Finite Group Databasebeta

← #30593963

Subgroups — #30593963

Order 15616.

730 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461642C211yesmaximal, characteristic
2#21460993C211yesmaximal, characteristic
3#21445728C211yesmaximal, characteristic
4C22×C22⋊#6923C412yes—
5C2×#14519834—21no—
6C2×#14519834—21no—
7C2×C22⋊#92420C412yescomplemented
8C2×(C2×#6923)⋊C4—21no—
9C2×(C2×#6923)⋊C4—21no—
10C23×C4×D61C2211yescharacteristic
11C2×C22⋊#92418C411yescharacteristic, complemented
12C2×#14519689—21no—
13C2×#14519689—21no—
14C2×C22⋊C8×C61C411yescharacteristic, complemented
15C23×#6923—22no—
16C22×#92420—22no—
17C2×C22⋊#6923—22no—
18C2×C22⋊#6923—42no—
19C2×C22⋊#6923—42no—
20C2×C22⋊#6923C814yescomplemented
21#14519834—42no—
22#14519834—41no—
23#14519834—41no—
24C22⋊#92420—42no—
25(C2×#6923)⋊C4—41no—
26(C2×#6923)⋊C4—41no—
27(C2×#6923)⋊C4—42no—
28C24×D61C2×C411yescharacteristic
29C23×Dic61C2×C411yescharacteristic
30C22×C4×D61—42no—
31C22×C4×D61—41no—
32C22×C4×D61—41no—
33C22×C4×D61—42no—
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D411yescharacteristic
37C22×C4×D61Q811yescharacteristic
38C22×#92418—21no—
39C22⋊#92418—41no—
40#14519689—42no—
41#14519689—42no—
42C23×C4×C61C2×C411yescharacteristic
43C22×C8×C61—21no—
44C22⋊C8×C61—41no—
45C24×C61C4211yescharacteristic
46C23×D61—22no—
47C23×D61—21no—
48C23×D61—21no—
49C23×D61—41no—
50C23×D61—41no—
51C23×D61—41no—
52C23×D61—41no—
53C23×D61C22⋊C411yescharacteristic
54C23×D61C4⋊C411yescharacteristic
55C23×D61C2×C812yes—
56C23×D61M1612yes—
57C22×#6923—24no—
58C22×#6923—42no—
59C22×#6923—42no—
60C22×#6923—42no—
61C22×#6923—42no—
62C22×#6923—42no—
63C22×#6923—42no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C4⋊C411yescharacteristic
70C22×Dic61—22no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C4⋊C411yescharacteristic
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×C4×D61—48no—
90C2×C4×D61—48no—
91C22⋊#6923—44no—
92C22⋊#6923—44no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61#9511yescharacteristic
109C23×C61C4×C811yescharacteristic
110C23×C61#9711yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—22no—
122C22×D61—22no—
123C22×D61—22no—
124C22×D61—22no—
125C22×D61—42no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—44no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C22×D61—44no—
135C22×D61C22⋊C812yes—
136C22×D61#9912yes—
137C22×D61#10011yescharacteristic
138C22×D61#10111yescharacteristic
139C22×D61C4⋊C812yes—
140C2×#6923—44no—
141C2×#6923—44no—
142C2×#6923—44no—
143C2×#6923—82no—
144C2×#6923—82no—
145C2×#6923—82no—
146C2×#6923—82no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61#9911yescharacteristic
155C2×C4×C61#9911yescharacteristic
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—44no—
162C2×Dic61#9912yes—
163C4×D61—42no—
164C4×D61—42no—
165C4×D61—44no—
166C4×D61—42no—
167C4×D61—42no—
168C4×D61—44no—
169#92420—82no—
170C8×C61—81no—
171#92418—81no—
172#7032—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61#33611yescharacteristic
184C22×C61#34211yescharacteristic
185C22×C61#34211yescharacteristic
186C22×C61#34211yescharacteristic
187C22×C61#34311yescharacteristic
188C22×C61#34411yescharacteristic
189C22×C61#34411yescharacteristic
190C2×D61—22no—
191C2×D61—22no—
192C2×D61—22no—
193C2×D61—21no—
194C2×D61—21no—
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—22no—
198C2×D61—22no—
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—44no—
202C2×D61—44no—
203C2×D61—44no—
204C2×D61—44no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61#32312yes—
210C2×D61#32412yes—
211#6923—84no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—41no—
215Dic61—22no—
216Dic61—41no—
217#1779—611no—
218#1779—611no—
219C22⋊#95—611no—
220C2×C61—41no—
221C2×C61—41no—
222C2×C61#128011yescharacteristic
223C2×C61#128211yescharacteristic
224C2×C61#128211yescharacteristic
225C2×C61#130411yescharacteristic
226C2×C61#130511yescharacteristic
227C2×C61#130511yescharacteristic
228C2×C61#130611yescharacteristic
229D61—22no—
230D61—22no—
231D61—42no—
232C24×C4—611no—
233C22×C22⋊C4—612no—
234C2×C22⋊C8—612no—
235C2×C22⋊C8—611no—
236C2×C22⋊C8—1221no—
237C2×C22⋊C8—1221no—
238C2×C22⋊C8—1221no—
239C2×C22⋊C8—1221no—
240C2×C22⋊C8#692311yescharacteristic, complemented
241C2×#95—1221no—
242C2×#95—1221no—
243C61#703211yescharacteristic, complemented, Sylow
244C25—611no—
245C23×C4—611no—
246C23×C4—611no—
247C23×C4—611no—
248C23×C4—611no—
249C23×C4—611no—
250C23×C4—1222no—
251C23×C4—2441no—
252C23×C4—2441no—
253C23×C4—2442no—
254C23×C4—2442no—
255C23×C4C2×#692311yescharacteristic
256C22×C8—21no—
257C22×C8—1222no—
258C22×C8—1221no—
259C2×C22⋊C4—614no—
260C2×C22⋊C4—1222no—
261C2×C22⋊C4—2442no—
262C2×C22⋊C4—2442no—
263C22⋊C8—41no—
264C22⋊C8—2442no—
265C22⋊C8—2442no—
266C22⋊C8—2442no—
267C22⋊C8—2441no—
268C22⋊C8—2441no—
269C22⋊C8—2441no—
270C22⋊C8—2442no—
271#95—2442no—
272#95—2441no—
273#95—2441no—
274C24—611no—
275C24—611no—
276C24—612no—
277C24—612no—
278C24—1221no—
279C24—1222no—
280C24—1221no—
281C24—2441no—
282C24—2441no—
283C24—2441no—
284C24—2441no—
285C24C4×#692311yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—1222no—
293C22×C4—1222no—
294C22×C4—1222no—
295C22×C4—1222no—
296C22×C4—1222no—
297C22×C4—1221no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1224no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4—2441no—
308C22×C4—2448no—
309C22×C4—2448no—
310C22×C4—2441no—
311C22×C4—2441no—
312C22×C4—2442no—
313C22×C4—2442no—
314C22×C4—2442no—
315C22×C4—2442no—
316C22×C4—2442no—
317C22×C4—2442no—
318C22×C4C4⋊#692311yescharacteristic
319C22×C4C22⋊#692311yescharacteristic
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2442no—
326C2×C8—2442no—
327C2×C8—2442no—
328C2×C8—2441no—
329C22⋊C4—2444no—
330C22⋊C4—2444no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—612no—
338C23—612no—
339C23—611no—
340C23—611no—
341C23—612no—
342C23—1222no—
343C23—1222no—
344C23—1222no—
345C23—1222no—
346C23—1221no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—2442no—
357C23—2442no—
358C23—2442no—
359C23—2442no—
360C23—2444no—
361C23—2442no—
362C23—2442no—
363C23—2442no—
364C23—2442no—
365C23—2444no—
366C23(C2×#6923)⋊C411yescharacteristic
367C23C8×#692311yescharacteristic
368C23#1451983111yescharacteristic
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—612no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—4882no—
383C2×C4—4882no—
384C2×C4—4882no—
385C2×C4—4882no—
386C2×C4—2442no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2444no—
391C2×C4—2444no—
392C2×C4—2444no—
393C2×C4—2444no—
394C2×C4—2444no—
395C2×C4—2444no—
396C2×C4#1451983511yescharacteristic
397C2×C4#1451983611yescharacteristic
398C8—81no—
399C8—4881no—
400C8—4882no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—612no—
412C22—612no—
413C22—1222no—
414C22—1222no—
415C22—1222no—
416C22—1221no—
417C22—1221no—
418C22—1221no—
419C22—1221no—
420C22—1222no—
421C22—1222no—
422C22—1222no—
423C22—1222no—
424C22—2444no—
425C22—2444no—
426C22—2444no—
427C22—2444no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22—2441no—
432C22(C2×#6923)⋊C811yescharacteristic
433C22#1684063911yescharacteristic
434C22#1684063911yescharacteristic
435C22#1684064011yescharacteristic
436C22#1684064111yescharacteristic
437C22#1684064411yescharacteristic
438C22#1684064511yescharacteristic
439C4—21no—
440C4—21no—
441C4—41no—
442C4—1222no—
443C4—4884no—
444C4—2441no—
445C2—41no—
446C2—41no—
447C2—1222no—
448C2—1222no—
449C2—2442no—
450C2#2146065611yescharacteristic
451C2#2146066011yescharacteristic
452C2#2146066111yescharacteristic
453C2#2146071811yescharacteristic
454C2#2146071911yescharacteristic
455C2#2146072111yescharacteristic
456C2#2146072311yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC23×C61C4×C8
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC23×C61#95
prime radicalC24×D61C2×C4
cosocleC23×C4×D61C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7032
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
7. C2×C22⋊#92420C4semidirect
11. C2×C22⋊#92418C4semidirect
14. C2×C22⋊C8×C61C4semidirect
20. C2×C22⋊#6923C8semidirect
240. C2×C22⋊C8#6923semidirect
243. C61#7032semidirect

Maximal subgroups

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

subgroupindex
#214616422
#214609932
#214457282
#703261