Finite Group Databasebeta

← #21453892

Subgroups — #21453892

Order 7808.

456 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519772C211yesmaximal, characteristic, complemented
2C2×#14519770C211yesmaximal, characteristic, complemented
3#16839695C211yesmaximal, characteristic, complemented
4#16839694C211yesmaximal, characteristic, complemented
5#16839693C211yesmaximal, characteristic, complemented
6#16839686C211yesmaximal, characteristic, complemented
7#16839685C211yesmaximal, characteristic, complemented
8#16839685C211yesmaximal, characteristic, complemented
9#16839684C211yesmaximal, characteristic, complemented
10#16839684C211yesmaximal, characteristic, complemented
11#16839678C211yesmaximal, characteristic
12#16839677C211yesmaximal, characteristic
13#16839677C211yesmaximal, characteristic
14#16839631C211yesmaximal, characteristic, complemented
15C61×#396C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17#14519772—24no—
18#14519770—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C23×D61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—41no—
62C2×C22⋊D61—41no—
63C2×C22⋊D61—41no—
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C4⋊C4×C61—22no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—22no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊Dic61—22no—
78C22⋊Dic61—22no—
79C22⋊Dic61—41no—
80#11758198—22no—
81#11758198—22no—
82#11758198—22no—
83#11758198—41no—
84#11758198—41no—
85#11758198—41no—
86C4⋊Dic61—22no—
87C4⋊Dic61—22no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196—41no—
94#11758196—41no—
95#11758196—41no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61D414yescomplemented
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61C2411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61C2×D412yes—
132C22⋊D61—44no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61C2×D412yes—
153C2×Dic61C2×D412yes—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C22×C61H(5,𝔽2)11yescharacteristic
163C22×C61H(5,𝔽2)11yescharacteristic
164C22×C61H(5,𝔽2)11yescharacteristic
165C22×C612−1+411yescharacteristic
166C22×C612−1+411yescharacteristic
167C22×C612−1+411yescharacteristic
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C4×C61—22no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—41no—
181Dic61—22no—
182Dic61—22no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188#2823—611nomaximal, Sylow
189C2×C61—81no—
190C2×C61#53711yescharacteristic
191C2×C61#53711yescharacteristic
192C2×C61#53711yescharacteristic
193C2×C61#56011yescharacteristic
194C2×C61#56311yescharacteristic
195C2×C61#56311yescharacteristic
196C2×C61#56311yescharacteristic
197D61—81no—
198C2×#126—611no—
199C2×#126—611no—
200#398—611no—
201#398—611no—
202#398—611no—
203#396—611no—
204#396—611no—
205#396—611no—
206#396—611no—
207#396—611no—
208#396D6111yescharacteristic, complemented
209#394—611no—
210#394—611no—
211#394—611no—
212#384—611no—
213C61#282311yescharacteristic, complemented, Sylow
214C22×D4—611no—
215#126—1224no—
216#126—1224no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4C2×D6111yescharacteristic
230C2×C4⋊C4C2×D6111yescharacteristic
231C2×C4⋊C4C2×D6111yescharacteristic
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—611no—
241C2×C22⋊C4C2×D6111yescharacteristic
242C2×C22⋊C4C2×D6111yescharacteristic
243C2×C22⋊C4C2×D6111yescharacteristic
244C2×C42—611no—
245#95—611no—
246#95—611no—
247#95—611no—
248#95—611no—
249#95—611no—
250#95C2×D6111yescharacteristic
251C24—611no—
252C24C22×D6111yescharacteristic
253C2×D4—2441no—
254C2×D4—2441no—
255C2×D4—2441no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4C22×D6111yescharacteristic
264C22×C4C22×D6111yescharacteristic
265C22×C4C22×D6111yescharacteristic
266C22×C4C22×D6111yescharacteristic
267C22×C4C22×D6111yescharacteristic
268C22×C4C22×D6111yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—1222no—
273C4⋊C4—1222no—
274C4⋊C4—1222no—
275C4⋊C4—1222no—
276C4⋊C4—1222no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C22⋊C4—22no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—1222no—
288C22⋊C4—1222no—
289C22⋊C4—1222no—
290C22⋊C4—1222no—
291C22⋊C4—1222no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C42—614no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—1221no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23C23×D6111yescharacteristic
312D4—2444no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—612no—
331C2×C4—612no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4D4×D6112yes—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22C2×D4×D6111yescharacteristic
367C22#1451982211yescharacteristic
368C22#1451982211yescharacteristic
369C22#1451982311yescharacteristic
370C22#1451982411yescharacteristic
371C22#1451982411yescharacteristic
372C22#1451982511yescharacteristic
373C4—22no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—1222no—
380C4—1222no—
381C4—2441no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4—2441no—
386C2—81no—
387C2—4881no—
388C2#1684033911yescharacteristic
389C2#1684034111yescharacteristic
390C2#1684034211yescharacteristic
391C2#1684050011yescharacteristic
392C2#1684051311yescharacteristic
393C2#1684051311yescharacteristic
394C2#1684051411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#396C2
hypercenter#396D61
hypocenterC61#2823
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14519772C2semidirect
2. C2×#14519770C2semidirect
3. #16839695C2semidirect
4. #16839694C2semidirect
5. #16839693C2semidirect
6. #16839686C2semidirect
7. #16839685C2semidirect
8. #16839685C2semidirect
9. #16839684C2semidirect
10. #16839684C2semidirect
14. #16839631C2semidirect
15. C61×#396C2semidirect
98. C4×Dic61D4semidirect
208. #396D61semidirect
213. C61#2823semidirect