Finite Group Databasebeta

← #34192730

Subgroups — #34192730

Order 20224.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23764163C211yesmaximal, characteristic
2#23764158C211yesmaximal, characteristic
3#23763527C211yesmaximal, characteristic
4#23761283C211yesmaximal, characteristic
5#23761241C211yesmaximal, characteristic
6#23761241C211yesmaximal, characteristic
7C79×#2571C211yesmaximal, characteristic
8C2×#14579094—21no—
9C2×#14579092—21no—
10C2×C4⋊(C79⋊C8)C2211yescharacteristic
11C2×C4⋊(C79⋊C8)C2211yescharacteristic
12C2×C4×C79⋊C8C2211yescharacteristic
13#19098433C2211yescharacteristic
14#19098325—22no—
15#19098325—21no—
16#19098325—21no—
17#400×C79—22no—
18#389×C79—21no—
19#389×C79—21no—
20#384×C79C2211yescharacteristic
21#382×C79—21no—
22#382×C79—21no—
23C4×C4⋊C4×C79C2211yescharacteristic
24C4×C4⋊C4×C79C2211yescharacteristic
25C22×C79⋊C8—21no—
26C22×C79⋊C8—21no—
27C22×C79⋊C8—21no—
28C2×C4⋊Dic79—21no—
29C2×C4⋊Dic79—21no—
30C2×C4⋊Dic79—21no—
31#14579094—42no—
32#14579092—42no—
33C4⋊(C79⋊C8)—21no—
34C4⋊(C79⋊C8)—21no—
35C4⋊(C79⋊C8)Q812yes—
36C4⋊(C79⋊C8)Q812yes—
37C4×C79⋊C8—21no—
38C4×C79⋊C8Q812yes—
39C2×C4⋊C4×C79—21no—
40C2×C4⋊C4×C79—21no—
41C2×C4⋊C4×C79—22no—
42C2×C4⋊C4×C79D411yescharacteristic
43C2×C4⋊C4×C79D411yescharacteristic
44C2×C4⋊C4×C79D411yescharacteristic
45C2×C4⋊C4×C79D411yescharacteristic
46C2×C4⋊C4×C79D412yes—
47C2×C42×C79—21no—
48C2×C42×C79—21no—
49C2×C42×C79C2311yescharacteristic
50#95×C79—22no—
51#95×C79—22no—
52#95×C79—22no—
53#95×C79—21no—
54#95×C79—21no—
55C22×Dic79—41no—
56C2×C79⋊C8—22no—
57C2×C79⋊C8—22no—
58C2×C79⋊C8—22no—
59C2×C79⋊C8—41no—
60C2×C79⋊C8—41no—
61C2×C79⋊C8—41no—
62C2×C79⋊C8—41no—
63C2×C79⋊C8—41no—
64C2×C79⋊C8—41no—
65C4⋊Dic79—42no—
66C4⋊Dic79—41no—
67C4⋊Dic79—41no—
68C4⋊Dic79—41no—
69C4⋊Dic79—41no—
70C22×C4×C79—21no—
71C22×C4×C79—21no—
72C22×C4×C79—21no—
73C22×C4×C79—21no—
74C22×C4×C79—22no—
75C22×C4×C79C2×D411yescharacteristic
76C22×C4×C79C2×D411yescharacteristic
77C22×C4×C79C2×D411yescharacteristic
78C4⋊C4×C79—21no—
79C4⋊C4×C79—21no—
80C4⋊C4×C79—21no—
81C4⋊C4×C79—21no—
82C4⋊C4×C79—21no—
83C4⋊C4×C79—21no—
84C4⋊C4×C79—21no—
85C4⋊C4×C79—21no—
86C4⋊C4×C79—42no—
87C4⋊C4×C79—41no—
88C4⋊C4×C79—41no—
89C4⋊C4×C79—41no—
90C4⋊C4×C79—41no—
91C4⋊C4×C79—82no—
92C42×C79—41no—
93C42×C79—41no—
94C42×C79—41no—
95C42×C79—41no—
96C42×C79C2×Q811yescharacteristic
97C42×C79C2×Q811yescharacteristic
98C42×C79C2×Q811yescharacteristic
99C42×C79#4111yescharacteristic
100C23×C79#12011yescharacteristic
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—41no—
104C2×C4×C79—41no—
105C2×C4×C79—41no—
106C2×C4×C79—41no—
107C2×C4×C79—42no—
108C2×C4×C79—41no—
109C2×C4×C79—41no—
110C2×C4×C79—41no—
111C2×C4×C79—41no—
112C2×C4×C79—42no—
113C2×C4×C79—41no—
114C2×C4×C79—41no—
115C2×C4×C79—42no—
116C2×C4×C79—41no—
117C2×C4×C79—41no—
118C2×C4×C79C22⋊Q811yescharacteristic
119C2×C4×C79C22⋊Q811yescharacteristic
120C2×C4×C79C22⋊Q811yescharacteristic
121C2×C4×C79C4⋊Q811yescharacteristic
122C2×C4×C79C4⋊Q811yescharacteristic
123C2×C4×C79C4⋊Q811yescharacteristic
124C2×C4×C79#13511yescharacteristic
125C2×C4×C79#13511yescharacteristic
126C2×C4×C79#13511yescharacteristic
127C2×C4×C79#13511yescharacteristic
128C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C79#13711yescharacteristic
131C2×C4×C79#13711yescharacteristic
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C79⋊C8—42no—
136C79⋊C8—42no—
137C79⋊C8—42no—
138C22×C79#39511yescharacteristic
139C22×C79#44911yescharacteristic
140C22×C79#44911yescharacteristic
141C22×C79#45211yescharacteristic
142C22×C79#45211yescharacteristic
143C22×C79#45411yescharacteristic
144C22×C79#45511yescharacteristic
145C4×C79—21no—
146C4×C79—21no—
147C4×C79—81no—
148C4×C79—81no—
149C4×C79—82no—
150C4×C79—81no—
151C4×C79—81no—
152C4×C79#47811yescharacteristic
153C4×C79#47811yescharacteristic
154C4×C79#47911yescharacteristic
155C4×C79#47911yescharacteristic
156C4×C79#49911yescharacteristic
157C4×C79#49911yescharacteristic
158C4×C79#50111yescharacteristic
159C4×C79#50111yescharacteristic
160Dic79—161no—
161#10578—791nomaximal, Sylow
162C2×C79#162811yescharacteristic
163C2×C79#163811yescharacteristic
164C2×C79#164011yescharacteristic
165C2×C79#164611yescharacteristic
166C2×C79#205911yescharacteristic
167C2×C79#205911yescharacteristic
168C2×C79#206111yescharacteristic
169#2571D7911yescharacteristic
170#1948—791no—
171#1947—791no—
172#1834—791no—
173#1296—791no—
174#1279—791no—
175#1279—791no—
176C79#1057811yescharacteristic, complemented, Sylow
177C2×#107—1581no—
178C2×#106—1581no—
179C2×C4⋊C8—791no—
180C2×C4⋊C8—791no—
181C2×C4×C8—791no—
182#400—22no—
183#389—21no—
184#389—21no—
185#384—791no—
186#384C2×D7911yescharacteristic
187#382—21no—
188#382—21no—
189C4×C4⋊C4C2×D7911yescharacteristic
190C4×C4⋊C4C2×D7911yescharacteristic
191#340—1582no—
192#340—1581no—
193#340—1581no—
194C22×C8—1581no—
195C22×C8—1581no—
196C22×C8—1581no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—1581no—
201C2×C4⋊C4—1581no—
202C2×C4⋊C4—1581no—
203C2×C4⋊C4C22⋊D7911yescharacteristic
204C2×C4⋊C4C22⋊D7911yescharacteristic
205C2×C4⋊C4C22⋊D7911yescharacteristic
206C2×C4⋊C4C22⋊D7911yescharacteristic
207C2×C4⋊C4C22⋊D7912yes—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42C22×D7911yescharacteristic
211#107—3162no—
212#106—3162no—
213C4⋊C8—792no—
214C4⋊C8—792no—
215C4⋊C8—1581no—
216C4⋊C8—1581no—
217C4×C8—792no—
218C4×C8—1581no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95—21no—
223#95—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—3161no—
230C22×C4C2×C22⋊D7911yescharacteristic
231C22×C4C2×C22⋊D7911yescharacteristic
232C22×C4C2×C22⋊D7911yescharacteristic
233C2×C8—3161no—
234C2×C8—3161no—
235C2×C8—3161no—
236C2×C8—3161no—
237C2×C8—3161no—
238C2×C8—3161no—
239C2×C8—1582no—
240C2×C8—1582no—
241C2×C8—1582no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—82no—
256C4⋊C4—3162no—
257C4⋊C4—3161no—
258C4⋊C4—3161no—
259C4⋊C4—3161no—
260C4⋊C4—3161no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42Q8×D7911yescharacteristic
266C42Q8×D7911yescharacteristic
267C42Q8×D7911yescharacteristic
268C42#1192962511yescharacteristic
269C23#1457913011yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—6321no—
288C2×C4—6321no—
289C2×C4—6321no—
290C2×C4#1457913711yescharacteristic
291C2×C4#1457913711yescharacteristic
292C2×C4#1457913711yescharacteristic
293C2×C4#1457915911yescharacteristic
294C2×C4#1457915911yescharacteristic
295C2×C4#1457915911yescharacteristic
296C2×C4#1457918111yescharacteristic
297C2×C4#1457918111yescharacteristic
298C2×C4#1457918111yescharacteristic
299C2×C4#1457918111yescharacteristic
300C2×C4#1457918611yescharacteristic
301C2×C4#1457918611yescharacteristic
302C2×C4#1457919111yescharacteristic
303C2×C4#1457919111yescharacteristic
304C8—3162no—
305C8—3162no—
306C8—3162no—
307C22#1909848211yescharacteristic
308C22#1909870811yescharacteristic
309C22#1909870811yescharacteristic
310C22#1909872511yescharacteristic
311C22#1909872511yescharacteristic
312C22#1909873611yescharacteristic
313C22#1909874111yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—82no—
319C4—81no—
320C4—81no—
321C4—12641no—
322C4#1909886011yescharacteristic
323C4#1909886011yescharacteristic
324C4#1909886711yescharacteristic
325C4#1909886711yescharacteristic
326C4#1909896211yescharacteristic
327C4#1909896211yescharacteristic
328C4#1909897311yescharacteristic
329C4#1909897311yescharacteristic
330C2#2376251011yescharacteristic
331C2#2376257211yescharacteristic
332C2#2376258611yescharacteristic
333C2#2376262811yescharacteristic
334C2#2376473511yescharacteristic
335C2#2376473511yescharacteristic
336C2#2376474711yescharacteristic
subgroupG/H
centerC23#14579130
commutator, cosocleC2×C42×C79C23
FrattiniC2×C42C22×D79
FittingC79×#2571C2
socle, prime radicalC23×C79#120
hypercenter#2571D79
hypocenterC79#10578
LCSG ▷ C2×C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
176. C79#10578semidirect

Maximal subgroups

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

subgroupindex
#237641632
#237641582
#237635272
#237612832
#237612412
C79×#25712
#1057879