Finite Group Databasebeta

← #21457871

Subgroups — #21457871

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840451C211yesmaximal, characteristic
2Q8×C22⋊D61C211yesmaximal, characteristic
3#16840129C211yesmaximal, characteristic, complemented
4#16840103C211yesmaximal, characteristic, complemented
5#16840091C211yesmaximal, characteristic, complemented
6#16840067C211yesmaximal, characteristic, complemented
7#16840020C211yesmaximal, characteristic, complemented
8#16840002C211yesmaximal, characteristic, complemented
9#16839971C211yesmaximal, characteristic, complemented
10#16839919C211yesmaximal, characteristic, complemented
11#16839918C211yesmaximal, characteristic, complemented
12#16839866C211yesmaximal, characteristic, complemented
13#16839831C211yesmaximal, characteristic
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#419C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×Dic244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758202C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519775—21no—
22#14519775C2211yescharacteristic
23#14519770—21no—
24#14519769—21no—
25#14519768C2211yescharacteristic
26#14519759—21no—
27#14519757C2211yescharacteristic
28#14519756—21no—
29#14519756C2211yescharacteristic
30#14519756C2211yescharacteristic
31#14519753—21no—
32#14519753C2211yescharacteristic
33Q8×Dic61C2211yescharacteristic
34#14519742C2211yescharacteristic
35C4×C22⋊D61—21no—
36C4×C22⋊D61C2211yescharacteristic
37#14519734—21no—
38C4⋊C4×D61C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54#117×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61C2311yescharacteristic
66C2×C22⋊D61D411yescharacteristic
67Q8×D61—22no—
68Q8×D61—41no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C2311yescharacteristic
72C2×Dic122—21no—
73C2×Dic122C2311yescharacteristic
74C2×Dic122C2311yescharacteristic
75M16×C61—41no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C42×C61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61D411yescharacteristic
85#11758202—22no—
86#11758202—41no—
87#11758198—21no—
88#11758198—21no—
89#11758198D411yescharacteristic
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109Dic244—41no—
110C8×D61—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61C2×D411yescharacteristic
113Q8×C61—21no—
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—42no—
117Q8×C61#4112yes—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—22no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—42no—
138C4×D61—42no—
139Dic122—21no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—42no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61#13712yes—
155C4×C61—22no—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61C2×#4111yescharacteristic
161C4×C61H(5,𝔽2)11yescharacteristic
162Dic61—21no—
163Dic61—21no—
164Dic61—21no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169#3312—611nomaximal, Sylow
170C2×C61—41no—
171C2×C61#54611yescharacteristic
172C2×C61C2×#13711yescharacteristic
173C2×C61#57811yescharacteristic
174D61—22no—
175#552—611no—
176D4×Q8—611no—
177#491—611no—
178#485—611no—
179#483—611no—
180#479—611no—
181#470—611no—
182#467—611no—
183#462—611no—
184#451—611no—
185#451—611no—
186#441—611no—
187#435—611no—
188#419D6111yescharacteristic, complemented
189C2×#103—611no—
190C61#331211yescharacteristic, complemented, Sylow
191C22×Q8—611no—
192C22×Q8C2×D6111yescharacteristic
193C2×Q16—611no—
194C2×Q16—611no—
195C2×Q16—611no—
196C2×M16C2×D6111yescharacteristic
197C22×C8—611no—
198C4⋊Q8—611no—
199C4⋊Q8—1221no—
200#126—1221no—
201#125—611no—
202#125—1221no—
203#123—1221no—
204C22⋊Q8—611no—
205C22⋊Q8—611no—
206C22⋊Q8—611no—
207C22⋊Q8—611no—
208C22⋊Q8—1221no—
209C22⋊Q8—1221no—
210C4×Q8—611no—
211C4×Q8—611no—
212C4×D4—611no—
213C4×D4—1221no—
214#117—1221no—
215#117C2×D6111yescharacteristic
216C2×C4⋊C4—611no—
217#107—611no—
218#106—611no—
219#106—611no—
220C4⋊C8—611no—
221#103—611no—
222#103—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#103—611no—
227#103C2×D6111yescharacteristic
228#103C2×D6111yescharacteristic
229#103C2×D6111yescharacteristic
230#103C2×D6111yescharacteristic
231C22⋊C8—611no—
232C22⋊C8—611no—
233#97—611no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—611no—
238C2×Q8—611no—
239C2×Q8—1221no—
240C2×Q8—1222no—
241C2×Q8—2441no—
242C2×Q8C22×D6111yescharacteristic
243C2×Q8C22×D6111yescharacteristic
244C2×D4—611no—
245C22×C4—21no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4C22×D6111yescharacteristic
250Q16—1222no—
251Q16—2441no—
252Q16—2441no—
253M16—41no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—2441no—
257C2×C8C22×D6111yescharacteristic
258C2×C8C22×D6111yescharacteristic
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4C22×D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—611no—
277C22⋊C4—611no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C42—21no—
283C42—611no—
284C42—1221no—
285C42—1221no—
286C23—611no—
287C23D4×D6111yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8—1221no—
293Q8—1221no—
294Q8—1221no—
295Q8—1221no—
296Q8—2442no—
297Q8#1175822212yes—
298D4—1222no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—2442no—
316C2×C4—2442no—
317C2×C4D4×D6111yescharacteristic
318C2×C4C23×D6111yescharacteristic
319C8—21no—
320C8—21no—
321C8—1221no—
322C8—1221no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—612no—
327C22—1221no—
328C22—1221no—
329C22C2×D4×D6111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—1221no—
336C4—1221no—
337C4—1221no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C4—2441no—
342C4C2×#1175822211yescharacteristic
343C4#1451982211yescharacteristic
344C2—41no—
345C2—1222no—
346C2#1684040211yescharacteristic
347C2#137×D6111yescharacteristic
348C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#419C2
socleC22×C61C22×D4
hypercenter#419D61
hypocenterC61#3312
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #16840129C2semidirect
4. #16840103C2semidirect
5. #16840091C2semidirect
6. #16840067C2semidirect
7. #16840020C2semidirect
8. #16840002C2semidirect
9. #16839971C2semidirect
10. #16839919C2semidirect
11. #16839918C2semidirect
12. #16839866C2semidirect
14. #103×D61C2semidirect
15. C61×#419C2semidirect
188. #419D61semidirect
190. C61#3312semidirect