Finite Group Databasebeta

← #30605188

Subgroups — #30605188

Order 15616.

582 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461680C211yesmaximal, characteristic, complemented
2#21461076C211yesmaximal, characteristic, complemented
3#21460816C212yesmaximal, complemented
4#21460797C212yesmaximal, complemented
5#21449098C211yesmaximal, characteristic
6C2×#14519836—21no—
7#16840733—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840607—21no—
11#16840606C2212yes—
12C2×C4×D244C2211yescharacteristic
13C2×C4×C22⋊D61—21no—
14C2×C4×C22⋊D61—21no—
15#16839698—21no—
16#16839697C411yescharacteristic, complemented
17#16839697C2211yescharacteristic
18#16839671—21no—
19#16839670C411yescharacteristic, complemented
20#16839670C2211yescharacteristic
21#16839608C411yescharacteristic, complemented
22C2×C4×D4×C61C411yescharacteristic, complemented
23C2×#11758213—41no—
24C2×C4⋊#6923—41no—
25C2×C22⋊#6923—22no—
26#14519836—42no—
27#14519834—41no—
28C22⋊#92420—22no—
29(C2×#6923)⋊C4—41no—
30C22×D244D411yescharacteristic
31C22×C22⋊D61—21no—
32C22×C22⋊D61—21no—
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C4×D244—41no—
36C4×D244—41no—
37C4×C22⋊D61—44no—
38C4×C22⋊D61—44no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198C2×C411yescharacteristic
47C2×#11758198C2311yescharacteristic
48C2×C4×Dic61—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51#14519684C2×C411yescharacteristic
52C22×D4×C61C2×C411yescharacteristic
53C23×C4×C61—21no—
54C4×D4×C61—41no—
55C4×D4×C61—41no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C42×C61C2×C411yescharacteristic
59C24×C61—21no—
60C23×D61C22⋊C411yescharacteristic
61C23×D61C2×D411yescharacteristic
62C22×#6923—42no—
63C2×D4×C61—41no—
64C2×D4×C61—42no—
65C22×C4×C61—21no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C2×C22⋊D61—42no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—41no—
87C2×D244—41no—
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C22⋊#6923—42no—
95C22⋊#6923—42no—
96C2×#92420—42no—
97C4⋊#6923—82no—
98#11758213—82no—
99C4⋊C4×C61—41no—
100C22⋊C4×C61—42no—
101C42×C61—21no—
102C42×C61—21no—
103C22⋊Dic61—42no—
104C22⋊Dic61—42no—
105#11758198—41no—
106#11758198—41no—
107#11758198—42no—
108#11758198—42no—
109C4⋊Dic61—41no—
110#11758196—42no—
111#11758196—42no—
112C4×Dic61—24no—
113C23×C61—22no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61C2×C22⋊C411yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61AGL(1,ℤ/8)11yescharacteristic
131C22×D61#13711yescharacteristic
132C2×#6923—82no—
133C2×#6923—82no—
134C2×#6923—82no—
135D4×C61—42no—
136D4×C61—42no—
137C2×C4×C61—22no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—82no—
147C2×C4×C61—82no—
148C2×C4×C61#9911yescharacteristic
149C2×C4×C61#9911yescharacteristic
150C22⋊D61—44no—
151C22⋊D61—44no—
152C22⋊D61—48no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163D244—42no—
164D244—42no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—81no—
168C4×D61—81no—
169#92420—82no—
170#11821—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61C2×#9911yescharacteristic
181C22×C61#41711yescharacteristic
182C22×C61#42111yescharacteristic
183C2×D61—21no—
184C2×D61—21no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—42no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—81no—
194C2×D61—81no—
195#6923—162no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—81no—
200C4×C61#35312yes—
201Dic61—42no—
202Dic61—42no—
203Dic61—41no—
204Dic61—41no—
205#2397—611no—
206#1799—611no—
207#1465—611no—
208#1352—612no—
209#1343—612no—
210C2×C61—21no—
211C2×C61—21no—
212C2×C61—82no—
213C2×C61#151311yescharacteristic
214C2×C61#212011yescharacteristic
215C2×C61C2×#35311yescharacteristic
216D61—41no—
217D61—41no—
218D61—81no—
219C2×C4×D4—611no—
220C2×C4×D4—1221no—
221C2×C4×D4—1221no—
222C2×C4×D4#692311yescharacteristic, complemented
223C2×#99—1221no—
224#407—1221no—
225#399—611no—
226#399—611no—
227#399—1221no—
228#392—611no—
229#392—611no—
230#392—1221no—
231#380—1221no—
232#376—611no—
233#342—612no—
234#324—1221no—
235#323—612no—
236C61#1182111yescharacteristic, complemented, Sylow
237C22×D4—611no—
238C22×D4—1221no—
239C22×D4—1221no—
240C22×D4C2×#692311yescharacteristic
241C23×C4—21no—
242C23×C4—611no—
243C23×C4—611no—
244C2×M16—2441no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—2441no—
248C4×D4—2441no—
249C4×D4—2444no—
250C4×D4—2444no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—2441no—
255C2×C4⋊C4C2×#692311yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—611no—
258C2×C22⋊C4—611no—
259C2×C22⋊C4—1221no—
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1222no—
264C2×C42—1221no—
265C2×C42C2×#692311yescharacteristic
266#99—2442no—
267C22⋊C8—1222no—
268C22⋊C8—2441no—
269#95—611no—
270#95—611no—
271#95—1221no—
272#95—2441no—
273C24—21no—
274C24—611no—
275C24—611no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2442no—
283C2×D4—2442no—
284C2×D4—2442no—
285C2×D4—2442no—
286C2×D4—2441no—
287C2×D4—2441no—
288C2×D4—2442no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—2442no—
303C22×C4—2442no—
304C22×C4—2442no—
305C22×C4C22⋊#692311yescharacteristic
306C22×C4C22⋊#692311yescharacteristic
307C22×C4C22×#692311yescharacteristic
308M16—4882no—
309C2×C8—2442no—
310C4⋊C4—41no—
311C4⋊C4—4882no—
312C4⋊C4—2441no—
313C4⋊C4—2442no—
314C4⋊C4—2442no—
315C22⋊C4—42no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C22⋊C4—2442no—
319C22⋊C4—2442no—
320C22⋊C4—2442no—
321C22⋊C4—2442no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C42—21no—
325C42—21no—
326C42—1224no—
327C23—22no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—611no—
335C23—611no—
336C23—1221no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23C2×C22⋊#692311yescharacteristic
346D4—42no—
347D4—42no—
348D4—2442no—
349D4—2442no—
350D4—2448no—
351D4—2444no—
352D4—2444no—
353C2×C4—22no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—4881no—
369C2×C4—4881no—
370C2×C4—4882no—
371C2×C4—4882no—
372C2×C4—4882no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2442no—
378C2×C4—2442no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4#1451983511yescharacteristic
382C2×C4#1451983511yescharacteristic
383C8—4882no—
384C22—21no—
385C22—21no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—1221no—
394C22—1221no—
395C22—4881no—
396C22—4881no—
397C22—2442no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22—2441no—
402C22—2441no—
403C22—2441no—
404C22—2441no—
405C22C2×#1451983511yescharacteristic
406C22#1684075311yescharacteristic
407C22#1684075911yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—81no—
412C4—9762no—
413C4—2442no—
414C4—2442no—
415C4—2441no—
416C4—2441no—
417C4#1684066612yes—
418C2—21no—
419C2—21no—
420C2—82no—
421C2—4881no—
422C2—2441no—
423C2—2441no—
424C2#2146123411yescharacteristic
425C2#2146207011yescharacteristic
426C2C2×#1684066611yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C2×#99
prime radical#21449098C2
cosocleC2×#11758198C23
hypercenterC2×C4×D4#6923
hypocenterC61#11821
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461680C2semidirect
2. #21461076C2semidirect
3. #21460816C2semidirect
4. #21460797C2semidirect
16. #16839697C4semidirect
19. #16839670C4semidirect
21. #16839608C4semidirect
22. C2×C4×D4×C61C4semidirect
222. C2×C4×D4#6923semidirect
236. C61#11821semidirect

Maximal subgroups

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

subgroupindex
#214616802
#214610762
#214608162
#214607972
#214490982
#1182161