Finite Group Databasebeta

← #21449518

Subgroups — #21449518

Order 7808.

608 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519775C211yesmaximal, characteristic, complemented
2C2×#14519754C211yesmaximal, characteristic
3C22×#11758196C211yesmaximal, characteristic
4#16839693C211yesmaximal, characteristic, complemented
5#16839692C211yesmaximal, characteristic, complemented
6#16839682C211yesmaximal, characteristic, complemented
7#16839681C211yesmaximal, characteristic, complemented
8#16839657C211yesmaximal, characteristic, complemented
9#16839657C211yesmaximal, characteristic, complemented
10#16839635C211yesmaximal, characteristic
11#16839634C211yesmaximal, characteristic
12#16839631C211yesmaximal, characteristic, complemented
13#16839620C211yesmaximal, characteristic
14C22⋊C4×Dic61C211yesmaximal, characteristic
15C2×C22⋊Q8×C61C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18C23×Dic61C2211yescharacteristic
19#14519775—24no—
20#14519754—24no—
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196—24no—
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758196C2211yescharacteristic
34C2×#11758196C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C4×Dic61C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C22×Q8×C61C2211yescharacteristic
48C23×C4×C61C2211yescharacteristic
49C22⋊Q8×C61—24no—
50C2×C4⋊C4×C61C2211yescharacteristic
51C2×C4⋊C4×C61C2211yescharacteristic
52C2×C4⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C2×Q8×C61—22no—
57C2×Q8×C61—22no—
58C2×Q8×C61—41no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—41no—
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—41no—
73C22×Dic61Q814yescomplemented
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C2×Dic122—22no—
83C2×Dic122—22no—
84C2×Dic122—41no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—22no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61D414yes—
90C22⋊Dic61—22no—
91C22⋊Dic61Q814yescomplemented
92C4⋊Dic61—22no—
93#11758196—22no—
94#11758196—22no—
95#11758196—22no—
96#11758196—22no—
97#11758196—22no—
98#11758196—22no—
99#11758196—22no—
100#11758196—22no—
101#11758196—22no—
102#11758196—41no—
103#11758196—41no—
104#11758196D414yes—
105C4×Dic61—22no—
106C4×Dic61—22no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61C2×D412yes—
112C23×C61C2×Q812yes—
113C23×C61C2×Q812yes—
114C23×C61C2411yescharacteristic
115Q8×C61—44no—
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×C61—44no—
132C2×C4×C61C2×D412yes—
133C2×C4×C61C2×D412yes—
134C2×C4×C61C2×D412yes—
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—28no—
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×Dic61C2×D412yes—
155C2×Dic61C2×D412yes—
156C2×Dic61C2×Q812yes—
157C2×Dic61C2×Q812yes—
158C2×Dic61C2×Q812yes—
159C2×Dic61C2×Q812yes—
160C2×Dic61#4112yes—
161Dic122—44no—
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61C4⋊Q814yescomplemented
169C22×C61C22×D411yescharacteristic
170C22×C61C22×D411yescharacteristic
171C22×C61C22×Q811yescharacteristic
172C22×C61C22×Q811yescharacteristic
173C22×C61C2×#4111yescharacteristic
174C22×C61H(5,𝔽2)11yescharacteristic
175C22×C612−1+411yescharacteristic
176C4×C61—22no—
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—41no—
182Dic61—22no—
183Dic61—22no—
184Dic61—22no—
185Dic61—22no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189Dic61C22⋊Q814yescomplemented
190#2440—611nomaximal, Sylow
191C2×C61—24no—
192C2×C61C2×C22⋊Q811yescharacteristic
193C2×C61C2×C4⋊Q811yescharacteristic
194C2×C61#54411yescharacteristic
195C2×C61D4211yescharacteristic
196C2×C61#54711yescharacteristic
197C2×C61D4×Q811yescharacteristic
198C2×C61#55411yescharacteristic
199C2×C4⋊Q8—611no—
200C2×C22⋊Q8—611no—
201C2×C22⋊Q8D6111yescharacteristic
202C22×C4⋊C4—611no—
203#398—611no—
204#398—611no—
205#395—611no—
206#395—611no—
207#389—611no—
208#389—611no—
209#385—611no—
210#385—611no—
211#384—611no—
212#380—611no—
213C4×C22⋊C4—611no—
214C61#244011yescharacteristic, complemented, Sylow
215C22×Q8—611no—
216C22×Q8C2×D6111yescharacteristic
217C23×C4—611no—
218C23×C4—611no—
219C23×C4C2×D6111yescharacteristic
220C4⋊Q8—1224no—
221C22⋊Q8—24no—
222C22⋊Q8—1224no—
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—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1224no—
237C2×C4⋊C4C2×D6111yescharacteristic
238C2×C4⋊C4C2×D6111yescharacteristic
239C2×C4⋊C4C2×D6111yescharacteristic
240C2×C22⋊C4—611no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4C2×D6111yescharacteristic
243C2×C22⋊C4C2×D6111yescharacteristic
244C2×C42—611no—
245C2×C42—611no—
246#95—611no—
247#95—611no—
248#95—611no—
249#95—611no—
250#95—611no—
251#95—611no—
252#95—611no—
253#95—611no—
254C24C22×D6111yescharacteristic
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—1222no—
259C2×Q8—1222no—
260C2×Q8—2441no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—611no—
265C22×C4—614no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—2441no—
278C22×C4C22×D6111yescharacteristic
279C22×C4C22×D6111yescharacteristic
280C22×C4C22×D6111yescharacteristic
281C22×C4C22×D6111yescharacteristic
282C22×C4C22×D6111yescharacteristic
283C22×C4C22×D6111yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—614no—
288C4⋊C4—1222no—
289C4⋊C4—1222no—
290C4⋊C4—1222no—
291C4⋊C4—1222no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—1222no—
295C4⋊C4—1222no—
296C4⋊C4—1222no—
297C4⋊C4—1222no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C22⋊C4—22no—
301C22⋊C4—614no—
302C22⋊C4—1222no—
303C22⋊C4C22⋊D6114yes—
304C42—1222no—
305C42—1222no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23Q8×D6112yes—
311C23Q8×D6112yes—
312C23C2×C22⋊D6112yes—
313C23C23×D6111yescharacteristic
314Q8—44no—
315Q8—2444no—
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—21no—
331C2×C4—44no—
332C2×C4—612no—
333C2×C4—612no—
334C2×C4—612no—
335C2×C4—612no—
336C2×C4—612no—
337C2×C4—612no—
338C2×C4—612no—
339C2×C4—1228no—
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—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—2444no—
358C2×C4D4×D6112yes—
359C2×C4C2×C22⋊D6112yes—
360C2×C4C2×C22⋊D6112yes—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22#1451977514yescomplemented
368C22C2×D4×D6111yescharacteristic
369C22C22×C22⋊D6111yescharacteristic
370C22C2×Q8×D6111yescharacteristic
371C22C2×Q8×D6111yescharacteristic
372C22#41×D6111yescharacteristic
373C22#1451982211yescharacteristic
374C22#1451982411yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—614no—
382C4—1222no—
383C4—1222no—
384C4—1222no—
385C4—1222no—
386C4—2441no—
387C4—2441no—
388C4—2441no—
389C2—24no—
390C2C22⋊Q8×D6111yescharacteristic
391C2C2×#1451977511yescharacteristic
392C2#1684039111yescharacteristic
393C2D4×C22⋊D6111yescharacteristic
394C2#1684041111yescharacteristic
395C2#1684042511yescharacteristic
396C2#1684046611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C22⋊Q8×C61C2
hypercenterC2×C22⋊Q8D61
hypocenterC61#2440
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14519775C2semidirect
4. #16839693C2semidirect
5. #16839692C2semidirect
6. #16839682C2semidirect
7. #16839681C2semidirect
8. #16839657C2semidirect
9. #16839657C2semidirect
12. #16839631C2semidirect
73. C22×Dic61Q8semidirect
91. C22⋊Dic61Q8semidirect
168. C22×C61C4⋊Q8semidirect
189. Dic61C22⋊Q8semidirect
214. C61#2440semidirect
367. C22#14519775semidirect