Finite Group Databasebeta

← #21457371

Subgroups — #21457371

Order 7808.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519799C211yesmaximal, characteristic, complemented
3#16840422C211yesmaximal, characteristic, complemented
4#16840414C211yesmaximal, characteristic, complemented
5#16840155C211yesmaximal, characteristic, complemented
6#16840009C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839971C211yesmaximal, characteristic, complemented
9#16839922C211yesmaximal, characteristic, complemented
10#16839922C211yesmaximal, characteristic, complemented
11#16839919C211yesmaximal, characteristic, complemented
12#16839910C211yesmaximal, characteristic, complemented
13#16839861C211yesmaximal, characteristic, complemented
14#16839833C211yesmaximal, characteristic, complemented
15C61×#467C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758222C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519809—24no—
21#14519799—24no—
22C2×Dic244C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758202C2211yescharacteristic
25C2×#11758190C2211yescharacteristic
26C2×#11758190C2211yescharacteristic
27C2×#11758201C2211yescharacteristic
28C2×#11758201C2211yescharacteristic
29C2×D488C2211yescharacteristic
30C2×#11758189C2211yescharacteristic
31#14519775C2211yescharacteristic
32#14519766C2211yescharacteristic
33#14519763—21no—
34#14519762—21no—
35#14519759—21no—
36#14519757C2211yescharacteristic
37#14519755—21no—
38#14519752C2211yescharacteristic
39#14519750—21no—
40#14519750—21no—
41#14519742C2211yescharacteristic
42#14519739—21no—
43#14519739C2211yescharacteristic
44C4×C22⋊D61C2211yescharacteristic
45C4⋊C4×D61—21no—
46#14519706C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519697C2211yescharacteristic
51C22⋊#92418C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519687C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic
56C22⋊Q8×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#107×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#103×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61D411yescharacteristic
67#11758226—22no—
68#11758226—41no—
69Q8×D61—22no—
70Q8×D61—41no—
71#11758222—22no—
72#11758222—22no—
73#11758222—41no—
74#11758222—41no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61C2311yescharacteristic
85C2×Dic122—21no—
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88Q16×C61—22no—
89C2×C8×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61C2311yescharacteristic
95C4⋊C4×C61C2311yescharacteristic
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C22⋊Dic61D411yescharacteristic
99#11758202—22no—
100#11758202—41no—
101#11758201—22no—
102#11758201—41no—
103#11758198—21no—
104#11758198—21no—
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
122#11758189—22no—
123C23×C61C2×D411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2411yescharacteristic
139C22⋊D61—41no—
140C22⋊D61—42no—
141C22⋊D61—42no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—21no—
148D244—21no—
149D244—21no—
150D244—42no—
151D244—42no—
152D244C2×D412yes—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—42no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—42no—
160Dic122—21no—
161Dic122—21no—
162Dic122—21no—
163Dic122—42no—
164Dic122C2×D412yes—
165C8×C61—21no—
166C8×C61C2×D412yes—
167#92418—21no—
168#92418—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61C22×D411yescharacteristic
173C2×D61—21no—
174C2×D61—22no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C4×C61—21no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61C22×D411yescharacteristic
188C4×C61H(5,𝔽2)11yescharacteristic
189Dic61—22no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—41no—
194#3269—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61D4211yescharacteristic
197C2×C61#57511yescharacteristic
198C2×C61#57811yescharacteristic
199D61—41no—
200D61—42no—
201D61—81no—
202C2×#137—611no—
203C2×#135—611no—
204#548—611no—
205#547—611no—
206#497—611no—
207#468—611no—
208#467D6111yescharacteristic, complemented
209#463—611no—
210#462—611no—
211#452—611no—
212#452—611no—
213#451—611no—
214#449—611no—
215#440—611no—
216#435—611no—
217C61#326911yescharacteristic, complemented, Sylow
218C2×#41—611no—
219C2×#41—611no—
220C2×#41—611no—
221C22×Q8—611no—
222#137—1224no—
223#135—1224no—
224C2×Q16—611no—
225C2×Q16—611no—
226C2×Q16—611no—
227C2×Q16C2×D6111yescharacteristic
228C2×SD16—611no—
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×D8—611no—
233C2×M16—611no—
234C22×C8C2×D6111yescharacteristic
235C4⋊Q8—611no—
236#124—611no—
237#124—1221no—
238#123—1221no—
239#123—1221no—
240C22⋊Q8—611no—
241C22⋊Q8—1221no—
242C22⋊Q8C2×D6111yescharacteristic
243C22⋊Q8C2×D6111yescharacteristic
244#121—611no—
245#121—1221no—
246#121—1221no—
247C4×Q8—611no—
248C4×D4—611no—
249C4×D4—611no—
250C4×D4—1221no—
251C2×C4⋊C4—1221no—
252#107C2×D6111yescharacteristic
253C4⋊C8—611no—
254#103—611no—
255#103—611no—
256#103C2×D6111yescharacteristic
257#103C2×D6111yescharacteristic
258#102—611no—
259#102—611no—
260C22⋊C8—611no—
261C22⋊C8—611no—
262#97—611no—
263#41—1222no—
264#41—1222no—
265#41—1222no—
266#41—2441no—
267#41—2441no—
268#41—2441no—
269C2×Q8—611no—
270C2×Q8—611no—
271C2×Q8—1221no—
272C2×Q8—1222no—
273C2×Q8—2441no—
274C2×Q8C22×D6111yescharacteristic
275C2×Q8C22×D6111yescharacteristic
276C2×D4—611no—
277C2×D4—611no—
278C2×D4—611no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C22×C4—611no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4C22×D6111yescharacteristic
290Q16—22no—
291Q16—1222no—
292Q16—1222no—
293Q16—2441no—
294SD16—614no—
295SD16—1222no—
296SD16—1222no—
297SD16—2441no—
298D8—1222no—
299M16—1222no—
300C2×C8—22no—
301C2×C8—611no—
302C2×C8—611no—
303C2×C8C22×D6111yescharacteristic
304C2×C8C22×D6111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—611no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4C22×D6111yescharacteristic
313C4⋊C4C22×D6111yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—611no—
317C22⋊C4—611no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C42—611no—
324C42—1221no—
325C23—611no—
326C23—1221no—
327C23—1221no—
328C23D4×D6111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—612no—
334Q8—1221no—
335Q8—1221no—
336Q8—1221no—
337Q8—2442no—
338D4—612no—
339D4—1221no—
340D4—1221no—
341D4—1221no—
342D4—2442no—
343D4—2442no—
344D4—2441no—
345D4—2442no—
346D4—2442no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4—2442no—
365C2×C4D4×D6111yescharacteristic
366C2×C4C23×D6111yescharacteristic
367C8—21no—
368C8—1221no—
369C8—1221no—
370C8D4×D6112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1222no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—1221no—
390C4—1221no—
391C4—1221no—
392C4—1222no—
393C4—2441no—
394C4C2×D4×D6111yescharacteristic
395C4#1451982311yescharacteristic
396C2—41no—
397C2—4881no—
398C2—2441no—
399C2—2442no—
400C2#1684039611yescharacteristic
401C2#1684055911yescharacteristic
402C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#467C2
socleC22×C61C22×D4
hypercenter#467D61
hypocenterC61#3269
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519799C2semidirect
3. #16840422C2semidirect
4. #16840414C2semidirect
5. #16840155C2semidirect
6. #16840009C2semidirect
7. #16839980C2semidirect
8. #16839971C2semidirect
9. #16839922C2semidirect
10. #16839922C2semidirect
11. #16839919C2semidirect
12. #16839910C2semidirect
13. #16839861C2semidirect
14. #16839833C2semidirect
15. C61×#467C2semidirect
121. #11758190D4semidirect
208. #467D61semidirect
217. C61#3269semidirect