Finite Group Databasebeta

← #34179062

Subgroups — #34179062

Order 20224.

570 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C79⋊C8C211yesmaximal, characteristic
2#23763269C211yesmaximal, characteristic, complemented
3C2×D4⋊(C79⋊C8)C211yesmaximal, characteristic
4C2×#19098285C211yesmaximal, characteristic, complemented
5#23761241C211yesmaximal, characteristic, complemented
6#23761235C211yesmaximal, characteristic, complemented
7C4×#102×C79C211yesmaximal, characteristic
8C23×C79⋊C8—21no—
9D4×C79⋊C8—22no—
10D4×C79⋊C8C414yescomplemented
11C2×C4⋊(C79⋊C8)C2211yescharacteristic
12C2×C4⋊(C79⋊C8)C2211yescharacteristic
13C2×C22⋊(C79⋊C8)—21no—
14C2×#14579072—21no—
15C2×C4×C79⋊C8C2211yescharacteristic
16C2×C4×C79⋊C8C2211yescharacteristic
17#19098318—21no—
18D4⋊(C79⋊C8)C414yescomplemented
19#19098285—22no—
20C2×C4×D4×C79C2211yescharacteristic
21C2×#102×C79C412yes—
22C2×C4×C8×C79C2211yescharacteristic
23C4×C4⋊C4×C79C2211yescharacteristic
24#340×C79C412yes—
25C22×C79⋊C8—21no—
26C22×C79⋊C8—21no—
27C22×C79⋊C8—21no—
28C22×C79⋊C8—24no—
29C22×C79⋊C8—42no—
30C22×C79⋊C8—42no—
31C22×C79⋊C8D411yescharacteristic
32C22×C79⋊C8D411yescharacteristic
33C4⋊(C79⋊C8)—21no—
34C4⋊(C79⋊C8)—21no—
35C4⋊(C79⋊C8)C2×C412yes—
36C4⋊(C79⋊C8)C2×C412yes—
37C22⋊(C79⋊C8)—24no—
38#14579072—42no—
39C4×C79⋊C8—21no—
40C4×C79⋊C8C2×C412yes—
41C4×C79⋊C8C2×C412yes—
42C4×C79⋊C8D412yes—
43C22×D4×C79C2×C411yescharacteristic
44C23×C4×C79—21no—
45C22×C8×C79C2×C412yes—
46C4×D4×C79—21no—
47C4×D4×C79—21no—
48C4×D4×C79C2×C412yes—
49C4×D4×C79C2×C412yes—
50C2×C4⋊C4×C79C2×C412yes—
51C2×C4⋊C4×C79C2×C411yescharacteristic
52C2×C22⋊C4×C79—21no—
53C2×C42×C79—21no—
54C2×C42×C79C2311yescharacteristic
55#102×C79—24no—
56C4×C8×C79—21no—
57C4×C8×C79—21no—
58#95×C79—21no—
59C2×C79⋊C8—22no—
60C2×C79⋊C8—22no—
61C2×C79⋊C8—22no—
62C2×C79⋊C8—21no—
63C2×C79⋊C8—21no—
64C2×C79⋊C8—42no—
65C2×C79⋊C8—48no—
66C2×C79⋊C8—41no—
67C2×C79⋊C8—41no—
68C2×C79⋊C8—41no—
69C2×C79⋊C8—41no—
70C2×C79⋊C8C22⋊C412yes—
71C2×C79⋊C8C22⋊C412yes—
72C2×C79⋊C8D812yes—
73C2×C79⋊C8SD1612yes—
74C24×C79—21no—
75C2×D4×C79—21no—
76C2×D4×C79—22no—
77C2×D4×C79C4212yes—
78C2×D4×C79M1614yes—
79C22×C4×C79—21no—
80C22×C4×C79—22no—
81C22×C4×C79—22no—
82C22×C4×C79—22no—
83C22×C4×C79—41no—
84C22×C4×C79—41no—
85C22×C4×C79—41no—
86C22×C4×C79—41no—
87C22×C4×C79C22×C411yescharacteristic
88C22×C4×C79C2×D411yescharacteristic
89C22×C4×C79#4111yescharacteristic
90C2×C8×C79—22no—
91C2×C8×C79—22no—
92C2×C8×C79—22no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79—22no—
95C4⋊C4×C79—22no—
96C4⋊C4×C79C4212yes—
97C22⋊C4×C79—22no—
98C22⋊C4×C79—22no—
99C42×C79—41no—
100C42×C79—41no—
101C42×C79C22×C411yescharacteristic
102C42×C79C22×C411yescharacteristic
103C42×C79C2×D411yescharacteristic
104C42×C79#4111yescharacteristic
105C23×C79—22no—
106C23×C79—24no—
107C23×C79—41no—
108C23×C79—41no—
109C23×C79—42no—
110C23×C79C4×D411yescharacteristic
111D4×C79—22no—
112D4×C79—24no—
113D4×C79#9714yescomplemented
114C2×C4×C79—22no—
115C2×C4×C79—22no—
116C2×C4×C79—41no—
117C2×C4×C79—41no—
118C2×C4×C79—42no—
119C2×C4×C79—42no—
120C2×C4×C79—42no—
121C2×C4×C79—42no—
122C2×C4×C79—42no—
123C2×C4×C79—42no—
124C2×C4×C79—42no—
125C2×C4×C79C2×C4211yescharacteristic
126C2×C4×C79C2×C22⋊C411yescharacteristic
127C2×C4×C79#11711yescharacteristic
128C2×C4×C79C4×D411yescharacteristic
129C2×C4×C79C4×D411yescharacteristic
130C2×C4×C79C4×D411yescharacteristic
131C2×C4×C79C2×M1612yes—
132C2×C4×C79#13112yes—
133C2×C4×C79C2×D811yescharacteristic
134C2×C4×C79C2×SD1611yescharacteristic
135C2×C4×C79#13511yescharacteristic
136C2×C4×C79#13511yescharacteristic
137C8×C79—42no—
138C79⋊C8—22no—
139C79⋊C8—42no—
140C79⋊C8—42no—
141C79⋊C8—42no—
142C79⋊C8#10214yescomplemented
143C22×C79—24no—
144C22×C79—44no—
145C22×C79—44no—
146C22×C79—42no—
147C22×C79—42no—
148C22×C79C4×C22⋊C411yescharacteristic
149C22×C79#43512yes—
150C22×C79C4×D811yescharacteristic
151C22×C79C4×SD1611yescharacteristic
152C22×C79#44412yes—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—42no—
156C4×C79—82no—
157C4×C79C2×#9711yescharacteristic
158C4×C79#40511yescharacteristic
159C4×C79C2×#10211yescharacteristic
160C4×C79#41611yescharacteristic
161C4×C79#43512yes—
162C4×C79C4×D811yescharacteristic
163C4×C79C4×SD1611yescharacteristic
164#8202—791nomaximal, Sylow
165C2×C79—44no—
166C2×C79#158112yes—
167C2×C79#158212yes—
168C2×C79#175211yescharacteristic
169C2×C79C4×#10211yescharacteristic
170C2×C79#176511yescharacteristic
171C2×C8×D4—791no—
172#1770—791no—
173C4×#102D7911yescharacteristic
174C2×D4⋊C8—791no—
175C2×#322—791no—
176#1279—791no—
177#1277—791no—
178C79#820211yescharacteristic, complemented, Sylow
179C23×C8—1581no—
180C2×C4×D4C2×D7911yescharacteristic
181C8×D4—794no—
182C8×D4—1582no—
183C2×C4⋊C8—791no—
184C2×C4⋊C8—791no—
185C2×#102Dic7912yes—
186C2×C22⋊C8—1581no—
187C2×#97—1581no—
188C2×C4×C8—791no—
189C2×C4×C8—791no—
190C2×C4×C8C2×D7911yescharacteristic
191C4×C4⋊C4C2×D7911yescharacteristic
192#340Dic7912yes—
193#336—1581no—
194D4⋊C8—794no—
195#322—1582no—
196C22×D4C2×Dic7911yescharacteristic
197C23×C4—21no—
198C22×C8—3162no—
199C22×C8—3162no—
200C22×C8—791no—
201C22×C8—791no—
202C22×C8—1584no—
203C22×C8—1581no—
204C22×C8—1581no—
205C22×C8—1581no—
206C22×C8C2×Dic7912yes—
207C4×D4—21no—
208C4×D4—21no—
209C4×D4C4×D7912yes—
210C4×D4C4×D7912yes—
211C2×C4⋊C4C2×Dic7912yes—
212C2×C4⋊C4C2×Dic7911yescharacteristic
213C2×C22⋊C4—21no—
214C2×C42—21no—
215C2×C42C22×D7911yescharacteristic
216C4⋊C8—792no—
217C4⋊C8—792no—
218C4⋊C8—1581no—
219C4⋊C8—1581no—
220#102—24no—
221C22⋊C8—1584no—
222#97—3162no—
223C4×C8—21no—
224C4×C8—21no—
225C4×C8—792no—
226C4×C8—792no—
227C4×C8—792no—
228C4×C8—1581no—
229#95—21no—
230C24—21no—
231C2×D4—21no—
232C2×D4—22no—
233C2×D4C4×Dic7912yes—
234C2×D4#1192960814yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22×Dic7911yescharacteristic
244C22×C4D4×D7911yescharacteristic
245C22×C4#1192962311yescharacteristic
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—3162no—
250C2×C8—3161no—
251C2×C8—3161no—
252C2×C8—3161no—
253C2×C8—3161no—
254C2×C8—3168no—
255C2×C8—792no—
256C2×C8—792no—
257C2×C8—792no—
258C2×C8—792no—
259C2×C8—1582no—
260C2×C8—1582no—
261C2×C8—1582no—
262C2×C8—1581no—
263C2×C8—1581no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4C4×Dic7912yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42—41no—
271C42—41no—
272C42C2×C4×D7911yescharacteristic
273C42C2×C4×D7911yescharacteristic
274C42D4×D7911yescharacteristic
275C42#1192962311yescharacteristic
276C23—24no—
277C23—22no—
278C23—41no—
279C23—41no—
280C23—42no—
281C23D4×Dic7911yescharacteristic
282D4—24no—
283D4—22no—
284D4#1457907214yescomplemented
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4C2×C4×Dic7911yescharacteristic
297C2×C4C22⋊C4×D7911yescharacteristic
298C2×C4#1457911711yescharacteristic
299C2×C4(C22⋊D79)⋊C411yescharacteristic
300C2×C4(C22⋊D79)⋊C411yescharacteristic
301C2×C4D4×Dic7911yescharacteristic
302C2×C4C2×#1192960812yes—
303C2×C4#1457916812yes—
304C2×C4D8×D7911yescharacteristic
305C2×C4SD16×D7911yescharacteristic
306C2×C4#1457918011yescharacteristic
307C2×C4#1457918211yescharacteristic
308C8—42no—
309C8—3162no—
310C8—3162no—
311C8—3162no—
312C8—794no—
313C8—1582no—
314C22—24no—
315C22—42no—
316C22—42no—
317C22—44no—
318C22—44no—
319C22C22⋊C4×Dic7911yescharacteristic
320C22#1909863512yes—
321C22D8×Dic7911yescharacteristic
322C22SD16×Dic7911yescharacteristic
323C22#1909868512yes—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—82no—
328C4C2×#1457907211yescharacteristic
329C4#1909851911yescharacteristic
330C4#102×D7911yescharacteristic
331C4#1909855611yescharacteristic
332C4#1909863512yes—
333C4#1909864311yescharacteristic
334C4#1909865411yescharacteristic
335C2—44no—
336C2#2376223012yes—
337C2#2376223712yes—
338C2#2376317811yescharacteristic
339C2#102×Dic7911yescharacteristic
340C2#2376324711yescharacteristic
subgroupG/H
centerC22×C4D4×D79
commutatorC2×C4×C79C2×C42
FrattiniC2×C42C22×D79
FittingC4×#102×C79C2
socleC23×C79C4×D4
prime radicalC22×D4×C79C2×C4
cosocleC2×C42×C79C23
hypercenterC4×#102D79
hypocenterC79#8202
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #23763269C2semidirect
4. C2×#19098285C2semidirect
5. #23761241C2semidirect
6. #23761235C2semidirect
10. D4×C79⋊C8C4semidirect
18. D4⋊(C79⋊C8)C4semidirect
113. D4×C79#97semidirect
142. C79⋊C8#102semidirect
178. C79#8202semidirect
284. D4#14579072semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C79⋊C82
#237632692
C2×D4⋊(C79⋊C8)2
C2×#190982852
#237612412
#237612352
C4×#102×C792
#820279