Finite Group Databasebeta

← #21454657

Subgroups — #21454657

Order 7808.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic
2#16840244C211yesmaximal, characteristic
3#16840238C211yesmaximal, characteristic, complemented
4#16839869C211yesmaximal, characteristic, complemented
5#16839867C211yesmaximal, characteristic, complemented
6#16839861C211yesmaximal, characteristic, complemented
7#16839860C211yesmaximal, characteristic, complemented
8#16839854C211yesmaximal, characteristic, complemented
9C4×#11758190C211yesmaximal, characteristic, complemented
10#16839847C211yesmaximal, characteristic, complemented
11#16839803C211yesmaximal, characteristic, complemented
12#16839757C211yesmaximal, characteristic
13#103×D61C211yesmaximal, characteristic, complemented
14#16839716C211yesmaximal, characteristic, complemented
15C4×Q16×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18#14519809C418yescomplemented
19C2×#11758202C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758201C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23C2×C8×D61C2211yescharacteristic
24Q8×Dic61C2211yescharacteristic
25Q8×Dic61C2211yescharacteristic
26C4×Dic122—21no—
27C4×Dic122C2211yescharacteristic
28#14519742—21no—
29#14519742C2211yescharacteristic
30C4×D244—21no—
31C4×D244C2211yescharacteristic
32#14519739—21no—
33#14519739C2211yescharacteristic
34#14519735—21no—
35#14519735C2211yescharacteristic
36#14519734—21no—
37#14519734—21no—
38#14519734C2211yescharacteristic
39C4⋊C4×D61—21no—
40C4⋊C4×D61C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519688C2211yescharacteristic
51#14519687C2211yescharacteristic
52C8×Dic61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic
59C4×C8×C61C2211yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62#11758226—22no—
63#11758226C2×C414yes—
64Q8×D61—22no—
65Q8×D61C2×C414yescomplemented
66C2×D244—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122C2311yescharacteristic
76Q16×C61C2×C414yescomplemented
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C42×C61—21no—
84C42×C61—21no—
85C42×C61C2311yescharacteristic
86#11758202C2×C414yescomplemented
87#11758201C2×C414yescomplemented
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198D411yescharacteristic
92#11758198D411yescharacteristic
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758190C2×C414yescomplemented
111#11758189C2×C414yescomplemented
112C8×D61—22no—
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61C22×C412yes—
118Q8×C61C22×C412yes—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—24no—
133D244—21no—
134D244C22×C412yes—
135C4×D61—24no—
136C4×D61—24no—
137C4×D61—81no—
138C4×D61—81no—
139C4×D61—81no—
140C4×D61C22×C412yes—
141C4×D61#4112yes—
142Dic122—21no—
143Dic122—24no—
144Dic122C22×C412yes—
145C8×C61—21no—
146C8×C61C22×C412yes—
147#92418—21no—
148#92418C22×C412yes—
149C22×C61C22×D411yescharacteristic
150C2×D61—21no—
151C2×D61—21no—
152C2×D61—22no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61C4×D412yes—
156C4×C61—22no—
157C4×C61—22no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61C23×C411yescharacteristic
163C4×C61C2×#4111yescharacteristic
164Dic61—22no—
165Dic61—21no—
166Dic61—21no—
167Dic61—41no—
168Dic61—41no—
169Dic61C4×D412yes—
170#2947—611nomaximal, Sylow
171C2×C61C2×C4×D411yescharacteristic
172C2×C61#57711yescharacteristic
173C2×C61#57811yescharacteristic
174D61—22no—
175D61—42no—
176C2×#137—611no—
177#520—611no—
178#519—611no—
179#441—611no—
180#441—611no—
181#440—611no—
182#440—611no—
183C4×Q16—611no—
184C4×Q16D6111yescharacteristic, complemented
185C4×SD16—611no—
186C4×SD16—611no—
187#428—611no—
188#416—611no—
189C2×#103—611no—
190#405—611no—
191C61#294711yescharacteristic, complemented, Sylow
192C2×#41—611no—
193C22×Q8—611no—
194#137—618no—
195C2×Q16—611no—
196C2×Q16C2×D6111yescharacteristic
197C2×SD16—611no—
198C2×SD16—611no—
199C2×M16—611no—
200C22×C8—611no—
201C4×Q8—611no—
202C4×Q8—611no—
203C4×Q8—611no—
204C4×Q8—611no—
205C4×Q8—1221no—
206C4×Q8—1221no—
207C4×Q8C2×D6111yescharacteristic
208C4×Q8C2×D6111yescharacteristic
209C4×D4—611no—
210C4×D4—611no—
211C4×D4—1221no—
212C4×D4—1221no—
213#117—611no—
214#117—611no—
215#117—1221no—
216#117—1221no—
217#117—1221no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1221no—
220#107—611no—
221#107C2×D6111yescharacteristic
222#106—611no—
223#106—611no—
224#103—611no—
225#103—611no—
226#103—611no—
227#103—611no—
228#103C2×D6111yescharacteristic
229#103C2×D6111yescharacteristic
230#102—611no—
231#102—611no—
232#97—611no—
233#97—611no—
234C4×C8—611no—
235C4×C8C2×D6111yescharacteristic
236#41—614no—
237#41—1222no—
238C2×Q8—614no—
239C2×Q8—611no—
240C2×Q8—1221no—
241C2×Q8—1222no—
242C2×Q8C22×D6111yescharacteristic
243C2×Q8C22×D6111yescharacteristic
244C2×D4—611no—
245C2×D4—1221no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252Q16—614no—
253Q16C4×D6114yescomplemented
254SD16—614no—
255SD16—614no—
256M16—614no—
257C2×C8—611no—
258C2×C8—611no—
259C2×C8—1222no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C22⋊C4—611no—
276C22⋊C4—611no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C42—21no—
281C42—21no—
282C42—611no—
283C42—1221no—
284C42—1221no—
285C42—1221no—
286C42—1221no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C23—611no—
290C23—1221no—
291Q8—21no—
292Q8—21no—
293Q8—612no—
294Q8—1224no—
295Q8—1221no—
296Q8C2×C4×D6112yes—
297Q8C2×C4×D6112yes—
298D4—612no—
299D4—1224no—
300D4—1221no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—611no—
306C2×C4—612no—
307C2×C4—612no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—1224no—
311C2×C4—1224no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4D4×D6111yescharacteristic
319C2×C4D4×D6111yescharacteristic
320C2×C4C23×D6111yescharacteristic
321C8—21no—
322C8—612no—
323C8—1221no—
324C8C2×C4×D6112yes—
325C22—612no—
326C22—1221no—
327C22—1221no—
328C22—1222no—
329C22—2441no—
330C22—2441no—
331C22C2×D4×D6111yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—612no—
339C4—1222no—
340C4—1221no—
341C4—1221no—
342C4—2441no—
343C4—2441no—
344C4C22×C4×D6111yescharacteristic
345C4#41×D6111yescharacteristic
346C2—1222no—
347C2—2442no—
348C2C4×D4×D6111yescharacteristic
349C2#1684056911yescharacteristic
350C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC4×Q16×C61C2
socleC22×C61C22×D4
hypercenterC4×Q16D61
hypocenterC61#2947
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. #16840238C2semidirect
4. #16839869C2semidirect
5. #16839867C2semidirect
6. #16839861C2semidirect
7. #16839860C2semidirect
8. #16839854C2semidirect
9. C4×#11758190C2semidirect
10. #16839847C2semidirect
11. #16839803C2semidirect
13. #103×D61C2semidirect
14. #16839716C2semidirect
15. C4×Q16×C61C2semidirect
18. #14519809C4semidirect
65. Q8×D61C2×C4semidirect
76. Q16×C61C2×C4semidirect
86. #11758202C2×C4semidirect
87. #11758201C2×C4semidirect
110. #11758190C2×C4semidirect
111. #11758189C2×C4semidirect
184. C4×Q16D61semidirect
191. C61#2947semidirect
253. Q16C4×D61semidirect