Finite Group Databasebeta

← #1992×D79 #34292832

Subgroups — #1992×D79 #34292832

Order 20224.

1294 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D79C211yesmaximal, characteristic
2C2×#97×D79C211yesmaximal, characteristic
3#384×D79C211yesmaximal, characteristic
4#23764370C211yesmaximal, characteristic, complemented
5#23764369C211yesmaximal, characteristic, complemented
6#23764368C211yesmaximal, characteristic, complemented
7#23764367C214yesmaximal, complemented
8#340×D79C214yesmaximal
9C79×#1992C211yesmaximal, characteristic, complemented
10C22×C8×D79C2212yes—
11C2×#14579153C2211yescharacteristic
12C2×#14579152C2212yes—
13C2×#14579151—22no—
14#125×D79—24no—
15#125×D79C418yescomplemented
16C2×C4⋊C4×D79—22no—
17C2×C4⋊C4×D79—22no—
18C2×C4⋊C4×D79C2212yes—
19C2×C4⋊C4×D79C2212yes—
20C2×C42×D79C2211yescharacteristic
21C2×#14579072C2211yescharacteristic
22C2×#14579071C2212yes—
23#97×D79—24no—
24#19098433C2211yescharacteristic
25#19098432—22no—
26#19098432C2212yes—
27#19098326C2214yes—
28#19098325C2214yes—
29#19098325C2214yes—
30C2×#125×C79C2211yescharacteristic
31C2×#97×C79C2211yescharacteristic
32#384×C79C2211yescharacteristic
33#340×C79C2214yes—
34C22×C4×D79—22no—
35C22×C4×D79—22no—
36C22×C4×D79D412yes—
37C22×C4×D79C2311yescharacteristic
38C22×C79⋊C8C2312yes—
39C2×C8×D79—24no—
40C2×C8×D79—24no—
41C2×C8×D79Q818yes—
42#14579153—22no—
43#14579153C2×C414yescomplemented
44#14579152—24no—
45#14579152C2×C418yescomplemented
46#14579151—216no—
47C2×C4⋊Dic79—22no—
48C2×C4⋊Dic79—22no—
49C2×C4⋊Dic79C2312yes—
50C2×C4⋊Dic79C2312yes—
51C2×Dic79⋊C4—22no—
52C2×Dic79⋊C4—22no—
53C2×Dic79⋊C4—22no—
54C2×Dic79⋊C4—22no—
55C2×Dic79⋊C4—24no—
56C4⋊C4×D79—216no—
57C4⋊C4×D79—24no—
58C4⋊C4×D79—28no—
59C4⋊C4×D79—48no—
60C4⋊C4×D79C2×C418yes—
61C2×C4×Dic79D412yes—
62C2×C4×Dic79C2311yescharacteristic
63C42×D79C2×C414yes—
64C42×D79D414yes—
65#14579072—22no—
66#14579071—24no—
67C22×C8×C79C2312yes—
68#125×C79—22no—
69#125×C79C2×C414yescomplemented
70C2×C4⋊C4×C79—22no—
71C2×C4⋊C4×C79—22no—
72C2×C4⋊C4×C79C2312yes—
73C2×C4⋊C4×C79C2312yes—
74C2×C42×C79C2311yescharacteristic
75#97×C79—22no—
76C23×D79C2×D411yescharacteristic
77C22×Dic79—22no—
78C22×Dic79—22no—
79C22×Dic79C2×D412yes—
80C22×Dic79C2×D411yescharacteristic
81C2×C4×D79—28no—
82C2×C4×D79—24no—
83C2×C4×D79—24no—
84C2×C4×D79—44no—
85C2×C4×D79—44no—
86C2×C4×D79—48no—
87C2×C4×D79—44no—
88C2×C4×D79C22⋊C418yes—
89C2×C4×D79C22×C412yes—
90C2×C4×D79C2×D412yes—
91C2×C4×D79C2×Q814yes—
92C2×C4×D79#4114yes—
93C2×C79⋊C8—22no—
94C2×C79⋊C8—22no—
95C2×C79⋊C8C2×Q814yes—
96C8×D79—216no—
97C4⋊Dic79—28no—
98C4⋊Dic79—22no—
99C4⋊Dic79—24no—
100C4⋊Dic79—44no—
101C4⋊Dic79C22×C414yes—
102Dic79⋊C4—28no—
103Dic79⋊C4—28no—
104Dic79⋊C4—28no—
105Dic79⋊C4—48no—
106Dic79⋊C4—44no—
107C4×Dic79C22⋊C418yes—
108C4×Dic79C22×C412yes—
109C4×Dic79C2×D412yes—
110C22×C4×C79—22no—
111C22×C4×C79—22no—
112C22×C4×C79C2×D412yes—
113C22×C4×C79C2411yescharacteristic
114C2×C8×C79—22no—
115C2×C8×C79—22no—
116C2×C8×C79C2×Q814yes—
117C4⋊C4×C79—28no—
118C4⋊C4×C79—22no—
119C4⋊C4×C79—24no—
120C4⋊C4×C79—44no—
121C4⋊C4×C79C22×C414yes—
122C42×C79C22×C412yes—
123C42×C79C2×D412yes—
124C23×C79C22×D411yescharacteristic
125C22×D79C2×C22⋊C412yes—
126C22×D79#12412yes—
127C22×D79C4⋊Q812yes—
128C22×D79AGL(1,ℤ/8)14yes—
129C22×D79#13714yes—
130C2×C4×C79—22no—
131C2×C4×C79—22no—
132C2×C4×C79—24no—
133C2×C4×C79—42no—
134C2×C4×C79—42no—
135C2×C4×C79—42no—
136C2×C4×C79—44no—
137C2×C4×C79C2×C22⋊C414yes—
138C2×C4×C79C23×C411yescharacteristic
139C2×C4×C79C22×D411yescharacteristic
140C2×C4×C79C22×Q812yes—
141C2×C4×C79C2×#4112yes—
142C2×Dic79—22no—
143C2×Dic79—22no—
144C2×Dic79—24no—
145C2×Dic79—42no—
146C2×Dic79—42no—
147C2×Dic79—42no—
148C2×Dic79—44no—
149C2×Dic79C2×C22⋊C414yes—
150C2×Dic79C2×C22⋊C412yes—
151C2×Dic79#12412yes—
152C2×Dic79C4⋊Q812yes—
153C4×D79—216no—
154C4×D79—416no—
155C4×D79—88no—
156C4×D79C4×Q818yes—
157C4×D79C22⋊Q818yes—
158C8×C79—24no—
159C79⋊C8—24no—
160C22×C79C22×C22⋊C411yescharacteristic
161C22×C79C2×#12411yescharacteristic
162C22×C79C2×C4⋊Q811yescharacteristic
163C22×C79C2×AGL(1,ℤ/8)12yes—
164C22×C79C2×#13712yes—
165C2×D79#39114yes—
166C2×D79#41718yes—
167C2×D79#49014yes—
168C2×D79#49114yes—
169C2×D79#50118yes—
170C4×C79—24no—
171C4×C79—44no—
172C4×C79—82no—
173C4×C79C2×C4×Q812yes—
174C4×C79C2×C22⋊Q812yes—
175Dic79—24no—
176Dic79—44no—
177Dic79—82no—
178Dic79#39114yes—
179C2×#1992—791nomaximal, Sylow
180C2×C79C2×#39111yescharacteristic
181C2×C79C2×#41712yes—
182C2×C79C2×#49011yescharacteristic
183C2×C79C2×#49111yescharacteristic
184C2×C79C2×#50112yes—
185D79#199218yesdirect product factor
186C22×#125—791no—
187C22×#97—791no—
188C2×#384—791no—
189#1992—791no—
190#1992—791no—
191#1992—794no—
192#1992—791no—
193#1992D7911yescharacteristic, direct product factor
194C2×#340—794no—
195C79C2×#199211yescharacteristic, complemented, Sylow
196C23×C8—792no—
197C2×#125—798no—
198C2×#125—792no—
199C2×#125—791no—
200C2×#125—1582no—
201C2×#125—1584no—
202C2×#125C2×D7911yescharacteristic
203C22×C4⋊C4—792no—
204C22×C4⋊C4—792no—
205C22×C4⋊C4—1582no—
206C22×C4⋊C4—1582no—
207C22×C42—791no—
208C2×#97—792no—
209C2×#97—791no—
210C2×#97—1584no—
211C2×#97C2×D7911yescharacteristic
212#384—792no—
213#384—791no—
214#384—1582no—
215#384C2×D7911yescharacteristic
216#340—794no—
217#340—794no—
218#340—794no—
219#340C2×D7914yes—
220C23×C4—791no—
221C23×C4—792no—
222C23×C4—1582no—
223C23×C4—1582no—
224C22×C8—792no—
225C22×C8—798no—
226C22×C8—1584no—
227C22×C8—1584no—
228C22×C8C22×D7912yes—
229#125—22no—
230#125—798no—
231#125—794no—
232#125—15816no—
233#125—1584no—
234#125—1582no—
235#125C4×D7914yescomplemented
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—3168no—
239C2×C4⋊C4—792no—
240C2×C4⋊C4—798no—
241C2×C4⋊C4—792no—
242C2×C4⋊C4—1588no—
243C2×C4⋊C4—1584no—
244C2×C4⋊C4—15816no—
245C2×C4⋊C4—1582no—
246C2×C4⋊C4—1584no—
247C2×C4⋊C4—1582no—
248C2×C4⋊C4—1582no—
249C2×C4⋊C4—1582no—
250C2×C4⋊C4—1582no—
251C2×C4⋊C4—1582no—
252C2×C4⋊C4C22×D7912yes—
253C2×C4⋊C4C22×D7912yes—
254C2×C42—792no—
255C2×C42—791no—
256C2×C42—794no—
257C2×C42—794no—
258C2×C42C22×D7911yescharacteristic
259#97—22no—
260#97—1584no—
261#97—1582no—
262C24—791no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—3164no—
266C22×C4—3164no—
267C22×C4—3168no—
268C22×C4—3164no—
269C22×C4—791no—
270C22×C4—794no—
271C22×C4—794no—
272C22×C4—792no—
273C22×C4—792no—
274C22×C4—792no—
275C22×C4—798no—
276C22×C4—1588no—
277C22×C4—1584no—
278C22×C4—1584no—
279C22×C4—1582no—
280C22×C4—1582no—
281C22×C4D4×D7912yes—
282C22×C4C23×D7911yescharacteristic
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—794no—
286C2×C8—15816no—
287C2×C8—1582no—
288C2×C8—1582no—
289C2×C8Q8×D7914yes—
290C4⋊C4—28no—
291C4⋊C4—22no—
292C4⋊C4—24no—
293C4⋊C4—44no—
294C4⋊C4—3164no—
295C4⋊C4—3164no—
296C4⋊C4—3168no—
297C4⋊C4—794no—
298C4⋊C4—1588no—
299C4⋊C4—1588no—
300C4⋊C4—1588no—
301C4⋊C4—1584no—
302C4⋊C4—1588no—
303C4⋊C4—1582no—
304C4⋊C4C2×C4×D7914yes—
305C42—798no—
306C42—792no—
307C42—792no—
308C42C2×C4×D7912yes—
309C42D4×D7912yes—
310C23—792no—
311C23—792no—
312C23—794no—
313C23—794no—
314C23—792no—
315C23C2×D4×D7911yescharacteristic
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—31616no—
324C2×C4—3162no—
325C2×C4—3162no—
326C2×C4—3162no—
327C2×C4—3164no—
328C2×C4—792no—
329C2×C4—792no—
330C2×C4—792no—
331C2×C4—798no—
332C2×C4—798no—
333C2×C4—794no—
334C2×C4—6328no—
335C2×C4—15816no—
336C2×C4—1584no—
337C2×C4—1582no—
338C2×C4—1582no—
339C2×C4C22⋊C4×D7914yes—
340C2×C4C22×C4×D7911yescharacteristic
341C2×C4C2×D4×D7911yescharacteristic
342C2×C4C2×Q8×D7912yes—
343C2×C4#41×D7912yes—
344C8—24no—
345C8—1584no—
346C22—798no—
347C22—794no—
348C22—794no—
349C22—794no—
350C22—798no—
351C22C2×C22⋊C4×D7911yescharacteristic
352C22#124×D7911yescharacteristic
353C22C4⋊Q8×D7911yescharacteristic
354C22AGL(1,ℤ/8)×D7912yes—
355C22#137×D7912yes—
356C4—24no—
357C4—44no—
358C4—82no—
359C4—3164no—
360C4—794no—
361C4—6322no—
362C4—1584no—
363C4C4×Q8×D7912yes—
364C4C22⋊Q8×D7912yes—
365C2—798no—
366C2#391×D7911yescharacteristic
367C2#417×D7912yes—
368C2#490×D7911yescharacteristic
369C2#491×D7911yescharacteristic
370C2#501×D7912yes—
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1992C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
cosocleC22×C4×C79C24
hypercenter#1992D79
hypocenterC79C2×#1992
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
4. #23764370C2semidirect
5. #23764369C2semidirect
6. #23764368C2semidirect
7. #23764367C2semidirect
9. C79×#1992C2semidirect
15. #125×D79C4semidirect
43. #14579153C2×C4semidirect
45. #14579152C2×C4semidirect
69. #125×C79C2×C4semidirect
185. D79#1992direct (N × H)
193. #1992D79direct (N × H)
195. C79C2×#1992semidirect
235. #125C4×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#125×D792
C2×#97×D792
#384×D792
#237643702
#237643692
#237643682
#237643672
#340×D792
C79×#19922
C2×#199279