Finite Group Databasebeta

← #30600469

Subgroups — #30600469

Order 15616.

478 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 96 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#21462466C211yesmaximal, characteristic
2#21461333C211yesmaximal, characteristic, complemented
3D61⋊#332C211yesmaximal, characteristic, complemented
4#21461115C211yesmaximal, characteristic
5#21460709C211yesmaximal, characteristic, complemented
6#21460688C211yesmaximal, characteristic, complemented
7#21455631C211yesmaximal, characteristic
8C2×#14519864—21no—
9#16840780C2211yescharacteristic
10#16840769—21no—
11#16840768—22no—
12#16840767C2211yescharacteristic
13#16840765—21no—
14C2×#14519844—21no—
15D61⋊(C4⋊C8)C2211yescharacteristic
16D61⋊(C4⋊C8)C2211yescharacteristic
17#16840622—22no—
18#16840621—21no—
19#16840621—21no—
20#16840612—21no—
21D4⋊#92420—21no—
22C4⋊Q8×D61C2211yescharacteristic
23C4×#11758224C2211yescharacteristic
24#16840058C411yescharacteristic
25#16840054C411yescharacteristic
26#16840052C411yescharacteristic
27#16840046—21no—
28#16840040—21no—
29#16839801—21no—
30#16839784C2211yescharacteristic
31#16839760—21no—
32C61×#476C411yescharacteristic
33#14519864—42no—
34#14519864—42no—
35C2×#11758213—21no—
36C2×#11758217—22no—
37C2×D61⋊C8—21no—
38C2×D61⋊C8—21no—
39C22×#92420—22no—
40#14519844—22no—
41#14519844—21no—
42#14519844—21no—
43#14519844—21no—
44#14519844D411yescharacteristic
45#14519844D411yescharacteristic
46#14519844D412yes—
47C4⋊#92420—22no—
48C4⋊#92420—21no—
49C4⋊#92420—21no—
50#14519834—21no—
51C4×#92420—21no—
52C2×#11758224D411yescharacteristic
53C2×Q8×D61—21no—
54C2×#11758189—21no—
55#14519777C2×C411yescharacteristic
56#14519776—21no—
57#14519776—21no—
58#14519775—21no—
59C4×Dic122C2×C411yescharacteristic
60#14519742D411yescharacteristic
61D4×Dic61D411yescharacteristic
62C4×C22⋊D61—21no—
63#14519737—21no—
64#14519735D411yescharacteristic
65#14519733—21no—
66C4⋊C4×D61—21no—
67C4⋊C4×D61—21no—
68C2×C4×Dic61—21no—
69C42×D61C2311yescharacteristic
70#14519711—21no—
71#14519710—21no—
72#14519708—21no—
73C4⋊#92418C2×C411yescharacteristic
74#14519706—21no—
75#14519702—21no—
76#14519700—21no—
77#14519698—21no—
78C4⋊Q8×C61C2×C411yescharacteristic
79C4×D4×C61C2×C411yescharacteristic
80#106×C61—21no—
81C4⋊C8×C61C2×C411yescharacteristic
82#102×C61—21no—
83C2×Q8×C61—21no—
84C2×D4×C61C22⋊C411yescharacteristic
85C22×C4×C61—21no—
86C2×C22⋊D61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89Q8×D61—81no—
90Q8×D61—81no—
91#11758224—21no—
92#11758224—21no—
93#11758224SD1612yes—
94#11758224Q1612yes—
95C2×C4×D61—41no—
96C2×C4×D61C2×D411yescharacteristic
97C2×C4×D61#4111yescharacteristic
98C2×C4×D61#4111yescharacteristic
99C2×Dic122—21no—
100C2×Dic122—41no—
101C2×Dic122C22⋊C411yescharacteristic
102#11758217—44no—
103C2×#92420—21no—
104C2×#92420—21no—
105C2×#92420—22no—
106C2×#92420—44no—
107C2×#92420—41no—
108C2×#92420—41no—
109#11758213—41no—
110#11758213—41no—
111D61⋊C8—41no—
112D61⋊C8—41no—
113D61⋊C8—81no—
114C2×C8×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61C22⋊C411yescharacteristic
118C22⋊C4×C61—21no—
119C42×C61C22×C411yescharacteristic
120C22⋊Dic61—21no—
121#11758198—21no—
122C4⋊Dic61—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61C22⋊C411yescharacteristic
125#11758196—21no—
126#11758196—21no—
127#11758196—41no—
128#11758196—41no—
129C4×Dic61—21no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61C2×D411yescharacteristic
133C4×Dic61C2×D411yescharacteristic
134C4×Dic61C2×D411yescharacteristic
135C2×#92418—21no—
136#11758189—41no—
137#11758189—41no—
138C23×C61—21no—
139C22×D61#12311yescharacteristic
140Q8×C61—81no—
141D4×C61—21no—
142D4×C61#10312yes—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—81no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C22⋊D61—22no—
150C22⋊D61—22no—
151C2×Dic61—21no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—21no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61#12011yescharacteristic
159C2×Dic61#12111yescharacteristic
160C2×Dic61#12111yescharacteristic
161C4×D61—21no—
162C4×D61—21no—
163C4×D61—41no—
164C4×D61—82no—
165C4×D61C2×SD1611yescharacteristic
166C4×D61C2×Q1611yescharacteristic
167C4×D61AGL(1,ℤ/8)11yescharacteristic
168C4×D61#13711yescharacteristic
169Dic122—21no—
170Dic122—81no—
171Dic122—81no—
172Dic122—81no—
173Dic122#10312yes—
174#92420—41no—
175#92420—41no—
176#92420—42no—
177#92420—81no—
178#92420—81no—
179C8×C61—41no—
180#92418—41no—
181#9167—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61#38611yescharacteristic
186C2×D61—21no—
187C2×D61—21no—
188C2×D61#48311yescharacteristic
189C2×D61#48411yescharacteristic
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—41no—
193C4×C61—81no—
194C4×C61C2×#10311yescharacteristic
195C4×C61#41711yescharacteristic
196Dic61—22no—
197Dic61—21no—
198Dic61—41no—
199Dic61—81no—
200Dic61#45011yescharacteristic
201Dic61#45111yescharacteristic
202Dic61#47111yescharacteristic
203Dic61#47211yescharacteristic
204#3079—611no—
205#2906—611no—
206#1548—611no—
207C2×#332—611no—
208#1477—611no—
209#1301—611no—
210#1292—611no—
211C2×C61—42no—
212C2×C61#187211yescharacteristic
213C2×C61#190211yescharacteristic
214C2×C61#190711yescharacteristic
215D61—21no—
216D61—21no—
217C2×#131—1221no—
218C2×C4⋊Q8—611no—
219C4×#41—611no—
220#477—611no—
221#477—611no—
222#476—611no—
223#476#692311yescharacteristic
224#475—1221no—
225#474—1221no—
226#431—611no—
227#428—1221no—
228#424—1222no—
229#424—1221no—
230#423—611no—
231#423—611no—
232#423—1221no—
233C2×C4⋊C8—611no—
234C2×C4⋊C8—611no—
235C2×C4⋊C8—1221no—
236#417—1221no—
237#333—1222no—
238#332—1221no—
239#332—1221no—
240Q8⋊C8—1221no—
241D4⋊C8—1221no—
242C61#916711yescharacteristic, complemented, Sylow
243C2×#41—611no—
244C22×Q8—1221no—
245#131—2442no—
246#131—2442no—
247C2×M16—1221no—
248C2×M16—1221no—
249C2×M16—1222no—
250C22×C8—1221no—
251C22×C8—1222no—
252C22×C8—1221no—
253C4⋊Q8—611no—
254C4⋊Q8—1221no—
255C4⋊Q8—1221no—
256C4⋊Q8—1221no—
257C4⋊Q8C2×#692311yescharacteristic
258C4×Q8—611no—
259C4×Q8—611no—
260C4×D4—611no—
261C4×D4—1221no—
262C4×D4—1221no—
263C4×D4C2×#692311yescharacteristic
264#117—611no—
265#117—1221no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1221no—
268C2×C42—611no—
269C2×C42—1221no—
270#107—1221no—
271#107—1221no—
272#106—21no—
273#106—1221no—
274C4⋊C8—611no—
275C4⋊C8—611no—
276C4⋊C8—612no—
277C4⋊C8—611no—
278C4⋊C8—1221no—
279C4⋊C8—1221no—
280C4⋊C8—1221no—
281C4⋊C8—1221no—
282C4⋊C8—1221no—
283C4⋊C8—1221no—
284C4⋊C8—1222no—
285C4⋊C8—1222no—
286C4⋊C8C2×#692311yescharacteristic
287#103—1221no—
288#103—1221no—
289#102—21no—
290#102—1221no—
291C22⋊C8—1221no—
292C4×C8—1221no—
293#41—612no—
294#41—612no—
295#41—1221no—
296#41—1221no—
297C2×Q8—21no—
298C2×Q8—611no—
299C2×Q8—1221no—
300C2×Q8—4881no—
301C2×Q8—4881no—
302C2×Q8—2441no—
303C2×D4—1221no—
304C2×D4C22⋊#692311yescharacteristic
305C22×C4—21no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—2441no—
312M16—2441no—
313M16—2441no—
314M16—2441no—
315M16—2441no—
316M16—2444no—
317C2×C8—21no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—1222no—
321C2×C8—1221no—
322C2×C8—4881no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8—2441no—
327C2×C8—2444no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—611no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C4⋊C4C22⋊#692311yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C42—611no—
342C42—611no—
343C42—611no—
344C42—1221no—
345C42—1221no—
346C42—1221no—
347C42C22×#692311yescharacteristic
348C23—21no—
349C23—611no—
350Q8—81no—
351Q8—612no—
352Q8—1221no—
353Q8—4881no—
354Q8—4881no—
355Q8—4881no—
356D4—21no—
357D4—1222no—
358D4—1222no—
359D4#1451984012yes—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—611no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—4882no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4C2×C22⋊#692311yescharacteristic
382C2×C4D4×#692311yescharacteristic
383C2×C4D4×#692311yescharacteristic
384C8—41no—
385C8—4881no—
386C8—4881no—
387C8—2441no—
388C8—2441no—
389C8—2442no—
390C8—2441no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—611no—
395C22—611no—
396C22—1221no—
397C22—1221no—
398C22#1684071011yescharacteristic
399C4—21no—
400C4—21no—
401C4—41no—
402C4—81no—
403C4—611no—
404C4—611no—
405C4—611no—
406C4—611no—
407C4—1222no—
408C4—1221no—
409C4—4881no—
410C4—2441no—
411C4C2×#1451984011yescharacteristic
412C4#1684075311yescharacteristic
413C2—42no—
414C2—1221no—
415C2—1221no—
416C2#2146180411yescharacteristic
417C2#2146184811yescharacteristic
418C2#2146185811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#476C4
socleC22×C61#386
prime radicalC2×#11758224D4
cosocleC42×D61C23
hypercenter#476#6923
hypocenterC61#9167
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #21461333C2semidirect
3. D61⋊#332C2semidirect
5. #21460709C2semidirect
6. #21460688C2semidirect
242. C61#9167semidirect

Maximal subgroups

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

subgroupindex
#214624662
#214613332
D61⋊#3322
#214611152
#214607092
#214606882
#214556312
#916761