Finite Group Databasebeta

← #21457546

Subgroups — #21457546

Order 7808.

494 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519799C211yesmaximal, characteristic, complemented
2C2×#14519798C211yesmaximal, characteristic, complemented
3#16840430C211yesmaximal, characteristic, complemented
4#16840414C211yesmaximal, characteristic, complemented
5#16840133C211yesmaximal, characteristic, complemented
6#16839992C211yesmaximal, characteristic, complemented
7#16839971C211yesmaximal, characteristic, complemented
8#16839956C211yesmaximal, characteristic, complemented
9#16839925C211yesmaximal, characteristic, complemented
10#16839922C211yesmaximal, characteristic, complemented
11#16839910C211yesmaximal, characteristic, complemented
12#16839905C211yesmaximal, characteristic, complemented
13#16839849C211yesmaximal, characteristic, complemented
14C8×C22⋊D61C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758222C2211yescharacteristic
19C2×#11758224C2211yescharacteristic
20#14519799—24no—
21#14519798—24no—
22C2×Dic244C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758190C2211yescharacteristic
26C2×#11758200C2211yescharacteristic
27C2×#11758201C2211yescharacteristic
28C2×D488C2211yescharacteristic
29C2×#11758199C2211yescharacteristic
30C2×C8×D61C2211yescharacteristic
31#14519775C2211yescharacteristic
32#14519773—21no—
33#14519773C2211yescharacteristic
34#14519762—21no—
35#14519759—21no—
36#14519757C2211yescharacteristic
37#14519752C2211yescharacteristic
38#14519750—21no—
39#14519750—21no—
40#14519749—21no—
41#14519742C2211yescharacteristic
42#14519739C2211yescharacteristic
43C4×C22⋊D61C2211yescharacteristic
44#14519737—21no—
45C4⋊C4×D61—21no—
46#14519706C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519697C2211yescharacteristic
51C22⋊#92418C2211yescharacteristic
52#14519689C2211yescharacteristic
53C8×Dic61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic
56C22⋊Q8×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic
58#106×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C22×Dic61—21no—
72#11758226—22no—
73#11758226—41no—
74#11758224—22no—
75#11758224—41no—
76#11758222—22no—
77#11758222—22no—
78#11758222—41no—
79#11758222—41no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61C2311yescharacteristic
89C2×Dic122C2311yescharacteristic
90C2×Dic122C2311yescharacteristic
91SD16×C61—22no—
92C2×C8×C61—22no—
93C2×C8×C61C2311yescharacteristic
94C2×C8×C61C2311yescharacteristic
95C4⋊C4×C61—21no—
96C4⋊C4×C61C2311yescharacteristic
97C4⋊C4×C61C2311yescharacteristic
98C22⋊C4×C61—21no—
99C22⋊C4×C61—21no—
100C22⋊Dic61D411yescharacteristic
101#11758202—22no—
102#11758201—41no—
103#11758200—41no—
104#11758199—22no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198D411yescharacteristic
109C4⋊Dic61—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196D411yescharacteristic
114C4×Dic61—21no—
115C4×Dic61C2311yescharacteristic
116C2×#92418C2311yescharacteristic
117C2×#92418C2311yescharacteristic
118Dic244—22no—
119D488—22no—
120#11758190—22no—
121#11758190D414yescomplemented
122C8×D61—22no—
123C23×C61—21no—
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61C2×D411yescharacteristic
128Q8×C61—21no—
129Q8×C61—21no—
130D4×C61—21no—
131D4×C61—21no—
132D4×C61—81no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2411yescharacteristic
140C22⋊D61—22no—
141C22⋊D61—42no—
142C22⋊D61—42no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C22⋊D61—81no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—42no—
149C2×Dic61C2×D411yescharacteristic
150C2×Dic61C2×D411yescharacteristic
151C2×Dic61C2×D411yescharacteristic
152D244—21no—
153D244—21no—
154D244—21no—
155D244—42no—
156D244—81no—
157D244C2×D412yes—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—42no—
163C4×D61—42no—
164Dic122—21no—
165Dic122—21no—
166Dic122—21no—
167Dic122C2×D412yes—
168C8×C61—21no—
169C8×C61C2×D412yes—
170#92418—21no—
171#92418—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61C22×D411yescharacteristic
179C2×D61—21no—
180C2×D61—22no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C4×C61—21no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61C22×D411yescharacteristic
193C4×C61H(5,𝔽2)11yescharacteristic
194Dic61—22no—
195Dic61—21no—
196Dic61—21no—
197Dic61—41no—
198Dic61#13512yescomplemented
199#3284—611nomaximal, Sylow
200C2×C61—41no—
201C2×C61—81no—
202C2×C61D4211yescharacteristic
203C2×C61C2×#13511yescharacteristic
204C2×C61#57711yescharacteristic
205D61—41no—
206D61—42no—
207D61—81no—
208C2×#135—611no—
209C2×#135—611no—
210#550—611no—
211#547—611no—
212#492—611no—
213#465—611no—
214#465D6111yescharacteristic, complemented
215#462—611no—
216#459—611no—
217#452—611no—
218#452—611no—
219#449—611no—
220#449—611no—
221C4×SD16—611no—
222C8×D4—611no—
223C61#328411yescharacteristic, complemented, Sylow
224C2×#41—611no—
225C2×#41—611no—
226C2×#41—611no—
227C2×#41—611no—
228#135—1224no—
229#135—1224no—
230C2×Q16—611no—
231C2×Q16—611no—
232C2×SD16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16C2×D6111yescharacteristic
237C2×D8—611no—
238C2×D8—611no—
239C22×C8—611no—
240C22×C8C2×D6111yescharacteristic
241C4⋊Q8—611no—
242#127—611no—
243#127—1221no—
244#123—1221no—
245#123—1221no—
246C22⋊Q8—611no—
247C22⋊Q8C2×D6111yescharacteristic
248#121—611no—
249#121—1221no—
250#121—1221no—
251#121—1221no—
252#121C2×D6111yescharacteristic
253C4×Q8—611no—
254C4×D4—611no—
255C4×D4—611no—
256C4×D4—1221no—
257C2×C4⋊C4—1221no—
258#106C2×D6111yescharacteristic
259C4⋊C8—611no—
260#103—611no—
261#103—611no—
262#103C2×D6111yescharacteristic
263#102—611no—
264#102—611no—
265#102C2×D6111yescharacteristic
266C22⋊C8—611no—
267C22⋊C8—611no—
268C4×C8—611no—
269#41—1222no—
270#41—1222no—
271#41—1222no—
272#41—1222no—
273#41—2441no—
274#41—2441no—
275#41—2441no—
276#41—2441no—
277C2×Q8—611no—
278C2×Q8—611no—
279C2×Q8C22×D6111yescharacteristic
280C2×D4—21no—
281C2×D4—611no—
282C2×D4—611no—
283C2×D4—611no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4C22×D6111yescharacteristic
292C22×C4—611no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4C22×D6111yescharacteristic
299Q16—1222no—
300Q16—1222no—
301SD16—22no—
302SD16—614no—
303SD16—1222no—
304SD16—2441no—
305SD16—2441no—
306D8—1222no—
307D8—1222no—
308C2×C8—22no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8—1222no—
312C2×C8C22×D6111yescharacteristic
313C2×C8C22×D6111yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4C22×D6111yescharacteristic
321C4⋊C4C22×D6111yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—611no—
325C22⋊C4—611no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C42—611no—
330C42—1221no—
331C23—21no—
332C23—611no—
333C23—1221no—
334C23—1221no—
335C23D4×D6111yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—612no—
339Q8—1221no—
340Q8—1221no—
341Q8—1221no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—612no—
346D4—1222no—
347D4—1221no—
348D4—1221no—
349D4—1221no—
350D4—4881no—
351D4—4881no—
352D4—2442no—
353D4—2442no—
354D4—2442no—
355D4—2442no—
356D4—2442no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2442no—
374C2×C4D4×D6111yescharacteristic
375C2×C4C23×D6111yescharacteristic
376C8—21no—
377C8—1221no—
378C8—1221no—
379C8D4×D6112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—1221no—
387C22—1221no—
388C22—1221no—
389C22—1222no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22C2×D4×D6111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—612no—
401C4—1221no—
402C4—1221no—
403C4—1222no—
404C4—2441no—
405C4C2×D4×D6111yescharacteristic
406C4#1451982311yescharacteristic
407C2—41no—
408C2—81no—
409C2—4881no—
410C2—2441no—
411C2—2442no—
412C2#1684039611yescharacteristic
413C2#135×D6111yescharacteristic
414C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3284
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#14519799C2semidirect
2. C2×#14519798C2semidirect
3. #16840430C2semidirect
4. #16840414C2semidirect
5. #16840133C2semidirect
6. #16839992C2semidirect
7. #16839971C2semidirect
8. #16839956C2semidirect
9. #16839925C2semidirect
10. #16839922C2semidirect
11. #16839910C2semidirect
12. #16839905C2semidirect
13. #16839849C2semidirect
14. C8×C22⋊D61C2semidirect
15. C61×#465C2semidirect
121. #11758190D4semidirect
198. Dic61#135semidirect
214. #465D61semidirect
223. C61#3284semidirect