Finite Group Databasebeta

← #21450760

Subgroups — #21450760

Order 7808.

948 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519773C211yesmaximal, characteristic, complemented
2C2×#14519773C212yesmaximal, complemented
3C2×#14519750C212yesmaximal, complemented
4C2×#14519749C212yesmaximal, complemented
5C2×#14519737C211yesmaximal, characteristic, complemented
6#16839672C211yesmaximal, characteristic, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839670C211yesmaximal, characteristic, complemented
9#16839662C212yesmaximal, complemented
10#16839613C211yesmaximal, characteristic, complemented
11C61×#392C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C2212yes—
15C22×C22⋊D61C2212yes—
16C22×C22⋊D61C2212yes—
17C22×C22⋊D61C2212yes—
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519773—28no—
22#14519773—24no—
23#14519750—28no—
24#14519749—28no—
25#14519737—24no—
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2212yes—
28C2×C22⋊Dic61C2212yes—
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2212yes—
31C2×#11758198C2212yes—
32C2×C4×Dic61C2212yes—
33C2×C4×Dic61C2211yescharacteristic
34#14519684C2211yescharacteristic
35C22×D4×C61C2212yes—
36C22×D4×C61C2211yescharacteristic
37C2×C22⋊C4×C61C2211yescharacteristic
38C2×C22⋊C4×C61C2212yes—
39#95×C61C2211yescharacteristic
40C24×C61C2312yes—
41C24×C61C2311yescharacteristic
42C23×D61C2312yes—
43C23×D61C2311yescharacteristic
44C2×D4×C61—24no—
45C2×D4×C61—24no—
46C2×D4×C61—22no—
47C2×D4×C61—42no—
48C2×D4×C61—42no—
49C22×C4×C61C2311yescharacteristic
50C22×C4×C61C2311yescharacteristic
51C22×C4×C61C2312yes—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—24no—
54C2×C22⋊D61—22no—
55C2×C22⋊D61—24no—
56C2×C22⋊D61—24no—
57C2×C22⋊D61—24no—
58C2×C22⋊D61—24no—
59C2×C22⋊D61—24no—
60C2×C22⋊D61—24no—
61C2×C22⋊D61—24no—
62C2×C22⋊D61—22no—
63C2×C22⋊D61—24no—
64C2×C22⋊D61—42no—
65C2×C22⋊D61—42no—
66C2×C22⋊D61D414yescomplemented
67C22×Dic61—22no—
68C22×Dic61—24no—
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2312yes—
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C2×D244—24no—
74C2×D244—24no—
75C2×D244—22no—
76C2×D244—42no—
77C2×D244—42no—
78C2×C4×D61—22no—
79C2×C4×D61—24no—
80C22⋊C4×C61—22no—
81C22⋊C4×C61—24no—
82C22⋊Dic61—24no—
83#11758198—22no—
84#11758198—24no—
85#11758198—24no—
86#11758196—22no—
87#11758196D418yescomplemented
88C4×Dic61—24no—
89C4×Dic61D414yescomplemented
90C23×C61—21no—
91C23×C61—22no—
92C23×C61—21no—
93C23×C61—22no—
94C23×C61—22no—
95C23×C61—22no—
96C23×C61—22no—
97C23×C61—22no—
98C23×C61—22no—
99C23×C61—22no—
100C23×C61—22no—
101C23×C61C2×D412yes—
102C23×C61C2411yescharacteristic
103C22×D61—21no—
104C22×D61—22no—
105C22×D61—21no—
106C22×D61—22no—
107C22×D61—22no—
108C22×D61—22no—
109C22×D61—22no—
110C22×D61—22no—
111C22×D61—22no—
112C22×D61—22no—
113C22×D61—22no—
114C22×D61C2×D412yes—
115D4×C61—48no—
116D4×C61—44no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—21no—
121C2×C4×C61—22no—
122C2×C4×C61C2×D412yes—
123C2×C4×C61C2×D414yes—
124C22⋊D61—28no—
125C22⋊D61—48no—
126C22⋊D61—48no—
127C22⋊D61—48no—
128C22⋊D61—48no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—44no—
134C2×Dic61C2×D414yes—
135C2×Dic61C2×D412yes—
136C2×Dic61C2×D412yes—
137C2×Dic61C2×D412yes—
138C2×Dic61C2×D414yes—
139C2×Dic61#4112yes—
140D244—48no—
141D244—44no—
142C4×D61—44no—
143C22×C61—22no—
144C22×C61—24no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61—42no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—42no—
155C22×C61C22×D411yescharacteristic
156C22×C61C22×D411yescharacteristic
157C22×C61C22×D412yes—
158C22×C61C2×#4111yescharacteristic
159C22×C61H(5,𝔽2)12yes—
160C2×D61—22no—
161C2×D61—24no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—42no—
165C2×D61—42no—
166C2×D61—42no—
167C2×D61—42no—
168C2×D61—42no—
169C2×D61—42no—
170C2×D61—42no—
171C2×D61—42no—
172C4×C61—22no—
173C4×C61—24no—
174C4×C61—41no—
175Dic61—24no—
176Dic61—41no—
177Dic61#12114yescomplemented
178Dic61#12714yescomplemented
179#2541—611nomaximal, Sylow
180C2×C61—42no—
181C2×C61—82no—
182C2×C61C2×#12111yescharacteristic
183C2×C61C2×#12711yescharacteristic
184C2×C61#53511yescharacteristic
185C2×C61D4212yes—
186C2×C61#55012yes—
187D61—42no—
188D61—82no—
189C2×#127—611no—
190C2×#127—612no—
191C2×#121—612no—
192C2×#121—612no—
193C2×C4×D4—611no—
194#392—611no—
195#392—611no—
196#392—611no—
197#392D6111yescharacteristic, complemented
198#390—612no—
199C4×C4⋊C4—611no—
200C61#254111yescharacteristic, complemented, Sylow
201C22×D4—611no—
202C22×D4—612no—
203C22×D4—612no—
204C22×D4—612no—
205C22×D4—612no—
206C22×D4—612no—
207C22×D4—611no—
208C22×D4C2×D6112yes—
209C22×D4C2×D6111yescharacteristic
210C23×C4—611no—
211C23×C4—611no—
212#127—1224no—
213#127—1228no—
214#121—1228no—
215#121—1228no—
216C4×D4—1224no—
217C2×C4⋊C4—612no—
218C2×C4⋊C4—611no—
219C2×C22⋊C4—612no—
220C2×C22⋊C4—611no—
221C2×C22⋊C4—612no—
222C2×C22⋊C4—612no—
223C2×C22⋊C4C2×D6111yescharacteristic
224C2×C22⋊C4C2×D6112yes—
225C2×C42—611no—
226C2×C42—612no—
227#95—611no—
228#95C2×D6111yescharacteristic
229C24—611no—
230C24—612no—
231C24C22×D6112yes—
232C24C22×D6111yescharacteristic
233C2×D4—24no—
234C2×D4—24no—
235C2×D4—22no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—614no—
239C2×D4—1224no—
240C2×D4—1222no—
241C2×D4—1222no—
242C2×D4—1224no—
243C2×D4—1224no—
244C2×D4—1224no—
245C2×D4—1224no—
246C2×D4—1224no—
247C2×D4—1224no—
248C2×D4—1224no—
249C2×D4—1224no—
250C2×D4—1224no—
251C2×D4—1224no—
252C2×D4—1224no—
253C2×D4—1222no—
254C2×D4—2442no—
255C2×D4—2442no—
256C2×D4—2442no—
257C2×D4—2442no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—612no—
261C22×C4—611no—
262C22×C4—1222no—
263C22×C4—1224no—
264C22×C4—1222no—
265C22×C4—1224no—
266C22×C4C22×D6111yescharacteristic
267C22×C4C22×D6111yescharacteristic
268C22×C4C22×D6112yes—
269C4⋊C4—618no—
270C4⋊C4—1222no—
271C22⋊C4—22no—
272C22⋊C4—24no—
273C22⋊C4—1224no—
274C22⋊C4—1224no—
275C22⋊C4—1222no—
276C22⋊C4—1224no—
277C42—614no—
278C42—1224no—
279C23—21no—
280C23—22no—
281C23—21no—
282C23—22no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—612no—
291C23—1221no—
292C23—1222no—
293C23—1221no—
294C23—1222no—
295C23—1222no—
296C23—1222no—
297C23—1222no—
298C23—1222no—
299C23—1222no—
300C23—1222no—
301C23—1222no—
302C23D4×D6112yes—
303C23C23×D6111yescharacteristic
304D4—48no—
305D4—44no—
306D4—1228no—
307D4—2448no—
308D4—2444no—
309D4—2448no—
310D4—2448no—
311D4—2448no—
312D4—2448no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—612no—
319C2×C4—612no—
320C2×C4—612no—
321C2×C4—614no—
322C2×C4—612no—
323C2×C4—614no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—1221no—
328C2×C4—2444no—
329C2×C4—2444no—
330C2×C4D4×D6112yes—
331C2×C4D4×D6114yes—
332C22—22no—
333C22—24no—
334C22—41no—
335C22—41no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—42no—
344C22—1222no—
345C22—1224no—
346C22—2442no—
347C22—2442no—
348C22—2442no—
349C22—2442no—
350C22—2442no—
351C22—2442no—
352C22—2442no—
353C22—2441no—
354C22—2441no—
355C22—2442no—
356C22C2×D4×D6111yescharacteristic
357C22C2×D4×D6111yescharacteristic
358C22C2×D4×D6112yes—
359C22#41×D6111yescharacteristic
360C22#1451982212yes—
361C4—22no—
362C4—24no—
363C4—41no—
364C4—614no—
365C4—614no—
366C4—1224no—
367C4—2441no—
368C2—42no—
369C2—82no—
370C2—4882no—
371C2—2442no—
372C2#121×D6111yescharacteristic
373C2#127×D6111yescharacteristic
374C2#1684032711yescharacteristic
375C2#1684039412yes—
376C2#1684043012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2541
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519773C2semidirect
2. C2×#14519773C2semidirect
3. C2×#14519750C2semidirect
4. C2×#14519749C2semidirect
5. C2×#14519737C2semidirect
6. #16839672C2semidirect
7. #16839671C2semidirect
8. #16839670C2semidirect
9. #16839662C2semidirect
10. #16839613C2semidirect
11. C61×#392C2semidirect
66. C2×C22⋊D61D4semidirect
87. #11758196D4semidirect
89. C4×Dic61D4semidirect
177. Dic61#121semidirect
178. Dic61#127semidirect
197. #392D61semidirect
200. C61#2541semidirect