Finite Group Databasebeta

← #29576747

Subgroups — #29576747

Order 15616.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456940C211yesmaximal, characteristic
2#21446651C211yesmaximal, characteristic
3#21444491C211yesmaximal, characteristic, complemented
4#21444378C211yesmaximal, characteristic
5#21443677C211yesmaximal, characteristic, complemented
6#21443648C211yesmaximal, characteristic, complemented
7C61×#2327C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840165C412yescomplemented
10#16840110C412yescomplemented
11#16840075—22no—
12#16840039—22no—
13#16839815C2211yescharacteristic
14#16839815C2211yescharacteristic
15#16839786C2211yescharacteristic
16C2×#14519705—21no—
17C2×#14519705—21no—
18#16839508—22no—
19#16839495—22no—
20C2×C4⋊Q8×C61C2211yescharacteristic
21C2×C4×Q8×C61—21no—
22C61×#391—21no—
23C61×#387—22no—
24C61×#387—22no—
25C61×#382C2211yescharacteristic
26C61×#376C2211yescharacteristic
27C2×#11758222—21no—
28C2×#11758194—21no—
29#14519777C2×C411yescharacteristic
30#14519774C2×C411yescharacteristic
31#14519765—21no—
32#14519751—21no—
33#14519751—21no—
34C4×D244—21no—
35C4×D244—21no—
36#14519710—24no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41#14519705—42no—
42#14519705—42no—
43#14519697—24no—
44C22⋊#92418—21no—
45C22⋊#92418—21no—
46C4×#92418—21no—
47C4×#92418C2×C412yes—
48C22×Q8×C61—21no—
49C4⋊Q8×C61—21no—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61C2×C412yes—
52C4⋊Q8×C61D412yes—
53C4×Q8×C61—42no—
54C4×Q8×C61—42no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—22no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61D412yes—
59C2×C42×C61—22no—
60C2×C42×C61D411yescharacteristic
61C2×C42×C61D411yescharacteristic
62C2×C42×C61C2311yescharacteristic
63#95×C61—24no—
64#95×C61—21no—
65#95×C61—21no—
66#95×C61—21no—
67#95×C61D412yes—
68C2×Q8×C61—22no—
69C2×Q8×C61—22no—
70C2×Q8×C61—41no—
71C2×Q8×C61—41no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C22×C4×C61—21no—
75C22×C4×C61—22no—
76C22×C4×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C2×C22⋊D61—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×C4×D61—41no—
90C2×Dic122—21no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—44no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61C22⋊C414yes—
98C42×C61—21no—
99C42×C61—21no—
100C42×C61—21no—
101C42×C61—44no—
102C42×C61D812yes—
103C42×C61C22×C411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106C42×C61#4111yescharacteristic
107#11758198—41no—
108#11758198—41no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111#11758194—41no—
112#11758194—41no—
113C2×#92418—22no—
114C2×#92418—41no—
115C2×#92418—41no—
116C23×C61#12011yescharacteristic
117C22×D61—41no—
118Q8×C61—42no—
119Q8×C61—42no—
120Q8×C61—42no—
121Q8×C61—42no—
122C2×C4×C61—24no—
123C2×C4×C61—22no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—41no—
131C2×C4×C61—42no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61C2×C22⋊C411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12311yescharacteristic
142C2×C4×C61C2×D811yescharacteristic
143C2×C4×C61#13511yescharacteristic
144C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C22⋊D61—81no—
147C22⋊D61—81no—
148C2×Dic61—41no—
149D244—42no—
150D244—41no—
151D244—41no—
152D244—81no—
153C4×D61—81no—
154C4×D61—81no—
155Dic122—41no—
156Dic122—41no—
157#92418—42no—
158#92418—81no—
159#92418—81no—
160#9300—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61#38611yescharacteristic
164C22×C61#44711yescharacteristic
165C22×C61#44911yescharacteristic
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—42no—
174C4×C61—44no—
175C4×C61—82no—
176C4×C61—81no—
177C4×C61C4×D811yescharacteristic
178C4×C61#44211yescharacteristic
179C4×C61#45911yescharacteristic
180C4×C61#46311yescharacteristic
181Dic61—81no—
182#3226—611no—
183#2327D6111yescharacteristic, complemented
184#1963—611no—
185#1546—611no—
186#1517—611no—
187#1286—611no—
188#1274—611no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61#187911yescharacteristic
192C2×C61#190511yescharacteristic
193C2×C61#191211yescharacteristic
194D61—161no—
195#532—611no—
196C2×C4⋊Q8C2×D6111yescharacteristic
197C2×C4×Q8—21no—
198#500—612no—
199#486—612no—
200#480—1222no—
201#474—1222no—
202#431—611no—
203#431—611no—
204#423—611no—
205C2×#104—1221no—
206C2×#104—1221no—
207#391—21no—
208#387—22no—
209#387—22no—
210#382C2×D6111yescharacteristic
211#376C2×D6111yescharacteristic
212#332—1222no—
213#327—1222no—
214C61#930011yescharacteristic, complemented, Sylow
215C2×#41—1221no—
216C22×Q8—21no—
217C2×M16—1221no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—611no—
221C4⋊Q8C4×D6112yes—
222C4⋊Q8D24412yes—
223#127—611no—
224#124—1221no—
225#121—1221no—
226#121—1221no—
227C4×Q8—42no—
228C4×Q8—42no—
229C4×D4—1221no—
230C4×D4—1221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C22⋊D6112yes—
235C2×C42—22no—
236C2×C42C22⋊D6111yescharacteristic
237C2×C42C22⋊D6111yescharacteristic
238C2×C42C22×D6111yescharacteristic
239#107—1224no—
240C4⋊C8—1221no—
241C4⋊C8—1221no—
242C4⋊C8—1221no—
243C4⋊C8—1221no—
244#104—2442no—
245#104—2442no—
246#102—1224no—
247C22⋊C8—1221no—
248C22⋊C8—1221no—
249C4×C8—612no—
250C4×C8—1221no—
251#95—24no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95C22⋊D6112yes—
256#41—2441no—
257#41—2441no—
258#41—2441no—
259#41—2441no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—2441no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—2441no—
276C22×C4C2×C22⋊D6111yescharacteristic
277C22×C4C2×C22⋊D6111yescharacteristic
278C22×C4C2×C22⋊D6111yescharacteristic
279M16—2441no—
280M16—2441no—
281C2×C8—1222no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—44no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4#1175819814yes—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—44no—
299C42#1175819912yes—
300C42C2×C4×D6111yescharacteristic
301C42C2×D24411yescharacteristic
302C42#1175822211yescharacteristic
303C42#1175822211yescharacteristic
304C23—2441no—
305C23#1451974611yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—42no—
309Q8—42no—
310Q8—2441no—
311Q8—2441no—
312D4—4881no—
313D4—4881no—
314D4—4881no—
315D4—2442no—
316D4—2441no—
317D4—2441no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—2441no—
335C2×C4C2×#1175819811yescharacteristic
336C2×C4C4×C22⋊D6111yescharacteristic
337C2×C4C4×C22⋊D6111yescharacteristic
338C2×C4#1451975111yescharacteristic
339C2×C4#1451975111yescharacteristic
340C2×C4#1451976011yescharacteristic
341C2×C4C2×#1175819911yescharacteristic
342C2×C4#1451979711yescharacteristic
343C2×C4#1451980211yescharacteristic
344C2×C4#1451980311yescharacteristic
345C8—4881no—
346C8—4881no—
347C8—2442no—
348C22—21no—
349C22—21no—
350C22—4881no—
351C22—4881no—
352C22—4881no—
353C22#1683964111yescharacteristic
354C22#1683989611yescharacteristic
355C22#1683990711yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—81no—
364C4—4881no—
365C4C4×#1175819911yescharacteristic
366C4#1683987211yescharacteristic
367C4#1683995711yescharacteristic
368C4#1683997711yescharacteristic
369C2—21no—
370C2—21no—
371C2—9761no—
372C2#2144616711yescharacteristic
373C2#2144631311yescharacteristic
374C2#2144635611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2327C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#2327D61
hypocenterC61#9300
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
3. #21444491C2semidirect
5. #21443677C2semidirect
6. #21443648C2semidirect
7. C61×#2327C2semidirect
9. #16840165C4semidirect
10. #16840110C4semidirect
183. #2327D61semidirect
214. C61#9300semidirect

Maximal subgroups

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

subgroupindex
#214569402
#214466512
#214444912
#214443782
#214436772
#214436482
C61×#23272
#930061