Finite Group Databasebeta

← #29573638

Subgroups — #29573638

Order 15616.

480 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 85 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#21448762C211yesmaximal, characteristic
2C4×#14519691C211yesmaximal, characteristic
3#21444155C211yesmaximal, characteristic
4#21443705C211yesmaximal, characteristic, complemented
5#21443673C211yesmaximal, characteristic, complemented
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1297C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D61C2211yescharacteristic
9C2×#14519691—21no—
10#16839726C2211yescharacteristic
11#16839650—21no—
12#16839646—21no—
13#16839638—21no—
14#16839629C411yescharacteristic, complemented
15#16839625C2211yescharacteristic
16#16839621C411yescharacteristic, complemented
17C4×#11758198—21no—
18C4×C22⋊Dic61C2211yescharacteristic
19#16839607C411yescharacteristic, complemented
20#95×D61C411yescharacteristic, complemented
21#16839528—21no—
22#16839487—21no—
23#16839485—21no—
24C61×#407C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊D61D411yescharacteristic
28C22×C4×D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C2×#11758194—21no—
31C4×C22⋊D61—21no—
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34C4×C22⋊D61—21no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61D411yescharacteristic
40C2×#11758198—21no—
41C2×#11758198D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61C2×C411yescharacteristic
45#14519691—24no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55#14519684C2×C411yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C2×M16×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C42×C61—21no—
61C2×C42×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66#95×C61C2×C411yescharacteristic
67C24×C61C2×D411yescharacteristic
68C23×D61C22⋊C411yescharacteristic
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61—81no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—41no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—41no—
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C2×C4×D61—21no—
90C2×C4×D61—21no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C4×D61—81no—
94C2×C4×D61—81no—
95M16×C61—81no—
96C2×C8×C61—41no—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—42no—
99C22⋊C4×C61—41no—
100C42×C61—81no—
101C42×C61—81no—
102C22⋊Dic61—21no—
103C22⋊Dic61—21no—
104C22⋊Dic61—22no—
105C22⋊Dic61—41no—
106C22⋊Dic61—81no—
107#11758198—21no—
108#11758198—21no—
109#11758198—42no—
110#11758196—21no—
111#11758196—21no—
112#11758196—81no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—42no—
116C4×Dic61—81no—
117#11758194—81no—
118C2×#92418—41no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61C2×C22⋊C411yescharacteristic
124C23×C61#12311yescharacteristic
125C23×C61#12311yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61#10412yes—
131C2×C4×C61—22no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61#11711yescharacteristic
147C2×C4×C61#11711yescharacteristic
148C2×C4×C61#12311yescharacteristic
149C2×C4×C61#12311yescharacteristic
150C22⋊D61—42no—
151C22⋊D61—42no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—42no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—81no—
167C2×Dic61—81no—
168C4×D61—81no—
169C4×D61—81no—
170C4×D61—84no—
171C8×C61—81no—
172#92418—81no—
173#8776—611nomaximal, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—81no—
183C22×C61—81no—
184C22×C61#38111yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C22×C61#42111yescharacteristic
187C2×D61—22no—
188C2×D61—42no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—42no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—42no—
197C4×C61—81no—
198C4×C61—82no—
199Dic61—41no—
200Dic61—41no—
201Dic61—41no—
202Dic61—81no—
203Dic61—81no—
204Dic61—82no—
205#2353—611no—
206C4×#99—611no—
207#1465—611no—
208#1297—611no—
209#1297D6111yescharacteristic, complemented
210#1284—611no—
211#1284—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—41no—
215C2×C61—41no—
216C2×C61#182611yescharacteristic
217C2×C61#182711yescharacteristic
218C2×C61#182811yescharacteristic
219D61—42no—
220C2×C4×D4—611no—
221C2×#99—1221no—
222#407—611no—
223#407C2×D6111yescharacteristic
224#388—1221no—
225#387—1221no—
226#386—1221no—
227#383—611no—
228#381—611no—
229#380—611no—
230C4×C22⋊C4—611no—
231C4×C22⋊C4—1221no—
232C4×C22⋊C4C2×D6111yescharacteristic
233C4×C22⋊C4C2×D6111yescharacteristic
234#376—611no—
235C2×#95—611no—
236#342—1221no—
237#324—1221no—
238#323—1221no—
239C61#877611yescharacteristic, complemented, Sylow
240C22×D4—611no—
241C23×C4—611no—
242C23×C4—1221no—
243C23×C4C22×D6111yescharacteristic
244C2×M16—21no—
245C2×M16—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248C4×D4—1221no—
249C4×D4—1221no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—1221no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—611no—
255C2×C22⋊C4—611no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—611no—
262C2×C42—1221no—
263C2×C42—1221no—
264#99—1224no—
265C22⋊C8—21no—
266C22⋊C8—21no—
267C22⋊C8—1221no—
268C22⋊C8—1221no—
269#95—21no—
270#95—611no—
271#95—611no—
272#95—1221no—
273#95—1221no—
274#95—1221no—
275#95—1221no—
276#95—1221no—
277#95—1221no—
278#95C4×D6111yescharacteristic
279#95C4×D6111yescharacteristic
280C24—611no—
281C24D4×D6111yescharacteristic
282C2×D4—1222no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—2441no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—81no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—4881no—
298C22×C4—4881no—
299C22×C4—2442no—
300C22×C4—2442no—
301C22×C4—2441no—
302C22×C4C2×C4×D6111yescharacteristic
303C22×C4#1175822211yescharacteristic
304C22×C4#1175822211yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4#1175822411yescharacteristic
307C22×C4#1175822611yescharacteristic
308M16—81no—
309M16—4881no—
310C2×C8—41no—
311C2×C8—2441no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—4881no—
315C22⋊C4—22no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1222no—
323C22⋊C4—4881no—
324C22⋊C4—2442no—
325C22⋊C4—2441no—
326C42—81no—
327C42—81no—
328C42—1221no—
329C42—1221no—
330C42—4881no—
331C42—2442no—
332C23—21no—
333C23—21no—
334C23—41no—
335C23—41no—
336C23—612no—
337C23—1221no—
338C23—1221no—
339C23—2441no—
340C23—2441no—
341C23C22⋊C4×D6111yescharacteristic
342C23#1451975911yescharacteristic
343C23#1451976211yescharacteristic
344D4—2442no—
345D4—2442no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—4881no—
367C2×C4—4881no—
368C2×C4—4884no—
369C2×C4—4881no—
370C2×C4—4881no—
371C2×C4—2441no—
372C2×C4—2442no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4—2441no—
377C2×C4—2441no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4#1451973411yescharacteristic
381C2×C4#1451973511yescharacteristic
382C2×C4#1451975911yescharacteristic
383C2×C4#1451976211yescharacteristic
384C8—81no—
385C8—4881no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—81no—
395C22—81no—
396C22—1222no—
397C22—2442no—
398C22—2442no—
399C22—2441no—
400C22—2441no—
401C22#1683962411yescharacteristic
402C22#104×D6111yescharacteristic
403C22#1683977711yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—82no—
411C4—4881no—
412C4—4881no—
413C4—4882no—
414C4—2441no—
415C4—2441no—
416C4—2441no—
417C2—21no—
418C2—21no—
419C2—41no—
420C2—41no—
421C2—2442no—
422C2#2144591711yescharacteristic
423C2#2144592211yescharacteristic
424C2#2144592611yescharacteristic
subgroupG/H
centerC22#16839624
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#8776
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
4. #21443705C2semidirect
5. #21443673C2semidirect
6. #21443672C2semidirect
7. C61×#1297C2semidirect
14. #16839629C4semidirect
16. #16839621C4semidirect
19. #16839607C4semidirect
20. #95×D61C4semidirect
209. #1297D61semidirect
239. C61#8776semidirect

Maximal subgroups

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

subgroupindex
#214487622
C4×#145196912
#214441552
#214437052
#214436732
#214436722
C61×#12972
#877661