Finite Group Databasebeta

← #34186872

Subgroups — #34186872

Order 20224.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23763516C211yesmaximal, characteristic
2#23763255C211yesmaximal, characteristic
3C4×Dic79⋊C8C211yesmaximal, characteristic
4C2×#19098315C211yesmaximal, characteristic
5C2×#19098314C211yesmaximal, characteristic
6#23761234C211yesmaximal, characteristic
7C79×#1277C211yesmaximal, characteristic
8C2×C4⋊(C79⋊C8)C2211yescharacteristic
9C2×C4⋊(C79⋊C8)C2211yescharacteristic
10C2×Dic79⋊C8C411yescharacteristic
11C2×Dic79⋊C8C411yescharacteristic
12C2×#14579071—21no—
13C2×C4×C79⋊C8C2211yescharacteristic
14C42×Dic79C2211yescharacteristic
15#19098317—21no—
16#19098317—21no—
17#19098317—21no—
18#19098317C411yescharacteristic
19#19098317C411yescharacteristic
20#19098315—22no—
21#19098314—22no—
22C2×C4⋊C8×C79C2211yescharacteristic
23C2×C4⋊C8×C79C2211yescharacteristic
24C2×C4×C8×C79C2211yescharacteristic
25C22×C79⋊C8—21no—
26C22×C79⋊C8—21no—
27C22×C79⋊C8C2×C411yescharacteristic
28C22×C79⋊C8C2×C411yescharacteristic
29C2×C4×Dic79C2×C411yescharacteristic
30C2×C4×Dic79C2×C411yescharacteristic
31C2×C4×Dic79D411yescharacteristic
32C2×C4×Dic79D411yescharacteristic
33C2×C4×Dic79Q811yescharacteristic
34C2×C4×Dic79Q811yescharacteristic
35C4⋊(C79⋊C8)—21no—
36C4⋊(C79⋊C8)—21no—
37C4⋊(C79⋊C8)—21no—
38C4⋊(C79⋊C8)D412yes—
39Dic79⋊C8—22no—
40Dic79⋊C8—22no—
41#14579071—42no—
42C4×C79⋊C8—21no—
43C4×C79⋊C8—21no—
44C22×C8×C79—21no—
45C22×C8×C79—21no—
46C22×C8×C79C2×C411yescharacteristic
47C22×C8×C79C2×C411yescharacteristic
48C2×C42×C79C2311yescharacteristic
49C4⋊C8×C79—21no—
50C4⋊C8×C79—21no—
51C4⋊C8×C79—21no—
52C4⋊C8×C79Q812yes—
53C4×C8×C79—21no—
54C4×C8×C79—21no—
55C22×Dic79C4⋊C411yescharacteristic
56C22×Dic79C4⋊C411yescharacteristic
57C22×Dic79C4⋊C411yescharacteristic
58C22×Dic79C4⋊C411yescharacteristic
59C2×C79⋊C8—21no—
60C2×C79⋊C8—21no—
61C2×C79⋊C8—22no—
62C2×C79⋊C8—21no—
63C2×C79⋊C8—21no—
64C2×C79⋊C8—21no—
65C2×C79⋊C8—41no—
66C2×C79⋊C8—41no—
67C2×C79⋊C8—41no—
68C2×C79⋊C8—41no—
69C2×C79⋊C8—41no—
70C2×C79⋊C8M1612yes—
71C4×Dic79—22no—
72C4×Dic79—21no—
73C4×Dic79—21no—
74C4×Dic79—21no—
75C4×Dic79—21no—
76C4×Dic79—21no—
77C4×Dic79—21no—
78C4×Dic79—21no—
79C4×Dic79—21no—
80C4×Dic79—41no—
81C22×C4×C79C22×C411yescharacteristic
82C22×C4×C79C2×D411yescharacteristic
83C22×C4×C79C2×Q811yescharacteristic
84C2×C8×C79—21no—
85C2×C8×C79—21no—
86C2×C8×C79—22no—
87C2×C8×C79—21no—
88C2×C8×C79—21no—
89C2×C8×C79—21no—
90C2×C8×C79—41no—
91C2×C8×C79—41no—
92C2×C8×C79—41no—
93C2×C8×C79—41no—
94C2×C8×C79—41no—
95C2×C8×C79M1612yes—
96C42×C79C2×D411yescharacteristic
97C42×C79C2×Q811yescharacteristic
98C42×C79#4111yescharacteristic
99C42×C79#4111yescharacteristic
100C23×C79C2×C4⋊C411yescharacteristic
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79C4×D411yescharacteristic
104C2×C4×C79C4×Q811yescharacteristic
105C2×C4×C79#12111yescharacteristic
106C2×C4×C79C22⋊Q811yescharacteristic
107C2×C4×C79#12511yescharacteristic
108C2×C4×C79C4⋊Q811yescharacteristic
109C2×C4×C79C2×M1611yescharacteristic
110C2×C4×C79C2×M1611yescharacteristic
111C2×C4×C79#13111yescharacteristic
112C2×C4×C79#13111yescharacteristic
113C2×C4×C79#13511yescharacteristic
114C2×C4×C79#13511yescharacteristic
115C2×C4×C79AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C79#13711yescharacteristic
117C2×Dic79—21no—
118C2×Dic79—21no—
119C2×Dic79—21no—
120C2×Dic79—21no—
121C2×Dic79—21no—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79#10812yes—
129C8×C79—22no—
130C8×C79—41no—
131C8×C79—42no—
132C8×C79—81no—
133C79⋊C8—22no—
134C79⋊C8—41no—
135C79⋊C8—42no—
136C79⋊C8—81no—
137C22×C79#38911yescharacteristic
138C22×C79#42311yescharacteristic
139C22×C79#42411yescharacteristic
140C22×C79#42711yescharacteristic
141C22×C79#42811yescharacteristic
142C22×C79C2×#10811yescharacteristic
143C22×C79#43011yescharacteristic
144C4×C79—21no—
145C4×C79—21no—
146C4×C79#43511yescharacteristic
147C4×C79#43511yescharacteristic
148C4×C79#44611yescharacteristic
149C4×C79#44611yescharacteristic
150C4×C79#46311yescharacteristic
151C4×C79#46411yescharacteristic
152C4×C79#47811yescharacteristic
153C4×C79#47911yescharacteristic
154Dic79—22no—
155Dic79—41no—
156Dic79—41no—
157Dic79—41no—
158#9606—791nomaximal, Sylow
159C2×C79#156811yescharacteristic
160C2×C79#156911yescharacteristic
161C2×C79#157211yescharacteristic
162C2×C79#157411yescharacteristic
163C2×C79#194011yescharacteristic
164C2×C79#194911yescharacteristic
165C2×C79#195011yescharacteristic
166#1831—791no—
167#1767—791no—
168C4×C4⋊C8—791no—
169C2×#335—791no—
170C2×#334—791no—
171#1277—791no—
172#1277D7911yescharacteristic
173C79#960611yescharacteristic, complemented, Sylow
174C2×C4⋊C8—791no—
175C2×C4⋊C8—791no—
176C2×C4⋊C8—791no—
177C2×C4⋊C8—791no—
178C2×C4⋊C8C2×D7911yescharacteristic
179C2×C4⋊C8C2×D7911yescharacteristic
180C2×#97—1581no—
181C2×C4×C8—791no—
182C2×C4×C8C2×D7911yescharacteristic
183C43—791no—
184#336—791no—
185#336—791no—
186#336—1581no—
187#336—1581no—
188#336—1581no—
189#335—1582no—
190#334—1582no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—791no—
194C22×C8—791no—
195C22×C8—1581no—
196C22×C8—1581no—
197C22×C8C4×D7911yescharacteristic
198C22×C8C4×D7911yescharacteristic
199C2×C42—791no—
200C2×C42—791no—
201C2×C42—791no—
202C2×C42—791no—
203C2×C42—791no—
204C2×C42—791no—
205C2×C42C22×D7911yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—792no—
210C4⋊C8—1582no—
211C4⋊C8—1582no—
212C4⋊C8—1581no—
213C4⋊C8—1581no—
214C4⋊C8—1581no—
215C4⋊C8Dic15812yes—
216#97—3162no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—1581no—
220C4×C8—1581no—
221C22×C4—791no—
222C22×C4—791no—
223C22×C4—791no—
224C22×C4—791no—
225C22×C4C2×C4×D7911yescharacteristic
226C22×C4D4×D7911yescharacteristic
227C22×C4Q8×D7911yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—3161no—
240C2×C8—3161no—
241C2×C8—3161no—
242C2×C8—3161no—
243C2×C8—3161no—
244C2×C8—792no—
245C2×C8—1581no—
246C2×C8—1582no—
247C2×C8—1581no—
248C2×C8—1581no—
249C2×C8—1581no—
250C2×C8—1581no—
251C2×C8#1192960712yes—
252C42—3161no—
253C42—1582no—
254C42—1581no—
255C42—1581no—
256C42—1581no—
257C42—1581no—
258C42—1581no—
259C42—1581no—
260C42—1581no—
261C42—1581no—
262C42D4×D7911yescharacteristic
263C42C2×Dic15811yescharacteristic
264C42#1192962311yescharacteristic
265C42#1192962411yescharacteristic
266C23C4⋊C4×D7911yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—792no—
270C2×C4—1581no—
271C2×C4—1581no—
272C2×C4—1581no—
273C2×C4—1581no—
274C2×C4—1581no—
275C2×C4—1581no—
276C2×C4—1581no—
277C2×C4—1581no—
278C2×C4—1581no—
279C2×C4—1581no—
280C2×C4—1581no—
281C2×C4(C22⋊D79)⋊C411yescharacteristic
282C2×C4C4×Dic15811yescharacteristic
283C2×C4#1457913411yescharacteristic
284C2×C4#1457913811yescharacteristic
285C2×C4#1457915111yescharacteristic
286C2×C4#1457916011yescharacteristic
287C2×C4M16×D7911yescharacteristic
288C2×C4C2×#1192960711yescharacteristic
289C2×C4#1457916711yescharacteristic
290C2×C4#1457916911yescharacteristic
291C2×C4#1457918211yescharacteristic
292C2×C4#1457918211yescharacteristic
293C2×C4#1457918511yescharacteristic
294C2×C4#1457919311yescharacteristic
295C8—22no—
296C8—41no—
297C8—42no—
298C8—81no—
299C8—3161no—
300C8—3162no—
301C8—6321no—
302C8—1582no—
303C22#1909846011yescharacteristic
304C22#1909858511yescharacteristic
305C22#1909858811yescharacteristic
306C22#1909859811yescharacteristic
307C22#1909860411yescharacteristic
308C22#108×D7911yescharacteristic
309C22#1909861011yescharacteristic
310C4—21no—
311C4—21no—
312C4—3161no—
313C4—3161no—
314C4—3161no—
315C4—1582no—
316C4#1909863111yescharacteristic
317C4#1909863711yescharacteristic
318C4#1909869111yescharacteristic
319C4#1909869311yescharacteristic
320C4#1909877711yescharacteristic
321C4#1909878811yescharacteristic
322C4#1909886511yescharacteristic
323C4#1909886811yescharacteristic
324C2#2376216011yescharacteristic
325C2#2376216611yescharacteristic
326C2#2376217711yescharacteristic
327C2#2376219011yescharacteristic
328C2#2376412211yescharacteristic
329C2#2376416711yescharacteristic
330C2#2376417411yescharacteristic
subgroupG/H
centerC22×C4D4×D79
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1277C2
socle, prime radicalC23×C79C2×C4⋊C4
cosocleC2×C42×C79C23
hypercenter#1277D79
hypocenterC79#9606
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
173. C79#9606semidirect

Maximal subgroups

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

subgroupindex
#237635162
#237632552
C4×Dic79⋊C82
C2×#190983152
C2×#190983142
#237612342
C79×#12772
#960679