Finite Group Databasebeta

← #30595427

Subgroups — #30595427

Order 15616.

662 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461676C211yesmaximal, characteristic, complemented
2#21461480C211yesmaximal, characteristic, complemented
3#21460637C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5C4×#14519752C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519844—21no—
8C2×#14519834—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519752C411yescharacteristic
13C2×C4×D244—21no—
14C2×C4×D244C411yescharacteristic
15C2×C42×D61C2211yescharacteristic
16#16839663C2211yescharacteristic
17#16839661C2211yescharacteristic
18#16839654—21no—
19#16839640—21no—
20#16839619C411yescharacteristic
21C4×#11758198—21no—
22C4×C4⋊C4×C61C411yescharacteristic
23C2×D61⋊C8—24no—
24C2×D61⋊C8—42no—
25C2×D61⋊C8—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519844—42no—
29#14519834—42no—
30C22×D244—21no—
31C22×D244C2×C411yescharacteristic
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36#14519752—22no—
37#14519752C814yescomplemented
38C4×D244—42no—
39C4×D244—42no—
40C4×D244—42no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51C42×D61—42no—
52#14519684—21no—
53#14519684—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58#95×C61—21no—
59C23×D61—21no—
60C23×D61C22⋊C411yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×D244—24no—
71C2×D244—21no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244—42no—
75C2×D244—42no—
76C2×D244C2×C812yescomplemented
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61C2×C812yes—
89C2×C4×D61M1612yes—
90C2×C4×D61D812yes—
91C2×C4×D61SD1612yes—
92C2×#92420—24no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98D61⋊C8—48no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61C2×C812yescomplemented
102C42×C61—22no—
103C42×C61—42no—
104#11758198—24no—
105#11758198—42no—
106#11758198—42no—
107#11758198—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198—41no—
111C4⋊Dic61—41no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
114C4×Dic61—22no—
115C4×Dic61—41no—
116C4×Dic61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—22no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61C22⋊C812yes—
130C22×D61#10212yes—
131C22×D61#10412yes—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—22no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61#9912yes—
145C2×C4×C61#10212yes—
146C2×C4×C61C22×C811yescharacteristic
147C2×C4×C61C2×M1611yescharacteristic
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61C22⋊C812yes—
158C2×Dic61C2×D811yescharacteristic
159C2×Dic61C2×SD1611yescharacteristic
160C2×Dic61AGL(1,ℤ/8)11yescharacteristic
161C2×Dic61#13711yescharacteristic
162D244—42no—
163D244—42no—
164D244—48no—
165C4×D61—24no—
166C4×D61—24no—
167C4×D61—42no—
168C4×D61—42no—
169C4×D61—42no—
170C4×D61—42no—
171C4×D61—84no—
172#92420—44no—
173#92420—82no—
174#7586—611nomaximal, Sylow
175C22×C61C2×C22⋊C811yescharacteristic
176C22×C61C2×#9911yescharacteristic
177C22×C61#41311yescharacteristic
178C22×C61C2×#10211yescharacteristic
179C22×C61#41711yescharacteristic
180C22×C61C2×#10411yescharacteristic
181C22×C61#42111yescharacteristic
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—22no—
186C2×D61—22no—
187C2×D61—22no—
188C2×D61—42no—
189C2×D61—42no—
190C2×D61—42no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61D4⋊C814yes—
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—22no—
199C4×C61—22no—
200C4×C61—42no—
201C4×C61—81no—
202Dic61—22no—
203Dic61—21no—
204Dic61—21no—
205Dic61—21no—
206Dic61—21no—
207Dic61—81no—
208C4×#121—611no—
209#1797—611no—
210C2×#336—611no—
211#1271—612no—
212#1270—612no—
213C2×C61#145911yescharacteristic
214C2×C61C2×D4⋊C811yescharacteristic
215C2×C61#147711yescharacteristic
216C2×C61#150411yescharacteristic
217C2×C61#151911yescharacteristic
218C2×C61#153211yescharacteristic
219C2×C61#154711yescharacteristic
220D61—24no—
221D61—82no—
222C23×C8—1221no—
223C2×#121—611no—
224C2×C4×D4—611no—
225C2×C4×D4—1221no—
226C22×C42—611no—
227C2×C4⋊C8—1221no—
228C2×C22⋊C8—1221no—
229#390—611no—
230#389—611no—
231#388—1221no—
232#386—1221no—
233#380—611no—
234C4×C4⋊C4#692311yescharacteristic
235C4×C22⋊C4—1221no—
236#336—612no—
237#336—612no—
238#336—1221no—
239C61#758611yescharacteristic, complemented, Sylow
240C22×D4—611no—
241C22×D4—1221no—
242C23×C4—611no—
243C23×C4—611no—
244C23×C4—611no—
245C23×C4—1221no—
246C22×C8—1222no—
247C22×C8—1224no—
248C22×C8—1222no—
249C22×C8—2442no—
250C22×C8—2442no—
251#121—614no—
252#121—1222no—
253C4×D4—2442no—
254C4×D4—2442no—
255C4×D4—2442no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4C2×#692311yescharacteristic
259C2×C4⋊C4C2×#692311yescharacteristic
260C2×C22⋊C4—1221no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C42—21no—
266C2×C42—611no—
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—2442no—
270C2×C42C2×#692311yescharacteristic
271C4⋊C8—2442no—
272C22⋊C8—2442no—
273#95—21no—
274#95—1221no—
275#95—1221no—
276C24—611no—
277C24—1221no—
278C2×D4—612no—
279C2×D4—1224no—
280C2×D4—1221no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2442no—
284C2×D4—2442no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—612no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—1221no—
299C22×C4—2441no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4—2442no—
304C22×C4—2442no—
305C22×C4—2442no—
306C22×C4C22⋊#692311yescharacteristic
307C22×C4C22⋊#692311yescharacteristic
308C22×C4C22×#692311yescharacteristic
309C2×C8—1224no—
310C2×C8—2442no—
311C2×C8—2442no—
312C2×C8—2442no—
313C2×C8—2442no—
314C2×C8—2448no—
315C2×C8—2442no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4D61⋊C812yescomplemented
322C22⋊C4—1224no—
323C22⋊C4—2441no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C22⋊C4—2441no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C42—22no—
330C42—42no—
331C42—1222no—
332C42—2441no—
333C42—2441no—
334C23—612no—
335C23—612no—
336C23—612no—
337C23—1221no—
338C23—1221no—
339C23—1221no—
340C23—1221no—
341C23—1222no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23—2441no—
348C23C2×C22⋊#692311yescharacteristic
349D4—2442no—
350D4—2442no—
351D4—2448no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—612no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—1224no—
370C2×C4—1224no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—4884no—
378C2×C4—2442no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4#1451983612yes—
386C2×C4#1451983912yes—
387C2×C4C2×D61⋊C811yescharacteristic
388C2×C4D61⋊M1611yescharacteristic
389C8—4882no—
390C8—2444no—
391C22—614no—
392C22—1222no—
393C22—1222no—
394C22—1222no—
395C22—1222no—
396C22—1222no—
397C22—1222no—
398C22—4881no—
399C22—4881no—
400C22—4881no—
401C22—4881no—
402C22—2442no—
403C22—2442no—
404C22—2442no—
405C22D61⋊(C22⋊C8)11yescharacteristic
406C22C2×#1451983611yescharacteristic
407C22#1684074811yescharacteristic
408C22C2×#1451983911yescharacteristic
409C22#1684075311yescharacteristic
410C22D61⋊#10411yescharacteristic
411C22#1684076111yescharacteristic
412C4—22no—
413C4—21no—
414C4—21no—
415C4—22no—
416C4—42no—
417C4—81no—
418C4—1221no—
419C4—1221no—
420C4—1222no—
421C4—1221no—
422C4—1221no—
423C4—4881no—
424C2—1224no—
425C2—4882no—
426C2#2146105611yescharacteristic
427C2D61⋊(D4⋊C8)11yescharacteristic
428C2#2146111711yescharacteristic
429C2#2146120711yescharacteristic
430C2#2146125611yescharacteristic
431C2#2146129611yescharacteristic
432C2#2146133011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#7586
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461676C2semidirect
2. #21461480C2semidirect
3. #21460637C2semidirect
4. #21460636C2semidirect
37. #14519752C8semidirect
76. C2×D244C2×C8semidirect
101. C4⋊C4×C61C2×C8semidirect
239. C61#7586semidirect
321. C4⋊C4D61⋊C8semidirect

Maximal subgroups

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

subgroupindex
#214616762
#214614802
#214606372
#214606362
C4×#145197522
#758661