Finite Group Databasebeta

← #34179267

Subgroups — #34179267

Order 20224.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772094C211yesmaximal, characteristic
2#23763176C211yesmaximal, characteristic, complemented
3#23761892C211yesmaximal, characteristic
4#23761889C211yesmaximal, characteristic
5#23761288C211yesmaximal, characteristic, complemented
6#23761286C211yesmaximal, characteristic, complemented
7C8×C22⋊C4×C79C211yesmaximal, characteristic, complemented
8C2×#14579167C411yescharacteristic, complemented
9#19099074C2211yescharacteristic
10#19098634—21no—
11#19098634—21no—
12C8×C22⋊D79—21no—
13C8×C22⋊D79—21no—
14#19098589C411yescharacteristic, complemented
15#19098529C411yescharacteristic, complemented
16#19098527C2211yescharacteristic
17C2×C22⋊(C79⋊C8)C2211yescharacteristic
18#19098518C411yescharacteristic, complemented
19C2×#14579071—21no—
20C4×C22⋊Dic79C2211yescharacteristic
21#19098317—21no—
22#19098301C412yescomplemented
23#19098299C412yescomplemented
24#19098298C412yescomplemented
25#19098296C412yescomplemented
26C23×C8×C79C2211yescharacteristic
27C2×C22⋊C8×C79C2211yescharacteristic
28C2×C4×C8×C79—21no—
29C4×C22⋊C4×C79C2211yescharacteristic
30#336×C79—21no—
31C2×#11929624C2×C411yescharacteristic
32#14579167—42no—
33C2×#11929608C2×C411yescharacteristic
34C2×#11929608C2×C411yescharacteristic
35C2×#11929607—21no—
36C22×C79⋊C8—21no—
37C2×C8×D79—21no—
38#14579144—21no—
39#14579140C2×C411yescharacteristic
40#14579140C2×C411yescharacteristic
41#14579135C2×C411yescharacteristic
42#14579135C2×C411yescharacteristic
43#14579130—21no—
44C4×C22⋊D79—21no—
45C4×C22⋊D79—21no—
46#14579120C2×C411yescharacteristic
47C2×C22⋊Dic79—21no—
48C2×C4×Dic79—21no—
49Dic79⋊C8—21no—
50Dic79⋊C8—21no—
51C22⋊(C79⋊C8)—21no—
52C22⋊(C79⋊C8)—21no—
53C22⋊(C79⋊C8)—21no—
54C22⋊(C79⋊C8)C2×C412yes—
55(C2×D79)⋊C8—21no—
56(C2×D79)⋊C8—21no—
57#14579071—21no—
58#14579071—42no—
59C8×Dic79—21no—
60C79⋊#95C2×C412yes—
61C23×C4×C79C2311yescharacteristic
62C22×C8×C79—21no—
63C22×C8×C79—42no—
64C22×C8×C79C2×C411yescharacteristic
65C22×C8×C79C2×C411yescharacteristic
66C22×C8×C79D411yescharacteristic
67C22×C8×C79D411yescharacteristic
68C22×C8×C79D411yescharacteristic
69C22×C8×C79D411yescharacteristic
70C2×C22⋊C4×C79—21no—
71C2×C42×C79—21no—
72C22⋊C8×C79—21no—
73C22⋊C8×C79C2×C412yes—
74C4×C8×C79—42no—
75#95×C79C2×C412yes—
76#11929624—41no—
77#11929624—41no—
78C2×Dic158C4211yescharacteristic
79C2×D316C4211yescharacteristic
80C2×C22⋊D79—21no—
81C2×C22⋊D79—21no—
82C2×C22⋊D79—21no—
83C22×Dic79—22no—
84C2×C4×D79—21no—
85#11929608—41no—
86#11929608—41no—
87#11929607—42no—
88C2×C79⋊C8—21no—
89C2×C79⋊C8—21no—
90C2×C79⋊C8—22no—
91C2×C79⋊C8—41no—
92C2×C79⋊C8—41no—
93C8×D79—42no—
94C4⋊Dic79C4211yescharacteristic
95C4⋊Dic79C4211yescharacteristic
96Dic79⋊C4—21no—
97Dic79⋊C4—21no—
98C22⋊Dic79—21no—
99C22⋊Dic79—21no—
100C22⋊Dic79—21no—
101C22⋊Dic79—42no—
102(C2×D79)⋊C4—21no—
103(C2×D79)⋊C4—21no—
104C4×Dic79—21no—
105C4×Dic79—41no—
106C4×Dic79—41no—
107C24×C79#4111yescharacteristic
108C22×C4×C79—22no—
109C22×C4×C79—41no—
110C22×C4×C79—41no—
111C22×C4×C79C22×C411yescharacteristic
112C22×C4×C79C22×C411yescharacteristic
113C22×C4×C79C22×C411yescharacteristic
114C22×C4×C79C2×D411yescharacteristic
115C22×C4×C79C2×D411yescharacteristic
116C22×C4×C79#4111yescharacteristic
117C2×C8×C79—22no—
118C2×C8×C79—22no—
119C2×C8×C79—22no—
120C2×C8×C79—22no—
121C2×C8×C79—41no—
122C2×C8×C79—41no—
123C2×C8×C79—41no—
124C2×C8×C79—41no—
125C2×C8×C79—41no—
126C2×C8×C79C22⋊C411yescharacteristic
127C2×C8×C79C22⋊C411yescharacteristic
128C2×C8×C79C22⋊C411yescharacteristic
129C2×C8×C79C22⋊C411yescharacteristic
130C22⋊C4×C79—24no—
131C42×C79—41no—
132C42×C79—41no—
133C23×C79—22no—
134C23×C79—22no—
135C23×C79—41no—
136C23×C79#11711yescharacteristic
137C23×C79C4×D411yescharacteristic
138C23×C79C4×D411yescharacteristic
139C22×D79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—21no—
146C2×C4×C79—24no—
147C2×C4×C79—41no—
148C2×C4×C79—41no—
149C2×C4×C79—41no—
150C2×C4×C79—42no—
151C2×C4×C79—42no—
152C2×C4×C79C2×C4211yescharacteristic
153C2×C4×C79C2×C22⋊C411yescharacteristic
154C2×C4×C79C4×D411yescharacteristic
155C2×C4×C79C4×D411yescharacteristic
156C22⋊D79—42no—
157C22⋊D79—42no—
158C22⋊D79—42no—
159C2×Dic79—21no—
160C2×Dic79—21no—
161C2×Dic79—21no—
162C2×Dic79—42no—
163C2×Dic79—42no—
164C2×Dic79—42no—
165D316—41no—
166C4×D79—41no—
167C4×D79—41no—
168Dic158—41no—
169C8×C79—21no—
170C8×C79—21no—
171C8×C79—21no—
172C8×C79—42no—
173C8×C79#9912yes—
174C79⋊C8—42no—
175C79⋊C8—41no—
176C79⋊C8—41no—
177C22×C79—21no—
178C22×C79—21no—
179C22×C79—21no—
180C22×C79—21no—
181C22×C79—21no—
182C22×C79—21no—
183C22×C79—21no—
184C22×C79—44no—
185C22×C79C4×C22⋊C411yescharacteristic
186C22×C79#44312yes—
187C22×C79#44412yes—
188C2×D79—41no—
189C2×D79—41no—
190C2×D79—41no—
191C4×C79—21no—
192C4×C79—21no—
193C4×C79—21no—
194C4×C79—44no—
195C4×C79C2×#9911yescharacteristic
196C4×C79#41011yescharacteristic
197Dic79—41no—
198Dic79—41no—
199Dic79—41no—
200Dic79—82no—
201#8240—791nomaximal, Sylow
202C2×C79—22no—
203C2×C79—22no—
204C2×C79—41no—
205C2×C79C4×#9911yescharacteristic
206C2×C79#176411yescharacteristic
207C2×C79#176511yescharacteristic
208D79—81no—
209#2929—791no—
210#1752—791no—
211C8×C22⋊C4D7911yescharacteristic, complemented
212#1501—791no—
213#1501—791no—
214#1298—791no—
215#1297—791no—
216C79#824011yescharacteristic, complemented, Sylow
217C2×#131—791no—
218C23×C8C2×D7911yescharacteristic
219#525—791no—
220#435—1581no—
221#435—1581no—
222C8×D4—1581no—
223C8×D4—1581no—
224#424—791no—
225#408—791no—
226#407—791no—
227C2×C22⋊C8—791no—
228C2×C22⋊C8C2×D7911yescharacteristic
229#405—791no—
230C2×#97—1581no—
231C2×C4×C8—21no—
232C4×C22⋊C4—791no—
233C4×C22⋊C4C2×D7911yescharacteristic
234#336—21no—
235#336—1581no—
236#328—792no—
237#328—792no—
238#327—792no—
239#327—792no—
240C2×#41—791no—
241C23×C4C22×D7911yescharacteristic
242#131—3162no—
243C2×M16—791no—
244C2×M16—791no—
245C2×M16—1581no—
246C22×C8—21no—
247C22×C8—42no—
248C22×C8—1581no—
249C22×C8—1581no—
250C22×C8C4×D7911yescharacteristic
251C22×C8C4×D7911yescharacteristic
252C22×C8D31611yescharacteristic
253C22×C8D31611yescharacteristic
254C22×C8C22⋊D7911yescharacteristic
255C22×C8C22⋊D7911yescharacteristic
256#123—1581no—
257C22⋊Q8—791no—
258C22⋊Q8—791no—
259#121—791no—
260#121—791no—
261#120—1581no—
262C4×D4—1581no—
263C4×D4—1581no—
264#117—791no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—1581no—
267C2×C42—21no—
268C2×C42—1581no—
269C4⋊C8—1581no—
270C4⋊C8—1581no—
271C22⋊C8—21no—
272C22⋊C8—792no—
273C22⋊C8—1581no—
274C22⋊C8—1581no—
275C22⋊C8—1581no—
276C22⋊C8—1581no—
277C22⋊C8—1581no—
278C22⋊C8C4×D7912yes—
279#97—3162no—
280#97—1581no—
281C4×C8—42no—
282C4×C8—1581no—
283#95—792no—
284#95C4×D7912yes—
285C24#1192962411yescharacteristic
286#41—3161no—
287#41—3161no—
288C2×Q8—791no—
289C2×D4—791no—
290C2×D4—1581no—
291C2×D4—1581no—
292C2×D4—1581no—
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—1582no—
297C22×C4—1581no—
298C22×C4C2×C4×D7911yescharacteristic
299C22×C4C2×C4×D7911yescharacteristic
300C22×C4C2×C4×D7911yescharacteristic
301C22×C4C2×C22⋊D7911yescharacteristic
302C22×C4C2×D31611yescharacteristic
303C22×C4#1192962411yescharacteristic
304M16—3162no—
305M16—3161no—
306M16—3161no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—3162no—
317C2×C8—3161no—
318C2×C8—3161no—
319C2×C8—1581no—
320C2×C8—1581no—
321C2×C8—1582no—
322C2×C8(C2×D79)⋊C411yescharacteristic
323C2×C8(C2×D79)⋊C411yescharacteristic
324C2×C8(C2×D79)⋊C411yescharacteristic
325C2×C8(C2×D79)⋊C411yescharacteristic
326C4⋊C4—791no—
327C4⋊C4—791no—
328C4⋊C4—1581no—
329C4⋊C4—1581no—
330C22⋊C4—24no—
331C22⋊C4—3162no—
332C22⋊C4—1581no—
333C22⋊C4—1581no—
334C22⋊C4—1581no—
335C22⋊C4—1581no—
336C22⋊C4—1581no—
337C42—41no—
338C42—41no—
339C42—3161no—
340C42—3161no—
341C42—1581no—
342C23—22no—
343C23—22no—
344C23—41no—
345C23—1581no—
346C23#1457911811yescharacteristic
347C23C4×C22⋊D7911yescharacteristic
348C23C4×D31611yescharacteristic
349Q8—3161no—
350D4—3161no—
351D4—3162no—
352D4—3162no—
353D4—3162no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—24no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—3161no—
367C2×C4—3161no—
368C2×C4—3162no—
369C2×C4—3162no—
370C2×C4—3162no—
371C2×C4—1581no—
372C2×C4—1581no—
373C2×C4—1581no—
374C2×C4C42×D7911yescharacteristic
375C2×C4C2×(C2×D79)⋊C411yescharacteristic
376C2×C4C4×C22⋊D7911yescharacteristic
377C2×C4C4×D31611yescharacteristic
378C8—21no—
379C8—21no—
380C8—21no—
381C8—42no—
382C8—3162no—
383C8—3161no—
384C8—3161no—
385C8#1457907512yes—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—3161no—
395C22—3161no—
396C22—3161no—
397C22C4×(C2×D79)⋊C411yescharacteristic
398C22#1909868112yes—
399C22#1909868312yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—44no—
404C4—3161no—
405C4—3161no—
406C4—3161no—
407C4—6322no—
408C4C2×#1457907511yescharacteristic
409C4#1909853611yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—6321no—
414C2C4×#1457907511yescharacteristic
415C2#2376323711yescharacteristic
416C2#2376324611yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D79)⋊C4
commutatorC2×C4×C79C2×C42
FrattiniC23×C4C22×D79
FittingC8×C22⋊C4×C79C2
socleC22×C79C4×C22⋊C4
prime radical#19099074C22
cosocleC23×C4×C79C23
hypercenterC8×C22⋊C4D79
hypocenterC79#8240
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #23763176C2semidirect
5. #23761288C2semidirect
6. #23761286C2semidirect
7. C8×C22⋊C4×C79C2semidirect
8. C2×#14579167C4semidirect
14. #19098589C4semidirect
15. #19098529C4semidirect
18. #19098518C4semidirect
22. #19098301C4semidirect
23. #19098299C4semidirect
24. #19098298C4semidirect
25. #19098296C4semidirect
211. C8×C22⋊C4D79semidirect
216. C79#8240semidirect

Maximal subgroups

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

subgroupindex
#237720942
#237631762
#237618922
#237618892
#237612882
#237612862
C8×C22⋊C4×C792
#824079