Finite Group Databasebeta

← #21446269

Subgroups — #21446269

Order 7808.

598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14519745C211yesmaximal, characteristic
2C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
3C2×#14519692C211yesmaximal, characteristic, complemented
4#16839617C211yesmaximal, characteristic, complemented
5#16839528C211yesmaximal, characteristic, complemented
6#16839528C211yesmaximal, characteristic, complemented
7C2×#99×C61C211yesmaximal, characteristic, complemented
8C24×D61C2211yescharacteristic
9C22×C22⋊D61C412yescomplemented
10C22×C4×D61—21no—
11#14519745—21no—
12#14519745—22no—
13#14519745—21no—
14C2×C22⋊Dic61C2211yescharacteristic
15C2×C22⋊Dic61C2211yescharacteristic
16C2×C22⋊Dic61C2211yescharacteristic
17C2×#11758198—21no—
18C2×#11758198—22no—
19C2×#11758198C412yescomplemented
20C22⋊C4×D61—22no—
21C22⋊C4×D61—22no—
22#14519692—22no—
23C22×D4×C61C2211yescharacteristic
24C2×C22⋊C4×C61C2211yescharacteristic
25C2×C22⋊C4×C61C2211yescharacteristic
26#99×C61—22no—
27C24×C61C2×C411yescharacteristic, complemented
28C24×C61C2311yescharacteristic
29C23×D61—21no—
30C23×D61—21no—
31C23×D61—21no—
32C23×D61—21no—
33C23×D61—44no—
34C23×D61C2×C412yes—
35C23×D61D411yescharacteristic
36C23×D61D412yes—
37C23×D61D411yescharacteristic
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61—21no—
41C2×D4×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C2×C411yescharacteristic, complemented
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—44no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61C2×C412yescomplemented
53C2×C4×D61—24no—
54C2×C4×D61—44no—
55C22⋊C4×C61—21no—
56C22⋊C4×C61—21no—
57C22⋊C4×C61—21no—
58C22⋊C4×C61D412yescomplemented
59C22⋊Dic61—21no—
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62C22⋊Dic61—21no—
63C22⋊Dic61—21no—
64C22⋊Dic61D412yescomplemented
65#11758198—24no—
66#11758198—22no—
67#11758198—22no—
68#11758198—44no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—42no—
73C23×C61—42no—
74C23×C61C22×C411yescharacteristic
75C23×C61C2×D411yescharacteristic
76C23×C61C2×D411yescharacteristic
77C23×C61C2×D411yescharacteristic
78C23×C61C2×D411yescharacteristic
79C23×C61#4111yescharacteristic
80C23×C61#4111yescharacteristic
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—24no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—21no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—21no—
90C22×D61—24no—
91C22×D61—24no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—44no—
96C22×D61—44no—
97C22×D61—44no—
98C22×D61—44no—
99C22×D61C22⋊C412yes—
100C22×D61C22⋊C412yes—
101D4×C61—41no—
102D4×C61—41no—
103D4×C61—41no—
104D4×C61—41no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61—41no—
112C22⋊D61—44no—
113C22⋊D61—44no—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C4×D61—48no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—42no—
130C22×C61—81no—
131C22×C61—81no—
132C22×C61C2×C22⋊C411yescharacteristic
133C22×C61C4×D411yescharacteristic
134C22×C61C4×D411yescharacteristic
135C22×C61#12011yescharacteristic
136C22×C61#12111yescharacteristic
137C22×C61#12111yescharacteristic
138C22×C61#12311yescharacteristic
139C2×D61—24no—
140C2×D61—24no—
141C2×D61—22no—
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—22no—
145C2×D61—22no—
146C2×D61—44no—
147C2×D61—44no—
148C2×D61—44no—
149C2×D61—44no—
150C2×D61—42no—
151C2×D61—42no—
152C2×D61#9914yescomplemented
153C4×C61—42no—
154C4×C61—41no—
155C4×C61—81no—
156Dic61—42no—
157Dic61—42no—
158Dic61—81no—
159#1898—611nomaximal, Sylow
160C2×C61—21no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61—21no—
166C2×C61—81no—
167C2×C61#38611yescharacteristic
168C2×C61C2×#9912yes—
169D61—24no—
170D61—42no—
171C2×#120—611no—
172C22×C22⋊C4—611no—
173C2×#99—611no—
174C2×#99D6111yescharacteristic, complemented
175#379—611no—
176#342—611no—
177#342—611no—
178C61#189811yescharacteristic, complemented, Sylow
179C25—611no—
180C22×D4—612no—
181C22×D4C2×D6111yescharacteristic
182C23×C4—1221no—
183#120—1221no—
184#120—1222no—
185#120—1221no—
186C2×C22⋊C4—611no—
187C2×C22⋊C4—611no—
188C2×C22⋊C4—612no—
189C2×C22⋊C4—611no—
190C2×C22⋊C4—1222no—
191C2×C22⋊C4—1221no—
192C2×C22⋊C4—1222no—
193C2×C22⋊C4—1222no—
194C2×C22⋊C4C2×D6111yescharacteristic
195C2×C22⋊C4C2×D6111yescharacteristic
196#99—22no—
197#99—1222no—
198C24—611no—
199C24—612no—
200C24—612no—
201C24—611no—
202C24—1221no—
203C24—1221no—
204C24—1221no—
205C24—1221no—
206C24—2444no—
207C24C4×D6111yescharacteristic, complemented
208C24C22×D6111yescharacteristic
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—1222no—
216C2×D4—1222no—
217C2×D4—2444no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—612no—
221C22×C4—1224no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—2444no—
225C22×C4C4×D6111yescharacteristic, complemented
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—612no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C22⋊C4—1224no—
233C22⋊C4—1221no—
234C22⋊C4—1221no—
235C22⋊C4—1221no—
236C22⋊C4—1221no—
237C22⋊C4—1221no—
238C22⋊C4—2444no—
239C22⋊C4C22⋊D6112yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—42no—
244C23—42no—
245C23—612no—
246C23—612no—
247C23—1224no—
248C23—1224no—
249C23—1224no—
250C23—1221no—
251C23—1221no—
252C23—1222no—
253C23—1222no—
254C23—1221no—
255C23—1222no—
256C23—1222no—
257C23—1221no—
258C23—2442no—
259C23—2442no—
260C23—2442no—
261C23—2444no—
262C23—2444no—
263C23—2444no—
264C23—2444no—
265C23C2×C4×D6111yescharacteristic
266C23#1175822211yescharacteristic
267C23D4×D6111yescharacteristic
268C23D4×D6111yescharacteristic
269C23D4×D6111yescharacteristic
270C23#1175822411yescharacteristic
271C23C2×C22⋊D6111yescharacteristic
272D4—41no—
273D4—41no—
274D4—41no—
275D4—41no—
276D4—2444no—
277D4—2444no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—1222no—
286C2×C4—1222no—
287C2×C4—2448no—
288C2×C4—2442no—
289C2×C4—2441no—
290C2×C4—2442no—
291C2×C4—2442no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—42no—
300C22—41no—
301C22—81no—
302C22—81no—
303C22—614no—
304C22—1224no—
305C22—1224no—
306C22—1222no—
307C22—1222no—
308C22—1222no—
309C22—1222no—
310C22—1222no—
311C22—2444no—
312C22—2444no—
313C22—2444no—
314C22—2444no—
315C22—2442no—
316C22—2442no—
317C22C22⋊C4×D6111yescharacteristic
318C22#1451973711yescharacteristic
319C22C4×C22⋊D6111yescharacteristic
320C22#1451974511yescharacteristic
321C22#1451974811yescharacteristic
322C22#1451975011yescharacteristic
323C22#1451975911yescharacteristic
324C4—42no—
325C4—41no—
326C4—81no—
327C4—4881no—
328C4—2442no—
329C4—2442no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2—21no—
335C2—21no—
336C2—81no—
337C2—1224no—
338C2—2442no—
339C2#1683963811yescharacteristic
340C2#99×D6112yes—
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC24C22×D61
FittingC2×#99×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#99D61
hypocenterC61#1898
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D61C2semidirect
3. C2×#14519692C2semidirect
4. #16839617C2semidirect
5. #16839528C2semidirect
6. #16839528C2semidirect
7. C2×#99×C61C2semidirect
9. C22×C22⋊D61C4semidirect
19. C2×#11758198C4semidirect
27. C24×C61C2×C4semidirect
46. C22×C4×C61C2×C4semidirect
52. C22×Dic61C2×C4semidirect
58. C22⋊C4×C61D4semidirect
64. C22⋊Dic61D4semidirect
152. C2×D61#99semidirect
174. C2×#99D61semidirect
178. C61#1898semidirect
207. C24C4×D61semidirect
225. C22×C4C4×D61semidirect
239. C22⋊C4C22⋊D61semidirect