Finite Group Databasebeta

← #34186690

Subgroups — #34186690

Order 20224.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23764362C211yesmaximal, characteristic
2#23764158C211yesmaximal, characteristic
3#23763269C211yesmaximal, characteristic
4C2×#19098312C211yesmaximal, characteristic
5#23761284C211yesmaximal, characteristic
6#23761234C211yesmaximal, characteristic
7C79×#1987C211yesmaximal, characteristic
8C2×#14579094—21no—
9C2×C4⋊(C79⋊C8)C2211yescharacteristic
10C2×C4⋊(C79⋊C8)C2211yescharacteristic
11C2×#14579072—21no—
12C2×C4×C79⋊C8C2211yescharacteristic
13#19098433C2211yescharacteristic
14#19098325—21no—
15#19098325—21no—
16#19098325—21no—
17#19098318—21no—
18#19098312C414yescomplemented
19C2×C4⋊Q8×C79C2211yescharacteristic
20C2×C4⋊C8×C79C2211yescharacteristic
21C4×C4⋊C4×C79C2211yescharacteristic
22#340×C79—21no—
23#340×C79—21no—
24C22×C79⋊C8—21no—
25C22×C79⋊C8—21no—
26C22×C79⋊C8D411yescharacteristic
27C22×C79⋊C8D411yescharacteristic
28C2×C4⋊Dic79—21no—
29C2×C4⋊Dic79—21no—
30C2×C4⋊Dic79—21no—
31#14579094—42no—
32C4⋊(C79⋊C8)—21no—
33C4⋊(C79⋊C8)—21no—
34C4⋊(C79⋊C8)C2×C412yes—
35C4⋊(C79⋊C8)C2×C412yes—
36#14579072—42no—
37C4×C79⋊C8—21no—
38C4×C79⋊C8—21no—
39C22×Q8×C79—21no—
40C22×C8×C79—21no—
41C4⋊Q8×C79—21no—
42C4⋊Q8×C79—21no—
43C4⋊Q8×C79—21no—
44C4⋊Q8×C79C2×C412yes—
45C2×C4⋊C4×C79—21no—
46C2×C4⋊C4×C79—21no—
47C2×C4⋊C4×C79D411yescharacteristic
48C2×C4⋊C4×C79D411yescharacteristic
49C2×C42×C79—21no—
50C2×C42×C79C2311yescharacteristic
51C4⋊C8×C79—21no—
52C4⋊C8×C79—21no—
53#95×C79—21no—
54C22×Dic79—41no—
55C2×C79⋊C8—22no—
56C2×C79⋊C8—22no—
57C2×C79⋊C8—21no—
58C2×C79⋊C8—21no—
59C2×C79⋊C8—21no—
60C2×C79⋊C8—21no—
61C2×C79⋊C8—21no—
62C2×C79⋊C8—41no—
63C2×C79⋊C8—41no—
64C2×C79⋊C8—41no—
65C2×C79⋊C8—41no—
66C2×C79⋊C8Q1612yes—
67C4⋊Dic79—41no—
68C4⋊Dic79—41no—
69C4⋊Dic79—41no—
70C4⋊Dic79—41no—
71C4⋊Dic79—81no—
72C2×Q8×C79—22no—
73C2×Q8×C79—41no—
74C2×Q8×C79—81no—
75C2×Q8×C79—81no—
76C22×C4×C79—21no—
77C22×C4×C79—21no—
78C22×C4×C79—41no—
79C22×C4×C79C2×D411yescharacteristic
80C22×C4×C79C2×D411yescharacteristic
81C22×C4×C79#4111yescharacteristic
82C2×C8×C79—41no—
83C2×C8×C79—41no—
84C2×C8×C79—41no—
85C4⋊C4×C79—22no—
86C4⋊C4×C79—22no—
87C4⋊C4×C79—21no—
88C4⋊C4×C79—21no—
89C4⋊C4×C79—21no—
90C4⋊C4×C79—21no—
91C4⋊C4×C79—41no—
92C4⋊C4×C79—41no—
93C42×C79—41no—
94C42×C79—41no—
95C42×C79C22×C411yescharacteristic
96C42×C79#4111yescharacteristic
97C42×C79#4111yescharacteristic
98C42×C79#4111yescharacteristic
99C23×C79#12111yescharacteristic
100Q8×C79—82no—
101Q8×C79—82no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—42no—
105C2×C4×C79—41no—
106C2×C4×C79—41no—
107C2×C4×C79—41no—
108C2×C4×C79—41no—
109C2×C4×C79—41no—
110C2×C4×C79—41no—
111C2×C4×C79—81no—
112C2×C4×C79—81no—
113C2×C4×C79#11711yescharacteristic
114C2×C4×C79C4×D411yescharacteristic
115C2×C4×C79C4×D411yescharacteristic
116C2×C4×C79#12311yescharacteristic
117C2×C4×C79#12411yescharacteristic
118C2×C4×C79#12611yescharacteristic
119C2×C4×C79C2×Q1611yescharacteristic
120C2×C4×C79#13511yescharacteristic
121C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C79#13711yescharacteristic
124C2×C4×C79#13711yescharacteristic
125C2×C4×C79#13711yescharacteristic
126C2×C4×C79#13711yescharacteristic
127C2×Dic79—81no—
128C2×Dic79—81no—
129C2×Dic79—81no—
130C8×C79—81no—
131C79⋊C8—22no—
132C79⋊C8—42no—
133C79⋊C8—42no—
134C79⋊C8—41no—
135C22×C79#38811yescharacteristic
136C22×C79#46211yescharacteristic
137C22×C79#46311yescharacteristic
138C22×C79#46811yescharacteristic
139C22×C79#47011yescharacteristic
140C22×C79#47111yescharacteristic
141C22×C79#47211yescharacteristic
142C4×C79—21no—
143C4×C79—21no—
144C4×C79—82no—
145C4×C79—81no—
146C4×C79—81no—
147C4×C79C4×Q1611yescharacteristic
148C4×C79#44011yescharacteristic
149C4×C79#44011yescharacteristic
150C4×C79#44111yescharacteristic
151C4×C79#48411yescharacteristic
152C4×C79#48511yescharacteristic
153C4×C79#48911yescharacteristic
154C4×C79#49111yescharacteristic
155Dic79—161no—
156#9576—791nomaximal, Sylow
157C2×C79#169211yescharacteristic
158C2×C79#169611yescharacteristic
159C2×C79#169711yescharacteristic
160C2×C79#170311yescharacteristic
161C2×C79#192811yescharacteristic
162C2×C79#193111yescharacteristic
163C2×C79#193511yescharacteristic
164#1990—791no—
165#1987D7911yescharacteristic
166#1947—791no—
167#1770—791no—
168C2×#333—791no—
169#1296—791no—
170#1277—791no—
171C79#957611yescharacteristic, complemented, Sylow
172C2×C4⋊Q8C2×D7911yescharacteristic
173C2×#107—1581no—
174C2×C4⋊C8—791no—
175C2×C4⋊C8—791no—
176C2×C4⋊C8C2×D7911yescharacteristic
177C2×#97—1581no—
178C2×C4×C8—791no—
179#384—791no—
180C4×C4⋊C4C2×D7911yescharacteristic
181#340—21no—
182#340—21no—
183#340—1581no—
184#340—1581no—
185#340—1581no—
186#336—1581no—
187#333—794no—
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—791no—
191C22×C8—791no—
192C22×C8—1581no—
193C22×C8—1581no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C4×D7912yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—1581no—
201C2×C4⋊C4—1581no—
202C2×C4⋊C4—1581no—
203C2×C4⋊C4C22⋊D7911yescharacteristic
204C2×C4⋊C4C22⋊D7911yescharacteristic
205C2×C42—21no—
206C2×C42C22×D7911yescharacteristic
207#107—3162no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—792no—
211C4⋊C8—792no—
212C4⋊C8—1581no—
213C4⋊C8—1581no—
214#97—3162no—
215C4×C8—1581no—
216C4×C8—1581no—
217#95—21no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—3161no—
226C22×C4D4×D7911yescharacteristic
227C22×C4C2×C22⋊D7911yescharacteristic
228C22×C4#1192962311yescharacteristic
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—3161no—
233C2×C8—3161no—
234C2×C8—3161no—
235C2×C8—3161no—
236C2×C8—792no—
237C2×C8—1582no—
238C2×C8—1582no—
239C2×C8—1581no—
240C2×C8—1581no—
241C2×C8—1581no—
242C2×C8—1581no—
243C2×C8—1581no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—3161no—
253C4⋊C4—3161no—
254C4⋊C4—3161no—
255C4⋊C4—3161no—
256C4⋊C4—6321no—
257C42—41no—
258C42—41no—
259C42C2×C4×D7911yescharacteristic
260C42#1192962311yescharacteristic
261C42#1192962311yescharacteristic
262C42#1192962411yescharacteristic
263C23#1457913311yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—6321no—
278C2×C4—6321no—
279C2×C4—6321no—
280C2×C4#1457911711yescharacteristic
281C2×C4(C22⋊D79)⋊C411yescharacteristic
282C2×C4C4×C22⋊D7911yescharacteristic
283C2×C4#1457914311yescharacteristic
284C2×C4#1457914811yescharacteristic
285C2×C4#1457915411yescharacteristic
286C2×C4Q16×D7911yescharacteristic
287C2×C4#1457918211yescharacteristic
288C2×C4#1457918611yescharacteristic
289C2×C4#1457918811yescharacteristic
290C2×C4#1457919111yescharacteristic
291C2×C4#1457919211yescharacteristic
292C2×C4#1457919211yescharacteristic
293C2×C4#1457919311yescharacteristic
294C8—81no—
295C8—3161no—
296C8—3162no—
297C8—3162no—
298C8—1582no—
299C22#1909845711yescharacteristic
300C22#1909877111yescharacteristic
301C22#1909878011yescharacteristic
302C22#1909881111yescharacteristic
303C22#1909881911yescharacteristic
304C22#1909882411yescharacteristic
305C22#1909883111yescharacteristic
306C4—21no—
307C4—21no—
308C4—81no—
309C4—82no—
310C4—81no—
311C4—12641no—
312C4#1909865511yescharacteristic
313C4#1909866111yescharacteristic
314C4#1909866611yescharacteristic
315C4#1909866811yescharacteristic
316C4#1909889711yescharacteristic
317C4#1909890211yescharacteristic
318C4#1909892211yescharacteristic
319C4#1909893111yescharacteristic
320C2#2376290811yescharacteristic
321C2#2376292611yescharacteristic
322C2#2376293511yescharacteristic
323C2#2376297711yescharacteristic
324C2#2376404411yescharacteristic
325C2#2376406511yescharacteristic
326C2#2376409311yescharacteristic
subgroupG/H
centerC23#14579133
commutatorC42×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1987C2
socle, prime radicalC23×C79#121
cosocleC2×C42×C79C23
hypercenter#1987D79
hypocenterC79#9576
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
18. #19098312C4semidirect
171. C79#9576semidirect

Maximal subgroups

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

subgroupindex
#237643622
#237641582
#237632692
C2×#190983122
#237612842
#237612342
C79×#19872
#957679