Finite Group Databasebeta

← #30607439

Subgroups — #30607439

Order 15616.

412 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D61⋊#443C211yesmaximal, characteristic
2D61⋊#365C211yesmaximal, characteristic, complemented
3D61⋊#360C211yesmaximal, characteristic
4#21461922C211yesmaximal, characteristic, complemented
5#21460883C211yesmaximal, characteristic, complemented
6#21460862C211yesmaximal, characteristic, complemented
7#360×D61C211yesmaximal, characteristic
8D61⋊#131—21no—
9D61⋊M32C2211yescharacteristic
10#16840806—21no—
11#16840805—21no—
12#16840805—21no—
13#16840804—21no—
14D61⋊#108C2211yescharacteristic
15C2×#14519845C2211yescharacteristic
16D61⋊#104—21no—
17C2×C8×#6923C2211yescharacteristic
18#16840713—21no—
19#16840687—21no—
20#16840686—21no—
21#16840679—21no—
22#16840678—21no—
23#16840635—21no—
24#135×D61C2211yescharacteristic
25M32×D61C2211yescharacteristic
26#106×D61C2211yescharacteristic
27#16839573C411yescharacteristic, complemented
28#16839572C411yescharacteristic, complemented
29#16839571C411yescharacteristic, complemented
30C61×#360C411yescharacteristic, complemented
31#14519865—21no—
32#14519865—21no—
33#14519864—21no—
34#14519864—21no—
35#14519864—41no—
36#14519864—41no—
37D61⋊M16—21no—
38D61⋊M16—41no—
39C2×D61⋊C8—41no—
40C2×D61⋊C8D411yescharacteristic
41C2×C4⋊#6923—21no—
42C2×C4⋊#6923—41no—
43C2×C4×#6923D411yescharacteristic
44#14519852—21no—
45#14519851—21no—
46D61⋊C16—21no—
47#14519848—21no—
48#14519847D411yescharacteristic
49#14519847D411yescharacteristic
50#14519845—21no—
51#14519845—21no—
52#14519842—21no—
53#14519842—21no—
54#14519841—21no—
55#14519841—21no—
56C8×#6923—21no—
57C8×#6923—21no—
58(C2×#6923)⋊C4—41no—
59#41×D61—21no—
60#14519800D411yescharacteristic
61#14519799C2×C411yescharacteristic
62#14519798—21no—
63#14519797—21no—
64#14519796D411yescharacteristic
65Q16×D61Q811yescharacteristic
66SD16×D61—21no—
67D8×D61Q811yescharacteristic
68C2×C8×D61C2311yescharacteristic
69C4⋊C4×D61—21no—
70#14519717C2×C411yescharacteristic
71#14519716—21no—
72C16×D61—21no—
73#14519709C2×C411yescharacteristic
74#14519708—21no—
75#135×C61C2×C411yescharacteristic
76M32×C61C2×C411yescharacteristic
77#106×C61C2×C411yescharacteristic
78C22×#6923—21no—
79C22×#6923—41no—
80#41×C61—21no—
81#11758226—21no—
82Q8×D61—21no—
83#11758224—21no—
84#11758224—41no—
85D4×D61—21no—
86D4×D61—41no—
87#11758222—21no—
88#11758222—41no—
89C2×C4×D61—41no—
90C2×C4×D61—41no—
91C2×C4×D61C2×D411yescharacteristic
92#11758217—41no—
93#11758217—41no—
94#11758217—41no—
95C2×#92420—21no—
96C2×#92420—41no—
97C2×#92420—41no—
98C4⋊#6923—41no—
99C4⋊#6923—41no—
100C4⋊#6923—82no—
101C4×#6923—21no—
102C4×#6923—21no—
103#11758213—21no—
104#11758213—21no—
105#11758213—41no—
106#11758213—41no—
107D61⋊C8—21no—
108D61⋊C8—41no—
109D61⋊C8—41no—
110D61⋊C8—41no—
111D61⋊C8SD1611yescharacteristic
112D61⋊C8SD1611yescharacteristic
113Q16×C61C4⋊C411yescharacteristic, complemented
114SD16×C61—21no—
115D8×C61C4⋊C411yescharacteristic, complemented
116C2×C8×C61C22×C411yescharacteristic
117C4⋊C4×C61—21no—
118#11758202—21no—
119#11758201—21no—
120#11758200—21no—
121#11758199—21no—
122C4⋊Dic61—21no—
123#11758196—41no—
124C2×#92418#4111yescharacteristic
125Dic244C4⋊C411yescharacteristic, complemented
126D488C4⋊C411yescharacteristic, complemented
127#11758190—21no—
128C8×D61C2×D411yescharacteristic
129C8×D61C2×D411yescharacteristic
130C8×D61C2×Q811yescharacteristic
131C8×D61#4111yescharacteristic
132#11758187—41no—
133C16×C61—21no—
134#11758185—21no—
135C22×D61—41no—
136C22×D61AGL(1,ℤ/8)11yescharacteristic
137C2×#6923—22no—
138C2×#6923—41no—
139C2×#6923—41no—
140C2×#6923—81no—
141C2×#6923—81no—
142C2×#6923—81no—
143Q8×C61—21no—
144D4×C61—21no—
145D4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61C4×D411yescharacteristic
149C22⋊D61—41no—
150C22⋊D61—41no—
151C22⋊D61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61AGL(1,ℤ/8)11yescharacteristic
155D244—21no—
156D244—41no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—81no—
161C4×D61—81no—
162C4×D61#12011yescharacteristic
163C4×D61C22⋊Q811yescharacteristic
164C4×D61C2×SD1611yescharacteristic
165C4×D61#13511yescharacteristic
166Dic122—21no—
167Dic122—41no—
168#92420—21no—
169#92420—21no—
170#92420—41no—
171#92420—41no—
172C8×C61C2×C4⋊C411yescharacteristic
173C8×C61C4×D411yescharacteristic
174#92418C22⋊Q811yescharacteristic
175#92418#12311yescharacteristic
176#12950—611nomaximal, Sylow
177C22×C61—41no—
178C22×C61#44211yescharacteristic
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—41no—
182C2×D61—81no—
183C2×D61—81no—
184C2×D61#44911yescharacteristic
185C2×D61#47611yescharacteristic
186#6923—42no—
187#6923—161no—
188C4×C61—41no—
189C4×C61—81no—
190C4×C61#38511yescharacteristic
191C4×C61C4×SD1611yescharacteristic
192Dic61—41no—
193Dic61—81no—
194Dic61#45011yescharacteristic
195Dic61#47811yescharacteristic
196C2×#443—611no—
197C2×#365—611no—
198C2×#360—611no—
199C2×#360—611no—
200#1941—611no—
201#1383—611no—
202#1376—611no—
203C2×C61—21no—
204C2×C61—81no—
205C2×C61#186411yescharacteristic
206D61—21no—
207D61—81no—
208D61#223011yescharacteristic
209D61#223111yescharacteristic
210C2×#135—611no—
211C2×#131—1221no—
212C2×M32—611no—
213C2×M32—611no—
214#443—1221no—
215#443—1221no—
216#443—1221no—
217#443—1221no—
218C2×#108—611no—
219C2×#106—611no—
220C2×#106—611no—
221C2×#104—1221no—
222C2×C4×C8—611no—
223#389—1221no—
224#365—1221no—
225#365—1221no—
226#360—611no—
227#360—611no—
228#360—611no—
229#360—1221no—
230#360—1221no—
231#360#692311yescharacteristic, complemented
232#340—1221no—
233C61#1295011yescharacteristic, complemented, Sylow
234C2×#41—1221no—
235#135—611no—
236#135—611no—
237#135—611no—
238#135—1221no—
239#135—1221no—
240#135C2×#692311yescharacteristic
241C2×Q16—611no—
242C2×SD16—1221no—
243C2×D8—611no—
244#131—1221no—
245#131—1221no—
246#131—1221no—
247#131—1221no—
248#131—2441no—
249#131—2441no—
250C2×M16—1221no—
251C2×M16—2441no—
252C22×C8—611no—
253C22×C8—611no—
254C22×C8—2441no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4—2441no—
258C2×C42—611no—
259M32—611no—
260M32—1221no—
261M32—1221no—
262M32—1221no—
263M32C2×#692311yescharacteristic
264C2×C16—1221no—
265C2×C16—1221no—
266#108—611no—
267#108—611no—
268#108—1221no—
269#106—611no—
270#106—1221no—
271#106—1221no—
272#106—1221no—
273#106C2×#692311yescharacteristic
274#104—1221no—
275#104—1221no—
276#104—1221no—
277#104—1221no—
278C4×C8—1221no—
279C4×C8—1221no—
280#95—2441no—
281#41—21no—
282#41—1221no—
283#41—1221no—
284#41—1221no—
285#41—2441no—
286#41—2441no—
287C2×Q8—1221no—
288C2×D4—1221no—
289C2×D4—2441no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295Q16—611no—
296Q16—1221no—
297Q16C4⋊#692311yescharacteristic, complemented
298SD16—21no—
299SD16—1221no—
300SD16—1221no—
301SD16—1221no—
302D8—611no—
303D8—1221no—
304D8C4⋊#692311yescharacteristic, complemented
305M16—1221no—
306M16—1221no—
307M16—2441no—
308M16—2441no—
309M16—2441no—
310M16—2441no—
311M16—2441no—
312C2×C8—611no—
313C2×C8—611no—
314C2×C8—611no—
315C2×C8—611no—
316C2×C8—611no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8—1221no—
320C2×C8—1221no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8C22×#692311yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—1221no—
329C4⋊C4—4882no—
330C4⋊C4—2441no—
331C4⋊C4—2441no—
332C4⋊C4—2441no—
333C42—1221no—
334C42—1221no—
335C16—21no—
336C16—1221no—
337C16—2441no—
338C23—611no—
339C23—2441no—
340Q8—21no—
341Q8—1221no—
342Q8—2441no—
343D4—21no—
344D4—41no—
345D4—1221no—
346D4—2441no—
347D4—2441no—
348D4—2441no—
349D4—2441no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—1222no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—4881no—
362C2×C4—4881no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4D4×#692311yescharacteristic
371C8—611no—
372C8—611no—
373C8—1221no—
374C8—1221no—
375C8—2441no—
376C8—2441no—
377C8C2×C4⋊#692311yescharacteristic
378C8D4×#692311yescharacteristic
379C22—41no—
380C22—611no—
381C22—611no—
382C22—1221no—
383C22—1221no—
384C22—4881no—
385C22—4881no—
386C22—2441no—
387C22#1684080311yescharacteristic
388C4—41no—
389C4—81no—
390C4—611no—
391C4—611no—
392C4—9761no—
393C4—4881no—
394C4—2442no—
395C4—2441no—
396C4#1684070911yescharacteristic
397C4SD16×#692311yescharacteristic
398C2—21no—
399C2—81no—
400C2—611no—
401C2—611no—
402C2—1221no—
403C2—4881no—
404C2#2146178411yescharacteristic
subgroupG/H
centerC2#21461784
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#360C4
socleC2×C61#1864
prime radical#135×D61C22
cosocleC2×C8×D61C23
hypercenter#360#6923
hypocenterC61#12950
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. D61⋊#365C2semidirect
4. #21461922C2semidirect
5. #21460883C2semidirect
6. #21460862C2semidirect
27. #16839573C4semidirect
28. #16839572C4semidirect
29. #16839571C4semidirect
30. C61×#360C4semidirect
113. Q16×C61C4⋊C4semidirect
115. D8×C61C4⋊C4semidirect
125. Dic244C4⋊C4semidirect
126. D488C4⋊C4semidirect
231. #360#6923semidirect
233. C61#12950semidirect
297. Q16C4⋊#6923semidirect
304. D8C4⋊#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4432
D61⋊#3652
D61⋊#3602
#214619222
#214608832
#214608622
#360×D612
#1295061