Finite Group Databasebeta

← #30600296

Subgroups — #30600296

Order 15616.

674 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 674 conjugacy classes of subgroups — too many to draw. Only its 110 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#21462668C211yesmaximal, characteristic, complemented
2#21461057C211yesmaximal, characteristic, complemented
3C2×#16840606C212yesmaximal, complemented
4#21460662C212yesmaximal, complemented
5#21448476C211yesmaximal, characteristic
6#16840789—24no—
7#16840779—21no—
8D61⋊(C22⋊C8)—21no—
9C2×C22⋊#92420C2212yes—
10C2×C22⋊#92420C2212yes—
11#16840608—21no—
12#16840606—21no—
13#16840606—24no—
14C2×#14519747C411yescharacteristic
15C2×#14519737C2211yescharacteristic
16C22×#11758198C2211yescharacteristic
17#16839663—21no—
18#16839652—21no—
19#16839651—21no—
20#16839641C411yescharacteristic
21#16839640—21no—
22#16839617C411yescharacteristic
23C22⋊C4×Dic61C2211yescharacteristic
24C61×#385C411yescharacteristic
25C2×D61⋊C8—22no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519844—22no—
29#14519834—22no—
30C22⋊#92420—22no—
31C22⋊#92420—22no—
32C22⋊#92420—22no—
33C22⋊#92420D414yescomplemented
34C4×#92420—22no—
35C24×D61C2×C411yescharacteristic
36C22×D244—21no—
37C22×C22⋊D61C2×C411yescharacteristic
38C23×Dic61C2311yescharacteristic
39C22×C4×D61D411yescharacteristic
40#14519747—22no—
41#14519747C814yescomplemented
42#14519737—22no—
43#14519737—22no—
44C2×#11758196D411yescharacteristic
45C2×C22⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—22no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—22no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198D411yescharacteristic
55C2×C4×Dic61—21no—
56C2×C4×Dic61D411yescharacteristic
57#14519684—21no—
58#14519684—21no—
59C23×C4×C61C2×C411yescharacteristic
60C2×C4⋊C4×C61—21no—
61C2×C22⋊C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61C2×C411yescharacteristic
63#95×C61—21no—
64C24×C61C22×C411yescharacteristic
65C23×D61—21no—
66C23×D61—22no—
67C23×D61—21no—
68C23×D61—22no—
69C23×D61—81no—
70C23×D61—81no—
71C23×D61C22⋊C411yescharacteristic
72C23×D61C2×C812yescomplemented
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—22no—
76C22×C4×C61—81no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61C2×C812yes—
82C2×C22⋊D61M1612yes—
83C22×Dic61—21no—
84C22×Dic61—81no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C2×D412yes—
87C22×Dic61C2×D411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C22×Dic61#4112yes—
90C2×D244—24no—
91C2×D244—81no—
92C2×D244—81no—
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—81no—
96C2×#92420—24no—
97C2×#92420—42no—
98C2×#92420—82no—
99C2×#92420—82no—
100D61⋊C8—82no—
101C4⋊C4×C61—81no—
102C22⋊C4×C61—22no—
103C22⋊C4×C61—21no—
104C22⋊C4×C61C2×C812yescomplemented
105C22⋊Dic61—22no—
106#11758198—24no—
107#11758198—22no—
108#11758198—41no—
109#11758198—42no—
110#11758198—41no—
111#11758198—81no—
112#11758198—81no—
113#11758198—81no—
114#11758196—22no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61—81no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61C2×C22⋊C411yescharacteristic
121C23×C61C4×D412yes—
122C23×C61C22×C811yescharacteristic
123C23×C61C2×M1611yescharacteristic
124C23×C61#13112yes—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—22no—
128C22×D61—24no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135C22×D61—41no—
136C22×D61—41no—
137C22×D61—42no—
138C22×D61—82no—
139C22×D61—82no—
140C22×D61—82no—
141C22×D61—82no—
142C22×D61—84no—
143C22×D61C22⋊C812yes—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—22no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—82no—
155C22⋊D61—24no—
156C22⋊D61—24no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—41no—
160C2×Dic61—42no—
161C2×Dic61—42no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61C22⋊C812yes—
167C2×Dic61#12011yescharacteristic
168C2×Dic61#12112yes—
169C2×Dic61#12311yescharacteristic
170D244—84no—
171C4×D61—42no—
172C4×D61—81no—
173#92420—44no—
174#92420—82no—
175#9107—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—22no—
178C22×C61—21no—
179C22×C61—22no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—42no—
183C22×C61#38611yescharacteristic
184C22×C61C2×C22⋊C811yescharacteristic
185C22×C61#40811yescharacteristic
186C22×C61C8×D412yes—
187C22×C61#43512yes—
188C2×D61—22no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—42no—
192C2×D61—42no—
193C2×D61—42no—
194C2×D61—42no—
195C2×D61—81no—
196C2×D61—81no—
197C2×D61—81no—
198C2×D61—84no—
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—84no—
202C4×C61—42no—
203C4×C61—41no—
204C4×C61—41no—
205C4×C61—81no—
206Dic61—22no—
207Dic61—21no—
208Dic61—22no—
209Dic61—21no—
210Dic61—81no—
211#2972—611no—
212#2321—611no—
213#1459—611no—
214C2×#323—612no—
215#1282—612no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61—22no—
219C2×C61—22no—
220C2×C61#186911yescharacteristic
221C2×C61#191311yescharacteristic
222C2×C61#191411yescharacteristic
223D61—42no—
224D61—82no—
225C2×#120—611no—
226C2×C4×D4—611no—
227C22×C22⋊C4—611no—
228C8×D4—1224no—
229#431—1221no—
230C2×C22⋊C8—612no—
231C2×C22⋊C8—612no—
232C2×C22⋊C8—1221no—
233#390—1221no—
234#388—1221no—
235#388—1221no—
236#386—611no—
237#386—1221no—
238#385#692311yescharacteristic
239#379—611no—
240C4×C22⋊C4—611no—
241#324—1221no—
242#323—1224no—
243#323—1221no—
244C61#910711yescharacteristic, complemented, Sylow
245C25—611no—
246C22×D4—611no—
247C22×D4—1221no—
248C23×C4—611no—
249C23×C4—611no—
250C23×C4C2×#692311yescharacteristic
251C22×C8—1222no—
252C22×C8—1222no—
253C22×C8—1222no—
254#120—614no—
255#120—1222no—
256C4×D4—1222no—
257C4×D4—1222no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—611no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1222no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1222no—
270C2×C22⋊C4C2×#692311yescharacteristic
271C2×C22⋊C4C2×#692311yescharacteristic
272C2×C42—611no—
273C2×C42—1221no—
274C4⋊C8—1222no—
275C22⋊C8—614no—
276C22⋊C8—1222no—
277C22⋊C8—1222no—
278C22⋊C8—1222no—
279C22⋊C8—1222no—
280C4×C8—1222no—
281#95—21no—
282#95—1221no—
283#95—1221no—
284C24—611no—
285C24—612no—
286C24—1222no—
287C24—1221no—
288C24—1222no—
289C24—1221no—
290C24—4881no—
291C24—4881no—
292C24C22×#692311yescharacteristic
293C2×D4—612no—
294C2×D4—612no—
295C2×D4—1224no—
296C2×D4—1222no—
297C2×D4—1222no—
298C2×D4—4881no—
299C2×D4—4881no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—81no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—612no—
308C22×C4—612no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312C22×C4—4881no—
313C22×C4—4881no—
314C22×C4C22⋊#692311yescharacteristic
315C22×C4C22⋊#692311yescharacteristic
316C2×C8—1224no—
317C2×C8—4882no—
318C2×C8—4882no—
319C2×C8—4882no—
320C2×C8—2442no—
321C4⋊C4—81no—
322C4⋊C4—1222no—
323C22⋊C4—22no—
324C22⋊C4—21no—
325C22⋊C4—1222no—
326C22⋊C4—1224no—
327C22⋊C4—1222no—
328C22⋊C4—4881no—
329C22⋊C4—4881no—
330C22⋊C4—4881no—
331C22⋊C4—2441no—
332C22⋊C4—2442no—
333C22⋊C4—2441no—
334C22⋊C4D61⋊C812yescomplemented
335C42—1221no—
336C42—1221no—
337C42—4881no—
338C23—41no—
339C23—41no—
340C23—612no—
341C23—1221no—
342C23—1221no—
343C23—1224no—
344C23—1222no—
345C23—4882no—
346C23—4882no—
347C23—4884no—
348C23—4882no—
349C23—4882no—
350C23—2441no—
351C23—2441no—
352C23—2441no—
353C23—2441no—
354C23—2441no—
355C23—2441no—
356C23—2441no—
357C23—2441no—
358C23—2442no—
359C23C2×C22⋊#692311yescharacteristic
360C23D4×#692312yes—
361C23C2×D61⋊C811yescharacteristic
362C23D61⋊M1611yescharacteristic
363C23#1451986512yes—
364D4—1224no—
365D4—1224no—
366D4—4884no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—82no—
378C2×C4—611no—
379C2×C4—612no—
380C2×C4—611no—
381C2×C4—612no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—4881no—
385C2×C4—2442no—
386C2×C4—2441no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4—2441no—
392C2×C4—2441no—
393C8—4882no—
394C8—2444no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—1222no—
403C22—4884no—
404C22—4884no—
405C22—4881no—
406C22—4881no—
407C22—4881no—
408C22—4881no—
409C22—4881no—
410C22—2442no—
411C22—2442no—
412C22—2442no—
413C22—2442no—
414C22—2441no—
415C22—2441no—
416C22#1684071011yescharacteristic
417C22D61⋊(C22⋊C8)11yescharacteristic
418C22#1684073711yescharacteristic
419C22#1684079012yes—
420C22#1684079212yes—
421C4—42no—
422C4—41no—
423C4—41no—
424C4—81no—
425C4—1222no—
426C4—1222no—
427C4—1221no—
428C4—1221no—
429C4—4881no—
430C2—21no—
431C2—21no—
432C2—22no—
433C2—22no—
434C2—4882no—
435C2—2442no—
436C2#2146179511yescharacteristic
437C2#2146186911yescharacteristic
438C2#2146187011yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC61×#385C4
socleC22×C61#386
prime radicalC2×#14519747C4
cosocleC23×Dic61C23
hypercenter#385#6923
hypocenterC61#9107
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #21462668C2semidirect
2. #21461057C2semidirect
3. C2×#16840606C2semidirect
4. #21460662C2semidirect
33. C22⋊#92420D4semidirect
41. #14519747C8semidirect
72. C23×D61C2×C8semidirect
104. C22⋊C4×C61C2×C8semidirect
244. C61#9107semidirect
334. C22⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
#214626682
#214610572
C2×#168406062
#214606622
#214484762
#910761