Finite Group Databasebeta

← #29576860

Subgroups — #29576860

Order 15616.

512 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455307C211yesmaximal, characteristic
2#21454927C211yesmaximal, characteristic
3#21446771C211yesmaximal, characteristic, complemented
4#21445840C211yesmaximal, characteristic
5#21444490C211yesmaximal, characteristic, complemented
6#21443693C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8C2×#14519810—21no—
9C2×#14519777C2211yescharacteristic
10C4×#11758222C2211yescharacteristic
11#16839973—21no—
12#16839973C412yescomplemented
13#16839968—21no—
14#16839968C412yescomplemented
15C8×Dic122—21no—
16C8×D244—21no—
17#16839825—22no—
18#16839814—21no—
19#16839786C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C4⋊C8×D61—21no—
22C2×#14519705—21no—
23#16839772—21no—
24#16839524—22no—
25#16839522—21no—
26#16839507—21no—
27#16839507—21no—
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C22×Dic122—21no—
33#14519810—42no—
34#14519810—42no—
35C2×Dic244—22no—
36C2×#11758190—22no—
37C2×#11758194—21no—
38C22×#92418D412yes—
39C2×C8×D61—22no—
40#14519777—21no—
41#14519777—21no—
42#14519777—21no—
43#14519777C2×C412yes—
44C4×Dic122C2×C411yescharacteristic
45C4×Dic122D411yescharacteristic
46C4×D244C2×C411yescharacteristic
47C4×D244D411yescharacteristic
48C4×C22⋊D61—21no—
49C4×C22⋊D61—21no—
50#14519736D411yescharacteristic
51#14519734—21no—
52C2×C4⋊Dic61—21no—
53C2×C4⋊Dic61—21no—
54C42×D61—21no—
55C4⋊#92418—21no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418—21no—
59#14519706—22no—
60#14519705—42no—
61#14519702—22no—
62#14519702—22no—
63#14519689—22no—
64C8×Dic61—22no—
65C2×M16×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C42×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61C2×C412yes—
71C4⋊C8×C61D411yescharacteristic
72C4⋊C8×C61D411yescharacteristic
73C22⋊C8×C61—21no—
74C4×C8×C61—21no—
75#95×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C2×C22⋊D61—21no—
81C22×Dic61—41no—
82#11758222—21no—
83#11758222—21no—
84#11758222D812yes—
85#11758222SD1612yes—
86C2×D244C22⋊C411yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×Dic122—22no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×Dic122—41no—
96C2×Dic122C22⋊C411yescharacteristic
97M16×C61—41no—
98M16×C61—41no—
99C2×C8×C61—22no—
100C2×C8×C61—21no—
101C2×C8×C61—21no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—41no—
104C42×C61—41no—
105C42×C61—41no—
106C42×C61C22×C411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61#4111yescharacteristic
110C22⋊Dic61—21no—
111#11758198—21no—
112#11758198—21no—
113C4⋊Dic61—22no—
114C4⋊Dic61—22no—
115C4⋊Dic61—41no—
116C4⋊Dic61—41no—
117C4⋊Dic61C22⋊C411yescharacteristic
118C4⋊Dic61C22⋊C411yescharacteristic
119#11758196—21no—
120#11758196—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123C4×Dic61—21no—
124#11758194—41no—
125#11758194—41no—
126C2×#92418—22no—
127C2×#92418—42no—
128C2×#92418—41no—
129Dic244—44no—
130#11758190—44no—
131C8×D61—82no—
132C23×C61#12111yescharacteristic
133C22×D61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—81no—
139C2×C4×C61—81no—
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61C2×SD1611yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C22⋊D61—22no—
151C22⋊D61—22no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—42no—
156C2×Dic61—81no—
157C2×Dic61—81no—
158D244—21no—
159D244#10212yes—
160C4×D61—22no—
161C4×D61—22no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—81no—
165Dic122—21no—
166Dic122—42no—
167Dic122—42no—
168Dic122—81no—
169Dic122—81no—
170Dic122#10212yes—
171C8×C61—42no—
172C8×C61—41no—
173C8×C61—41no—
174#92418—42no—
175#92418—81no—
176#9316—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61#38611yescharacteristic
180C22×C61#46511yescharacteristic
181C22×C61#46611yescharacteristic
182C2×D61—22no—
183C2×D61—41no—
184C2×D61—41no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—82no—
189C4×C61C2×#10211yescharacteristic
190C4×C61#41611yescharacteristic
191C4×C61#45511yescharacteristic
192C4×C61#45611yescharacteristic
193C4×C61#46511yescharacteristic
194C4×C61#46611yescharacteristic
195Dic61—22no—
196Dic61—41no—
197Dic61—41no—
198Dic61—82no—
199#3039—611no—
200#2988—611no—
201#1988—611no—
202#1806—611no—
203#1546—611no—
204#1303D6111yescharacteristic, complemented
205#1292—611no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61#188211yescharacteristic
209C2×C61#189311yescharacteristic
210C2×C61#190211yescharacteristic
211D61—42no—
212C2×#137—1221no—
213C2×C4⋊Q8—611no—
214C4×#41—611no—
215#462—612no—
216#462—1221no—
217#461—612no—
218#461—1221no—
219C8×Q8—1221no—
220C8×D4—1221no—
221C8×D4—1222no—
222#431—1221no—
223#431C2×D6111yescharacteristic
224#423—611no—
225#423C2×D6111yescharacteristic
226C2×C4⋊C8—611no—
227C2×C4⋊C8—1221no—
228C2×#104—1221no—
229#419—1221no—
230C4×C4⋊C4C2×D6111yescharacteristic
231#340—1222no—
232#339—1221no—
233#332—1221no—
234#332—1221no—
235C61#931611yescharacteristic, complemented, Sylow
236C2×#41—611no—
237C22×Q8—1221no—
238#137—2442no—
239#137—2442no—
240C2×Q16—1222no—
241C2×SD16—1222no—
242C2×M16—21no—
243C2×M16—1221no—
244C22×C8—612no—
245C22×C8—1222no—
246C4⋊Q8—612no—
247C4⋊Q8—1221no—
248C4⋊Q8—1221no—
249C4⋊Q8—1221no—
250C4×Q8—611no—
251C4×Q8—611no—
252C4×D4—611no—
253C4×D4—611no—
254C4×D4—1221no—
255C4×D4—1221no—
256#117—611no—
257#117—1221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C42—21no—
262C2×C42—1221no—
263C2×C42C22×D6111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—1222no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270C4⋊C8C4×D6112yes—
271C4⋊C8D24411yescharacteristic
272C4⋊C8D24411yescharacteristic
273#104—2442no—
274#103—1222no—
275#103—1222no—
276C22⋊C8—21no—
277C22⋊C8—1222no—
278C4×C8—21no—
279C4×C8—1222no—
280#95—21no—
281#41—612no—
282#41—612no—
283#41—1221no—
284#41—1221no—
285C2×Q8—611no—
286C2×Q8—1222no—
287C2×Q8—2441no—
288C2×Q8—2441no—
289C2×Q8—2441no—
290C2×Q8—2441no—
291C2×Q8—2441no—
292C2×D4—611no—
293C2×D4—1221no—
294C22×C4—41no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—2441no—
299C22×C4#1175822211yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4D4×D6111yescharacteristic
302Q16—2444no—
303SD16—2444no—
304M16—41no—
305M16—41no—
306M16—2441no—
307M16—2441no—
308C2×C8—22no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—1222no—
312C2×C8—4882no—
313C2×C8—2441no—
314C2×C8—2442no—
315C4⋊C4—22no—
316C4⋊C4—41no—
317C4⋊C4—611no—
318C4⋊C4—611no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C4⋊C4—1222no—
322C4⋊C4—1222no—
323C4⋊C4—2441no—
324C4⋊C4—2441no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C42—41no—
329C42—41no—
330C42—1221no—
331C42—1221no—
332C42—1221no—
333C42C2×C4×D6111yescharacteristic
334C42C2×D24411yescharacteristic
335C42D4×D6111yescharacteristic
336C42#1175822611yescharacteristic
337C23—1221no—
338C23#1451975011yescharacteristic
339Q8—612no—
340Q8—1221no—
341Q8—4881no—
342Q8—4881no—
343Q8—2442no—
344Q8—2442no—
345D4—612no—
346D4—1222no—
347D4—1222no—
348D4—1221no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—1221no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—4881no—
361C2×C4—4881no—
362C2×C4—4881no—
363C2×C4—2442no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4C22⋊C4×D6111yescharacteristic
367C2×C4#1451973911yescharacteristic
368C2×C4C4×D24411yescharacteristic
369C2×C4#1451974711yescharacteristic
370C2×C4#1451975211yescharacteristic
371C2×C4#1451976211yescharacteristic
372C2×C4D8×D6111yescharacteristic
373C2×C4SD16×D6111yescharacteristic
374C2×C4#1451979811yescharacteristic
375C2×C4#1451980011yescharacteristic
376C8—41no—
377C8—41no—
378C8—42no—
379C8—4881no—
380C8—2442no—
381C22—21no—
382C22—21no—
383C22—1222no—
384C22—2441no—
385C22—2441no—
386C22#1683964011yescharacteristic
387C22#1683999411yescharacteristic
388C22#1683999711yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—1222no—
394C4—4882no—
395C4—2441no—
396C4—2441no—
397C4#102×D6111yescharacteristic
398C4#1683975711yescharacteristic
399C4#1683994111yescharacteristic
400C4#1683994611yescharacteristic
401C4#1683999211yescharacteristic
402C4#1683999911yescharacteristic
403C2—21no—
404C2—21no—
405C2—2442no—
406C2#2144618911yescharacteristic
407C2#2144624611yescharacteristic
408C2#2144629111yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9316
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #21446771C2semidirect
5. #21444490C2semidirect
6. #21443693C2semidirect
7. C61×#1303C2semidirect
12. #16839973C4semidirect
14. #16839968C4semidirect
204. #1303D61semidirect
235. C61#9316semidirect

Maximal subgroups

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

subgroupindex
#214553072
#214549272
#214467712
#214458402
#214444902
#214436932
C61×#13032
#931661