Finite Group Databasebeta

← #29833430

Subgroups — #29833430

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458953C211yesmaximal, characteristic
2#21454737C211yesmaximal, characteristic, complemented
3#21447703C214yesmaximal, complemented
4#21447698C214yesmaximal, complemented
5#21447613C211yesmaximal, characteristic, complemented
6C2×#16839569C211yesmaximal, characteristic, complemented
7C2×#16839568C211yesmaximal, characteristic, complemented
8#21447416C211yesmaximal, characteristic, complemented
9C61×#2957C211yesmaximal, characteristic, complemented
10C2×#14519799C2211yescharacteristic
11#16840528—21no—
12#16840203C412yescomplemented
13#16840202C412yescomplemented
14#16840198C412yescomplemented
15#16840197C412yescomplemented
16#16840192C2214yes—
17C2×#14519717C2211yescharacteristic
18C22×#11758185C2211yescharacteristic
19#16839885—22no—
20#16839880C2214yescomplemented
21C2×#14519713C2211yescharacteristic
22#16839780—21no—
23#16839591C2214yescomplemented
24#16839569C2212yescomplemented
25#16839569C2212yescomplemented
26#16839568C2212yescomplemented
27#16839568C2212yescomplemented
28#16839538C2212yescomplemented
29C4×#11758185C2212yescomplemented
30C2×#135×C61C2211yescharacteristic
31C61×#568—21no—
32C61×#444—22no—
33C61×#443C2214yescomplemented
34C2×#108×C61C2211yescharacteristic
35C61×#421—21no—
36C61×#405C2211yescharacteristic
37C2×#11758222—21no—
38#14519799—21no—
39#14519799—21no—
40#14519799C2×C412yes—
41#14519799C2312yes—
42C2×Dic244C2×C411yescharacteristic
43C2×#11758190—21no—
44C2×D488C2×C411yescharacteristic
45#14519785—42no—
46#14519783—24no—
47C2×#11758194—21no—
48M16×D61—42no—
49#14519723C2×C414yes—
50#14519721C2×C414yes—
51#14519720C2×C414yes—
52#14519718C2×C414yes—
53#14519717C2×C412yes—
54#14519717C2×C412yes—
55C2×#11758185—21no—
56C2×#11758185—21no—
57C2×#11758185C2311yescharacteristic
58C2×#11758185C2311yescharacteristic
59C2×#11758185C2312yes—
60#14519713—21no—
61#14519713C2312yes—
62#14519705—24no—
63C2×#41×C61—21no—
64#135×C61—21no—
65#135×C61—21no—
66#135×C61C2×C412yes—
67#135×C61C2312yes—
68C2×Q16×C61C2×C411yescharacteristic
69C2×SD16×C61—21no—
70C2×D8×C61C2×C411yescharacteristic
71#131×C61—24no—
72#131×C61—42no—
73C2×M16×C61—21no—
74C2×M16×C61—42no—
75C2×M16×C61D411yescharacteristic
76C22×C8×C61C2311yescharacteristic
77#117×C61D411yescharacteristic
78#108×C61—21no—
79#108×C61C2312yes—
80#104×C61—24no—
81#97×C61D412yes—
82C4×C8×C61C2312yes—
83#41×C61—22no—
84#41×C61—22no—
85#41×C61—41no—
86#41×C61—41no—
87C2×Q8×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61C2×D411yescharacteristic
92C2×C22⋊D61—41no—
93#11758222—22no—
94#11758222—22no—
95#11758222—41no—
96#11758222—41no—
97C2×D244—21no—
98C2×C4×D61—41no—
99C2×Dic122—21no—
100Q16×C61—21no—
101Q16×C61C22×C412yes—
102SD16×C61—22no—
103SD16×C61—22no—
104D8×C61—21no—
105D8×C61C22×C412yes—
106M16×C61—22no—
107M16×C61—41no—
108M16×C61—44no—
109M16×C61D812yes—
110M16×C61D812yes—
111C2×C8×C61—41no—
112C2×C8×C61—44no—
113C2×C8×C61C22×C411yescharacteristic
114C2×C8×C61C22×C411yescharacteristic
115C2×C8×C61C2×D411yescharacteristic
116C2×C8×C61C2×D412yes—
117C2×C8×C61#4111yescharacteristic
118C2×C8×C61#4111yescharacteristic
119C2×C8×C61C2411yescharacteristic
120C4⋊C4×C61—21no—
121C22⋊C4×C61—21no—
122C42×C61C2×D412yes—
123#11758194—22no—
124#11758194—41no—
125C2×#92418—41no—
126Dic244—21no—
127Dic244C22×C412yes—
128D488—21no—
129D488C22×C412yes—
130#11758190—22no—
131#11758190—22no—
132#11758189—44no—
133C8×D61—44no—
134#11758185—21no—
135#11758185—21no—
136#11758185C22×C414yes—
137C23×C61—41no—
138C23×C61#13511yescharacteristic
139C22×D61—41no—
140Q8×C61—22no—
141Q8×C61—41no—
142D4×C61—22no—
143D4×C61—42no—
144D4×C61—42no—
145D4×C61—41no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61C4×D411yescharacteristic
151C2×C4×C61C4×D411yescharacteristic
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61#13511yescharacteristic
155C2×C4×C61C22×D411yescharacteristic
156C22⋊D61—42no—
157C22⋊D61—42no—
158C2×Dic61—41no—
159D244—22no—
160D244—41no—
161C4×D61—42no—
162C4×D61—42no—
163Dic122—22no—
164Dic122—41no—
165C8×C61—42no—
166C8×C61C4×D411yescharacteristic
167C8×C61C4×D411yescharacteristic
168C8×C61C2×D814yes—
169C8×C61C23×C411yescharacteristic
170C8×C61C2×#4111yescharacteristic
171#92418—42no—
172#33464—611nomaximal, Sylow
173C22×C61—41no—
174C22×C61—42no—
175C22×C61—161no—
176C22×C61C4×D811yescharacteristic
177C22×C61C4×D811yescharacteristic
178C22×C61C2×#13511yescharacteristic
179C2×D61—42no—
180C2×D61—161no—
181C4×C61—42no—
182C4×C61—42no—
183C4×C61C4×D811yescharacteristic
184C4×C61C4×D811yescharacteristic
185C4×C61C2×C4×D411yescharacteristic
186C4×C61C22×D811yescharacteristic
187Dic61—42no—
188#3414—611no—
189#2957—611no—
190#2957D6111yescharacteristic, complemented
191#2179—614no—
192#2178—614no—
193#2161—611no—
194C2×#359—611no—
195C2×#359—611no—
196#2108—611no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—82no—
201C2×C61C2×C4×D811yescharacteristic
202D61—82no—
203C2×#135—611no—
204C2×#135C2×D6111yescharacteristic
205#568—21no—
206#568—1221no—
207#510—612no—
208#510—612no—
209#509—612no—
210#509—612no—
211#508—614no—
212C2×M32—611no—
213C22×C16—611no—
214#444—22no—
215#444—1222no—
216#443—614no—
217#443C2×D6114yescomplemented
218C2×#108—611no—
219C2×#108C2×D6111yescharacteristic
220#421—21no—
221#421—1221no—
222#405C2×D6111yescharacteristic
223#368—614no—
224#359—612no—
225#359—612no—
226#359—612no—
227#359—612no—
228#346—612no—
229C4×C16—612no—
230C61#3346411yescharacteristic, complemented, Sylow
231C2×#41—21no—
232C2×#41—1221no—
233#135—21no—
234#135—21no—
235#135—612no—
236#135—612no—
237#135—1221no—
238#135—1221no—
239#135C4×D6112yes—
240#135C22×D6112yes—
241C2×Q16—611no—
242C2×Q16C4×D6111yescharacteristic
243C2×SD16—21no—
244C2×SD16—1221no—
245C2×D8—611no—
246C2×D8C4×D6111yescharacteristic
247#131—24no—
248#131—42no—
249#131—1224no—
250#131—2442no—
251C2×M16—21no—
252C2×M16—42no—
253C2×M16—1221no—
254C2×M16—2442no—
255C2×M16C22⋊D6111yescharacteristic
256C22×C8C22×D6111yescharacteristic
257#117C22⋊D6111yescharacteristic
258Q32—614no—
259SD32—614no—
260SD32—614no—
261D16—614no—
262M32—612no—
263M32—612no—
264C2×C16—612no—
265C2×C16—611no—
266C2×C16—611no—
267C2×C16—1221no—
268C2×C16—1221no—
269#108—21no—
270#108—612no—
271#108—1221no—
272#108C22×D6112yes—
273#104—24no—
274#104—1224no—
275#97C22⋊D6112yes—
276C4×C8C22×D6112yes—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—1222no—
282#41—1222no—
283#41—2441no—
284#41—2441no—
285C2×Q8—21no—
286C2×Q8—1221no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—1221no—
290C2×D4—2441no—
291C22×C4—41no—
292C22×C4—2441no—
293C22×C4C2×C22⋊D6111yescharacteristic
294Q16—21no—
295Q16—612no—
296Q16—1221no—
297Q16C2×C4×D6112yes—
298SD16—22no—
299SD16—22no—
300SD16—1222no—
301SD16—1222no—
302D8—21no—
303D8—612no—
304D8—1221no—
305D8C2×C4×D6112yes—
306M16—22no—
307M16—41no—
308M16—44no—
309M16—1222no—
310M16—2441no—
311M16—2444no—
312M16#1175819912yes—
313M16#1175819912yes—
314C2×C8—41no—
315C2×C8—44no—
316C2×C8—2441no—
317C2×C8—2444no—
318C2×C8C2×C4×D6111yescharacteristic
319C2×C8C2×C4×D6111yescharacteristic
320C2×C8#1175822211yescharacteristic
321C2×C8#1175822211yescharacteristic
322C2×C8C2×C22⋊D6111yescharacteristic
323C2×C8C2×C22⋊D6112yes—
324C2×C8C23×D6111yescharacteristic
325C4⋊C4—21no—
326C22⋊C4—21no—
327C42C2×C22⋊D6112yes—
328C16—614no—
329C16—1221no—
330C16—1221no—
331C23—41no—
332C23—2441no—
333C23#1451979711yescharacteristic
334Q8—22no—
335Q8—41no—
336Q8—1222no—
337Q8—2441no—
338D4—22no—
339D4—42no—
340D4—42no—
341D4—41no—
342D4—1222no—
343D4—2442no—
344D4—2442no—
345D4—2441no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—2441no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4C4×C22⋊D6111yescharacteristic
354C2×C4C4×C22⋊D6111yescharacteristic
355C2×C4C2×#1175819911yescharacteristic
356C2×C4C2×#1175819911yescharacteristic
357C2×C4#1451979711yescharacteristic
358C2×C4C22×C22⋊D6111yescharacteristic
359C8—42no—
360C8—2442no—
361C8C4×C22⋊D6111yescharacteristic
362C8C4×C22⋊D6111yescharacteristic
363C8C2×#1175819914yes—
364C8C22×C4×D6111yescharacteristic
365C8C2×#1175822211yescharacteristic
366C22—41no—
367C22—42no—
368C22—161no—
369C22—9761no—
370C22—2442no—
371C22C4×#1175819911yescharacteristic
372C22C4×#1175819911yescharacteristic
373C22C2×#1451979711yescharacteristic
374C4—42no—
375C4—42no—
376C4—2442no—
377C4C4×#1175819911yescharacteristic
378C4C4×#1175819911yescharacteristic
379C4C2×C4×C22⋊D6111yescharacteristic
380C4C22×#1175819911yescharacteristic
381C2—21no—
382C2—21no—
383C2—21no—
384C2—82no—
385C2—4882no—
386C2C2×C4×#1175819911yescharacteristic
subgroupG/H
centerC4C22×#11758199
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC61×#2957C2
socleC2×C61C2×C4×D8
prime radical#21458953C2
cosocleC2×C8×C61C24
hypercenter#2957D61
hypocenterC61#33464
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×M16 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #21454737C2semidirect
3. #21447703C2semidirect
4. #21447698C2semidirect
5. #21447613C2semidirect
6. C2×#16839569C2semidirect
7. C2×#16839568C2semidirect
8. #21447416C2semidirect
9. C61×#2957C2semidirect
12. #16840203C4semidirect
13. #16840202C4semidirect
14. #16840198C4semidirect
15. #16840197C4semidirect
20. #16839880C22semidirect
23. #16839591C22semidirect
24. #16839569C22semidirect
25. #16839569C22semidirect
26. #16839568C22semidirect
27. #16839568C22semidirect
28. #16839538C22semidirect
29. C4×#11758185C22semidirect
33. C61×#443C22semidirect
190. #2957D61semidirect
217. #443C2×D61semidirect
230. C61#33464semidirect

Maximal subgroups

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

subgroupindex
#214589532
#214547372
#214477032
#214476982
#214476132
C2×#168395692
C2×#168395682
#214474162
C61×#29572
#3346461