Finite Group Databasebeta

← #30595549

Subgroups — #30595549

Order 15616.

630 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 106 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#21461747C211yesmaximal, characteristic, complemented
2#21461605C211yesmaximal, characteristic, complemented
3#21460636C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5C4×#14519773C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519832—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519773C411yescharacteristic
13C2×C4×D244C411yescharacteristic
14C2×C4×C22⋊D61—21no—
15C2×C4×C22⋊D61—21no—
16#16839665C2211yescharacteristic
17#16839663C2211yescharacteristic
18#16839662—21no—
19#16839662—21no—
20#16839631C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22C2×C4×D4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—24no—
26#14519832—42no—
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30C22×C4×D61—21no—
31#14519773—22no—
32#14519773—22no—
33C4×D244—42no—
34C4×C22⋊D61—44no—
35C4×C22⋊D61—42no—
36C4×C22⋊D61—42no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61C2311yescharacteristic
51C22×D4×C61C2×C411yescharacteristic
52C23×C4×C61—21no—
53C4×D4×C61—42no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C24×C61—21no—
58C23×D61—21no—
59C2×D4×C61—21no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61M1612yes—
63C22×C4×C61—21no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C2×C22⋊D61—24no—
71C2×C22⋊D61—24no—
72C2×C22⋊D61—42no—
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—42no—
76C22×Dic61—21no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C2×D244—21no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244M1612yes—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×#92420—24no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—42no—
96C42×C61—22no—
97C22⋊Dic61—41no—
98C22⋊Dic61—41no—
99C22⋊Dic61—42no—
100#11758198—42no—
101#11758198—41no—
102#11758198—41no—
103#11758198—42no—
104C4⋊Dic61—41no—
105#11758196—42no—
106#11758196—42no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—22no—
110C4×Dic61—22no—
111C4×Dic61—41no—
112C4×Dic61—41no—
113C4×Dic61D812yes—
114C4×Dic61SD1612yes—
115C23×C61—22no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61C2×C22⋊C411yescharacteristic
123C22×D61—22no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130D4×C61—42no—
131D4×C61—42no—
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—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—84no—
142C2×C4×C61#10012yes—
143C2×C4×C61#10212yes—
144C2×C4×C61C2×M1611yescharacteristic
145C2×C4×C61C2×M1611yescharacteristic
146C22⋊D61—48no—
147C22⋊D61—48no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61#10212yes—
160C2×Dic61#10412yes—
161C2×Dic61C2×D811yescharacteristic
162C2×Dic61C2×SD1611yescharacteristic
163C2×Dic61AGL(1,ℤ/8)12yes—
164D244—42no—
165D244—42no—
166C4×D61—84no—
167#92420—44no—
168#92420—82no—
169#7621—611nomaximal, Sylow
170C22×C61—42no—
171C22×C61—42no—
172C22×C61—42no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61#40711yescharacteristic
178C22×C61#41011yescharacteristic
179C22×C61C2×#10011yescharacteristic
180C22×C61C2×#10211yescharacteristic
181C22×C61#41811yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C22×C61#42111yescharacteristic
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C4×C61—22no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—22no—
195C4×C61—81no—
196Dic61—22no—
197Dic61—22no—
198Dic61—21no—
199Dic61—21no—
200Dic61—22no—
201Dic61—81no—
202C4×#127—611no—
203#1839—611no—
204#1767—611no—
205#1270—612no—
206#1270—612no—
207C2×C61—82no—
208C2×C61#146611yescharacteristic
209C2×C61#148611yescharacteristic
210C2×C61#149011yescharacteristic
211C2×C61#150211yescharacteristic
212C2×C61#151411yescharacteristic
213C2×C61#153011yescharacteristic
214C2×C61#154511yescharacteristic
215D61—82no—
216C2×#127—611no—
217C2×C4×D4—611no—
218C2×C4×D4—1221no—
219C2×C4×D4—1221no—
220C2×C4×D4#692311yescharacteristic
221C2×C4⋊C8—1221no—
222C2×#97—1221no—
223#390—611no—
224#390—611no—
225#390—1221no—
226#390—1221no—
227#384—611no—
228C43—611no—
229#336—612no—
230#336—612no—
231#336—1221no—
232#336—1221no—
233C61#762111yescharacteristic, complemented, Sylow
234C22×D4—611no—
235C22×D4—1221no—
236C22×D4—1221no—
237C22×D4C2×#692311yescharacteristic
238C23×C4—21no—
239C23×C4—1221no—
240C22×C8—1222no—
241C22×C8—1222no—
242#127—1222no—
243#127—1222no—
244C4×D4—42no—
245C4×D4—2442no—
246C4×D4—2442no—
247C4×D4—2442no—
248C4×D4—2444no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4C2×#692311yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C42—611no—
260C2×C42—611no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—611no—
265C2×C42C2×#692311yescharacteristic
266C4⋊C8—1224no—
267#97—2442no—
268C24—21no—
269C24—1221no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—612no—
274C2×D4—1224no—
275C2×D4—1224no—
276C2×D4—1221no—
277C2×D4—2441no—
278C2×D4—2441no—
279C2×D4—2442no—
280C2×D4—2442no—
281C2×D4—2442no—
282C2×D4—2442no—
283C2×D4#1175821312yes—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—1221no—
293C22×C4—2442no—
294C22×C4—2442no—
295C22×C4—2442no—
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22⋊#692311yescharacteristic
298C22×C4C22×#692311yescharacteristic
299C2×C8—1224no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8—2442no—
304C2×C8—2442no—
305C4⋊C4—41no—
306C4⋊C4—2441no—
307C4⋊C4—2442no—
308C4⋊C4—2442no—
309C22⋊C4—42no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2442no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2442no—
316C22⋊C4—2442no—
317C42—22no—
318C42—612no—
319C42—612no—
320C42—1222no—
321C42—1222no—
322C42—1221no—
323C42—1221no—
324C42—2441no—
325C42—2441no—
326C23—22no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—1222no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23C2×C22⋊#692311yescharacteristic
341D4—42no—
342D4—42no—
343D4—2442no—
344D4—2442no—
345D4—2448no—
346D4—2448no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—84no—
357C2×C4—612no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—612no—
361C2×C4—612no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—4884no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4#1451983712yes—
375C2×C4#1451983912yes—
376C2×C4D61⋊M1611yescharacteristic
377C2×C4C2×#1175821311yescharacteristic
378C8—4882no—
379C8—2444no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—4881no—
388C22—4881no—
389C22—4881no—
390C22—4881no—
391C22—2442no—
392C22—2442no—
393C22—2442no—
394C22#1684073311yescharacteristic
395C22#1684074111yescharacteristic
396C22C2×#1451983711yescharacteristic
397C22C2×#1451983911yescharacteristic
398C22#1684075411yescharacteristic
399C22D61⋊#10411yescharacteristic
400C22#1684075911yescharacteristic
401C4—22no—
402C4—22no—
403C4—21no—
404C4—21no—
405C4—81no—
406C4—1222no—
407C4—1222no—
408C4—1221no—
409C4—1221no—
410C4—1222no—
411C4—4881no—
412C2—82no—
413C2—4882no—
414C2#2146107811yescharacteristic
415C2#2146114511yescharacteristic
416C2#2146115911yescharacteristic
417C2#2146119811yescharacteristic
418C2#2146123811yescharacteristic
419C2#2146128811yescharacteristic
420C2#2146132611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7621
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461747C2semidirect
2. #21461605C2semidirect
3. #21460636C2semidirect
4. #21460635C2semidirect
233. C61#7621semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214616052
#214606362
#214606352
C4×#145197732
#762161