Finite Group Databasebeta

← #21457403

Subgroups — #21457403

Order 7808.

488 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×#14519806C211yesmaximal, characteristic, complemented
2C2×#14519796C211yesmaximal, characteristic, complemented
3#16840432C211yesmaximal, characteristic, complemented
4#16840420C211yesmaximal, characteristic, complemented
5#16840012C211yesmaximal, characteristic, complemented
6#16839988C211yesmaximal, characteristic, complemented
7#16839981C211yesmaximal, characteristic, complemented
8#16839959C211yesmaximal, characteristic, complemented
9#16839921C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11#16839904C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839870C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758224C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519806—24no—
21#14519796—24no—
22C2×Dic244C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758200C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519773—21no—
30#14519763—21no—
31#14519754—21no—
32#14519753C2211yescharacteristic
33#14519750—21no—
34#14519749—21no—
35#14519749—21no—
36#14519748C2211yescharacteristic
37#14519748C2211yescharacteristic
38#14519748C2211yescharacteristic
39C4×Dic122C2211yescharacteristic
40C4×Dic122C2211yescharacteristic
41C4×D244C2211yescharacteristic
42D4×Dic61—21no—
43#14519737—21no—
44#14519709C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519698C2211yescharacteristic
51#14519698C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519689C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C2×D8×C61C2211yescharacteristic
57C2×D8×C61C2211yescharacteristic
58#127×C61C2211yescharacteristic
59#124×C61C2211yescharacteristic
60#97×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76Q8×D61—22no—
77Q8×D61—41no—
78#11758224—22no—
79#11758224—22no—
80#11758224—22no—
81#11758224—41no—
82#11758224—41no—
83#11758224—41no—
84C2×D244D411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61C2311yescharacteristic
87C2×C4×D61C2311yescharacteristic
88C2×Dic122—21no—
89C2×Dic122C2311yescharacteristic
90C2×Dic122C2311yescharacteristic
91SD16×C61—22no—
92SD16×C61—41no—
93D8×C61—22no—
94D8×C61—41no—
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C22⋊C4×C61—21no—
98C22⋊C4×C61—21no—
99C42×C61C2311yescharacteristic
100C22⋊Dic61—21no—
101C22⋊Dic61—21no—
102C22⋊Dic61—21no—
103#11758202—22no—
104#11758200—22no—
105#11758200—22no—
106#11758200—22no—
107#11758198—21no—
108#11758198D411yescharacteristic
109#11758198D411yescharacteristic
110C4⋊Dic61D411yescharacteristic
111C4⋊Dic61C2311yescharacteristic
112C4⋊Dic61C2311yescharacteristic
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116C4×Dic61—21no—
117C4×Dic61—21no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120Dic244D414yescomplemented
121#11758189—22no—
122C8×D61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C22×D61C2×D411yescharacteristic
127C22×D61C2×D411yescharacteristic
128Q8×C61—21no—
129Q8×C61—21no—
130D4×C61—21no—
131D4×C61—21no—
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—42no—
137D4×C61—81no—
138C2×C4×C61—21no—
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2×D411yescharacteristic
141C2×C4×C61C2411yescharacteristic
142C22⋊D61—42no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C22⋊D61—42no—
146C22⋊D61—81no—
147C22⋊D61—81no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61C2×D411yescharacteristic
156C2×Dic61C2×D411yescharacteristic
157D244—41no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—21no—
162C4×D61—42no—
163Dic122—21no—
164Dic122—21no—
165Dic122—42no—
166Dic122C2×D412yes—
167Dic122C2×D412yes—
168C8×C61—21no—
169C8×C61C2×D412yes—
170#92418—21no—
171#92418—21no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61C22×D411yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—41no—
191C4×C61C22×D411yescharacteristic
192C4×C61H(5,𝔽2)11yescharacteristic
193Dic61—22no—
194Dic61—22no—
195Dic61—21no—
196Dic61—21no—
197Dic61—41no—
198Dic61—41no—
199#3271—611nomaximal, Sylow
200C2×C61—81no—
201C2×C61—81no—
202C2×C61—81no—
203C2×C61D4211yescharacteristic
204C2×C61#57511yescharacteristic
205C2×C61#57711yescharacteristic
206D61—41no—
207D61—41no—
208C2×#137—611no—
209C2×#135—611no—
210#550—611no—
211#548—611no—
212#496D6111yescharacteristic, complemented
213#469—611no—
214#465—611no—
215#464—611no—
216#460—611no—
217#452—611no—
218#449—611no—
219#449—611no—
220#448—611no—
221#441—611no—
222#435—611no—
223C61#327111yescharacteristic, complemented, Sylow
224C2×#41—611no—
225C2×#41—611no—
226C2×#41—611no—
227C22×Q8—611no—
228#137—1224no—
229#135—1224no—
230C2×Q16—611no—
231C2×Q16—611no—
232C2×SD16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16C2×D6111yescharacteristic
236C2×SD16C2×D6111yescharacteristic
237C2×D8C2×D6111yescharacteristic
238C2×D8C2×D6111yescharacteristic
239C2×M16—611no—
240C22×C8—611no—
241#127—1221no—
242#127C2×D6111yescharacteristic
243#124—1221no—
244#124C2×D6111yescharacteristic
245C22⋊Q8—611no—
246C22⋊Q8—1221no—
247#121—611no—
248#121—611no—
249#121—611no—
250#121—1221no—
251#121—1221no—
252#121—1221no—
253C4×Q8—611no—
254C4×Q8—611no—
255C4×D4—611no—
256C4×D4—1221no—
257C4×D4—1221no—
258#106—611no—
259C4⋊C8—611no—
260#103—611no—
261#103—611no—
262#103—611no—
263#102—611no—
264#102—611no—
265#102—611no—
266C22⋊C8—611no—
267C22⋊C8—611no—
268#97C2×D6111yescharacteristic
269#41—1222no—
270#41—1222no—
271#41—1222no—
272#41—2441no—
273#41—2441no—
274#41—2441no—
275C2×Q8—611no—
276C2×Q8—611no—
277C2×Q8—1221no—
278C2×Q8—1222no—
279C2×Q8—2441no—
280C2×Q8C22×D6111yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—611no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4C22×D6111yescharacteristic
291C2×D4C22×D6111yescharacteristic
292C2×D4C22×D6111yescharacteristic
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299Q16—614no—
300Q16—1222no—
301SD16—22no—
302SD16—41no—
303SD16—1222no—
304SD16—1222no—
305SD16—1222no—
306D8—22no—
307D8—41no—
308M16—1222no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8—1222no—
312C2×C8C22×D6111yescharacteristic
313C2×C8C22×D6111yescharacteristic
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—611no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—611no—
323C22⋊C4—611no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C42—1221no—
329C42—1221no—
330C42C22×D6111yescharacteristic
331C23—21no—
332C23—21no—
333C23—21no—
334C23—611no—
335C23—611no—
336Q8—21no—
337Q8—21no—
338Q8—612no—
339Q8—612no—
340Q8—1221no—
341Q8—1221no—
342Q8—2442no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—81no—
351D4—4881no—
352D4—4881no—
353D4—2441no—
354D4—2442no—
355D4—2442no—
356D4—2442no—
357D4—2442no—
358C2×C4—21no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
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×C4D4×D6111yescharacteristic
374C2×C4D4×D6111yescharacteristic
375C2×C4C23×D6111yescharacteristic
376C8—21no—
377C8—1221no—
378C8—1221no—
379C8D4×D6112yes—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—1221no—
390C22—1221no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—1221no—
395C22C2×D4×D6111yescharacteristic
396C4—21no—
397C4—21no—
398C4—41no—
399C4—1221no—
400C4—1221no—
401C4—1222no—
402C4—1222no—
403C4—2441no—
404C4—2441no—
405C4C2×D4×D6111yescharacteristic
406C4#1451982211yescharacteristic
407C2—81no—
408C2—81no—
409C2—81no—
410C2—2441no—
411C2—2441no—
412C2#1684039711yescharacteristic
413C2#1684055811yescharacteristic
414C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3271
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
2. C2×#14519796C2semidirect
3. #16840432C2semidirect
4. #16840420C2semidirect
5. #16840012C2semidirect
6. #16839988C2semidirect
7. #16839981C2semidirect
8. #16839959C2semidirect
9. #16839921C2semidirect
10. #16839904C2semidirect
11. #16839904C2semidirect
12. #16839899C2semidirect
13. #16839870C2semidirect
14. #16839835C2semidirect
15. C61×#496C2semidirect
120. Dic244D4semidirect
212. #496D61semidirect
223. C61#3271semidirect