Finite Group Databasebeta

← #34183341

Subgroups — #34183341

Order 20224.

484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772485C211yesmaximal, characteristic
2#23766691C211yesmaximal, characteristic
3#23761848C212yesmaximal
4#23761294C212yesmaximal
5C4×#101×C79C211yesmaximal, characteristic
6C2×C4×Dic158C2211yescharacteristic
7#19098694—24no—
8#19098620—21no—
9#19098620C2212yes—
10#19098616—21no—
11#19098494—21no—
12#19098493C411yescharacteristic
13#19098493C411yescharacteristic
14#19098483C411yescharacteristic
15#19098483C411yescharacteristic
16#19098482—21no—
17C4×Dic79⋊C4—21no—
18C4×Dic79⋊C4—21no—
19#19098409C2211yescharacteristic
20#19098295—24no—
21C2×C4×Q8×C79C2211yescharacteristic
22C2×#101×C79—21no—
23C4×M16×C79C2212yes—
24#343×C79—21no—
25C22×Dic158C2×C411yescharacteristic
26C4×Dic158—22no—
27C4×Dic158—22no—
28C2×C4⋊Dic79C2×C411yescharacteristic
29C2×Dic79⋊C4—21no—
30C2×Dic79⋊C4—21no—
31C2×Dic79⋊C4—21no—
32C2×Dic79⋊C4—21no—
33C2×Dic79⋊C4—21no—
34C2×C4×Dic79—21no—
35C2×C4×Dic79—21no—
36C4⋊(C79⋊C8)—22no—
37C4⋊(C79⋊C8)—22no—
38C4⋊(C79⋊C8)D414yes—
39C22⋊(C79⋊C8)—22no—
40#14579072—22no—
41#14579072—22no—
42C4×C79⋊C8—22no—
43C79⋊#95—21no—
44C79⋊#95—21no—
45C79⋊#95—21no—
46C79⋊#95—21no—
47C79⋊#95—21no—
48C79⋊#95C2×C411yescharacteristic
49C79⋊#95C2×C411yescharacteristic
50C22×Q8×C79D411yescharacteristic
51C2×M16×C79—22no—
52C4×Q8×C79—22no—
53C4×Q8×C79—22no—
54C2×C4⋊C4×C79C2×C411yescharacteristic
55C2×C4⋊C4×C79C2×C411yescharacteristic
56C2×C4⋊C4×C79D411yescharacteristic
57C2×C42×C79D411yescharacteristic
58C2×C42×C79D411yescharacteristic
59C2×C42×C79C2311yescharacteristic
60#101×C79—24no—
61#97×C79—22no—
62C4×C8×C79—22no—
63C2×Dic158—22no—
64C2×Dic158—42no—
65C22×Dic79—21no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C22×Dic79—21no—
69C2×C79⋊C8—24no—
70C4⋊Dic79—22no—
71Dic79⋊C4—42no—
72Dic79⋊C4—42no—
73Dic79⋊C4—42no—
74Dic79⋊C4—42no—
75Dic79⋊C4—42no—
76C4×Dic79—24no—
77C4×Dic79—41no—
78C4×Dic79—41no—
79C2×Q8×C79—22no—
80C2×Q8×C79—22no—
81C2×Q8×C79—41no—
82C22×C4×C79C22⋊C411yescharacteristic
83C22×C4×C79C22⋊C411yescharacteristic
84C22×C4×C79C22⋊C411yescharacteristic
85C22×C4×C79C22⋊C411yescharacteristic
86C22×C4×C79C22×C411yescharacteristic
87C22×C4×C79C2×D411yescharacteristic
88C22×C4×C79C2×D411yescharacteristic
89M16×C79—24no—
90M16×C79—42no—
91C2×C8×C79—42no—
92C4⋊C4×C79—22no—
93C4⋊C4×C79—22no—
94C4⋊C4×C79—22no—
95C42×C79—21no—
96C42×C79—21no—
97C42×C79—21no—
98C42×C79—21no—
99C42×C79C2×D412yes—
100C42×C79#4112yes—
101C23×C79C2×C22⋊C411yescharacteristic
102Q8×C79—44no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—22no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—21no—
112C2×C4×C79—21no—
113C2×C4×C79—41no—
114C2×C4×C79—41no—
115C2×C4×C79—41no—
116C2×C4×C79#10412yes—
117C2×C4×C79C4×D412yes—
118C2×C4×C79#12011yescharacteristic
119C2×C4×C79#12112yes—
120C2×C4×C79#12311yescharacteristic
121C2×Dic79—22no—
122C2×Dic79—22no—
123C2×Dic79—22no—
124C2×Dic79—41no—
125C2×Dic79—41no—
126C2×Dic79—41no—
127C2×Dic79—41no—
128C2×Dic79—41no—
129C2×Dic79—41no—
130C2×Dic79—41no—
131C2×Dic79—41no—
132C2×Dic79—41no—
133Dic158—24no—
134Dic158—42no—
135C8×C79—44no—
136C79⋊C8—44no—
137C22×C79—21no—
138C22×C79—21no—
139C22×C79#38611yescharacteristic
140C22×C79C2×#10411yescharacteristic
141C22×C79#42111yescharacteristic
142C4×C79—22no—
143C4×C79—22no—
144C4×C79—21no—
145C4×C79—22no—
146C4×C79—41no—
147C4×C79—41no—
148C4×C79—41no—
149C4×C79#45612yes—
150Dic79—42no—
151Dic79—42no—
152Dic79—42no—
153Dic79—81no—
154#9030—791nomaximal, Sylow
155C2×C79—21no—
156C2×C79—21no—
157C2×C79#187111yescharacteristic
158C2×C79#188611yescharacteristic
159C2×C79#189111yescharacteristic
160#2983—791no—
161#2399—791no—
162C4×#101D7911yescharacteristic
163#1491—792no—
164#1300—792no—
165C79#903011yescharacteristic, complemented, Sylow
166C2×C4×Q8—791no—
167C2×C4×Q8C2×D7911yescharacteristic
168#446—1584no—
169#432—792no—
170#432—1581no—
171#431—1581no—
172C2×#101—21no—
173C4×M16C2×D7912yes—
174#398—791no—
175#398—791no—
176#398—1581no—
177#395—791no—
178#395—791no—
179#395—1581no—
180C4×C4⋊C4—1581no—
181C4×C4⋊C4—1581no—
182#376—791no—
183#343—21no—
184Q8⋊C8—1584no—
185C22×Q8—791no—
186C22×Q8C22⋊D7911yescharacteristic
187C2×M16—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—1582no—
191C4×Q8—1582no—
192C2×C4⋊C4—791no—
193C2×C4⋊C4—1581no—
194C2×C4⋊C4—1581no—
195C2×C4⋊C4—1581no—
196C2×C4⋊C4—1581no—
197C2×C4⋊C4—1581no—
198C2×C4⋊C4C4×D7911yescharacteristic
199C2×C4⋊C4C4×D7911yescharacteristic
200C2×C4⋊C4C22⋊D7911yescharacteristic
201C2×C42—1581no—
202C2×C42—1581no—
203C2×C42D31611yescharacteristic
204C2×C42D31611yescharacteristic
205C2×C42C22×D7911yescharacteristic
206C4⋊C8—794no—
207C4⋊C8—1582no—
208C4⋊C8—1582no—
209#101—24no—
210C22⋊C8—1582no—
211#97—22no—
212#97—1582no—
213#97—1582no—
214C4×C8—22no—
215C4×C8—1582no—
216#95—791no—
217#95—791no—
218#95—1581no—
219#95—1581no—
220#95—1581no—
221#95—1581no—
222#95—1581no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—3162no—
227C2×Q8—1582no—
228C22×C4—1581no—
229C22×C4—1581no—
230C22×C4—1581no—
231C22×C4—1581no—
232C22×C4(C2×D79)⋊C411yescharacteristic
233C22×C4(C2×D79)⋊C411yescharacteristic
234C22×C4(C2×D79)⋊C411yescharacteristic
235C22×C4(C2×D79)⋊C411yescharacteristic
236C22×C4C2×C4×D7911yescharacteristic
237C22×C4C2×C22⋊D7911yescharacteristic
238C22×C4C2×D31611yescharacteristic
239M16—24no—
240M16—42no—
241C2×C8—42no—
242C2×C8—1584no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—3162no—
247C4⋊C4—3162no—
248C4⋊C4—3162no—
249C4⋊C4—3162no—
250C4⋊C4—3162no—
251C4⋊C4—1582no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—3161no—
257C42—3161no—
258C42—1584no—
259C42D4×D7912yes—
260C42#1192962312yes—
261C23C2×(C2×D79)⋊C411yescharacteristic
262Q8—44no—
263Q8—3162no—
264Q8—1584no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—3161no—
279C2×C4—3161no—
280C2×C4—3161no—
281C2×C4—3161no—
282C2×C4—3161no—
283C2×C4—3161no—
284C2×C4—3161no—
285C2×C4—3161no—
286C2×C4—3161no—
287C2×C4—1582no—
288C2×C4—1582no—
289C2×C4—1582no—
290C2×C4#1457908912yes—
291C2×C4(C22⋊D79)⋊C412yes—
292C2×C4#1457913111yescharacteristic
293C2×C4#1457913312yes—
294C2×C4#1457914511yescharacteristic
295C8—44no—
296C8—3164no—
297C22—21no—
298C22—21no—
299C22#1909844011yescharacteristic
300C22C2×#1457908911yescharacteristic
301C22#1909858111yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—3162no—
310C4—3162no—
311C4—3162no—
312C4—6321no—
313C4#1909874812yes—
314C2—21no—
315C2—21no—
316C2#2376370011yescharacteristic
317C2#2376379111yescharacteristic
318C2#2376381611yescharacteristic
subgroupG/H
centerC2×C4#14579131
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC4×#101×C79C2
socleC22×C79#386
prime radicalC23×C79C2×C22⋊C4
cosocleC2×C42×C79C23
hypercenterC4×#101D79
hypocenterC79#9030
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
165. C79#9030semidirect

Maximal subgroups

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

subgroupindex
#237724852
#237666912
#237618482
#237612942
C4×#101×C792
#903079