Finite Group Databasebeta

← #23766397

Subgroups — #23766397

Order 10112.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579146C211yesmaximal, characteristic
2C2×C4×D316C211yesmaximal, characteristic
3C2×#14579118C211yesmaximal, characteristic, complemented
4#19098460C211yesmaximal, characteristic, complemented
5#19098454C211yesmaximal, characteristic, complemented
6#19098454C211yesmaximal, characteristic, complemented
7#19098449C211yesmaximal, characteristic, complemented
8#19098447C211yesmaximal, characteristic, complemented
9#19098441C211yesmaximal, characteristic
10#19098434C211yesmaximal, characteristic, complemented
11#19098434C211yesmaximal, characteristic, complemented
12C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
13#19098410C211yesmaximal, characteristic, complemented
14#95×D79C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C22×C4×D79C2211yescharacteristic
21#14579146C418yescomplemented
22C4×D316—24no—
23#14579118—24no—
24C2×C4⋊Dic79C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×(C2×D79)⋊C4C2211yescharacteristic
37C2×C4×Dic79C2211yescharacteristic
38C2×C4×Dic79C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C79⋊#95C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C42×C79C2211yescharacteristic
50C2×C42×C79C2211yescharacteristic
51C2×C42×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53#95×C79C2211yescharacteristic
54C23×D79C2311yescharacteristic
55C23×D79C2311yescharacteristic
56C2×D316—22no—
57C2×D316—22no—
58C2×D316C2×C414yes—
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C2×C4×D79—22no—
66C2×C4×D79—22no—
67C2×C4×D79—22no—
68C2×C4×D79—22no—
69C2×C4×D79—22no—
70C2×C4×D79—22no—
71C2×C4×D79—22no—
72C2×C4×D79—22no—
73C2×C4×D79—41no—
74C2×C4×D79—41no—
75C2×C4×D79—41no—
76C2×C4×D79C2×C414yescomplemented
77C4⋊Dic79—22no—
78Dic79⋊C4—22no—
79Dic79⋊C4—22no—
80Dic79⋊C4—41no—
81Dic79⋊C4C2×C414yescomplemented
82(C2×D79)⋊C4—22no—
83(C2×D79)⋊C4—22no—
84(C2×D79)⋊C4—22no—
85(C2×D79)⋊C4—41no—
86(C2×D79)⋊C4C2×C414yescomplemented
87(C2×D79)⋊C4C2×C414yescomplemented
88(C2×D79)⋊C4C2×C414yescomplemented
89(C2×D79)⋊C4D414yes—
90C4×Dic79—22no—
91C4×Dic79—41no—
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C22×C4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C4⋊C4×C79—22no—
100C4⋊C4×C79C2×C414yescomplemented
101C42×C79—22no—
102C42×C79—22no—
103C42×C79—22no—
104C23×C79C2411yescharacteristic
105C22×D79—21no—
106C22×D79—21no—
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—21no—
112C22×D79—21no—
113C22×D79—21no—
114C22×D79—21no—
115C22×D79C22×C412yes—
116C22×D79C22×C412yes—
117C22×D79C2×D412yes—
118C22×D79#4112yes—
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×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79C22×C412yes—
135C2×C4×C79C22×C412yes—
136C2×C4×C79C22×C412yes—
137C2×C4×C79C2×D412yes—
138C2×C4×C79#4112yes—
139C2×C4×C79#4112yes—
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—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79C22×C412yes—
156C2×Dic79C22×C412yes—
157C2×Dic79C2×D412yes—
158D316—28no—
159C4×D79—28no—
160C4×D79—44no—
161C4×D79—44no—
162C4×D79—44no—
163C22×C79C23×C411yescharacteristic
164C22×C79C22×D411yescharacteristic
165C22×C79C2×#4111yescharacteristic
166C22×C79C2×#4111yescharacteristic
167C22×C79C2×#4111yescharacteristic
168C22×C79H(5,𝔽2)11yescharacteristic
169C22×C792−1+411yescharacteristic
170C2×D79—22no—
171C2×D79—22no—
172C2×D79—22no—
173C2×D79—22no—
174C2×D79—22no—
175C2×D79—22no—
176C2×D79—22no—
177C2×D79—22no—
178C2×D79—22no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79C4×D414yes—
184C4×C79—22no—
185C4×C79—22no—
186C4×C79—22no—
187C4×C79—22no—
188C4×C79—22no—
189C4×C79—22no—
190C4×C79—41no—
191Dic79—22no—
192Dic79—22no—
193Dic79—22no—
194Dic79—41no—
195Dic79—41no—
196Dic79—41no—
197C2×C79C2×C4×D411yescharacteristic
198C2×C79C4×#4111yescharacteristic
199C2×C79#52011yescharacteristic
200C2×C79#54611yescharacteristic
201C2×C79#54711yescharacteristic
202C2×C79#55111yescharacteristic
203C2×C79#55211yescharacteristic
204D79—24no—
205D79—42no—
206#2359—791nomaximal, Sylow
207C79#235911yescharacteristic, complemented, Sylow
208C2×#123—791no—
209C2×C4×D4—791no—
210C2×#117—791no—
211#389—791no—
212#388—791no—
213#388—791no—
214#387—791no—
215#387—791no—
216#386—791no—
217#385—791no—
218#385—791no—
219C4×C4⋊C4D7911yescharacteristic, complemented
220C4×C22⋊C4—791no—
221C4×C22⋊C4—791no—
222C2×#95—791no—
223C22×D4—791no—
224C23×C4—791no—
225C23×C4—791no—
226C23×C4—791no—
227C23×C4—791no—
228#123—798no—
229C4×D4—1584no—
230#117—1584no—
231C2×C4⋊C4—791no—
232C2×C4⋊C4—791no—
233C2×C4⋊C4—791no—
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C4⋊C4C2×D7911yescharacteristic
237C2×C4⋊C4C2×D7911yescharacteristic
238C2×C22⋊C4—791no—
239C2×C22⋊C4—791no—
240C2×C22⋊C4—791no—
241C2×C22⋊C4—791no—
242C2×C22⋊C4—791no—
243C2×C22⋊C4—791no—
244C2×C22⋊C4—791no—
245C2×C22⋊C4—791no—
246C2×C42—791no—
247C2×C42—791no—
248C2×C42C2×D7911yescharacteristic
249C2×C42C2×D7911yescharacteristic
250C2×C42C2×D7911yescharacteristic
251#95—791no—
252#95—791no—
253#95—791no—
254#95—791no—
255#95—791no—
256#95—791no—
257#95—791no—
258#95—791no—
259#95C2×D7911yescharacteristic
260#95C2×D7911yescharacteristic
261C24—791no—
262C24—791no—
263C2×D4—794no—
264C2×D4—1582no—
265C2×D4—1582no—
266C22×C4—3161no—
267C22×C4—3161no—
268C22×C4—3161no—
269C22×C4—791no—
270C22×C4—791no—
271C22×C4—791no—
272C22×C4—794no—
273C22×C4—791no—
274C22×C4—791no—
275C22×C4—791no—
276C22×C4—1582no—
277C22×C4—1582no—
278C22×C4—1582no—
279C22×C4—1582no—
280C22×C4—1582no—
281C22×C4—1582no—
282C22×C4—1582no—
283C22×C4—1582no—
284C22×C4C22×D7911yescharacteristic
285C22×C4C22×D7911yescharacteristic
286C22×C4C22×D7911yescharacteristic
287C22×C4C22×D7911yescharacteristic
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7911yescharacteristic
290C22×C4C22×D7911yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—3161no—
293C4⋊C4—794no—
294C4⋊C4—1582no—
295C4⋊C4—1582no—
296C4⋊C4—1582no—
297C4⋊C4C4×D7914yescomplemented
298C22⋊C4—3161no—
299C22⋊C4—794no—
300C22⋊C4—794no—
301C22⋊C4—794no—
302C22⋊C4—794no—
303C22⋊C4—1582no—
304C22⋊C4—1582no—
305C22⋊C4—1582no—
306C42—22no—
307C42—22no—
308C42—22no—
309C42—3161no—
310C42—1582no—
311C23—792no—
312C23—792no—
313C23—792no—
314C23—792no—
315C23—1581no—
316C23—1581no—
317C23—1581no—
318C23—1581no—
319C23—1581no—
320C23—1581no—
321C23—1581no—
322C23—1581no—
323C23—1581no—
324C23—1581no—
325C23C23×D7911yescharacteristic
326D4—1588no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3164no—
343C2×C4—3164no—
344C2×C4—3164no—
345C2×C4—792no—
346C2×C4—792no—
347C2×C4—792no—
348C2×C4—1588no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4—1581no—
353C2×C4—1581no—
354C2×C4—1581no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4—1581no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4C2×C4×D7912yes—
365C2×C4C2×C4×D7912yes—
366C2×C4C2×C4×D7912yes—
367C2×C4D4×D7912yes—
368C2×C4#1192962412yes—
369C2×C4#1192962412yes—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22—3161no—
374C22—794no—
375C22—1582no—
376C22—1582no—
377C22—1582no—
378C22—1582no—
379C22—1582no—
380C22—1582no—
381C22—1582no—
382C22—1582no—
383C22—1582no—
384C22C22×C4×D7911yescharacteristic
385C22C2×D4×D7911yescharacteristic
386C22#41×D7911yescharacteristic
387C22C2×#1192962411yescharacteristic
388C22C2×#1192962411yescharacteristic
389C22#1457920711yescharacteristic
390C22#1457920911yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—22no—
397C4—41no—
398C4—3161no—
399C4—3161no—
400C4—3161no—
401C4—1582no—
402C4—1582no—
403C4—1582no—
404C2—3162no—
405C2—1584no—
406C2C4×D4×D7911yescharacteristic
407C2C4×#1192962411yescharacteristic
408C2#1909904511yescharacteristic
409C2#1909920911yescharacteristic
410C2#1909921411yescharacteristic
411C2#1909923711yescharacteristic
412C2#1909925411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
FittingC4×C4⋊C4×C79C2
socle, cosocleC23×C79C24
prime radicalC22×D316C22
hypercenterC4×C4⋊C4D79
hypocenterC79#2359
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#14579118C2semidirect
4. #19098460C2semidirect
5. #19098454C2semidirect
6. #19098454C2semidirect
7. #19098449C2semidirect
8. #19098447C2semidirect
10. #19098434C2semidirect
11. #19098434C2semidirect
12. C4×(C2×D79)⋊C4C2semidirect
13. #19098410C2semidirect
14. #95×D79C2semidirect
15. C4×C4⋊C4×C79C2semidirect
21. #14579146C4semidirect
76. C2×C4×D79C2×C4semidirect
81. Dic79⋊C4C2×C4semidirect
86. (C2×D79)⋊C4C2×C4semidirect
87. (C2×D79)⋊C4C2×C4semidirect
88. (C2×D79)⋊C4C2×C4semidirect
100. C4⋊C4×C79C2×C4semidirect
207. C79#2359semidirect
219. C4×C4⋊C4D79semidirect
297. C4⋊C4C4×D79semidirect