Finite Group Databasebeta

← #23766211

Subgroups — #23766211

Order 10112.

540 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579147C211yesmaximal, characteristic
2#19098468C211yesmaximal, characteristic, complemented
3#19098467C211yesmaximal, characteristic, complemented
4#19098454C211yesmaximal, characteristic, complemented
5#19098452C211yesmaximal, characteristic, complemented
6#19098451C211yesmaximal, characteristic, complemented
7#19098440C211yesmaximal, characteristic
8#19098439C211yesmaximal, characteristic
9#19098435C211yesmaximal, characteristic, complemented
10#19098434C211yesmaximal, characteristic, complemented
11#19098430C211yesmaximal, characteristic, complemented
12C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic79C211yesmaximal, characteristic, complemented
14#19098410C211yesmaximal, characteristic, complemented
15#388×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C23×Dic79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20#14579147C418yescomplemented
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×C22⋊Dic79C2211yescharacteristic
25C2×C22⋊Dic79C2211yescharacteristic
26C2×(C2×D79)⋊C4C2211yescharacteristic
27C2×(C2×D79)⋊C4C2211yescharacteristic
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×C4×Dic79C2211yescharacteristic
32C2×C4×Dic79C2211yescharacteristic
33C2×C4×Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C2×C4⋊C4×C79C2211yescharacteristic
46C2×C22⋊C4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C42×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52C23×D79C2311yescharacteristic
53C2×Dic158—41no—
54C2×Dic158—41no—
55C2×Dic158C2×C414yescomplemented
56C2×C22⋊D79—41no—
57C2×C22⋊D79—41no—
58C2×C22⋊D79C2×C414yes—
59C22×Dic79—22no—
60C22×Dic79—41no—
61C22×Dic79—41no—
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C2×C4×D79—22no—
70C2×C4×D79—41no—
71C2×C4×D79—41no—
72Dic79⋊C4—22no—
73Dic79⋊C4—22no—
74Dic79⋊C4—41no—
75C22⋊Dic79—22no—
76C22⋊Dic79C2×C414yescomplemented
77(C2×D79)⋊C4—22no—
78(C2×D79)⋊C4—41no—
79(C2×D79)⋊C4—41no—
80(C2×D79)⋊C4C2×C414yescomplemented
81(C2×D79)⋊C4C2×C414yescomplemented
82C4×Dic79—41no—
83C4×Dic79—41no—
84C4×Dic79—41no—
85C4×Dic79C2×C414yescomplemented
86C24×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—41no—
94C22⋊C4×C79—41no—
95C22⋊C4×C79—41no—
96C22⋊C4×C79C2×C414yescomplemented
97C42×C79—41no—
98C23×C79—21no—
99C23×C79—21no—
100C23×C79—21no—
101C23×C79—21no—
102C23×C79—21no—
103C23×C79—21no—
104C23×C79C22×C412yes—
105C23×C79C2411yescharacteristic
106C22×D79—21no—
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—21no—
112C22×D79C22×C412yes—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79C22×C412yes—
130C2×C4×C79C22×C412yes—
131C22⋊D79—44no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—44no—
149C2×Dic79C22×C412yes—
150C2×Dic79C22×C412yes—
151C2×Dic79C22×C412yes—
152C2×Dic79#4112yes—
153C2×Dic79#4112yes—
154C4×D79—44no—
155Dic158—44no—
156C22×C79—22no—
157C22×C79—22no—
158C22×C79—22no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79C23×C411yescharacteristic
164C22×C79C2×#4111yescharacteristic
165C22×C79C2×#4111yescharacteristic
166C22×C79H(5,𝔽2)11yescharacteristic
167C22×C79H(5,𝔽2)11yescharacteristic
168C22×C79H(5,𝔽2)11yescharacteristic
169C22×C792−1+411yescharacteristic
170C2×D79—22no—
171C2×D79—22no—
172C2×D79—22no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C4×C79—22no—
178C4×C79—22no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79—41no—
182C4×C79—41no—
183Dic79—22no—
184Dic79—22no—
185Dic79—22no—
186Dic79—22no—
187Dic79—22no—
188Dic79—41no—
189Dic79—41no—
190C2×C79—42no—
191C2×C79C4×#4111yescharacteristic
192C2×C79#51811yescharacteristic
193C2×C79#52011yescharacteristic
194C2×C79#53811yescharacteristic
195C2×C79#53811yescharacteristic
196C2×C79#54211yescharacteristic
197C2×C79#54211yescharacteristic
198D79—42no—
199#2337—791nomaximal, Sylow
200C79#233711yescharacteristic, complemented, Sylow
201C2×#124—791no—
202#391—791no—
203#391—791no—
204#388—791no—
205#388—791no—
206#388—791no—
207#388D7911yescharacteristic, complemented
208#386—791no—
209#386—791no—
210#385—791no—
211#385—791no—
212#383—791no—
213C4×C4⋊C4—791no—
214C4×C22⋊C4—791no—
215C4×C22⋊C4—791no—
216C22×Q8—791no—
217C22×D4—791no—
218C23×C4—791no—
219C23×C4—791no—
220#124—798no—
221C2×C4⋊C4—791no—
222C2×C4⋊C4—791no—
223C2×C4⋊C4—791no—
224C2×C4⋊C4C2×D7911yescharacteristic
225C2×C22⋊C4—791no—
226C2×C22⋊C4—791no—
227C2×C22⋊C4—791no—
228C2×C22⋊C4—791no—
229C2×C22⋊C4—791no—
230C2×C22⋊C4—791no—
231C2×C22⋊C4—791no—
232C2×C22⋊C4C2×D7911yescharacteristic
233C2×C22⋊C4C2×D7911yescharacteristic
234C2×C22⋊C4C2×D7911yescharacteristic
235C2×C42—791no—
236C2×C42—791no—
237C2×C42—791no—
238C2×C42—791no—
239C2×C42C2×D7911yescharacteristic
240#95—791no—
241#95—791no—
242#95—791no—
243#95—791no—
244#95—791no—
245#95—791no—
246#95—791no—
247#95—791no—
248#95—791no—
249#95—791no—
250#95C2×D7911yescharacteristic
251#95C2×D7911yescharacteristic
252C24—791no—
253C24C22×D7911yescharacteristic
254C2×Q8—3161no—
255C2×Q8—3161no—
256C2×Q8—794no—
257C2×D4—3161no—
258C2×D4—3161no—
259C2×D4—794no—
260C22×C4—3161no—
261C22×C4—3161no—
262C22×C4—3161no—
263C22×C4—3161no—
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—791no—
268C22×C4—791no—
269C22×C4—791no—
270C22×C4—791no—
271C22×C4—1582no—
272C22×C4—1582no—
273C22×C4C22×D7911yescharacteristic
274C22×C4C22×D7911yescharacteristic
275C22×C4C22×D7911yescharacteristic
276C22×C4C22×D7911yescharacteristic
277C22×C4C22×D7911yescharacteristic
278C22×C4C22×D7911yescharacteristic
279C4⋊C4—41no—
280C4⋊C4—3161no—
281C4⋊C4—1582no—
282C4⋊C4—1582no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—3161no—
286C22⋊C4—3161no—
287C22⋊C4—794no—
288C22⋊C4—794no—
289C22⋊C4—794no—
290C22⋊C4—1582no—
291C22⋊C4—1582no—
292C22⋊C4C4×D7914yescomplemented
293C42—41no—
294C42—3161no—
295C42—3161no—
296C42—3161no—
297C42—794no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—792no—
305C23—1581no—
306C23—1581no—
307C23—1581no—
308C23—1581no—
309C23—1581no—
310C23—1581no—
311C23C2×C4×D7912yes—
312C23C23×D7911yescharacteristic
313Q8—3164no—
314D4—3164no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—3164no—
332C2×C4—3164no—
333C2×C4—792no—
334C2×C4—792no—
335C2×C4—792no—
336C2×C4—792no—
337C2×C4—792no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4—1581no—
353C2×C4—1581no—
354C2×C4C2×C4×D7912yes—
355C2×C4C2×C4×D7912yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—1582no—
368C22—1582no—
369C22—1582no—
370C22C22×C4×D7911yescharacteristic
371C22#41×D7911yescharacteristic
372C22#41×D7911yescharacteristic
373C22#1457920611yescharacteristic
374C22#1457920611yescharacteristic
375C22#1457920711yescharacteristic
376C22#1457920811yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—3161no—
384C4—3161no—
385C4—1582no—
386C4—1582no—
387C4—1582no—
388C4—1582no—
389C4—1582no—
390C2—42no—
391C2—3162no—
392C2#1909903111yescharacteristic
393C2#1909903511yescharacteristic
394C2#1909904211yescharacteristic
395C2#1909914511yescharacteristic
396C2#1909914911yescharacteristic
397C2#1909917711yescharacteristic
398C2#1909917911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#388×C79C2
socle, cosocleC23×C79C24
prime radicalC22×C22⋊D79C22
hypercenter#388D79
hypocenterC79#2337
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #19098468C2semidirect
3. #19098467C2semidirect
4. #19098454C2semidirect
5. #19098452C2semidirect
6. #19098451C2semidirect
9. #19098435C2semidirect
10. #19098434C2semidirect
11. #19098430C2semidirect
12. C4×Dic79⋊C4C2semidirect
13. C22⋊C4×Dic79C2semidirect
14. #19098410C2semidirect
15. #388×C79C2semidirect
20. #14579147C4semidirect
55. C2×Dic158C2×C4semidirect
76. C22⋊Dic79C2×C4semidirect
80. (C2×D79)⋊C4C2×C4semidirect
81. (C2×D79)⋊C4C2×C4semidirect
85. C4×Dic79C2×C4semidirect
96. C22⋊C4×C79C2×C4semidirect
200. C79#2337semidirect
207. #388D79semidirect
292. C22⋊C4C4×D79semidirect