Finite Group Databasebeta

← #21459469

Subgroups — #21459469

Order 7808.

1492 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519825C211yesmaximal, characteristic, complemented
2C22×Q8×D61C211yesmaximal, characteristic, complemented
3#16840427C213yesmaximal, complemented
4Q8×C22⋊D61C211yesmaximal, characteristic, complemented
5#16840425C213yesmaximal, complemented
6#16840424C211yesmaximal, characteristic, complemented
7#16840423C211yesmaximal, characteristic, complemented
8#16840422C213yesmaximal, complemented
9#16840421C213yesmaximal, complemented
10#16840337C213yesmaximal, complemented
11#16840335C213yesmaximal, complemented
12#16840275C213yesmaximal, complemented
13#16840271C213yesmaximal, complemented
14#16840238C211yesmaximal, characteristic, complemented
15D4×Q8×C61C211yesmaximal, characteristic, complemented
16#14519825—28no—
17C2×#11758226C2213yes—
18C2×#11758226C2211yescharacteristic, complemented
19C2×#11758222C2213yes—
20C2×#11758222C2213yescomplemented
21C22×Dic122C2213yes—
22C2×Q8×D61—28no—
23C2×Q8×D61C2213yes—
24C2×Q8×D61C2213yes—
25C2×Q8×D61C2211yescharacteristic
26C2×Q8×D61C2211yescharacteristic
27C2×Q8×D61C2213yescomplemented
28C22×C4×D61C2213yes—
29#14519776C2216yescomplemented
30#14519775C2213yescomplemented
31#14519766C2213yescomplemented
32#14519765C2213yescomplemented
33#14519763C2216yescomplemented
34#14519762C2213yes—
35#14519762C2216yes—
36#14519759C2213yes—
37#14519757C2213yescomplemented
38#14519756C2213yescomplemented
39#14519755C2213yes—
40#14519755C2216yescomplemented
41#14519755C2216yescomplemented
42#14519754C2213yes—
43#14519753C2213yes—
44#14519753C2213yescomplemented
45#14519752C2213yes—
46#14519751C2213yes—
47#14519750C2213yes—
48#14519749C2213yes—
49#14519747C2213yes—
50#14519745C2211yescharacteristic
51Q8×Dic61C2211yescharacteristic, complemented
52C4×Dic122C2213yescomplemented
53#14519742C2213yescomplemented
54C4×D244C2213yes—
55#14519739C2216yes—
56C4×C22⋊D61C2213yes—
57C4×C22⋊D61C2213yes—
58#14519737C2216yes—
59#14519735C2213yes—
60#14519734C2213yes—
61C22×Q8×C61C2211yescharacteristic
62C22×Q8×C61C2211yescharacteristic, complemented
63C4⋊Q8×C61C2213yescomplemented
64C22⋊Q8×C61C2213yes—
65C22⋊Q8×C61C2213yescomplemented
66C4×Q8×C61C2211yescharacteristic, complemented
67C4×D4×C61C2213yes—
68C23×D61C2311yescharacteristic
69C2×Q8×C61—24no—
70C2×Q8×C61—24no—
71C2×Q8×C61C2313yes—
72C2×Q8×C61C2313yes—
73C2×Q8×C61C2311yescharacteristic
74C2×D4×C61C2311yescharacteristic
75C22×C4×C61C2313yes—
76C22×C4×C61C2313yes—
77C2×C22⋊D61C2311yescharacteristic
78C2×C22⋊D61C2313yes—
79C2×C22⋊D61C2313yes—
80C2×C22⋊D61C2311yescharacteristic
81C22×Dic61C2313yes—
82#11758226—24no—
83#11758226—212no—
84Q8×D61—24no—
85Q8×D61—212no—
86Q8×D61—212no—
87Q8×D61—212no—
88Q8×D61D418yescomplemented
89#11758222—212no—
90#11758222—212no—
91C2×D244C2313yes—
92C2×D244C2313yes—
93C2×D244C2313yes—
94C2×C4×D61—212no—
95C2×C4×D61C2313yes—
96C2×C4×D61C2313yes—
97C2×C4×D61C2313yes—
98C2×C4×D61C2313yes—
99C2×C4×D61C2316yes—
100C2×C4×D61C2313yes—
101C2×Dic122—212no—
102C2×Dic122C2316yes—
103C2×Dic122C2313yes—
104C2×Dic122C2313yes—
105C2×Dic122C2313yes—
106C4⋊C4×C61C2313yes—
107C4⋊C4×C61C2313yes—
108C4⋊C4×C61C2316yes—
109C22⋊C4×C61C2313yes—
110C22⋊C4×C61C2313yes—
111C42×C61C2313yes—
112C22⋊Dic61C2311yescharacteristic
113C22⋊Dic61C2313yes—
114#11758198C2311yescharacteristic
115#11758198C2313yes—
116#11758198C2316yes—
117#11758198C2313yes—
118#11758198C2313yes—
119#11758198C2316yes—
120#11758198C2311yescharacteristic
121#11758198C2313yes—
122C4⋊Dic61C2313yes—
123C4⋊Dic61C2313yes—
124#11758196C2313yes—
125#11758196C2313yes—
126#11758196C2316yes—
127#11758196C2313yes—
128#11758196C2313yes—
129C4×Dic61C2313yes—
130C4×Dic61C2316yes—
131C23×C61C2411yescharacteristic
132C23×C61C2411yescharacteristic
133C22×D61—22no—
134C22×D61—22no—
135C22×D61—22no—
136C22×D61C2413yes—
137C22×D61C2411yescharacteristic
138C22×D61C2411yescharacteristic
139Q8×C61—26no—
140Q8×C61—26no—
141Q8×C61C2×D414yes—
142D4×C61—22no—
143C2×C4×C61—26no—
144C2×C4×C61—26no—
145C2×C4×C61C2413yes—
146C2×C4×C61C2411yescharacteristic
147C2×C4×C61C2413yes—
148C2×C4×C61C2413yes—
149C2×C4×C61C2413yes—
150C22⋊D61—26no—
151C22⋊D61—22no—
152C22⋊D61—22no—
153C22⋊D61—26no—
154C2×Dic61—26no—
155C2×Dic61C2411yescharacteristic
156C2×Dic61C2413yes—
157C2×Dic61C2411yescharacteristic
158C2×Dic61C2413yes—
159C2×Dic61C2413yes—
160D244—26no—
161D244—26no—
162D244—26no—
163C4×D61—26no—
164C4×D61—26no—
165C4×D61—26no—
166C4×D61—26no—
167C4×D61—212no—
168C4×D61C2×D4112yes—
169Dic122—26no—
170Dic122—212no—
171Dic122—26no—
172Dic122C2×D4112yes—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C612−1+412yescomplemented
179C22×C61C2511yescharacteristic
180C2×D61—28no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—23no—
186C2×D61—23no—
187C2×D61—23no—
188C2×D61C22×D412yes—
189C2×D612−1+412yescomplemented
190C4×C61—23no—
191C4×C61—23no—
192C4×C61—23no—
193C4×C61—21no—
194C4×C61C22×D416yes—
195Dic61—23no—
196Dic61—21no—
197Dic61—21no—
198Dic61—23no—
199Dic61C22×D416yes—
200#3486—611nomaximal, Sylow
201C2×C61—22no—
202C2×C61—41no—
203C2×C61C23×D411yescharacteristic
204C2×C61C2×2−1+411yescharacteristic
205C2×C61C2×2−1+411yescharacteristic
206D61—22no—
207D61—22no—
208D61—43no—
209C2×2−1+4—611no—
210C23×Q8—611no—
211D4×Q8—611no—
212D4×Q8—613no—
213D4×Q8—613no—
214D4×Q8D6111yescharacteristic, complemented
215#548—611no—
216#548—613no—
217#548—611no—
218#548—613no—
219#536—613no—
220#536—613no—
221#525—613no—
222#525—613no—
223#519—611no—
224C61#348611yescharacteristic, complemented, Sylow
2252−1+4—1228no—
226C2×#41—613no—
227C2×#41—611no—
228C2×#41—613no—
229C2×#41—613no—
230C22×Q8—611no—
231C22×Q8—613no—
232C22×Q8—613no—
233C22×Q8—611no—
234C22×Q8—613no—
235C22×Q8—613no—
236C22×Q8—1228no—
237C22×Q8C2×D6111yescharacteristic
238C22×Q8C2×D6111yescharacteristic, complemented
239C23×C4—613no—
240C4⋊Q8—613no—
241C4⋊Q8—616no—
242C4⋊Q8C2×D6113yescomplemented
243#124—613no—
244#124—616no—
245#124—613no—
246#123—616no—
247#123—613no—
248#123—613no—
249C22⋊Q8—613no—
250C22⋊Q8—613no—
251C22⋊Q8—613no—
252C22⋊Q8—613no—
253C22⋊Q8—616no—
254C22⋊Q8—616no—
255C22⋊Q8—613no—
256C22⋊Q8—613no—
257C22⋊Q8C2×D6113yes—
258C22⋊Q8C2×D6113yescomplemented
259#121—613no—
260#121—613no—
261#121—613no—
262#121—613no—
263#120—611no—
264#120—613no—
265C4×Q8—611no—
266C4×Q8—613no—
267C4×Q8—613no—
268C4×Q8C2×D6111yescharacteristic, complemented
269C4×D4—613no—
270C4×D4—613no—
271C4×D4—616no—
272C4×D4—616no—
273C4×D4—613no—
274C4×D4C2×D6113yes—
275#117—613no—
276#117—613no—
277C24—611no—
278#41—12212no—
279#41—12212no—
280#41—12212no—
281#41—1224no—
282C2×Q8—24no—
283C2×Q8—24no—
284C2×Q8—618no—
285C2×Q8—613no—
286C2×Q8—616no—
287C2×Q8—613no—
288C2×Q8—613no—
289C2×Q8—12212no—
290C2×Q8—12212no—
291C2×Q8—12212no—
292C2×Q8—12212no—
293C2×Q8—1224no—
294C2×Q8C22×D6113yes—
295C2×Q8C22×D6113yes—
296C2×Q8C22×D6111yescharacteristic
297C2×D4—611no—
298C2×D4—613no—
299C2×D4—611no—
300C2×D4—613no—
301C2×D4—613no—
302C2×D4—613no—
303C2×D4—613no—
304C2×D4C22×D6111yescharacteristic
305C22×C4—613no—
306C22×C4—613no—
307C22×C4—613no—
308C22×C4—613no—
309C22×C4—616no—
310C22×C4—613no—
311C22×C4—613no—
312C22×C4—12212no—
313C22×C4C22×D6113yes—
314C22×C4C22×D6113yes—
315C4⋊C4—613no—
316C4⋊C4—613no—
317C4⋊C4—616no—
318C4⋊C4—613no—
319C4⋊C4—613no—
320C4⋊C4—613no—
321C4⋊C4—613no—
322C4⋊C4C22×D6113yes—
323C4⋊C4C22×D6116yes—
324C4⋊C4C22×D6113yes—
325C22⋊C4—611no—
326C22⋊C4—613no—
327C22⋊C4—613no—
328C22⋊C4—611no—
329C22⋊C4—613no—
330C22⋊C4—611no—
331C22⋊C4—613no—
332C22⋊C4—616no—
333C22⋊C4—616no—
334C22⋊C4—613no—
335C22⋊C4C22×D6113yes—
336C22⋊C4C22×D6113yes—
337C42—616no—
338C42—613no—
339C42C22×D6113yes—
340C23—611no—
341C23—611no—
342C23—613no—
343C23—1222no—
344C23—1222no—
345C23—1222no—
346C23C23×D6111yescharacteristic
347C23C23×D6111yescharacteristic
348Q8—26no—
349Q8—26no—
350Q8—6112no—
351Q8—12212no—
352Q8—1226no—
353Q8—1226no—
354Q8D4×D6114yes—
355D4—22no—
356D4—1226no—
357D4—1226no—
358D4—1226no—
359D4—1222no—
360D4—1222no—
361D4—1226no—
362D4—1226no—
363C2×C4—26no—
364C2×C4—26no—
365C2×C4—613no—
366C2×C4—6112no—
367C2×C4—611no—
368C2×C4—613no—
369C2×C4—613no—
370C2×C4—611no—
371C2×C4—1226no—
372C2×C4—12212no—
373C2×C4—1226no—
374C2×C4—1226no—
375C2×C4—1226no—
376C2×C4—1226no—
377C2×C4C23×D6113yes—
378C2×C4C23×D6111yescharacteristic
379C2×C4C23×D6113yes—
380C2×C4C23×D6113yes—
381C2×C4C23×D6113yes—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—612no—
388C22—612no—
389C22—1228no—
390C22—1221no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—1223no—
395C22—1223no—
396C22—1223no—
397C22#1451982512yescomplemented
398C22C24×D6111yescharacteristic
399C4—23no—
400C4—23no—
401C4—23no—
402C4—21no—
403C4—616no—
404C4—1221no—
405C4—1223no—
406C4—1221no—
407C4—1223no—
408C4C2×D4×D6116yes—
409C2—22no—
410C2—41no—
411C2—1222no—
412C2—1222no—
413C2—2443no—
414C2C22×D4×D6111yescharacteristic
415C22−1+4×D6111yescharacteristic
416C2C2×#1451982511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingD4×Q8×C61C2
hypercenterD4×Q8D61
hypocenterC61#3486
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14519825C2semidirect
2. C22×Q8×D61C2semidirect
3. #16840427C2semidirect
4. Q8×C22⋊D61C2semidirect
5. #16840425C2semidirect
6. #16840424C2semidirect
7. #16840423C2semidirect
8. #16840422C2semidirect
9. #16840421C2semidirect
10. #16840337C2semidirect
11. #16840335C2semidirect
12. #16840275C2semidirect
13. #16840271C2semidirect
14. #16840238C2semidirect
15. D4×Q8×C61C2semidirect
18. C2×#11758226C22semidirect
20. C2×#11758222C22semidirect
27. C2×Q8×D61C22semidirect
29. #14519776C22semidirect
30. #14519775C22semidirect
31. #14519766C22semidirect
32. #14519765C22semidirect
33. #14519763C22semidirect
37. #14519757C22semidirect
38. #14519756C22semidirect
40. #14519755C22semidirect
41. #14519755C22semidirect
44. #14519753C22semidirect
51. Q8×Dic61C22semidirect
52. C4×Dic122C22semidirect
53. #14519742C22semidirect
62. C22×Q8×C61C22semidirect
63. C4⋊Q8×C61C22semidirect
65. C22⋊Q8×C61C22semidirect
66. C4×Q8×C61C22semidirect
88. Q8×D61D4semidirect
178. C22×C612−1+4semidirect
189. C2×D612−1+4semidirect
214. D4×Q8D61semidirect
224. C61#3486semidirect
238. C22×Q8C2×D61semidirect
242. C4⋊Q8C2×D61semidirect
258. C22⋊Q8C2×D61semidirect
268. C4×Q8C2×D61semidirect
397. C22#14519825semidirect