Finite Group Databasebeta

← #21457369

Subgroups — #21457369

Order 7808.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519809C211yesmaximal, characteristic, complemented
2C2×#14519800C211yesmaximal, characteristic, complemented
3#16840424C211yesmaximal, characteristic, complemented
4#16840415C211yesmaximal, characteristic, complemented
5#16840154C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16840002C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839927C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11#16839916C211yesmaximal, characteristic, complemented
12#16839910C211yesmaximal, characteristic, complemented
13#16839860C211yesmaximal, characteristic, complemented
14#16839832C211yesmaximal, characteristic, complemented
15C61×#462C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758226C2211yescharacteristic
18C2×#11758226C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519809—24no—
21#14519800—24no—
22C2×#11758202C2211yescharacteristic
23C2×#11758202C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×#11758201C2211yescharacteristic
26C2×#11758201C2211yescharacteristic
27C2×#11758201C2211yescharacteristic
28C2×D488C2211yescharacteristic
29C2×#11758189C2211yescharacteristic
30C2×C8×D61C2211yescharacteristic
31#14519765—21no—
32#14519765C2211yescharacteristic
33#14519762—21no—
34#14519762—21no—
35#14519757—21no—
36#14519757C2211yescharacteristic
37#14519753C2211yescharacteristic
38#14519753C2211yescharacteristic
39#14519752—21no—
40#14519752—21no—
41#14519752C2211yescharacteristic
42C4×D244—21no—
43C4×D244C2211yescharacteristic
44C4×D244C2211yescharacteristic
45C4⋊C4×D61—21no—
46#14519710C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519689C2211yescharacteristic
52#14519689C2211yescharacteristic
53#14519688C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic
55C2×Q16×C61C2211yescharacteristic
56C4⋊Q8×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic
58C4⋊C8×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#103×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64#11758226—22no—
65#11758226—22no—
66#11758226—22no—
67#11758226—41no—
68#11758226—41no—
69#11758226—41no—
70Q8×D61—22no—
71Q8×D61—41no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244D411yescharacteristic
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61C2311yescharacteristic
85C2×C4×D61C2311yescharacteristic
86C2×Dic122—21no—
87C2×Dic122C2311yescharacteristic
88Q16×C61—22no—
89Q16×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61C2311yescharacteristic
96C42×C61—21no—
97C42×C61C2311yescharacteristic
98#11758202—22no—
99#11758202—41no—
100#11758201—22no—
101#11758201—41no—
102#11758201D414yescomplemented
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198D411yescharacteristic
111#11758198D411yescharacteristic
112C4⋊Dic61—21no—
113C4⋊Dic61D411yescharacteristic
114C4⋊Dic61C2311yescharacteristic
115#11758196—21no—
116#11758196—21no—
117C2×#92418C2311yescharacteristic
118C2×#92418C2311yescharacteristic
119D488—22no—
120#11758190—22no—
121#11758189—22no—
122C8×D61—22no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61C2×D411yescharacteristic
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61—21no—
130Q8×C61—21no—
131Q8×C61—21no—
132Q8×C61C2×D412yes—
133C2×C4×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
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146D244—21no—
147D244—41no—
148D244—42no—
149D244—42no—
150D244—42no—
151D244—42no—
152D244C2×D412yes—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161C4×D61—42no—
162Dic122—21no—
163Dic122—21no—
164Dic122—42no—
165C8×C61—21no—
166C8×C61—21no—
167#92418—21no—
168#92418C2×D412yes—
169C22×C61C22×D411yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—22no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C4×C61—22no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61C22×D411yescharacteristic
189C4×C61H(5,𝔽2)11yescharacteristic
190Dic61—21no—
191Dic61—21no—
192Dic61—41no—
193Dic61—41no—
194#3269—611nomaximal, Sylow
195C2×C61D4211yescharacteristic
196C2×C61#57511yescharacteristic
197C2×C61#57811yescharacteristic
198D61—41no—
199D61—41no—
200D61—42no—
201D61—81no—
202C2×#137—611no—
203C2×#135—611no—
204#548—611no—
205#547—611no—
206#497—611no—
207#468—611no—
208#467—611no—
209#463—611no—
210#462D6111yescharacteristic, complemented
211#452—611no—
212#452—611no—
213#451—611no—
214#449—611no—
215#440—611no—
216#435—611no—
217C61#326911yescharacteristic, complemented, Sylow
218C2×#41—611no—
219C2×#41—611no—
220C2×#41—611no—
221C22×Q8—611no—
222#137—1224no—
223#135—1224no—
224C2×Q16—611no—
225C2×Q16—611no—
226C2×Q16C2×D6111yescharacteristic
227C2×Q16C2×D6111yescharacteristic
228C2×SD16—611no—
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×D8—611no—
233C2×M16—611no—
234C22×C8—611no—
235C4⋊Q8C2×D6111yescharacteristic
236#124—611no—
237#124—1221no—
238#123—1221no—
239#123—1221no—
240C22⋊Q8—611no—
241C22⋊Q8—611no—
242C22⋊Q8—611no—
243C22⋊Q8—1221no—
244#121—611no—
245#121—1221no—
246#121—1221no—
247C4×Q8C2×D6111yescharacteristic
248C4×D4—611no—
249C4×D4—611no—
250C4×D4—1221no—
251C2×C4⋊C4—1221no—
252#107—611no—
253C4⋊C8C2×D6111yescharacteristic
254#103—611no—
255#103—611no—
256#103C2×D6111yescharacteristic
257#103C2×D6111yescharacteristic
258#102—611no—
259#102—611no—
260C22⋊C8—611no—
261C22⋊C8—611no—
262#97—611no—
263#41—1222no—
264#41—1222no—
265#41—1222no—
266#41—2441no—
267#41—2441no—
268#41—2441no—
269C2×Q8—611no—
270C2×Q8—1221no—
271C2×Q8—1222no—
272C2×Q8—2441no—
273C2×Q8C22×D6111yescharacteristic
274C2×Q8C22×D6111yescharacteristic
275C2×Q8C22×D6111yescharacteristic
276C2×D4—611no—
277C2×D4—611no—
278C2×D4—611no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290Q16—22no—
291Q16—22no—
292Q16—1222no—
293Q16—2441no—
294SD16—614no—
295SD16—1222no—
296SD16—1222no—
297SD16—2441no—
298D8—1222no—
299M16—1222no—
300C2×C8—611no—
301C2×C8—611no—
302C2×C8—1222no—
303C2×C8C22×D6111yescharacteristic
304C2×C8C22×D6111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—611no—
309C4⋊C4—611no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4C22×D6111yescharacteristic
314C22⋊C4—611no—
315C22⋊C4—611no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C42—21no—
324C42C22×D6111yescharacteristic
325C23—611no—
326C23—611no—
327C23—1221no—
328C23—1221no—
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—1221no—
335Q8—1221no—
336Q8—2442no—
337Q8D4×D6112yes—
338D4—612no—
339D4—1221no—
340D4—1221no—
341D4—1221no—
342D4—2441no—
343D4—2442no—
344D4—2442no—
345D4—2442no—
346D4—2442no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4D4×D6111yescharacteristic
365C2×C4D4×D6111yescharacteristic
366C2×C4C23×D6111yescharacteristic
367C8—21no—
368C8—21no—
369C8—612no—
370C8—1221no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1222no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—1221no—
391C4—1221no—
392C4—2441no—
393C4—2441no—
394C4C2×D4×D6111yescharacteristic
395C4#1451982311yescharacteristic
396C2—4881no—
397C2—2441no—
398C2—2441no—
399C2—2442no—
400C2#1684039611yescharacteristic
401C2#1684056111yescharacteristic
402C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3269
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519800C2semidirect
3. #16840424C2semidirect
4. #16840415C2semidirect
5. #16840154C2semidirect
6. #16840011C2semidirect
7. #16840002C2semidirect
8. #16839978C2semidirect
9. #16839927C2semidirect
10. #16839923C2semidirect
11. #16839916C2semidirect
12. #16839910C2semidirect
13. #16839860C2semidirect
14. #16839832C2semidirect
15. C61×#462C2semidirect
102. #11758201D4semidirect
210. #462D61semidirect
217. C61#3269semidirect