Finite Group Databasebeta

← #23773429

Subgroups — #23773429

Order 10112.

428 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099110C211yesmaximal, characteristic
2C4×Q8×D79C211yesmaximal, characteristic, complemented
3#19098883C211yesmaximal, characteristic, complemented
4#19098880C211yesmaximal, characteristic, complemented
5#19098847C211yesmaximal, characteristic, complemented
6#19098846C211yesmaximal, characteristic, complemented
7#19098762C211yesmaximal, characteristic, complemented
8#19098761C211yesmaximal, characteristic, complemented
9#19098703C211yesmaximal, characteristic, complemented
10#19098700C211yesmaximal, characteristic, complemented
11C4×#11929613C211yesmaximal, characteristic, complemented
12C4×#11929611C211yesmaximal, characteristic, complemented
13C4×#11929612C211yesmaximal, characteristic, complemented
14#19098614C211yesmaximal, characteristic, complemented
15C4×SD16×C79C211yesmaximal, characteristic, complemented
16C2×#11929624—21no—
17C2×Q8×D79C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21#14579160C2211yescharacteristic
22#14579157C2211yescharacteristic
23#14579147—21no—
24#14579136C2211yescharacteristic
25#14579134—21no—
26#14579132C2211yescharacteristic
27Q8×Dic79C2211yescharacteristic
28C4×Dic158—21no—
29C4×Dic158C2211yescharacteristic
30#14579126—21no—
31#14579126C2211yescharacteristic
32C4×D316C2211yescharacteristic
33C4×C22⋊D79—21no—
34C4⋊C4×D79—21no—
35C4⋊C4×D79C2211yescharacteristic
36C42×D79—21no—
37C42×D79C2211yescharacteristic
38#14579093C2211yescharacteristic
39#14579092C2211yescharacteristic
40#14579092C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579084C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C4×C79⋊C8C2211yescharacteristic
52C2×SD16×C79C2211yescharacteristic
53C4×Q8×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55#106×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C4×C8×C79C2211yescharacteristic
59#11929624—44no—
60C2×Dic158—21no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63Q8×D79—22no—
64Q8×D79—22no—
65C2×D316—21no—
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79D411yescharacteristic
74C2×C4×D79D411yescharacteristic
75C2×C4×D79C2311yescharacteristic
76#11929613—22no—
77#11929612—22no—
78#11929611—22no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91C4×Dic79—21no—
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79D411yescharacteristic
95C4×Dic79D411yescharacteristic
96C4×Dic79C2311yescharacteristic
97C2×Q8×C79C2311yescharacteristic
98C2×D4×C79C2311yescharacteristic
99C22×C4×C79—21no—
100SD16×C79—22no—
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79—21no—
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C42×C79—21no—
108C42×C79C2311yescharacteristic
109C23×C79—21no—
110C22×D79—21no—
111C22×D79C2×D411yescharacteristic
112Q8×C79—21no—
113Q8×C79#4112yescomplemented
114D4×C79—21no—
115D4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—42no—
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2×D411yescharacteristic
122C2×C4×C79C2411yescharacteristic
123C22⋊D79—42no—
124C22⋊D79—42no—
125C22⋊D79—42no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131C2×Dic79C2×D411yescharacteristic
132D316—21no—
133D316—21no—
134D316—42no—
135C4×D79—24no—
136C4×D79—21no—
137C4×D79—21no—
138C4×D79—41no—
139C4×D79—42no—
140C4×D79—42no—
141C4×D79SD1614yescomplemented
142Dic158—24no—
143Dic158—21no—
144Dic158—42no—
145Dic158#4112yescomplemented
146C8×C79—21no—
147C8×C79—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79C22×D411yescharacteristic
154C2×D79—21no—
155C2×D79—21no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C2×D79C2×SD1612yes—
160C4×C79—22no—
161C4×C79—21no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79C2×SD1612yes—
165C4×C79C2×#4111yescharacteristic
166C4×C79C2×#4111yescharacteristic
167Dic79—21no—
168Dic79—22no—
169Dic79—21no—
170Dic79—41no—
171Dic79—41no—
172Dic79C2×SD1612yes—
173C2×C79—81no—
174C2×C79#52511yescharacteristic
175C2×C79C22×SD1611yescharacteristic
176C2×C79#57511yescharacteristic
177D79—22no—
178D79—81no—
179#3103—791nomaximal, Sylow
180C79#310311yescharacteristic, complemented, Sylow
181#532—791no—
182C2×C4×Q8—791no—
183#481—791no—
184#481—791no—
185#475—791no—
186#475—791no—
187#460—791no—
188#460—791no—
189#448—791no—
190#448—791no—
191C4×SD16—791no—
192C4×SD16—791no—
193C4×SD16—791no—
194C4×SD16D7911yescharacteristic, complemented
195#431—791no—
196C2×#41—1581no—
197C22×Q8—791no—
198C2×SD16—791no—
199C2×SD16—791no—
200C2×SD16—791no—
201C2×SD16C2×D7911yescharacteristic
202C4⋊Q8—791no—
203#127—791no—
204#124—1581no—
205#121—791no—
206#121—791no—
207#121—1581no—
208C4×Q8—791no—
209C4×Q8—791no—
210C4×Q8—791no—
211C4×Q8—1581no—
212C4×Q8—1581no—
213C4×Q8C2×D7911yescharacteristic
214C4×D4—791no—
215C4×D4—1581no—
216C4×D4C2×D7911yescharacteristic
217C2×C4⋊C4—791no—
218C2×C4⋊C4—1581no—
219C2×C42—791no—
220C2×C42—1581no—
221#106—791no—
222#106—791no—
223#106—791no—
224#106C2×D7911yescharacteristic
225C4⋊C8—791no—
226C4⋊C8—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103C2×D7911yescharacteristic
231#102—791no—
232#102—791no—
233#102—791no—
234#102C2×D7911yescharacteristic
235C22⋊C8—791no—
236C22⋊C8—791no—
237C4×C8—791no—
238C4×C8C2×D7911yescharacteristic
239#41—3164no—
240C2×Q8—791no—
241C2×Q8—1581no—
242C2×Q8—1581no—
243C2×Q8—1582no—
244C2×Q8—1582no—
245C2×Q8C22×D7911yescharacteristic
246C2×D4—791no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4—1581no—
250C2×D4—1581no—
251C2×D4C22×D7911yescharacteristic
252C22×C4—21no—
253C22×C4—791no—
254C22×C4—791no—
255C22×C4—791no—
256C22×C4—1581no—
257C22×C4—1581no—
258C22×C4—1581no—
259SD16—22no—
260SD16—1582no—
261SD16—1582no—
262SD16—1582no—
263C2×C8—791no—
264C2×C8—791no—
265C2×C8C22×D7911yescharacteristic
266C2×C8C22×D7911yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4C22×D7911yescharacteristic
276C4⋊C4C22×D7911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C42—21no—
282C42—791no—
283C42—791no—
284C42—791no—
285C42—1581no—
286C42—1581no—
287C42—1581no—
288C42C22×D7911yescharacteristic
289C23—21no—
290C23—791no—
291C23—1581no—
292Q8—21no—
293Q8—3162no—
294Q8—792no—
295Q8—1584no—
296Q8—1581no—
297Q8#1192962412yescomplemented
298D4—21no—
299D4—21no—
300D4—3162no—
301D4—3162no—
302D4—3162no—
303D4—3162no—
304D4—1581no—
305D4—1581no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—3161no—
311C2×C4—3162no—
312C2×C4—3162no—
313C2×C4—791no—
314C2×C4—794no—
315C2×C4—791no—
316C2×C4—791no—
317C2×C4—1584no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4D4×D7911yescharacteristic
324C2×C4D4×D7911yescharacteristic
325C2×C4C23×D7911yescharacteristic
326C8—21no—
327C8—21no—
328C8—1581no—
329C8—1581no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—3161no—
334C22—3161no—
335C22—3161no—
336C22—792no—
337C22—1581no—
338C22—1581no—
339C22C2×D4×D7911yescharacteristic
340C4—22no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—3161no—
345C4—3161no—
346C4—792no—
347C4—1581no—
348C4—1582no—
349C4—1581no—
350C4SD16×D7912yes—
351C4#41×D7911yescharacteristic
352C4C2×#1192962411yescharacteristic
353C2—81no—
354C2—6321no—
355C2—1582no—
356C2#1909907211yescharacteristic
357C2C2×SD16×D7911yescharacteristic
358C2#1909936011yescharacteristic
subgroupG/H
centerC2×C4D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×SD16×C79C2
socleC22×C79C22×D4
prime radical#19099110C2
hypercenterC4×SD16D79
hypocenterC79#3103
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D79C2semidirect
3. #19098883C2semidirect
4. #19098880C2semidirect
5. #19098847C2semidirect
6. #19098846C2semidirect
7. #19098762C2semidirect
8. #19098761C2semidirect
9. #19098703C2semidirect
10. #19098700C2semidirect
11. C4×#11929613C2semidirect
12. C4×#11929611C2semidirect
13. C4×#11929612C2semidirect
14. #19098614C2semidirect
15. C4×SD16×C79C2semidirect
113. Q8×C79#41semidirect
141. C4×D79SD16semidirect
145. Dic158#41semidirect
180. C79#3103semidirect
194. C4×SD16D79semidirect
297. Q8#11929624semidirect