Finite Group Databasebeta

← #29590188

Subgroups — #29590188

Order 15616.

552 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 83 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#21449056C211yesmaximal, characteristic
2#21445550C211yesmaximal, characteristic, complemented
3#21444130C211yesmaximal, characteristic, complemented
4#21443819C211yesmaximal, characteristic, complemented
5#21443817C211yesmaximal, characteristic
6#21443815C211yesmaximal, characteristic
7C61×#1344C211yesmaximal, characteristic, complemented
8C2×#14519739C411yescharacteristic, complemented
9C2×#14519737—21no—
10C2×#14519733—21no—
11C2×#14519733C2211yescharacteristic
12#16839812—21no—
13#16839693C411yescharacteristic, complemented
14#16839686—21no—
15#16839680C411yescharacteristic, complemented
16#16839677—21no—
17#16839671C2211yescharacteristic
18#16839613C411yescharacteristic, complemented
19#16839609—21no—
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#397C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61D411yescharacteristic
30C22×C4×D61—21no—
31#14519739—41no—
32#14519739—41no—
33#14519737—42no—
34#14519737—42no—
35#14519733—24no—
36#14519733—41no—
37#14519733—41no—
38#14519733—42no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—41no—
42C2×#11758196C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61D411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61—41no—
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519706—41no—
55C22⋊#92418—21no—
56C8×Dic61—41no—
57#14519684—21no—
58#14519684C2×C411yescharacteristic
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61C2311yescharacteristic
63C22⋊C8×C61—21no—
64#95×C61—21no—
65#95×C61C2×C411yescharacteristic
66C24×C61C2×D411yescharacteristic
67C23×D61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×C22⋊D61—42no—
74C2×C22⋊D61—42no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—22no—
80C22×Dic61—21no—
81C22×Dic61—41no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61D812yes—
87C22×Dic61SD1612yes—
88C2×D244—41no—
89C2×D244—42no—
90C2×C4×D61—41no—
91C2×C4×D61—41no—
92C2×C4×D61—42no—
93C2×C4×D61—42no—
94C2×C8×C61—41no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊Dic61—22no—
102C22⋊Dic61—41no—
103C22⋊Dic61—41no—
104#11758198—42no—
105#11758198—42no—
106#11758198—42no—
107#11758198—42no—
108#11758196—41no—
109#11758196—41no—
110#11758196—42no—
111#11758196—44no—
112#11758196—42no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C4×Dic61—21no—
117C4×Dic61—44no—
118C4×Dic61—42no—
119C2×#92418—41no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61C2×C22⋊C411yescharacteristic
125C23×C61C2×D811yescharacteristic
126C23×C61C2×SD1611yescharacteristic
127C22×D61—22no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61—41no—
133C22×D61—41no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C22⋊D61—44no—
148C22⋊D61—44no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—22no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—22no—
155C2×Dic61—22no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—81no—
164C2×Dic61—81no—
165C2×Dic61#9911yescharacteristic
166C2×Dic61#9911yescharacteristic
167C2×Dic61#10212yes—
168C2×Dic61#10212yes—
169C2×Dic61#10412yes—
170D244—42no—
171D244—42no—
172C4×D61—82no—
173C4×D61—82no—
174C8×C61—81no—
175#92418—81no—
176#11691—611nomaximal, Sylow
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—81no—
186C22×C61C2×#9911yescharacteristic
187C22×C61C2×#10211yescharacteristic
188C22×C61C2×#10411yescharacteristic
189C2×D61—42no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—81no—
193C2×D61—81no—
194C2×D61—81no—
195C2×D61—81no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—81no—
199C4×C61—82no—
200C4×C61—81no—
201Dic61—22no—
202Dic61—42no—
203Dic61—41no—
204Dic61—41no—
205Dic61—82no—
206Dic61#32712yes—
207Dic61#32712yes—
208#2392—611no—
209#1740—611no—
210#1458—611no—
211#1344—611no—
212#1344D6111yescharacteristic, complemented
213#1343—611no—
214#1343—611no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—41no—
218C2×C61—41no—
219C2×C61C2×#32711yescharacteristic
220C2×C61#212011yescharacteristic
221C2×C61#212611yescharacteristic
222D61—82no—
223C2×C4×D4—611no—
224C2×C4×D4—1221no—
225C2×#117—611no—
226C2×#117—1221no—
227#431—1221no—
228#398—611no—
229#397C2×D6111yescharacteristic
230#396—1221no—
231#394—611no—
232#394—1221no—
233#392—611no—
234C4×C4⋊C4—611no—
235C4×C22⋊C4—1221no—
236#342—611no—
237#342—1221no—
238#342C2×D6111yescharacteristic
239#324—1221no—
240#323—611no—
241#323C2×D6111yescharacteristic
242C61#1169111yescharacteristic, complemented, Sylow
243C22×D4—611no—
244C22×D4—1221no—
245C23×C4—611no—
246C23×C4—1221no—
247C4×D4—2441no—
248C4×D4—2441no—
249C4×D4—2442no—
250C4×D4—2442no—
251#117—1224no—
252#117—2441no—
253#117—2441no—
254#117—2442no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—1221no—
258C2×C4⋊C4—1221no—
259C2×C4⋊C4—2441no—
260C2×C4⋊C4C4×D6111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266C2×C22⋊C4—1221no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4C22×D6111yescharacteristic
270C2×C42—611no—
271C2×C42—611no—
272C2×C42—1221no—
273C2×C42—2441no—
274C4⋊C8—2441no—
275C22⋊C8—21no—
276C22⋊C8—1221no—
277C4×C8—2441no—
278#95—21no—
279#95—611no—
280#95—1221no—
281#95C4×D6111yescharacteristic
282C24—1221no—
283C24D4×D6111yescharacteristic
284C2×D4—2441no—
285C2×D4—2442no—
286C2×D4—2442no—
287C2×D4—2442no—
288C2×D4—2441no—
289C2×D4—2441no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—612no—
296C22×C4—612no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1222no—
302C22×C4—1221no—
303C22×C4—2442no—
304C22×C4—2441no—
305C22×C4—2441no—
306C22×C4—2442no—
307C22×C4—2441no—
308C22×C4C2×C4×D6111yescharacteristic
309C22×C4D4×D6111yescharacteristic
310C2×C8—41no—
311C2×C8—2441no—
312C4⋊C4—41no—
313C4⋊C4—2441no—
314C4⋊C4—2441no—
315C4⋊C4—2442no—
316C4⋊C4—2442no—
317C4⋊C4—2444no—
318C22⋊C4—22no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—1222no—
324C22⋊C4—2442no—
325C22⋊C4—2442no—
326C22⋊C4—2442no—
327C22⋊C4—2442no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C42—1221no—
331C42—1221no—
332C42—1221no—
333C42—1221no—
334C42—2442no—
335C42—2444no—
336C23—21no—
337C23—21no—
338C23—41no—
339C23—41no—
340C23—1222no—
341C23—2441no—
342C23—2441no—
343C23—2441no—
344C23—2441no—
345C23—2441no—
346C23—2441no—
347C23C22⋊C4×D6111yescharacteristic
348C23D8×D6111yescharacteristic
349C23SD16×D6111yescharacteristic
350D4—2442no—
351D4—2442no—
352D4—2444no—
353D4—2444no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—611no—
368C2×C4—611no—
369C2×C4—612no—
370C2×C4—612no—
371C2×C4—612no—
372C2×C4—1222no—
373C2×C4—1222no—
374C2×C4—1222no—
375C2×C4—1222no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—1222no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—4882no—
382C2×C4—4882no—
383C2×C4—4881no—
384C2×C4—4881no—
385C2×C4—2442no—
386C2×C4—2441no—
387C2×C4—2441no—
388C2×C4—2441no—
389C2×C4—2441no—
390C8—81no—
391C8—4881no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22—4881no—
402C22—4881no—
403C22—4881no—
404C22—4881no—
405C22—2442no—
406C22—2442no—
407C22—2442no—
408C22#99×D6111yescharacteristic
409C22#102×D6111yescharacteristic
410C22#104×D6111yescharacteristic
411C4—41no—
412C4—41no—
413C4—81no—
414C4—82no—
415C4—81no—
416C4—612no—
417C4—612no—
418C4—1222no—
419C4—4882no—
420C4—2442no—
421C4—2441no—
422C4—2441no—
423C2—21no—
424C2—21no—
425C2—41no—
426C2—41no—
427C2—4882no—
428C2#327×D6111yescharacteristic
429C2#2144745911yescharacteristic
430C2#2144748311yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1344C2
socleC22×C61C2×#99
prime radical#16839671C22
cosocleC2×C22⋊C4×C61C23
hypercenter#1344D61
hypocenterC61#11691
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
2. #21445550C2semidirect
3. #21444130C2semidirect
4. #21443819C2semidirect
7. C61×#1344C2semidirect
8. C2×#14519739C4semidirect
13. #16839693C4semidirect
15. #16839680C4semidirect
18. #16839613C4semidirect
212. #1344D61semidirect
242. C61#11691semidirect

Maximal subgroups

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

subgroupindex
#214490562
#214455502
#214441302
#214438192
#214438172
#214438152
C61×#13442
#1169161