Finite Group Databasebeta

← #34305974

Subgroups — #34305974

Order 20224.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D79C211yesmaximal, characteristic
2#23766276C212yesmaximal
3#23764139C211yesmaximal, characteristic, complemented
4#23763974C212yesmaximal, complemented
5#23763968C212yesmaximal, complemented
6#23763489C212yesmaximal
7#23763422C211yesmaximal, characteristic
8#23763300C211yesmaximal, characteristic, complemented
9#23763297C211yesmaximal, characteristic, complemented
10#23763177C211yesmaximal, characteristic
11C79×#1943C211yesmaximal, characteristic, complemented
12C22×C8×D79C2211yescharacteristic
13C2×C4⋊C4×D79C2212yes—
14C2×#14579095C2211yescharacteristic
15C2×#14579094C2212yes—
16#107×D79C418yescomplemented
17C2×#14579093C2211yescharacteristic
18C2×(C2×D79)⋊C8C2211yescharacteristic
19C2×#14579071C2211yescharacteristic
20#19098462C2212yes—
21#19098450—22no—
22#19098444—22no—
23#19098420—22no—
24#19098420C2212yes—
25C4⋊C4×Dic79C2212yes—
26C4×C4⋊Dic79C2212yes—
27C4×(C2×D79)⋊C4C2211yescharacteristic
28#19098410—22no—
29#19098326C2212yes—
30#19098325C2212yes—
31#19098325C2212yes—
32#19098325C2212yes—
33#19098318C2211yescharacteristic
34#19098317C2211yescharacteristic
35C2×#107×C79C2211yescharacteristic
36C2×#106×C79C2211yescharacteristic
37C2×#97×C79C2211yescharacteristic
38#389×C79C2212yes—
39#340×C79C2212yes—
40C22×C4×D79—22no—
41C22×C4×D79C2311yescharacteristic
42C22×C79⋊C8C2311yescharacteristic
43C22×C79⋊C8C2311yescharacteristic
44C2×C8×D79—22no—
45C2×C8×D79—22no—
46C2×C8×D79C2×C414yes—
47C2×C4⋊Dic79—22no—
48C2×C4⋊Dic79C2312yes—
49C2×C4⋊Dic79C2312yes—
50C2×Dic79⋊C4—22no—
51C4⋊C4×D79—24no—
52C4⋊C4×D79C2×C418yes—
53C2×(C2×D79)⋊C4—22no—
54C2×(C2×D79)⋊C4D412yes—
55C2×C4×Dic79—22no—
56C2×C4×Dic79—22no—
57C2×C4×Dic79C2311yescharacteristic
58#14579095C2×C414yes—
59#14579094C2×C418yes—
60#14579093—22no—
61(C2×D79)⋊C8—22no—
62#14579071—22no—
63C79⋊#95—22no—
64C79⋊#95—22no—
65C79⋊#95—22no—
66C79⋊#95—22no—
67C79⋊#95D412yes—
68C22×C8×C79C2311yescharacteristic
69C22×C8×C79C2311yescharacteristic
70C2×C4⋊C4×C79—22no—
71C2×C4⋊C4×C79C2312yes—
72C2×C4⋊C4×C79C2312yes—
73C2×C42×C79C2311yescharacteristic
74#107×C79C2×C414yes—
75#106×C79—22no—
76#97×C79—22no—
77#95×C79—22no—
78C23×D79C2×D411yescharacteristic
79C22×Dic79—22no—
80C22×Dic79—22no—
81C22×Dic79C2×D412yes—
82C22×Dic79C2×D411yescharacteristic
83C2×C4×D79—28no—
84C2×C4×D79—21no—
85C2×C4×D79—21no—
86C2×C4×D79—21no—
87C2×C4×D79—21no—
88C2×C4×D79—82no—
89C2×C4×D79—82no—
90C2×C4×D79C22×C412yes—
91C2×C4×D79#4112yes—
92C2×C79⋊C8—21no—
93C2×C79⋊C8—21no—
94C2×C79⋊C8—21no—
95C2×C79⋊C8—21no—
96C2×C79⋊C8—21no—
97C2×C79⋊C8C22×C412yes—
98C8×D79—28no—
99C4⋊Dic79—22no—
100C4⋊Dic79—22no—
101C4⋊Dic79—22no—
102C4⋊Dic79—82no—
103C4⋊Dic79C22×C414yes—
104Dic79⋊C4—28no—
105(C2×D79)⋊C4—24no—
106(C2×D79)⋊C4—44no—
107C4×Dic79—21no—
108C4×Dic79—21no—
109C4×Dic79—82no—
110C4×Dic79—82no—
111C22×C4×C79—22no—
112C22×C4×C79—22no—
113C22×C4×C79C2×D412yes—
114C22×C4×C79C2411yescharacteristic
115C2×C8×C79—21no—
116C2×C8×C79—21no—
117C2×C8×C79—21no—
118C2×C8×C79C22×C412yes—
119C2×C8×C79#4112yes—
120C2×C8×C79#4112yes—
121C4⋊C4×C79—22no—
122C4⋊C4×C79—22no—
123C4⋊C4×C79—22no—
124C4⋊C4×C79—82no—
125C4⋊C4×C79C22×C414yes—
126C42×C79—21no—
127C42×C79—21no—
128C23×C79C22×D411yescharacteristic
129C22×D79—21no—
130C22×D79—21no—
131C22×D79—22no—
132C22×D79C4×D412yes—
133C22×D79#13714yes—
134C2×C4×C79—24no—
135C2×C4×C79—22no—
136C2×C4×C79—22no—
137C2×C4×C79—22no—
138C2×C4×C79—42no—
139C2×C4×C79—42no—
140C2×C4×C79—42no—
141C2×C4×C79—42no—
142C2×C4×C79—42no—
143C2×C4×C79C23×C411yescharacteristic
144C2×C4×C79C2×#4111yescharacteristic
145C2×C4×C79C2×#4111yescharacteristic
146C2×C4×C79C2×#4111yescharacteristic
147C2×C4×C792−1+411yescharacteristic
148C2×C4×C792−1+411yescharacteristic
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—24no—
152C2×Dic79—22no—
153C2×Dic79—22no—
154C2×Dic79—22no—
155C2×Dic79—42no—
156C2×Dic79—42no—
157C2×Dic79—42no—
158C2×Dic79—42no—
159C2×Dic79—42no—
160C2×Dic79C4×D412yes—
161C4×D79—22no—
162C4×D79—22no—
163C4×D79—22no—
164C4×D79—22no—
165C4×D79—88no—
166C8×C79—41no—
167C8×C79#11714yes—
168C79⋊C8—22no—
169C79⋊C8—41no—
170C22×C79C2×C4×D411yescharacteristic
171C22×C79#54711yescharacteristic
172C22×C79#54711yescharacteristic
173C22×C79C2×#13712yes—
174C22×C79#57612yes—
175C2×D79—24no—
176C2×D79—24no—
177C2×D79—22no—
178C2×D79—22no—
179C2×D79#44114yes—
180C4×C79—42no—
181C4×C79—44no—
182C4×C79—82no—
183C4×C79C2×#11711yescharacteristic
184C4×C79#51911yescharacteristic
185C4×C79#55211yescharacteristic
186C4×C79#55211yescharacteristic
187Dic79—22no—
188Dic79—42no—
189Dic79—44no—
190Dic79—82no—
191#22618—791nomaximal, Sylow
192C2×C79#234411yescharacteristic
193C2×C79C2×#44111yescharacteristic
194C2×C79#294811yescharacteristic
195C2×C79#334612yes—
196C2×C79#334612yes—
197D79—24no—
198C22×#107—791no—
199#2345—792no—
200#1943—791no—
201#1943D7911yescharacteristic, complemented
202#1918—792no—
203#1918—792no—
204#1824—792no—
205#1807—791no—
206#1776—791no—
207#1776—791no—
208#1752—791no—
209C79#2261811yescharacteristic, complemented, Sylow
210C23×C8—791no—
211C22×C4⋊C4—792no—
212C2×#107—791no—
213C2×#107—792no—
214C2×#107—798no—
215C2×#107C2×D7911yescharacteristic
216C2×#106—791no—
217C2×#106C2×D7911yescharacteristic
218C2×C22⋊C8—791no—
219C2×#97—791no—
220C2×#97C2×D7911yescharacteristic
221#389—792no—
222#389C2×D7912yes—
223#387—1582no—
224#387—1582no—
225#380—792no—
226#380—1582no—
227C4×C4⋊C4—792no—
228C4×C4⋊C4—792no—
229C4×C22⋊C4—791no—
230C4×C22⋊C4—1582no—
231#340—792no—
232#340—792no—
233#340—792no—
234#340—792no—
235#340C2×D7912yes—
236#336—791no—
237#336—791no—
238C23×C4—791no—
239C23×C4—1582no—
240C22×C8—791no—
241C22×C8—794no—
242C22×C8—791no—
243C22×C8—1582no—
244C22×C8—1582no—
245C22×C8C22×D7911yescharacteristic
246C22×C8C22×D7911yescharacteristic
247C2×C4⋊C4—22no—
248C2×C4⋊C4—792no—
249C2×C4⋊C4—798no—
250C2×C4⋊C4—792no—
251C2×C4⋊C4—1584no—
252C2×C4⋊C4—1582no—
253C2×C4⋊C4—1582no—
254C2×C4⋊C4C22×D7912yes—
255C2×C4⋊C4C22×D7912yes—
256C2×C22⋊C4—792no—
257C2×C22⋊C4—1582no—
258C2×C42—791no—
259C2×C42—1582no—
260C2×C42—1582no—
261C2×C42C22×D7911yescharacteristic
262#107—794no—
263#107—798no—
264#107C4×D7914yes—
265#106—22no—
266#106—1582no—
267C22⋊C8—1582no—
268#97—22no—
269#97—1582no—
270#95—22no—
271#95—792no—
272#95—1582no—
273#95—1582no—
274#95—1582no—
275#95—1582no—
276C24—791no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—791no—
280C22×C4—792no—
281C22×C4—792no—
282C22×C4—792no—
283C22×C4—6322no—
284C22×C4—6322no—
285C22×C4—1588no—
286C22×C4—1582no—
287C22×C4—1582no—
288C22×C4—1581no—
289C22×C4—1581no—
290C22×C4—1581no—
291C22×C4—1581no—
292C22×C4D4×D7912yes—
293C22×C4C23×D7911yescharacteristic
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—792no—
298C2×C8—1581no—
299C2×C8—1581no—
300C2×C8—1581no—
301C2×C8—1581no—
302C2×C8—1581no—
303C2×C8—1588no—
304C2×C8C2×C4×D7912yes—
305C2×C8#1192962312yes—
306C2×C8#1192962512yes—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—82no—
311C4⋊C4—794no—
312C4⋊C4—6322no—
313C4⋊C4—1588no—
314C4⋊C4—1582no—
315C4⋊C4—1582no—
316C4⋊C4—1582no—
317C4⋊C4C2×C4×D7914yes—
318C22⋊C4—3164no—
319C22⋊C4—1584no—
320C42—21no—
321C42—21no—
322C42—6322no—
323C42—6322no—
324C42—1581no—
325C42—1581no—
326C23—792no—
327C23—794no—
328C23—1581no—
329C23—1581no—
330C23—1582no—
331C23C2×D4×D7911yescharacteristic
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—3162no—
342C2×C4—3162no—
343C2×C4—3162no—
344C2×C4—3162no—
345C2×C4—3162no—
346C2×C4—792no—
347C2×C4—6328no—
348C2×C4—1582no—
349C2×C4—1584no—
350C2×C4—1582no—
351C2×C4—1582no—
352C2×C4—1581no—
353C2×C4—1581no—
354C2×C4—1582no—
355C2×C4—1582no—
356C2×C4—1582no—
357C2×C4—1582no—
358C2×C4C22×C4×D7911yescharacteristic
359C2×C4#41×D7911yescharacteristic
360C2×C4C2×#1192962311yescharacteristic
361C2×C4C2×#1192962511yescharacteristic
362C2×C4#1457920811yescharacteristic
363C2×C4#1457920911yescharacteristic
364C8—41no—
365C8—3161no—
366C8—1582no—
367C8#1457911914yes—
368C22—794no—
369C22—1582no—
370C22—1584no—
371C22—1584no—
372C22—1582no—
373C22C4×D4×D7911yescharacteristic
374C22#1909921311yescharacteristic
375C22#1909921611yescharacteristic
376C22#137×D7912yes—
377C22#1909936712yes—
378C4—44no—
379C4—42no—
380C4—82no—
381C4—3164no—
382C4—3162no—
383C4—6322no—
384C4—1582no—
385C4C2×#1457911911yescharacteristic
386C4#1909903911yescharacteristic
387C4#1909924711yescharacteristic
388C4#1909925111yescharacteristic
389C2—1584no—
390C2#2376626811yescharacteristic
391C2#441×D7911yescharacteristic
392C2#2377224911yescharacteristic
393C2#2377588012yes—
394C2#2377588412yes—
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1943C2
socleC23×C79C22×D4
prime radicalC23×D79C2×D4
cosocleC22×C4×C79C24
hypercenter#1943D79
hypocenterC79#22618
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
3. #23764139C2semidirect
4. #23763974C2semidirect
5. #23763968C2semidirect
8. #23763300C2semidirect
9. #23763297C2semidirect
11. C79×#1943C2semidirect
16. #107×D79C4semidirect
201. #1943D79semidirect
209. C79#22618semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D792
#237662762
#237641392
#237639742
#237639682
#237634892
#237634222
#237633002
#237632972
#237631772
C79×#19432
#2261879