Finite Group Databasebeta

← #1831×D79 #34288409

Subgroups — #1831×D79 #34288409

Order 20224.

1246 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C8×D79C212yesmaximal
2C43×D79C211yesmaximal, characteristic
3#23763517C211yesmaximal, characteristic, complemented
4#23763516C212yesmaximal, complemented
5#23763515C214yesmaximal, complemented
6#336×D79C214yesmaximal
7C79×#1831C211yesmaximal, characteristic, complemented
8C22×C8×D79C2214yes—
9C2×C42×D79C412yes—
10C2×C42×D79C411yescharacteristic
11C2×C42×D79C411yescharacteristic
12C2×C42×D79C2212yes—
13C2×C42×D79C2211yescharacteristic
14C2×C4⋊(C79⋊C8)C2212yes—
15C2×Dic79⋊C8C2214yes—
16C4⋊C8×D79—28no—
17C42×Dic79C412yes—
18C42×Dic79C411yescharacteristic
19C42×Dic79C411yescharacteristic
20C42×Dic79C2212yes—
21C42×Dic79C2211yescharacteristic
22#19098318C2214yes—
23#19098317C2218yes—
24C2×C4⋊C8×C79C2212yes—
25C43×C79C2211yescharacteristic
26#336×C79C2214yes—
27C22×C4×D79C2×C411yescharacteristic
28C22×C4×D79C2×C412yes—
29C22×C4×D79C2×C412yes—
30C22×C4×D79C2×C411yescharacteristic
31C22×C4×D79C2311yescharacteristic
32C22×C79⋊C8C2314yes—
33C2×C8×D79—28no—
34C2×C8×D79—216no—
35C2×C4×Dic79C2×C412yes—
36C2×C4×Dic79C2×C412yes—
37C2×C4×Dic79C2×C412yes—
38C2×C4×Dic79C2×C412yes—
39C2×C4×Dic79C2×C412yes—
40C2×C4×Dic79C2×C412yes—
41C2×C4×Dic79C2×C411yescharacteristic
42C2×C4×Dic79C2×C411yescharacteristic
43C2×C4×Dic79C2×C411yescharacteristic
44C2×C4×Dic79C2×C411yescharacteristic
45C2×C4×Dic79C2×C412yes—
46C2×C4×Dic79C2312yes—
47C2×C4×Dic79C2311yescharacteristic
48C42×D79—28no—
49C42×D79—24no—
50C42×D79—28no—
51C42×D79C818yescomplemented
52C42×D79D414yes—
53C42×D79Q814yes—
54C4⋊(C79⋊C8)—24no—
55Dic79⋊C8—28no—
56C22×C8×C79C2314yes—
57C2×C42×C79C2×C412yes—
58C2×C42×C79C2×C411yescharacteristic
59C2×C42×C79C2×C411yescharacteristic
60C2×C42×C79C2312yes—
61C2×C42×C79C2311yescharacteristic
62C4⋊C8×C79—24no—
63C23×D79C22×C411yescharacteristic
64C22×Dic79C22×C411yescharacteristic
65C22×Dic79C22×C412yes—
66C22×Dic79C22×C412yes—
67C22×Dic79C22×C411yescharacteristic
68C22×Dic79C22×C411yescharacteristic
69C2×C4×D79—24no—
70C2×C4×D79—24no—
71C2×C4×D79—24no—
72C2×C4×D79—24no—
73C2×C4×D79—24no—
74C2×C4×D79C4⋊C414yes—
75C2×C4×D79C4⋊C414yes—
76C2×C4×D79C2×C818yes—
77C2×C4×D79C2×C814yes—
78C2×C4×D79M1618yes—
79C2×C4×D79M1614yes—
80C2×C4×D79C2×D412yes—
81C2×C4×D79C2×Q812yes—
82C2×C4×D79#4118yes—
83C2×C79⋊C8—24no—
84C2×C79⋊C8—28no—
85C8×D79—416no—
86C4×Dic79—24no—
87C4×Dic79—24no—
88C4×Dic79—24no—
89C4×Dic79—24no—
90C4×Dic79—24no—
91C4×Dic79—24no—
92C4×Dic79—22no—
93C4×Dic79—24no—
94C4×Dic79C4⋊C414yes—
95C4×Dic79C4⋊C414yes—
96C4×Dic79C2×C818yescomplemented
97C4×Dic79C2×C814yescomplemented
98C4×Dic79C2×D412yes—
99C4×Dic79C2×Q812yes—
100C22×C4×C79C22×C411yescharacteristic
101C22×C4×C79C22×C412yes—
102C22×C4×C79C22×C412yes—
103C22×C4×C79C22×C411yescharacteristic
104C22×C4×C79C2411yescharacteristic
105C2×C8×C79—24no—
106C2×C8×C79—28no—
107C42×C79—24no—
108C42×C79—22no—
109C42×C79—24no—
110C42×C79C2×C814yescomplemented
111C42×C79C2×D412yes—
112C42×C79C2×Q812yes—
113C23×C79C23×C411yescharacteristic
114C22×D79C2×C4⋊C412yes—
115C22×D79#11714yes—
116C22×D79C22×C812yes—
117C22×D79C2×M1612yes—
118C22×D79C2×M1614yes—
119C2×C4×C79—22no—
120C2×C4×C79—22no—
121C2×C4×C79—22no—
122C2×C4×C79—22no—
123C2×C4×C79—22no—
124C2×C4×C79C2×C4⋊C412yes—
125C2×C4×C79C2×C4⋊C412yes—
126C2×C4×C79C22×C814yes—
127C2×C4×C79C22×C812yes—
128C2×C4×C79C2×M1614yes—
129C2×C4×C79C2×M1612yes—
130C2×C4×C79C22×D411yescharacteristic
131C2×C4×C79C22×Q811yescharacteristic
132C2×C4×C79C2×#4114yes—
133C2×Dic79—22no—
134C2×Dic79—22no—
135C2×Dic79—22no—
136C2×Dic79—22no—
137C2×Dic79—22no—
138C2×Dic79C2×C4⋊C412yes—
139C2×Dic79C2×C4⋊C412yes—
140C2×Dic79C2×C4⋊C412yes—
141C2×Dic79#11714yes—
142C2×Dic79C22×C814yes—
143C2×Dic79C22×C812yes—
144C2×Dic79C2×M1614yes—
145C2×Dic79C2×M1612yes—
146C4×D79—28no—
147C4×D79—216no—
148C4×D79—216no—
149C4×D79C4⋊C8116yes—
150C4×D79#12418yes—
151C4×D79#12518yes—
152C8×C79—44no—
153C79⋊C8—44no—
154C22×C79C22×C4⋊C411yescharacteristic
155C22×C79C2×#11712yes—
156C22×C79C23×C811yescharacteristic
157C22×C79C22×M1611yescharacteristic
158C22×C79C22×M1612yes—
159C2×D79#38214yes—
160C2×D79C2×C4⋊C814yes—
161C2×D79#42314yes—
162C2×D79#43118yes—
163C2×D79#43218yes—
164C4×C79—22no—
165C4×C79—24no—
166C4×C79—24no—
167C4×C79C2×C4⋊C814yes—
168C4×C79C2×#12412yes—
169C4×C79C2×#12512yes—
170Dic79—22no—
171Dic79—24no—
172Dic79—24no—
173Dic79#38214yes—
174Dic79C2×C4⋊C814yes—
175C2×#1831—791nomaximal, Sylow
176C2×C79C2×#38211yescharacteristic
177C2×C79C22×C4⋊C811yescharacteristic
178C2×C79C2×#42311yescharacteristic
179C2×C79C2×#43112yes—
180C2×C79C2×#43212yes—
181D79#183118yesdirect product factor
182C22×C4⋊C8—792no—
183C2×C43—791no—
184#1831—792no—
185#1831—791no—
186#1831—794no—
187#1831D7911yescharacteristic, direct product factor
188C2×#336—794no—
189C79C2×#183111yescharacteristic, complemented, Sylow
190C23×C8—794no—
191C22×C42—791no—
192C22×C42—791no—
193C22×C42—792no—
194C22×C42—791no—
195C22×C42—792no—
196C2×C4⋊C8—794no—
197C2×C4⋊C8—792no—
198C2×C4⋊C8—1588no—
199C2×C4⋊C8C2×D7912yes—
200C43—792no—
201C43—791no—
202C43—792no—
203C43—791no—
204C43—791no—
205C43C2×D7911yescharacteristic
206#336—798no—
207#336—794no—
208#336C2×D7914yes—
209C23×C4—791no—
210C23×C4—791no—
211C23×C4—791no—
212C23×C4—792no—
213C23×C4—792no—
214C22×C8—794no—
215C22×C8—1588no—
216C22×C8—15816no—
217C22×C8C22×D7914yes—
218C2×C42—791no—
219C2×C42—791no—
220C2×C42—792no—
221C2×C42—791no—
222C2×C42—791no—
223C2×C42—798no—
224C2×C42—794no—
225C2×C42—794no—
226C2×C42—792no—
227C2×C42—792no—
228C2×C42—792no—
229C2×C42—792no—
230C2×C42—792no—
231C2×C42—792no—
232C2×C42—791no—
233C2×C42—792no—
234C2×C42—1588no—
235C2×C42—1584no—
236C2×C42—1588no—
237C2×C42C4×D7912yes—
238C2×C42C4×D7911yescharacteristic
239C2×C42C4×D7911yescharacteristic
240C2×C42C22×D7912yes—
241C2×C42C22×D7911yescharacteristic
242C4⋊C8—24no—
243C4⋊C8—1588no—
244C4⋊C8—1584no—
245C24—791no—
246C22×C4—791no—
247C22×C4—791no—
248C22×C4—792no—
249C22×C4—798no—
250C22×C4—794no—
251C22×C4—794no—
252C22×C4—794no—
253C22×C4—792no—
254C22×C4—791no—
255C22×C4—792no—
256C22×C4—792no—
257C22×C4—794no—
258C22×C4—798no—
259C22×C4—798no—
260C22×C4—1584no—
261C22×C4—1584no—
262C22×C4—1584no—
263C22×C4—1584no—
264C22×C4—1584no—
265C22×C4C2×C4×D7911yescharacteristic
266C22×C4C2×C4×D7912yes—
267C22×C4C2×C4×D7912yes—
268C22×C4C2×C4×D7911yescharacteristic
269C22×C4C23×D7911yescharacteristic
270C2×C8—28no—
271C2×C8—24no—
272C2×C8—31616no—
273C2×C8—1588no—
274C2×C8—1584no—
275C42—24no—
276C42—24no—
277C42—22no—
278C42—792no—
279C42—794no—
280C42—794no—
281C42—798no—
282C42—794no—
283C42—792no—
284C42—1584no—
285C42—1584no—
286C42—1584no—
287C42—1584no—
288C42—1584no—
289C42—1584no—
290C42—1584no—
291C42—1582no—
292C42C8×D7914yescomplemented
293C42D4×D7912yes—
294C42Q8×D7912yes—
295C23—792no—
296C23—794no—
297C23—792no—
298C23—792no—
299C23—794no—
300C23C22×C4×D7911yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—792no—
307C2×C4—792no—
308C2×C4—794no—
309C2×C4—792no—
310C2×C4—792no—
311C2×C4—798no—
312C2×C4—798no—
313C2×C4—7916no—
314C2×C4—792no—
315C2×C4—794no—
316C2×C4—794no—
317C2×C4—1588no—
318C2×C4—15816no—
319C2×C4—15816no—
320C2×C4—1582no—
321C2×C4—1582no—
322C2×C4—1582no—
323C2×C4—1582no—
324C2×C4—1582no—
325C2×C4C4⋊C4×D7912yes—
326C2×C4C4⋊C4×D7912yes—
327C2×C4C2×C8×D7914yes—
328C2×C4C2×C8×D7912yes—
329C2×C4M16×D7914yes—
330C2×C4M16×D7912yes—
331C2×C4C2×D4×D7911yescharacteristic
332C2×C4C2×Q8×D7911yescharacteristic
333C2×C4#41×D7914yes—
334C8—44no—
335C8—3164no—
336C22—794no—
337C22—794no—
338C22—794no—
339C22—798no—
340C22—798no—
341C22C2×C4⋊C4×D7911yescharacteristic
342C22#117×D7912yes—
343C22C22×C8×D7911yescharacteristic
344C22C2×M16×D7911yescharacteristic
345C22C2×M16×D7912yes—
346C4—22no—
347C4—24no—
348C4—24no—
349C4—794no—
350C4—794no—
351C4—1582no—
352C4—1584no—
353C4—1584no—
354C4C4⋊C8×D7914yes—
355C4#124×D7912yes—
356C4#125×D7912yes—
357C2—798no—
358C2#382×D7911yescharacteristic
359C2C2×C4⋊C8×D7911yescharacteristic
360C2#423×D7911yescharacteristic
361C2#431×D7912yes—
362C2#432×D7912yes—
subgroupG/H
center, FrattiniC22×C4C23×D79
commutatorC22×C79C23×C8
FittingC79×#1831C2
socleC23×C79C23×C4
prime radicalC23×D79C22×C4
cosocleC22×C4×C79C24
hypercenter#1831D79
hypocenterC79C2×#1831
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ #1831

Complements

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

NH ≅ G/Ntype
3. #23763517C2semidirect
4. #23763516C2semidirect
5. #23763515C2semidirect
7. C79×#1831C2semidirect
51. C42×D79C8semidirect
96. C4×Dic79C2×C8semidirect
97. C4×Dic79C2×C8semidirect
110. C42×C79C2×C8semidirect
181. D79#1831direct (N × H)
187. #1831D79direct (N × H)
189. C79C2×#1831semidirect
292. C42C8×D79semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D792
C43×D792
#237635172
#237635162
#237635152
#336×D792
C79×#18312
C2×#183179