Finite Group Databasebeta

← #21455372

Subgroups — #21455372

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×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519798C211yesmaximal, characteristic
3#16840332C211yesmaximal, characteristic, complemented
4#16840244C211yesmaximal, characteristic, complemented
5#16839982C211yesmaximal, characteristic, complemented
6#16839976C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839972C211yesmaximal, characteristic, complemented
9#16839970C211yesmaximal, characteristic, complemented
10#16839968C211yesmaximal, characteristic, complemented
11#16839966C211yesmaximal, characteristic, complemented
12#16839787C211yesmaximal, characteristic, complemented
13#16839760C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#464C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19#14519809—24no—
20#14519798—24no—
21C2×#11758202C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758190C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758201C2211yescharacteristic
26C2×#11758199C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519777C2211yescharacteristic
30#14519775C2211yescharacteristic
31#14519764C2211yescharacteristic
32#14519759—21no—
33#14519759—21no—
34#14519754—21no—
35#14519754—21no—
36Q8×Dic61C2211yescharacteristic
37C4×D244—21no—
38C4×D244C2211yescharacteristic
39#14519739—21no—
40#14519739C2211yescharacteristic
41#14519734—21no—
42#14519734C2211yescharacteristic
43C4⋊C4×D61—21no—
44C4⋊C4×D61C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic
46#14519706C2211yescharacteristic
47#14519706C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519701C2211yescharacteristic
51#14519700C2211yescharacteristic
52#14519700C2211yescharacteristic
53#14519698C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66#11758226—22no—
67#11758226D414yes—
68Q8×D61—22no—
69Q8×D61—22no—
70#11758224—22no—
71#11758224—22no—
72C2×D244—21no—
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82C2×Dic122C2311yescharacteristic
83Q16×C61—22no—
84SD16×C61—22no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C42×C61—21no—
92C42×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758202—22no—
96#11758202—22no—
97#11758201—22no—
98#11758199—22no—
99#11758198—21no—
100#11758198—21no—
101#11758198D411yescharacteristic
102#11758198D411yescharacteristic
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109#11758196—21no—
110#11758196D411yescharacteristic
111#11758196D411yescharacteristic
112C4×Dic61—21no—
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116#11758190—22no—
117#11758190—22no—
118#11758189—22no—
119C8×D61—22no—
120C23×C61—21no—
121C22×D61—21no—
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126Q8×C61C2×D412yes—
127D4×C61—21no—
128D4×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
135C22⋊D61—42no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143D244—24no—
144D244—21no—
145D244C2×D412yes—
146C4×D61—24no—
147C4×D61—42no—
148C4×D61—81no—
149C4×D61—81no—
150C4×D61—81no—
151C4×D61C2×D412yes—
152C4×D61#4112yes—
153Dic122—21no—
154Dic122—21no—
155Dic122—21no—
156Dic122—21no—
157Dic122—42no—
158C8×C61—21no—
159C8×C61—21no—
160#92418—21no—
161#92418—21no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61C22×D411yescharacteristic
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—22no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61#12112yes—
172C4×C61—22no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61C22×D411yescharacteristic
178C4×C61C2×#4111yescharacteristic
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182Dic61—41no—
183Dic61—41no—
184Dic61#12112yes—
185#3046—611nomaximal, Sylow
186C2×C61—81no—
187C2×C61C2×#12111yescharacteristic
188C2×C61#57711yescharacteristic
189C2×C61#57811yescharacteristic
190D61—22no—
191D61—42no—
192C2×#137—611no—
193C2×#135—611no—
194#536—611no—
195#520—611no—
196#464—611no—
197#464D6111yescharacteristic, complemented
198#463—611no—
199#463—611no—
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×Q16C2×D6111yescharacteristic
216C2×SD16—611no—
217C2×SD16—611no—
218C2×SD16—611no—
219C2×SD16C2×D6111yescharacteristic
220C2×D8—611no—
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×Q8C2×D6111yescharacteristic
233C4×D4—611no—
234C4×D4—611no—
235C4×D4—1221no—
236C4×D4—1221no—
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—1221no—
260C2×Q8—1222no—
261C2×Q8—1222no—
262C2×Q8C22×D6111yescharacteristic
263C2×Q8C22×D6111yescharacteristic
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4C22×D6111yescharacteristic
268C22×C4—611no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275Q16—22no—
276Q16—1222no—
277Q16—1222no—
278SD16—22no—
279SD16—1222no—
280SD16—1222no—
281SD16—1222no—
282D8—1222no—
283M16—1222no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—1222no—
287C2×C8C22×D6111yescharacteristic
288C2×C8C22×D6111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—611no—
291C4⋊C4—611no—
292C4⋊C4—611no—
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—611no—
303C22⋊C4—611no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—21no—
309C42—611no—
310C42—1221no—
311C42C22×D6111yescharacteristic
312C23—21no—
313C23—611no—
314C23—1221no—
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—1221no—
319Q8—1221no—
320Q8—1221no—
321Q8—1221no—
322Q8—2442no—
323Q8D4×D6112yes—
324D4—21no—
325D4—21no—
326D4—612no—
327D4—1224no—
328D4—1221no—
329D4—2442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
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—4881no—
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—41no—
355C22—41no—
356C22—41no—
357C22—612no—
358C22—1221no—
359C22—1221no—
360C22—1222no—
361C22—2441no—
362C22—2441no—
363C22C2×D4×D6111yescharacteristic
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—612no—
370C4—1221no—
371C4—1221no—
372C4—2441no—
373C4—2441no—
374C4—2441no—
375C4C2×D4×D6111yescharacteristic
376C4#41×D6111yescharacteristic
377C2—81no—
378C2—1222no—
379C2—2442no—
380C2#121×D6111yescharacteristic
381C2#1684056911yescharacteristic
382C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61#3046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
3. #16840332C2semidirect
4. #16840244C2semidirect
5. #16839982C2semidirect
6. #16839976C2semidirect
7. #16839974C2semidirect
8. #16839972C2semidirect
9. #16839970C2semidirect
10. #16839968C2semidirect
11. #16839966C2semidirect
12. #16839787C2semidirect
13. #16839760C2semidirect
14. #103×D61C2semidirect
15. C61×#464C2semidirect
197. #464D61semidirect
207. C61#3046semidirect