Finite Group Databasebeta

← #30603027

Subgroups — #30603027

Order 15616.

1066 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 170 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
1C2×#16840734C212yesmaximal
2#21462383C211yesmaximal, characteristic, complemented
3C2×#16840643C212yesmaximal, complemented
4#21461525C211yesmaximal, characteristic, complemented
5#21448199C211yesmaximal, characteristic
6C22×#11758217C2212yes—
7C22×#11758217C2212yes—
8#16840734—24no—
9#16840734C418yescomplemented
10C2×#14519834—24no—
11#16840726—24no—
12C4×#11758217—22no—
13#16840643—24no—
14#16840642—22no—
15C23×C4×D61C2211yescharacteristic
16C2×#14519733C2211yescharacteristic
17C2×#14519733C2211yescharacteristic
18#16839625C411yescharacteristic
19#16839621—22no—
20#16839617C411yescharacteristic
21#16839617C411yescharacteristic
22#16839609—22no—
23C61×#381C411yescharacteristic
24C2×#11758217—22no—
25C2×#11758217—22no—
26C2×#11758217—22no—
27C2×#11758217—22no—
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C2×#11758217—22no—
32C2×#11758217—22no—
33C2×#11758217C2×C414yes—
34C2×#11758217C2×C414yes—
35C2×#11758217D414yes—
36C22×#92420—22no—
37C22×#92420D414yes—
38#14519834—216no—
39#14519832—24no—
40C4×#92420—24no—
41C24×D61C2×C411yescharacteristic
42C23×Dic61C2311yescharacteristic
43C22×C4×D61—22no—
44C22×C4×D61—22no—
45C22×C4×D61—21no—
46C22×C4×D61—21no—
47C22×C4×D61—22no—
48C22×C4×D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61C2×C414yes—
51#14519733—22no—
52#14519733—22no—
53#14519733—22no—
54#14519733—22no—
55C2×#11758196—21no—
56C2×#11758196D412yes—
57C2×C22⋊Dic61C2×C411yescharacteristic
58C2×C22⋊Dic61C2×C411yescharacteristic
59C2×#11758198—22no—
60C2×#11758198—22no—
61C2×C4×Dic61—21no—
62C2×C4×Dic61D412yes—
63#14519684—22no—
64C23×C4×C61C2×C411yescharacteristic
65C2×C22⋊C4×C61C2×C411yescharacteristic
66C2×C22⋊C4×C61C2×C411yescharacteristic
67#95×C61—22no—
68C24×C61C22×C411yescharacteristic
69C23×D61—21no—
70C23×D61—22no—
71C23×D61—21no—
72C23×D61—22no—
73C23×D61—44no—
74C23×D61C4212yes—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61—22no—
79C22×C4×C61—21no—
80C22×C4×C61C4212yes—
81C22×C4×C61C22⋊C412yes—
82C22×Dic61—21no—
83C22×Dic61C22⋊C412yes—
84C22×Dic61C22×C412yes—
85C22×Dic61C2×D412yes—
86C22×Dic61C2×D412yes—
87C22×Dic61C2×D411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61#4112yes—
90C22×Dic61#4112yes—
91C22×Dic61#4112yes—
92C2×C4×D61—24no—
93C2×C4×D61—24no—
94C2×C4×D61—24no—
95C2×C4×D61—24no—
96C2×C4×D61—24no—
97C2×C4×D61—24no—
98C2×C4×D61—41no—
99C2×C4×D61—42no—
100C2×C4×D61—42no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—41no—
108#11758217—24no—
109#11758217—24no—
110#11758217—24no—
111#11758217—24no—
112#11758217—24no—
113#11758217—24no—
114#11758217—42no—
115#11758217—42no—
116C2×#92420—24no—
117C2×#92420—24no—
118C2×#92420—24no—
119C2×#92420—42no—
120C2×#92420—42no—
121C2×#92420C22⋊C418yescomplemented
122C22⋊C4×C61—22no—
123C22⋊C4×C61—22no—
124C22⋊Dic61—22no—
125C22⋊Dic61—22no—
126#11758198—44no—
127#11758198—44no—
128#11758196—24no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61—22no—
132C4×Dic61—22no—
133C4×Dic61—42no—
134C23×C61—42no—
135C23×C61C2×C4211yescharacteristic
136C23×C61C2×C22⋊C411yescharacteristic
137C23×C61#11711yescharacteristic
138C23×C61C4×D412yes—
139C23×C61C4×D412yes—
140C22×D61—24no—
141C22×D61—28no—
142C22×D61—22no—
143C22×D61—24no—
144C22×D61—44no—
145C22×D61—44no—
146C22×D61—48no—
147C22×D61—42no—
148C22×D61—44no—
149C22×D61—41no—
150C22×D61—42no—
151C22×D61—41no—
152C2×C4×C61—22no—
153C2×C4×C61—24no—
154C2×C4×C61—22no—
155C2×C4×C61—41no—
156C2×C4×C61—42no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×Dic61—22no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—41no—
165C2×Dic61C2×C22⋊C412yes—
166C2×Dic61#11712yes—
167C2×Dic61C4×D412yes—
168C2×Dic61C4×D412yes—
169C2×Dic61C4×D412yes—
170C2×Dic61C4×D412yes—
171C2×Dic61#12011yescharacteristic
172C2×Dic61#12112yes—
173C2×Dic61#12112yes—
174C2×Dic61#12112yes—
175C2×Dic61#12312yes—
176C2×Dic61#12311yescharacteristic
177C2×Dic61#12411yescharacteristic
178C2×Dic61#12412yes—
179C2×Dic61#12612yes—
180C2×Dic61#12711yescharacteristic
181C4×D61—44no—
182C4×D61—44no—
183C4×D61—44no—
184C4×D61—44no—
185#92420—28no—
186#92420—44no—
187#10937—611nomaximal, Sylow
188C22×C61—22no—
189C22×C61—24no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—42no—
193C22×C61C4×C22⋊C411yescharacteristic
194C22×C61C4×C22⋊C412yes—
195C22×C61#38611yescharacteristic
196C22×C61#38812yes—
197C22×C61#39011yescharacteristic
198C2×D61—24no—
199C2×D61—28no—
200C2×D61—44no—
201C2×D61—42no—
202C2×D61—44no—
203C2×D61—48no—
204C2×D61—44no—
205C2×D61—42no—
206C4×C61—42no—
207C4×C61—42no—
208C4×C61—81no—
209Dic61—42no—
210Dic61—81no—
211Dic61#38612yes—
212Dic61#38812yes—
213Dic61#38812yes—
214Dic61#39012yes—
215C2×#407—612no—
216#2873—611no—
217#2280—611no—
218C2×#344—612no—
219#1742—611no—
220C2×C61—21no—
221C2×C61—21no—
222C2×C61—22no—
223C2×C61—22no—
224C2×C61#143711yescharacteristic
225C2×C61#189112yes—
226D61—44no—
227C24×C4—611no—
228C22×M16—612no—
229C22×M16—612no—
230C2×#117—611no—
231C2×#117—611no—
232#407—618no—
233#407—1224no—
234C2×C22⋊C8—1224no—
235#405—1224no—
236C4×M16—1222no—
237#381—611no—
238#381#692311yescharacteristic
239#380—1222no—
240#379—611no—
241#379—611no—
242C4×C22⋊C4—1222no—
243#344—1224no—
244#343—1222no—
245C61#1093711yescharacteristic, complemented, Sylow
246C25—611no—
247C23×C4—611no—
248C23×C4—614no—
249C23×C4—1222no—
250C23×C4—1222no—
251C23×C4—1222no—
252C23×C4—1221no—
253C23×C4—1221no—
254C23×C4—1222no—
255C23×C4—1222no—
256C23×C4C2×#692311yescharacteristic
257C2×M16—614no—
258C2×M16—614no—
259C2×M16—614no—
260C2×M16—1222no—
261C2×M16—1222no—
262C2×M16—1222no—
263C2×M16—1222no—
264C2×M16—1222no—
265C2×M16—1222no—
266C2×M16—1222no—
267C2×M16—1222no—
268C2×M16—1222no—
269C22×C8—614no—
270C22×C8—1222no—
271#117—1222no—
272#117—1222no—
273#117—1222no—
274#117—1222no—
275C2×C4⋊C4—612no—
276C2×C4⋊C4—1221no—
277C2×C22⋊C4—611no—
278C2×C22⋊C4—611no—
279C2×C22⋊C4—1222no—
280C2×C22⋊C4—1222no—
281C2×C22⋊C4C2×#692311yescharacteristic
282C2×C22⋊C4C2×#692311yescharacteristic
283C2×C42—612no—
284C2×C42—1221no—
285C22⋊C8—12216no—
286#97—1224no—
287C4×C8—1224no—
288#95—22no—
289#95—1222no—
290C24—612no—
291C24—1221no—
292C24—1222no—
293C24—1221no—
294C24—1222no—
295C24—2444no—
296C24C22×#692311yescharacteristic
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—612no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—612no—
306C22×C4—612no—
307C22×C4—612no—
308C22×C4—612no—
309C22×C4—612no—
310C22×C4—612no—
311C22×C4—1224no—
312C22×C4—1224no—
313C22×C4—1224no—
314C22×C4—1224no—
315C22×C4—1224no—
316C22×C4—1224no—
317C22×C4—1221no—
318C22×C4—2441no—
319C22×C4—2442no—
320C22×C4—2441no—
321C22×C4—2442no—
322C22×C4—2442no—
323C22×C4—2442no—
324C22×C4—2442no—
325C22×C4—2442no—
326C22×C4—2441no—
327C22×C4—2441no—
328C22×C4C4×#692312yes—
329C22×C4C22⋊#692312yes—
330M16—1224no—
331M16—1224no—
332M16—1224no—
333M16—1224no—
334M16—1224no—
335M16—1224no—
336M16—2442no—
337M16—2442no—
338C2×C8—618no—
339C2×C8—1224no—
340C2×C8—1224no—
341C2×C8—1224no—
342C2×C8—2442no—
343C2×C8—2442no—
344C4⋊C4—1224no—
345C4⋊C4—2441no—
346C4⋊C4—2441no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—1222no—
350C22⋊C4—1222no—
351C22⋊C4—2444no—
352C22⋊C4—2444no—
353C42—1222no—
354C42—1222no—
355C42—2442no—
356C23—42no—
357C23—1224no—
358C23—1228no—
359C23—1222no—
360C23—1224no—
361C23—2442no—
362C23—2444no—
363C23—2444no—
364C23—2444no—
365C23—2448no—
366C23—2441no—
367C23—2442no—
368C23—2441no—
369C23C2×C4×#692311yescharacteristic
370C23C2×C22⋊#692311yescharacteristic
371C23#1451985611yescharacteristic
372C23D4×#692312yes—
373C23D4×#692312yes—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—611no—
384C2×C4—612no—
385C2×C4—611no—
386C2×C4—612no—
387C2×C4—612no—
388C2×C4—612no—
389C2×C4—612no—
390C2×C4—612no—
391C2×C4—611no—
392C2×C4—611no—
393C2×C4—612no—
394C2×C4—612no—
395C2×C4—612no—
396C2×C4—612no—
397C2×C4—612no—
398C2×C4—612no—
399C2×C4—1222no—
400C2×C4—2444no—
401C2×C4—2444no—
402C2×C4—2444no—
403C2×C4—2444no—
404C2×C4—2442no—
405C2×C4—2441no—
406C2×C4—2442no—
407C8—1228no—
408C8—2444no—
409C22—22no—
410C22—24no—
411C22—41no—
412C22—41no—
413C22—42no—
414C22—1224no—
415C22—1228no—
416C22—2444no—
417C22—2442no—
418C22—2444no—
419C22—2448no—
420C22—2442no—
421C22—2444no—
422C22C4×C22⋊#692311yescharacteristic
423C22C22⋊C4×#692312yes—
424C22#1684071011yescharacteristic
425C22#1684071212yes—
426C22#1684071411yescharacteristic
427C4—42no—
428C4—42no—
429C4—81no—
430C4—612no—
431C4—612no—
432C4—612no—
433C4—612no—
434C4—4881no—
435C4—2442no—
436C2—21no—
437C2—21no—
438C2—22no—
439C2—22no—
440C2—2444no—
441C2#2146100011yescharacteristic
442C2#2146183112yes—
subgroupG/H
centerC22#16840710
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#381C4
socleC22×C61#386
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenter#381#6923
hypocenterC61#10937
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #21462383C2semidirect
3. C2×#16840643C2semidirect
4. #21461525C2semidirect
9. #16840734C4semidirect
121. C2×#92420C22⋊C4semidirect
245. C61#10937semidirect

Maximal subgroups

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

subgroupindex
C2×#168407342
#214623832
C2×#168406432
#214615252
#214481992
#1093761