Finite Group Databasebeta

← #29576003

Subgroups — #29576003

Order 15616.

502 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454847C211yesmaximal, characteristic
2#21451688C211yesmaximal, characteristic
3C4×#14519693C211yesmaximal, characteristic
4#21444421C211yesmaximal, characteristic, complemented
5#21443685C211yesmaximal, characteristic, complemented
6#21443684C211yesmaximal, characteristic, complemented
7C61×#1528C211yesmaximal, characteristic, complemented
8C2×C4×D244C2211yescharacteristic
9#16839835—22no—
10#16839832—22no—
11#16839819C2211yescharacteristic
12C2×#14519693—21no—
13#16839724—21no—
14C22⋊C8×D61—21no—
15C4×#11758194C2211yescharacteristic
16#16839697C411yescharacteristic
17#16839697C411yescharacteristic
18#16839692—21no—
19#16839688C411yescharacteristic
20#16839688C411yescharacteristic
21#16839679—21no—
22#16839633—21no—
23#16839633—21no—
24#16839630C2211yescharacteristic
25#16839530—21no—
26#16839504—22no—
27C2×#125×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#330—22no—
31C22×D244D411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×#11758194—21no—
35C2×#11758189—22no—
36C2×C8×D61—22no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198C2×C411yescharacteristic
49C2×#11758198C2×C411yescharacteristic
50C4⋊#92418—21no—
51#14519693—24no—
52C22⋊#92418—21no—
53#14519689—22no—
54#14519689—22no—
55#14519688—21no—
56#14519688D412yes—
57C4×#92418—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684C2×C411yescharacteristic
63#14519684C2×C411yescharacteristic
64C2×M16×C61—21no—
65#125×C61—21no—
66#125×C61—21no—
67#125×C61—21no—
68#125×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C4⋊C4×C61C2×C411yescharacteristic
73C2×C42×C61C2311yescharacteristic
74C4⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76#97×C61—21no—
77#97×C61D412yes—
78C4×C8×C61—21no—
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C2×D244—22no—
91C2×D244—21no—
92C2×D244—21no—
93C2×D244—41no—
94C2×C4×D61—21no—
95C2×C4×D61—21no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—81no—
99C2×C4×D61—81no—
100M16×C61—22no—
101M16×C61—41no—
102C2×C8×C61—22no—
103C2×C8×C61—41no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C42×C61#4111yescharacteristic
116#11758198—21no—
117#11758198—21no—
118#11758198—21no—
119#11758198—21no—
120#11758198—42no—
121#11758198—42no—
122#11758198—81no—
123#11758198—81no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126#11758196—81no—
127#11758196—81no—
128#11758194—22no—
129#11758194—41no—
130C2×#92418—22no—
131C2×#92418—41no—
132#11758189—82no—
133C8×D61—82no—
134C23×C61C2×C22⋊C411yescharacteristic
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61#10412yes—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61—41no—
155C2×C4×C61C4×D411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12311yescharacteristic
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—41no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171D244—42no—
172D244—42no—
173C4×D61—42no—
174C4×D61—42no—
175C4×D61—81no—
176C4×D61—81no—
177C8×C61—42no—
178C8×C61—42no—
179#92418—42no—
180#92418—42no—
181#9189—611nomaximal, Sylow
182C22×C61—21no—
183C22×C61—21no—
184C22×C61#38611yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C22×C61#42111yescharacteristic
187C2×D61—22no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—81no—
196C2×D61—81no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—21no—
202C4×C61—21no—
203C4×C61—81no—
204C4×C61—81no—
205Dic61—41no—
206Dic61—41no—
207Dic61—81no—
208Dic61—81no—
209#2973—611no—
210#2633—611no—
211C4×#100—611no—
212#1528—611no—
213#1528D6111yescharacteristic, complemented
214#1288—611no—
215#1288—611no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61#187111yescharacteristic
219C2×C61#191111yescharacteristic
220C2×C61#191511yescharacteristic
221D61—42no—
222D61—81no—
223C2×#125C2×D6111yescharacteristic
224C2×C4×D4—611no—
225#435—1222no—
226#435—1222no—
227#432—611no—
228#432C2×D6111yescharacteristic
229C2×#100—1221no—
230#407—1221no—
231C2×C22⋊C8—1221no—
232C4×M16—611no—
233C4×M16C2×D6111yescharacteristic
234#399—611no—
235#399—611no—
236#398—1221no—
237#397—611no—
238#397—611no—
239#394—1221no—
240#385—1221no—
241#385—1221no—
242#383—611no—
243#343—1221no—
244#330—22no—
245#330—1222no—
246C61#918911yescharacteristic, complemented, Sylow
247C22×D4—611no—
248C23×C4—611no—
249C23×C4—611no—
250C2×M16—21no—
251C2×M16—1222no—
252C2×M16—1221no—
253C22×C8—1222no—
254#125—21no—
255#125—21no—
256#125—21no—
257#125—21no—
258C4×D4—1221no—
259C4×D4—1221no—
260C4×D4—1221no—
261C4×D4—1221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C4⋊C4C4×D6111yescharacteristic
268C2×C4⋊C4C4×D6111yescharacteristic
269C2×C22⋊C4—611no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C22⋊C4—1221no—
275C2×C42C22×D6111yescharacteristic
276C4⋊C8—21no—
277C4⋊C8—1221no—
278#100—1224no—
279C22⋊C8—21no—
280C22⋊C8—1222no—
281C22⋊C8—1222no—
282C22⋊C8—1221no—
283#97—21no—
284#97—612no—
285#97—1221no—
286#97C22⋊D6112yes—
287C4×C8—21no—
288C4×C8—1221no—
289#95—611no—
290#95—611no—
291#95—1221no—
292#95—1221no—
293#95—1221no—
294#95—1221no—
295C24—611no—
296C24—611no—
297C2×D4—1222no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—2441no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—4881no—
312C22×C4—4881no—
313C22×C4C2×C4×D6111yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C22×C4D4×D6111yescharacteristic
316M16—22no—
317M16—41no—
318M16—1222no—
319M16—4882no—
320M16—2441no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—1222no—
324C2×C8—4882no—
325C2×C8—2441no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—1221no—
335C4⋊C4—1221no—
336C4⋊C4—4881no—
337C4⋊C4—4881no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—4881no—
343C22⋊C4—4881no—
344C22⋊C4—2442no—
345C22⋊C4—2442no—
346C42#1175822211yescharacteristic
347C42D4×D6111yescharacteristic
348C42#1175822411yescharacteristic
349C42C2×C22⋊D6111yescharacteristic
350C23—612no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—2441no—
357C23—2441no—
358C23—2441no—
359C23—2441no—
360C23C22⋊C4×D6111yescharacteristic
361D4—2442no—
362D4—2442no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—4881no—
376C2×C4—4881no—
377C2×C4—2442no—
378C2×C4—2442no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4#1451973711yescharacteristic
388C2×C4C4×C22⋊D6111yescharacteristic
389C2×C4#1451974511yescharacteristic
390C2×C4#1451974811yescharacteristic
391C2×C4#1451975011yescharacteristic
392C2×C4#1451975911yescharacteristic
393C8—42no—
394C8—42no—
395C8—2442no—
396C8—2442no—
397C22—21no—
398C22—21no—
399C22—1222no—
400C22—4881no—
401C22—4881no—
402C22—2442no—
403C22—2442no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22#1683963811yescharacteristic
410C22#104×D6111yescharacteristic
411C22#1683977711yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—4881no—
421C4—4881no—
422C4—2441no—
423C4—2441no—
424C2—21no—
425C2—21no—
426C2—4881no—
427C2—2442no—
428C2#2144611811yescharacteristic
429C2#2144634811yescharacteristic
430C2#2144636811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1528C2
socleC22×C61#386
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1528D61
hypocenterC61#9189
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
4. #21444421C2semidirect
5. #21443685C2semidirect
6. #21443684C2semidirect
7. C61×#1528C2semidirect
213. #1528D61semidirect
246. C61#9189semidirect

Maximal subgroups

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

subgroupindex
#214548472
#214516882
C4×#145196932
#214444212
#214436852
#214436842
C61×#15282
#918961