Finite Group Databasebeta

← #29598174

Subgroups — #29598174

Order 15616.

450 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#21454529C211yesmaximal, characteristic
2#21447574C211yesmaximal, characteristic, complemented
3C2×#16839547C211yesmaximal, characteristic, complemented
4C2×#16839546C211yesmaximal, characteristic, complemented
5C2×#16839545C211yesmaximal, characteristic, complemented
6C2×C16×Dic61C211yesmaximal, characteristic, complemented
7C2×C61×#350C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9#16840308C411yescharacteristic
10C2×#14519717C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12#16839838—22no—
13C8×C22⋊D61—22no—
14#16839785C411yescharacteristic
15#16839730C411yescharacteristic
16#16839729C411yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18#16839580—22no—
19#16839547—22no—
20#16839546—22no—
21#16839545—22no—
22C16×Dic61—22no—
23C2×#131×C61C2211yescharacteristic
24C2×M32×C61C2211yescharacteristic
25C22×C16×C61C2211yescharacteristic
26C61×#350—22no—
27C2×#11758222C2×C411yescharacteristic
28#14519783—21no—
29#14519783—21no—
30#14519783—21no—
31#14519783—21no—
32C2×#11758194C2×C411yescharacteristic
33C2×#11758189—21no—
34C22×#92418C2×C411yescharacteristic
35C2×C8×D61—21no—
36#14519775C811yescharacteristic
37#14519773C811yescharacteristic
38#14519766C811yescharacteristic
39#14519764C811yescharacteristic
40#14519749—22no—
41C4×C22⋊D61—22no—
42C2×C4×Dic61C2×C411yescharacteristic
43#14519717—21no—
44#14519717—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185—21no—
48C2×#11758185D412yescomplemented
49#14519706—22no—
50C22⋊#92418—22no—
51#14519689—22no—
52C8×Dic61D412yes—
53C8×Dic61D412yes—
54C2×#41×C61C2×C411yescharacteristic
55#131×C61—21no—
56#131×C61—21no—
57#131×C61—21no—
58#131×C61—21no—
59C2×M16×C61—21no—
60C2×M16×C61C2×C411yescharacteristic
61C22×C8×C61—21no—
62C22×C8×C61C2311yescharacteristic
63M32×C61—21no—
64M32×C61—21no—
65C2×C16×C61—21no—
66C2×C16×C61—21no—
67C2×C16×C61—21no—
68C2×C16×C61D412yescomplemented
69#41×C61—21no—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61—21no—
73C2×Q8×C61C2×C811yescharacteristic
74C2×D4×C61—21no—
75C2×D4×C61C2×C811yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61C22×C411yescharacteristic
78C2×C22⋊D61—21no—
79C2×C22⋊D61—22no—
80C22×Dic61M1612yes—
81#11758222—21no—
82#11758222—21no—
83#11758222—21no—
84#11758222—21no—
85C2×D244C2×C811yescharacteristic
86C2×C4×D61—21no—
87C2×Dic122C2×C811yescharacteristic
88M16×C61—21no—
89M16×C61—21no—
90M16×C61—41no—
91M16×C61—41no—
92C2×C8×C61—21no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61#4111yescharacteristic
100C2×C8×C61#4111yescharacteristic
101C22⋊Dic61—22no—
102#11758198—22no—
103#11758196—22no—
104C4×Dic61C22⋊C412yes—
105C4×Dic61C2×C811yescharacteristic
106C4×Dic61C2×C811yescharacteristic
107#11758194—21no—
108#11758194—21no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418C22⋊C412yes—
113#11758189—41no—
114#11758189—41no—
115C8×D61—41no—
116C8×D61—41no—
117C16×C61—22no—
118C16×C61—41no—
119#11758185—22no—
120#11758185—41no—
121C23×C61—21no—
122C23×C61C2×M1611yescharacteristic
123C22×D61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—41no—
129D4×C61—41no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61#13111yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C22⋊D61—41no—
140C22⋊D61—41no—
141C22⋊D61—44no—
142C2×Dic61—24no—
143C2×Dic61—21no—
144C2×Dic61C22⋊C812yes—
145C2×Dic61C22⋊C812yes—
146D244—21no—
147D244—21no—
148C4×D61—41no—
149C4×D61—41no—
150Dic122—21no—
151Dic122—21no—
152C8×C61—41no—
153C8×C61#12111yescharacteristic
154C8×C61#12111yescharacteristic
155C8×C61#12411yescharacteristic
156C8×C61#12711yescharacteristic
157#92418—22no—
158#92418—41no—
159#13191—611nomaximal, Sylow
160C22×C61—22no—
161C22×C61—42no—
162C22×C61—41no—
163C22×C61C2×C22⋊C811yescharacteristic
164C22×C61#43611yescharacteristic
165C22×C61#43611yescharacteristic
166C2×D61—42no—
167C2×D61—41no—
168C4×C61—41no—
169C4×C61#39011yescharacteristic
170C4×C61#40811yescharacteristic
171C4×C61C8×D411yescharacteristic
172C4×C61C8×D411yescharacteristic
173Dic61—22no—
174Dic61—41no—
175Dic61#35014yescomplemented
176#2931—611no—
177#2150—611no—
178C2×#350—611no—
179C2×#350—611no—
180C2×#350—611no—
181C2×#350D6111yescharacteristic, complemented
182C2×C4×C16—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—81no—
186C2×C61#195411yescharacteristic
187C2×C61C2×#35012yes—
188D61—81no—
189C2×#131—611no—
190C2×#131C2×D6111yescharacteristic
191#532—611no—
192C2×M32—611no—
193C2×M32C2×D6111yescharacteristic
194C22×C16—611no—
195C22×C16C2×D6111yescharacteristic
196#436—1222no—
197C8×D4—1222no—
198#423—611no—
199#408—611no—
200#408—611no—
201C2×C4×C8—611no—
202C4⋊C16—1222no—
203#350—22no—
204#350—1222no—
205#350—1222no—
206#350—1222no—
207C4×C16—1222no—
208C61#1319111yescharacteristic, complemented, Sylow
209C2×#41—611no—
210C2×#41C4×D6111yescharacteristic
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—1221no—
216#131—1221no—
217#131—1221no—
218#131—1221no—
219C2×M16—21no—
220C2×M16—611no—
221C2×M16—1221no—
222C2×M16C4×D6111yescharacteristic
223C22×C8—21no—
224C22×C8—611no—
225C22×C8—1221no—
226C22×C8C22×D6111yescharacteristic
227C4⋊Q8—611no—
228#127—611no—
229#124—611no—
230#124—611no—
231#121—1222no—
232C4×D4—1222no—
233C2×C42—611no—
234M32—21no—
235M32—21no—
236M32—1221no—
237M32—1221no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—612no—
242C2×C16—1221no—
243C2×C16—1221no—
244C2×C16—1221no—
245C2×C16C22⋊D6112yescomplemented
246C4⋊C8—1222no—
247C22⋊C8—1222no—
248C22⋊C8—1222no—
249C4×C8—612no—
250C4×C8—612no—
251#41—21no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—1221no—
256#41—1221no—
257#41—1221no—
258#41—1221no—
259C2×Q8—611no—
260C2×Q8C8×D6111yescharacteristic
261C2×D4—21no—
262C2×D4—611no—
263C2×D4—1222no—
264C2×D4—1221no—
265C2×D4C8×D6111yescharacteristic
266C22×C4—21no—
267C22×C4—612no—
268C22×C4—1221no—
269C22×C4C2×C4×D6111yescharacteristic
270M16—21no—
271M16—21no—
272M16—41no—
273M16—41no—
274M16—1221no—
275M16—1221no—
276M16—2441no—
277M16—2441no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—612no—
282C2×C8—1221no—
283C2×C8—1221no—
284C2×C8—1221no—
285C2×C8—2441no—
286C2×C8—2441no—
287C2×C8#1175822211yescharacteristic
288C2×C8D4×D6111yescharacteristic
289C2×C8D4×D6111yescharacteristic
290C2×C8D4×D6111yescharacteristic
291C2×C8#1175822411yescharacteristic
292C2×C8C2×C22⋊D6111yescharacteristic
293C4⋊C4—1222no—
294C22⋊C4—1222no—
295C22⋊C4—1222no—
296C42—612no—
297C42—611no—
298C42—611no—
299C16—22no—
300C16—41no—
301C16—1222no—
302C16—2441no—
303C23—21no—
304C23—1221no—
305C23M16×D6111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—1221no—
309Q8—1221no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—1221no—
315D4—1221no—
316D4—2444no—
317D4—2441no—
318D4—2441no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—612no—
323C2×C4—612no—
324C2×C4—1224no—
325C2×C4—1221no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4C22⋊C4×D6111yescharacteristic
329C2×C4#1451973711yescharacteristic
330C2×C4C4×C22⋊D6111yescharacteristic
331C2×C4C2×C8×D6111yescharacteristic
332C2×C4#1451978311yescharacteristic
333C2×C4#1451978511yescharacteristic
334C8—41no—
335C8—1222no—
336C8—2441no—
337C8#1451974911yescharacteristic
338C8#1451975011yescharacteristic
339C8#1451976311yescharacteristic
340C8#1451977311yescharacteristic
341C22—22no—
342C22—42no—
343C22—41no—
344C22—2442no—
345C22—2441no—
346C22C22⋊C8×D6111yescharacteristic
347C22#1683983711yescharacteristic
348C22#1683983811yescharacteristic
349C4—41no—
350C4—614no—
351C4—1222no—
352C4—2441no—
353C4#1683966211yescharacteristic
354C4#1683972711yescharacteristic
355C4#1683982511yescharacteristic
356C4C8×C22⋊D6111yescharacteristic
357C2—21no—
358C2—21no—
359C2—81no—
360C2—4881no—
361C2#2144661111yescharacteristic
362C2#350×D6112yes—
subgroupG/H
centerC2×C8D4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#350C2
socleC22×C61C2×C22⋊C8
prime radical#16840308C4
cosocleC22×C8×C61C23
hypercenterC2×#350D61
hypocenterC61#13191
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. #21447574C2semidirect
3. C2×#16839547C2semidirect
4. C2×#16839546C2semidirect
5. C2×#16839545C2semidirect
6. C2×C16×Dic61C2semidirect
7. C2×C61×#350C2semidirect
48. C2×#11758185D4semidirect
68. C2×C16×C61D4semidirect
175. Dic61#350semidirect
181. C2×#350D61semidirect
208. C61#13191semidirect
245. C2×C16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214545292
#214475742
C2×#168395472
C2×#168395462
C2×#168395452
C2×C16×Dic612
C2×C61×#3502
#1319161