Finite Group Databasebeta

← #21457406

Subgroups — #21457406

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×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519800C211yesmaximal, characteristic, complemented
3#16840434C211yesmaximal, characteristic, complemented
4#16840424C211yesmaximal, characteristic, complemented
5#16840151C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16839992C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839962C211yesmaximal, characteristic, complemented
10#16839927C211yesmaximal, characteristic, complemented
11#16839910C211yesmaximal, characteristic, complemented
12#16839910C211yesmaximal, characteristic, complemented
13#16839902C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#441C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic
18C2×#11758226C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519809—24no—
21#14519800—24no—
22C2×#11758202C2211yescharacteristic
23C2×#11758190C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758201C2211yescharacteristic
26C2×#11758201C2211yescharacteristic
27C2×#11758201C2211yescharacteristic
28C2×D488C2211yescharacteristic
29C2×D488C2211yescharacteristic
30C2×#11758189C2211yescharacteristic
31C2×C8×D61C2211yescharacteristic
32#14519774—21no—
33#14519774C2211yescharacteristic
34#14519765—21no—
35#14519765C2211yescharacteristic
36#14519757—21no—
37#14519757C2211yescharacteristic
38#14519752—21no—
39#14519752—21no—
40#14519752—21no—
41#14519752C2211yescharacteristic
42#14519752C2211yescharacteristic
43#14519752C2211yescharacteristic
44C4×D244—21no—
45C4×D244—21no—
46C4×D244C2211yescharacteristic
47C4⋊#92418C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519697C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519689C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic
56C4×Q8×C61C2211yescharacteristic
57#106×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#97×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63#11758226—22no—
64#11758226—22no—
65#11758226—22no—
66#11758226—41no—
67#11758226—41no—
68#11758226—41no—
69Q8×D61—22no—
70Q8×D61—41no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244D411yescharacteristic
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×D244C2311yescharacteristic
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61C2311yescharacteristic
88C2×C4×D61C2311yescharacteristic
89C2×Dic122—21no—
90C2×Dic122C2311yescharacteristic
91Q16×C61D414yescomplemented
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61C2311yescharacteristic
97C4⋊C4×C61C2311yescharacteristic
98C42×C61—21no—
99C42×C61—21no—
100C42×C61C2311yescharacteristic
101#11758202—22no—
102#11758201—22no—
103#11758201—22no—
104#11758201—22no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198D411yescharacteristic
112#11758198D411yescharacteristic
113C4⋊Dic61—21no—
114C4⋊Dic61D411yescharacteristic
115C2×#92418C2311yescharacteristic
116C2×#92418C2311yescharacteristic
117D488—22no—
118D488—41no—
119#11758190—22no—
120#11758190—41no—
121#11758189—22no—
122C8×D61—22no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61C2×D411yescharacteristic
127C22×D61C2×D411yescharacteristic
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61C2×D412yes—
131Q8×C61C2×D412yes—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2411yescharacteristic
139C2×Dic61—21no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142D244—21no—
143D244—21no—
144D244—21no—
145D244—21no—
146D244—21no—
147D244—21no—
148D244—41no—
149D244—42no—
150D244—42no—
151D244—42no—
152D244—42no—
153D244—42no—
154D244—81no—
155D244—81no—
156D244—81no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—42no—
162C4×D61—42no—
163C4×D61—42no—
164C4×D61—42no—
165Dic122—21no—
166Dic122—21no—
167Dic122—42no—
168C8×C61—21no—
169C8×C61C2×D412yes—
170#92418—21no—
171#92418—21no—
172C22×C61C22×D411yescharacteristic
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
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—22no—
189C4×C61—22no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61C22×D411yescharacteristic
195C4×C61H(5,𝔽2)11yescharacteristic
196Dic61—21no—
197Dic61—21no—
198Dic61—41no—
199#3271—611nomaximal, Sylow
200C2×C61D4211yescharacteristic
201C2×C61#57511yescharacteristic
202C2×C61#57711yescharacteristic
203D61—41no—
204D61—41no—
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#441D6111yescharacteristic, complemented
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×Q16C2×D6111yescharacteristic
232C2×SD16—611no—
233C2×SD16—611no—
234C2×SD16—611no—
235C2×SD16—611no—
236C2×SD16—611no—
237C2×D8—611no—
238C2×D8—611no—
239C2×M16—611no—
240C22×C8—611no—
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×Q8C2×D6111yescharacteristic
254C4×Q8C2×D6111yescharacteristic
255C4×D4—611no—
256C4×D4—1221no—
257C4×D4—1221no—
258#106C2×D6111yescharacteristic
259C4⋊C8—611no—
260#103—611no—
261#103C2×D6111yescharacteristic
262#103C2×D6111yescharacteristic
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—1221no—
277C2×Q8—1222no—
278C2×Q8—2441no—
279C2×Q8C22×D6111yescharacteristic
280C2×Q8C22×D6111yescharacteristic
281C2×D4—611no—
282C2×D4—611no—
283C2×D4—611no—
284C2×D4—611no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—1221no—
292C2×D4—1221no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299Q16—1222no—
300Q16D24414yescomplemented
301SD16—1222no—
302SD16—1222no—
303SD16—1222no—
304SD16—1222no—
305SD16—2441no—
306D8—1222no—
307D8—2441no—
308M16—1222no—
309C2×C8—611no—
310C2×C8—611no—
311C2×C8—1222no—
312C2×C8C22×D6111yescharacteristic
313C2×C8C22×D6111yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—611no—
317C4⋊C4—1221no—
318C4⋊C4C22×D6111yescharacteristic
319C4⋊C4C22×D6111yescharacteristic
320C22⋊C4—611no—
321C22⋊C4—611no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C42—21no—
329C42—21no—
330C42C22×D6111yescharacteristic
331C23—611no—
332C23—611no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336Q8—21no—
337Q8—21no—
338Q8—1221no—
339Q8—1221no—
340Q8—2442no—
341Q8C2×D24412yes—
342Q8C2×D24412yes—
343D4—1221no—
344D4—1221no—
345D4—1221no—
346D4—1221no—
347D4—1221no—
348D4—1221no—
349D4—4881no—
350D4—4881no—
351D4—4881no—
352D4—2441no—
353D4—2442no—
354D4—2442no—
355D4—2442no—
356D4—2442no—
357D4—2442no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—611no—
363C2×C4—611no—
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—
379C8C2×D24412yes—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—1221no—
385C22—1221no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22C2×D4×D6111yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—1221no—
403C4—1221no—
404C4—2441no—
405C4C22×D24411yescharacteristic
406C4#1451982311yescharacteristic
407C2—4881no—
408C2—4881no—
409C2—4881no—
410C2—2441no—
411C2—2441no—
412C2D4×D24411yescharacteristic
413C2#1684056111yescharacteristic
414C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#441C2
socleC22×C61C22×D4
hypercenter#441D61
hypocenterC61#3271
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519800C2semidirect
3. #16840434C2semidirect
4. #16840424C2semidirect
5. #16840151C2semidirect
6. #16840016C2semidirect
7. #16839992C2semidirect
8. #16839984C2semidirect
9. #16839962C2semidirect
10. #16839927C2semidirect
11. #16839910C2semidirect
12. #16839910C2semidirect
13. #16839902C2semidirect
14. #16839835C2semidirect
15. C61×#441C2semidirect
91. Q16×C61D4semidirect
221. #441D61semidirect
223. C61#3271semidirect
300. Q16D244semidirect