Finite Group Databasebeta

← #30605184

Subgroups — #30605184

Order 15616.

626 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 70 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#21461679C211yesmaximal, characteristic, complemented
2#21461078C211yesmaximal, characteristic, complemented
3#21460814C212yesmaximal, complemented
4#21460797C212yesmaximal, complemented
5#21449032C211yesmaximal, characteristic
6#16840783—21no—
7C2×#14519835—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840606C2212yes—
11#16840605—21no—
12C2×C4×C22⋊D61—21no—
13C2×C4×C22⋊D61C2211yescharacteristic
14#16839681C411yescharacteristic, complemented
15#16839676—21no—
16#16839676C411yescharacteristic, complemented
17#16839673C2211yescharacteristic
18#16839670—21no—
19#16839670C2211yescharacteristic
20C4×C22⋊Dic61—21no—
21C4×C22⋊Dic61C411yescharacteristic, complemented
22C22×#41×C61C411yescharacteristic, complemented
23C2×C4⋊#6923—41no—
24C2×C22⋊#6923—22no—
25C4⋊#92420—41no—
26#14519835—42no—
27C22⋊#92420—22no—
28#14519832—41no—
29(C2×#6923)⋊C4—41no—
30C22×C22⋊D61—21no—
31C22×C22⋊D61D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C4×C22⋊D61—41no—
34C4×C22⋊D61—41no—
35C4×C22⋊D61—44no—
36C2×#11758196—21no—
37C2×#11758196C2×C411yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44C2×#11758198C2311yescharacteristic
45C2×C4×Dic61—21no—
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C2×#41×C61—44no—
52C2×#41×C61—41no—
53C2×#41×C61—41no—
54C22×Q8×C61C2×C411yescharacteristic
55C22×D4×C61—21no—
56C22×D4×C61C2×C411yescharacteristic
57C23×C4×C61—21no—
58C23×C4×C61C2×C411yescharacteristic
59C24×C61—21no—
60C24×C61C22⋊C411yescharacteristic
61C23×D61C2×D411yescharacteristic
62C22×#6923—42no—
63#41×C61—44no—
64#41×C61—44no—
65#41×C61—44no—
66#41×C61—44no—
67C2×Q8×C61—42no—
68C2×Q8×C61—41no—
69C2×D4×C61—42no—
70C2×D4×C61—41no—
71C2×D4×C61—42no—
72C2×D4×C61—42no—
73C2×D4×C61—42no—
74C22×C4×C61—24no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—42no—
79C22×C4×C61—42no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22×C411yescharacteristic
84C2×C22⋊D61—21no—
85C2×C22⋊D61—21no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—42no—
89C2×C22⋊D61—42no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C2×D411yescharacteristic
97C2×C4×D61—21no—
98C2×C4×D61—21no—
99C2×C4×D61—42no—
100C22⋊#6923—42no—
101C22⋊#6923—42no—
102C2×#92420—42no—
103C4⋊#6923—82no—
104C22⋊Dic61—41no—
105C22⋊Dic61—42no—
106C22⋊Dic61—42no—
107C22⋊Dic61—42no—
108C22⋊Dic61—42no—
109#11758198—41no—
110#11758198—42no—
111#11758196—41no—
112#11758196—42no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—42no—
116C23×C61—22no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61C2×C22⋊C411yescharacteristic
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61AGL(1,ℤ/8)11yescharacteristic
134C22×D61#13711yescharacteristic
135C2×#6923—82no—
136C2×#6923—82no—
137C2×#6923—82no—
138Q8×C61—42no—
139Q8×C61—42no—
140D4×C61—42no—
141D4×C61—48no—
142D4×C61—42no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
145C2×C4×C61—21no—
146C2×C4×C61—44no—
147C2×C4×C61—42no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—44no—
151C2×C4×C61—42no—
152C2×C4×C61—41no—
153C2×C4×C61#9911yescharacteristic
154C2×C4×C61#9911yescharacteristic
155C22⋊D61—42no—
156C22⋊D61—42no—
157C22⋊D61—44no—
158C22⋊D61—44no—
159C2×Dic61—22no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C4×D61—42no—
173C4×D61—81no—
174#92420—82no—
175#11820—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—42no—
179C22×C61—42no—
180C22×C61—41no—
181C22×C61—42no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—81no—
185C22×C61—81no—
186C22×C61—81no—
187C22×C61—81no—
188C22×C61—81no—
189C22×C61—81no—
190C22×C61C2×#9911yescharacteristic
191C22×C61#41711yescharacteristic
192C22×C61#42111yescharacteristic
193C2×D61—21no—
194C2×D61—21no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—81no—
200#6923—162no—
201C4×C61—21no—
202C4×C61—42no—
203C4×C61—41no—
204C4×C61AΣL(1,𝔽16)12yes—
205Dic61—42no—
206Dic61—41no—
207Dic61—41no—
208Dic61—41no—
209Dic61—81no—
210#2388—611no—
211#1799—611no—
212#1466—611no—
213#1351—612no—
214#1343—612no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—81no—
218C2×C61—82no—
219C2×C61#151311yescharacteristic
220C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
221C2×C61#212611yescharacteristic
222D61—41no—
223D61—41no—
224C22×#41#692311yescharacteristic, complemented
225C2×C4×D4—611no—
226C2×C4×D4—1221no—
227#432—1221no—
228C2×#99—1221no—
229#395—611no—
230#394—611no—
231#394—1221no—
232#393—611no—
233#392—611no—
234#392—1221no—
235#380—1221no—
236C4×C22⋊C4—611no—
237C4×C22⋊C4—1221no—
238#342—612no—
239#323—612no—
240#323—1221no—
241C61#1182011yescharacteristic, complemented, Sylow
242C2×#41—44no—
243C2×#41—41no—
244C2×#41—41no—
245C22×Q8C2×#692311yescharacteristic
246C22×D4—21no—
247C22×D4—611no—
248C22×D4—1221no—
249C22×D4C2×#692311yescharacteristic
250C23×C4—21no—
251C23×C4—611no—
252C23×C4C2×#692311yescharacteristic
253C4×D4—2441no—
254C4×D4—2441no—
255C4×D4—2444no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—2441no—
259C2×C22⋊C4—611no—
260C2×C22⋊C4—611no—
261C2×C22⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C22⋊C4—1221no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1222no—
267C2×C42—611no—
268C2×C42—1221no—
269C4⋊C8—2441no—
270#99—2442no—
271C22⋊C8—1222no—
272#97—2441no—
273#95—611no—
274#95—611no—
275#95—1221no—
276#95—1221no—
277#95—2441no—
278C24—21no—
279C24—611no—
280C24C22⋊#692311yescharacteristic
281#41—44no—
282#41—44no—
283#41—44no—
284#41—44no—
285C2×Q8—42no—
286C2×Q8—41no—
287C2×D4—41no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2442no—
297C2×D4—2442no—
298C2×D4—2441no—
299C2×D4—2441no—
300C22×C4—24no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—2442no—
316C22×C4—2442no—
317C22×C4C22⋊#692311yescharacteristic
318C22×C4C22×#692311yescharacteristic
319C2×C8—2442no—
320C4⋊C4—4882no—
321C4⋊C4—2441no—
322C4⋊C4—2442no—
323C22⋊C4—2441no—
324C22⋊C4—2442no—
325C22⋊C4—2441no—
326C22⋊C4—2442no—
327C22⋊C4—2442no—
328C22⋊C4—2442no—
329C22⋊C4—2442no—
330C22⋊C4—2442no—
331C22⋊C4—2442no—
332C42—1221no—
333C42—1221no—
334C42—2442no—
335C23—22no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—611no—
348C23—611no—
349C23—1221no—
350C23—1221no—
351C23—2441no—
352C23—2441no—
353C23C2×C22⋊#692311yescharacteristic
354Q8—42no—
355Q8—42no—
356D4—42no—
357D4—48no—
358D4—42no—
359D4—2442no—
360D4—2442no—
361D4—2444no—
362D4—2444no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—1222no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1221no—
379C2×C4—4881no—
380C2×C4—4882no—
381C2×C4—4882no—
382C2×C4—4882no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2442no—
389C2×C4—2441no—
390C2×C4—2441no—
391C2×C4#1451983511yescharacteristic
392C2×C4#1451983511yescharacteristic
393C8—4882no—
394C22—21no—
395C22—21no—
396C22—42no—
397C22—42no—
398C22—41no—
399C22—42no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—1221no—
409C22—1221no—
410C22—4881no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22C2×#1451983511yescharacteristic
416C22#1684075311yescharacteristic
417C22#1684075911yescharacteristic
418C4—21no—
419C4—42no—
420C4—41no—
421C4—9762no—
422C4—4881no—
423C4—2442no—
424C4—2441no—
425C4—2441no—
426C4—2441no—
427C4#1684066212yes—
428C2—21no—
429C2—21no—
430C2—82no—
431C2—81no—
432C2—2441no—
433C2—2441no—
434C2#2146123411yescharacteristic
435C2C2×#1684066211yescharacteristic
436C2#2146209011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×#41×C61C4
socleC22×C61C2×#99
prime radical#21449032C2
cosocleC2×#11758198C23
hypercenterC22×#41#6923
hypocenterC61#11820
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. #21461679C2semidirect
2. #21461078C2semidirect
3. #21460814C2semidirect
4. #21460797C2semidirect
14. #16839681C4semidirect
16. #16839676C4semidirect
21. C4×C22⋊Dic61C4semidirect
22. C22×#41×C61C4semidirect
224. C22×#41#6923semidirect
241. C61#11820semidirect

Maximal subgroups

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

subgroupindex
#214616792
#214610782
#214608142
#214607972
#214490322
#1182061