Finite Group Databasebeta

← #29591038

Subgroups — #29591038

Order 15616.

536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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#21450716C211yesmaximal, characteristic
2#21445807C211yesmaximal, characteristic, complemented
3#21443820C212yesmaximal, complemented
4#21443817C212yesmaximal, complemented
5C61×#1459C211yesmaximal, characteristic, complemented
6C2×#14519748—21no—
7C2×C4×D244C411yescharacteristic, complemented
8C2×#14519692—21no—
9#16839687C411yescharacteristic, complemented
10#16839687C2211yescharacteristic
11#16839671C411yescharacteristic, complemented
12#16839671C2211yescharacteristic
13#16839641—21no—
14#16839641—21no—
15#16839628C411yescharacteristic, complemented
16#16839622—21no—
17#16839619—21no—
18#16839529C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#324—21no—
22C61×#323C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C22×C22⋊D61—21no—
26C22×C4×D61—21no—
27#14519748—42no—
28#14519748—42no—
29C4×D244—41no—
30C4×D244—41no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—41no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—22no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40#14519692—42no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—41no—
45#14519684C2×C411yescharacteristic
46#14519684C2×C411yescharacteristic
47C22×D4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C22×C8×C61—41no—
51C4×D4×C61—41no—
52C4×D4×C61—41no—
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61C2311yescharacteristic
56C2×C42×C61C2×C411yescharacteristic
57C22⋊C8×C61—22no—
58C22⋊C8×C61—41no—
59C24×C61C22⋊C411yescharacteristic
60C24×C61C2×D411yescharacteristic
61C23×D61—21no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61D812yes—
65C2×D4×C61SD1612yes—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—81no—
71C22×C4×C61—81no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—81no—
83C2×C22⋊D61—81no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—42no—
88C2×D244—41no—
89C2×D244—42no—
90C2×C4×D61—42no—
91C2×C4×D61—42no—
92C2×C4×D61—42no—
93C2×C8×C61—42no—
94C2×C8×C61—82no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C42×C61—21no—
99C42×C61—21no—
100C22⋊Dic61—42no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103C22⋊Dic61—42no—
104C22⋊Dic61—42no—
105#11758198—41no—
106#11758198—41no—
107#11758198—81no—
108#11758198—81no—
109C4⋊Dic61—42no—
110C4⋊Dic61—41no—
111C4⋊Dic61—82no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61#10212yes—
121C23×C61C2×C22⋊C411yescharacteristic
122C23×C61C2×D811yescharacteristic
123C23×C61C2×SD1611yescharacteristic
124C22×D61—22no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131D4×C61—42no—
132D4×C61—42no—
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—42no—
140C2×C4×C61—42no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61#9911yescharacteristic
147C2×C4×C61#9911yescharacteristic
148C2×C4×C61#10212yes—
149C22⋊D61—84no—
150C22⋊D61—82no—
151C22⋊D61—82no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—82no—
162C2×Dic61—82no—
163C2×Dic61—82no—
164D244—42no—
165D244—42no—
166C4×D61—84no—
167C8×C61—82no—
168#11875—611nomaximal, Sylow
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—22no—
173C22×C61—21no—
174C22×C61—42no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—81no—
182C22×C61—81no—
183C22×C61C2×#9911yescharacteristic
184C22×C61C2×#10211yescharacteristic
185C22×C61#42111yescharacteristic
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—42no—
189C2×D61—81no—
190C2×D61—81no—
191C2×D61—81no—
192C2×D61—81no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—22no—
196C4×C61—41no—
197C4×C61—41no—
198C4×C61—41no—
199Dic61—81no—
200Dic61—81no—
201Dic61—81no—
202Dic61—162no—
203#2535—611no—
204#1799—611no—
205#1459D6111yescharacteristic, complemented
206#1344—612no—
207#1343—612no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61—41no—
211C2×C61—42no—
212C2×C61—41no—
213C2×C61#151911yescharacteristic
214C2×C61#212011yescharacteristic
215C2×C61#212711yescharacteristic
216D61—82no—
217C2×#121—1221no—
218C2×C4×D4—611no—
219C2×C4×D4C2×D6111yescharacteristic
220C2×#99—1221no—
221C2×C22⋊C8—21no—
222#397—611no—
223#397—611no—
224#392—611no—
225#392—611no—
226#386—1221no—
227#386—1221no—
228#382—611no—
229#380—1221no—
230#380—1221no—
231#342—612no—
232#324—21no—
233#323C2×D6112yes—
234C61#1187511yescharacteristic, complemented, Sylow
235C22×D4—611no—
236C22×D4—1221no—
237C22×D4—1221no—
238C22×D4D24411yescharacteristic
239C23×C4—1221no—
240C23×C4D24411yescharacteristic
241C23×C4C22⋊D6111yescharacteristic
242C22×C8—41no—
243#121—2442no—
244#121—2442no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—2441no—
248C4×D4—2441no—
249C2×C4⋊C4—611no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—2441no—
252C2×C4⋊C4C22⋊D6111yescharacteristic
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1222no—
259C2×C22⋊C4C4×D6111yescharacteristic
260C2×C22⋊C4C22×D6111yescharacteristic
261C2×C42C4×D6111yescharacteristic
262#99—2442no—
263C22⋊C8—22no—
264C22⋊C8—41no—
265#95—611no—
266#95—611no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270#95—2441no—
271C24—1221no—
272C24#1175819811yescharacteristic
273C24C2×D24411yescharacteristic
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—4881no—
277C2×D4—4881no—
278C2×D4—2441no—
279C2×D4—2442no—
280C2×D4—2442no—
281C2×D4—2442no—
282C2×D4—2442no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4#1175819012yes—
286C2×D4D48812yes—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—81no—
292C22×C4—81no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—2442no—
297C22×C4—2442no—
298C22×C4—2442no—
299C22×C4—2442no—
300C22×C4#1175819811yescharacteristic
301C22×C4#1175819811yescharacteristic
302C22×C4#1175819811yescharacteristic
303C22×C4C2×C4×D6111yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305C2×C8—42no—
306C2×C8—82no—
307C4⋊C4—41no—
308C4⋊C4—4882no—
309C4⋊C4—2441no—
310C4⋊C4—2442no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—4881no—
314C22⋊C4—4881no—
315C22⋊C4—2442no—
316C22⋊C4—2442no—
317C22⋊C4—2442no—
318C22⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2441no—
322C42—21no—
323C42—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—1222no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23#1451969912yes—
340C23C2×#1175819811yescharacteristic
341C23C2×D48811yescharacteristic
342C23C2×#1175819011yescharacteristic
343D4—42no—
344D4—42no—
345D4—4884no—
346D4—4882no—
347D4—4882no—
348D4—2442no—
349D4—2442no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—4884no—
364C2×C4—4882no—
365C2×C4—4882no—
366C2×C4—4882no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2441no—
376C2×C4#1451969111yescharacteristic
377C2×C4#1451969111yescharacteristic
378C2×C4#1451969912yes—
379C8—82no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—42no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—81no—
394C22—4881no—
395C22—4881no—
396C22—4881no—
397C22—4881no—
398C22—2442no—
399C22—2442no—
400C22—2442no—
401C22C2×#1451969111yescharacteristic
402C22C2×#1451969911yescharacteristic
403C22#1683977811yescharacteristic
404C4—22no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—9762no—
411C4—4881no—
412C4—4881no—
413C4—4881no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—42no—
418C2—41no—
419C2—4882no—
420C2#2144438811yescharacteristic
421C2#2144746111yescharacteristic
422C2#2144748611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1459C2
socleC22×C61C2×#99
prime radical#21450716C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1459D61
hypocenterC61#11875
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #21445807C2semidirect
3. #21443820C2semidirect
4. #21443817C2semidirect
5. C61×#1459C2semidirect
7. C2×C4×D244C4semidirect
9. #16839687C4semidirect
11. #16839671C4semidirect
15. #16839628C4semidirect
205. #1459D61semidirect
234. C61#11875semidirect

Maximal subgroups

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

subgroupindex
#214507162
#214458072
#214438202
#214438172
C61×#14592
#1187561