Finite Group Databasebeta

← #29576035

Subgroups — #29576035

Order 15616.

524 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454381C211yesmaximal, characteristic
2#21451588C211yesmaximal, characteristic
3#21444492C211yesmaximal, characteristic, complemented
4#21444490C211yesmaximal, characteristic, complemented
5#21444131C211yesmaximal, characteristic
6#21443677C211yesmaximal, characteristic, complemented
7C61×#1286C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519757—21no—
11C2×#14519734C2211yescharacteristic
12#16839815C2211yescharacteristic
13#16839787—22no—
14#16839787—22no—
15#16839786C2211yescharacteristic
16#16839785—21no—
17#16839694—21no—
18#16839694C412yes—
19#16839689—21no—
20#16839689C412yes—
21#16839667—21no—
22#16839509—22no—
23#16839507—22no—
24#16839487—21no—
25#16839485—21no—
26C61×#431C2211yescharacteristic
27C61×#423C2211yescharacteristic
28C61×#382C2211yescharacteristic
29C22×Dic122—21no—
30C22×C4×D61D411yescharacteristic
31C2×#11758194—21no—
32C2×#11758189—22no—
33M16×D61—42no—
34M16×D61—42no—
35C2×C8×D61—22no—
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777—21no—
40#14519757—42no—
41#14519757—42no—
42#14519734—21no—
43#14519734—21no—
44#14519734—21no—
45#14519734—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61—22no—
48C2×C4⋊Dic61C2×C412yes—
49C2×#11758196C2×C411yescharacteristic
50C2×#11758196D411yescharacteristic
51C2×#11758198—22no—
52C2×#11758198C2×C411yescharacteristic
53C2×#11758198D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C4⋊#92418—21no—
56C4⋊#92418—21no—
57C4⋊#92418D412yes—
58#14519706—24no—
59C22⋊#92418—21no—
60C4×#92418—21no—
61#14519684—22no—
62#14519684—22no—
63C2×M16×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61D412yes—
69C22⋊C8×C61—21no—
70C4×C8×C61—21no—
71#95×C61—21no—
72#95×C61C2×C412yes—
73C23×D61C22⋊C411yescharacteristic
74C22×C4×C61—22no—
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—22no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61D812yes—
87C2×C4×D61SD1612yes—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94M16×C61—41no—
95M16×C61—41no—
96C2×C8×C61—22no—
97C2×C8×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104#11758198—21no—
105#11758198—21no—
106#11758198—21no—
107#11758198—21no—
108#11758198—44no—
109C4⋊Dic61—22no—
110C4⋊Dic61—22no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61—44no—
114#11758196—21no—
115#11758196—21no—
116#11758196—21no—
117#11758196—21no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120#11758194—41no—
121#11758194—41no—
122C2×#92418—22no—
123C2×#92418—41no—
124#11758189—44no—
125C8×D61—44no—
126C23×C61C2×C22⋊C411yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61#10212yes—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×C4×C61C2×D811yescharacteristic
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C61#13711yescharacteristic
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61#10212yes—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—22no—
161Dic122—81no—
162Dic122—81no—
163Dic122—81no—
164Dic122—81no—
165C8×C61—42no—
166C8×C61—81no—
167#92418—42no—
168#92418—81no—
169#9195—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#38611yescharacteristic
173C22×C61C2×#10211yescharacteristic
174C22×C61#41711yescharacteristic
175C2×D61—22no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—42no—
179C2×D61—81no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—82no—
185C4×C61#44711yescharacteristic
186C4×C61#44811yescharacteristic
187C4×C61#48011yescharacteristic
188C4×C61#48111yescharacteristic
189Dic61—22no—
190Dic61—41no—
191Dic61—41no—
192Dic61—82no—
193#2905—611no—
194#2621—611no—
195#1546—611no—
196#1546—611no—
197#1458—611no—
198#1286—611no—
199#1286D6111yescharacteristic, complemented
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#187411yescharacteristic
203C2×C61#190911yescharacteristic
204C2×C61#191511yescharacteristic
205D61—42no—
206C22×M16—1221no—
207C2×C4⋊Q8—611no—
208C2×C22⋊Q8—1221no—
209C2×#117—611no—
210#431—611no—
211#431C2×D6111yescharacteristic
212#424—1222no—
213#424—1222no—
214#423—611no—
215#423—1221no—
216#423C2×D6111yescharacteristic
217#398—612no—
218#398—1221no—
219#397—612no—
220#397—1221no—
221#391—1221no—
222#382C2×D6111yescharacteristic
223#332—1222no—
224#332—1222no—
225#324—1221no—
226#323—1221no—
227C61#919511yescharacteristic, complemented, Sylow
228C22×Q8—1221no—
229C23×C4—611no—
230C2×M16—21no—
231C2×M16—1222no—
232C2×M16—1221no—
233C2×M16—2442no—
234C2×M16—2442no—
235C22×C8—1222no—
236C4⋊Q8—1221no—
237C4⋊Q8—1221no—
238C4⋊Q8—1221no—
239C4⋊Q8—1221no—
240C22⋊Q8—2442no—
241C22⋊Q8—2442no—
242#117—1221no—
243#117—1221no—
244#117—1221no—
245#117—1221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—611no—
249C2×C4⋊C4—612no—
250C2×C4⋊C4—1222no—
251C2×C4⋊C4—1221no—
252C2×C22⋊C4—611no—
253C2×C22⋊C4—611no—
254C2×C22⋊C4—1222no—
255C2×C42—611no—
256C2×C42C22×D6111yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—612no—
260C4⋊C8—1224no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C4⋊C8D24412yes—
264C22⋊C8—21no—
265C22⋊C8—1221no—
266C4×C8—21no—
267C4×C8—1221no—
268#95—21no—
269#95—1222no—
270#95—1222no—
271#95C4×D6112yes—
272C24—611no—
273C2×Q8—2441no—
274C2×Q8—2441no—
275C2×Q8—2441no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×Q8—2441no—
279C22×C4—22no—
280C22×C4—611no—
281C22×C4—612no—
282C22×C4—612no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1222no—
290C22×C4C2×C4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4D4×D6111yescharacteristic
293M16—41no—
294M16—41no—
295M16—2444no—
296M16—2441no—
297M16—2441no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—1222no—
301C2×C8—2444no—
302C2×C8—2441no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1222no—
310C4⋊C4—1222no—
311C4⋊C4—2444no—
312C4⋊C4—2441no—
313C4⋊C4—2441no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—2444no—
319C42—1221no—
320C42—1221no—
321C42C2×D24411yescharacteristic
322C42#1175822211yescharacteristic
323C42D4×D6111yescharacteristic
324C42#1175822611yescharacteristic
325C23—612no—
326C23—1221no—
327C23—1221no—
328C23—2441no—
329C23—2441no—
330C23C22⋊C4×D6111yescharacteristic
331Q8—4881no—
332Q8—4881no—
333Q8—4881no—
334Q8—4881no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—612no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4#1451973911yescharacteristic
355C2×C4C4×D24411yescharacteristic
356C2×C4#1451974711yescharacteristic
357C2×C4#1451975011yescharacteristic
358C2×C4#1451975211yescharacteristic
359C2×C4#1451976211yescharacteristic
360C2×C4D8×D6111yescharacteristic
361C2×C4SD16×D6111yescharacteristic
362C2×C4#1451980411yescharacteristic
363C2×C4#1451980911yescharacteristic
364C8—42no—
365C8—81no—
366C8—4881no—
367C8—2442no—
368C22—21no—
369C22—21no—
370C22—1222no—
371C22—4881no—
372C22—2442no—
373C22—2441no—
374C22—2441no—
375C22#1683964011yescharacteristic
376C22#102×D6111yescharacteristic
377C22#1683976211yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—1222no—
384C4—4882no—
385C4—2441no—
386C4—2441no—
387C4#1683989711yescharacteristic
388C4#1683990211yescharacteristic
389C4#1684007711yescharacteristic
390C4#1684008211yescharacteristic
391C2—21no—
392C2—21no—
393C2—2442no—
394C2#2144613511yescharacteristic
395C2#2144634011yescharacteristic
396C2#2144637011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1286C2
socleC22×C61#386
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1286D61
hypocenterC61#9195
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
3. #21444492C2semidirect
4. #21444490C2semidirect
6. #21443677C2semidirect
7. C61×#1286C2semidirect
199. #1286D61semidirect
227. C61#9195semidirect

Maximal subgroups

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

subgroupindex
#214543812
#214515882
#214444922
#214444902
#214441312
#214436772
C61×#12862
#919561