Finite Group Databasebeta

← #2110×D79 #34440924

Subgroups — #2110×D79 #34440924

Order 20224.

738 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D79C212yesmaximal
2#405×D79C211yesmaximal, characteristic
3#23765005C211yesmaximal, characteristic, complemented
4#23765004C212yesmaximal, complemented
5#23765003C214yesmaximal, complemented
6#347×D79C214yesmaximal, complemented
7C79×#2110C211yesmaximal, characteristic, complemented
8C2×M16×D79C411yescharacteristic
9C22×C8×D79C2211yescharacteristic
10#117×D79C411yescharacteristic
11C2×#14579101C2212yes—
12C2×#14579100C414yescomplemented
13M32×D79C414yescomplemented
14M32×D79C414yescomplemented
15M32×D79C2214yes—
16M32×D79C2214yes—
17C2×C16×D79C414yescomplemented
18#19098521C411yescharacteristic
19#19098520C2212yes—
20#19098519C411yescharacteristic
21#19098518C2211yescharacteristic
22#19098517C412yes—
23#97×D79C2212yes—
24C4×C8×D79C412yes—
25#19098341C2214yescomplemented
26#19098340C2218yescomplemented
27C2×M32×C79C2212yes—
28#405×C79C2211yescharacteristic
29#347×C79C2214yescomplemented
30C22×C4×D79C2×C411yescharacteristic
31C2×#11929608C2×C411yescharacteristic
32C2×#11929607C2×C412yes—
33M16×D79—22no—
34M16×D79—22no—
35C22×C79⋊C8C2×C411yescharacteristic
36C2×C8×D79C2×C412yes—
37C2×C8×D79C2×C411yescharacteristic
38C2×C8×D79C2×C411yescharacteristic
39C2×C8×D79C2×C412yes—
40C2×C8×D79C2×C412yes—
41C2×C8×D79C2×C412yes—
42C2×C8×D79C2×C412yes—
43C2×C8×D79C2311yescharacteristic
44C2×C8×D79C2311yescharacteristic
45#14579120C2×C411yescharacteristic
46#14579119—21no—
47#14579118C2×C412yes—
48#14579117—21no—
49C4⋊C4×D79—21no—
50C22⋊C4×D79—21no—
51C42×D79C2×C412yes—
52#14579101C2×C414yescomplemented
53#14579101C2314yes—
54#14579100C2×C418yes—
55#14579100C2×C418yescomplemented
56C2×C79⋊C16C2×C414yescomplemented
57C16×D79C2×C418yes—
58C16×D79C2×C418yescomplemented
59#14579072C2×C412yes—
60#14579071C2×C412yes—
61#14579071C2312yes—
62C4×C79⋊C8C2×C412yes—
63C8×Dic79C2×C412yes—
64C8×Dic79C2×C412yes—
65C2×M16×C79C2×C411yescharacteristic
66C22×C8×C79C2311yescharacteristic
67#117×C79C2×C411yescharacteristic
68M32×C79C2×C414yescomplemented
69M32×C79C2314yes—
70C2×C16×C79C2×C414yescomplemented
71#97×C79C2312yes—
72C4×C8×C79C2×C412yes—
73C23×D79M1611yescharacteristic
74C22×Dic79M1611yescharacteristic
75C2×C4×D79—22no—
76C2×C4×D79C4212yes—
77C2×C4×D79C4212yes—
78C2×C4×D79M1612yes—
79C2×C4×D79M1612yes—
80C2×C4×D79M1611yescharacteristic
81C2×C4×D79M1611yescharacteristic
82C2×C4×D79C22×C411yescharacteristic
83C2×C4×D79C22×C411yescharacteristic
84#11929608—22no—
85#11929607—24no—
86C2×C79⋊C8C4212yes—
87C2×C79⋊C8C4212yes—
88C2×C79⋊C8C22×C412yes—
89C2×C79⋊C8C22×C411yescharacteristic
90C2×C79⋊C8C22×C411yescharacteristic
91C8×D79—22no—
92C8×D79—22no—
93C8×D79C4211yescharacteristic
94C8×D79C4211yescharacteristic
95C8×D79C4212yes—
96C8×D79C4211yescharacteristic
97C8×D79C4211yescharacteristic
98C8×D79C4212yes—
99C8×D79C22×C412yes—
100C8×D79C22×C412yes—
101C8×D79C22×C412yes—
102C8×D79C22×C412yes—
103C4⋊Dic79—21no—
104Dic79⋊C4—22no—
105C22⋊Dic79—21no—
106(C2×D79)⋊C4—22no—
107C4×Dic79—22no—
108C4×Dic79C22×C412yes—
109C79⋊C16C22×C418yes—
110C22×C4×C79C22×C411yescharacteristic
111M16×C79—22no—
112C2×C8×C79C22×C412yes—
113C2×C8×C79C22×C412yes—
114C2×C8×C79C22×C412yes—
115C2×C8×C79C22×C411yescharacteristic
116C2×C8×C79C2411yescharacteristic
117C4⋊C4×C79—21no—
118C22⋊C4×C79—21no—
119C42×C79C22×C412yes—
120C16×C79C22×C418yes—
121C23×C79C2×M1611yescharacteristic
122C22×D79—42no—
123C22×D79#9712yes—
124C22×D79#9712yes—
125C22×D79C2×M1611yescharacteristic
126C22×D79C2×M1611yescharacteristic
127C2×C4×C79—22no—
128C2×C4×C79C2×C4212yes—
129C2×C4×C79C2×M1612yes—
130C2×C4×C79C2×M1611yescharacteristic
131C2×C4×C79C23×C411yescharacteristic
132C2×Dic79—22no—
133C2×Dic79#9712yes—
134C2×Dic79#9712yes—
135C2×Dic79C2×M1611yescharacteristic
136C2×Dic79C2×M1611yescharacteristic
137C4×D79—44no—
138C4×D79#9712yes—
139C4×D79#9712yes—
140C4×D79#9712yes—
141C4×D79#9712yes—
142C4×D79C2×C4212yes—
143C4×D79C2×C4211yescharacteristic
144C4×D79C2×C4211yescharacteristic
145C4×D79C2×M1611yescharacteristic
146C4×D79C2×M1611yescharacteristic
147C4×D79C2×M1612yes—
148C8×C79—22no—
149C8×C79C2×C4211yescharacteristic
150C8×C79C2×C4211yescharacteristic
151C8×C79C23×C412yes—
152C79⋊C8—22no—
153C79⋊C8C2×C4212yes—
154C79⋊C8C2×C4211yescharacteristic
155C79⋊C8C2×C4211yescharacteristic
156C22×C79—41no—
157C22×C79C2×#9712yes—
158C22×C79C22×M1611yescharacteristic
159C2×D79—24no—
160C2×D79—22no—
161C2×D79—42no—
162C2×D79—41no—
163C2×D79C2×#9712yes—
164C2×D79C2×#9711yescharacteristic
165C2×D79C2×#9711yescharacteristic
166C4×C79—42no—
167C4×C79C2×#9712yes—
168C4×C79C22×C4211yescharacteristic
169C4×C79C22×M1611yescharacteristic
170Dic79—42no—
171Dic79C2×#9711yescharacteristic
172Dic79C2×#9711yescharacteristic
173Dic79C2×#9712yes—
174C2×#2110—791nomaximal, Sylow
175C2×C79—21no—
176C2×C79—22no—
177C2×C79C22×#9711yescharacteristic
178D79—22no—
179D79—21no—
180D79#211012yesdirect product factor
181C22×M32—792no—
182C2×#405—791no—
183#2110—792no—
184#2110—791no—
185#2110—794no—
186#2110D7911yescharacteristic, direct product factor
187C2×#347—794no—
188C79C2×#211011yescharacteristic, complemented, Sylow
189C22×M16—791no—
190C23×C8—791no—
191C2×#117—791no—
192C2×M32—792no—
193C2×M32—794no—
194C2×M32—794no—
195C2×M32—794no—
196C2×M32—794no—
197C2×M32—794no—
198C2×M32C2×D7912yes—
199C22×C16—794no—
200#405—791no—
201#405—791no—
202#405—791no—
203#405—792no—
204#405—792no—
205#405C2×D7911yescharacteristic
206C2×#97—792no—
207C2×C4×C8—792no—
208#347—798no—
209#347—794no—
210#347C2×D7914yescomplemented
211C23×C4—791no—
212C2×M16—791no—
213C2×M16—792no—
214C2×M16—1582no—
215C2×M16—1582no—
216C2×M16C4×D7911yescharacteristic
217C22×C8—791no—
218C22×C8—791no—
219C22×C8—791no—
220C22×C8—792no—
221C22×C8—792no—
222C22×C8—792no—
223C22×C8—792no—
224C22×C8—791no—
225C22×C8—791no—
226C22×C8—792no—
227C22×C8C22×D7911yescharacteristic
228#117—791no—
229#117—792no—
230#117—1581no—
231#117—1581no—
232#117C4×D7911yescharacteristic
233C2×C4⋊C4—1581no—
234C2×C22⋊C4—1581no—
235C2×C42—792no—
236M32—794no—
237M32—794no—
238M32—798no—
239M32—798no—
240M32C4×D7914yescomplemented
241M32C22×D7914yes—
242C2×C16—794no—
243C2×C16—798no—
244C2×C16—798no—
245C2×C16C4×D7914yescomplemented
246#97—792no—
247#97—792no—
248#97—792no—
249#97C22×D7912yes—
250C4×C8—792no—
251C4×C8—792no—
252C4×C8—792no—
253C4×C8C4×D7912yes—
254C24—791no—
255C22×C4—791no—
256C22×C4—792no—
257C22×C4—792no—
258C22×C4—791no—
259C22×C4—791no—
260C22×C4—792no—
261C22×C4—792no—
262C22×C4—791no—
263C22×C4—791no—
264C22×C4—1582no—
265C22×C4C2×C4×D7911yescharacteristic
266M16—22no—
267M16—1584no—
268M16—1582no—
269C2×C8—792no—
270C2×C8—792no—
271C2×C8—791no—
272C2×C8—791no—
273C2×C8—791no—
274C2×C8—791no—
275C2×C8—792no—
276C2×C8—791no—
277C2×C8—791no—
278C2×C8—792no—
279C2×C8—792no—
280C2×C8—792no—
281C2×C8—792no—
282C2×C8—792no—
283C2×C8—792no—
284C2×C8—1582no—
285C2×C8—1582no—
286C2×C8C2×C4×D7912yes—
287C2×C8C2×C4×D7911yescharacteristic
288C2×C8C2×C4×D7912yes—
289C2×C8C2×C4×D7912yes—
290C2×C8C23×D7911yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—1582no—
293C4⋊C4—1581no—
294C22⋊C4—21no—
295C22⋊C4—1582no—
296C22⋊C4—1581no—
297C42—792no—
298C42—1582no—
299C42C2×C4×D7912yes—
300C16—798no—
301C16C2×C4×D7918yes—
302C23—3162no—
303C23—792no—
304C23—791no—
305C23—792no—
306C23—791no—
307C23M16×D7911yescharacteristic
308C2×C4—22no—
309C2×C4—3164no—
310C2×C4—792no—
311C2×C4—792no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—792no—
316C2×C4—791no—
317C2×C4—792no—
318C2×C4—792no—
319C2×C4—792no—
320C2×C4—792no—
321C2×C4—791no—
322C2×C4—791no—
323C2×C4—792no—
324C2×C4—1582no—
325C2×C4C42×D7912yes—
326C2×C4M16×D7911yescharacteristic
327C2×C4M16×D7912yes—
328C2×C4C22×C4×D7911yescharacteristic
329C8—22no—
330C8—791no—
331C8—791no—
332C8—792no—
333C8—1582no—
334C8C42×D7911yescharacteristic
335C8C42×D7911yescharacteristic
336C8C22×C4×D7912yes—
337C22—41no—
338C22—3161no—
339C22—3162no—
340C22—791no—
341C22—791no—
342C22—792no—
343C22—1582no—
344C22—1584no—
345C22#97×D7912yes—
346C22C2×M16×D7911yescharacteristic
347C4—42no—
348C4—3162no—
349C4—791no—
350C4—791no—
351C4—792no—
352C4#97×D7912yes—
353C4C2×C42×D7911yescharacteristic
354C4C2×M16×D7911yescharacteristic
355C2—21no—
356C2—22no—
357C2—792no—
358C2—1581no—
359C2—1582no—
360C2C2×#97×D7911yescharacteristic
subgroupG/H
centerC8C42×D79
commutatorC4×C79C22×C42
FrattiniC2×C8C23×D79
FittingC79×#2110C2
socleC2×C79C22×#97
prime radicalC23×D79M16
cosocleC2×C8×C79C24
hypercenter#2110D79
hypocenterC79C2×#2110
LCSG ▷ C4×C79 ▷ C79
UCSC1 ◁ C8 ◁ #2110

Complements

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

NH ≅ G/Ntype
3. #23765005C2semidirect
4. #23765004C2semidirect
5. #23765003C2semidirect
6. #347×D79C2semidirect
7. C79×#2110C2semidirect
12. C2×#14579100C4semidirect
13. M32×D79C4semidirect
14. M32×D79C4semidirect
17. C2×C16×D79C4semidirect
25. #19098341C22semidirect
26. #19098340C22semidirect
29. #347×C79C22semidirect
52. #14579101C2×C4semidirect
55. #14579100C2×C4semidirect
56. C2×C79⋊C16C2×C4semidirect
58. C16×D79C2×C4semidirect
68. M32×C79C2×C4semidirect
70. C2×C16×C79C2×C4semidirect
180. D79#2110direct (N × H)
186. #2110D79direct (N × H)
188. C79C2×#2110semidirect
210. #347C2×D79semidirect
240. M32C4×D79semidirect
245. C2×C16C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D792
#405×D792
#237650052
#237650042
#237650032
#347×D792
C79×#21102
C2×#211079