Finite Group Databasebeta

← #30595530

Subgroups — #30595530

Order 15616.

634 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 110 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#21461675C211yesmaximal, characteristic, complemented
2#21461482C211yesmaximal, characteristic, complemented
3#21460637C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#121×Dic61C211yesmaximal, characteristic
6C22×#11758217—21no—
7C2×#14519844—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×D4×Dic61—21no—
13C2×D4×Dic61C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839665C2211yescharacteristic
16#16839661C2211yescharacteristic
17#16839655—21no—
18#16839642—21no—
19#16839622C411yescharacteristic
20C4⋊C4×Dic61C411yescharacteristic
21C22⋊C4×Dic61—21no—
22C2×#121×C61C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—42no—
25C2×#11758217—42no—
26C22×#92420—22no—
27C22×#92420—22no—
28#14519844—42no—
29C22⋊#92420—42no—
30C23×Dic61—21no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33D4×Dic61—42no—
34D4×Dic61—42no—
35D4×Dic61—42no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×D4×C61—21no—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61C2×C411yescharacteristic
55#121×C61—22no—
56#121×C61—22no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C24×C61—21no—
60C24×C61C22⋊C411yescharacteristic
61C2×D4×C61—24no—
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C2×D4×C61—42no—
66C2×D4×C61—42no—
67C2×D4×C61M1612yescomplemented
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×Dic61—22no—
76C22×Dic61—22no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—42no—
84C22×Dic61—42no—
85C22×Dic61—42no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61D812yes—
89C22×Dic61SD1612yes—
90C22×Dic61C2×D411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92#11758217—48no—
93C2×#92420—24no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C2×#92420—42no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61M1612yescomplemented
101C22⋊C4×C61—24no—
102C22⋊Dic61—42no—
103C22⋊Dic61—42no—
104C22⋊Dic61—41no—
105C22⋊Dic61—41no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112C4×Dic61—22no—
113C4×Dic61—22no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C4×Dic61—42no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—22no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61#10212yes—
131C23×C61C2×C22⋊C411yescharacteristic
132D4×C61—42no—
133D4×C61—42no—
134D4×C61—48no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—22no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61C2×M1611yescharacteristic
146C2×C4×C61C2×M1611yescharacteristic
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—24no—
152C2×Dic61—24no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—84no—
165C2×Dic61#9912yes—
166C2×Dic61#10212yes—
167C2×Dic61#10412yes—
168C2×Dic61C2×D811yescharacteristic
169C2×Dic61C2×SD1611yescharacteristic
170C2×Dic61AGL(1,ℤ/8)11yescharacteristic
171C2×Dic61#13711yescharacteristic
172#92420—44no—
173#92420—82no—
174#7616—611nomaximal, Sylow
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—42no—
183C22×C61—42no—
184C22×C61—42no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61#40711yescharacteristic
190C22×C61C2×#9911yescharacteristic
191C22×C61#41311yescharacteristic
192C22×C61C2×#10211yescharacteristic
193C22×C61#41711yescharacteristic
194C22×C61C2×#10411yescharacteristic
195C22×C61#42111yescharacteristic
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—41no—
199C4×C61—42no—
200Dic61—21no—
201Dic61—21no—
202Dic61—21no—
203Dic61—21no—
204Dic61—41no—
205Dic61—81no—
206Dic61—81no—
207Dic61#32714yes—
208C4×#121—611no—
209#1797—611no—
210#1728—611no—
211#1271—612no—
212#1270—612no—
213C2×C61—42no—
214C2×C61—82no—
215C2×C61#146511yescharacteristic
216C2×C61#148611yescharacteristic
217C2×C61#148911yescharacteristic
218C2×C61C2×#32711yescharacteristic
219C2×C61#151311yescharacteristic
220C2×C61#152911yescharacteristic
221C2×C61#154711yescharacteristic
222C22×M16—1221no—
223C2×#121#692311yescharacteristic
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—611no—
235C4×C22⋊C4—1221no—
236#336—612no—
237#336—612no—
238#336—1221no—
239C61#761611yescharacteristic, complemented, Sylow
240C22×D4—21no—
241C22×D4C2×#692311yescharacteristic
242C23×C4—611no—
243C23×C4—611no—
244C23×C4—1221no—
245C23×C4C2×#692311yescharacteristic
246C2×M16—1224no—
247C2×M16—2442no—
248C2×M16—2442no—
249C22×C8—1222no—
250C22×C8—1222no—
251#121—22no—
252#121—22no—
253C4×D4—2442no—
254C4×D4—2442no—
255C4×D4—2442no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4C2×#692311yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C42—611no—
266C2×C42—611no—
267C2×C42—611no—
268C2×C42—611no—
269C2×C42—1221no—
270C2×C42—2442no—
271C4⋊C8—2442no—
272C22⋊C8—2442no—
273#95—1221no—
274#95—1221no—
275#95—1221no—
276C24—21no—
277C24C22⋊#692311yescharacteristic
278C2×D4—24no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4#1175821712yescomplemented
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—611no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—1222no—
297C22×C4—1222no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1221no—
302C22×C4—2442no—
303C22×C4—2442no—
304C22×C4—2442no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4C22⋊#692311yescharacteristic
308C22×C4C22×#692311yescharacteristic
309M16—2448no—
310C2×C8—1224no—
311C2×C8—2442no—
312C2×C8—2442no—
313C2×C8—2442no—
314C2×C8—2442no—
315C2×C8—2442no—
316C4⋊C4—21no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4#1175821712yescomplemented
322C22⋊C4—24no—
323C22⋊C4—2441no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C22⋊C4—2441no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C42—1222no—
330C42—1222no—
331C42—2441no—
332C42—2441no—
333C42—2442no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—22no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#1451983912yes—
348C23C2×C22⋊#692311yescharacteristic
349D4—42no—
350D4—42no—
351D4—48no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—612no—
363C2×C4—612no—
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—1221no—
378C2×C4—4884no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4C2×#1175821711yescharacteristic
388C2×C4C2×#1175821711yescharacteristic
389C8—4882no—
390C8—2444no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—42no—
399C22—42no—
400C22—42no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22#1684073211yescharacteristic
406C22D61⋊#9911yescharacteristic
407C22#1684074911yescharacteristic
408C22C2×#1451983911yescharacteristic
409C22#1684075311yescharacteristic
410C22D61⋊#10411yescharacteristic
411C22#1684076011yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—42no—
416C4—614no—
417C4—1221no—
418C4—1221no—
419C4—1221no—
420C4—1221no—
421C4—4881no—
422C4—4881no—
423C4—2441no—
424C2—42no—
425C2—82no—
426C2#2146107511yescharacteristic
427C2#2146114411yescharacteristic
428C2#2146115411yescharacteristic
429C2D61⋊#32711yescharacteristic
430C2#2146123511yescharacteristic
431C2#2146128511yescharacteristic
432C2#2146133111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#121×C61C4
socleC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#121#6923
hypocenterC61#7616
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461675C2semidirect
2. #21461482C2semidirect
3. #21460637C2semidirect
4. #21460635C2semidirect
67. C2×D4×C61M16semidirect
100. C4⋊C4×C61M16semidirect
239. C61#7616semidirect
284. C2×D4#11758217semidirect
321. C4⋊C4#11758217semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214614822
#214606372
#214606352
#121×Dic612
#761661