Finite Group Databasebeta

← #23768997

Subgroups — #23768997

Order 10112.

518 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579155C211yesmaximal, characteristic, complemented
2#19098496C211yesmaximal, characteristic, complemented
3#19098486C211yesmaximal, characteristic, complemented
4#19098485C211yesmaximal, characteristic, complemented
5#19098479C211yesmaximal, characteristic
6#19098463C211yesmaximal, characteristic
7#19098458C211yesmaximal, characteristic, complemented
8#19098457C211yesmaximal, characteristic, complemented
9#19098454C211yesmaximal, characteristic, complemented
10#19098453C211yesmaximal, characteristic, complemented
11#19098447C211yesmaximal, characteristic, complemented
12#19098442C211yesmaximal, characteristic
13#19098436C211yesmaximal, characteristic, complemented
14C4×C4⋊Dic79C211yesmaximal, characteristic, complemented
15C2×#117×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79C2211yescharacteristic
17#14579155—24no—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C23×C4×C79C2211yescharacteristic
46#117×C79—24no—
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C22⋊C4×C79C2211yescharacteristic
51C2×C42×C79C2211yescharacteristic
52C2×C42×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C2×C22⋊D79—22no—
55C2×C22⋊D79—22no—
56C2×C22⋊D79—41no—
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C4⋊Dic79—22no—
65C4⋊Dic79—22no—
66Dic79⋊C4—22no—
67Dic79⋊C4—22no—
68Dic79⋊C4—22no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4—41no—
72C22⋊Dic79—22no—
73C22⋊Dic79—22no—
74C22⋊Dic79—41no—
75(C2×D79)⋊C4—22no—
76(C2×D79)⋊C4—22no—
77(C2×D79)⋊C4—22no—
78(C2×D79)⋊C4—22no—
79(C2×D79)⋊C4—22no—
80(C2×D79)⋊C4—41no—
81C4×Dic79—41no—
82C4×Dic79—41no—
83C24×C79C2311yescharacteristic
84C22×C4×C79—22no—
85C22×C4×C79—22no—
86C22×C4×C79—22no—
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—22no—
94C4⋊C4×C79—22no—
95C22⋊C4×C79—22no—
96C22⋊C4×C79—22no—
97C42×C79—22no—
98C42×C79D414yescomplemented
99C23×C79—21no—
100C23×C79—21no—
101C23×C79—21no—
102C23×C79—21no—
103C23×C79—21no—
104C23×C79—21no—
105C23×C79#4112yes—
106C23×C79C2411yescharacteristic
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—21no—
112C22×D79—21no—
113C22×D79—21no—
114C2×C4×C79—28no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79C2×D412yes—
130C2×C4×C79C2×D412yes—
131C2×C4×C79C2×D412yes—
132C2×C4×C79#4112yes—
133C22⋊D79—44no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79#4112yes—
154C2×Dic79#4112yes—
155C22×C79—22no—
156C22×C79—22no—
157C22×C79—22no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79C22×D411yescharacteristic
163C22×C79C2×#4111yescharacteristic
164C22×C79C2×#4111yescharacteristic
165C22×C79C2×#4111yescharacteristic
166C22×C79C2×#4111yescharacteristic
167C22×C79H(5,𝔽2)11yescharacteristic
168C22×C792−1+411yescharacteristic
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C4×C79—22no—
177C4×C79—22no—
178C4×C79—22no—
179C4×C79—22no—
180C4×C79—41no—
181C4×C79—41no—
182Dic79—22no—
183Dic79—22no—
184Dic79—41no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188Dic79—41no—
189C2×C79—42no—
190C2×C79#52511yescharacteristic
191C2×C79#53211yescharacteristic
192C2×C79#53711yescharacteristic
193C2×C79#55111yescharacteristic
194C2×C79#55211yescharacteristic
195C2×C79#55311yescharacteristic
196C2×C79#55611yescharacteristic
197D79—81no—
198#2601—791nomaximal, Sylow
199C79#260111yescharacteristic, complemented, Sylow
200C2×#126—791no—
201C2×#117D7911yescharacteristic, complemented
202#398—791no—
203#396—791no—
204#396—791no—
205#394—791no—
206#390—791no—
207#389—791no—
208#388—791no—
209#388—791no—
210#388—791no—
211#387—791no—
212#386—791no—
213#385—791no—
214C4×C4⋊C4—791no—
215C22×D4—791no—
216C23×C4C2×D7911yescharacteristic
217#126—1584no—
218#117—24no—
219C2×C4⋊C4—791no—
220C2×C4⋊C4—791no—
221C2×C4⋊C4—791no—
222C2×C4⋊C4—791no—
223C2×C4⋊C4—791no—
224C2×C4⋊C4—791no—
225C2×C4⋊C4—791no—
226C2×C4⋊C4—791no—
227C2×C4⋊C4C2×D7911yescharacteristic
228C2×C4⋊C4C2×D7911yescharacteristic
229C2×C22⋊C4—791no—
230C2×C22⋊C4—791no—
231C2×C22⋊C4—791no—
232C2×C22⋊C4—791no—
233C2×C22⋊C4—791no—
234C2×C22⋊C4—791no—
235C2×C22⋊C4—791no—
236C2×C22⋊C4—791no—
237C2×C22⋊C4—791no—
238C2×C22⋊C4C2×D7911yescharacteristic
239C2×C22⋊C4C2×D7911yescharacteristic
240C2×C42—791no—
241C2×C42—791no—
242C2×C42C2×D7911yescharacteristic
243C2×C42C2×D7911yescharacteristic
244#95—791no—
245#95—791no—
246#95—791no—
247#95—791no—
248#95—791no—
249#95—791no—
250#95—791no—
251#95—791no—
252C24—791no—
253C24C22×D7911yescharacteristic
254C2×D4—3161no—
255C2×D4—1582no—
256C2×D4—1582no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—791no—
261C22×C4—791no—
262C22×C4—791no—
263C22×C4—791no—
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4C22×D7911yescharacteristic
268C22×C4C22×D7911yescharacteristic
269C22×C4C22×D7911yescharacteristic
270C22×C4C22×D7911yescharacteristic
271C22×C4C22×D7911yescharacteristic
272C22×C4C22×D7911yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—3161no—
276C4⋊C4—1582no—
277C4⋊C4—1582no—
278C4⋊C4—1582no—
279C4⋊C4—1582no—
280C4⋊C4—1582no—
281C4⋊C4—1582no—
282C4⋊C4—1582no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—3161no—
286C22⋊C4—3161no—
287C22⋊C4—1582no—
288C22⋊C4—1582no—
289C22⋊C4—1582no—
290C22⋊C4—1582no—
291C22⋊C4—1582no—
292C22⋊C4—1582no—
293C22⋊C4—1582no—
294C42—22no—
295C42—3161no—
296C42—3161no—
297C42C22⋊D7914yescomplemented
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—1581no—
305C23—1581no—
306C23—1581no—
307C23—1581no—
308C23—1581no—
309C23—1581no—
310C23—1581no—
311C23#1192962412yes—
312C23C23×D7911yescharacteristic
313D4—3164no—
314C2×C4—28no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—792no—
330C2×C4—792no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4C2×C22⋊D7912yes—
351C2×C4C2×C22⋊D7912yes—
352C2×C4C2×C22⋊D7912yes—
353C2×C4#1192962412yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22C22×C22⋊D7911yescharacteristic
369C22#41×D7911yescharacteristic
370C22#41×D7911yescharacteristic
371C22C2×#1192962411yescharacteristic
372C22C2×#1192962411yescharacteristic
373C22#1457920711yescharacteristic
374C22#1457920811yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—3161no—
382C4—3161no—
383C4—3161no—
384C4—3161no—
385C4—3161no—
386C4—1582no—
387C4—1582no—
388C2—42no—
389C2—6321no—
390C2#1909907411yescharacteristic
391C2#1909910911yescharacteristic
392C2#1909914111yescharacteristic
393C2#1909923711yescharacteristic
394C2#1909924611yescharacteristic
395C2#1909925711yescharacteristic
396C2#1909928111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#117×C79C2
prime radicalC22×C22⋊D79C22
hypercenterC2×#117D79
hypocenterC79#2601
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#14579155C2semidirect
2. #19098496C2semidirect
3. #19098486C2semidirect
4. #19098485C2semidirect
7. #19098458C2semidirect
8. #19098457C2semidirect
9. #19098454C2semidirect
10. #19098453C2semidirect
11. #19098447C2semidirect
13. #19098436C2semidirect
14. C4×C4⋊Dic79C2semidirect
15. C2×#117×C79C2semidirect
98. C42×C79D4semidirect
199. C79#2601semidirect
201. C2×#117D79semidirect
297. C42C22⋊D79semidirect