Finite Group Databasebeta

← #29596923

Subgroups — #29596923

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458921C211yesmaximal, characteristic, complemented
2C2×#16839885C211yesmaximal, characteristic
3#21447448C211yesmaximal, characteristic, complemented
4#21447446C211yesmaximal, characteristic, complemented
5#21447439C211yesmaximal, characteristic, complemented
6#21443903C211yesmaximal, characteristic, complemented
7C61×#1375C211yesmaximal, characteristic, complemented
8C2×#14519799C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10C2×#14519783C2211yescharacteristic
11#16840180—22no—
12#16840178—22no—
13C2×#14519717C2211yescharacteristic
14C2×#14519717C2211yescharacteristic
15M32×D61—22no—
16#16839885—22no—
17#16839885—22no—
18C2×#14519713C411yescharacteristic
19C2×#14519705C411yescharacteristic
20C2×#14519705C411yescharacteristic
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#14519799—22no—
30#14519799—22no—
31C2×Dic244C811yescharacteristic
32C2×#11758190C811yescharacteristic
33C2×#11758190C811yescharacteristic
34C2×D488C811yescharacteristic
35#14519783—21no—
36#14519783—21no—
37#14519783—21no—
38#14519783—21no—
39#14519783—21no—
40#14519783—21no—
41#14519783D412yes—
42#14519783D412yes—
43C2×#11758194C2×C411yescharacteristic
44C2×#11758194C2×C411yescharacteristic
45C2×#11758189—21no—
46C2×#11758189—21no—
47C2×C8×D61—21no—
48C2×C8×D61—21no—
49#14519717—21no—
50#14519717—21no—
51#14519717—21no—
52#14519717D412yes—
53#14519716—24no—
54C2×#11758185—21no—
55C2×#11758185—21no—
56C16×D61—24no—
57#14519713—22no—
58#14519705—22no—
59#14519705—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×C61D412yes—
69#97×C61—21no—
70#97×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22×C411yescharacteristic
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75#11758222—21no—
76#11758222—21no—
77#11758222—21no—
78#11758222—21no—
79#11758222—21no—
80#11758222—21no—
81#11758222C22⋊C412yes—
82#11758222M1612yes—
83C2×D244C2×C811yescharacteristic
84C2×D244C2×C811yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×Dic122C2×C811yescharacteristic
88C2×Dic122C2×C811yescharacteristic
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61C2×C811yescharacteristic
92C2×C8×C61C2×C811yescharacteristic
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×C61—21no—
101#11758194—21no—
102#11758194—21no—
103#11758194—21no—
104#11758194C22⋊C412yes—
105C2×#92418—21no—
106C2×#92418—21no—
107Dic244—22no—
108D488—22no—
109#11758190—22no—
110#11758190—22no—
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×C61#13111yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—81no—
128C2×C4×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C22×C811yescharacteristic
132C2×C4×C61C2×M1611yescharacteristic
133C2×C4×C61#13111yescharacteristic
134C22⋊D61—22no—
135C22⋊D61—22no—
136C22⋊D61—41no—
137C22⋊D61—41no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140D244—21no—
141D244—21no—
142D244—21no—
143D244C22⋊C812yes—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—41no—
147C4×D61—41no—
148Dic122—21no—
149Dic122—21no—
150Dic122—21no—
151Dic122C22⋊C812yes—
152C8×C61—21no—
153C8×C61—21no—
154C8×C61#12011yescharacteristic
155C8×C61#12111yescharacteristic
156C8×C61#12111yescharacteristic
157C8×C61#12311yescharacteristic
158#92418—22no—
159#92418—41no—
160#12986—611nomaximal, Sylow
161C22×C61—41no—
162C22×C61#40811yescharacteristic
163C22×C61C8×D411yescharacteristic
164C22×C61#43511yescharacteristic
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—81no—
168C2×D61—81no—
169C4×C61—81no—
170C4×C61#38611yescharacteristic
171C4×C61C2×C22⋊C811yescharacteristic
172C4×C61C8×D411yescharacteristic
173C4×C61#43511yescharacteristic
174Dic61—22no—
175Dic61—41no—
176#3407—611no—
177C2×#444—611no—
178#2117—611no—
179#2117—611no—
180#2115—611no—
181#1377—611no—
182#1375D6111yescharacteristic, complemented
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#186911yescharacteristic
187D61—42no—
188D61—81no—
189C2×#135—611no—
190C2×#131—611no—
191C2×#131—611no—
192#504—1222no—
193#504—1222no—
194C2×M32—611no—
195C2×M32—611no—
196C2×M32—1222no—
197C2×M32C2×D6111yescharacteristic
198C2×M32C2×D6111yescharacteristic
199#444—1222no—
200#444—1222no—
201C2×#108—611no—
202C2×#104—611no—
203C2×#104—611no—
204C2×#97C2×D6111yescharacteristic
205#350—1222no—
206#350—1222no—
207#349—1222no—
208C61#1298611yescharacteristic, complemented, Sylow
209C2×#41—611no—
210C2×#41—611no—
211#135—1222no—
212#135—1222no—
213C2×Q16—611no—
214C2×SD16—611no—
215C2×SD16—611no—
216C2×D8—611no—
217#131—612no—
218#131—612no—
219#131—1221no—
220#131—1221no—
221#131—1221no—
222#131—1221no—
223#131—1221no—
224#131—1221no—
225C2×M16—611no—
226C2×M16—611no—
227C2×M16—1221no—
228C2×M16—1221no—
229C22×C8—1221no—
230C22×C8—1221no—
231C22×C8C4×D6111yescharacteristic
232C22×C8C22×D6111yescharacteristic
233C2×C42C4×D6111yescharacteristic
234M32—21no—
235M32—21no—
236M32—21no—
237M32—21no—
238M32—612no—
239M32—1224no—
240M32—1221no—
241M32—1221no—
242M32—1221no—
243C2×C16—21no—
244C2×C16—1224no—
245C2×C16—1221no—
246C2×C16—1221no—
247C2×C16D24412yes—
248#108—1222no—
249#104—1222no—
250#104—1222no—
251#97—21no—
252#97—21no—
253#41—612no—
254#41—612no—
255#41—1221no—
256#41—1221no—
257#41—1221no—
258#41—1221no—
259#41—1221no—
260#41—1221no—
261C2×Q8—611no—
262C2×Q8—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—1221no—
267C22×C4—21no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4C2×C4×D6111yescharacteristic
271Q16—1222no—
272SD16—1222no—
273SD16—1222no—
274D8—1222no—
275M16—612no—
276M16—1221no—
277M16—1222no—
278M16—1222no—
279M16—1221no—
280M16—1221no—
281M16—2441no—
282M16—2441no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—1221no—
286C2×C8—1222no—
287C2×C8—1222no—
288C2×C8—1221no—
289C2×C8—2441no—
290C2×C8—2441no—
291C2×C8C8×D6111yescharacteristic
292C2×C8C8×D6111yescharacteristic
293C2×C8C2×D24411yescharacteristic
294C2×C8#1175822211yescharacteristic
295C2×C8D4×D6111yescharacteristic
296C2×C8D4×D6111yescharacteristic
297C2×C8D4×D6111yescharacteristic
298C2×C8#1175822611yescharacteristic
299C42—21no—
300C42—21no—
301C16—22no—
302C16—41no—
303C16—1222no—
304C16—2441no—
305C23—1221no—
306C23—1221no—
307C23#1451978511yescharacteristic
308Q8—612no—
309Q8—1221no—
310Q8—1221no—
311Q8—1221no—
312D4—612no—
313D4—1222no—
314D4—1222no—
315D4—1221no—
316D4—1221no—
317D4—1221no—
318D4—2441no—
319D4—2441no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—1221no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1221no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4C22⋊C4×D6111yescharacteristic
329C2×C4#1451973911yescharacteristic
330C2×C4C4×D24411yescharacteristic
331C2×C4C2×C8×D6111yescharacteristic
332C2×C4M16×D6111yescharacteristic
333C2×C4#1451978311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1222no—
337C8—2441no—
338C8#1451974711yescharacteristic
339C8#1451975011yescharacteristic
340C8#1451975211yescharacteristic
341C8#1451976211yescharacteristic
342C22—41no—
343C22—1222no—
344C22—4881no—
345C22—4881no—
346C22—2441no—
347C22#1683972711yescharacteristic
348C22#1683982711yescharacteristic
349C22#1683983511yescharacteristic
350C4—81no—
351C4—1222no—
352C4—2441no—
353C4#1683964011yescharacteristic
354C4C22⋊C8×D6111yescharacteristic
355C4C8×D24411yescharacteristic
356C4#1683983211yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—4881no—
361C2—2442no—
362C2#2144611011yescharacteristic
subgroupG/H
centerC4#16839640
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1375C2
socleC2×C61#1869
prime radicalC2×#14519799C4
cosocleC22×C8×C61C23
hypercenter#1375D61
hypocenterC61#12986
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. #21443903C2semidirect
7. C61×#1375C2semidirect
182. #1375D61semidirect
208. C61#12986semidirect

Maximal subgroups

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

subgroupindex
#214589212
C2×#168398852
#214474482
#214474462
#214474392
#214439032
C61×#13752
#1298661