Finite Group Databasebeta

← #21452189

Subgroups — #21452189

Order 7808.

592 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519756C211yesmaximal, characteristic, complemented
2C2×#14519755C211yesmaximal, characteristic, complemented
3C2×#14519753C211yesmaximal, characteristic, complemented
4#16839685C211yesmaximal, characteristic, complemented
5#16839685C211yesmaximal, characteristic, complemented
6#16839684C211yesmaximal, characteristic, complemented
7#16839684C211yesmaximal, characteristic, complemented
8#16839682C211yesmaximal, characteristic, complemented
9#16839681C211yesmaximal, characteristic, complemented
10#16839662C211yesmaximal, characteristic
11#16839661C211yesmaximal, characteristic, complemented
12#16839657C211yesmaximal, characteristic, complemented
13#16839641C211yesmaximal, characteristic
14#16839638C211yesmaximal, characteristic
15C2×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19#14519756—24no—
20#14519755—24no—
21#14519753—24no—
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
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
56C23×D61C2311yescharacteristic
57C2×Q8×C61—22no—
58C2×Q8×C61—22no—
59C2×Q8×C61—41no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—41no—
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—41no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61Q814yescomplemented
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—41no—
82C2×Dic122—22no—
83C2×Dic122—22no—
84C2×Dic122—41no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61D414yescomplemented
88C22⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C22⋊Dic61—22no—
91C22⋊Dic61—22no—
92C22⋊Dic61—41no—
93#11758198—22no—
94#11758198—22no—
95#11758198—22no—
96#11758198—22no—
97#11758198—41no—
98C4⋊Dic61—22no—
99C4⋊Dic61—22no—
100C4⋊Dic61—41no—
101#11758196—22no—
102#11758196—22no—
103#11758196—22no—
104#11758196—22no—
105#11758196—41no—
106#11758196—41no—
107#11758196D414yescomplemented
108C4×Dic61—41no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61C2×Q812yes—
116C23×C61C2411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61C2×Q812yes—
124Q8×C61—44no—
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—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—44no—
140C2×C4×C61C2×D412yes—
141C2×C4×C61C2×D412yes—
142C2×C4×C61C2×D412yes—
143C2×C4×C61C2×D412yes—
144C22⋊D61—44no—
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—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61C2×D412yes—
164C2×Dic61C2×D412yes—
165C2×Dic61C2×Q812yes—
166C4×D61—44no—
167Dic122—44no—
168C22×C61—22no—
169C22×C61—22no—
170C22×C61—22no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61C22×D411yescharacteristic
176C22×C61C22×D411yescharacteristic
177C22×C61C22×Q811yescharacteristic
178C22×C61H(5,𝔽2)11yescharacteristic
179C22×C61H(5,𝔽2)11yescharacteristic
180C22×C612−1+411yescharacteristic
181C22×C612−1+411yescharacteristic
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C4×C61—22no—
190C4×C61—22no—
191C4×C61—22no—
192C4×C61—22no—
193C4×C61—41no—
194C4×C61—41no—
195Dic61—22no—
196Dic61—22no—
197Dic61—22no—
198Dic61—41no—
199Dic61—41no—
200Dic61—41no—
201Dic61—41no—
202#2683—611nomaximal, Sylow
203C2×C61—42no—
204C2×C61#53711yescharacteristic
205C2×C61#53711yescharacteristic
206C2×C61#54311yescharacteristic
207C2×C61D4211yescharacteristic
208C2×C61D4×Q811yescharacteristic
209C2×C61D4×Q811yescharacteristic
210C2×C61#56311yescharacteristic
211D61—42no—
212C2×C22⋊Q8—611no—
213C2×C22⋊Q8—611no—
214C2×C22⋊Q8—611no—
215C2×C22⋊Q8D6111yescharacteristic, complemented
216#396—611no—
217#396—611no—
218#396—611no—
219#396—611no—
220#395—611no—
221#395—611no—
222#390—611no—
223#389—611no—
224#389—611no—
225#386—611no—
226#386—611no—
227C61#268311yescharacteristic, complemented, Sylow
228C22×Q8—611no—
229C22×Q8C2×D6111yescharacteristic
230C22×D4—611no—
231C23×C4—611no—
232C23×C4C2×D6111yescharacteristic
233C22⋊Q8—24no—
234C22⋊Q8—1224no—
235C22⋊Q8—1224no—
236C22⋊Q8—1224no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4C2×D6111yescharacteristic
248C2×C4⋊C4C2×D6111yescharacteristic
249C2×C4⋊C4C2×D6111yescharacteristic
250C2×C22⋊C4—611no—
251C2×C22⋊C4—611no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—611no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—611no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4C2×D6111yescharacteristic
259C2×C22⋊C4C2×D6111yescharacteristic
260C2×C42—611no—
261#95—611no—
262#95—611no—
263#95—611no—
264#95—611no—
265#95—611no—
266#95—611no—
267C24—611no—
268C24C22×D6111yescharacteristic
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—1222no—
273C2×Q8—1222no—
274C2×Q8—2441no—
275C2×D4—614no—
276C2×D4—2441no—
277C2×D4—2441no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—41no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—2441no—
291C22×C4C22×D6111yescharacteristic
292C22×C4C22×D6111yescharacteristic
293C22×C4C22×D6111yescharacteristic
294C22×C4C22×D6111yescharacteristic
295C22×C4C22×D6111yescharacteristic
296C22×C4C22×D6111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—614no—
300C4⋊C4—1222no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—1222no—
304C4⋊C4—1222no—
305C4⋊C4—1222no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C4⋊C4—2441no—
309C4⋊C4C22⋊D6114yescomplemented
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—1222no—
313C22⋊C4—1222no—
314C22⋊C4—1222no—
315C22⋊C4—1222no—
316C22⋊C4—1222no—
317C22⋊C4—1222no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C42—2441no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—612no—
328C23—1221no—
329C23—1221no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23Q8×D6112yes—
335C23C23×D6111yescharacteristic
336Q8—44no—
337Q8—2444no—
338D4—2444no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—44no—
354C2×C4—612no—
355C2×C4—612no—
356C2×C4—612no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—2444no—
376C2×C4D4×D6112yes—
377C2×C4C2×C22⋊D6112yes—
378C2×C4C2×C22⋊D6112yes—
379C2×C4C2×C22⋊D6112yes—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—1222no—
388C22—1222no—
389C22—1222no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22C2×D4×D6111yescharacteristic
395C22C22×C22⋊D6111yescharacteristic
396C22C2×Q8×D6111yescharacteristic
397C22#1451982211yescharacteristic
398C22#1451982311yescharacteristic
399C22#1451982411yescharacteristic
400C22#1451982511yescharacteristic
401C4—22no—
402C4—22no—
403C4—22no—
404C4—22no—
405C4—41no—
406C4—41no—
407C4—1222no—
408C4—1222no—
409C4—1222no—
410C4—2441no—
411C4—2441no—
412C4—2441no—
413C4—2441no—
414C2—42no—
415C2—2442no—
416C2#1684034011yescharacteristic
417C2#1684034211yescharacteristic
418C2#1684038711yescharacteristic
419C2D4×C22⋊D6111yescharacteristic
420C2#1684042511yescharacteristic
421C2Q8×C22⋊D6111yescharacteristic
422C2#1684051311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C22⋊Q8×C61C2
hypercenterC2×C22⋊Q8D61
hypocenterC61#2683
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×#14519756C2semidirect
2. C2×#14519755C2semidirect
3. C2×#14519753C2semidirect
4. #16839685C2semidirect
5. #16839685C2semidirect
6. #16839684C2semidirect
7. #16839684C2semidirect
8. #16839682C2semidirect
9. #16839681C2semidirect
11. #16839661C2semidirect
12. #16839657C2semidirect
15. C2×C22⋊Q8×C61C2semidirect
71. C2×C22⋊D61Q8semidirect
87. C4⋊C4×C61D4semidirect
107. #11758196D4semidirect
215. C2×C22⋊Q8D61semidirect
227. C61#2683semidirect
309. C4⋊C4C22⋊D61semidirect