Finite Group Databasebeta

← #21457564

Subgroups — #21457564

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11758202C211yesmaximal, characteristic, complemented
2C2×Q16×D61C211yesmaximal, characteristic, complemented
3Q8×C22⋊D61C211yesmaximal, characteristic
4#16840425C211yesmaximal, characteristic
5#16840140C211yesmaximal, characteristic, complemented
6#16840002C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839971C211yesmaximal, characteristic, complemented
9#16839970C211yesmaximal, characteristic, complemented
10#16839920C211yesmaximal, characteristic, complemented
11#16839919C211yesmaximal, characteristic, complemented
12#16839916C211yesmaximal, characteristic, complemented
13#16839854C211yesmaximal, characteristic, complemented
14#16839825C211yesmaximal, characteristic
15C61×#451C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×Dic244C2211yescharacteristic
20C2×Dic244C2211yescharacteristic
21C2×#11758202—24no—
22C2×#11758202C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758202C2211yescharacteristic
25C2×#11758202C2211yescharacteristic
26C2×#11758202C2211yescharacteristic
27Q16×D61—24no—
28C22×#92418C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic
30#14519776—21no—
31#14519775—21no—
32#14519775C2211yescharacteristic
33#14519775C2211yescharacteristic
34#14519757C2211yescharacteristic
35#14519756—21no—
36#14519756C2211yescharacteristic
37#14519755—21no—
38#14519754—21no—
39#14519753—21no—
40#14519753C2211yescharacteristic
41Q8×Dic61C2211yescharacteristic
42#14519742C2211yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61C2211yescharacteristic
45#14519737—21no—
46#14519710C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519701C2211yescharacteristic
51#14519700C2211yescharacteristic
52#14519689C2211yescharacteristic
53C8×Dic61C2211yescharacteristic
54C22×Q8×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic
56C2×Q16×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic
61C2×Q8×C61—21no—
62C2×Q8×C61—22no—
63C2×Q8×C61—41no—
64C2×Q8×C61C2311yescharacteristic
65C2×Q8×C61C2311yescharacteristic
66C2×Q8×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71Q8×D61—22no—
72Q8×D61—22no—
73Q8×D61—41no—
74Q8×D61—41no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×Dic122—22no—
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122—21no—
82C2×Dic122—41no—
83C2×Dic122C2311yescharacteristic
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86Q16×C61—22no—
87Q16×C61—41no—
88C2×C8×C61C2311yescharacteristic
89C2×C8×C61C2311yescharacteristic
90C4⋊C4×C61—21no—
91C4⋊C4×C61C2311yescharacteristic
92C22⋊C4×C61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61D411yescharacteristic
95#11758202—22no—
96#11758202—22no—
97#11758202—22no—
98#11758202—22no—
99#11758202D414yescomplemented
100#11758198—21no—
101#11758198—21no—
102#11758198D411yescharacteristic
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196—21no—
108#11758196—21no—
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196D411yescharacteristic
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117C2×#92418—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120Dic244—22no—
121Dic244—41no—
122C8×D61—22no—
123C23×C61C2×D411yescharacteristic
124C22×D61C2×D411yescharacteristic
125Q8×C61—21no—
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—42no—
131Q8×C61C2×D412yes—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—42no—
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2411yescharacteristic
141C22⋊D61Q1614yescomplemented
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—42no—
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149C2×Dic61C2×D411yescharacteristic
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—42no—
153C4×D61—42no—
154Dic122—21no—
155Dic122—21no—
156Dic122—21no—
157Dic122—21no—
158Dic122—21no—
159Dic122—42no—
160Dic122—42no—
161Dic122—42no—
162Dic122C2×D412yes—
163C8×C61—21no—
164C8×C61—21no—
165#92418—21no—
166#92418C2×D412yes—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61C2×Q1612yescomplemented
170C22×C61C22×D411yescharacteristic
171C2×D61—21no—
172C2×D61—21no—
173C2×D61C2×Q1612yescomplemented
174C4×C61—21no—
175C4×C61—22no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61C22×D411yescharacteristic
180C4×C61H(5,𝔽2)11yescharacteristic
181Dic61—22no—
182Dic61—21no—
183Dic61—21no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187Dic61C2×Q1612yescomplemented
188D4×Q16—611nomaximal, Sylow
189C2×C61—22no—
190C2×C61D4211yescharacteristic
191C2×C61C22×Q1611yescharacteristic
192C2×C61#57811yescharacteristic
193D61—22no—
194C22×Q16—611no—
195C22×Q16—611no—
196D4×Q8—611no—
197D4×Q8—611no—
198#494—611no—
199#467—611no—
200#467—611no—
201#462—611no—
202#462—611no—
203#451—611no—
204#451—611no—
205#451—611no—
206#451D6111yescharacteristic, complemented
207C4×Q16—611no—
208C8×D4—611no—
209C61D4×Q1611yescharacteristic, complemented, Sylow
210C22×Q8—611no—
211C22×Q8—611no—
212C22×Q8—611no—
213C22×Q8C2×D6111yescharacteristic
214C2×Q16—611no—
215C2×Q16—611no—
216C2×Q16—611no—
217C2×Q16—611no—
218C2×Q16—611no—
219C2×Q16—611no—
220C2×Q16—611no—
221C2×Q16—1224no—
222C2×Q16—1224no—
223C2×Q16C2×D6111yescharacteristic
224C2×Q16C2×D6111yescharacteristic
225C22×C8—611no—
226C22×C8—611no—
227C4⋊Q8—611no—
228C4⋊Q8—611no—
229C4⋊Q8—1221no—
230C4⋊Q8—1221no—
231C22⋊Q8—611no—
232C22⋊Q8—611no—
233C22⋊Q8—611no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236C22⋊Q8—1221no—
237C22⋊Q8—1221no—
238C22⋊Q8C2×D6111yescharacteristic
239C4×Q8—611no—
240C4×Q8—611no—
241C4×D4—611no—
242C4×D4—1221no—
243C4×D4—1221no—
244#107—611no—
245C4⋊C8—611no—
246#103—611no—
247#103—611no—
248#103—611no—
249#103—611no—
250#103C2×D6111yescharacteristic
251#103C2×D6111yescharacteristic
252C22⋊C8—611no—
253C22⋊C8C2×D6111yescharacteristic
254C4×C8—611no—
255C2×Q8—21no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—611no—
259C2×Q8—611no—
260C2×Q8—611no—
261C2×Q8—1221no—
262C2×Q8—1221no—
263C2×Q8—1222no—
264C2×Q8—1221no—
265C2×Q8—1222no—
266C2×Q8—1222no—
267C2×Q8—2441no—
268C2×Q8—2441no—
269C2×Q8—2441no—
270C2×Q8C22×D6111yescharacteristic
271C2×Q8C22×D6111yescharacteristic
272C2×Q8C22×D6111yescharacteristic
273C2×D4—611no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4C22×D6111yescharacteristic
280Q16—22no—
281Q16—41no—
282Q16—614no—
283Q16—1222no—
284Q16—1222no—
285Q16—1222no—
286Q16—1222no—
287Q16—1222no—
288Q16—2441no—
289C2×C8—611no—
290C2×C8—611no—
291C2×C8—1222no—
292C2×C8—1222no—
293C2×C8C22×D6111yescharacteristic
294C2×C8C22×D6111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—611no—
297C4⋊C4—611no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4C22×D6111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—611no—
310C22⋊C4—611no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C42—611no—
315C42—1221no—
316C42—1221no—
317C23—611no—
318C23D4×D6111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—612no—
326Q8—1221no—
327Q8—1221no—
328Q8—1221no—
329Q8—1221no—
330Q8—1221no—
331Q8—2442no—
332Q8—2442no—
333Q8—2442no—
334Q8D4×D6112yes—
335D4—614no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4D4×D6111yescharacteristic
356C2×C4C23×D6111yescharacteristic
357C8—21no—
358C8—21no—
359C8—612no—
360C8—1221no—
361C22—21no—
362C22—21no—
363C22—612no—
364C22—1221no—
365C22—1221no—
366C22Q16×D6112yescomplemented
367C22C2×D4×D6111yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—612no—
374C4—1221no—
375C4—1221no—
376C4—1222no—
377C4—2441no—
378C4—2441no—
379C4—2441no—
380C4C2×D4×D6111yescharacteristic
381C4#1451982211yescharacteristic
382C2—22no—
383C2—1222no—
384C2#1684039411yescharacteristic
385C2C2×Q16×D6111yescharacteristic
386C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#451C2
socleC22×C61C22×D4
hypercenter#451D61
hypocenterC61D4×Q16
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
1. C22×#11758202C2semidirect
2. C2×Q16×D61C2semidirect
5. #16840140C2semidirect
6. #16840002C2semidirect
7. #16840001C2semidirect
8. #16839971C2semidirect
9. #16839970C2semidirect
10. #16839920C2semidirect
11. #16839919C2semidirect
12. #16839916C2semidirect
13. #16839854C2semidirect
15. C61×#451C2semidirect
99. #11758202D4semidirect
141. C22⋊D61Q16semidirect
169. C22×C61C2×Q16semidirect
173. C2×D61C2×Q16semidirect
187. Dic61C2×Q16semidirect
206. #451D61semidirect
209. C61D4×Q16semidirect
366. C22Q16×D61semidirect