Finite Group Databasebeta

← #23773658

Subgroups — #23773658

Order 10112.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099178C211yesmaximal, characteristic, complemented
2#19099042C211yesmaximal, characteristic, complemented
3#19098900C211yesmaximal, characteristic, complemented
4#19098875C211yesmaximal, characteristic, complemented
5#19098857C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098784C211yesmaximal, characteristic, complemented
8#19098776C211yesmaximal, characteristic, complemented
9#19098726C211yesmaximal, characteristic, complemented
10#19098705C211yesmaximal, characteristic
11#19098663C211yesmaximal, characteristic, complemented
12#19098663C211yesmaximal, characteristic, complemented
13C4×Dic316C211yesmaximal, characteristic, complemented
14#19098622C211yesmaximal, characteristic, complemented
15C4×D8×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×Dic316C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20#14579160C2211yescharacteristic
21#14579154—21no—
22#14579148C2211yescharacteristic
23#14579147—21no—
24#14579144—21no—
25#14579141C2211yescharacteristic
26#14579140—21no—
27#14579132C2211yescharacteristic
28C4×Dic158C2211yescharacteristic
29C4×Dic158C2211yescharacteristic
30#14579126C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32C4×C22⋊D79—21no—
33(C22⋊D79)⋊C4—21no—
34#14579118C2211yescharacteristic
35#14579117—21no—
36C2×Dic79⋊C4—21no—
37C4⋊C4×D79C2211yescharacteristic
38#14579095C2211yescharacteristic
39#14579094C2211yescharacteristic
40#14579094C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579084C2211yescharacteristic
46#14579084C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579072C2211yescharacteristic
52C2×D8×C79C2211yescharacteristic
53C4×D4×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55#107×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C4×C8×C79C2211yescharacteristic
59#11929623—22no—
60#11929623—22no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×Dic158C2311yescharacteristic
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C2×C4×D79—21no—
69C2×C4×D79C2311yescharacteristic
70Dic316—22no—
71#11929612—22no—
72#11929612—22no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C4⋊Dic79—21no—
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4D411yescharacteristic
84Dic79⋊C4D411yescharacteristic
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4D411yescharacteristic
91(C2×D79)⋊C4D411yescharacteristic
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96C2×D4×C79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C22×C4×C79—21no—
100D8×C79—22no—
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C22×D79C2×D411yescharacteristic
111D4×C79—21no—
112D4×C79—21no—
113D4×C79—21no—
114D4×C79#4112yes—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—81no—
118C2×C4×C79—81no—
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2411yescharacteristic
122C22⋊D79—24no—
123C22⋊D79—81no—
124C2×Dic79—24no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—81no—
130C2×Dic79C2×D411yescharacteristic
131C2×Dic79C2×D411yescharacteristic
132C2×Dic79C2×D411yescharacteristic
133C4×D79—21no—
134C4×D79—21no—
135C4×D79—81no—
136Dic158—21no—
137Dic158—21no—
138Dic158—21no—
139Dic158—81no—
140Dic158#4112yes—
141C8×C79—21no—
142C8×C79—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—22no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79C22×D411yescharacteristic
152C2×D79—21no—
153C2×D79—21no—
154C2×D79—21no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79C2×#4111yescharacteristic
160C4×C79C2×#4111yescharacteristic
161Dic79—22no—
162Dic79—21no—
163Dic79—21no—
164Dic79—21no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168C2×C79—42no—
169C2×C79—81no—
170C2×C79#52511yescharacteristic
171C2×C79#57611yescharacteristic
172C2×C79#57811yescharacteristic
173D79—41no—
174#3124—791nomaximal, Sylow
175C79#312411yescharacteristic, complemented, Sylow
176#542—791no—
177#520—791no—
178#484—791no—
179#480—791no—
180#477—791no—
181#474—791no—
182#464—791no—
183#463—791no—
184#452—791no—
185#449—791no—
186#440—791no—
187#440—791no—
188C4×Q16—791no—
189C4×D8D7911yescharacteristic, complemented
190#433—791no—
191C2×#41—791no—
192C2×Q16—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×D8C2×D7911yescharacteristic
196C4⋊Q8—791no—
197#126—1581no—
198#124—791no—
199#124—1581no—
200#123—1581no—
201C22⋊Q8—791no—
202C22⋊Q8—1581no—
203#121—791no—
204C4×Q8—791no—
205C4×Q8—791no—
206C4×Q8—791no—
207C4×D4—791no—
208C4×D4—1581no—
209C4×D4—1581no—
210C4×D4C2×D7911yescharacteristic
211C4×D4C2×D7911yescharacteristic
212#117—791no—
213#117—1581no—
214C2×C4⋊C4—791no—
215C2×C4⋊C4—1581no—
216#107—791no—
217#107—791no—
218#107—791no—
219#107C2×D7911yescharacteristic
220C4⋊C8—791no—
221C4⋊C8—791no—
222#103—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#102—791no—
227#102—791no—
228#102C2×D7911yescharacteristic
229#102C2×D7911yescharacteristic
230C22⋊C8—791no—
231C22⋊C8—791no—
232#97—791no—
233C4×C8C2×D7911yescharacteristic
234#41—1582no—
235#41—1582no—
236C2×Q8—791no—
237C2×Q8—791no—
238C2×Q8—1581no—
239C2×D4—1581no—
240C2×D4—1581no—
241C2×D4C22×D7911yescharacteristic
242C2×D4C22×D7911yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—791no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4—1581no—
249Q16—1582no—
250SD16—1582no—
251SD16—1582no—
252D8—22no—
253C2×C8—791no—
254C2×C8—791no—
255C2×C8C22×D7911yescharacteristic
256C2×C8C22×D7911yescharacteristic
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4C22×D7911yescharacteristic
268C4⋊C4C22×D7911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—791no—
272C22⋊C4—791no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C42—791no—
279C42—1581no—
280C42—1581no—
281C42—1581no—
282C42C22×D7911yescharacteristic
283C23—21no—
284C23—21no—
285C23—791no—
286Q8—792no—
287Q8—6321no—
288Q8—1581no—
289Q8—1581no—
290Q8—1581no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—6321no—
295D4—1584no—
296D4#1192962412yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—791no—
302C2×C4—791no—
303C2×C4—791no—
304C2×C4—6321no—
305C2×C4—6321no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1584no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4D4×D7911yescharacteristic
314C2×C4D4×D7911yescharacteristic
315C2×C4C23×D7911yescharacteristic
316C8—21no—
317C8—21no—
318C8—1581no—
319C8—1581no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—1581no—
327C22—1581no—
328C22—1581no—
329C22C2×D4×D7911yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4—1581no—
338C4—1582no—
339C4—1581no—
340C4—1581no—
341C4#41×D7911yescharacteristic
342C4C2×#1192962411yescharacteristic
343C2—42no—
344C2—81no—
345C2—3161no—
346C2#1909907211yescharacteristic
347C2#1909936411yescharacteristic
348C2#1909937711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×D8×C79C2
socleC22×C79C22×D4
prime radical#19098705C2
hypercenterC4×D8D79
hypocenterC79#3124
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #19099178C2semidirect
2. #19099042C2semidirect
3. #19098900C2semidirect
4. #19098875C2semidirect
5. #19098857C2semidirect
6. #19098841C2semidirect
7. #19098784C2semidirect
8. #19098776C2semidirect
9. #19098726C2semidirect
11. #19098663C2semidirect
12. #19098663C2semidirect
13. C4×Dic316C2semidirect
14. #19098622C2semidirect
15. C4×D8×C79C2semidirect
175. C79#3124semidirect
189. C4×D8D79semidirect