Finite Group Databasebeta

← #21452136

Subgroups — #21452136

Order 7808.

544 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×#14519776C211yesmaximal, characteristic, complemented
2C2×#14519776C211yesmaximal, characteristic, complemented
3C2×#14519757C211yesmaximal, characteristic
4C2×#14519755C211yesmaximal, characteristic
5#16839697C211yesmaximal, characteristic
6#16839696C211yesmaximal, characteristic, complemented
7#16839683C211yesmaximal, characteristic, complemented
8#16839682C211yesmaximal, characteristic, complemented
9#16839675C211yesmaximal, characteristic
10#16839654C211yesmaximal, characteristic
11#16839651C211yesmaximal, characteristic
12#16839645C211yesmaximal, characteristic, complemented
13#16839643C211yesmaximal, characteristic, complemented
14#16839633C211yesmaximal, characteristic
15C61×#398C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C22×Dic122C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519776—24no—
21#14519776—24no—
22#14519757—24no—
23#14519755—24no—
24C2×C4⋊Dic61C2211yescharacteristic
25C2×C4⋊Dic61C2211yescharacteristic
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C4⋊C4×C61C2211yescharacteristic
51C2×C4⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55C23×D61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—41no—
73C2×Dic122—22no—
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—22no—
77C2×Dic122—22no—
78C2×Dic122—22no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—22no—
84C4⋊C4×C61—22no—
85C4⋊C4×C61—22no—
86#11758198—22no—
87#11758198—22no—
88#11758198—22no—
89#11758198—22no—
90#11758198—41no—
91#11758198Q814yescomplemented
92C4⋊Dic61—22no—
93C4⋊Dic61—22no—
94C4⋊Dic61D414yes—
95#11758196—22no—
96#11758196—22no—
97#11758196—22no—
98#11758196—22no—
99#11758196—41no—
100#11758196D414yes—
101C4×Dic61—22no—
102C4×Dic61—22no—
103C23×C61C2411yescharacteristic
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61C2×Q812yes—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
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—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61C2×D412yes—
130C2×C4×C61C2×D412yes—
131C2×C4×C61C2×Q812yes—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61C2×D412yes—
149C2×Dic61C2×D412yes—
150C2×Dic61C2×D412yes—
151C2×Dic61C2×D412yes—
152C2×Dic61C2×Q812yes—
153C4×D61—44no—
154Dic122—44no—
155Dic122—44no—
156Dic122—44no—
157C22×C61C22×D411yescharacteristic
158C22×C61C22×D411yescharacteristic
159C22×C61C22×Q811yescharacteristic
160C22×C61H(5,𝔽2)11yescharacteristic
161C22×C612−1+411yescharacteristic
162C22×C612−1+411yescharacteristic
163C22×C612−1+411yescharacteristic
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C4×C61—22no—
172C4×C61—22no—
173C4×C61—22no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—41no—
178Dic61—22no—
179Dic61—22no—
180Dic61—22no—
181Dic61—22no—
182Dic61—22no—
183Dic61—41no—
184Dic61—41no—
185#2677—611nomaximal, Sylow
186C2×C61#53611yescharacteristic
187C2×C61#53611yescharacteristic
188C2×C61#54411yescharacteristic
189C2×C61D4211yescharacteristic
190C2×C61D4×Q811yescharacteristic
191C2×C61D4×Q811yescharacteristic
192C2×C61#56311yescharacteristic
193D61—42no—
194C2×C4⋊Q8—611no—
195C2×C4⋊Q8—611no—
196C2×C22⋊Q8—611no—
197C2×C22⋊Q8—611no—
198#399—611no—
199#398—611no—
200#398D6111yescharacteristic, complemented
201#395—611no—
202#395—611no—
203#393—611no—
204#388—611no—
205#388—611no—
206#387—611no—
207#387—611no—
208#385—611no—
209C61#267711yescharacteristic, complemented, Sylow
210C22×Q8—611no—
211C22×Q8—611no—
212C22×Q8—611no—
213C23×C4—611no—
214C4⋊Q8—1224no—
215C4⋊Q8—1224no—
216C22⋊Q8—1224no—
217C22⋊Q8—1224no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4C2×D6111yescharacteristic
228C2×C4⋊C4C2×D6111yescharacteristic
229C2×C4⋊C4C2×D6111yescharacteristic
230C2×C4⋊C4C2×D6111yescharacteristic
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—611no—
237C2×C42—611no—
238C2×C42—611no—
239#95—611no—
240#95—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95—611no—
246#95C2×D6111yescharacteristic
247#95C2×D6111yescharacteristic
248#95C2×D6111yescharacteristic
249C24—611no—
250C2×Q8—1222no—
251C2×Q8—1222no—
252C2×Q8—1222no—
253C2×Q8—1222no—
254C2×Q8—1222no—
255C2×Q8—1222no—
256C2×Q8—2441no—
257C2×Q8—2441no—
258C2×Q8—2441no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—1222no—
267C22×C4—1222no—
268C22×C4—2441no—
269C22×C4C22×D6111yescharacteristic
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273C22×C4C22×D6111yescharacteristic
274C22×C4C22×D6111yescharacteristic
275C22×C4C22×D6111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—614no—
281C4⋊C4—614no—
282C4⋊C4—1222no—
283C4⋊C4—1222no—
284C4⋊C4—1222no—
285C4⋊C4—1222no—
286C4⋊C4—1222no—
287C4⋊C4—1222no—
288C4⋊C4—2441no—
289C22⋊C4—614no—
290C22⋊C4—1222no—
291C22⋊C4—1222no—
292C22⋊C4—1222no—
293C22⋊C4—1222no—
294C22⋊C4—2441no—
295C42—1222no—
296C42—1222no—
297C23—612no—
298C23—1221no—
299C23—1221no—
300C23—1221no—
301C23—1221no—
302C23—1221no—
303C23—1221no—
304C23C23×D6111yescharacteristic
305Q8—2444no—
306Q8—2444no—
307Q8—2444no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—612no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—612no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—2444no—
348C2×C4D4×D6112yes—
349C2×C4D4×D6112yes—
350C2×C4Q8×D6112yes—
351C22—1222no—
352C22—1222no—
353C22—1222no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22C2×D4×D6111yescharacteristic
359C22C2×D4×D6111yescharacteristic
360C22C2×Q8×D6111yescharacteristic
361C22#1451982311yescharacteristic
362C22#1451982411yescharacteristic
363C22#1451982411yescharacteristic
364C22#1451982511yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—1222no—
373C4—1222no—
374C4—1222no—
375C4—1222no—
376C4—1222no—
377C4—2441no—
378C4—2441no—
379C2—2442no—
380C2#1684033411yescharacteristic
381C2#1684033511yescharacteristic
382C2#1684039211yescharacteristic
383C2#1684039611yescharacteristic
384C2#1684042511yescharacteristic
385C2#1684042711yescharacteristic
386C2#1684051611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2677
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
2. C2×#14519776C2semidirect
6. #16839696C2semidirect
7. #16839683C2semidirect
8. #16839682C2semidirect
12. #16839645C2semidirect
13. #16839643C2semidirect
15. C61×#398C2semidirect
91. #11758198Q8semidirect
200. #398D61semidirect
209. C61#2677semidirect