Finite Group Databasebeta

← #29589619

Subgroups — #29589619

Order 15616.

534 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 71 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#21450712C211yesmaximal, characteristic
2#21444158C211yesmaximal, characteristic, complemented
3#21444134C211yesmaximal, characteristic, complemented
4#21443748C211yesmaximal, characteristic, complemented
5#21443748C211yesmaximal, characteristic, complemented
6#21443747C211yesmaximal, characteristic, complemented
7C61×#1316C211yesmaximal, characteristic, complemented
8C2×#14519761C411yescharacteristic
9C2×#14519746C411yescharacteristic
10C2×#14519737C2211yescharacteristic
11C22×C22⋊Dic61C411yescharacteristic
12#16839816—21no—
13C22⋊C8×D61—21no—
14#16839685—21no—
15#16839677—21no—
16#16839655—21no—
17#16839638—21no—
18#16839623C2211yescharacteristic
19#16839620C411yescharacteristic
20#16839487—21no—
21#16839486C2211yescharacteristic
22#16839486C2211yescharacteristic
23#16839485—21no—
24C61×#379C2211yescharacteristic
25C61×#323C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C22×C22⋊D61—21no—
28C22×C22⋊D61C2×C411yescharacteristic
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C22×C4×D61D411yescharacteristic
32C2×C8×D61—41no—
33#14519761—42no—
34#14519746—42no—
35#14519737—41no—
36#14519737—41no—
37C2×C4⋊Dic61—21no—
38C2×#11758196—21no—
39C2×#11758196D411yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—41no—
44C2×C22⋊Dic61—41no—
45C2×C22⋊Dic61C2×C411yescharacteristic
46C2×#11758198—21no—
47C2×#11758198D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519706—41no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519689—41no—
53#14519687—41no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C25×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61C2311yescharacteristic
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C24×C61—21no—
65C24×C61—21no—
66C24×C61—21no—
67C24×C61—42no—
68C24×C61—41no—
69C24×C61—41no—
70C24×C61—81no—
71C24×C61C22×C411yescharacteristic
72C23×D61C22⋊C411yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C2×C22⋊D61—81no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—81no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C22⋊C411yescharacteristic
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—81no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—42no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—81no—
104C22⋊Dic61—42no—
105C22⋊Dic61—42no—
106C22⋊Dic61—41no—
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109#11758198—41no—
110#11758198—42no—
111C4⋊Dic61—42no—
112#11758196—41no—
113#11758196—81no—
114C4×Dic61—21no—
115C4×Dic61—21no—
116C2×#92418—41no—
117C2×#92418—41no—
118C8×D61—82no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—22no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61—41no—
127C23×C61—42no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—42no—
132C23×C61—81no—
133C23×C61—81no—
134C23×C61—84no—
135C23×C61—82no—
136C23×C61—82no—
137C23×C61—81no—
138C23×C61—81no—
139C23×C61C2×C22⋊C411yescharacteristic
140C23×C61#13111yescharacteristic
141C23×C61#13111yescharacteristic
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—41no—
145C22×D61—41no—
146C22×D61#10012yes—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C22⋊D61—42no—
155C22⋊D61—42no—
156C22⋊D61—84no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171C2×Dic61—81no—
172C2×Dic61—81no—
173C2×Dic61#9911yescharacteristic
174C2×Dic61#9911yescharacteristic
175C4×D61—42no—
176C4×D61—81no—
177C8×C61—81no—
178C8×C61—81no—
179#92418—81no—
180#92418—81no—
181#11560—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—42no—
189C22×C61—42no—
190C22×C61—42no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—42no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—82no—
197C22×C61—82no—
198C22×C61—82no—
199C22×C61—82no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61#40811yescharacteristic
203C22×C61C2×#9911yescharacteristic
204C22×C61C2×#10011yescharacteristic
205C2×D61—22no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—42no—
209C2×D61—81no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61—81no—
213Dic61—21no—
214Dic61—21no—
215Dic61—41no—
216Dic61—41no—
217Dic61—81no—
218Dic61—81no—
219#2534—611no—
220#1466—611no—
221#1459—611no—
222#1317—611no—
223#1317—611no—
224#1316—611no—
225#1316D6111yescharacteristic, complemented
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—41no—
229C2×C61—41no—
230C2×C61—82no—
231C2×C61#147111yescharacteristic
232C2×C61#212011yescharacteristic
233C2×C61#212111yescharacteristic
234D61—42no—
235C2×#123—611no—
236C2×#120—611no—
237C2×C4×D4—611no—
238C22×C22⋊C4—611no—
239#432—1221no—
240C2×C22⋊C8—1221no—
241#396—1221no—
242#394—1221no—
243#388—1221no—
244#386—1221no—
245#381—611no—
246#380—611no—
247#379C2×D6111yescharacteristic
248#324—1221no—
249#323—611no—
250#323—611no—
251#323—1221no—
252#323C2×D6111yescharacteristic
253#323C2×D6111yescharacteristic
254C61#1156011yescharacteristic, complemented, Sylow
255C25C4×D6111yescharacteristic
256C22×D4—611no—
257C22×D4—1221no—
258C23×C4—611no—
259C23×C4—611no—
260C23×C4—611no—
261C22×C8—2441no—
262#123—2442no—
263#120—2442no—
264C4×D4—2441no—
265C4×D4—2441no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—1221no—
268C2×C4⋊C4—1221no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C22⋊C4—1221no—
276C2×C22⋊C4—1221no—
277C2×C22⋊C4—2441no—
278C2×C22⋊C4—2441no—
279C2×C22⋊C4C4×D6111yescharacteristic
280C2×C22⋊C4C22×D6111yescharacteristic
281C2×C42—611no—
282C4⋊C8—2441no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—1221no—
286C22⋊C8—1221no—
287C22⋊C8—2441no—
288#97—2441no—
289#95—1221no—
290#95—1221no—
291#95—1221no—
292C24—21no—
293C24—21no—
294C24—21no—
295C24—41no—
296C24—42no—
297C24—41no—
298C24—81no—
299C24—611no—
300C24C2×C4×D6111yescharacteristic
301C2×D4—1222no—
302C2×D4—1221no—
303C2×D4—1221no—
304C2×D4—4881no—
305C2×D4—2441no—
306C2×D4—2442no—
307C2×D4—2442no—
308C22×C4—21no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—1221no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1221no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4—1221no—
320C22×C4—4881no—
321C22×C4—4881no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4D4×D6111yescharacteristic
325C22×C4D4×D6111yescharacteristic
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—4882no—
329C2×C8—2441no—
330C2×C8—2441no—
331C4⋊C4—4881no—
332C4⋊C4—2441no—
333C4⋊C4—2442no—
334C22⋊C4—41no—
335C22⋊C4—42no—
336C22⋊C4—41no—
337C22⋊C4—81no—
338C22⋊C4—2441no—
339C22⋊C4—2442no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2442no—
343C22⋊C4—2442no—
344C22⋊C4—2441no—
345C42—1221no—
346C42—1221no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—42no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—81no—
361C23—81no—
362C23—82no—
363C23—82no—
364C23—84no—
365C23—81no—
366C23—81no—
367C23—612no—
368C23—1221no—
369C23—1221no—
370C23—2441no—
371C23—2441no—
372C23C22⋊C4×D6111yescharacteristic
373C23#1451978311yescharacteristic
374C23#1451978511yescharacteristic
375D4—4884no—
376D4—2442no—
377D4—2442no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—611no—
386C2×C4—611no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—4881no—
392C2×C4—4881no—
393C2×C4—4881no—
394C2×C4—4881no—
395C2×C4—4881no—
396C2×C4—2442no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2441no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C8—81no—
406C8—81no—
407C8—4881no—
408C8—4881no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—41no—
414C22—41no—
415C22—42no—
416C22—42no—
417C22—42no—
418C22—41no—
419C22—41no—
420C22—42no—
421C22—81no—
422C22—81no—
423C22—82no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—1222no—
430C22—4881no—
431C22—2442no—
432C22—2441no—
433C22—2441no—
434C22#1683972711yescharacteristic
435C22#99×D6111yescharacteristic
436C22#100×D6111yescharacteristic
437C4—41no—
438C4—41no—
439C4—81no—
440C4—1221no—
441C4—1221no—
442C4—4881no—
443C4—4881no—
444C4—2441no—
445C4—2441no—
446C2—21no—
447C2—21no—
448C2—41no—
449C2—41no—
450C2—82no—
451C2—2442no—
452C2#2144417711yescharacteristic
453C2#2144745711yescharacteristic
454C2#2144746211yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1316C2
socleC22×C61C2×#99
prime radicalC2×#14519746C4
cosocleC2×C22⋊C4×C61C23
hypercenter#1316D61
hypocenterC61#11560
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1316

Complements

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

NH ≅ G/Ntype
2. #21444158C2semidirect
3. #21444134C2semidirect
4. #21443748C2semidirect
5. #21443748C2semidirect
6. #21443747C2semidirect
7. C61×#1316C2semidirect
225. #1316D61semidirect
254. C61#11560semidirect

Maximal subgroups

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

subgroupindex
#214507122
#214441582
#214441342
#214437482
#214437472
C61×#13162
#1156061