Finite Group Databasebeta

← #21449413

Subgroups — #21449413

Order 7808.

564 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519776C211yesmaximal, characteristic, complemented
2C2×#14519755C211yesmaximal, characteristic
3C2×#14519755C211yesmaximal, characteristic
4C2×#14519742C211yesmaximal, characteristic, complemented
5#16839696C211yesmaximal, characteristic, complemented
6#16839686C211yesmaximal, characteristic
7#16839684C211yesmaximal, characteristic
8#16839666C211yesmaximal, characteristic, complemented
9#16839659C211yesmaximal, characteristic, complemented
10#16839658C211yesmaximal, characteristic, complemented
11#16839657C211yesmaximal, characteristic, complemented
12#16839654C211yesmaximal, characteristic
13#16839652C211yesmaximal, characteristic
14#16839609C211yesmaximal, characteristic
15C61×#398C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19#14519776—24no—
20#14519755—24no—
21#14519755—24no—
22#14519742—24no—
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
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
41C2×C4×Dic61C2211yescharacteristic
42C2×C4×Dic61C2211yescharacteristic
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—22no—
73C2×Dic122—22no—
74C2×Dic122—22no—
75C2×Dic122—22no—
76C2×Dic122—22no—
77C2×Dic122—22no—
78C2×Dic122D414yes—
79C4⋊C4×C61—22no—
80C4⋊C4×C61—22no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—22no—
83#11758198—22no—
84#11758198—22no—
85#11758198—22no—
86#11758198—22no—
87#11758198—22no—
88#11758198Q814yescomplemented
89C4⋊Dic61—22no—
90C4⋊Dic61—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196—22no—
94#11758196—22no—
95#11758196—22no—
96#11758196—22no—
97#11758196—22no—
98#11758196D414yes—
99C4×Dic61—22no—
100C4×Dic61—22no—
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×Dic61C2×D412yes—
147C2×Dic61C2×D412yes—
148C2×Dic61C2×D412yes—
149C2×Dic61C2×D412yes—
150C2×Dic61C2×Q812yes—
151C2×Dic61#4112yes—
152C2×Dic61#4112yes—
153C4×D61—44no—
154Dic122—28no—
155Dic122—44no—
156C22×C61C22×D411yescharacteristic
157C22×C61C22×D411yescharacteristic
158C22×C61C22×Q811yescharacteristic
159C22×C61C2×#4111yescharacteristic
160C22×C61C2×#4111yescharacteristic
161C22×C612−1+411yescharacteristic
162C22×C612−1+411yescharacteristic
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C4×C61—22no—
171C4×C61—22no—
172C4×C61—22no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—41no—
177Dic61—22no—
178Dic61—22no—
179Dic61—22no—
180Dic61—22no—
181Dic61—41no—
182Dic61—41no—
183Dic61#12114yes—
184#2429—611nomaximal, Sylow
185C2×C61C2×#12111yescharacteristic
186C2×C61#53311yescharacteristic
187C2×C61#54111yescharacteristic
188C2×C61#54711yescharacteristic
189C2×C61#54811yescharacteristic
190C2×C61D4×Q811yescharacteristic
191C2×C61D4×Q811yescharacteristic
192D61—42no—
193C2×C4⋊Q8—611no—
194C2×C22⋊Q8—611no—
195C2×C22⋊Q8—611no—
196C2×C4×Q8—611no—
197#398—611no—
198#398D6111yescharacteristic, complemented
199#396—611no—
200#396—611no—
201#391—611no—
202#389—611no—
203#389—611no—
204#389—611no—
205#388—611no—
206#388—611no—
207C4×C22⋊C4—611no—
208C61#242911yescharacteristic, complemented, Sylow
209C22×Q8—611no—
210C22×Q8—611no—
211C23×C4—611no—
212C4⋊Q8—1224no—
213C22⋊Q8—1224no—
214C22⋊Q8—1224no—
215C4×Q8—1224no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
227C2×C4⋊C4C2×D6111yescharacteristic
228C2×C4⋊C4C2×D6111yescharacteristic
229C2×C4⋊C4C2×D6111yescharacteristic
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—611no—
240#95—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95C2×D6111yescharacteristic
246#95C2×D6111yescharacteristic
247#95C2×D6111yescharacteristic
248C24—611no—
249C2×Q8—614no—
250C2×Q8—1222no—
251C2×Q8—1222no—
252C2×Q8—1222no—
253C2×Q8—1222no—
254C2×Q8—1222no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4C22×D6111yescharacteristic
266C22×C4C22×D6111yescharacteristic
267C22×C4C22×D6111yescharacteristic
268C22×C4C22×D6111yescharacteristic
269C22×C4C22×D6111yescharacteristic
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—614no—
277C4⋊C4—1222no—
278C4⋊C4—1222no—
279C4⋊C4—1222no—
280C4⋊C4—1222no—
281C4⋊C4—1222no—
282C4⋊C4—1222no—
283C4⋊C4—1222no—
284C4⋊C4—1222no—
285C4⋊C4—1222no—
286C22⋊C4—614no—
287C22⋊C4—1222no—
288C22⋊C4—1222no—
289C22⋊C4—1222no—
290C22⋊C4—1222no—
291C22⋊C4—1222no—
292C42—1222no—
293C42—1222no—
294C42—1222no—
295C42—1222no—
296C23—612no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23—1221no—
301C23—1221no—
302C23—1221no—
303C23C23×D6111yescharacteristic
304Q8—1228no—
305Q8—2444no—
306C2×C4—21no—
307C2×C4—21no—
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—612no—
325C2×C4—612no—
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—2444no—
346C2×C4D4×D6112yes—
347C2×C4D4×D6112yes—
348C2×C4Q8×D6112yes—
349C22—1222no—
350C22—1222no—
351C22—1222no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22C2×D4×D6111yescharacteristic
357C22C2×D4×D6111yescharacteristic
358C22C2×Q8×D6111yescharacteristic
359C22#41×D6111yescharacteristic
360C22#41×D6111yescharacteristic
361C22#1451982411yescharacteristic
362C22#1451982511yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—614no—
371C4—1222no—
372C4—1222no—
373C4—1222no—
374C4—1222no—
375C4—2441no—
376C4—2441no—
377C2—2442no—
378C2#121×D6111yescharacteristic
379C2#1684031811yescharacteristic
380C2#1684037111yescharacteristic
381C2#1684041011yescharacteristic
382C2#1684042211yescharacteristic
383C2#1684042511yescharacteristic
384C2#1684042711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2429
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
4. C2×#14519742C2semidirect
5. #16839696C2semidirect
8. #16839666C2semidirect
9. #16839659C2semidirect
10. #16839658C2semidirect
11. #16839657C2semidirect
15. C61×#398C2semidirect
88. #11758198Q8semidirect
198. #398D61semidirect
208. C61#2429semidirect