Finite Group Databasebeta

← #29576862

Subgroups — #29576862

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#21455302C211yesmaximal, characteristic
2#21454928C211yesmaximal, characteristic
3#21445840C211yesmaximal, characteristic
4#21444491C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443694C211yesmaximal, characteristic, complemented
7C61×#1988C211yesmaximal, characteristic, complemented
8C2×#14519808—21no—
9C4×#11758222C2211yescharacteristic
10#16839969—21no—
11#16839969C412yescomplemented
12#16839964—21no—
13#16839964C412yescomplemented
14#16839886—21no—
15#16839827—21no—
16C8×C22⋊D61—22no—
17#16839815C2211yescharacteristic
18#16839814—21no—
19#16839786C2211yescharacteristic
20#16839786C2211yescharacteristic
21C4⋊C8×D61—21no—
22C2×#14519705—21no—
23#16839771—21no—
24#16839522—21no—
25#16839508—21no—
26#16839508—21no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C4×C4⋊C4×C61C2211yescharacteristic
30C61×#340—22no—
31C2×#11758222D411yescharacteristic
32#14519808—42no—
33#14519808—42no—
34C2×#11758202—22no—
35C2×#11758201—22no—
36C2×#11758194—21no—
37C2×#11758194—21no—
38C2×C8×D61—22no—
39C4×Dic122C2×C411yescharacteristic
40C4×Dic122D411yescharacteristic
41C4×D244C2×C411yescharacteristic
42C4×D244D411yescharacteristic
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45#14519736D411yescharacteristic
46#14519734—21no—
47C42×D61—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C4⋊#92418C2×C412yes—
52C4⋊#92418D411yescharacteristic
53C4⋊#92418D411yescharacteristic
54#14519706—22no—
55#14519705—42no—
56#14519701—22no—
57#14519701—22no—
58C22⋊#92418—21no—
59#14519689—22no—
60C4×#92418—21no—
61C8×Dic61—22no—
62C22×Q8×C61—21no—
63C22×C8×C61D412yes—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61C2×C412yes—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C42×C61—21no—
72C2×C42×C61C2311yescharacteristic
73C4⋊C8×C61—21no—
74C4⋊C8×C61—21no—
75#95×C61—21no—
76C2×Q8×C61—22no—
77C2×Q8×C61—41no—
78C2×Q8×C61—41no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C2×C22⋊D61—21no—
88#11758222—21no—
89#11758222—21no—
90#11758222D812yes—
91#11758222SD1612yes—
92C2×D244C22⋊C411yescharacteristic
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×Dic122C22⋊C411yescharacteristic
97C2×C8×C61—22no—
98C2×C8×C61—42no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—22no—
101C4⋊C4×C61—22no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C42×C61—41no—
106C42×C61—41no—
107C42×C61C22×C411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61#4111yescharacteristic
111C22⋊Dic61—21no—
112#11758202—44no—
113#11758201—44no—
114#11758198—21no—
115#11758198—21no—
116C4⋊Dic61C22⋊C411yescharacteristic
117C4⋊Dic61C22⋊C411yescharacteristic
118#11758196—21no—
119#11758196—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123#11758194—41no—
124#11758194—41no—
125#11758194—41no—
126#11758194—41no—
127C2×#92418—22no—
128C2×#92418—21no—
129C2×#92418—21no—
130C2×#92418—41no—
131C8×D61—82no—
132C23×C61#12111yescharacteristic
133C22×D61—21no—
134Q8×C61—42no—
135Q8×C61—42no—
136Q8×C61—81no—
137Q8×C61—81no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—81no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C4×D411yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12311yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C2×SD1611yescharacteristic
155C2×C4×C61#13511yescharacteristic
156C2×C4×C61#13511yescharacteristic
157C22⋊D61—22no—
158C22⋊D61—22no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162D244—21no—
163D244#10212yes—
164C4×D61—22no—
165C4×D61—22no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—81no—
169Dic122—21no—
170Dic122#10212yes—
171C8×C61—42no—
172#92418—42no—
173#92418—41no—
174#92418—41no—
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×C61—82no—
190C4×C61C2×#10211yescharacteristic
191C4×C61#41611yescharacteristic
192C4×C61#45511yescharacteristic
193C4×C61#45611yescharacteristic
194C4×C61#46511yescharacteristic
195C4×C61#46611yescharacteristic
196Dic61—22no—
197Dic61—41no—
198Dic61—41no—
199#3039—611no—
200#2988—611no—
201#1988D6111yescharacteristic, complemented
202#1806—611no—
203#1546—611no—
204#1303—611no—
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⋊Q8C2×D6111yescharacteristic
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—611no—
223#431—1221no—
224#423—611no—
225#423—611no—
226C2×C4⋊C8—1221no—
227C2×C4⋊C8C2×D6111yescharacteristic
228C2×#104—1221no—
229#419—1221no—
230C4×C4⋊C4C2×D6111yescharacteristic
231#340—22no—
232#339—1221no—
233#332—1221no—
234#332—1221no—
235C61#931611yescharacteristic, complemented, Sylow
236C2×#41—611no—
237C22×Q8—21no—
238#137—2442no—
239#137—2442no—
240C2×Q16—1222no—
241C2×SD16—1222no—
242C2×M16—1221no—
243C2×M16—1221no—
244C22×C8—1222no—
245C22×C8C22⋊D6112yes—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C4×D6112yes—
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—21no—
260C2×C4⋊C4—21no—
261C2×C42—21no—
262C2×C42—1221no—
263C2×C42C22×D6111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—612no—
267C4⋊C8—611no—
268C4⋊C8—611no—
269C4⋊C8—1222no—
270C4⋊C8—1221no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273#104—2442no—
274#103—1222no—
275#103—1222no—
276C22⋊C8—1222no—
277C22⋊C8—1221no—
278C4×C8—1222no—
279C4×C8—1221no—
280#95—21no—
281#41—612no—
282#41—612no—
283#41—1221no—
284#41—1221no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—611no—
292C2×D4—611no—
293C2×D4—1221no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4D4×D6111yescharacteristic
300C22×C4#1175822411yescharacteristic
301C22×C4C2×C22⋊D6111yescharacteristic
302Q16—2444no—
303SD16—2444no—
304M16—2441no—
305M16—2441no—
306M16—2441no—
307M16—2441no—
308C2×C8—22no—
309C2×C8—42no—
310C2×C8—1222no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—4882no—
314C2×C8—2441no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—611no—
322C4⋊C4—611no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C42—41no—
329C42—41no—
330C42—1221no—
331C42—1221no—
332C42—1221no—
333C42C2×C4×D6111yescharacteristic
334C42#1175822211yescharacteristic
335C42D4×D6111yescharacteristic
336C42D4×D6111yescharacteristic
337C23—1221no—
338C23#1451974811yescharacteristic
339Q8—42no—
340Q8—42no—
341Q8—81no—
342Q8—81no—
343Q8—612no—
344Q8—1221no—
345D4—612no—
346D4—1222no—
347D4—1222no—
348D4—1221no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—1221no—
359C2×C4—1222no—
360C2×C4—1222no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—4881no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4C22⋊C4×D6111yescharacteristic
367C2×C4#1451973711yescharacteristic
368C2×C4C4×C22⋊D6111yescharacteristic
369C2×C4#1451974511yescharacteristic
370C2×C4#1451975011yescharacteristic
371C2×C4#1451975911yescharacteristic
372C2×C4D8×D6111yescharacteristic
373C2×C4SD16×D6111yescharacteristic
374C2×C4#1451979611yescharacteristic
375C2×C4#1451979811yescharacteristic
376C8—42no—
377C8—4881no—
378C8—2441no—
379C8—2441no—
380C8—2442no—
381C22—21no—
382C22—21no—
383C22—1222no—
384C22—2441no—
385C22—2441no—
386C22#1683963811yescharacteristic
387C22#1683998811yescharacteristic
388C22#1683999511yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—82no—
394C4—1222no—
395C4—2441no—
396C4—2441no—
397C4#102×D6111yescharacteristic
398C4#1683975511yescharacteristic
399C4#1683993911yescharacteristic
400C4#1683994411yescharacteristic
401C4#1683999011yescharacteristic
402C4#1683999711yescharacteristic
403C2—21no—
404C2—21no—
405C2—2442no—
406C2#2144619111yescharacteristic
407C2#2144624411yescharacteristic
408C2#2144628911yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1988C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1988D61
hypocenterC61#9316
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #21444491C2semidirect
5. #21443722C2semidirect
6. #21443694C2semidirect
7. C61×#1988C2semidirect
11. #16839969C4semidirect
13. #16839964C4semidirect
201. #1988D61semidirect
235. C61#9316semidirect

Maximal subgroups

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

subgroupindex
#214553022
#214549282
#214458402
#214444912
#214437222
#214436942
C61×#19882
#931661