Finite Group Databasebeta

← #29596935

Subgroups — #29596935

Order 15616.

466 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458921C211yesmaximal, characteristic, complemented
2#21454538C211yesmaximal, characteristic
3#21447448C211yesmaximal, characteristic, complemented
4#21447446C211yesmaximal, characteristic, complemented
5#21447439C211yesmaximal, characteristic, complemented
6#21443899C211yesmaximal, characteristic, complemented
7C61×#1375C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9C2×#14519783C2211yescharacteristic
10#16840312C411yescharacteristic
11#16840180—22no—
12#16840178—22no—
13C2×#14519717C2211yescharacteristic
14C2×#14519717C2211yescharacteristic
15M32×D61—22no—
16#16839835—22no—
17#16839835—22no—
18#16839786C411yescharacteristic
19#16839728C411yescharacteristic
20#16839728C411yescharacteristic
21#16839547—22no—
22#16839545—22no—
23#16839543—22no—
24C2×M32×C61C2211yescharacteristic
25C2×M32×C61C2211yescharacteristic
26C2×#97×C61C2211yescharacteristic
27C2×#11758222C2×C411yescharacteristic
28C2×#11758222C2×C411yescharacteristic
29#14519783—21no—
30#14519783—21no—
31#14519783—21no—
32#14519783—21no—
33#14519783—21no—
34#14519783—21no—
35#14519783—21no—
36#14519783—21no—
37C2×#11758194C2×C411yescharacteristic
38C2×#11758194C2×C411yescharacteristic
39C2×#11758189—21no—
40C2×#11758189D412yes—
41C2×C8×D61—21no—
42C2×C8×D61D412yes—
43#14519777C811yescharacteristic
44#14519774C811yescharacteristic
45#14519765C811yescharacteristic
46#14519765C811yescharacteristic
47#14519751—22no—
48C4×D244—22no—
49#14519717—21no—
50#14519717—21no—
51#14519717—21no—
52#14519717—21no—
53#14519716—24no—
54C2×#11758185—21no—
55C2×#11758185D412yescomplemented
56C16×D61—24no—
57C4⋊#92418—22no—
58#14519689—22no—
59#14519689—22no—
60C22×C8×C61C2×C411yescharacteristic
61C22×C8×C61C2311yescharacteristic
62C2×C42×C61C2×C411yescharacteristic
63M32×C61—21no—
64M32×C61—21no—
65M32×C61—21no—
66M32×C61—21no—
67C2×C16×C61—21no—
68C2×C16×C61D412yescomplemented
69#97×C61—21no—
70#97×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C2×C22⋊D61—21no—
74C2×C22⋊D61M1612yes—
75#11758222—21no—
76#11758222—21no—
77#11758222—21no—
78#11758222—21no—
79#11758222—21no—
80#11758222—21no—
81#11758222—21no—
82#11758222—21no—
83C2×D244—22no—
84C2×D244C2×C811yescharacteristic
85C2×D244C2×C811yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61C22⋊C412yes—
88C2×Dic122C2×C811yescharacteristic
89C2×Dic122C2×C811yescharacteristic
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C2×C8×C61#4111yescharacteristic
99C42×C61—21no—
100C42×C61C2×C811yescharacteristic
101C42×C61C2×C811yescharacteristic
102#11758198—22no—
103#11758198—22no—
104C4⋊Dic61—22no—
105#11758194—21no—
106#11758194—21no—
107#11758194—21no—
108#11758194—21no—
109C2×#92418—21no—
110C2×#92418C22⋊C412yes—
111#11758189—22no—
112#11758189—22no—
113#11758189—41no—
114#11758189—41no—
115C8×D61—22no—
116C8×D61—22no—
117C8×D61—41no—
118C8×D61—41no—
119C16×C61—22no—
120C16×C61—41no—
121#11758185—22no—
122#11758185—41no—
123C23×C61C2×M1611yescharacteristic
124C22×D61—21no—
125C22×D61C22⋊C812yes—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—81no—
129C2×C4×C61C2×C22⋊C411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C22×C811yescharacteristic
133C2×C4×C61#13111yescharacteristic
134C2×C4×C61#13111yescharacteristic
135C22⋊D61—22no—
136C22⋊D61—22no—
137C22⋊D61—41no—
138C22⋊D61—41no—
139C2×Dic61—21no—
140C2×Dic61C22⋊C812yes—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—82no—
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—41no—
149C4×D61—41no—
150Dic122—21no—
151Dic122—21no—
152Dic122—21no—
153Dic122—21no—
154C8×C61—41no—
155C8×C61#12011yescharacteristic
156C8×C61#12111yescharacteristic
157C8×C61#12111yescharacteristic
158C8×C61#12311yescharacteristic
159#92418—22no—
160#92418—41no—
161#12988—611nomaximal, Sylow
162C22×C61—41no—
163C22×C61C2×C22⋊C811yescharacteristic
164C22×C61#43511yescharacteristic
165C22×C61#43511yescharacteristic
166C2×D61—22no—
167C2×D61—42no—
168C2×D61—42no—
169C2×D61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61#38611yescharacteristic
173C4×C61#40811yescharacteristic
174C4×C61C8×D411yescharacteristic
175C4×C61C8×D411yescharacteristic
176Dic61—22no—
177Dic61—41no—
178#3407—611no—
179#2932—611no—
180#2117—611no—
181#2117—611no—
182#2115—611no—
183#1375—611no—
184#1375D6111yescharacteristic, complemented
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61#186911yescharacteristic
189D61—42no—
190D61—81no—
191C2×#131—611no—
192C2×#131—611no—
193#532—611no—
194#504—1222no—
195#504—1222no—
196C2×M32—611no—
197C2×M32—611no—
198C2×M32—1222no—
199C2×M32C2×D6111yescharacteristic
200C2×M32C2×D6111yescharacteristic
201#435—1222no—
202#435—1222no—
203#423—611no—
204#408—611no—
205#408—611no—
206C2×#97C2×D6111yescharacteristic
207#350—1222no—
208#350—1222no—
209#349—1222no—
210C61#1298811yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×#41—611no—
213#131—1221no—
214#131—1221no—
215#131—1221no—
216#131—1221no—
217#131—1221no—
218#131—1221no—
219#131—1221no—
220#131—1221no—
221C2×M16—611no—
222C2×M16—612no—
223C2×M16—611no—
224C2×M16—1221no—
225C22×C8—612no—
226C22×C8—1221no—
227C22×C8C4×D6111yescharacteristic
228C22×C8C22×D6111yescharacteristic
229C4⋊Q8—611no—
230#127—611no—
231#124—611no—
232#124—611no—
233#121—1222no—
234C4×D4—1222no—
235C2×C42C4×D6111yescharacteristic
236M32—21no—
237M32—21no—
238M32—21no—
239M32—21no—
240M32—1224no—
241M32—1221no—
242M32—1221no—
243M32—1221no—
244M32—1221no—
245C2×C16—21no—
246C2×C16—612no—
247C2×C16—1224no—
248C2×C16—1221no—
249C2×C16D24412yescomplemented
250C4⋊C8—1222no—
251C22⋊C8—1222no—
252C22⋊C8—1222no—
253#97—21no—
254#97—21no—
255#41—1221no—
256#41—1221no—
257#41—1221no—
258#41—1221no—
259#41—1221no—
260#41—1221no—
261#41—1221no—
262#41—1221no—
263C2×Q8—611no—
264C2×Q8—611no—
265C2×D4—612no—
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—1222no—
269C2×D4—1221no—
270C22×C4—21no—
271C22×C4—612no—
272C22×C4—1221no—
273C22×C4C2×C4×D6111yescharacteristic
274M16—1221no—
275M16—1221no—
276M16—1222no—
277M16—1222no—
278M16—1221no—
279M16—1221no—
280M16—2441no—
281M16—2441no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—612no—
286C2×C8—1222no—
287C2×C8—1222no—
288C2×C8—1221no—
289C2×C8—2441no—
290C2×C8—2441no—
291C2×C8C2×D24411yescharacteristic
292C2×C8#1175822211yescharacteristic
293C2×C8D4×D6111yescharacteristic
294C2×C8D4×D6111yescharacteristic
295C2×C8D4×D6111yescharacteristic
296C2×C8#1175822611yescharacteristic
297C4⋊C4—1222no—
298C22⋊C4—1222no—
299C22⋊C4—1222no—
300C42—21no—
301C42C8×D6111yescharacteristic
302C42C8×D6111yescharacteristic
303C16—22no—
304C16—41no—
305C16—1222no—
306C16—2441no—
307C23—612no—
308C23—1221no—
309C23M16×D6111yescharacteristic
310Q8—1221no—
311Q8—1221no—
312Q8—1221no—
313Q8—1221no—
314D4—1222no—
315D4—1222no—
316D4—1221no—
317D4—1221no—
318D4—1221no—
319D4—1221no—
320D4—4882no—
321D4—2441no—
322D4—2441no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—81no—
326C2×C4—612no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1221no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4C22⋊C4×D6111yescharacteristic
333C2×C4#1451973911yescharacteristic
334C2×C4C4×D24411yescharacteristic
335C2×C4C2×C8×D6111yescharacteristic
336C2×C4#1451978311yescharacteristic
337C2×C4#1451978511yescharacteristic
338C8—41no—
339C8—1222no—
340C8—2441no—
341C8#1451974711yescharacteristic
342C8#1451975011yescharacteristic
343C8#1451975211yescharacteristic
344C8#1451976211yescharacteristic
345C22—41no—
346C22—1222no—
347C22—2442no—
348C22—2442no—
349C22—2441no—
350C22C22⋊C8×D6111yescharacteristic
351C22#1683983211yescharacteristic
352C22#1683983511yescharacteristic
353C4—41no—
354C4—41no—
355C4—1222no—
356C4—2441no—
357C4#1683964011yescharacteristic
358C4#1683972711yescharacteristic
359C4#1683982711yescharacteristic
360C4C8×D24411yescharacteristic
361C2—21no—
362C2—21no—
363C2—21no—
364C2—4881no—
365C2—2442no—
366C2#2144611011yescharacteristic
subgroupG/H
centerC4#16839640
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1375C2
socleC2×C61#1869
prime radical#16840312C4
cosocleC22×C8×C61C23
hypercenter#1375D61
hypocenterC61#12988
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C8 ◁ #1375

Complements

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

NH ≅ G/Ntype
1. #21458921C2semidirect
3. #21447448C2semidirect
4. #21447446C2semidirect
5. #21447439C2semidirect
6. #21443899C2semidirect
7. C61×#1375C2semidirect
55. C2×#11758185D4semidirect
68. C2×C16×C61D4semidirect
184. #1375D61semidirect
210. C61#12988semidirect
249. C2×C16D244semidirect

Maximal subgroups

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

subgroupindex
#214589212
#214545382
#214474482
#214474462
#214474392
#214438992
C61×#13752
#1298861