Finite Group Databasebeta

← #21455344

Subgroups — #21455344

Order 7808.

458 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic
2C2×Q16×D61C211yesmaximal, characteristic, complemented
3#16840337C211yesmaximal, characteristic
4#16840238C211yesmaximal, characteristic, complemented
5#16839987C211yesmaximal, characteristic, complemented
6#16839986C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839971C211yesmaximal, characteristic, complemented
10#16839970C211yesmaximal, characteristic, complemented
11#16839969C211yesmaximal, characteristic, complemented
12#16839787C211yesmaximal, characteristic, complemented
13#16839769C211yesmaximal, characteristic, complemented
14#16839757C211yesmaximal, characteristic
15C61×#462C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19#14519809—24no—
20C2×Dic244C2211yescharacteristic
21C2×#11758202C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24Q16×D61—24no—
25C2×#11758190C2211yescharacteristic
26C2×#11758201C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519775C2211yescharacteristic
30#14519766C2211yescharacteristic
31#14519765C2211yescharacteristic
32#14519762—21no—
33#14519762—21no—
34#14519755—21no—
35#14519755—21no—
36Q8×Dic61C2211yescharacteristic
37C4×Dic122—21no—
38C4×Dic122C2211yescharacteristic
39#14519742—21no—
40#14519742C2211yescharacteristic
41#14519735—21no—
42#14519735C2211yescharacteristic
43#14519734—21no—
44#14519734C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic
46#14519706C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519701C2211yescharacteristic
51#14519700C2211yescharacteristic
52#14519699C2211yescharacteristic
53#14519697C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic
56C4⋊Q8×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#103×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64#11758226—22no—
65#11758226—22no—
66Q8×D61—22no—
67Q8×D61—22no—
68Q8×D61—22no—
69Q8×D61D414yes—
70C2×D244—21no—
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×Dic122C2311yescharacteristic
79C2×Dic122C2311yescharacteristic
80Q16×C61—22no—
81Q16×C61—22no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61C2311yescharacteristic
88C42×C61—21no—
89C42×C61C2311yescharacteristic
90#11758202—22no—
91#11758202—22no—
92#11758202—22no—
93#11758201—22no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198D411yescharacteristic
100#11758198D411yescharacteristic
101C4⋊Dic61—21no—
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196D411yescharacteristic
108#11758196D411yescharacteristic
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116Dic244—22no—
117#11758190—22no—
118#11758189—22no—
119C8×D61—22no—
120C22×D61—21no—
121C22×D61C2×D411yescharacteristic
122Q8×C61—21no—
123Q8×C61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126Q8×C61—21no—
127Q8×C61C2×D412yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143D244—42no—
144C4×D61—24no—
145C4×D61—42no—
146C4×D61—42no—
147C4×D61C2×D412yes—
148C4×D61#4112yes—
149Dic122—21no—
150Dic122—24no—
151Dic122—21no—
152Dic122—21no—
153Dic122—42no—
154Dic122C2×D412yes—
155C8×C61—21no—
156C8×C61—21no—
157#92418—21no—
158#92418—21no—
159C22×C61C22×D411yescharacteristic
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61#12112yes—
166C4×C61—22no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C22×D411yescharacteristic
173C4×C61C2×#4111yescharacteristic
174Dic61—22no—
175Dic61—21no—
176Dic61—21no—
177Dic61—41no—
178Dic61—41no—
179Dic61#12112yes—
180#3044—611nomaximal, Sylow
181C2×C61C2×#12111yescharacteristic
182C2×C61#57811yescharacteristic
183C2×C61#57811yescharacteristic
184D61—22no—
185D61—81no—
186C2×#137—611no—
187C22×Q16—611no—
188#536—611no—
189#519—611no—
190#464—611no—
191#464—611no—
192#464—611no—
193#464—611no—
194#462—611no—
195#462—611no—
196#462—611no—
197#462D6111yescharacteristic, complemented
198#424—611no—
199#419—611no—
200#416—611no—
201C61#304411yescharacteristic, complemented, Sylow
202C2×#41—611no—
203C22×Q8—611no—
204C22×Q8—611no—
205#137—1224no—
206C2×Q16—611no—
207C2×Q16—611no—
208C2×Q16—611no—
209C2×Q16—611no—
210C2×Q16—1224no—
211C2×Q16C2×D6111yescharacteristic
212C2×Q16C2×D6111yescharacteristic
213C2×SD16—611no—
214C2×SD16—611no—
215C2×M16—611no—
216C22×C8—611no—
217C4⋊Q8—611no—
218C4⋊Q8C2×D6111yescharacteristic
219#124—611no—
220#124—611no—
221#123—1221no—
222#123—1221no—
223C22⋊Q8—1221no—
224C22⋊Q8—1221no—
225C4×Q8—611no—
226C4×Q8—611no—
227C4×Q8—611no—
228C4×Q8—1221no—
229C4×Q8—1221no—
230C4×Q8C2×D6111yescharacteristic
231#117—611no—
232#117—611no—
233#117—1221no—
234#117—1221no—
235C4⋊C8—611no—
236C4⋊C8—611no—
237C4⋊C8—611no—
238C4⋊C8C2×D6111yescharacteristic
239#103—611no—
240#103—611no—
241#103—611no—
242#103—611no—
243#103C2×D6111yescharacteristic
244#103C2×D6111yescharacteristic
245#102—611no—
246#102—611no—
247#41—1222no—
248#41—1222no—
249C2×Q8—614no—
250C2×Q8—611no—
251C2×Q8—611no—
252C2×Q8—1221no—
253C2×Q8—1221no—
254C2×Q8—1222no—
255C2×Q8—1222no—
256C2×Q8—1222no—
257C2×Q8C22×D6111yescharacteristic
258C2×Q8C22×D6111yescharacteristic
259C2×Q8C22×D6111yescharacteristic
260C2×D4—611no—
261C2×D4—1221no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266Q16—22no—
267Q16—22no—
268Q16—1222no—
269Q16—1222no—
270Q16—1222no—
271Q16—1222no—
272SD16—1222no—
273SD16—1222no—
274M16—1222no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8—1222no—
278C2×C8C22×D6111yescharacteristic
279C2×C8C22×D6111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4C22×D6111yescharacteristic
292C22⋊C4—611no—
293C22⋊C4—611no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—21no—
300C42—611no—
301C42—1221no—
302C42—1221no—
303C42—1221no—
304C42—1221no—
305C42C22×D6111yescharacteristic
306C23—611no—
307C23—1221no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—612no—
314Q8—1224no—
315Q8—1221no—
316Q8—1221no—
317Q8—1221no—
318Q8—2442no—
319Q8D4×D6112yes—
320D4—1221no—
321D4—1221no—
322D4—2442no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—611no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1224no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4D4×D6111yescharacteristic
339C2×C4D4×D6111yescharacteristic
340C2×C4C23×D6111yescharacteristic
341C8—21no—
342C8—21no—
343C8—1221no—
344C8—1221no—
345C22—612no—
346C22—1221no—
347C22—1221no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22C2×D4×D6111yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—612no—
359C4—1222no—
360C4—1221no—
361C4—1221no—
362C4—2441no—
363C4—2441no—
364C4C2×D4×D6111yescharacteristic
365C4#41×D6111yescharacteristic
366C2—1222no—
367C2—4881no—
368C2#121×D6111yescharacteristic
369C2#1684057511yescharacteristic
370C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3044
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D61C2semidirect
4. #16840238C2semidirect
5. #16839987C2semidirect
6. #16839986C2semidirect
7. #16839985C2semidirect
8. #16839984C2semidirect
9. #16839971C2semidirect
10. #16839970C2semidirect
11. #16839969C2semidirect
12. #16839787C2semidirect
13. #16839769C2semidirect
15. C61×#462C2semidirect
197. #462D61semidirect
201. C61#3044semidirect