Finite Group Databasebeta

← #34288756

Subgroups — #34288756

Order 20224.

1110 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098619C212yesmaximal
2C43×D79C211yesmaximal, characteristic
3#23763552C211yesmaximal, characteristic, complemented
4#23763516C212yesmaximal, complemented
5#23763377C214yesmaximal
6#23763255C214yesmaximal, complemented
7C79×#1842C211yesmaximal, characteristic, complemented
8C2×C42×D79C412yes—
9C2×C42×D79C411yescharacteristic
10C2×C42×D79C411yescharacteristic
11C2×C42×D79C2212yes—
12C2×C42×D79C2211yescharacteristic
13#19098619—28no—
14C2×C4⋊(C79⋊C8)C2214yes—
15C2×C4⋊(C79⋊C8)C2212yes—
16C2×(C2×D79)⋊C8C2214yes—
17C2×#14579071C2214yes—
18C42×Dic79C412yes—
19C42×Dic79C411yescharacteristic
20C42×Dic79C411yescharacteristic
21C42×Dic79C2212yes—
22C42×Dic79C2211yescharacteristic
23#19098317C2218yes—
24C2×C4⋊C8×C79C2214yes—
25C2×C4⋊C8×C79C2212yes—
26C43×C79C2211yescharacteristic
27C22×C4×D79C2×C412yes—
28C22×C4×D79C2×C411yescharacteristic
29C22×C4×D79C2×C411yescharacteristic
30C22×C4×D79C2×C412yes—
31C22×C4×D79C2311yescharacteristic
32C22×C79⋊C8C2314yes—
33C2×C4×Dic79C2×C412yes—
34C2×C4×Dic79C2×C412yes—
35C2×C4×Dic79C2×C412yes—
36C2×C4×Dic79C2×C412yes—
37C2×C4×Dic79C2×C412yes—
38C2×C4×Dic79C2×C412yes—
39C2×C4×Dic79C2×C412yes—
40C2×C4×Dic79C2×C411yescharacteristic
41C2×C4×Dic79C2×C411yescharacteristic
42C2×C4×Dic79C2×C411yescharacteristic
43C2×C4×Dic79C2×C411yescharacteristic
44C2×C4×Dic79C2312yes—
45C2×C4×Dic79C2311yescharacteristic
46C42×D79—24no—
47C42×D79—24no—
48C42×D79—24no—
49C42×D79—28no—
50C42×D79—24no—
51C42×D79D414yes—
52C42×D79Q814yes—
53C4⋊(C79⋊C8)—24no—
54C4⋊(C79⋊C8)—28no—
55(C2×D79)⋊C8—28no—
56#14579071—28no—
57C22×C8×C79C2314yes—
58C2×C42×C79C2×C412yes—
59C2×C42×C79C2×C411yescharacteristic
60C2×C42×C79C2×C411yescharacteristic
61C2×C42×C79C2311yescharacteristic
62C2×C42×C79C2312yes—
63C4⋊C8×C79—24no—
64C4⋊C8×C79—28no—
65C23×D79C22×C411yescharacteristic
66C22×Dic79C22×C411yescharacteristic
67C22×Dic79C22×C411yescharacteristic
68C22×Dic79C22×C411yescharacteristic
69C22×Dic79C22×C412yes—
70C22×Dic79C22×C412yes—
71C2×C4×D79—24no—
72C2×C4×D79—24no—
73C2×C4×D79—24no—
74C2×C4×D79—24no—
75C2×C4×D79—24no—
76C2×C4×D79—22no—
77C2×C4×D79—22no—
78C2×C4×D79—24no—
79C2×C4×D79—22no—
80C2×C4×D79—22no—
81C2×C4×D79C4⋊C414yes—
82C2×C4×D79C4⋊C414yes—
83C2×C4×D79M1618yes—
84C2×C4×D79C2×D412yes—
85C2×C4×D79C2×Q812yes—
86C2×C79⋊C8—24no—
87C2×C79⋊C8—28no—
88C4×Dic79—24no—
89C4×Dic79—24no—
90C4×Dic79—24no—
91C4×Dic79—24no—
92C4×Dic79—24no—
93C4×Dic79—24no—
94C4×Dic79—22no—
95C4×Dic79—24no—
96C4×Dic79—22no—
97C4×Dic79—22no—
98C4×Dic79C4⋊C414yes—
99C4×Dic79C4⋊C414yes—
100C4×Dic79M1614yes—
101C4×Dic79C2×D412yes—
102C4×Dic79C2×Q812yes—
103C22×C4×C79C22×C411yescharacteristic
104C22×C4×C79C22×C412yes—
105C22×C4×C79C22×C411yescharacteristic
106C22×C4×C79C22×C412yes—
107C22×C4×C79C2411yescharacteristic
108C2×C8×C79—24no—
109C2×C8×C79—28no—
110C42×C79—22no—
111C42×C79—24no—
112C42×C79M1614yes—
113C42×C79C2×D412yes—
114C42×C79C2×Q812yes—
115C42×C79#4114yes—
116C42×C79#4114yes—
117C23×C79C23×C411yescharacteristic
118C22×D79—22no—
119C22×D79—21no—
120C22×D79—21no—
121C22×D79C2×C4⋊C412yes—
122C22×D79C2×M1614yes—
123C2×C4×C79—22no—
124C2×C4×C79—22no—
125C2×C4×C79—22no—
126C2×C4×C79C2×C4⋊C412yes—
127C2×C4×C79C2×C4⋊C412yes—
128C2×C4×C79#11714yes—
129C2×C4×C79#11714yes—
130C2×C4×C79C2×M1612yes—
131C2×C4×C79C2×M1614yes—
132C2×C4×C79C2×M1612yes—
133C2×C4×C79C2×M1614yes—
134C2×C4×C79C22×D411yescharacteristic
135C2×C4×C79C22×Q811yescharacteristic
136C2×C4×C79C2×#4112yes—
137C2×C4×C79C2×#4112yes—
138C2×Dic79—22no—
139C2×Dic79—22no—
140C2×Dic79—22no—
141C2×Dic79—22no—
142C2×Dic79—21no—
143C2×Dic79—22no—
144C2×Dic79—21no—
145C2×Dic79—22no—
146C2×Dic79C2×C4⋊C412yes—
147C2×Dic79C2×C4⋊C412yes—
148C2×Dic79C2×C4⋊C412yes—
149C2×Dic79C2×M1614yes—
150C2×Dic79C2×M1614yes—
151C4×D79—216no—
152C4×D79—28no—
153C4×D79—22no—
154C4×D79—22no—
155C4×D79—24no—
156C4×D79—28no—
157C4×D79—216no—
158C8×C79—44no—
159C79⋊C8—44no—
160C22×C79C22×C4⋊C411yescharacteristic
161C22×C79C2×#11712yes—
162C22×C79C22×M1612yes—
163C22×C79C22×M1611yescharacteristic
164C22×C79C22×M1611yescharacteristic
165C2×D79—22no—
166C2×D79—24no—
167C2×D79—24no—
168C2×D79—22no—
169C2×D79#42314yes—
170C4×C79—22no—
171C4×C79—24no—
172C4×C79#42314yes—
173C4×C79#43218yescomplemented
174C4×C79#53211yescharacteristic
175C4×C79#53211yescharacteristic
176C4×C79#53312yes—
177Dic79—22no—
178Dic79—22no—
179Dic79—24no—
180Dic79—24no—
181Dic79—22no—
182#20810—791nomaximal, Sylow
183C2×C79#228511yescharacteristic
184C2×C79C2×#42311yescharacteristic
185C2×C79C2×#42311yescharacteristic
186C2×C79C2×#43212yes—
187C2×C79#292012yes—
188D79—24no—
189C2×#432—792no—
190C2×C43—791no—
191#1842—791no—
192#1842D7911yescharacteristic, complemented
193#1831—792no—
194#1797—794no—
195#1767—794no—
196C79#2081011yescharacteristic, complemented, Sylow
197C22×C42—791no—
198C22×C42—792no—
199C22×C42—791no—
200C22×C42—792no—
201C22×C42—791no—
202#432—1588no—
203C2×C4⋊C8—794no—
204C2×C4⋊C8—792no—
205C2×C4⋊C8C2×D7914yes—
206C2×C4⋊C8C2×D7912yes—
207C2×C22⋊C8—794no—
208C2×#97—794no—
209C43—791no—
210C43—792no—
211C43—791no—
212C43—792no—
213C43—791no—
214C43C2×D7911yescharacteristic
215#336—798no—
216C23×C4—791no—
217C23×C4—791no—
218C23×C4—792no—
219C23×C4—791no—
220C23×C4—792no—
221C22×C8—794no—
222C22×C8C22×D7914yes—
223C2×C42—791no—
224C2×C42—791no—
225C2×C42—791no—
226C2×C42—791no—
227C2×C42—794no—
228C2×C42—794no—
229C2×C42—792no—
230C2×C42—792no—
231C2×C42—792no—
232C2×C42—792no—
233C2×C42—792no—
234C2×C42—792no—
235C2×C42—791no—
236C2×C42—792no—
237C2×C42—792no—
238C2×C42—1584no—
239C2×C42—1588no—
240C2×C42—1584no—
241C2×C42—1584no—
242C2×C42—1584no—
243C2×C42C4×D7912yes—
244C2×C42C4×D7911yescharacteristic
245C2×C42C4×D7911yescharacteristic
246C2×C42C22×D7911yescharacteristic
247C2×C42C22×D7912yes—
248C4⋊C8—24no—
249C4⋊C8—28no—
250C4⋊C8—1584no—
251C4⋊C8—1588no—
252C22⋊C8—1588no—
253#97—1588no—
254C24—791no—
255C22×C4—791no—
256C22×C4—791no—
257C22×C4—791no—
258C22×C4—792no—
259C22×C4—792no—
260C22×C4—792no—
261C22×C4—794no—
262C22×C4—794no—
263C22×C4—798no—
264C22×C4—792no—
265C22×C4—1584no—
266C22×C4—1584no—
267C22×C4—1584no—
268C22×C4—1582no—
269C22×C4—1582no—
270C22×C4—1584no—
271C22×C4—1584no—
272C22×C4—1582no—
273C22×C4—1582no—
274C22×C4—1584no—
275C22×C4C2×C4×D7911yescharacteristic
276C22×C4C2×C4×D7912yes—
277C22×C4C2×C4×D7911yescharacteristic
278C22×C4C2×C4×D7912yes—
279C22×C4C23×D7911yescharacteristic
280C2×C8—28no—
281C2×C8—24no—
282C2×C8—1588no—
283C2×C8—1584no—
284C42—22no—
285C42—24no—
286C42—792no—
287C42—794no—
288C42—794no—
289C42—794no—
290C42—792no—
291C42—1584no—
292C42—1584no—
293C42—1584no—
294C42—1582no—
295C42—1582no—
296C42—1584no—
297C42—1584no—
298C42—1584no—
299C42—1582no—
300C42—1584no—
301C42#1192960714yes—
302C42D4×D7912yes—
303C42Q8×D7912yes—
304C42#1192962314yes—
305C42#1192962514yes—
306C23—792no—
307C23—794no—
308C23—1582no—
309C23—1581no—
310C23—1581no—
311C23C22×C4×D7911yescharacteristic
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—792no—
316C2×C4—792no—
317C2×C4—792no—
318C2×C4—794no—
319C2×C4—794no—
320C2×C4—1588no—
321C2×C4—15816no—
322C2×C4—1582no—
323C2×C4—1582no—
324C2×C4—1582no—
325C2×C4—1582no—
326C2×C4—1581no—
327C2×C4—1582no—
328C2×C4—1581no—
329C2×C4—1582no—
330C2×C4—1588no—
331C2×C4—1582no—
332C2×C4—1582no—
333C2×C4—1584no—
334C2×C4—15816no—
335C2×C4C4⋊C4×D7912yes—
336C2×C4C4⋊C4×D7912yes—
337C2×C4#1457911914yes—
338C2×C4#1457911914yes—
339C2×C4M16×D7912yes—
340C2×C4M16×D7914yes—
341C2×C4C2×#1192960712yes—
342C2×C4C2×#1192960714yes—
343C2×C4C2×D4×D7911yescharacteristic
344C2×C4C2×Q8×D7911yescharacteristic
345C2×C4C2×#1192962312yes—
346C2×C4C2×#1192962512yes—
347C8—44no—
348C8—3164no—
349C22—794no—
350C22—1582no—
351C22—1582no—
352C22—1584no—
353C22—1584no—
354C22C2×C4⋊C4×D7911yescharacteristic
355C22C2×#1457911912yes—
356C22C2×M16×D7912yes—
357C22C2×M16×D7911yescharacteristic
358C22C22×#1192960711yescharacteristic
359C4—22no—
360C4—24no—
361C4—1582no—
362C4—1582no—
363C4—1582no—
364C4—1584no—
365C4—1584no—
366C4#1909858514yes—
367C4#1909861918yescomplemented
368C4#1909911111yescharacteristic
369C4#1909911411yescharacteristic
370C4#1909911812yes—
371C2—1584no—
372C2#2376580511yescharacteristic
373C2#423×D7911yescharacteristic
374C2C2×#1909858511yescharacteristic
375C2C2×#1909861912yes—
376C2#2377203212yes—
subgroupG/H
center, FrattiniC22×C4C23×D79
commutator, socleC23×C79C23×C4
FittingC79×#1842C2
prime radicalC23×D79C22×C4
cosocleC22×C4×C79C24
hypercenter#1842D79
hypocenterC79#20810
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ #1842

Complements

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

NH ≅ G/Ntype
3. #23763552C2semidirect
4. #23763516C2semidirect
6. #23763255C2semidirect
7. C79×#1842C2semidirect
173. C4×C79#432semidirect
192. #1842D79semidirect
196. C79#20810semidirect
367. C4#19098619semidirect

Maximal subgroups

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

subgroupindex
C2×#190986192
C43×D792
#237635522
#237635162
#237633772
#237632552
C79×#18422
#2081079