Finite Group Databasebeta

← #34183727

Subgroups — #34183727

Order 20224.

488 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772485C211yesmaximal, characteristic, complemented
2C2×#19098661C211yesmaximal, characteristic
3#23761790C211yesmaximal, characteristic
4#23761720C211yesmaximal, characteristic
5#23761244C211yesmaximal, characteristic, complemented
6#23761230C211yesmaximal, characteristic, complemented
7C79×#1479C211yesmaximal, characteristic, complemented
8C22×#11929611C411yescharacteristic
9C2×C4×D316C2211yescharacteristic
10#19098694—22no—
11#19098694—22no—
12#19098661—22no—
13#19098661—22no—
14#19098620—22no—
15#19098616C2211yescharacteristic
16#19098616C2211yescharacteristic
17C2×#14579094C411yescharacteristic
18C2×#14579085C411yescharacteristic
19C2×#14579081C411yescharacteristic
20C2×#14579072C2211yescharacteristic
21#19098290—22no—
22#19098286—22no—
23C2×C4×Q8×C79C2211yescharacteristic
24#431×C79C2211yescharacteristic
25#431×C79C2211yescharacteristic
26Q8⋊C8×C79—22no—
27C22×D316C2×C411yescharacteristic
28C22×C4×D79—21no—
29C2×#11929611—22no—
30C2×#11929611—22no—
31C2×#11929611—22no—
32C22×C79⋊C8C2×C411yescharacteristic
33C22×C79⋊C8C2×C411yescharacteristic
34C4×D316—21no—
35C4×D316—21no—
36C4×D316—21no—
37C4×D316—21no—
38C2×C4⋊Dic79C2×C411yescharacteristic
39C2×(C2×D79)⋊C4—21no—
40#14579094—22no—
41C4⋊(C79⋊C8)—24no—
42C4⋊(C79⋊C8)—21no—
43C4⋊(C79⋊C8)—21no—
44#14579085—22no—
45#14579081—22no—
46C22⋊(C79⋊C8)—21no—
47C22⋊(C79⋊C8)D412yes—
48#14579072—24no—
49#14579072—21no—
50#14579072—21no—
51C4×C79⋊C8—21no—
52C4×C79⋊C8D412yes—
53C22×Q8×C79C2×C411yescharacteristic
54C4×Q8×C79—21no—
55C4×Q8×C79—21no—
56C4×Q8×C79D412yes—
57C4×Q8×C79D412yes—
58C2×C4⋊C4×C79—21no—
59C2×C4⋊C4×C79C2×C411yescharacteristic
60C2×C42×C79—21no—
61C2×C42×C79C2311yescharacteristic
62C4⋊C8×C79—21no—
63C4⋊C8×C79—21no—
64C22⋊C8×C79—21no—
65C22⋊C8×C79—21no—
66C4×C8×C79—21no—
67C4×C8×C79—21no—
68C23×D79—21no—
69C2×D316—21no—
70C2×D316—21no—
71C2×D316—21no—
72C2×D316—21no—
73C2×D316—21no—
74C2×D316M1612yes—
75C22×Dic79—21no—
76C2×C4×D79—41no—
77C2×C4×D79—41no—
78C2×C4×D79—82no—
79#11929611—28no—
80C2×C79⋊C8—21no—
81C2×C79⋊C8—21no—
82C2×C79⋊C8—22no—
83C2×C79⋊C8—22no—
84C2×C79⋊C8—21no—
85C2×C79⋊C8—21no—
86C2×C79⋊C8—21no—
87C2×C79⋊C8M1612yes—
88C4⋊Dic79—21no—
89C4⋊Dic79—21no—
90(C2×D79)⋊C4—41no—
91(C2×D79)⋊C4—41no—
92C2×Q8×C79—21no—
93C2×Q8×C79—21no—
94C2×Q8×C79—21no—
95C2×Q8×C79—21no—
96C2×Q8×C79—21no—
97C2×Q8×C79C22⋊C412yes—
98C22×C4×C79—21no—
99C22×C4×C79—21no—
100C22×C4×C79C22×C411yescharacteristic
101C22×C4×C79C2×D411yescharacteristic
102C22×C4×C79#4111yescharacteristic
103C2×C8×C79—41no—
104C2×C8×C79—41no—
105C4⋊C4×C79—21no—
106C4⋊C4×C79—22no—
107C4⋊C4×C79—22no—
108C4⋊C4×C79C22⋊C412yes—
109C42×C79—22no—
110C42×C79—22no—
111C42×C79C2×D411yescharacteristic
112C42×C79C2×D411yescharacteristic
113C42×C79C2×D411yescharacteristic
114C42×C79#4111yescharacteristic
115C23×C79C4×D411yescharacteristic
116C22×D79—22no—
117C22×D79—41no—
118C22×D79—41no—
119C22×D79—81no—
120C22×D79—81no—
121Q8×C79—22no—
122Q8×C79—22no—
123Q8×C79—41no—
124Q8×C79—41no—
125C2×C4×C79—22no—
126C2×C4×C79—22no—
127C2×C4×C79—41no—
128C2×C4×C79—41no—
129C2×C4×C79—41no—
130C2×C4×C79—41no—
131C2×C4×C79—81no—
132C2×C4×C79C2×C22⋊C411yescharacteristic
133C2×C4×C79C4×D411yescharacteristic
134C2×C4×C79#12011yescharacteristic
135C2×C4×C79#12111yescharacteristic
136C2×C4×C79#12111yescharacteristic
137C2×C4×C79#12311yescharacteristic
138C2×C4×C79C2×M1611yescharacteristic
139C2×C4×C79C2×M1611yescharacteristic
140C2×C4×C79#13111yescharacteristic
141C2×C4×C79#13111yescharacteristic
142C2×Dic79—41no—
143C2×Dic79—81no—
144D316—22no—
145D316—22no—
146D316—41no—
147D316—41no—
148C4×D79—82no—
149C4×D79—82no—
150C8×C79—81no—
151C8×C79—81no—
152C79⋊C8—22no—
153C79⋊C8—42no—
154C79⋊C8—42no—
155C79⋊C8—41no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79#38611yescharacteristic
159C22×C79#43511yescharacteristic
160C22×C79#43611yescharacteristic
161C2×D79—42no—
162C2×D79—82no—
163C2×D79—81no—
164C2×D79—81no—
165C2×D79—82no—
166C4×C79—21no—
167C4×C79—21no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—42no—
171C4×C79—42no—
172C4×C79#40711yescharacteristic
173C4×C79#40811yescharacteristic
174C4×C79#43511yescharacteristic
175C4×C79#43611yescharacteristic
176Dic79—81no—
177#9094—791nomaximal, Sylow
178C2×C79—21no—
179C2×C79—21no—
180C2×C79#187011yescharacteristic
181C2×C79#190311yescharacteristic
182C2×C79#190511yescharacteristic
183D79—82no—
184#2983—791no—
185C2×#440—791no—
186#1479D7911yescharacteristic, complemented
187#1478—791no—
188#1460—791no—
189#1281—791no—
190#1275—791no—
191C79#909411yescharacteristic, complemented, Sylow
192C22×SD16—791no—
193C2×C4×Q8C2×D7911yescharacteristic
194C2×C4×D4—791no—
195#446—1582no—
196#446—1582no—
197#440—1582no—
198#440—1582no—
199#432—1582no—
200#431—791no—
201#431—791no—
202#431C2×D7911yescharacteristic
203#431C2×D7911yescharacteristic
204C2×#107—791no—
205C2×#103—791no—
206C2×#102—791no—
207C2×#97—791no—
208Q8⋊C8—22no—
209D4⋊C8—1582no—
210#323—1582no—
211C22×Q8C4×D7911yescharacteristic
212C22×D4—791no—
213C23×C4—1581no—
214C2×SD16—1582no—
215C2×SD16—1582no—
216C2×SD16—1582no—
217C22×C8—791no—
218C22×C8—791no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8D31612yes—
222C4×Q8C22⋊D7912yes—
223C4×D4—1581no—
224C4×D4—1581no—
225C4×D4—1581no—
226C4×D4—1581no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—791no—
229C2×C4⋊C4C4×D7911yescharacteristic
230C2×C22⋊C4—1581no—
231C2×C42—21no—
232C2×C42C22×D7911yescharacteristic
233#107—1582no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—1584no—
237C4⋊C8—1581no—
238C4⋊C8—1581no—
239#103—1582no—
240#102—1582no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—792no—
244C22⋊C8—1581no—
245#97—1584no—
246#97—1581no—
247#97—1581no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—792no—
251C4×C8—1581no—
252C24—1581no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8(C2×D79)⋊C412yes—
259C2×D4—792no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—3161no—
268C22×C4—3161no—
269C22×C4—6322no—
270C22×C4—1581no—
271C22×C4C2×C4×D7911yescharacteristic
272C22×C4D4×D7911yescharacteristic
273C22×C4#1192962311yescharacteristic
274SD16—1588no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—792no—
278C2×C8—1581no—
279C2×C8—1582no—
280C2×C8—1582no—
281C2×C8—1581no—
282C2×C8—1581no—
283C2×C8—1581no—
284C2×C8—1581no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—1581no—
289C4⋊C4—1581no—
290C4⋊C4(C2×D79)⋊C412yes—
291C22⋊C4—3161no—
292C22⋊C4—3161no—
293C42—22no—
294C42—22no—
295C42D4×D7911yescharacteristic
296C42C2×C22⋊D7911yescharacteristic
297C42C2×D31611yescharacteristic
298C42#1192962311yescharacteristic
299C23—3161no—
300C23—3161no—
301C23—6321no—
302C23—6321no—
303C23—1582no—
304C23(C22⋊D79)⋊C411yescharacteristic
305Q8—22no—
306Q8—22no—
307Q8—41no—
308Q8—41no—
309D4—3161no—
310D4—3161no—
311D4—1582no—
312D4—1582no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—3161no—
321C2×C4—6322no—
322C2×C4—6322no—
323C2×C4—6321no—
324C2×C4C2×(C2×D79)⋊C411yescharacteristic
325C2×C4(C22⋊D79)⋊C411yescharacteristic
326C2×C4#1457913111yescharacteristic
327C2×C4#1457913311yescharacteristic
328C2×C4#1457913311yescharacteristic
329C2×C4#1457914511yescharacteristic
330C2×C4M16×D7911yescharacteristic
331C2×C4M16×D7911yescharacteristic
332C2×C4#1457916711yescharacteristic
333C2×C4#1457916711yescharacteristic
334C8—81no—
335C8—81no—
336C8—3162no—
337C8—3162no—
338C8—3161no—
339C8—1582no—
340C22—21no—
341C22—21no—
342C22—3162no—
343C22—6322no—
344C22—6322no—
345C22—6321no—
346C22—6321no—
347C22#1909844011yescharacteristic
348C22#1909863711yescharacteristic
349C22#1909863811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—42no—
356C4—6321no—
357C4#1909852611yescharacteristic
358C4#1909852911yescharacteristic
359C4#1909863711yescharacteristic
360C4#1909863811yescharacteristic
361C2—21no—
362C2—21no—
363C2—6322no—
364C2#2376369511yescharacteristic
365C2#2376387811yescharacteristic
366C2#2376389211yescharacteristic
subgroupG/H
centerC22#19098440
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1479C2
socleC22×C79#386
prime radicalC22×D316C2×C4
cosocleC2×C42×C79C23
hypercenter#1479D79
hypocenterC79#9094
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
1. #23772485C2semidirect
5. #23761244C2semidirect
6. #23761230C2semidirect
7. C79×#1479C2semidirect
186. #1479D79semidirect
191. C79#9094semidirect

Maximal subgroups

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

subgroupindex
#237724852
C2×#190986612
#237617902
#237617202
#237612442
#237612302
C79×#14792
#909479