Finite Group Databasebeta

← #21457379

Subgroups — #21457379

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×#14519810C211yesmaximal, characteristic, complemented
2C2×#14519799C211yesmaximal, characteristic, complemented
3#16840421C211yesmaximal, characteristic, complemented
4#16840417C211yesmaximal, characteristic, complemented
5#16840156C211yesmaximal, characteristic, complemented
6#16840008C211yesmaximal, characteristic, complemented
7#16840003C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839973C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839926C211yesmaximal, characteristic, complemented
12#16839920C211yesmaximal, characteristic, complemented
13#16839909C211yesmaximal, characteristic, complemented
14#16839864C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758222C2211yescharacteristic
19C22×Dic122C2211yescharacteristic
20#14519810—24no—
21#14519799—24no—
22C2×Dic244C2211yescharacteristic
23C2×Dic244C2211yescharacteristic
24C2×Dic244C2211yescharacteristic
25C2×Dic244C2211yescharacteristic
26C2×#11758190C2211yescharacteristic
27C2×#11758190C2211yescharacteristic
28C2×#11758190C2211yescharacteristic
29C2×#11758190C2211yescharacteristic
30C2×D488C2211yescharacteristic
31#14519777C2211yescharacteristic
32#14519765C2211yescharacteristic
33#14519763—21no—
34#14519759—21no—
35#14519759—21no—
36#14519756C2211yescharacteristic
37#14519756C2211yescharacteristic
38#14519756C2211yescharacteristic
39#14519755—21no—
40#14519751C2211yescharacteristic
41#14519749—21no—
42#14519748—21no—
43C4×Dic122C2211yescharacteristic
44C4×D244C2211yescharacteristic
45#14519737—21no—
46C4⋊C4×D61—21no—
47#14519711C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519702C2211yescharacteristic
51#14519702C2211yescharacteristic
52#14519699C2211yescharacteristic
53#14519699C2211yescharacteristic
54C2×M16×C61C2211yescharacteristic
55C22×C8×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57C4⋊C8×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C22⋊C8×C61C2211yescharacteristic
60#97×C61C2211yescharacteristic
61C2×D4×C61D411yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69#11758222—22no—
70#11758222—22no—
71#11758222—22no—
72#11758222—41no—
73#11758222—41no—
74#11758222—41no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×Dic122—22no—
82C2×Dic122—21no—
83C2×Dic122—41no—
84C2×Dic122C2311yescharacteristic
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88M16×C61—22no—
89C2×C8×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61D411yescharacteristic
95C22⋊C4×C61D411yescharacteristic
96C22⋊C4×C61D411yescharacteristic
97C42×C61C2311yescharacteristic
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61C2311yescharacteristic
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113C4×Dic61—21no—
114Dic244—22no—
115Dic244—22no—
116Dic244—22no—
117Dic244—41no—
118D488—22no—
119#11758190—22no—
120#11758190—22no—
121#11758190—41no—
122#11758190D414yescomplemented
123C23×C61C2×D411yescharacteristic
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127D4×C61—41no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148D244—21no—
149D244—21no—
150D244—21no—
151D244C2×D412yes—
152C4×D61—42no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156Dic122—21no—
157Dic122—21no—
158Dic122—21no—
159Dic122—21no—
160Dic122—21no—
161Dic122—21no—
162Dic122—21no—
163Dic122—42no—
164Dic122C2×D412yes—
165C8×C61—21no—
166C8×C61—21no—
167C8×C61—21no—
168C8×C61C2×D412yes—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61C22×D411yescharacteristic
176C2×D61—22no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61C22×D411yescharacteristic
187C4×C61H(5,𝔽2)11yescharacteristic
188Dic61—22no—
189Dic61—41no—
190Dic61—41no—
191Dic61—41no—
192Dic61—41no—
193Dic61—41no—
194#3269—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61—41no—
197C2×C61D4211yescharacteristic
198C2×C61#57511yescharacteristic
199C2×C61#57811yescharacteristic
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#462—611no—
211#452—611no—
212#452—611no—
213#451—611no—
214#449—611no—
215#440—611no—
216#435D6111yescharacteristic, complemented
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×Q16—611no—
227C2×Q16—611no—
228C2×SD16—611no—
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×D8—611no—
233C2×M16C2×D6111yescharacteristic
234C22×C8C2×D6111yescharacteristic
235C4⋊Q8—611no—
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×Q8—611no—
248C4×D4—611no—
249C4×D4—1221no—
250C4×D4C2×D6111yescharacteristic
251C2×C4⋊C4—1221no—
252#107—611no—
253C4⋊C8C2×D6111yescharacteristic
254#103—611no—
255#103—611no—
256#103—611no—
257#103—611no—
258#102—611no—
259#102—611no—
260C22⋊C8C2×D6111yescharacteristic
261C22⋊C8C2×D6111yescharacteristic
262#97C2×D6111yescharacteristic
263#41—1222no—
264#41—1222no—
265#41—1222no—
266#41—2441no—
267#41—2441no—
268#41—2441no—
269C2×Q8—611no—
270C2×Q8—611no—
271C2×Q8—611no—
272C2×Q8—611no—
273C2×Q8—1222no—
274C2×Q8—1221no—
275C2×Q8—2441no—
276C2×D4—611no—
277C2×D4—611no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4D24411yescharacteristic
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4C22×D6111yescharacteristic
289C22×C4C22×D6111yescharacteristic
290Q16—1222no—
291Q16—1222no—
292Q16—1222no—
293Q16—2441no—
294SD16—614no—
295SD16—1222no—
296SD16—1222no—
297SD16—2441no—
298D8—1222no—
299M16—22no—
300C2×C8—22no—
301C2×C8C22×D6111yescharacteristic
302C2×C8C22×D6111yescharacteristic
303C2×C8C22×D6111yescharacteristic
304C2×C8C22×D6111yescharacteristic
305C4⋊C4—611no—
306C4⋊C4—611no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4D24411yescharacteristic
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4D24411yescharacteristic
322C22⋊C4D24411yescharacteristic
323C42—1221no—
324C42C22×D6111yescharacteristic
325C23—1221no—
326C23—1221no—
327C23C2×D24411yescharacteristic
328C23C2×D24411yescharacteristic
329Q8—612no—
330Q8—1221no—
331Q8—1221no—
332Q8—1221no—
333Q8—1221no—
334Q8—1221no—
335Q8—1221no—
336Q8—1221no—
337Q8—2442no—
338D4—41no—
339D4—612no—
340D4—1221no—
341D4—1221no—
342D4—1221no—
343D4—2442no—
344D4—2442no—
345D4—2442no—
346D4—2442no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4C2×D24411yescharacteristic
363C2×C4C2×D24411yescharacteristic
364C2×C4C2×D24411yescharacteristic
365C2×C4C2×D24411yescharacteristic
366C2×C4C23×D6111yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8D4×D6112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—1222no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C22×D24411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—1222no—
389C4—2441no—
390C4—2441no—
391C4—2441no—
392C4—2441no—
393C4—2441no—
394C4C2×D4×D6111yescharacteristic
395C4#1451982311yescharacteristic
396C2—41no—
397C2—41no—
398C2—4881no—
399C2—2442no—
400C2D4×D24411yescharacteristic
401C2#1684056211yescharacteristic
402C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3269
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14519810C2semidirect
2. C2×#14519799C2semidirect
3. #16840421C2semidirect
4. #16840417C2semidirect
5. #16840156C2semidirect
6. #16840008C2semidirect
7. #16840003C2semidirect
8. #16839978C2semidirect
9. #16839973C2semidirect
10. #16839926C2semidirect
11. #16839926C2semidirect
12. #16839920C2semidirect
13. #16839909C2semidirect
14. #16839864C2semidirect
15. C61×#435C2semidirect
122. #11758190D4semidirect
216. #435D61semidirect
217. C61#3269semidirect