Finite Group Databasebeta

← #21447068

Subgroups — #21447068

Order 7808.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#16840321C211yesmaximal, characteristic
2C2×#14519692C211yesmaximal, characteristic, complemented
3C2×#14519691C211yesmaximal, characteristic, complemented
4#16839641C211yesmaximal, characteristic, complemented
5#16839635C211yesmaximal, characteristic, complemented
6#16839528C211yesmaximal, characteristic, complemented
7C61×#386C211yesmaximal, characteristic, complemented
8C22×C22⋊D61C2211yescharacteristic
9#14519760—21no—
10#14519758—21no—
11#14519749—21no—
12#14519749—21no—
13#14519746—21no—
14#14519745—21no—
15C2×#11758196—21no—
16C2×C22⋊Dic61C2211yescharacteristic
17C2×C22⋊Dic61C2211yescharacteristic
18C2×C22⋊Dic61C2211yescharacteristic
19C2×#11758198—21no—
20#14519692—22no—
21#14519691—22no—
22#14519684—21no—
23#14519684—21no—
24C22×D4×C61C2211yescharacteristic
25C23×C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61—21no—
27C2×C22⋊C4×C61C2211yescharacteristic
28#95×C61—21no—
29C24×C61D411yescharacteristic
30C24×C61C2311yescharacteristic
31C23×D61D411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C22×C4×C61—21no—
39C22×C4×C61—21no—
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—42no—
43C22×C4×C61D411yescharacteristic
44C2×C22⋊D61—21no—
45C2×C22⋊D61—21no—
46C2×C22⋊D61—21no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—21no—
49C2×C22⋊D61—21no—
50C2×C22⋊D61—21no—
51C2×C22⋊D61—21no—
52C22×Dic61—21no—
53C22×Dic61—21no—
54C22×Dic61D411yescharacteristic
55C22×Dic61D411yescharacteristic
56C22×Dic61D411yescharacteristic
57C22⋊C4×C61—21no—
58C22⋊C4×C61—21no—
59C22⋊C4×C61—42no—
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62C22⋊Dic61—21no—
63C22⋊Dic61—21no—
64C22⋊Dic61—21no—
65C22⋊Dic61—21no—
66C22⋊Dic61—21no—
67C22⋊Dic61D412yescomplemented
68#11758198—21no—
69#11758198—21no—
70#11758198—42no—
71#11758196—21no—
72#11758196—21no—
73#11758196—42no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—41no—
78C23×C61—41no—
79C23×C61—41no—
80C23×C61—41no—
81C23×C61C2×D411yescharacteristic
82C23×C61C2×D411yescharacteristic
83C23×C61C2×D411yescharacteristic
84C23×C61C2×D411yescharacteristic
85C23×C61#4111yescharacteristic
86C23×C61#4111yescharacteristic
87C23×C61#4111yescharacteristic
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—41no—
92C22×D61—41no—
93D4×C61—41no—
94D4×C61—41no—
95D4×C61—41no—
96D4×C61—41no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C22⋊D61—41no—
111C22⋊D61—41no—
112C22⋊D61—41no—
113C22⋊D61—41no—
114C22⋊D61—81no—
115C22⋊D61—81no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—22no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—41no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61—41no—
139C22×C61—42no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—81no—
144C22×C61#12011yescharacteristic
145C22×C61#12111yescharacteristic
146C22×C61#12111yescharacteristic
147C22×C61#12111yescharacteristic
148C22×C61#12311yescharacteristic
149C22×C61#12311yescharacteristic
150C22×C61#12411yescharacteristic
151C2×D61—42no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—81no—
156C4×C61—41no—
157C4×C61—42no—
158C4×C61—81no—
159Dic61—42no—
160Dic61—41no—
161Dic61—41no—
162Dic61—41no—
163Dic61—81no—
164#2044—611nomaximal, Sylow
165C2×C61—21no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61—21no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61—81no—
172C2×C61#39411yescharacteristic
173C2×C61B(4,𝔽2)11yescharacteristic
174C2×C61#45811yescharacteristic
175D61—81no—
176#534—611no—
177C2×#99—611no—
178C2×#99—611no—
179#386—611no—
180#386D6111yescharacteristic, complemented
181#385—611no—
182#342—611no—
183C61#204411yescharacteristic, complemented, Sylow
184C22×D4—611no—
185C22×D4C2×D6111yescharacteristic
186C23×C4C2×D6111yescharacteristic
187#123—1221no—
188#123—1221no—
189#121—1221no—
190#121—1221no—
191#120—1221no—
192#120—1221no—
193C2×C4⋊C4—1221no—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—611no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—1221no—
199C2×C22⋊C4C2×D6111yescharacteristic
200#99—1222no—
201#99—1222no—
202#95—21no—
203#95—1221no—
204#95—1221no—
205C24—611no—
206C24C22⋊D6111yescharacteristic
207C24C22×D6111yescharacteristic
208C2×D4—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—1221no—
215C2×D4—1221no—
216C2×D4—1221no—
217C2×D4—1221no—
218C2×D4—1221no—
219C2×D4—1221no—
220C2×D4—1221no—
221C2×D4—1221no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4C22⋊D6111yescharacteristic
233C4⋊C4—1221no—
234C4⋊C4—1221no—
235C4⋊C4—2442no—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—42no—
239C22⋊C4—612no—
240C22⋊C4—1221no—
241C22⋊C4—1221no—
242C22⋊C4—1221no—
243C22⋊C4—1221no—
244C22⋊C4—1221no—
245C22⋊C4—1221no—
246C22⋊C4—1221no—
247C22⋊C4—1221no—
248C22⋊C4—1221no—
249C22⋊C4—2442no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—1221no—
258C23—1221no—
259C23—1221no—
260C23—2441no—
261C23—2441no—
262C23#1175822211yescharacteristic
263C23#1175822211yescharacteristic
264C23D4×D6111yescharacteristic
265C23D4×D6111yescharacteristic
266C23D4×D6111yescharacteristic
267C23#1175822411yescharacteristic
268C23C2×C22⋊D6111yescharacteristic
269D4—41no—
270D4—41no—
271D4—41no—
272D4—41no—
273D4—4881no—
274D4—4881no—
275D4—2441no—
276D4—2441no—
277D4—2441no—
278D4—2441no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1222no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22—4881no—
321C22—2442no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22#1451974511yescharacteristic
326C22#1451974911yescharacteristic
327C22#1451975011yescharacteristic
328C22#1451975011yescharacteristic
329C22#1451975911yescharacteristic
330C22#1451976011yescharacteristic
331C22#1451976311yescharacteristic
332C4—42no—
333C4—41no—
334C4—81no—
335C4—4881no—
336C4—2442no—
337C4—2441no—
338C4—2441no—
339C4—2441no—
340C2—21no—
341C2—21no—
342C2—21no—
343C2—21no—
344C2—21no—
345C2—21no—
346C2—81no—
347C2—4881no—
348C2#1683967711yescharacteristic
349C2#1683994811yescharacteristic
350C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC24×C61C23
FrattiniC24C22×D61
FittingC61×#386C2
socleC22×C61#120
hypercenter#386D61
hypocenterC61#2044
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#14519692C2semidirect
3. C2×#14519691C2semidirect
4. #16839641C2semidirect
5. #16839635C2semidirect
6. #16839528C2semidirect
7. C61×#386C2semidirect
67. C22⋊Dic61D4semidirect
180. #386D61semidirect
183. C61#2044semidirect