Finite Group Databasebeta

← #29575535

Subgroups — #29575535

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454859C211yesmaximal, characteristic, complemented
2#21448541C211yesmaximal, characteristic
3#21444210C211yesmaximal, characteristic, complemented
4#21444139C211yesmaximal, characteristic, complemented
5#21443647C211yesmaximal, characteristic, complemented
6#21443647C211yesmaximal, characteristic, complemented
7C61×#1478C211yesmaximal, characteristic, complemented
8C2×#14519773C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10#16839841—22no—
11#16839839—22no—
12#16839815C2211yescharacteristic
13#16839815C2211yescharacteristic
14#16839724—22no—
15#16839665C411yescharacteristic
16#16839663C411yescharacteristic
17#16839641—22no—
18#16839638—22no—
19#16839627C411yescharacteristic
20#16839608C2211yescharacteristic
21D4⋊#92418—22no—
22#16839485—22no—
23C2×C4×D4×C61C2211yescharacteristic
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C61×D4⋊C8—22no—
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—22no—
29C22×C4×D61D412yes—
30C2×#11758189—24no—
31#14519773—22no—
32#14519773—22no—
33C4×D244—21no—
34C4×D244—21no—
35C4×D244—21no—
36C4×D244—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C22⋊Dic61—22no—
39C2×#11758198—22no—
40C2×#11758198D412yes—
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C22⋊#92418—21no—
46C22⋊#92418—21no—
47#14519689—24no—
48C4×#92418—21no—
49C4×#92418D412yescomplemented
50#14519684—21no—
51#14519684—21no—
52#14519684—22no—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61—21no—
55C4×D4×C61—21no—
56C4×D4×C61—21no—
57C4×D4×C61—21no—
58C4×D4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61D412yescomplemented
68C24×C61—21no—
69C23×D61C22⋊C412yes—
70C2×D4×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61—21no—
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×D4×C61M1612yescomplemented
76C22×C4×C61—21no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—82no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C2×C22⋊D61—28no—
84C2×C22⋊D61—82no—
85C2×C22⋊D61—82no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61C22⋊C412yes—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—21no—
93C2×D244—21no—
94C2×D244—21no—
95C2×C4×D61—22no—
96C2×C4×D61—22no—
97C2×C4×D61—82no—
98C2×C8×C61—22no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C42×C61#4111yescharacteristic
108C22⋊Dic61—82no—
109#11758198—22no—
110#11758198—22no—
111#11758198—82no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61M1612yescomplemented
118C2×#92418—22no—
119C2×#92418—41no—
120#11758189—84no—
121C23×C61—22no—
122C23×C61—42no—
123C23×C61—42no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61C2×C22⋊C411yescharacteristic
127C22×D61—22no—
128C22×D61—22no—
129C22×D61—22no—
130C22×D61—42no—
131C22×D61—42no—
132D4×C61—22no—
133D4×C61—22no—
134D4×C61—41no—
135D4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—82no—
141C2×C4×C61—82no—
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61C4×D411yescharacteristic
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12311yescharacteristic
148C2×C4×C61C2×M1611yescharacteristic
149C2×C4×C61C2×M1611yescharacteristic
150C2×C4×C61#13111yescharacteristic
151C2×C4×C61#13111yescharacteristic
152C22⋊D61—88no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161D244—41no—
162D244—41no—
163D244—41no—
164D244—41no—
165C4×D61—44no—
166C4×D61—82no—
167C8×C61—42no—
168C8×C61—81no—
169#92418—42no—
170#92418—81no—
171#9105—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—44no—
175C22×C61—42no—
176C22×C61—82no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61#38611yescharacteristic
180C22×C61#40711yescharacteristic
181C22×C61#40811yescharacteristic
182C2×D61—44no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—82no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—81no—
192C4×C61#43511yescharacteristic
193C4×C61#43511yescharacteristic
194C4×C61#43611yescharacteristic
195C4×C61#43611yescharacteristic
196Dic61—42no—
197Dic61—42no—
198Dic61—81no—
199#2975—611no—
200#2328—611no—
201#1478—611no—
202#1478D6111yescharacteristic, complemented
203#1460—611no—
204#1274—611no—
205#1274—611no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—82no—
209C2×C61#187011yescharacteristic
210C2×C61#191011yescharacteristic
211C2×C61#191111yescharacteristic
212D61—82no—
213C2×#127—611no—
214C2×C4×D4—611no—
215C2×C4×D4C2×D6111yescharacteristic
216#436—1222no—
217#436—1222no—
218#431—611no—
219#431—611no—
220#431C2×D6111yescharacteristic
221#431C2×D6111yescharacteristic
222#407—1222no—
223#390—611no—
224#390—611no—
225#386—1222no—
226#386—1222no—
227#382—611no—
228#376—611no—
229D4⋊C8—22no—
230D4⋊C8—1222no—
231#323—1222no—
232C61#910511yescharacteristic, complemented, Sylow
233C22×D4—611no—
234C22×D4—1222no—
235C22×D4C4×D6111yescharacteristic
236C23×C4—21no—
237C23×C4—612no—
238C2×M16—1224no—
239#127—1222no—
240#127—1222no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248C4×D4—1221no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4C4×D6111yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—612no—
253C2×C22⋊C4—1222no—
254C2×C22⋊C4—1222no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42C22×D6111yescharacteristic
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—1224no—
265C22⋊C8—1221no—
266C22⋊C8—1221no—
267C4×C8—21no—
268C4×C8—612no—
269C4×C8—1221no—
270C4×C8C22⋊D6112yescomplemented
271#95—1222no—
272#95—1221no—
273#95—1221no—
274C24—21no—
275C24—612no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—1228no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—4882no—
289C2×D4—4882no—
290C2×D4#1175818912yescomplemented
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—82no—
295C22×C4—612no—
296C22×C4—1221no—
297C22×C4—1222no—
298C22×C4—1222no—
299C22×C4—1221no—
300C22×C4—4882no—
301C22×C4C2×C4×D6111yescharacteristic
302C22×C4D4×D6111yescharacteristic
303C22×C4D4×D6111yescharacteristic
304M16—4884no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—1222no—
308C2×C8—2441no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—1222no—
316C22⋊C4—1222no—
317C22⋊C4—4882no—
318C22⋊C4—4882no—
319C42—612no—
320C42—1221no—
321C42—1221no—
322C42—1221no—
323C42#1175822211yescharacteristic
324C42D4×D6111yescharacteristic
325C42#1175822411yescharacteristic
326C42C2×C22⋊D6111yescharacteristic
327C23—22no—
328C23—42no—
329C23—42no—
330C23—41no—
331C23—41no—
332C23—1222no—
333C23—1222no—
334C23—1222no—
335C23—2442no—
336C23—2442no—
337C23C22⋊C4×D6111yescharacteristic
338D4—22no—
339D4—22no—
340D4—41no—
341D4—41no—
342D4—4888no—
343D4—2441no—
344D4—2441no—
345D4—2441no—
346D4—2441no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—4882no—
356C2×C4—2444no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2442no—
363C2×C4#1451973711yescharacteristic
364C2×C4C4×C22⋊D6111yescharacteristic
365C2×C4#1451974511yescharacteristic
366C2×C4#1451974811yescharacteristic
367C2×C4#1451975011yescharacteristic
368C2×C4#1451975911yescharacteristic
369C2×C4M16×D6111yescharacteristic
370C2×C4C2×#1175818911yescharacteristic
371C2×C4#1451978311yescharacteristic
372C2×C4#1451978511yescharacteristic
373C8—42no—
374C8—81no—
375C8—4881no—
376C8—2442no—
377C22—21no—
378C22—21no—
379C22—44no—
380C22—42no—
381C22—82no—
382C22—81no—
383C22—81no—
384C22—4882no—
385C22—2444no—
386C22—2442no—
387C22—2442no—
388C22—2442no—
389C22#1683963811yescharacteristic
390C22#1683972411yescharacteristic
391C22#1683972711yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—4881no—
398C4—2442no—
399C4—2442no—
400C4#1683983011yescharacteristic
401C4#1683983311yescharacteristic
402C4#1683983711yescharacteristic
403C4#1683983811yescharacteristic
404C2—21no—
405C2—21no—
406C2—82no—
407C2—4882no—
408C2#2144611311yescharacteristic
409C2#2144634311yescharacteristic
410C2#2144634811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1478C2
socleC22×C61#386
prime radicalC2×#14519773C4
cosocleC2×C42×C61C23
hypercenter#1478D61
hypocenterC61#9105
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #21454859C2semidirect
3. #21444210C2semidirect
4. #21444139C2semidirect
5. #21443647C2semidirect
6. #21443647C2semidirect
7. C61×#1478C2semidirect
49. C4×#92418D4semidirect
67. C4×C8×C61D4semidirect
75. C2×D4×C61M16semidirect
117. C4×Dic61M16semidirect
202. #1478D61semidirect
232. C61#9105semidirect
270. C4×C8C22⋊D61semidirect
290. C2×D4#11758189semidirect

Maximal subgroups

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

subgroupindex
#214548592
#214485412
#214442102
#214441392
#214436472
C61×#14782
#910561