Finite Group Databasebeta

← #21457688

Subgroups — #21457688

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840470C211yesmaximal, characteristic
2Q8×C22⋊D61C211yesmaximal, characteristic
3#16840111C211yesmaximal, characteristic, complemented
4#16840098C211yesmaximal, characteristic, complemented
5#16840096C211yesmaximal, characteristic, complemented
6#16840055C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16840000C211yesmaximal, characteristic, complemented
9#16839970C211yesmaximal, characteristic, complemented
10#16839916C211yesmaximal, characteristic, complemented
11Q16×Dic61C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic
13C2×#14519701C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#451C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519775—21no—
22#14519775C2211yescharacteristic
23#14519767—21no—
24#14519757—21no—
25#14519756—21no—
26#14519756C2211yescharacteristic
27#14519754—21no—
28#14519753—21no—
29#14519753C2211yescharacteristic
30#14519753C2211yescharacteristic
31Q8×Dic61C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33C4×C22⋊D61—21no—
34C4×C22⋊D61C2211yescharacteristic
35#14519737—21no—
36C2×C4⋊Dic61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519701C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519700C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×Q8×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61D411yescharacteristic
68C22×Dic61—21no—
69Q8×D61—22no—
70Q8×D61—41no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77Q16×C61—22no—
78Q16×C61—41no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61D411yescharacteristic
86#11758202—41no—
87#11758198—21no—
88#11758198—21no—
89#11758198D411yescharacteristic
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C8×D61—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61C2×D411yescharacteristic
113Q8×C61—21no—
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—42no—
119Q8×C61#4112yes—
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—42no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61Q1614yescomplemented
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—81no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C4×D61—21no—
139C4×D61—21no—
140C4×D61—42no—
141C4×D61—81no—
142Dic122—21no—
143Dic122—21no—
144Dic122—42no—
145Dic122—81no—
146C8×C61—21no—
147C8×C61—21no—
148#92418—21no—
149#92418—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61C2×Q1612yes—
153C22×C61C22×D411yescharacteristic
154C2×D61—21no—
155C2×D61—21no—
156C2×D61C2×Q1612yes—
157C4×C61—22no—
158C4×C61—21no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61C2×#4111yescharacteristic
163C4×C61H(5,𝔽2)11yescharacteristic
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61C2×Q1612yes—
171#3299—611nomaximal, Sylow
172C2×C61—22no—
173C2×C61#54611yescharacteristic
174C2×C61C22×Q1611yescharacteristic
175C2×C61#57711yescharacteristic
176D61—22no—
177#554—611no—
178D4×Q8—611no—
179#487—611no—
180#484—611no—
181#484—611no—
182#477—611no—
183#467—611no—
184#467—611no—
185#462—611no—
186#451—611no—
187#451D6111yescharacteristic, complemented
188C4×Q16—611no—
189C8×D4—611no—
190C2×#103—611no—
191C2×#103—611no—
192C61#329911yescharacteristic, complemented, Sylow
193C22×Q8—611no—
194C22×Q8C2×D6111yescharacteristic
195C2×Q16—611no—
196C2×Q16C2×D6111yescharacteristic
197C2×Q16C2×D6111yescharacteristic
198C22×C8—611no—
199C22×C8—611no—
200C4⋊Q8—611no—
201C4⋊Q8—611no—
202C4⋊Q8—1221no—
203#125—1221no—
204C22⋊Q8—611no—
205C22⋊Q8—611no—
206C22⋊Q8—611no—
207C22⋊Q8—1221no—
208C22⋊Q8—1221no—
209C22⋊Q8—1221no—
210C22⋊Q8—1221no—
211C22⋊Q8C2×D6111yescharacteristic
212C4×Q8—611no—
213C4×Q8—611no—
214C4×D4—611no—
215C4×D4—1221no—
216C4×D4—1221no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219#107—611no—
220#107—611no—
221#107—611no—
222C4⋊C8—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103C2×D6111yescharacteristic
232#103C2×D6111yescharacteristic
233C22⋊C8—611no—
234C22⋊C8C2×D6111yescharacteristic
235C4×C8—611no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—611no—
240C2×Q8—1221no—
241C2×Q8—1221no—
242C2×Q8—1222no—
243C2×Q8—2441no—
244C2×Q8C22×D6111yescharacteristic
245C2×Q8C22×D6111yescharacteristic
246C2×Q8C22×D6111yescharacteristic
247C2×D4—611no—
248C22×C4—21no—
249C22×C4—611no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4C22×D6111yescharacteristic
254Q16—22no—
255Q16—41no—
256Q16—2441no—
257C2×C8—611no—
258C2×C8—611no—
259C2×C8—2441no—
260C2×C8—2441no—
261C2×C8C22×D6111yescharacteristic
262C2×C8C22×D6111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4C22×D6111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—611no—
281C22⋊C4—611no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C42—611no—
286C42—1221no—
287C42—1221no—
288C23—611no—
289C23D4×D6111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—1221no—
297Q8—1221no—
298Q8—4881no—
299Q8—2442no—
300Q8#1175822412yes—
301D4—614no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—611no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—2442no—
321C2×C4D4×D6111yescharacteristic
322C2×C4C23×D6111yescharacteristic
323C8—21no—
324C8—21no—
325C8—1221no—
326C8—1221no—
327C22—21no—
328C22—21no—
329C22—612no—
330C22—1221no—
331C22—1221no—
332C22Q16×D6112yes—
333C22C2×D4×D6111yescharacteristic
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—612no—
340C4—1221no—
341C4—1221no—
342C4—2441no—
343C4—2441no—
344C4—2441no—
345C4—2441no—
346C4C2×#1175822411yescharacteristic
347C4#1451982211yescharacteristic
348C2—22no—
349C2—1222no—
350C2#1684039911yescharacteristic
351C2C2×Q16×D6111yescharacteristic
352C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61#3299
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #16840111C2semidirect
4. #16840098C2semidirect
5. #16840096C2semidirect
6. #16840055C2semidirect
7. #16840001C2semidirect
8. #16840000C2semidirect
9. #16839970C2semidirect
10. #16839916C2semidirect
11. Q16×Dic61C2semidirect
13. C2×#14519701C2semidirect
14. #103×D61C2semidirect
15. C61×#451C2semidirect
129. C22⋊D61Q16semidirect
187. #451D61semidirect
192. C61#3299semidirect