Finite Group Databasebeta

← #29667885

Subgroups — #29667885

Order 15616.

772 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456963C211yesmaximal, characteristic, complemented
2#21456947C211yesmaximal, characteristic
3#21456378C211yesmaximal, characteristic
4#21456361C211yesmaximal, characteristic, complemented
5#21456276C211yesmaximal, characteristic
6#21445454C212yesmaximal, complemented
7#21445443C212yesmaximal, complemented
8#21445422C212yesmaximal, complemented
9#21445415C212yesmaximal, complemented
10C8×#11758194C211yesmaximal, characteristic, complemented
11C2×C61×#487C211yesmaximal, characteristic, complemented
12C2×#14519808—22no—
13#16840319C2211yescharacteristic
14#16840312C2211yescharacteristic
15#16840168—22no—
16#16840165C2212yes—
17#16840160C2211yescharacteristic
18#16840158C2212yes—
19#16840158C2212yes—
20#16840158C2212yes—
21#16840154—22no—
22#16840141C2212yes—
23#16840136C2212yes—
24#16840135C2211yescharacteristic
25#16840114C2212yes—
26#16840113C2211yescharacteristic
27#16840110C2212yes—
28#16840109C2211yescharacteristic
29#16840092—22no—
30#16840080—22no—
31#16840049—22no—
32#16840044—22no—
33#16839991—22no—
34C4×#11758190—22no—
35#16839815C2211yescharacteristic
36#16839802—22no—
37C4×#11758194C2211yescharacteristic
38#16839484C2212yes—
39C8×#92418C2212yes—
40C2×C4⋊Q8×C61C2211yescharacteristic
41C2×C4⋊Q8×C61C2211yescharacteristic
42C61×#487—22no—
43C61×#487C2212yes—
44C61×#487C2212yes—
45C2×#103×C61—22no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758222—21no—
48#14519808—48no—
49C2×#11758202—24no—
50C2×#11758190—22no—
51C2×#11758201—24no—
52C2×#11758194D412yes—
53#14519777C2311yescharacteristic
54#14519777C2311yescharacteristic
55#14519777C2311yescharacteristic
56#14519774C2311yescharacteristic
57#14519769—21no—
58#14519765—21no—
59#14519756—21no—
60#14519756—21no—
61#14519751—21no—
62#14519751—21no—
63C4×Dic122—21no—
64C4×Dic122—21no—
65C4×D244—21no—
66C4×D244—21no—
67#14519736—21no—
68#14519710—24no—
69#14519709—22no—
70#14519708—24no—
71#14519708—24no—
72#14519708—24no—
73C4⋊#92418D412yes—
74#14519702—22no—
75#14519700—24no—
76#14519699—22no—
77#14519697—24no—
78C22⋊#92418D412yes—
79#14519688D412yes—
80C4×#92418C2312yes—
81C4×#92418C2312yes—
82C22×Q8×C61—21no—
83C22×Q8×C61—21no—
84C22×C8×C61D412yes—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61—21no—
91C4⋊Q8×C61C2312yes—
92C4⋊Q8×C61C2312yes—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C42×C61C2311yescharacteristic
98#103×C61—24no—
99#103×C61—24no—
100C4×C8×C61D412yes—
101C4×C8×C61C2311yescharacteristic
102C4×C8×C61C2311yescharacteristic
103C2×Q8×C61—22no—
104C2×Q8×C61—22no—
105C2×Q8×C61—44no—
106C2×Q8×C61—41no—
107C2×Q8×C61—41no—
108C2×Q8×C61—44no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C2×C22⋊D61—41no—
115#11758222—44no—
116C2×D244—21no—
117C2×D244—21no—
118C2×D244—21no—
119C2×C4×D61—41no—
120C2×Dic122—21no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×C8×C61—42no—
124C2×C8×C61C2×D412yes—
125C2×C8×C61C2×D412yes—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—22no—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—41no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61C2411yescharacteristic
138C22⋊Dic61—41no—
139#11758202—48no—
140#11758201—48no—
141#11758198—41no—
142#11758198—41no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149#11758196—41no—
150#11758196—41no—
151C4×Dic61—41no—
152#11758194SD1618yescomplemented
153C2×#92418C2×D414yes—
154C2×#92418C2×D414yes—
155#11758190—44no—
156C23×C61#12711yescharacteristic
157C22×D61—41no—
158Q8×C61—44no—
159Q8×C61—44no—
160Q8×C61—82no—
161Q8×C61—82no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—82no—
167C2×C4×C61—82no—
168C2×C4×C61#12711yescharacteristic
169C2×C4×C61#12711yescharacteristic
170C2×C4×C61#12711yescharacteristic
171C2×C4×C61C2×SD1614yes—
172C2×C4×C61C22×D411yescharacteristic
173C2×C4×C61C22×D411yescharacteristic
174C2×C4×C61C22×D411yescharacteristic
175C22⋊D61—82no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179D244—42no—
180D244—42no—
181D244—42no—
182C4×D61—82no—
183Dic122—42no—
184Dic122—42no—
185Dic122—42no—
186C8×C61—22no—
187C8×C61—22no—
188#92418—24no—
189#92418C2×SD1618yes—
190#19624—611nomaximal, Sylow
191C22×C61—21no—
192C22×C61—21no—
193C22×C61#49212yes—
194C22×C61C2×#12711yescharacteristic
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—82no—
201C4×C61—82no—
202C4×C61#49212yes—
203C4×C61C22×SD1612yes—
204C4×C61#57512yes—
205C4×C61#57812yes—
206Dic61—81no—
207Dic61—81no—
208Dic61—81no—
209#3229—611no—
210#3227—611no—
211#3167—611no—
212#3165—611no—
213#3152—611no—
214C2×#487D6111yescharacteristic, complemented
215#1716—612no—
216#1714—612no—
217#1708—612no—
218#1707—612no—
219C8×M16—611no—
220C2×C61—22no—
221C2×C61C2×#49211yescharacteristic
222C2×C61#315311yescharacteristic
223C2×C61#315611yescharacteristic
224D61—161no—
225C2×#137—1222no—
226#533—611no—
227#532—611no—
228C2×C4⋊Q8C2×D6111yescharacteristic
229C2×C4⋊Q8C2×D6111yescharacteristic
230#501—1222no—
231#500—612no—
232#498—612no—
233#498—612no—
234#498—612no—
235#498—611no—
236#497—1222no—
237#494—612no—
238#492—612no—
239#492—611no—
240#487—22no—
241#487—612no—
242#487—611no—
243#487C2×D6112yes—
244#487C2×D6112yes—
245#486—612no—
246#486—611no—
247#483—1222no—
248#481—1222no—
249#476—1222no—
250#475—1222no—
251#465—1222no—
252C4×SD16—1222no—
253#431—611no—
254#428—1222no—
255C2×#103—22no—
256C4×M16—611no—
257C2×C4×C8C2×D6111yescharacteristic
258#322—612no—
259C82—612no—
260C61#1962411yescharacteristic, complemented, Sylow
261C2×#41—1221no—
262C22×Q8—21no—
263C22×Q8—21no—
264#137—2448no—
265C2×Q16—1224no—
266C2×SD16—1224no—
267C2×SD16—1222no—
268C2×M16—612no—
269C22×C8C22⋊D6112yes—
270C4⋊Q8—21no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—611no—
277C4⋊Q8—611no—
278C4⋊Q8—611no—
279C4⋊Q8C22×D6112yes—
280C4⋊Q8C22×D6112yes—
281#127—611no—
282#125—1221no—
283#124—1221no—
284C22⋊Q8—1221no—
285C22⋊Q8—1221no—
286#121—1221no—
287#121—1221no—
288C4×Q8—1221no—
289C4×Q8—1221no—
290C4×D4—1221no—
291C4×D4—1221no—
292#117—1221no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C42C22×D6111yescharacteristic
298#107—1224no—
299#106—1224no—
300#106—1224no—
301#106—1224no—
302#106—1222no—
303C4⋊C8—612no—
304#103—24no—
305#103—24no—
306#103—1224no—
307#103—1222no—
308#102—1224no—
309#102—1222no—
310C22⋊C8—612no—
311#97—612no—
312C4×C8—612no—
313C4×C8—612no—
314C4×C8C22⋊D6112yes—
315C4×C8C22×D6111yescharacteristic
316C4×C8C22×D6111yescharacteristic
317#41—2444no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—44no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×Q8—44no—
324C2×Q8—1221no—
325C2×Q8—1221no—
326C2×Q8—1221no—
327C2×D4—1221no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—2441no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—2441no—
334C22×C4D4×D6111yescharacteristic
335C22×C4D4×D6111yescharacteristic
336C22×C4C2×C22⋊D6111yescharacteristic
337Q16—2448no—
338SD16—2444no—
339SD16—2448no—
340M16—618no—
341C2×C8—42no—
342C2×C8—614no—
343C2×C8—614no—
344C2×C8C2×C22⋊D6112yes—
345C2×C8C2×C22⋊D6112yes—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—1221no—
355C4⋊C4—1221no—
356C4⋊C4—1221no—
357C4⋊C4—1221no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C22⋊C4—2441no—
363C22⋊C4—2441no—
364C22⋊C4—2441no—
365C42—2441no—
366C42D4×D6111yescharacteristic
367C42D4×D6111yescharacteristic
368C42C2×C22⋊D6111yescharacteristic
369C42C23×D6111yescharacteristic
370C23—2441no—
371C23#1451977311yescharacteristic
372Q8—44no—
373Q8—44no—
374Q8—82no—
375Q8—82no—
376Q8—2442no—
377Q8—2442no—
378Q8—2442no—
379D4—4882no—
380D4—2442no—
381D4—2442no—
382D4—2442no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—4882no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C2×C4#1451977311yescharacteristic
394C2×C4#1451977311yescharacteristic
395C2×C4#1451977311yescharacteristic
396C2×C4SD16×D6114yes—
397C2×C4C2×D4×D6111yescharacteristic
398C2×C4C2×D4×D6111yescharacteristic
399C2×C4C22×C22⋊D6111yescharacteristic
400C8—22no—
401C8—22no—
402C8—618no—
403C8—1224no—
404C22—21no—
405C22—21no—
406C22—4881no—
407C22—4881no—
408C22—4881no—
409C22#1684013312yes—
410C22C2×#1451977311yescharacteristic
411C4—21no—
412C4—21no—
413C4—82no—
414C4—82no—
415C4—4881no—
416C4—4881no—
417C4—4881no—
418C4#1684013312yes—
419C4C2×SD16×D6112yes—
420C4#1684056012yes—
421C4#1684057512yes—
422C2—22no—
423C2—9761no—
424C2C2×#1684013311yescharacteristic
425C2#2145628311yescharacteristic
426C2#2145630811yescharacteristic
subgroupG/H
centerC22C2×#14519773
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#487C2
socleC22×C61C2×#127
prime radical#16840312C22
hypercenterC2×#487D61
hypocenterC61#19624
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
1. #21456963C2semidirect
4. #21456361C2semidirect
6. #21445454C2semidirect
7. #21445443C2semidirect
8. #21445422C2semidirect
9. #21445415C2semidirect
10. C8×#11758194C2semidirect
11. C2×C61×#487C2semidirect
152. #11758194SD16semidirect
214. C2×#487D61semidirect
260. C61#19624semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214569632
#214569472
#214563782
#214563612
#214562762
#214454542
#214454432
#214454222
#214454152
C8×#117581942
C2×C61×#4872
#1962461