Finite Group Databasebeta

← #29575421

Subgroups — #29575421

Order 15616.

532 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454842C211yesmaximal, characteristic
2C2×#16839860C211yesmaximal, characteristic
3#21444211C211yesmaximal, characteristic
4#21444143C211yesmaximal, characteristic, complemented
5#21443663C211yesmaximal, characteristic, complemented
6#21443649C211yesmaximal, characteristic, complemented
7C61×#1479C211yesmaximal, characteristic, complemented
8C22×#11758201C411yescharacteristic
9C2×C4×D244C2211yescharacteristic
10#16839860—22no—
11#16839860—22no—
12C8×D244—22no—
13#16839827—22no—
14#16839815C2211yescharacteristic
15#16839815C2211yescharacteristic
16C2×#14519710C411yescharacteristic
17C2×#14519701C411yescharacteristic
18C2×#14519697C411yescharacteristic
19C22⋊C8×D61—22no—
20C2×#14519688C2211yescharacteristic
21#16839491—22no—
22#16839488—22no—
23C2×C4×Q8×C61C2211yescharacteristic
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C61×Q8⋊C8—22no—
27C22×D244C2×C411yescharacteristic
28C22×C4×D61—21no—
29C2×#11758201—22no—
30C2×#11758201—22no—
31C2×#11758201C814yescomplemented
32C22×#92418C2×C411yescharacteristic
33C22×#92418C2×C411yescharacteristic
34C2×C8×D61—24no—
35C4×D244—21no—
36C4×D244—21no—
37C4×D244D412yes—
38C4×D244D412yes—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758198—21no—
41#14519710—22no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44#14519701—22no—
45#14519697—22no—
46C22⋊#92418—21no—
47C22⋊#92418D412yes—
48#14519689—24no—
49#14519688—21no—
50#14519688—21no—
51C4×#92418—21no—
52C4×#92418—21no—
53C22×Q8×C61C2×C411yescharacteristic
54C4×Q8×C61—21no—
55C4×Q8×C61—21no—
56C4×Q8×C61—21no—
57C4×Q8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C42×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×C61D412yes—
68C23×D61—21no—
69C2×Q8×C61—21no—
70C2×Q8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61—21no—
73C2×Q8×C61—21no—
74C2×Q8×C61C2×C812yescomplemented
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×Dic61—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244C22⋊C412yes—
85C2×D244C2×C812yes—
86C2×D244M1612yes—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—82no—
90C2×C8×C61—22no—
91C2×C8×C61—41no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C42×C61—41no—
97C42×C61—41no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102#11758201—28no—
103#11758198—22no—
104#11758198—22no—
105C4⋊Dic61—21no—
106C4⋊Dic61C22⋊C412yes—
107C2×#92418—21no—
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418—22no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—41no—
114C2×#92418C2×C812yescomplemented
115C8×D61—84no—
116C23×C61C4×D411yescharacteristic
117C22×D61—22no—
118C22×D61—22no—
119C22×D61—22no—
120C22×D61—81no—
121C22×D61—81no—
122Q8×C61—22no—
123Q8×C61—22no—
124Q8×C61—41no—
125Q8×C61—41no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—81no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12311yescharacteristic
139C2×C4×C61C22×C811yescharacteristic
140C2×C4×C61C2×M1611yescharacteristic
141C2×C4×C61#13111yescharacteristic
142C2×C4×C61#13111yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—81no—
145D244—22no—
146D244—22no—
147D244—22no—
148D244C22⋊C814yes—
149C4×D61—44no—
150C4×D61—82no—
151C8×C61—42no—
152C8×C61—81no—
153#92418—22no—
154#92418—42no—
155#92418—41no—
156#92418—81no—
157#9087—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61#38611yescharacteristic
161C22×C61C8×D411yescharacteristic
162C22×C61#43511yescharacteristic
163C2×D61—24no—
164C2×D61—42no—
165C2×D61—42no—
166C2×D61—82no—
167C2×D61—82no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—42no—
173C4×C61—81no—
174C4×C61C2×C22⋊C811yescharacteristic
175C4×C61#40811yescharacteristic
176C4×C61C8×D411yescharacteristic
177C4×C61#43511yescharacteristic
178Dic61—42no—
179#2972—611no—
180C2×#440—611no—
181#1479D6111yescharacteristic, complemented
182#1478—611no—
183#1461—611no—
184#1281—611no—
185#1275—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61#186911yescharacteristic
189C2×C61#190211yescharacteristic
190C2×C61#190411yescharacteristic
191D61—44no—
192C22×SD16—611no—
193C2×C4×Q8C2×D6111yescharacteristic
194C2×C4×D4—611no—
195#440—1222no—
196#440—1222no—
197C8×D4—1222no—
198C8×D4—1222no—
199#431—611no—
200#431—611no—
201#431C2×D6111yescharacteristic
202#431C2×D6111yescharacteristic
203C2×#107—611no—
204C2×#103—611no—
205C2×#102—611no—
206C2×C22⋊C8—1222no—
207C2×#97—611no—
208Q8⋊C8—22no—
209D4⋊C8—1222no—
210#324—1222no—
211C61#908711yescharacteristic, complemented, Sylow
212C22×Q8C4×D6111yescharacteristic
213C22×D4—611no—
214C23×C4—1221no—
215C2×SD16—614no—
216C2×SD16—1222no—
217C2×SD16—1222no—
218C22×C8—611no—
219C22×C8—611no—
220C22×C8—1224no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×D4—612no—
226C4×D4—612no—
227C4×D4—1221no—
228C4×D4—1221no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4C4×D6111yescharacteristic
232C2×C22⋊C4—1221no—
233C2×C42—21no—
234C2×C42C22×D6111yescharacteristic
235#107—1222no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—1221no—
239C4⋊C8—1221no—
240#103—1222no—
241#102—1222no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—612no—
245C22⋊C8—1224no—
246C22⋊C8—1221no—
247#97—1221no—
248#97—1221no—
249C4×C8—21no—
250C4×C8—1221no—
251C4×C8—1221no—
252C4×C8C22⋊D6112yes—
253C24—1221no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8C8×D6112yescomplemented
260C2×D4—612no—
261C2×D4—612no—
262C2×D4—612no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—1221no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—4882no—
272C22×C4C2×C4×D6111yescharacteristic
273C22×C4D4×D6111yescharacteristic
274C22×C4#1175822411yescharacteristic
275SD16—1228no—
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—612no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—1221no—
282C2×C8—1222no—
283C2×C8—1221no—
284C2×C8—1221no—
285C2×C8—4884no—
286C2×C8—2441no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—612no—
292C4⋊C4—1221no—
293C22⋊C4—1222no—
294C22⋊C4—1222no—
295C42—41no—
296C42—41no—
297C42#1175822211yescharacteristic
298C42D4×D6111yescharacteristic
299C42D4×D6111yescharacteristic
300C42C2×C22⋊D6111yescharacteristic
301C23—1222no—
302C23—1222no—
303C23—1222no—
304C23—4881no—
305C23—4881no—
306C23#1451973711yescharacteristic
307Q8—22no—
308Q8—22no—
309Q8—41no—
310Q8—41no—
311D4—614no—
312D4—1222no—
313D4—1222no—
314D4—1222no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—1222no—
323C2×C4—4882no—
324C2×C4—4881no—
325C2×C4—2444no—
326C2×C4C22⋊C4×D6111yescharacteristic
327C2×C4C4×C22⋊D6111yescharacteristic
328C2×C4#1451974511yescharacteristic
329C2×C4#1451974811yescharacteristic
330C2×C4#1451975011yescharacteristic
331C2×C4#1451975911yescharacteristic
332C2×C4C2×C8×D6111yescharacteristic
333C2×C4M16×D6111yescharacteristic
334C2×C4#1451978311yescharacteristic
335C2×C4#1451978511yescharacteristic
336C8—42no—
337C8—81no—
338C8—1222no—
339C8—4881no—
340C8—2442no—
341C8—2441no—
342C22—21no—
343C22—21no—
344C22—1224no—
345C22—4882no—
346C22—4882no—
347C22—2442no—
348C22—2442no—
349C22#1683963811yescharacteristic
350C22#1683982511yescharacteristic
351C22#1683983611yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—42no—
357C4—81no—
358C4—2442no—
359C4C22⋊C8×D6111yescharacteristic
360C4#1683972711yescharacteristic
361C4C8×C22⋊D6111yescharacteristic
362C4#1683983111yescharacteristic
363C2—21no—
364C2—21no—
365C2—2444no—
366C2#2144610811yescharacteristic
367C2#2144628911yescharacteristic
368C2#2144630311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1479C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1479D61
hypocenterC61#9087
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #21444143C2semidirect
5. #21443663C2semidirect
6. #21443649C2semidirect
7. C61×#1479C2semidirect
31. C2×#11758201C8semidirect
74. C2×Q8×C61C2×C8semidirect
114. C2×#92418C2×C8semidirect
181. #1479D61semidirect
211. C61#9087semidirect
259. C2×Q8C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214548422
C2×#168398602
#214442112
#214441432
#214436632
#214436492
C61×#14792
#908761