Finite Group Databasebeta

← #30595375

Subgroups — #30595375

Order 15616.

884 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 146 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#21461673C211yesmaximal, characteristic, complemented
2C4×C22⋊#92420C211yesmaximal, characteristic, complemented
3#21460636C214yesmaximal, complemented
4C2×#16839663C211yesmaximal, characteristic
5C2×C4⋊#92420—21no—
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C4×#92420—21no—
9#16840628C2212yescomplemented
10#16840628C2212yescomplemented
11C23×D244C411yescharacteristic
12C22×#11758198—21no—
13C22×#11758198—21no—
14C22×C4×Dic61C2211yescharacteristic
15#16839663—21no—
16#16839663—21no—
17#16839663C412yes—
18#16839663C2212yes—
19C22×C4⋊C4×C61C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—42no—
23C22⋊#92420—24no—
24C22⋊#92420—42no—
25C4×#92420—42no—
26C24×D61—21no—
27C22×D244—21no—
28C22×D244—22no—
29C22×D244—42no—
30C22×D244—42no—
31C22×D244C814yescomplemented
32C22×D244C2×C412yes—
33C23×Dic61D411yescharacteristic
34C23×Dic61D411yescharacteristic
35C2×#11758198—22no—
36C2×#11758198—22no—
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198—44no—
40C2×#11758198—42no—
41C2×#11758198—42no—
42C2×C4×Dic61—42no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47C23×C4×C61—21no—
48C23×C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—42no—
51C2×C4⋊C4×C61C2×C412yes—
52C24×C61C22⋊C411yescharacteristic
53C23×D61—24no—
54C23×D61—22no—
55C23×D61—42no—
56C23×D61—42no—
57C23×D61—42no—
58C23×D61—42no—
59C23×D61—42no—
60C23×D61—42no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C2×C812yes—
69C22×C4×C61M1612yes—
70C22×C4×C61C22×C411yescharacteristic
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61D812yes—
79C22×Dic61SD1612yes—
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×D244—24no—
83C2×D244—22no—
84C2×D244—48no—
85C2×D244—42no—
86C2×D244—42no—
87C2×D244—42no—
88C2×D244—42no—
89C2×D244—48no—
90C2×D244C2×C814yes—
91C2×#92420—24no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C4⋊C4×C61—42no—
98C4⋊C4×C61—42no—
99#11758198—44no—
100#11758198—44no—
101#11758198—42no—
102#11758198—42no—
103#11758198—44no—
104C4×Dic61—22no—
105C4×Dic61—22no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61C22⋊C812yes—
113C23×C61#10212yes—
114C23×C61#10412yes—
115C23×C61C2×C22⋊C411yescharacteristic
116C22×D61—24no—
117C22×D61—48no—
118C22×D61—48no—
119C22×D61—48no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61—42no—
126C22×D61—84no—
127C22×D61—84no—
128C22×D61—84no—
129C22×D61—84no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—24no—
133C2×C4×C61—24no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—84no—
138C2×C4×C61C22⋊C812yes—
139C2×C4×C61#9912yes—
140C2×C4×C61#10012yes—
141C2×C4×C61C22×C811yescharacteristic
142C2×C4×C61C2×M1611yescharacteristic
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—44no—
155C2×Dic61#10212yes—
156C2×Dic61C2×D811yescharacteristic
157C2×Dic61C2×SD1611yescharacteristic
158C2×Dic61AGL(1,ℤ/8)12yes—
159D244—44no—
160D244—44no—
161D244—48no—
162#92420—44no—
163#92420—82no—
164#7572—611nomaximal, Sylow
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—22no—
170C22×C61—22no—
171C22×C61D4⋊C814yes—
172C22×C61C2×C22⋊C811yescharacteristic
173C22×C61C2×#9911yescharacteristic
174C22×C61C2×#10011yescharacteristic
175C22×C61C2×#10211yescharacteristic
176C22×C61#41811yescharacteristic
177C22×C61C2×#10411yescharacteristic
178C22×C61#42111yescharacteristic
179C2×D61—44no—
180C2×D61—44no—
181C2×D61—44no—
182C2×D61—816no—
183C2×D61—82no—
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—82no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—82no—
190C4×C61#32314yes—
191Dic61—22no—
192Dic61—21no—
193Dic61—22no—
194Dic61—21no—
195Dic61—41no—
196C2×#390—611no—
197#1797—611no—
198C4×C22⋊C8—611no—
199#1270—614no—
200C2×C61—24no—
201C2×C61C2×#32311yescharacteristic
202C2×C61C2×D4⋊C811yescharacteristic
203C2×C61#147811yescharacteristic
204C2×C61#150711yescharacteristic
205C2×C61#151911yescharacteristic
206C2×C61#152711yescharacteristic
207C2×C61#154511yescharacteristic
208D61—84no—
209C23×D4—611no—
210C22×C4⋊C4#692311yescharacteristic
211C22×C22⋊C4—1221no—
212C22×C22⋊C4—1221no—
213C22×C42—611no—
214C2×C4⋊C8—1221no—
215C2×C22⋊C8—1221no—
216C2×C22⋊C8—1221no—
217C2×C4×C8—1221no—
218#390—612no—
219#390—612no—
220#390—1221no—
221#390—1221no—
222#336—612no—
223#336—612no—
224C61#757211yescharacteristic, complemented, Sylow
225C25—1221no—
226C22×D4—614no—
227C22×D4—612no—
228C22×D4—1222no—
229C22×D4—1221no—
230C22×D4—2442no—
231C22×D4—2442no—
232C23×C4—21no—
233C23×C4—611no—
234C23×C4—611no—
235C23×C4C2×#692311yescharacteristic
236C22×C8—1222no—
237C22×C8—1222no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4C2×#692312yes—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1222no—
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—2442no—
246C2×C22⋊C4—2442no—
247C2×C22⋊C4—2444no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—2442no—
253C4⋊C8—2442no—
254C22⋊C8—1224no—
255C22⋊C8—2442no—
256C4×C8—2442no—
257C24—1224no—
258C24—1222no—
259C24—2442no—
260C24—2442no—
261C24—2442no—
262C24—2442no—
263C24—2442no—
264C24—2442no—
265C24C22⋊#692311yescharacteristic
266C2×D4—614no—
267C2×D4—1224no—
268C2×D4—1222no—
269C2×D4—2442no—
270C2×D4—2442no—
271C2×D4—2448no—
272C2×D4—2448no—
273C2×D4—2442no—
274C2×D4—2442no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—612no—
285C22×C4—612no—
286C22×C4—611no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4D61⋊C812yes—
293C22×C4#1175821312yes—
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22×#692311yescharacteristic
296C2×C8—1224no—
297C2×C8—2442no—
298C2×C8—2442no—
299C2×C8—2442no—
300C2×C8—2442no—
301C2×C8—2442no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C22⋊C4—2444no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C22⋊C4—2444no—
308C22⋊C4—2444no—
309C42—1222no—
310C42—1222no—
311C42—2441no—
312C42—2441no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—1224no—
318C23—4884no—
319C23—4884no—
320C23—4884no—
321C23—4884no—
322C23—2448no—
323C23—2448no—
324C23—2442no—
325C23—2442no—
326C23—2442no—
327C23—2442no—
328C23—2442no—
329C23—2442no—
330C23—2448no—
331C23#1451983412yes—
332C23#1451983912yes—
333C23#1451984212yes—
334C23C2×C22⋊#692311yescharacteristic
335D4—2444no—
336D4—2444no—
337D4—2448no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—84no—
346C2×C4—612no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—612no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—2442no—
360C2×C4—2442no—
361C2×C4—2444no—
362C2×C4#1451983412yes—
363C2×C4#1451983612yes—
364C2×C4#1451983712yes—
365C2×C4C2×D61⋊C811yescharacteristic
366C2×C4C2×#1175821311yescharacteristic
367C8—4882no—
368C8—2444no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—48816no—
376C22—4882no—
377C22—4882no—
378C22—4882no—
379C22—4882no—
380C22—2444no—
381C22—2444no—
382C22—2444no—
383C22#1684061014yes—
384C22C2×#1451983411yescharacteristic
385C22C2×#1451983611yescharacteristic
386C22C2×#1451983711yescharacteristic
387C22C2×#1451983911yescharacteristic
388C22#1684075411yescharacteristic
389C22C2×#1451984211yescharacteristic
390C22#1684076111yescharacteristic
391C4—21no—
392C4—21no—
393C4—82no—
394C4—1221no—
395C4—1222no—
396C4—1221no—
397C4—1222no—
398C4—2441no—
399C4#1684060614yes—
400C2—24no—
401C2—4884no—
402C2C2×#1684060611yescharacteristic
403C2C2×#1684061011yescharacteristic
404C2#2146112011yescharacteristic
405C2#2146121611yescharacteristic
406C2#2146125611yescharacteristic
407C2#2146128011yescharacteristic
408C2#2146132611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#7572
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461673C2semidirect
2. C4×C22⋊#92420C2semidirect
3. #21460636C2semidirect
9. #16840628C22semidirect
10. #16840628C22semidirect
31. C22×D244C8semidirect
224. C61#7572semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
#214606362
C2×#168396632
#757261