Finite Group Databasebeta

← #30601793

Subgroups — #30601793

Order 15616.

602 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461735C211yesmaximal, characteristic, complemented
2C4×#14519844C211yesmaximal, characteristic, complemented
3C2×#16840622C212yesmaximal, complemented
4C2×#16840620C212yesmaximal
5#21454174C211yesmaximal, characteristic
6C2×#14519844C2212yes—
7C2×#14519844C2212yes—
8C2×C4×#92420—21no—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12#16840622—24no—
13#16840620—24no—
14C2×#14519775C2211yescharacteristic
15C2×#14519773C2211yescharacteristic
16C2×#14519766C411yescharacteristic
17C2×#14519765C411yescharacteristic
18C2×#14519764C411yescharacteristic
19#16839662—21no—
20#16839662—21no—
21#16839662—21no—
22#16839662—21no—
23C42×Dic61C2211yescharacteristic
24C2×#124×C61C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30#14519844D414yes—
31C4×#92420—42no—
32C22×Dic122C2×C411yescharacteristic
33C22×D244C2×C411yescharacteristic
34C22×C22⋊D61—21no—
35C22×C22⋊D61—21no—
36#14519775—22no—
37#14519775—22no—
38#14519773—22no—
39#14519773—22no—
40#14519766—42no—
41#14519765—42no—
42#14519764—42no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61C2311yescharacteristic
57C22×Q8×C61C2×C411yescharacteristic
58C22×D4×C61C2×C411yescharacteristic
59#124×C61—42no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C42×C61C2×C411yescharacteristic
63C24×C61—21no—
64C23×D61—21no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×D4×C61—22no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C22×C4×C61—21no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C2×C22⋊D61—42no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C22×Dic61—21no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C2×D411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C2×D244—22no—
89C2×D244—41no—
90C2×D244—41no—
91C2×Dic122—22no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×#92420—24no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C22⋊C4×C61—42no—
101C22⋊C4×C61—42no—
102C42×C61—22no—
103C22⋊Dic61—42no—
104C22⋊Dic61—42no—
105#11758198—42no—
106#11758198—42no—
107#11758198—42no—
108#11758198—42no—
109#11758196—42no—
110#11758196—41no—
111#11758196—41no—
112C4×Dic61—22no—
113C4×Dic61—22no—
114C4×Dic61—22no—
115C4×Dic61—22no—
116C4×Dic61—21no—
117C4×Dic61—21no—
118C4×Dic61C2×D412yes—
119C4×Dic61#4112yes—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61C2×C22⋊C411yescharacteristic
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C22×D61—41no—
135Q8×C61—82no—
136D4×C61—82no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61#10012yes—
148C2×C4×C61C4×D412yes—
149C22⋊D61—82no—
150C22⋊D61—82no—
151C22⋊D61—82no—
152C22⋊D61—82no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61#10012yes—
162C2×Dic61#12112yes—
163C2×Dic61#12411yescharacteristic
164C2×Dic61#12711yescharacteristic
165C2×Dic61#13512yes—
166C2×Dic61#13512yes—
167C2×Dic61#13512yes—
168C2×Dic61AGL(1,ℤ/8)11yescharacteristic
169C2×Dic61#13711yescharacteristic
170D244—82no—
171Dic122—82no—
172#92420—44no—
173#92420—82no—
174#9699—611nomaximal, Sylow
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61—81no—
181C22×C61—81no—
182C22×C61#39011yescharacteristic
183C22×C61C2×#10011yescharacteristic
184C22×C61C2×#10011yescharacteristic
185C22×C61#41611yescharacteristic
186C22×C61#41611yescharacteristic
187C22×C61#41611yescharacteristic
188C22×C61#41711yescharacteristic
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C4×C61—22no—
197C4×C61—22no—
198C4×C61—41no—
199C4×C61—81no—
200Dic61—22no—
201Dic61—41no—
202Dic61—81no—
203Dic61#46312yes—
204Dic61#46412yes—
205Dic61#48812yes—
206Dic61#49512yes—
207#2858—611no—
208#1831—611no—
209C4×C4⋊C8—611no—
210C2×#333—612no—
211C2×#331—612no—
212C2×C61—161no—
213C2×C61#154311yescharacteristic
214C2×C61#154311yescharacteristic
215C2×C61#155111yescharacteristic
216C2×C61#155111yescharacteristic
217C2×C61#195811yescharacteristic
218C2×C61#196511yescharacteristic
219C2×C61#198311yescharacteristic
220D61—161no—
221C2×C4⋊Q8—611no—
222C2×#127—611no—
223C2×#124—611no—
224C2×#124—611no—
225C2×#124—611no—
226C2×#124#692311yescharacteristic
227C2×C4⋊C8—612no—
228C2×C4⋊C8—612no—
229C2×C4×C8—1221no—
230#390—1221no—
231#390—1221no—
232#390—1221no—
233#390—1221no—
234C43—611no—
235#336—1221no—
236#336—1221no—
237#336—1221no—
238#333—1224no—
239#331—1224no—
240C61#969911yescharacteristic, complemented, Sylow
241C22×Q8—611no—
242C22×Q8C2×#692311yescharacteristic
243C22×D4—611no—
244C22×D4—1221no—
245C22×D4—1221no—
246C22×D4C2×#692311yescharacteristic
247C22×C8—1222no—
248C22×C8—1222no—
249C4⋊Q8—1222no—
250C4⋊Q8—1222no—
251#127—1222no—
252#127—1222no—
253#124—42no—
254#124—2442no—
255#124—2442no—
256#124—2442no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—611no—
270C2×C42—611no—
271C2×C42—611no—
272C2×C42—611no—
273C2×C42C2×#692311yescharacteristic
274C4⋊C8—614no—
275C4⋊C8—1222no—
276C4⋊C8—1222no—
277C4⋊C8—1222no—
278C4×C8—2442no—
279C24—21no—
280C24—1221no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—1222no—
285C2×Q8—2441no—
286C2×Q8—2441no—
287C2×D4—22no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—1222no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2442no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2442no—
297C2×D4—2442no—
298C2×D4—2442no—
299C2×D4—2441no—
300C2×D4—2441no—
301C22×C4—21no—
302C22×C4—611no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—1221no—
307C22×C4C22⋊#692311yescharacteristic
308C22×C4C22⋊#692311yescharacteristic
309C22×C4C22×#692311yescharacteristic
310C2×C8—1224no—
311C2×C8—2442no—
312C2×C8—2442no—
313C2×C8—2442no—
314C2×C8—2442no—
315C2×C8—2442no—
316C4⋊C4—2442no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—2442no—
322C22⋊C4—2442no—
323C22⋊C4—2442no—
324C22⋊C4—2442no—
325C22⋊C4—2442no—
326C22⋊C4—2442no—
327C42—22no—
328C42—612no—
329C42—612no—
330C42—1221no—
331C42—1222no—
332C42—1221no—
333C42—1222no—
334C42—1222no—
335C42—1222no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23—2441no—
348C23—2441no—
349C23—2441no—
350C23C2×C22⋊#692311yescharacteristic
351Q8—82no—
352Q8—4882no—
353D4—82no—
354D4—4882no—
355D4—4882no—
356D4—4882no—
357D4—4882no—
358D4—4882no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—612no—
370C2×C4—611no—
371C2×C4—611no—
372C2×C4—612no—
373C2×C4—612no—
374C2×C4—612no—
375C2×C4—611no—
376C2×C4—611no—
377C2×C4—612no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4#1451983712yes—
387C2×C4D4×#692312yes—
388C8—4882no—
389C8—2444no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—4881no—
398C22—4881no—
399C22—4881no—
400C22—4881no—
401C22—4881no—
402C22—4881no—
403C22—4881no—
404C22#1684071411yescharacteristic
405C22C2×#1451983711yescharacteristic
406C22D61⋊#10011yescharacteristic
407C22#1684075211yescharacteristic
408C22#1684075211yescharacteristic
409C22#1684075211yescharacteristic
410C22#1684075311yescharacteristic
411C4—22no—
412C4—22no—
413C4—41no—
414C4—81no—
415C4—612no—
416C4—612no—
417C4—612no—
418C4—612no—
419C4—1222no—
420C4—4881no—
421C4—2441no—
422C2—161no—
423C2—9761no—
424C2#2146132211yescharacteristic
425C2#2146132311yescharacteristic
426C2#2146133811yescharacteristic
427C2#2146133911yescharacteristic
428C2#2146194811yescharacteristic
429C2#2146196111yescharacteristic
430C2#2146198711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C22
cosocleC2×C4×Dic61C23
hypercenterC2×#124#6923
hypocenterC61#9699
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #21461735C2semidirect
2. C4×#14519844C2semidirect
3. C2×#16840622C2semidirect
240. C61#9699semidirect

Maximal subgroups

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

subgroupindex
#214617352
C4×#145198442
C2×#168406222
C2×#168406202
#214541742
#969961