Finite Group Databasebeta

← #21450079

Subgroups — #21450079

Order 7808.

546 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519770C211yesmaximal, characteristic, complemented
2C22×C4⋊Dic61C211yesmaximal, characteristic, complemented
3#16839704C211yesmaximal, characteristic, complemented
4#16839702C211yesmaximal, characteristic, complemented
5#16839687C211yesmaximal, characteristic, complemented
6#16839685C211yesmaximal, characteristic, complemented
7#16839655C211yesmaximal, characteristic, complemented
8#16839649C211yesmaximal, characteristic, complemented
9#16839647C211yesmaximal, characteristic, complemented
10#16839642C211yesmaximal, characteristic
11#16839642C211yesmaximal, characteristic
12#16839635C211yesmaximal, characteristic, complemented
13#16839620C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic
16C23×Dic61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18#14519770—24no—
19C2×C4⋊Dic61—24no—
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C22×D4×C61C2211yescharacteristic
47C23×C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C24×C61C2311yescharacteristic
55C2×D4×C61—22no—
56C2×D4×C61—22no—
57C2×D4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22⋊C4×C61—22no—
81C22⋊C4×C61—22no—
82C22⋊C4×C61—22no—
83C22⋊Dic61—22no—
84C22⋊Dic61—22no—
85C22⋊Dic61—22no—
86C22⋊Dic61—22no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C4⋊Dic61—22no—
90C4⋊Dic61—22no—
91C4⋊Dic61—22no—
92C4⋊Dic61D414yescomplemented
93#11758196—22no—
94#11758196—22no—
95#11758196—22no—
96#11758196—41no—
97C4×Dic61—22no—
98C4×Dic61—41no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61#4112yes—
111C23×C61#4112yes—
112C23×C61#4112yes—
113C23×C61C2411yescharacteristic
114D4×C61—44no—
115C2×C4×C61—28no—
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×C61C2×D412yes—
130C2×C4×C61#4112yes—
131C2×Dic61—21no—
132C2×Dic61—21no—
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×Dic61—21no—
153C2×Dic61—44no—
154C2×Dic61—44no—
155C2×Dic61C2×D412yes—
156C2×Dic61C2×D412yes—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—22no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61#12614yescomplemented
171C22×C61C22×D411yescharacteristic
172C22×C61C2×#4111yescharacteristic
173C22×C61C2×#4111yescharacteristic
174C22×C61C2×#4111yescharacteristic
175C22×C61C2×#4111yescharacteristic
176C22×C61H(5,𝔽2)11yescharacteristic
177C22×C612−1+411yescharacteristic
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183Dic61—22no—
184Dic61—22no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189Dic61—41no—
190Dic61—41no—
191#2481—611nomaximal, Sylow
192C2×C61—24no—
193C2×C61—81no—
194C2×C61#52511yescharacteristic
195C2×C61C2×#12611yescharacteristic
196C2×C61#53911yescharacteristic
197C2×C61#54611yescharacteristic
198C2×C61#54811yescharacteristic
199C2×C61#55211yescharacteristic
200C2×C61#55311yescharacteristic
201C2×#126—611no—
202C22×C4⋊C4—611no—
203#400—611no—
204#400—611no—
205#397—611no—
206#396—611no—
207#388—611no—
208#387—611no—
209#387—611no—
210#386—611no—
211#386—611no—
212#386D6111yescharacteristic
213#385—611no—
214#380—611no—
215C4×C22⋊C4—611no—
216C61#248111yescharacteristic, complemented, Sylow
217C22×D4C2×D6111yescharacteristic
218C23×C4—611no—
219C23×C4—611no—
220C23×C4C2×D6111yescharacteristic
221#126—1224no—
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⋊C4—611no—
230C2×C4⋊C4—1224no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—611no—
236C2×C22⋊C4—611no—
237C2×C22⋊C4C2×D6111yescharacteristic
238C2×C22⋊C4C2×D6111yescharacteristic
239C2×C22⋊C4C2×D6111yescharacteristic
240C2×C42—611no—
241C2×C42—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95—611no—
246#95—611no—
247#95—611no—
248#95—611no—
249#95—611no—
250#95—611no—
251#95—611no—
252#95C2×D6111yescharacteristic
253#95C2×D6111yescharacteristic
254C24C22×D6111yescharacteristic
255C24C22×D6111yescharacteristic
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—1222no—
273C22×C4—1222no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4C22×D6111yescharacteristic
277C22×C4C22×D6111yescharacteristic
278C22×C4C22×D6111yescharacteristic
279C22×C4C22×D6111yescharacteristic
280C22×C4C22×D6111yescharacteristic
281C4⋊C4—614no—
282C4⋊C4—1222no—
283C4⋊C4—1222no—
284C4⋊C4—1222no—
285C4⋊C4—1222no—
286C4⋊C4—1222no—
287C4⋊C4—1222no—
288C4⋊C4—2441no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—1222no—
293C22⋊C4—1222no—
294C22⋊C4—1222no—
295C22⋊C4—1222no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C42—1222no—
299C42—2441no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23#1175822212yes—
312C23#1175822412yes—
313C23#1175822412yes—
314C23C23×D6111yescharacteristic
315D4—44no—
316C2×C4—28no—
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×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—2444no—
355C2×C4—2444no—
356C2×C4D4×D6112yes—
357C2×C4#1175822412yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22#1451977014yescomplemented
372C22C2×D4×D6111yescharacteristic
373C22C2×#1175822411yescharacteristic
374C22C2×#1175822411yescharacteristic
375C22C2×#1175822411yescharacteristic
376C22C2×#1175822211yescharacteristic
377C22#1451982311yescharacteristic
378C22#1451982411yescharacteristic
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—1222no—
385C4—1222no—
386C4—2441no—
387C4—2441no—
388C4—2441no—
389C4—2441no—
390C4—2441no—
391C4—2441no—
392C2—24no—
393C2—81no—
394C2#1684026811yescharacteristic
395C2C2×#1451977011yescharacteristic
396C2#1684035611yescharacteristic
397C2#1684040811yescharacteristic
398C2#1684041811yescharacteristic
399C2#1684045211yescharacteristic
400C2#1684046411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2481
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14519770C2semidirect
2. C22×C4⋊Dic61C2semidirect
3. #16839704C2semidirect
4. #16839702C2semidirect
5. #16839687C2semidirect
6. #16839685C2semidirect
7. #16839655C2semidirect
8. #16839649C2semidirect
9. #16839647C2semidirect
12. #16839635C2semidirect
13. #16839620C2semidirect
14. C22⋊C4×Dic61C2semidirect
92. C4⋊Dic61D4semidirect
170. C22×C61#126semidirect
216. C61#2481semidirect
371. C22#14519770semidirect