Finite Group Databasebeta

← #21455370

Subgroups — #21455370

Order 7808.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519806C211yesmaximal, characteristic, complemented
2C2×#14519796C211yesmaximal, characteristic
3#16840332C211yesmaximal, characteristic, complemented
4#16840241C211yesmaximal, characteristic, complemented
5#16839983C211yesmaximal, characteristic, complemented
6#16839981C211yesmaximal, characteristic, complemented
7#16839975C211yesmaximal, characteristic, complemented
8#16839973C211yesmaximal, characteristic, complemented
9#16839971C211yesmaximal, characteristic, complemented
10#16839967C211yesmaximal, characteristic, complemented
11#16839965C211yesmaximal, characteristic, complemented
12#16839787C211yesmaximal, characteristic, complemented
13#16839760C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19#14519806—24no—
20#14519796—24no—
21C2×Dic244C2211yescharacteristic
22C2×Dic244C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758200C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519777C2211yescharacteristic
30#14519775C2211yescharacteristic
31#14519764C2211yescharacteristic
32#14519759—21no—
33#14519759—21no—
34#14519754—21no—
35#14519754—21no—
36C4×Dic122C2211yescharacteristic
37#14519742C2211yescharacteristic
38D4×Dic61C2211yescharacteristic
39C4×C22⋊D61—21no—
40#14519737—21no—
41#14519734C2211yescharacteristic
42#14519733—21no—
43C2×#11758196—21no—
44C4⋊C4×D61C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic
46#14519706C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519701C2211yescharacteristic
51#14519700C2211yescharacteristic
52#14519700C2211yescharacteristic
53#14519698C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57C4×D4×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70Q8×D61—22no—
71Q8×D61—22no—
72#11758224—22no—
73#11758224—22no—
74#11758224—22no—
75#11758224D414yes—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122—21no—
80C2×Dic122C2311yescharacteristic
81C2×Dic122C2311yescharacteristic
82C2×Dic122C2311yescharacteristic
83SD16×C61—22no—
84D8×C61—22no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C42×C61C2311yescharacteristic
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758202—22no—
96#11758200—22no—
97#11758200—22no—
98#11758200—22no—
99#11758198D411yescharacteristic
100#11758198D411yescharacteristic
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108#11758196—21no—
109#11758196D411yescharacteristic
110#11758196D411yescharacteristic
111C4×Dic61—21no—
112C4×Dic61—21no—
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116Dic244—22no—
117Dic244—22no—
118#11758189—22no—
119C8×D61—22no—
120C23×C61—21no—
121C23×C61—21no—
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61C2×D412yes—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—81no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—24no—
136C22⋊D61—42no—
137C2×Dic61—21no—
138C2×Dic61—24no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—42no—
143C2×Dic61—81no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147C4×D61—42no—
148C4×D61—81no—
149C4×D61C2×D412yes—
150C4×D61#4112yes—
151Dic122—21no—
152Dic122—21no—
153Dic122—21no—
154Dic122—21no—
155Dic122—21no—
156Dic122—42no—
157Dic122C2×D412yes—
158C8×C61—21no—
159C8×C61—21no—
160#92418—21no—
161#92418—21no—
162C22×C61—22no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61C22×D411yescharacteristic
169C2×D61—21no—
170C2×D61—21no—
171C2×D61#12112yes—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61C22×D411yescharacteristic
177C4×C61C2×#4111yescharacteristic
178Dic61—22no—
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182Dic61—41no—
183Dic61—41no—
184Dic61#12112yes—
185#3046—611nomaximal, Sylow
186C2×C61—42no—
187C2×C61—81no—
188C2×C61C2×#12111yescharacteristic
189C2×C61#57711yescharacteristic
190C2×C61#57811yescharacteristic
191D61—22no—
192C2×#137—611no—
193C2×#135—611no—
194#536—611no—
195#520—611no—
196#464—611no—
197#464—611no—
198#463—611no—
199#463D6111yescharacteristic, complemented
200#462—611no—
201#462—611no—
202#461—611no—
203#461—611no—
204#424—611no—
205#417—611no—
206C2×#103—611no—
207C61#304611yescharacteristic, complemented, Sylow
208C2×#41—611no—
209C2×#41—611no—
210C22×Q8—611no—
211#137—1224no—
212#135—1224no—
213C2×Q16—611no—
214C2×Q16—611no—
215C2×Q16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×SD16—611no—
219C2×SD16C2×D6111yescharacteristic
220C2×D8C2×D6111yescharacteristic
221C2×M16—611no—
222C22×C8—611no—
223C4⋊Q8—611no—
224C4⋊Q8—611no—
225#124—611no—
226#124C2×D6111yescharacteristic
227#123—1221no—
228#123—1221no—
229C22⋊Q8—1221no—
230C22⋊Q8—1221no—
231C4×Q8—611no—
232C4×Q8—611no—
233C4×D4—611no—
234C4×D4—1221no—
235C4×D4—1221no—
236C4×D4C2×D6111yescharacteristic
237#117—611no—
238#117—1221no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1221no—
241C4⋊C8—611no—
242C4⋊C8—611no—
243C4⋊C8—611no—
244C4⋊C8C2×D6111yescharacteristic
245#103—611no—
246#103—611no—
247#103—611no—
248#103—611no—
249#103—611no—
250#103C2×D6111yescharacteristic
251#102—611no—
252#102C2×D6111yescharacteristic
253#41—614no—
254#41—1222no—
255#41—1222no—
256#41—1222no—
257C2×Q8—611no—
258C2×Q8—611no—
259C2×Q8—611no—
260C2×Q8—1221no—
261C2×Q8—1222no—
262C2×Q8—1222no—
263C2×Q8C22×D6111yescharacteristic
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4C22×D6111yescharacteristic
267C2×D4C22×D6111yescharacteristic
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275Q16—1222no—
276Q16—1222no—
277Q16—1222no—
278SD16—22no—
279SD16—1222no—
280SD16—1222no—
281SD16—1222no—
282D8—22no—
283M16—1222no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—1222no—
287C2×C8C22×D6111yescharacteristic
288C2×C8C22×D6111yescharacteristic
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—611no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4C22×D6111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—611no—
304C22⋊C4—611no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—611no—
309C42—1221no—
310C42—1221no—
311C42C22×D6111yescharacteristic
312C23—21no—
313C23—21no—
314C23—611no—
315Q8—21no—
316Q8—21no—
317Q8—612no—
318Q8—1221no—
319Q8—1221no—
320Q8—1221no—
321Q8—1221no—
322Q8—1221no—
323Q8—2442no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—1224no—
328D4—2442no—
329D4D4×D6112yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—611no—
334C2×C4—612no—
335C2×C4—612no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—1224no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4D4×D6111yescharacteristic
348C2×C4D4×D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—1221no—
353C8—1221no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—612no—
361C22—1221no—
362C22—1221no—
363C22C2×D4×D6111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—612no—
369C4—1222no—
370C4—1221no—
371C4—1221no—
372C4—2441no—
373C4—2441no—
374C4—2441no—
375C4C2×D4×D6111yescharacteristic
376C4#41×D6111yescharacteristic
377C2—42no—
378C2—81no—
379C2—1222no—
380C2#121×D6111yescharacteristic
381C2#1684057211yescharacteristic
382C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
3. #16840332C2semidirect
4. #16840241C2semidirect
5. #16839983C2semidirect
6. #16839981C2semidirect
7. #16839975C2semidirect
8. #16839973C2semidirect
9. #16839971C2semidirect
10. #16839967C2semidirect
11. #16839965C2semidirect
12. #16839787C2semidirect
13. #16839760C2semidirect
14. #103×D61C2semidirect
15. C61×#463C2semidirect
199. #463D61semidirect
207. C61#3046semidirect