacteristic
34C4⋊C4×D79C2211yescharacteristic
35C4⋊C4×D79C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579094C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41#14579092C2211yescharacteristic
42#14579092C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579084C2211yescharacteristic
46#14579084C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52#121×C79C2211yescharacteristic
53C2×C4⋊C4×C79C2211yescharacteristic
54#106×C79C2211yescharacteristic
55#106×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61#11929623—22no—
62#11929623—22no—
63C2×Dic158D411yescharacteristic
64C2×Dic158C2311yescharacteristic
65C2×D316D411yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79D411yescharacteristic
69C2×C22⋊D79D411yescharacteristic
70C22×Dic79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79C2311yescharacteristic
75C2×C4×D79C2311yescharacteristic
76#11929607—22no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C8×D79—22no—
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C22×C4×C79—21no—
100C22×C4×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79—21no—
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79C2×D411yescharacteristic
111C22×D79C2×D411yescharacteristic
112D4×C79—21no—
113D4×C79—21no—
114D4×C79—81no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—81no—
121C2×C4×C79C2×D411yescharacteristic
122C2×C4×C79C2411yescharacteristic
123C22⋊D79—22no—
124C22⋊D79—22no—
125C22⋊D79—42no—
126C22⋊D79—81no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—42no—
132C2×Dic79C2×D411yescharacteristic
133C2×Dic79C2×D411yescharacteristic
134D316—22no—
135C4×D79—21no—
136C4×D79—21no—
137C4×D79—81no—
138C4×D79—81no—
139C4×D79—81no—
140C4×D79#4112yes—
141C4×D79#4112yes—
142Dic158—22no—
143Dic158—21no—
144Dic158—21no—
145C8×C79—21no—
146C8×C79—21no—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79C22×D411yescharacteristic
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—21no—
159C2×D79—21no—
160C2×D79—21no—
161C2×D79#12312yes—
162C4×C79—21no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79C2×#4111yescharacteristic
167C4×C79C2×#4111yescharacteristic
168Dic79—21no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173Dic79#12312yes—
174C2×C79—41no—
175C2×C79—81no—
176C2×C79C2×#12311yescharacteristic
177C2×C79#57711yescharacteristic
178C2×C79#57711yescharacteristic
179D79—22no—
180D79—41no—
181#3099—791nomaximal, Sylow
182C79#309911yescharacteristic, complemented, Sylow
183#537—791no—
184#520—791no—
185#485—791no—
186#485—791no—
187#483—791no—
188#483—791no—
189#482—791no—
190#482—791no—
191#481—791no—
192#481D7911yescharacteristic, complemented
193#428—791no—
194C2×#106—791no—
195#417—791no—
196#416—791no—
197#408—791no—
198C2×#41—791no—
199C2×#41—791no—
200C2×M16—791no—
201C22×C8—791no—
202C22⋊Q8—791no—
203C22⋊Q8—791no—
204C22⋊Q8—1581no—
205#121—791no—
206#121—1581no—
207#121—1581no—
208#121—1581no—
209#121C2×D7911yescharacteristic
210C4×Q8—1581no—
211C4×D4—1581no—
212C4×D4—1581no—
213C4×D4—1581no—
214#117—791no—
215#117—791no—
216#117—791no—
217C2×C4⋊C4—791no—
218C2×C4⋊C4—791no—
219C2×C4⋊C4—791no—
220C2×C4⋊C4C2×D7911yescharacteristic
221#107—791no—
222#107—791no—
223#106—791no—
224#106—791no—
225#106—791no—
226#106—791no—
227#106C2×D7911yescharacteristic
228#106C2×D7911yescharacteristic
229#103—791no—
230#103—791no—
231#103—791no—
232#103—791no—
233#102—791no—
234#102—791no—
235#102C2×D7911yescharacteristic
236#102C2×D7911yescharacteristic
237C22⋊C8—791no—
238C22⋊C8—791no—
239C22⋊C8—791no—
240C22⋊C8C2×D7911yescharacteristic
241#41—1582no—
242#41—1582no—
243#41—1582no—
244#41—1582no—
245C2×Q8—791no—
246C2×Q8—791no—
247C2×D4—21no—
248C2×D4—791no—
249C2×D4—791no—
250C2×D4—791no—
251C2×D4—1581no—
252C2×D4—1581no—
253C2×D4C22×D7911yescharacteristic
254C22×C4—21no—
255C22×C4—791no—
256C22×C4—791no—
257C22×C4—1581no—
258C22×C4—1581no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4C22×D7911yescharacteristic
262M16—1582no—
263C2×C8—791no—
264C2×C8—791no—
265C2×C8—1582no—
266C2×C8C22×D7911yescharacteristic
267C2×C8C22×D7911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—791no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4C22×D7911yescharacteristic
278C4⋊C4C22×D7911yescharacteristic
279C4⋊C4C22×D7911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C42—1581no—
288C42—1581no—
289C42—1581no—
290C23—21no—
291C23—791no—
292C23—791no—
293C23D4×D7911yescharacteristic
294Q8—1582no—
295Q8—1581no—
296Q8—1581no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—3162no—
301D4—6321no—
302D4—1582no—
303D4—1582no—
304D4—1582no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—3162no—
312C2×C4—791no—
313C2×C4—792no—
314C2×C4—792no—
315C2×C4—791no—
316C2×C4—6321no—
317C2×C4—6321no—
318C2×C4—6321no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4—1581no—
325C2×C4D4×D7911yescharacteristic
326C2×C4C23×D7911yescharacteristic
327C8—21no—
328C8—21no—
329C8—1581no—
330C8—1581no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—792no—
338C22—1581no—
339C22—1581no—
340C22—1581no—
341C22—1581no—
342C22—1581no—
343C22C2×D4×D7911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3161no—
349C4—3161no—
350C4—3161no—
351C4—3161no—
352C4—792no—
353C4—1581no—
354C4#41×D7911yescharacteristic
355C4#41×D7911yescharacteristic
356C2—41no—
357C2—81no—
358C2—3161no—
359C2—1582no—
360C2#123×D7911yescharacteristic
361C2#1909936911yescharacteristic
362C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#481×C79C2
socleC22×C79C22×D4
prime radical#19099142C2
hypercenter#481D79
hypocenterC79#3099
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #19099044C2semidirect
3. #19098907C2semidirect
4. #19098905C2semidirect
5. #19098895C2semidirect
6. #19098893C2semidirect
7. #19098885C2semidirect
8. #19098884C2semidirect
9. #19098880C2semidirect
10. #19098602C2semidirect
11. #106×D79C2semidirect
12. #19098561C2semidirect
13. #19098556C2semidirect
14. #19098528C2semidirect
15. #481×C79C2semidirect
182. C79#3099semidirect
192. #481D79semidirect