Finite Group Databasebeta

← #21455289

Subgroups — #21455289

Order 7808.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519806C211yesmaximal, characteristic, complemented
3#16840311C211yesmaximal, characteristic
4C4×Q8×D61C211yesmaximal, characteristic, complemented
5#16839985C211yesmaximal, characteristic, complemented
6#16839984C211yesmaximal, characteristic, complemented
7#16839981C211yesmaximal, characteristic, complemented
8#16839971C211yesmaximal, characteristic, complemented
9#16839970C211yesmaximal, characteristic, complemented
10#16839961C211yesmaximal, characteristic, complemented
11#16839960C211yesmaximal, characteristic, complemented
12#16839784C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C61×#464C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19#14519809—24no—
20#14519806—24no—
21C2×Dic244C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758201C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×#11758189C2211yescharacteristic
29#14519775C2211yescharacteristic
30#14519773C2211yescharacteristic
31#14519765C2211yescharacteristic
32#14519750—21no—
33#14519750—21no—
34Q8×Dic61C2211yescharacteristic
35C4×Dic122—21no—
36C4×Dic122C2211yescharacteristic
37#14519742—21no—
38#14519742C2211yescharacteristic
39#14519737—21no—
40#14519737—21no—
41C4⋊C4×D61—21no—
42C4⋊C4×D61C2211yescharacteristic
43C42×D61—21no—
44C42×D61C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic
46#14519706C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519700C2211yescharacteristic
51#14519699C2211yescharacteristic
52#14519698C2211yescharacteristic
53#14519697C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68#11758226—22no—
69#11758226—22no—
70Q8×D61—22no—
71Q8×D61D414yescomplemented
72#11758224—22no—
73#11758224—22no—
74C2×D244—21no—
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61D411yescharacteristic
80C2×C4×D61D411yescharacteristic
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83C2×Dic122C2311yescharacteristic
84C2×Dic122C2311yescharacteristic
85Q16×C61—22no—
86SD16×C61—22no—
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C42×C61—21no—
94C42×C61C2311yescharacteristic
95#11758202—22no—
96#11758202—22no—
97#11758201—22no—
98#11758200—22no—
99#11758198—21no—
100#11758198—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61D411yescharacteristic
112C4×Dic61D411yescharacteristic
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116Dic244—22no—
117#11758190—22no—
118#11758189—22no—
119#11758189—22no—
120C23×C61—21no—
121C22×D61—21no—
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126Q8×C61C2×D412yes—
127D4×C61—21no—
128D4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—42no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—42no—
148C4×D61—24no—
149C4×D61—22no—
150C4×D61—41no—
151C4×D61—42no—
152C4×D61—42no—
153C4×D61C2×D412yes—
154C4×D61#4112yes—
155Dic122—21no—
156Dic122—24no—
157Dic122—21no—
158Dic122—21no—
159Dic122C2×D412yes—
160C8×C61—21no—
161C8×C61—21no—
162#92418—21no—
163#92418—21no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C22×D411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61#12112yes—
174C4×C61—22no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61C22×D411yescharacteristic
180C4×C61C2×#4111yescharacteristic
181Dic61—22no—
182Dic61—21no—
183Dic61—41no—
184Dic61—41no—
185Dic61#12112yes—
186Dic61#13712yescomplemented
187#3037—611nomaximal, Sylow
188C2×C61—81no—
189C2×C61C2×#12111yescharacteristic
190C2×C61C2×#13711yescharacteristic
191C2×C61#57511yescharacteristic
192D61—22no—
193D61—81no—
194C2×#137—611no—
195C2×#137—611no—
196#532—611no—
197C2×C4×Q8—611no—
198#464—611no—
199#464—611no—
200#464—611no—
201#464D6111yescharacteristic, complemented
202#462—611no—
203#462—611no—
204#460—611no—
205#460—611no—
206#423—611no—
207#417—611no—
208#417—611no—
209C61#303711yescharacteristic, complemented, Sylow
210C2×#41—611no—
211C2×#41—611no—
212C22×Q8—611no—
213#137—1224no—
214#137—1224no—
215C2×Q16—611no—
216C2×Q16—611no—
217C2×Q16—611no—
218C2×Q16C2×D6111yescharacteristic
219C2×SD16—611no—
220C2×SD16—611no—
221C2×SD16—611no—
222C2×SD16C2×D6111yescharacteristic
223C2×M16—611no—
224C2×M16—611no—
225C4⋊Q8—611no—
226#127—611no—
227#124—611no—
228#124C2×D6111yescharacteristic
229#121—1221no—
230#121—1221no—
231C4×Q8—611no—
232C4×Q8—611no—
233C4×Q8—611no—
234C4×Q8—1221no—
235C4×Q8—1221no—
236C4×Q8C2×D6111yescharacteristic
237C4×D4—1221no—
238C4×D4—1221no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C2×C42—611no—
242C2×C42—1221no—
243C4⋊C8—611no—
244C4⋊C8—611no—
245C4⋊C8—611no—
246C4⋊C8C2×D6111yescharacteristic
247#103—611no—
248#103—611no—
249#103—611no—
250#103C2×D6111yescharacteristic
251#102—611no—
252#102—611no—
253#102—611no—
254#102C2×D6111yescharacteristic
255#41—1222no—
256#41—1222no—
257#41—1222no—
258#41—1222no—
259C2×Q8—614no—
260C2×Q8—611no—
261C2×Q8—611no—
262C2×Q8—1221no—
263C2×Q8—1222no—
264C2×Q8C22×D6111yescharacteristic
265C2×Q8C22×D6111yescharacteristic
266C2×D4—611no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4C22×D6111yescharacteristic
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279Q16—22no—
280Q16—1222no—
281Q16—1222no—
282Q16—1222no—
283SD16—22no—
284SD16—1222no—
285SD16—1222no—
286SD16—1222no—
287M16—1222no—
288M16—1222no—
289C2×C8—611no—
290C2×C8—611no—
291C2×C8C22×D6111yescharacteristic
292C2×C8C22×D6111yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—611no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4C22×D6111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C42—21no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—1221no—
311C42—1221no—
312C42—1221no—
313C42C22×D6111yescharacteristic
314C23—21no—
315C23—611no—
316C23—1221no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—612no—
321Q8—1224no—
322Q8—1221no—
323Q8—1221no—
324Q8—1221no—
325Q8D4×D6112yes—
326D4—21no—
327D4—21no—
328D4—1221no—
329D4—1221no—
330D4—2442no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—611no—
342C2×C4—1222no—
343C2×C4—1224no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—2441no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4D4×D6111yescharacteristic
352C2×C4D4×D6111yescharacteristic
353C2×C4C23×D6111yescharacteristic
354C8—21no—
355C8—21no—
356C8—1221no—
357C8—1221no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—612no—
362C22—1221no—
363C22—1221no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22C2×D4×D6111yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—612no—
374C4—612no—
375C4—1222no—
376C4—1221no—
377C4—2441no—
378C4—2441no—
379C4C2×D4×D6111yescharacteristic
380C4#41×D6111yescharacteristic
381C2—81no—
382C2—1222no—
383C2—4881no—
384C2#121×D6111yescharacteristic
385C2#137×D6111yescharacteristic
386C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61#3037
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519806C2semidirect
4. C4×Q8×D61C2semidirect
5. #16839985C2semidirect
6. #16839984C2semidirect
7. #16839981C2semidirect
8. #16839971C2semidirect
9. #16839970C2semidirect
10. #16839961C2semidirect
11. #16839960C2semidirect
12. #16839784C2semidirect
13. #16839762C2semidirect
14. #16839760C2semidirect
15. C61×#464C2semidirect
71. Q8×D61D4semidirect
186. Dic61#137semidirect
201. #464D61semidirect
209. C61#3037semidirect