Finite Group Databasebeta

← #21455487

Subgroups — #21455487

Order 7808.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519798C211yesmaximal, characteristic, complemented
2C2×#14519785C211yesmaximal, characteristic, complemented
3#16840342C211yesmaximal, characteristic, complemented
4#16840341C211yesmaximal, characteristic, complemented
5#16840009C211yesmaximal, characteristic, complemented
6#16840008C211yesmaximal, characteristic, complemented
7#16840005C211yesmaximal, characteristic, complemented
8#16840002C211yesmaximal, characteristic, complemented
9#16840001C211yesmaximal, characteristic, complemented
10#16839997C211yesmaximal, characteristic, complemented
11#16839996C211yesmaximal, characteristic, complemented
12#107×D61C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758224C2211yescharacteristic
19#14519798—24no—
20C2×#11758202C2211yescharacteristic
21C2×#11758190C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23#14519785—24no—
24C2×#11758189C2211yescharacteristic
25C2×#11758189C2211yescharacteristic
26C22×#92418C2211yescharacteristic
27C2×C8×D61C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519757C2211yescharacteristic
30#14519756C2211yescharacteristic
31#14519755—21no—
32#14519754—21no—
33#14519753C2211yescharacteristic
34#14519752—21no—
35#14519752C2211yescharacteristic
36#14519751C2211yescharacteristic
37#14519750—21no—
38#14519750—21no—
39#14519750—21no—
40#14519749—21no—
41#14519748—21no—
42#14519748C2211yescharacteristic
43C4⋊C4×D61C2211yescharacteristic
44C4⋊C4×D61C2211yescharacteristic
45#14519711C2211yescharacteristic
46#14519710C2211yescharacteristic
47#14519710C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519701C2211yescharacteristic
50#14519700C2211yescharacteristic
51#14519699C2211yescharacteristic
52#14519698C2211yescharacteristic
53#14519697C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C2×M16×C61C2211yescharacteristic
56C22⋊Q8×C61C2211yescharacteristic
57#121×C61C2211yescharacteristic
58#107×C61C2211yescharacteristic
59#103×C61C2211yescharacteristic
60#102×C61C2211yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61D411yescharacteristic
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71#11758226—22no—
72#11758226—22no—
73#11758224—22no—
74#11758224—22no—
75#11758222—22no—
76#11758222—22no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244D411yescharacteristic
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61C2311yescharacteristic
85C2×C4×D61C2311yescharacteristic
86C2×Dic122D411yescharacteristic
87C2×Dic122C2311yescharacteristic
88SD16×C61—22no—
89M16×C61—22no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61C2311yescharacteristic
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99#11758202—22no—
100#11758199—22no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61C2311yescharacteristic
107C4⋊Dic61C2311yescharacteristic
108#11758196—21no—
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112C2×#92418—22no—
113C2×#92418C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115#11758190—22no—
116#11758189—22no—
117#11758189—22no—
118C8×D61—22no—
119C8×D61D414yescomplemented
120C23×C61—21no—
121C23×C61C2×D411yescharacteristic
122C22×D61—21no—
123C22×D61C2×D411yescharacteristic
124C22×D61C2×D411yescharacteristic
125Q8×C61—21no—
126Q8×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—81no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—22no—
138C22⋊D61—22no—
139C22⋊D61—42no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148D244—22no—
149D244—21no—
150D244—21no—
151D244—42no—
152D244—81no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—42no—
156C4×D61—81no—
157C4×D61—81no—
158C4×D61C2×D412yes—
159C4×D61#4112yes—
160Dic122—22no—
161Dic122—21no—
162Dic122—21no—
163C8×C61—21no—
164C8×C61C2×D412yes—
165#92418—21no—
166#92418C2×D412yes—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61C22×D411yescharacteristic
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61#12112yes—
183C4×C61—21no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61C22×D411yescharacteristic
188C4×C61C2×#4111yescharacteristic
189Dic61—21no—
190Dic61—41no—
191Dic61—41no—
192Dic61—41no—
193Dic61#12112yes—
194#3061—611nomaximal, Sylow
195C2×C61—41no—
196C2×C61—81no—
197C2×C61C2×#12111yescharacteristic
198C2×C61#57611yescharacteristic
199C2×C61#57811yescharacteristic
200D61—22no—
201D61—41no—
202D61—81no—
203C2×#135—611no—
204C2×#131—611no—
205#537—611no—
206#537—611no—
207#468—611no—
208#468—611no—
209#468—611no—
210#468D6111yescharacteristic, complemented
211#467—611no—
212#467—611no—
213#466—611no—
214#466—611no—
215C2×#107—611no—
216#417—611no—
217#417—611no—
218C61#306111yescharacteristic, complemented, Sylow
219C2×#41—611no—
220C2×#41—611no—
221C2×#41—611no—
222#135—1224no—
223C2×Q16—611no—
224C2×SD16—611no—
225C2×SD16C2×D6111yescharacteristic
226C2×D8—611no—
227#131—1224no—
228C2×M16—611no—
229C2×M16—611no—
230C2×M16C2×D6111yescharacteristic
231C22×C8—611no—
232C22×C8—611no—
233C22×C8—611no—
234C22⋊Q8—611no—
235C22⋊Q8—611no—
236C22⋊Q8—611no—
237C22⋊Q8—1221no—
238C22⋊Q8—1221no—
239C22⋊Q8C2×D6111yescharacteristic
240#121—611no—
241#121—611no—
242#121—611no—
243#121—1221no—
244#121—1221no—
245#121—1221no—
246#121—1221no—
247#121—1221no—
248#121—1221no—
249#121C2×D6111yescharacteristic
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252#107—611no—
253#107—611no—
254#107—611no—
255#107C2×D6111yescharacteristic
256#103—611no—
257#103—611no—
258#103—611no—
259#103C2×D6111yescharacteristic
260#102—611no—
261#102—611no—
262#102—611no—
263#102C2×D6111yescharacteristic
264#41—1222no—
265#41—1222no—
266#41—1222no—
267#41—1222no—
268#41—1222no—
269#41—1222no—
270C2×Q8—611no—
271C2×Q8—611no—
272C2×Q8C22×D6111yescharacteristic
273C2×D4—21no—
274C2×D4—611no—
275C2×D4—611no—
276C2×D4—611no—
277C2×D4—611no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4C22×D6111yescharacteristic
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4C22×D6111yescharacteristic
291Q16—1222no—
292SD16—22no—
293SD16—1222no—
294D8—1222no—
295M16—22no—
296M16—1222no—
297M16—1222no—
298C2×C8—611no—
299C2×C8—614no—
300C2×C8—611no—
301C2×C8—1222no—
302C2×C8—1222no—
303C2×C8C22×D6111yescharacteristic
304C2×C8C22×D6111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—611no—
307C4⋊C4—611no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4C22×D6111yescharacteristic
314C4⋊C4C22×D6111yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C23—21no—
324C23—611no—
325C23—611no—
326C23—1221no—
327C23D4×D6111yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—1222no—
331Q8—1221no—
332Q8—1221no—
333D4—21no—
334D4—21no—
335D4—81no—
336D4—1222no—
337D4—1222no—
338D4—1222no—
339D4—1221no—
340D4—1221no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—2442no—
345D4—2442no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—611no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—611no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—4881no—
361C2×C4—4881no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4D4×D6111yescharacteristic
365C2×C4C23×D6111yescharacteristic
366C8—21no—
367C8—612no—
368C8—1221no—
369C8D4×D6112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—612no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—1221no—
381C22—1221no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22C2×D4×D6111yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—612no—
391C4—1221no—
392C4—2441no—
393C4—2441no—
394C4—2441no—
395C4C2×D4×D6111yescharacteristic
396C4#41×D6111yescharacteristic
397C2—41no—
398C2—81no—
399C2—1222no—
400C2—4881no—
401C2—2441no—
402C2#121×D6111yescharacteristic
403C2#1684056611yescharacteristic
404C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3061
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14519798C2semidirect
2. C2×#14519785C2semidirect
3. #16840342C2semidirect
4. #16840341C2semidirect
5. #16840009C2semidirect
6. #16840008C2semidirect
7. #16840005C2semidirect
8. #16840002C2semidirect
9. #16840001C2semidirect
10. #16839997C2semidirect
11. #16839996C2semidirect
12. #107×D61C2semidirect
13. #16839762C2semidirect
14. #16839760C2semidirect
15. C61×#468C2semidirect
119. C8×D61D4semidirect
210. #468D61semidirect
218. C61#3061semidirect