Finite Group Databasebeta

← #21457409

Subgroups — #21457409

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×#14519810C211yesmaximal, characteristic, complemented
2C2×#14519799C211yesmaximal, characteristic, complemented
3#16840433C211yesmaximal, characteristic, complemented
4#16840421C211yesmaximal, characteristic, complemented
5#16840151C211yesmaximal, characteristic, complemented
6#16840015C211yesmaximal, characteristic, complemented
7#16839991C211yesmaximal, characteristic, complemented
8#16839985C211yesmaximal, characteristic, complemented
9#16839963C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839909C211yesmaximal, characteristic, complemented
12#16839909C211yesmaximal, characteristic, complemented
13#16839903C211yesmaximal, characteristic, complemented
14#16839870C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758222C2211yescharacteristic
19C22×Dic122C2211yescharacteristic
20#14519810—24no—
21#14519799—24no—
22C2×Dic244C2211yescharacteristic
23C2×Dic244C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758190C2211yescharacteristic
26C2×#11758190C2211yescharacteristic
27C2×#11758190C2211yescharacteristic
28C2×#11758190C2211yescharacteristic
29C2×D488C2211yescharacteristic
30C2×D488C2211yescharacteristic
31#14519774C2211yescharacteristic
32#14519773—21no—
33#14519765C2211yescharacteristic
34#14519763—21no—
35#14519756C2211yescharacteristic
36#14519755—21no—
37#14519751C2211yescharacteristic
38#14519751C2211yescharacteristic
39#14519751C2211yescharacteristic
40#14519750—21no—
41#14519750—21no—
42#14519749—21no—
43C4×Dic122C2211yescharacteristic
44C4×Dic122C2211yescharacteristic
45#14519739—21no—
46#14519737—21no—
47#14519709C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519702C2211yescharacteristic
51#14519699C2211yescharacteristic
52#14519699C2211yescharacteristic
53#14519699C2211yescharacteristic
54C2×M16×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57C4⋊C8×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C22⋊C8×C61C2211yescharacteristic
60#97×C61C2211yescharacteristic
61C2×D4×C61D411yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C22×Dic61—21no—
71#11758222—22no—
72#11758222—22no—
73#11758222—22no—
74#11758222—41no—
75#11758222—41no—
76#11758222—41no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×Dic122—22no—
86C2×Dic122—21no—
87C2×Dic122—41no—
88C2×Dic122C2311yescharacteristic
89C2×Dic122C2311yescharacteristic
90C2×Dic122C2311yescharacteristic
91M16×C61—22no—
92C2×C8×C61—22no—
93C2×C8×C61C2311yescharacteristic
94C2×C8×C61C2311yescharacteristic
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C4⋊C4×C61D411yescharacteristic
98C22⋊C4×C61D411yescharacteristic
99C22⋊C4×C61D411yescharacteristic
100C42×C61C2311yescharacteristic
101C22⋊Dic61—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107C4⋊Dic61C2311yescharacteristic
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114Dic244—22no—
115Dic244D414yescomplemented
116D488—22no—
117D488—41no—
118#11758190—22no—
119#11758190—22no—
120#11758190—22no—
121#11758190—22no—
122#11758190—41no—
123C23×C61C2×D411yescharacteristic
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128D4×C61—41no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—81no—
143C22⋊D61—81no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—42no—
150D244—21no—
151D244—21no—
152D244—21no—
153D244—21no—
154D244—21no—
155D244—21no—
156D244—42no—
157D244—81no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161Dic122—21no—
162Dic122—21no—
163Dic122—21no—
164Dic122—21no—
165Dic122—42no—
166Dic122C2×D412yes—
167Dic122C2×D412yes—
168C8×C61—21no—
169C8×C61—21no—
170C8×C61—21no—
171C8×C61C2×D412yes—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61C22×D411yescharacteristic
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61C22×D411yescharacteristic
193C4×C61H(5,𝔽2)11yescharacteristic
194Dic61—22no—
195Dic61—22no—
196Dic61—41no—
197Dic61—41no—
198Dic61—41no—
199#3271—611nomaximal, Sylow
200C2×C61—41no—
201C2×C61—41no—
202C2×C61D4211yescharacteristic
203C2×C61#57511yescharacteristic
204C2×C61#57711yescharacteristic
205D61—81no—
206D61—81no—
207D61—81no—
208C2×#137—611no—
209C2×#135—611no—
210#550—611no—
211#548—611no—
212#496—611no—
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#435D6111yescharacteristic, complemented
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×SD16—611no—
236C2×SD16—611no—
237C2×D8—611no—
238C2×D8—611no—
239C2×M16C2×D6111yescharacteristic
240C22×C8C2×D6111yescharacteristic
241#127—611no—
242#127—1221no—
243#124—611no—
244#124—1221no—
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—1221no—
256C4×D4—1221no—
257C4×D4C2×D6111yescharacteristic
258#106—611no—
259C4⋊C8C2×D6111yescharacteristic
260#103—611no—
261#103—611no—
262#103—611no—
263#102—611no—
264#102—611no—
265#102—611no—
266C22⋊C8C2×D6111yescharacteristic
267C22⋊C8C2×D6111yescharacteristic
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—611no—
278C2×Q8—1222no—
279C2×Q8—1221no—
280C2×Q8—2441no—
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×D4—1221no—
292C2×D4D24411yescharacteristic
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4C22×D6111yescharacteristic
298C22×C4C22×D6111yescharacteristic
299Q16—614no—
300Q16—1222no—
301SD16—1222no—
302SD16—1222no—
303SD16—1222no—
304SD16—1222no—
305SD16—2441no—
306D8—1222no—
307D8—2441no—
308M16—22no—
309C2×C8—22no—
310C2×C8C22×D6111yescharacteristic
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C2×C8C22×D6111yescharacteristic
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4D24411yescharacteristic
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4D24411yescharacteristic
327C22⋊C4D24411yescharacteristic
328C42—1221no—
329C42—1221no—
330C42C22×D6111yescharacteristic
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23C2×D24411yescharacteristic
335C23C2×D24411yescharacteristic
336Q8—612no—
337Q8—612no—
338Q8—1221no—
339Q8—1221no—
340Q8—1221no—
341Q8—1221no—
342Q8—2442no—
343D4—41no—
344D4—1221no—
345D4—1221no—
346D4—1221no—
347D4—1221no—
348D4—1221no—
349D4—1221no—
350D4—4881no—
351D4—4881no—
352D4—4881no—
353D4—2442no—
354D4—2442no—
355D4—2442no—
356D4—2442no—
357D4—2442no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4C2×D24411yescharacteristic
372C2×C4C2×D24411yescharacteristic
373C2×C4C2×D24411yescharacteristic
374C2×C4C2×D24411yescharacteristic
375C2×C4C23×D6111yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8D4×D6112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22C22×D24411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—1222no—
401C4—1222no—
402C4—2441no—
403C4—2441no—
404C4—2441no—
405C4C2×D4×D6111yescharacteristic
406C4#1451982311yescharacteristic
407C2—41no—
408C2—41no—
409C2—4881no—
410C2—4881no—
411C2—4881no—
412C2D4×D24411yescharacteristic
413C2#1684056211yescharacteristic
414C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3271
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
2. C2×#14519799C2semidirect
3. #16840433C2semidirect
4. #16840421C2semidirect
5. #16840151C2semidirect
6. #16840015C2semidirect
7. #16839991C2semidirect
8. #16839985C2semidirect
9. #16839963C2semidirect
10. #16839926C2semidirect
11. #16839909C2semidirect
12. #16839909C2semidirect
13. #16839903C2semidirect
14. #16839870C2semidirect
15. C61×#435C2semidirect
115. Dic244D4semidirect
222. #435D61semidirect
223. C61#3271semidirect