Finite Group Databasebeta

← #34181337

Subgroups — #34181337

Order 20224.

438 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098687C211yesmaximal, characteristic
2#23763527C211yesmaximal, characteristic
3#23763406C211yesmaximal, characteristic
4#23763402C211yesmaximal, characteristic
5C2×#19098313C211yesmaximal, characteristic
6#23761284C211yesmaximal, characteristic
7C79×#1296C211yesmaximal, characteristic
8C2×C4×Dic158C2211yescharacteristic
9#19098687—22no—
10#19098687C414yescomplemented
11C2×C4⋊(C79⋊C8)C2211yescharacteristic
12C2×Dic79⋊C8—21no—
13C2×#14579086—21no—
14C2×#14579084—21no—
15C2×C4×C79⋊C8C2211yescharacteristic
16C2×C8×Dic79—21no—
17#19098433C2211yescharacteristic
18#19098326—21no—
19#19098325—21no—
20#19098325—21no—
21#19098325—21no—
22#19098313—22no—
23C2×C4⋊C8×C79C2211yescharacteristic
24C2×C4⋊C8×C79C2211yescharacteristic
25#384×C79C2211yescharacteristic
26C22×Dic158D411yescharacteristic
27C22×C79⋊C8—21no—
28C22×C79⋊C8D411yescharacteristic
29C22×C79⋊C8D411yescharacteristic
30C4×Dic158—21no—
31C4×Dic158—21no—
32C4×Dic158C2×C412yes—
33C4×Dic158Q812yes—
34C2×C4⋊Dic79—21no—
35C2×C4⋊Dic79—21no—
36C2×C4⋊Dic79—21no—
37C2×C4⋊Dic79D411yescharacteristic
38C2×Dic79⋊C4—21no—
39C2×C4×Dic79—21no—
40C4⋊(C79⋊C8)—21no—
41C4⋊(C79⋊C8)—21no—
42Dic79⋊C8—24no—
43#14579086—42no—
44#14579084—42no—
45C4×C79⋊C8C2×C412yes—
46C4×C79⋊C8D412yes—
47C8×Dic79—24no—
48C22×C8×C79—21no—
49C22×C8×C79—21no—
50C2×C4⋊C4×C79—21no—
51C2×C4⋊C4×C79—21no—
52C2×C4⋊C4×C79—21no—
53C2×C42×C79C2311yescharacteristic
54C4⋊C8×C79—21no—
55C4⋊C8×C79—21no—
56C4⋊C8×C79—21no—
57C4⋊C8×C79C2×C412yes—
58C2×Dic158—21no—
59C2×Dic158—21no—
60C2×Dic158—21no—
61C2×Dic158C4⋊C412yes—
62C2×Dic158SD1612yes—
63C2×Dic158SD1612yes—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C22×Dic79—41no—
67C2×C79⋊C8—21no—
68C2×C79⋊C8—21no—
69C2×C79⋊C8—21no—
70C2×C79⋊C8—21no—
71C2×C79⋊C8—41no—
72C2×C79⋊C8—41no—
73C2×C79⋊C8—41no—
74C2×C79⋊C8C22⋊C412yes—
75C2×C79⋊C8C22⋊C412yes—
76C4⋊Dic79—21no—
77C4⋊Dic79—41no—
78C4⋊Dic79—41no—
79C4⋊Dic79—41no—
80C4⋊Dic79—41no—
81C4⋊Dic79—81no—
82C4⋊Dic79C4⋊C412yes—
83Dic79⋊C4—22no—
84Dic79⋊C4—22no—
85C4×Dic79—22no—
86C4×Dic79—22no—
87C22×C4×C79—41no—
88C22×C4×C79C2×D411yescharacteristic
89C22×C4×C79C2×D411yescharacteristic
90C22×C4×C79#4111yescharacteristic
91C2×C8×C79—22no—
92C2×C8×C79—41no—
93C2×C8×C79—41no—
94C2×C8×C79—41no—
95C2×C8×C79—41no—
96C2×C8×C79—41no—
97C4⋊C4×C79—41no—
98C4⋊C4×C79—41no—
99C4⋊C4×C79—41no—
100C4⋊C4×C79—41no—
101C4⋊C4×C79—81no—
102C42×C79C22×C411yescharacteristic
103C42×C79C2×D411yescharacteristic
104C42×C79C2×Q811yescharacteristic
105C42×C79#4111yescharacteristic
106C23×C79#12111yescharacteristic
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—81no—
110C2×C4×C79—81no—
111C2×C4×C79—81no—
112C2×C4×C79C2×C22⋊C411yescharacteristic
113C2×C4×C79C2×C4⋊C411yescharacteristic
114C2×C4×C79#11711yescharacteristic
115C2×C4×C79#12111yescharacteristic
116C2×C4×C79C22⋊Q811yescharacteristic
117C2×C4×C79C22⋊Q811yescharacteristic
118C2×C4×C79C2×SD1611yescharacteristic
119C2×C4×C79C2×SD1611yescharacteristic
120C2×C4×C79#13511yescharacteristic
121C2×C4×C79#13511yescharacteristic
122C2×C4×C79#13511yescharacteristic
123C2×C4×C79#13511yescharacteristic
124C2×C4×C79#13711yescharacteristic
125C2×C4×C79#13711yescharacteristic
126C2×Dic79—22no—
127C2×Dic79—22no—
128C2×Dic79—22no—
129C2×Dic79—22no—
130C2×Dic79—41no—
131C2×Dic79—41no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135Dic158—22no—
136Dic158—22no—
137Dic158—22no—
138Dic158#10614yes—
139C8×C79—42no—
140C8×C79—81no—
141C79⋊C8—22no—
142C79⋊C8—22no—
143C79⋊C8—81no—
144C22×C79#38011yescharacteristic
145C22×C79#46411yescharacteristic
146C22×C79#46411yescharacteristic
147C22×C79#46511yescharacteristic
148C22×C79#46511yescharacteristic
149C22×C79#47211yescharacteristic
150C22×C79#47311yescharacteristic
151C4×C79—21no—
152C4×C79—21no—
153C4×C79—161no—
154C4×C79#41611yescharacteristic
155C4×C79#41911yescharacteristic
156C4×C79C2×#10611yescharacteristic
157C4×C79#42711yescharacteristic
158C4×C79#46511yescharacteristic
159C4×C79#46511yescharacteristic
160C4×C79#47911yescharacteristic
161C4×C79#47911yescharacteristic
162Dic79—24no—
163Dic79—42no—
164Dic79—161no—
165#8647—791nomaximal, Sylow
166C2×C79#167811yescharacteristic
167C2×C79#167811yescharacteristic
168C2×C79#168011yescharacteristic
169C2×C79#168011yescharacteristic
170C2×C79#180511yescharacteristic
171C2×C79#180711yescharacteristic
172C2×C79#181611yescharacteristic
173C2×C8×Q8—791no—
174#1834—791no—
175#1803—791no—
176#1803—791no—
177C2×#334—791no—
178#1296—791no—
179#1296D7911yescharacteristic
180C79#864711yescharacteristic, complemented, Sylow
181C2×C4×Q8—791no—
182C8×Q8—794no—
183C8×Q8—1582no—
184C2×C4⋊C8—791no—
185C2×C4⋊C8—1581no—
186C2×C4⋊C8C2×D7911yescharacteristic
187C2×C4⋊C8C2×D7911yescharacteristic
188C2×#103—1581no—
189C2×#103—1581no—
190C2×C4×C8—791no—
191C2×C4×C8—1581no—
192#384—791no—
193#384C2×D7911yescharacteristic
194#340—1581no—
195#340—1581no—
196#340—1581no—
197#340—1581no—
198#334—1582no—
199C22×Q8—791no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—791no—
203C22×C8—791no—
204C22×C8—1581no—
205C4×Q8—792no—
206C4×Q8—792no—
207C4×Q8—1581no—
208C4×Q8—1581no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—791no—
213C2×C4⋊C4—1581no—
214C2×C4⋊C4—1581no—
215C2×C4⋊C4—1581no—
216C2×C4⋊C4—1581no—
217C2×C42—1581no—
218C2×C42C22×D7911yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—1584no—
223C4⋊C8—1581no—
224C4⋊C8—1581no—
225C4⋊C8C4×D7912yes—
226#103—3162no—
227#103—3162no—
228C4×C8—792no—
229C4×C8—792no—
230C4×C8—1584no—
231C2×Q8—792no—
232C2×Q8—792no—
233C2×Q8—792no—
234C2×Q8—1581no—
235C2×Q8—1581no—
236C2×Q8—1581no—
237C22×C4—41no—
238C22×C4—3161no—
239C22×C4—1581no—
240C22×C4—1581no—
241C22×C4D4×D7911yescharacteristic
242C22×C4D4×D7911yescharacteristic
243C22×C4#1192962411yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—3161no—
251C2×C8—3161no—
252C2×C8—3161no—
253C2×C8—792no—
254C2×C8—792no—
255C2×C8—1581no—
256C2×C8—1581no—
257C2×C8—1581no—
258C2×C8—1581no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—3161no—
265C4⋊C4—3161no—
266C4⋊C4—3161no—
267C4⋊C4—3161no—
268C4⋊C4—792no—
269C4⋊C4—6321no—
270C4⋊C4—1582no—
271C4⋊C4—1581no—
272C4⋊C4—1582no—
273C42—1582no—
274C42—1582no—
275C42C2×C4×D7911yescharacteristic
276C42D4×D7911yescharacteristic
277C42Q8×D7911yescharacteristic
278C42#1192962411yescharacteristic
279C23#1457913411yescharacteristic
280Q8—794no—
281Q8—1582no—
282Q8—1582no—
283Q8—1582no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—3161no—
290C2×C4—3161no—
291C2×C4—6321no—
292C2×C4—6321no—
293C2×C4—6321no—
294C2×C4—1582no—
295C2×C4—1582no—
296C2×C4—1582no—
297C2×C4—1582no—
298C2×C4C22⋊C4×D7911yescharacteristic
299C2×C4C4⋊C4×D7911yescharacteristic
300C2×C4#1457911811yescharacteristic
301C2×C4#1457913411yescharacteristic
302C2×C4#1457913911yescharacteristic
303C2×C4#1457913911yescharacteristic
304C2×C4SD16×D7911yescharacteristic
305C2×C4SD16×D7911yescharacteristic
306C2×C4#1457918011yescharacteristic
307C2×C4#1457918011yescharacteristic
308C2×C4#1457918211yescharacteristic
309C2×C4#1457918411yescharacteristic
310C2×C4#1457919011yescharacteristic
311C2×C4#1457919311yescharacteristic
312C8—42no—
313C8—81no—
314C8—6321no—
315C8—1582no—
316C8—1582no—
317C22#1909842211yescharacteristic
318C22#1909878411yescharacteristic
319C22#1909878811yescharacteristic
320C22#1909879111yescharacteristic
321C22#1909879511yescharacteristic
322C22#1909883211yescharacteristic
323C22#1909883711yescharacteristic
324C4—21no—
325C4—21no—
326C4—161no—
327C4—3162no—
328C4—1584no—
329C4—12641no—
330C4#1909855611yescharacteristic
331C4#1909857011yescharacteristic
332C4#106×D7911yescharacteristic
333C4#1909860011yescharacteristic
334C4#1909879111yescharacteristic
335C4#1909879511yescharacteristic
336C4#1909886911yescharacteristic
337C4#1909887311yescharacteristic
338C2#2376281511yescharacteristic
339C2#2376281911yescharacteristic
340C2#2376282911yescharacteristic
341C2#2376283311yescharacteristic
342C2#2376341411yescharacteristic
343C2#2376342411yescharacteristic
344C2#2376346311yescharacteristic
subgroupG/H
centerC23#14579134
commutatorC42×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1296C2
socle, prime radicalC23×C79#121
cosocleC2×C42×C79C23
hypercenter#1296D79
hypocenterC79#8647
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
10. #19098687C4semidirect
180. C79#8647semidirect

Maximal subgroups

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

subgroupindex
C2×#190986872
#237635272
#237634062
#237634022
C2×#190983132
#237612842
C79×#12962
#864779