Finite Group Databasebeta

← #30600542

Subgroups — #30600542

Order 15616.

524 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462463C211yesmaximal, characteristic
2#21461328C212yesmaximal, complemented
3#21461053C211yesmaximal, characteristic
4#21460672C212yesmaximal, complemented
5#21451587C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7#16840779C2212yes—
8#16840769—24no—
9#16840765—21no—
10#16840765C2212yes—
11#16840621—24no—
12#16840607—21no—
13#16840606—21no—
14C2×#14519776C2211yescharacteristic
15C2×#14519755—21no—
16C2×#14519735C2211yescharacteristic
17#16839695—21no—
18#16839692C411yescharacteristic
19#16839691—21no—
20#16839689C411yescharacteristic
21#16839688C411yescharacteristic
22#16839666—21no—
23#16839626C2211yescharacteristic
24C61×#398C411yescharacteristic
25C2×#11758213—22no—
26D61⋊M16—42no—
27D61⋊M16—42no—
28C2×#11758217—22no—
29C2×D61⋊C8—22no—
30#14519844—22no—
31#14519844—22no—
32#14519844D414yes—
33C4⋊#92420—22no—
34C4⋊#92420—22no—
35C22⋊#92420—22no—
36C4×#92420—22no—
37C22×Dic122—21no—
38C22×C4×D61D411yescharacteristic
39#14519776—22no—
40#14519776—22no—
41#14519755—42no—
42#14519755—42no—
43#14519735—22no—
44#14519735—22no—
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198C2×C411yescharacteristic
53C2×#11758198D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61C2311yescharacteristic
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684C2×C411yescharacteristic
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C4⋊C4×C61C2×C411yescharacteristic
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66C23×D61C22⋊C411yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61D812yes—
82C2×C4×D61SD1612yes—
83C2×Dic122—41no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122—41no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89#11758217—42no—
90#11758217—42no—
91C2×#92420—24no—
92C2×#92420—42no—
93#11758213—44no—
94D61⋊C8—44no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—42no—
98#11758198—22no—
99#11758198—22no—
100#11758198—42no—
101#11758198—42no—
102C4⋊Dic61—22no—
103C4⋊Dic61—22no—
104#11758196—42no—
105#11758196—42no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61C2×D412yes—
111C4×Dic61#4112yes—
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61#10212yes—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61#10212yes—
130C2×C4×C61C4×D412yes—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#12011yescharacteristic
141C2×Dic61#12112yes—
142C2×Dic61#12311yescharacteristic
143C2×Dic61C2×D811yescharacteristic
144C2×Dic61C2×SD1611yescharacteristic
145C2×Dic61AGL(1,ℤ/8)11yescharacteristic
146C2×Dic61#13711yescharacteristic
147C4×D61—22no—
148C4×D61—22no—
149C4×D61—22no—
150C4×D61—22no—
151Dic122—81no—
152Dic122—81no—
153Dic122—81no—
154Dic122—81no—
155#92420—44no—
156#92420—82no—
157#9195—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61#38611yescharacteristic
161C22×C61C2×#10211yescharacteristic
162C22×C61#41711yescharacteristic
163C2×D61—22no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—42no—
167C2×D61—81no—
168C4×C61—22no—
169C4×C61—22no—
170C4×C61—41no—
171C4×C61—81no—
172C4×C61—81no—
173Dic61—22no—
174Dic61—41no—
175Dic61—81no—
176Dic61—81no—
177Dic61#44711yescharacteristic
178Dic61#44811yescharacteristic
179Dic61#48011yescharacteristic
180Dic61#48111yescharacteristic
181#2905—611no—
182#2621—611no—
183#1546—612no—
184#1458—611no—
185#1286—612no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61#187411yescharacteristic
189C2×C61#190911yescharacteristic
190C2×C61#191511yescharacteristic
191D61—42no—
192C22×M16—1221no—
193C2×C4⋊Q8—611no—
194C2×C22⋊Q8—1221no—
195C2×#117—611no—
196#431—612no—
197#424—1224no—
198#423—612no—
199#423—1221no—
200#398—611no—
201#398—1221no—
202#398#692311yescharacteristic
203#397—611no—
204#397—611no—
205#397—1221no—
206#391—1221no—
207#382—611no—
208#332—1224no—
209#324—1221no—
210#323—1221no—
211C61#919511yescharacteristic, complemented, Sylow
212C22×Q8—1221no—
213C23×C4—611no—
214C2×M16—1222no—
215C2×M16—1222no—
216C2×M16—2442no—
217C2×M16—2442no—
218C22×C8—1222no—
219C4⋊Q8—1222no—
220C4⋊Q8—1222no—
221C22⋊Q8—2442no—
222C22⋊Q8—2442no—
223#117—1222no—
224#117—1222no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4C2×#692311yescharacteristic
232C2×C4⋊C4C2×#692311yescharacteristic
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C42—611no—
238C2×C42—611no—
239C4⋊C8—614no—
240C4⋊C8—1222no—
241C4⋊C8—1222no—
242C4⋊C8—1222no—
243C4⋊C8—1222no—
244C22⋊C8—1222no—
245C4×C8—1222no—
246#95—21no—
247#95—611no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251#95—1221no—
252#95C2×#692311yescharacteristic
253C24—611no—
254C2×Q8—2441no—
255C2×Q8—2441no—
256C2×Q8—2441no—
257C2×Q8—2441no—
258C2×Q8—2441no—
259C2×Q8—2441no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—612no—
265C22×C4—612no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4C22⋊#692311yescharacteristic
274C22×C4C22⋊#692311yescharacteristic
275C22×C4C22×#692311yescharacteristic
276M16—2442no—
277M16—2442no—
278M16—2444no—
279C2×C8—1224no—
280C2×C8—2442no—
281C2×C8—2444no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—42no—
285C4⋊C4—1222no—
286C4⋊C4—1222no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
291C22⋊C4—1222no—
292C22⋊C4—1222no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C42—612no—
296C42—612no—
297C42—1221no—
298C42—1221no—
299C23—612no—
300C23—1221no—
301C23—1221no—
302C23—2441no—
303C23—2441no—
304C23C2×C22⋊#692311yescharacteristic
305Q8—4881no—
306Q8—4881no—
307Q8—4881no—
308Q8—4881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—612no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1222no—
330C2×C4—1222no—
331C2×C4—1221no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451983912yes—
341C2×C4D4×#692312yes—
342C8—4882no—
343C8—2444no—
344C22—21no—
345C22—21no—
346C22—1222no—
347C22—4881no—
348C22—2442no—
349C22—2441no—
350C22—2441no—
351C22#1684071011yescharacteristic
352C22C2×#1451983911yescharacteristic
353C22#1684075311yescharacteristic
354C4—22no—
355C4—22no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—611no—
360C4—611no—
361C4—611no—
362C4—611no—
363C4—1222no—
364C4—4881no—
365C4—4881no—
366C4—2441no—
367C2—21no—
368C2—21no—
369C2—2442no—
370C2#2146180611yescharacteristic
371C2#2146186111yescharacteristic
372C2#2146187111yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61#386
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#398#6923
hypocenterC61#9195
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #21461328C2semidirect
4. #21460672C2semidirect
211. C61#9195semidirect

Maximal subgroups

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

subgroupindex
#214624632
#214613282
#214610532
#214606722
#214515872
#919561