Finite Group Databasebeta

← #34188373

Subgroups — #34188373

Order 20224.

388 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23771785C211yesmaximal, characteristic
2#23763254C211yesmaximal, characteristic
3#23763148C211yesmaximal, characteristic
4#23761282C211yesmaximal, characteristic
5#23761282C211yesmaximal, characteristic
6#23761281C211yesmaximal, characteristic
7C79×#1295C211yesmaximal, characteristic
8C2×Dic79⋊C8—21no—
9C2×#14579072C2211yescharacteristic
10C2×#14579072C2211yescharacteristic
11#19098462C411yescharacteristic
12#19098462C411yescharacteristic
13#19098459C411yescharacteristic
14#19098459C411yescharacteristic
15#19098450—21no—
16#19098450—21no—
17#19098446—21no—
18#19098446—21no—
19#19098429C2211yescharacteristic
20C42×Dic79C2211yescharacteristic
21#19098317—21no—
22#19098317—21no—
23#19098317—21no—
24C2×#97×C79C2211yescharacteristic
25C2×#97×C79C2211yescharacteristic
26#382×C79C2211yescharacteristic
27C22×C79⋊C8—21no—
28C22×C79⋊C8—21no—
29C2×C4⋊Dic79—21no—
30C2×C4⋊Dic79—21no—
31C2×C4⋊Dic79C2×C411yescharacteristic
32C2×C4⋊Dic79C2×C411yescharacteristic
33C2×Dic79⋊C4—21no—
34C2×Dic79⋊C4—21no—
35C2×C4×Dic79C2×C411yescharacteristic
36C2×C4×Dic79C2×C411yescharacteristic
37C2×C4×Dic79D411yescharacteristic
38C2×C4×Dic79D411yescharacteristic
39C2×C4×Dic79D411yescharacteristic
40C2×C4×Dic79D411yescharacteristic
41Dic79⋊C8—24no—
42#14579072—21no—
43#14579072—21no—
44#14579072—21no—
45#14579072Q812yes—
46C79⋊#95—21no—
47C79⋊#95—21no—
48C79⋊#95—21no—
49C79⋊#95—21no—
50C79⋊#95—21no—
51C79⋊#95—21no—
52C22×C8×C79—21no—
53C22×C8×C79—21no—
54C2×C4⋊C4×C79C2×C411yescharacteristic
55C2×C4⋊C4×C79C2×C411yescharacteristic
56C2×C42×C79C2311yescharacteristic
57#97×C79—21no—
58#97×C79—21no—
59#97×C79—21no—
60#97×C79Q812yes—
61#95×C79—21no—
62#95×C79—21no—
63C22×Dic79—21no—
64C22×Dic79—21no—
65C22×Dic79C22⋊C411yescharacteristic
66C22×Dic79C22⋊C411yescharacteristic
67C22×Dic79C22⋊C411yescharacteristic
68C22×Dic79C22⋊C411yescharacteristic
69C2×C79⋊C8—22no—
70C2×C79⋊C8—22no—
71C2×C79⋊C8—41no—
72C2×C79⋊C8—41no—
73C2×C79⋊C8—41no—
74C2×C79⋊C8—41no—
75C4⋊Dic79—41no—
76C4⋊Dic79—41no—
77C4⋊Dic79—42no—
78C4⋊Dic79—42no—
79Dic79⋊C4—42no—
80Dic79⋊C4—42no—
81C4×Dic79—22no—
82C4×Dic79—41no—
83C4×Dic79—41no—
84C4×Dic79—41no—
85C4×Dic79—41no—
86C4×Dic79—41no—
87C22×C4×C79—21no—
88C22×C4×C79—21no—
89C22×C4×C79C22×C411yescharacteristic
90C22×C4×C79C2×D411yescharacteristic
91C22×C4×C79C2×D411yescharacteristic
92C2×C8×C79—22no—
93C2×C8×C79—22no—
94C2×C8×C79—41no—
95C2×C8×C79—41no—
96C2×C8×C79—41no—
97C2×C8×C79—41no—
98C4⋊C4×C79—41no—
99C4⋊C4×C79—41no—
100C42×C79C2×Q811yescharacteristic
101C42×C79C2×Q811yescharacteristic
102C42×C79#4111yescharacteristic
103C42×C79#4111yescharacteristic
104C23×C79C2×C22⋊C411yescharacteristic
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—41no—
112C2×C4×C79—41no—
113C2×C4×C79—41no—
114C2×C4×C79—41no—
115C2×C4×C79—41no—
116C2×C4×C79—41no—
117C2×C4×C79C4×Q811yescharacteristic
118C2×C4×C79C4×Q811yescharacteristic
119C2×C4×C79C22⋊Q811yescharacteristic
120C2×C4×C79C22⋊Q811yescharacteristic
121C2×C4×C79#12411yescharacteristic
122C2×C4×C79C4⋊Q811yescharacteristic
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—41no—
135C2×Dic79—41no—
136C2×Dic79—41no—
137C2×Dic79—41no—
138C2×Dic79—41no—
139C2×Dic79—41no—
140C2×Dic79#10412yes—
141C8×C79—42no—
142C8×C79—42no—
143C79⋊C8—42no—
144C79⋊C8—42no—
145C22×C79#39111yescharacteristic
146C22×C79#41311yescharacteristic
147C22×C79#41311yescharacteristic
148C22×C79C2×#10411yescharacteristic
149C22×C79#42111yescharacteristic
150C22×C79#42111yescharacteristic
151C22×C79#42111yescharacteristic
152C4×C79—21no—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—81no—
159C4×C79—81no—
160Dic79—22no—
161Dic79—41no—
162Dic79—41no—
163Dic79—41no—
164Dic79—81no—
165Dic79—81no—
166#9893—791nomaximal, Sylow
167C2×C79#152911yescharacteristic
168C2×C79#153211yescharacteristic
169C2×C79#153511yescharacteristic
170C2×C79#153511yescharacteristic
171C2×C79#198611yescharacteristic
172C2×C79#199511yescharacteristic
173C2×C79#199811yescharacteristic
174#2864—791no—
175#1767—791no—
176#1745—791no—
177#1295—791no—
178#1295—791no—
179#1295—791no—
180#1295D7911yescharacteristic
181C79#989311yescharacteristic, complemented, Sylow
182C2×C4⋊C8—1581no—
183C2×#97—791no—
184C2×#97—791no—
185C2×#97C2×D7911yescharacteristic
186C2×#97C2×D7911yescharacteristic
187#389—791no—
188#389—791no—
189#389—791no—
190#389—791no—
191#387—1581no—
192#387—1581no—
193#387—1581no—
194#387—1581no—
195#382—791no—
196#382C2×D7911yescharacteristic
197C43—791no—
198#336—1581no—
199#336—1581no—
200#336—1581no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—1581no—
204C22×C8—1581no—
205C2×C4⋊C4—791no—
206C2×C4⋊C4—791no—
207C2×C4⋊C4—1581no—
208C2×C4⋊C4—1581no—
209C2×C4⋊C4—1581no—
210C2×C4⋊C4—1581no—
211C2×C4⋊C4C4×D7911yescharacteristic
212C2×C4⋊C4C4×D7911yescharacteristic
213C2×C42—791no—
214C2×C42—791no—
215C2×C42—791no—
216C2×C42—791no—
217C2×C42—791no—
218C2×C42—791no—
219C2×C42C22×D7911yescharacteristic
220C4⋊C8—1584no—
221#97—21no—
222#97—21no—
223#97—21no—
224#97—792no—
225#97—1581no—
226#97—1581no—
227#97—1581no—
228#97Dic15812yes—
229#95—21no—
230#95—21no—
231#95—1581no—
232#95—1581no—
233#95—1581no—
234#95—1581no—
235#95—1581no—
236#95—1581no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—791no—
240C22×C4—791no—
241C22×C4—791no—
242C22×C4—791no—
243C22×C4—1581no—
244C22×C4—1581no—
245C22×C4C2×C4×D7911yescharacteristic
246C22×C4D4×D7911yescharacteristic
247C22×C4D4×D7911yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—3161no—
255C2×C8—3161no—
256C2×C8—3161no—
257C2×C8—3161no—
258C2×C8—1582no—
259C2×C8—1582no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—3161no—
263C4⋊C4—3161no—
264C4⋊C4—3162no—
265C4⋊C4—3162no—
266C4⋊C4—3162no—
267C4⋊C4—3162no—
268C42—3161no—
269C42—3161no—
270C42—3161no—
271C42—3161no—
272C42—3161no—
273C42—1582no—
274C42Q8×D7911yescharacteristic
275C42C2×Dic15811yescharacteristic
276C42#1192962311yescharacteristic
277C42#1192962411yescharacteristic
278C23C22⋊C4×D7911yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—3161no—
292C2×C4—3161no—
293C2×C4—3161no—
294C2×C4—3161no—
295C2×C4—3161no—
296C2×C4—3161no—
297C2×C4—792no—
298C2×C4—1581no—
299C2×C4—1581no—
300C2×C4—1581no—
301C2×C4—1581no—
302C2×C4—1581no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4#1457912611yescharacteristic
310C2×C4C4×Dic15811yescharacteristic
311C2×C4#1457913811yescharacteristic
312C2×C4#1457913911yescharacteristic
313C2×C4#1457914711yescharacteristic
314C2×C4#1457916011yescharacteristic
315C8—42no—
316C8—42no—
317C8—3162no—
318C8—3162no—
319C22#1909846711yescharacteristic
320C22#1909854411yescharacteristic
321C22#1909854611yescharacteristic
322C22#104×D7911yescharacteristic
323C22#1909857811yescharacteristic
324C22#1909857811yescharacteristic
325C22#1909857811yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4—6321no—
338C4—6321no—
339C4—1582no—
340C2#2376200411yescharacteristic
341C2#2376201911yescharacteristic
342C2#2376202811yescharacteristic
343C2#2376203011yescharacteristic
344C2#2376434211yescharacteristic
345C2#2376437911yescharacteristic
346C2#2376439111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D79
commutatorC22×C4×C79C22×C4
FrattiniC2×C42C22×D79
FittingC79×#1295C2
socle, prime radicalC23×C79C2×C22⋊C4
cosocleC2×C42×C79C23
hypercenter#1295D79
hypocenterC79#9893
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
181. C79#9893semidirect

Maximal subgroups

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

subgroupindex
#237717852
#237632542
#237631482
#237612822
#237612812
C79×#12952
#989379