Finite Group Databasebeta

← #21457388

Subgroups — #21457388

Order 7808.

472 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×#14519806C211yesmaximal, characteristic, complemented
2C2×Q16×D61C211yesmaximal, characteristic, complemented
3#16840427C211yesmaximal, characteristic, complemented
4#16840420C211yesmaximal, characteristic
5#16840017C211yesmaximal, characteristic, complemented
6#16839988C211yesmaximal, characteristic, complemented
7#16839981C211yesmaximal, characteristic, complemented
8#16839969C211yesmaximal, characteristic, complemented
9#16839921C211yesmaximal, characteristic, complemented
10#16839916C211yesmaximal, characteristic, complemented
11#16839916C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839870C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#497C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519806—24no—
21C2×Dic244C2211yescharacteristic
22C2×#11758202C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758202C2211yescharacteristic
25Q16×D61—24no—
26C2×#11758200C2211yescharacteristic
27C2×#11758189C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519776—21no—
30#14519763—21no—
31#14519755—21no—
32#14519755—21no—
33#14519754—21no—
34#14519753C2211yescharacteristic
35#14519753C2211yescharacteristic
36#14519753C2211yescharacteristic
37#14519750—21no—
38#14519748C2211yescharacteristic
39C4×Dic122C2211yescharacteristic
40C4×Dic122C2211yescharacteristic
41C4×D244C2211yescharacteristic
42#14519739—21no—
43#14519737—21no—
44#14519709C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519701C2211yescharacteristic
51#14519698C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519689C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic
56C2×SD16×C61C2211yescharacteristic
57C2×SD16×C61C2211yescharacteristic
58C4⋊Q8×C61C2211yescharacteristic
59#124×C61C2211yescharacteristic
60#97×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68Q8×D61—22no—
69Q8×D61—22no—
70Q8×D61—22no—
71Q8×D61—41no—
72Q8×D61—41no—
73Q8×D61—41no—
74#11758224—22no—
75#11758224—41no—
76C2×D244D411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61C2311yescharacteristic
81C2×C4×D61C2311yescharacteristic
82C2×Dic122—21no—
83C2×Dic122—21no—
84C2×Dic122—21no—
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87Q16×C61—22no—
88Q16×C61—41no—
89SD16×C61—22no—
90SD16×C61—41no—
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C42×C61C2311yescharacteristic
98C22⋊Dic61—21no—
99#11758202—22no—
100#11758202—22no—
101#11758202—22no—
102#11758200—22no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198D411yescharacteristic
107#11758198D411yescharacteristic
108C4⋊Dic61D411yescharacteristic
109C4⋊Dic61C2311yescharacteristic
110C4⋊Dic61C2311yescharacteristic
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116C4×Dic61—21no—
117C4×Dic61—21no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120Dic244D414yescomplemented
121#11758189—22no—
122C8×D61—22no—
123C23×C61—21no—
124C22×D61C2×D411yescharacteristic
125C22×D61C2×D411yescharacteristic
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131Q8×C61—21no—
132D4×C61—21no—
133D4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2411yescharacteristic
140C22⋊D61—42no—
141C22⋊D61—42no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—42no—
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149D244—22no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—42no—
157Dic122—21no—
158Dic122—21no—
159Dic122—42no—
160Dic122—42no—
161Dic122—42no—
162Dic122C2×D412yes—
163Dic122C2×D412yes—
164C8×C61—21no—
165C8×C61C2×D412yes—
166#92418—21no—
167#92418—21no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61C22×D411yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61#13712yescomplemented
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61C22×D411yescharacteristic
184C4×C61H(5,𝔽2)11yescharacteristic
185Dic61—22no—
186Dic61—22no—
187Dic61—21no—
188Dic61—21no—
189Dic61—41no—
190Dic61—41no—
191#3270—611nomaximal, Sylow
192C2×C61—81no—
193C2×C61D4211yescharacteristic
194C2×C61C2×#13711yescharacteristic
195C2×C61#57811yescharacteristic
196D61—22no—
197D61—41no—
198C2×#137—611no—
199C22×Q16—611no—
200D4×Q8—611no—
201#548—611no—
202#497D6111yescharacteristic, complemented
203#470—611no—
204#465—611no—
205#464—611no—
206#462—611no—
207#452—611no—
208#451—611no—
209#451—611no—
210#448—611no—
211#441—611no—
212#435—611no—
213C61#327011yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C22×Q8—611no—
216C22×Q8—611no—
217C22×Q8—611no—
218#137—1224no—
219C2×Q16—611no—
220C2×Q16—611no—
221C2×Q16—611no—
222C2×Q16—611no—
223C2×Q16—1224no—
224C2×Q16C2×D6111yescharacteristic
225C2×Q16C2×D6111yescharacteristic
226C2×SD16—611no—
227C2×SD16C2×D6111yescharacteristic
228C2×SD16C2×D6111yescharacteristic
229C2×M16—611no—
230C22×C8—611no—
231C4⋊Q8—1221no—
232C4⋊Q8C2×D6111yescharacteristic
233#124—1221no—
234#124C2×D6111yescharacteristic
235C22⋊Q8—611no—
236C22⋊Q8—611no—
237C22⋊Q8—611no—
238C22⋊Q8—1221no—
239C22⋊Q8—1221no—
240C22⋊Q8—1221no—
241#121—611no—
242#121—1221no—
243C4×Q8—611no—
244C4×Q8—611no—
245C4×D4—611no—
246C4×D4—1221no—
247C4×D4—1221no—
248#106—611no—
249C4⋊C8—611no—
250#103—611no—
251#103—611no—
252#103—611no—
253#103—611no—
254#103—611no—
255#102—611no—
256C22⋊C8—611no—
257C22⋊C8—611no—
258#97C2×D6111yescharacteristic
259#41—1222no—
260#41—2441no—
261C2×Q8—611no—
262C2×Q8—611no—
263C2×Q8—1221no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×Q8—1222no—
267C2×Q8—1222no—
268C2×Q8—1222no—
269C2×Q8—2441no—
270C2×Q8—2441no—
271C2×Q8—2441no—
272C2×Q8C22×D6111yescharacteristic
273C2×Q8C22×D6111yescharacteristic
274C2×Q8C22×D6111yescharacteristic
275C2×D4—611no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4C22×D6111yescharacteristic
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285Q16—22no—
286Q16—41no—
287Q16—614no—
288Q16—1222no—
289Q16—1222no—
290Q16—1222no—
291SD16—22no—
292SD16—41no—
293SD16—1222no—
294M16—1222no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8—1222no—
298C2×C8C22×D6111yescharacteristic
299C2×C8C22×D6111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—611no—
303C4⋊C4—611no—
304C4⋊C4—611no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—611no—
313C22⋊C4—611no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C42—1221no—
319C42—1221no—
320C42C22×D6111yescharacteristic
321C23—21no—
322C23—611no—
323C23—611no—
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—612no—
331Q8—612no—
332Q8—1221no—
333Q8—1221no—
334Q8—2442no—
335Q8—2442no—
336Q8—2442no—
337D4—21no—
338D4—21no—
339D4—1222no—
340D4—2442no—
341D4—2442no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—611no—
346C2×C4—611no—
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—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4D4×D6111yescharacteristic
360C2×C4D4×D6111yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—1221no—
364C8—1221no—
365C8D4×D6112yes—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—612no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—1221no—
382C4—1221no—
383C4—1222no—
384C4—1222no—
385C4—2441no—
386C4—2441no—
387C4C2×D4×D6111yescharacteristic
388C4#1451982211yescharacteristic
389C2—81no—
390C2—1222no—
391C2—2441no—
392C2#1684039711yescharacteristic
393C2#137×D6111yescharacteristic
394C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#497C2
socleC22×C61C22×D4
hypercenter#497D61
hypocenterC61#3270
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
2. C2×Q16×D61C2semidirect
3. #16840427C2semidirect
5. #16840017C2semidirect
6. #16839988C2semidirect
7. #16839981C2semidirect
8. #16839969C2semidirect
9. #16839921C2semidirect
10. #16839916C2semidirect
11. #16839916C2semidirect
12. #16839899C2semidirect
13. #16839870C2semidirect
14. #16839835C2semidirect
15. C61×#497C2semidirect
120. Dic244D4semidirect
177. C2×D61#137semidirect
202. #497D61semidirect
213. C61#3270semidirect