Finite Group Databasebeta

← #30600829

Subgroups — #30600829

Order 15616.

458 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462742C211yesmaximal, characteristic
2#21461997C211yesmaximal, characteristic, complemented
3#21461693C211yesmaximal, characteristic
4#21461333C211yesmaximal, characteristic, complemented
5#21460715C211yesmaximal, characteristic, complemented
6#21460688C211yesmaximal, characteristic, complemented
7#21455627C211yesmaximal, characteristic
8#16840812—21no—
9#16840797—21no—
10#16840794—22no—
11#16840782—21no—
12#16840780C2211yescharacteristic
13#16840767C2211yescharacteristic
14#16840765—21no—
15D61⋊(C4⋊C8)C2211yescharacteristic
16C2×#14519841—21no—
17C4×C4⋊#6923C2211yescharacteristic
18#16840635—22no—
19#16840632—21no—
20#16840622—21no—
21#16840622—21no—
22C4⋊Q8×D61C2211yescharacteristic
23C4×#11758224C2211yescharacteristic
24#16840056—21no—
25#16840050—21no—
26#16840048C411yescharacteristic, complemented
27#16840044C411yescharacteristic, complemented
28#16840042C411yescharacteristic, complemented
29#16839803—21no—
30#16839784C2211yescharacteristic
31#16839760—21no—
32C61×#474C411yescharacteristic, complemented
33C2×#11758213—21no—
34C2×#11758217—22no—
35C2×D61⋊C8D412yes—
36C2×C4⋊#6923—21no—
37C2×C4×#6923—21no—
38#14519844—21no—
39#14519844—21no—
40#14519844—21no—
41#14519844D411yescharacteristic
42#14519844D411yescharacteristic
43C4⋊#92420—22no—
44C4⋊#92420—21no—
45#14519841—42no—
46#14519834—21no—
47C22⋊#92420—22no—
48#14519832—22no—
49C4×#92420—21no—
50(C2×#6923)⋊C4—21no—
51C2×#11758224D411yescharacteristic
52C2×Q8×D61—21no—
53C2×#11758189—21no—
54#14519777C2×C411yescharacteristic
55#14519776—21no—
56#14519776—21no—
57#14519775—21no—
58C4×Dic122C2×C411yescharacteristic
59#14519742D411yescharacteristic
60D4×Dic61D411yescharacteristic
61C4×C22⋊D61—21no—
62#14519737—21no—
63#14519735D411yescharacteristic
64#14519733—21no—
65C4⋊C4×D61—21no—
66C4⋊C4×D61—21no—
67C2×C4×Dic61—21no—
68C42×D61C2311yescharacteristic
69#14519710—21no—
70#14519709—21no—
71#14519708—21no—
72C4⋊#92418C2×C411yescharacteristic
73#14519706—21no—
74#14519702—21no—
75#14519700—21no—
76#14519698—21no—
77C4⋊Q8×C61C2×C411yescharacteristic
78C4×D4×C61C2×C411yescharacteristic
79#107×C61—21no—
80C4⋊C8×C61C2×C411yescharacteristic
81#102×C61—21no—
82C22×#6923—41no—
83C2×Q8×C61—21no—
84C2×D4×C61C22⋊C411yescharacteristic
85C22×C4×C61—21no—
86C2×C22⋊D61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89Q8×D61—82no—
90#11758224—21no—
91#11758224—21no—
92#11758224—21no—
93#11758224—21no—
94C2×C4×D61—41no—
95C2×C4×D61C2×D411yescharacteristic
96C2×C4×D61C2×D411yescharacteristic
97C2×C4×D61#4111yescharacteristic
98C2×Dic122—21no—
99C2×Dic122—41no—
100C2×Dic122C22⋊C411yescharacteristic
101#11758217—82no—
102C2×#92420—21no—
103C2×#92420—21no—
104C2×#92420—22no—
105C2×#92420—41no—
106C4⋊#6923—22no—
107C4⋊#6923—41no—
108C4×#6923—41no—
109C4×#6923—41no—
110#11758213—41no—
111#11758213—41no—
112D61⋊C8—42no—
113C2×C8×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61C22⋊C411yescharacteristic
117C22⋊C4×C61—21no—
118C42×C61C22×C411yescharacteristic
119C22⋊Dic61—21no—
120#11758198—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61C22⋊C411yescharacteristic
124#11758196—21no—
125#11758196—21no—
126#11758196—41no—
127#11758196—41no—
128C4×Dic61—21no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61C2×D411yescharacteristic
132C4×Dic61C2×D411yescharacteristic
133C4×Dic61#4111yescharacteristic
134C2×#92418—21no—
135#11758189—41no—
136#11758189—41no—
137C23×C61—21no—
138C22×D61#12111yescharacteristic
139C2×#6923—42no—
140C2×#6923—81no—
141C2×#6923—81no—
142Q8×C61—81no—
143D4×C61—21no—
144D4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—41no—
147C2×C4×C61—81no—
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61C4×D411yescharacteristic
151C22⋊D61—41no—
152C22⋊D61—41no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61#12011yescharacteristic
161C2×Dic61#12111yescharacteristic
162C2×Dic61#12311yescharacteristic
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—41no—
166C4×D61—82no—
167C4×D61AGL(1,ℤ/8)11yescharacteristic
168C4×D61#13711yescharacteristic
169C4×D61#13711yescharacteristic
170C4×D61#13711yescharacteristic
171Dic122—21no—
172Dic122—21no—
173Dic122—82no—
174Dic122—81no—
175#92420—42no—
176#92420—41no—
177#92420—41no—
178#92420—81no—
179C8×C61—41no—
180#92418—41no—
181#9319—611nomaximal, Sylow
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61#38611yescharacteristic
186C2×D61—21no—
187C2×D61—21no—
188C2×D61#46811yescharacteristic
189C2×D61#47011yescharacteristic
190#6923—82no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—41no—
194C4×C61—81no—
195C4×C61#41711yescharacteristic
196C4×C61#41911yescharacteristic
197Dic61—21no—
198Dic61—41no—
199Dic61—41no—
200Dic61—81no—
201Dic61#45511yescharacteristic
202Dic61#45611yescharacteristic
203Dic61#46811yescharacteristic
204Dic61#47011yescharacteristic
205#3079—611no—
206#2989—611no—
207#1987—611no—
208#1806—611no—
209#1548—611no—
210#1303—611no—
211#1292—611no—
212C2×C61—81no—
213C2×C61#188211yescharacteristic
214C2×C61#189411yescharacteristic
215C2×C61#190311yescharacteristic
216D61—21no—
217D61—21no—
218C2×C4⋊Q8—611no—
219C4×#41—611no—
220#477—1221no—
221#476—1221no—
222#475—611no—
223#475—611no—
224#474—611no—
225#474#692311yescharacteristic, complemented
226#446—1221no—
227#436—1221no—
228#435—1222no—
229#432—1221no—
230#431—611no—
231#428—1221no—
232#423—611no—
233#423—611no—
234#423—1221no—
235C2×C4⋊C8—611no—
236C2×#104—1221no—
237#417—1221no—
238C4×C4⋊C4—611no—
239#340—1222no—
240#339—1221no—
241#333—1221no—
242#333—1221no—
243C61#931911yescharacteristic, complemented, Sylow
244C2×#41—611no—
245C22×Q8—1221no—
246C2×M16—1221no—
247C2×M16—1222no—
248C2×M16—1221no—
249C22×C8—612no—
250C4⋊Q8—611no—
251C4⋊Q8—1221no—
252C4⋊Q8—1221no—
253C4⋊Q8—1221no—
254C4⋊Q8C2×#692311yescharacteristic
255C4×Q8—611no—
256C4×Q8—611no—
257C4×D4—611no—
258C4×D4—1221no—
259C4×D4—1221no—
260C4×D4C2×#692311yescharacteristic
261#117—611no—
262#117—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1221no—
266C2×C42—611no—
267C2×C42—1221no—
268C2×C42—1221no—
269#107—21no—
270#107—1221no—
271#106—1221no—
272#106—1221no—
273C4⋊C8—611no—
274C4⋊C8—611no—
275C4⋊C8—611no—
276C4⋊C8—1221no—
277C4⋊C8—1221no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281C4⋊C8—1222no—
282C4⋊C8C2×#692311yescharacteristic
283#104—2442no—
284#103—1221no—
285#103—1221no—
286#102—21no—
287#102—1221no—
288C22⋊C8—1221no—
289C22⋊C8—1222no—
290#97—1222no—
291C4×C8—1221no—
292#95—1221no—
293#41—1221no—
294#41—1221no—
295#41—1221no—
296#41—1221no—
297C2×Q8—21no—
298C2×Q8—611no—
299C2×Q8—1221no—
300C2×Q8—4882no—
301C2×Q8—2441no—
302C2×D4—1221no—
303C2×D4C22⋊#692311yescharacteristic
304C22×C4—21no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—2441no—
311C22×C4—2441no—
312M16—4882no—
313M16—2441no—
314M16—2441no—
315M16—2441no—
316M16—2441no—
317C2×C8—21no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—1222no—
321C2×C8—1221no—
322C2×C8—2441no—
323C2×C8—2442no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—611no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1222no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4—2441no—
335C4⋊C4C22⋊#692311yescharacteristic
336C22⋊C4—21no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C42—611no—
340C42—611no—
341C42—611no—
342C42—1221no—
343C42—1221no—
344C42—1221no—
345C42—2441no—
346C42—2441no—
347C42C22×#692311yescharacteristic
348C23—21no—
349C23—611no—
350Q8—81no—
351Q8—1221no—
352Q8—1221no—
353Q8—4881no—
354Q8—4882no—
355D4—21no—
356D4—21no—
357D4—2441no—
358D4—2441no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—611no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—4882no—
374C2×C4—4881no—
375C2×C4—4881no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2442no—
382C2×C4—2441no—
383C2×C4C2×C22⋊#692311yescharacteristic
384C2×C4D4×#692311yescharacteristic
385C2×C4D4×#692311yescharacteristic
386C8—41no—
387C8—4881no—
388C8—2441no—
389C8—2442no—
390C8—2441no—
391C8—2441no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—611no—
396C22—611no—
397C22—1221no—
398C22—1221no—
399C22#1684071011yescharacteristic
400C4—21no—
401C4—21no—
402C4—41no—
403C4—81no—
404C4—611no—
405C4—611no—
406C4—611no—
407C4—611no—
408C4—1221no—
409C4—4882no—
410C4—4881no—
411C4—2441no—
412C4—2441no—
413C4#1684075311yescharacteristic
414C4#1684075511yescharacteristic
415C2—81no—
416C2—1221no—
417C2—1221no—
418C2#2146181811yescharacteristic
419C2#2146183411yescharacteristic
420C2#2146185011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#474C4
socleC22×C61#386
prime radicalC2×#11758224D4
cosocleC42×D61C23
hypercenter#474#6923
hypocenterC61#9319
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #21461997C2semidirect
4. #21461333C2semidirect
5. #21460715C2semidirect
6. #21460688C2semidirect
26. #16840048C4semidirect
27. #16840044C4semidirect
28. #16840042C4semidirect
32. C61×#474C4semidirect
225. #474#6923semidirect
243. C61#9319semidirect

Maximal subgroups

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

subgroupindex
#214627422
#214619972
#214616932
#214613332
#214607152
#214606882
#214556272
#931961