Finite Group Databasebeta

← #30600470

Subgroups — #30600470

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#21462467C211yesmaximal, characteristic
2#21461333C211yesmaximal, characteristic, complemented
3D61⋊#332C211yesmaximal, characteristic, complemented
4#21461117C211yesmaximal, characteristic
5#21460709C211yesmaximal, characteristic, complemented
6#21460688C211yesmaximal, characteristic, complemented
7#21455633C211yesmaximal, characteristic
8C2×#14519865—21no—
9#16840780C2211yescharacteristic
10#16840769—21no—
11#16840769—22no—
12#16840767—21no—
13#16840767C2211yescharacteristic
14D61⋊(C4⋊C8)—21no—
15D61⋊(C4⋊C8)C2211yescharacteristic
16D61⋊(C4⋊C8)C2211yescharacteristic
17#16840622—22no—
18#16840621—21no—
19#16840621—21no—
20Q8⋊#92420—21no—
21#16840610—21no—
22C4⋊Q8×D61C2211yescharacteristic
23C4×#11758226C2211yescharacteristic
24#16840057C411yescharacteristic
25#16840053C411yescharacteristic
26#16840049C411yescharacteristic
27#16840045—21no—
28#16840041—21no—
29#16839803—21no—
30#16839784C2211yescharacteristic
31#16839762—21no—
32C61×#477C411yescharacteristic
33#14519865—42no—
34#14519865—42no—
35C2×#11758213—22no—
36C2×#11758213—21no—
37C2×D61⋊C8—22no—
38C2×D61⋊C8—21no—
39C2×D61⋊C8—21no—
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×#11758226D411yescharacteristic
53C2×Q8×D61—21no—
54C2×#11758189—21no—
55#14519777C2×C411yescharacteristic
56#14519776—21no—
57#14519776—21no—
58#14519775—21no—
59Q8×Dic61D411yescharacteristic
60C4×D244—21no—
61C4×D244C2×C411yescharacteristic
62#14519739—21no—
63#14519739D411yescharacteristic
64#14519735—21no—
65#14519735D411yescharacteristic
66C4⋊C4×D61—21no—
67C4⋊C4×D61—21no—
68C42×D61—21no—
69C42×D61C2311yescharacteristic
70#14519710—21no—
71#14519709—21no—
72#14519708—21no—
73C4⋊#92418C2×C411yescharacteristic
74#14519706—21no—
75#14519701—21no—
76#14519699—21no—
77#14519697—21no—
78C4⋊Q8×C61C2×C411yescharacteristic
79C4×Q8×C61C2×C411yescharacteristic
80#107×C61—21no—
81C4⋊C8×C61C2×C411yescharacteristic
82#103×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61C22⋊C411yescharacteristic
85#11758226—21no—
86#11758226—21no—
87#11758226SD1612yes—
88#11758226Q1612yes—
89Q8×D61—81no—
90Q8×D61—81no—
91C2×D244—21no—
92C2×D244C22⋊C411yescharacteristic
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—41no—
97C2×C4×D61C2×D411yescharacteristic
98C2×C4×D61#4111yescharacteristic
99C2×C4×D61#4111yescharacteristic
100C2×Dic122—21no—
101C2×Dic122—41no—
102C2×#92420—21no—
103C2×#92420—22no—
104C2×#92420—21no—
105C2×#92420—41no—
106C2×#92420—41no—
107#11758213—44no—
108#11758213—41no—
109#11758213—41no—
110D61⋊C8—44no—
111D61⋊C8—41no—
112D61⋊C8—41no—
113D61⋊C8—81no—
114C2×C8×C61—21no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61C22⋊C411yescharacteristic
119C42×C61—21no—
120C42×C61C22×C411yescharacteristic
121#11758198—21no—
122#11758198—21no—
123#11758198—21no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61C22⋊C411yescharacteristic
128#11758196—41no—
129#11758196—41no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61C2×D411yescharacteristic
133C4×Dic61C2×D411yescharacteristic
134C4×Dic61C2×D411yescharacteristic
135C2×#92418—21no—
136#11758189—41no—
137#11758189—41no—
138C22×D61—21no—
139C22×D61#12311yescharacteristic
140Q8×C61—21no—
141Q8×C61—81no—
142Q8×C61#10312yes—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61#12011yescharacteristic
152C2×Dic61#12111yescharacteristic
153C2×Dic61#12111yescharacteristic
154D244—22no—
155D244—22no—
156D244—21no—
157D244#10312yes—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—21no—
161C4×D61—21no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—81no—
166C4×D61—82no—
167C4×D61C2×SD1611yescharacteristic
168C4×D61C2×Q1611yescharacteristic
169C4×D61AGL(1,ℤ/8)11yescharacteristic
170C4×D61#13711yescharacteristic
171Dic122—81no—
172Dic122—81no—
173Dic122—81no—
174#92420—41no—
175#92420—42no—
176#92420—41no—
177#92420—81no—
178#92420—81no—
179C8×C61—41no—
180#92418—41no—
181#9167—611nomaximal, Sylow
182C22×C61#38611yescharacteristic
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—22no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61#48311yescharacteristic
189C2×D61#48411yescharacteristic
190C4×C61—22no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—41no—
194C4×C61—81no—
195C4×C61C2×#10311yescharacteristic
196C4×C61#41711yescharacteristic
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#187211yescharacteristic
212C2×C61#190211yescharacteristic
213C2×C61#190711yescharacteristic
214D61—21no—
215D61—21no—
216D61—42no—
217C2×#131—1221no—
218C2×C4⋊Q8—611no—
219C4×#41—611no—
220#477—611no—
221#477#692311yescharacteristic
222#476—611no—
223#476—611no—
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×Q8C2×#692311yescharacteristic
260C4×D4—611no—
261C4×D4—611no—
262C4×D4—1221no—
263C4×D4—1221no—
264#117—611no—
265#117—1221no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4—1221no—
268C2×C42—611no—
269C2×C42—1221no—
270#107—21no—
271#107—1221no—
272#106—1221no—
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—21no—
288#103—1221no—
289#102—1221no—
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—1221no—
299C2×Q8—4881no—
300C2×Q8—4881no—
301C2×Q8—2441no—
302C2×Q8C22⋊#692311yescharacteristic
303C2×D4—611no—
304C2×D4—1221no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—1221no—
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—21no—
331C4⋊C4—611no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C4⋊C4C22⋊#692311yescharacteristic
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C42—21no—
342C42—611no—
343C42—611no—
344C42—611no—
345C42—1221no—
346C42—1221no—
347C42C22×#692311yescharacteristic
348C23—611no—
349C23—1221no—
350Q8—21no—
351Q8—81no—
352Q8—4881no—
353Q8—4881no—
354Q8—4881no—
355Q8#1451984012yes—
356D4—612no—
357D4—1222no—
358D4—1222no—
359D4—1221no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
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—1222no—
372C2×C4—1221no—
373C2×C4—1222no—
374C2×C4—1221no—
375C2×C4—4881no—
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—611no—
392C22—611no—
393C22—1221no—
394C22—1221no—
395C22—1222no—
396C22—2441no—
397C22—2441no—
398C22#1684071011yescharacteristic
399C4—22no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—81no—
404C4—611no—
405C4—611no—
406C4—611no—
407C4—611no—
408C4—1221no—
409C4—4881no—
410C4—2441no—
411C4C2×#1451984011yescharacteristic
412C4#1684075311yescharacteristic
413C2—1221no—
414C2—1221no—
415C2—2442no—
416C2#2146180411yescharacteristic
417C2#2146184911yescharacteristic
418C2#2146185811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#477C4
socleC22×C61#386
prime radicalC2×#11758226D4
cosocleC42×D61C23
hypercenter#477#6923
hypocenterC61#9167
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

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
#214624672
#214613332
D61⋊#3322
#214611172
#214607092
#214606882
#214556332
#916761