Finite Group Databasebeta

← #29571007

Subgroups — #29571007

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454514C211yesmaximal, characteristic
2#21445598C211yesmaximal, characteristic, complemented
3#21445597C211yesmaximal, characteristic, complemented
4#21444310C211yesmaximal, characteristic
5#21443707C211yesmaximal, characteristic, complemented
6#21443705C211yesmaximal, characteristic, complemented
7C61×#1501C211yesmaximal, characteristic
8C2×#14519784C411yescharacteristic, complemented
9C23×#92418C2211yescharacteristic
10#16839834—21no—
11#16839834—21no—
12D4×#92418—21no—
13D4×#92418—21no—
14#16839789C411yescharacteristic, complemented
15#16839729C411yescharacteristic, complemented
16#16839726C2211yescharacteristic
17C2×C22⋊#92418C2211yescharacteristic
18#16839718C411yescharacteristic, complemented
19C2×#14519688—21no—
20C2×#14519687—21no—
21C4×C22⋊Dic61C2211yescharacteristic
22#16839517—21no—
23#16839516—21no—
24#16839499C412yescomplemented
25#16839496C412yescomplemented
26C61×#525C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C4×C22⋊C4×C61C2211yescharacteristic
29C61×#328C412yescomplemented
30C61×#327C412yescomplemented
31#14519784—42no—
32C2×#11758194—21no—
33C2×#11758194C2×C411yescharacteristic
34C2×#11758194C2×C411yescharacteristic
35C22×#92418—21no—
36C22×#92418—21no—
37C22×#92418—42no—
38C22×#92418C2×C411yescharacteristic
39C22×#92418C2×C411yescharacteristic
40C22×#92418D411yescharacteristic
41C22×#92418D411yescharacteristic
42C22×#92418D411yescharacteristic
43C22×#92418D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C4×Dic61—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418C2×C412yes—
54#14519688—21no—
55#14519688—42no—
56#14519687—42no—
57C4×#92418—21no—
58#14519684C2×C412yes—
59C2×#41×C61C2×C411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C22×C8×C61—21no—
62#123×C61—21no—
63C22⋊Q8×C61C2×C411yescharacteristic
64C22⋊Q8×C61C2×C411yescharacteristic
65#121×C61C2×C411yescharacteristic
66#121×C61C2×C411yescharacteristic
67#120×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70#117×C61C2×C411yescharacteristic
71C2×C22⋊C4×C61—21no—
72C2×C42×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61C2×C412yes—
75#95×C61C2×C412yes—
76C24×C61#4111yescharacteristic
77#41×C61—41no—
78#41×C61—41no—
79C2×Q8×C61C4211yescharacteristic
80C2×D4×C61—21no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61C4211yescharacteristic
84C22×C4×C61—21no—
85C22×C4×C61—22no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×Dic61—22no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61C4211yescharacteristic
101C4⋊C4×C61C4211yescharacteristic
102C22⋊C4×C61—21no—
103C22⋊C4×C61—21no—
104C22⋊C4×C61—21no—
105C22⋊C4×C61—21no—
106C22⋊C4×C61—21no—
107C22⋊C4×C61—42no—
108C42×C61—21no—
109C42×C61—41no—
110C42×C61—41no—
111C22⋊Dic61—42no—
112C4×Dic61—41no—
113C4×Dic61—41no—
114#11758194—42no—
115#11758194—41no—
116#11758194—41no—
117C2×#92418—22no—
118C2×#92418—22no—
119C2×#92418—22no—
120C2×#92418—21no—
121C2×#92418—21no—
122C2×#92418—22no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418—41no—
126C2×#92418—41no—
127C2×#92418—41no—
128C2×#92418—42no—
129C2×#92418C22⋊C411yescharacteristic
130C2×#92418C22⋊C411yescharacteristic
131C2×#92418C22⋊C411yescharacteristic
132C2×#92418C22⋊C411yescharacteristic
133C23×C61—22no—
134C23×C61—22no—
135C23×C61—21no—
136C23×C61—41no—
137C23×C61#11711yescharacteristic
138C23×C61C4×D411yescharacteristic
139C23×C61C4×D411yescharacteristic
140Q8×C61—41no—
141D4×C61—41no—
142D4×C61—42no—
143D4×C61—42no—
144D4×C61—42no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61C2×C4211yescharacteristic
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61C4×D411yescharacteristic
165C2×C4×C61C4×D411yescharacteristic
166C2×Dic61—42no—
167C2×Dic61—42no—
168C2×Dic61—42no—
169C8×C61—42no—
170#92418—21no—
171#92418—21no—
172#92418—21no—
173#92418—42no—
174#92418—41no—
175#92418—41no—
176#92418#9912yes—
177#8239—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—44no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61C4×C22⋊C411yescharacteristic
190C22×C61#44412yes—
191C22×C61#44412yes—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—82no—
199C4×C61C2×#9911yescharacteristic
200C4×C61#41011yescharacteristic
201Dic61—82no—
202#2929—611no—
203#1752—611no—
204#1752—611no—
205#1501—611no—
206#1501D6111yescharacteristic
207#1298—611no—
208#1297—611no—
209C2×C61—22no—
210C2×C61—22no—
211C2×C61—41no—
212C2×C61—81no—
213C2×C61C4×#9911yescharacteristic
214C2×C61#176511yescharacteristic
215C2×C61#176511yescharacteristic
216C2×#131—611no—
217C23×C8—611no—
218#525C2×D6111yescharacteristic
219#435—1221no—
220#435—1221no—
221C8×D4—1221no—
222C8×D4—1221no—
223#424—611no—
224#408—611no—
225#407—611no—
226C2×C22⋊C8—611no—
227C2×C22⋊C8C2×D6111yescharacteristic
228#405—611no—
229C2×#97—1221no—
230C2×#97—1221no—
231C4×C22⋊C4—611no—
232C4×C22⋊C4C2×D6111yescharacteristic
233#336—1221no—
234#336—1221no—
235#328—612no—
236#328Dic6112yescomplemented
237#327—612no—
238#327Dic6112yescomplemented
239C61#823911yescharacteristic, complemented, Sylow
240C2×#41C4×D6111yescharacteristic
241C23×C4C22×D6111yescharacteristic
242#131—2442no—
243C2×M16—611no—
244C2×M16—611no—
245C2×M16—1221no—
246C22×C8—21no—
247C22×C8—611no—
248C22×C8—611no—
249C22×C8—611no—
250C22×C8—611no—
251C22×C8—611no—
252C22×C8—611no—
253C22×C8—1221no—
254C22×C8—1221no—
255C22×C8—2442no—
256#123—21no—
257C22⋊Q8C4×D6111yescharacteristic
258C22⋊Q8C2×Dic6111yescharacteristic
259#121C4×D6111yescharacteristic
260#121C2×Dic6111yescharacteristic
261#120—21no—
262C4×D4—21no—
263C4×D4—21no—
264#117C4×D6111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—1221no—
267C2×C42—21no—
268C2×C42—1221no—
269C4⋊C8—1221no—
270C4⋊C8—1221no—
271C22⋊C8—21no—
272C22⋊C8—612no—
273C22⋊C8—1221no—
274C22⋊C8—1221no—
275C22⋊C8—1221no—
276C22⋊C8—1221no—
277C22⋊C8—1221no—
278C22⋊C8C2×Dic6112yes—
279#97—1221no—
280#97—2442no—
281#97—2442no—
282C4×C8—1221no—
283#95—612no—
284#95C2×Dic6112yes—
285C24#1175822411yescharacteristic
286#41—41no—
287#41—41no—
288C2×Q8C4×Dic6111yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4C4×Dic6111yescharacteristic
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—1222no—
298C22×C4C2×C4×D6111yescharacteristic
299C22×C4C2×C4×D6111yescharacteristic
300C22×C4D4×D6111yescharacteristic
301C22×C4D4×D6111yescharacteristic
302C22×C4#1175822411yescharacteristic
303C22×C4C22×Dic6111yescharacteristic
304M16—2442no—
305M16—2441no—
306M16—2441no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—611no—
311C2×C8—611no—
312C2×C8—611no—
313C2×C8—611no—
314C2×C8—1222no—
315C2×C8—1222no—
316C2×C8—1222no—
317C2×C8—1221no—
318C2×C8—1221no—
319C2×C8—1222no—
320C2×C8—2442no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2441no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4C4×Dic6111yescharacteristic
329C4⋊C4C4×Dic6111yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—42no—
336C22⋊C4—2442no—
337C42—21no—
338C42—41no—
339C42—41no—
340C42—2441no—
341C42—2441no—
342C23—22no—
343C23—22no—
344C23—21no—
345C23—41no—
346C23#1451973311yescharacteristic
347C23#1451973711yescharacteristic
348C23D4×Dic6111yescharacteristic
349Q8—41no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—42no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4—2442no—
374C2×C4C2×C4×Dic6111yescharacteristic
375C2×C4C22⋊C4×D6111yescharacteristic
376C2×C4#1451973711yescharacteristic
377C2×C4D4×Dic6111yescharacteristic
378C8—42no—
379C8—612no—
380C8—1221no—
381C8—1221no—
382C8—1221no—
383C8—2442no—
384C8—2441no—
385C8—2441no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22C22⋊C4×Dic6111yescharacteristic
398C22#1683988112yes—
399C22#1683988412yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—82no—
407C4—4882no—
408C4#99×D6111yescharacteristic
409C4#1683973411yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—81no—
414C2#99×Dic6111yescharacteristic
415C2#2144566411yescharacteristic
416C2#2144566611yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1501C2
socleC22×C61C4×C22⋊C4
prime radicalC61×#525C22
cosocleC23×C4×C61C23
hypercenter#1501D61
hypocenterC61#8239
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #21445598C2semidirect
3. #21445597C2semidirect
5. #21443707C2semidirect
6. #21443705C2semidirect
8. C2×#14519784C4semidirect
14. #16839789C4semidirect
15. #16839729C4semidirect
18. #16839718C4semidirect
24. #16839499C4semidirect
25. #16839496C4semidirect
29. C61×#328C4semidirect
30. C61×#327C4semidirect
236. #328Dic61semidirect
238. #327Dic61semidirect
239. C61#8239semidirect

Maximal subgroups

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

subgroupindex
#214545142
#214455982
#214455972
#214443102
#214437072
#214437052
C61×#15012
#823961