Finite Group Databasebeta

← #29580424

Subgroups — #29580424

Order 15616.

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

normal subgroups only

This group has 574 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#21455763C211yesmaximal, characteristic
2#21450106C211yesmaximal, characteristic
3#21445919C211yesmaximal, characteristic
4#21444352C211yesmaximal, characteristic
5#21444149C211yesmaximal, characteristic
6#21443672C211yesmaximal, characteristic
7C61×#2583C211yesmaximal, characteristic
8C2×#14519736C2211yescharacteristic
9#16840100—22no—
10#16840095—21no—
11#16840090—21no—
12#16839802—21no—
13#16839771—21no—
14#16839726C2211yescharacteristic
15#16839726C2211yescharacteristic
16#16839701—21no—
17#16839692—21no—
18#16839643—22no—
19#16839635—21no—
20#16839625—21no—
21#16839625C2211yescharacteristic
22#16839522—22no—
23#16839499—22no—
24#16839488—22no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C22×C4⋊C4×C61C2211yescharacteristic
27C61×#398—21no—
28C61×#395—21no—
29C61×#389—22no—
30C61×#385—21no—
31C61×#385—21no—
32C4×C22⋊C4×C61C2211yescharacteristic
33C2×#11758194—21no—
34C2×#11758194—21no—
35#14519736—21no—
36#14519736—21no—
37#14519736—21no—
38#14519736—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—22no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C4×Dic61—21no—
45#14519710—22no—
46#14519708—22no—
47#14519701—22no—
48#14519701—22no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418D412yes—
53#14519684—22no—
54#14519684—22no—
55#14519684—22no—
56#14519684—21no—
57#14519684D412yes—
58C22×Q8×C61D411yescharacteristic
59C23×C4×C61D411yescharacteristic
60C23×C4×C61D411yescharacteristic
61C23×C4×C61C2311yescharacteristic
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C2×C4⋊C4×C61—22no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61—22no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—21no—
78C2×C42×C61D412yes—
79#95×C61—22no—
80#95×C61—22no—
81#95×C61—21no—
82C24×C61C2×D411yescharacteristic
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—42no—
86C22×C4×C61—22no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—42no—
96C22×C4×C61—42no—
97C22×C4×C61—42no—
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61#4111yescharacteristic
104C22×Dic61—22no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—44no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—82no—
117C22⋊C4×C61—24no—
118C22⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C42×C61—42no—
121C22⋊Dic61—42no—
122C22⋊Dic61—41no—
123C22⋊Dic61—41no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128#11758196—44no—
129C4×Dic61—41no—
130C4×Dic61—41no—
131#11758194—42no—
132#11758194—42no—
133C2×#92418—22no—
134C2×#92418—41no—
135C23×C61—22no—
136C23×C61—22no—
137C23×C61—41no—
138C23×C61#12011yescharacteristic
139C23×C61#12011yescharacteristic
140C23×C61#12111yescharacteristic
141Q8×C61—42no—
142Q8×C61—81no—
143C2×C4×C61—22no—
144C2×C4×C61—22no—
145C2×C4×C61—22no—
146C2×C4×C61—24no—
147C2×C4×C61—22no—
148C2×C4×C61—22no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—41no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—81no—
167C2×C4×C61#12011yescharacteristic
168C2×C4×C61#12111yescharacteristic
169C2×C4×C61#12111yescharacteristic
170C2×C4×C61#12711yescharacteristic
171C2×Dic61—42no—
172C2×Dic61—42no—
173C2×Dic61—42no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178#92418—42no—
179#92418—81no—
180#9945—611nomaximal, Sylow
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—44no—
189C22×C61#39211yescharacteristic
190C22×C61#45612yes—
191C22×C61#45812yes—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—44no—
197C4×C61—42no—
198C4×C61—81no—
199C4×C61—81no—
200C4×C61—81no—
201Dic61—82no—
202Dic61—81no—
203Dic61—81no—
204#3095—611no—
205#2583D6111yescharacteristic
206#2484—611no—
207#1826—611no—
208#1511—611no—
209#1463—611no—
210#1284—611no—
211C2×C61—22no—
212C2×C61—22no—
213C2×C61—41no—
214C2×C61#200511yescharacteristic
215C2×C61#201011yescharacteristic
216C2×C61#202211yescharacteristic
217C2×C22⋊Q8C2×D6111yescharacteristic
218C2×#117—611no—
219C22×C4⋊C4C2×D6111yescharacteristic
220#485—1222no—
221#484—1221no—
222#483—1221no—
223#428—1221no—
224#419—1221no—
225#407—611no—
226#407—611no—
227#400—1221no—
228#398—21no—
229#398—1221no—
230#395—21no—
231#389—22no—
232#387—1222no—
233#385—21no—
234#385—21no—
235#385—1221no—
236#381—611no—
237#381—1221no—
238C4×C22⋊C4C2×D6111yescharacteristic
239#339—1222no—
240#328—1222no—
241#324—1222no—
242C61#994511yescharacteristic, complemented, Sylow
243C22×Q8C22⋊D6111yescharacteristic
244C23×C4C22⋊D6111yescharacteristic
245C23×C4C22⋊D6111yescharacteristic
246C23×C4C22×D6111yescharacteristic
247C2×M16—1221no—
248C2×M16—1221no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253#117—1221no—
254#117—1221no—
255#117—1221no—
256#117—1221no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—1222no—
269C2×C4⋊C4C22⋊D6111yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—1221no—
273C2×C22⋊C4—1221no—
274C2×C42—1221no—
275C2×C42C22⋊D6112yes—
276#107—1222no—
277#106—1222no—
278#103—1222no—
279#103—1222no—
280C22⋊C8—612no—
281C22⋊C8—1221no—
282C22⋊C8—1221no—
283C22⋊C8—1221no—
284#95—22no—
285#95—22no—
286#95—21no—
287#95—612no—
288#95—1222no—
289#95—1222no—
290#95—1222no—
291#95—1221no—
292C24C2×C22⋊D6111yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—1222no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4D4×D6111yescharacteristic
312C22×C4D4×D6111yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C22×C4#1175822411yescharacteristic
315C22×C4C2×C22⋊D6111yescharacteristic
316C22×C4C2×C22⋊D6111yescharacteristic
317M16—2442no—
318M16—2442no—
319C2×C8—1222no—
320C2×C8—2441no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—44no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—82no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—2444no—
336C22⋊C4—24no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—2442no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C42—42no—
343C42—2441no—
344C42—2441no—
345C23—22no—
346C23—22no—
347C23—41no—
348C23#1451974511yescharacteristic
349C23#1451974611yescharacteristic
350C23#1451974911yescharacteristic
351Q8—42no—
352Q8—81no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—2442no—
378C2×C4—2442no—
379C2×C4—2442no—
380C2×C4—2442no—
381C2×C4—2442no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4#1451974511yescharacteristic
385C2×C4#1451974811yescharacteristic
386C2×C4#1451974911yescharacteristic
387C2×C4#1451977311yescharacteristic
388C8—4881no—
389C8—2442no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22#1683967011yescharacteristic
399C22#1683994412yes—
400C22#1683995212yes—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—44no—
406C4—42no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—4882no—
411C4—4881no—
412C4—4881no—
413C2—22no—
414C2—22no—
415C2—41no—
416C2#2144685511yescharacteristic
417C2#2144688411yescharacteristic
418C2#2144694811yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2583C2
socleC22×C61#392
prime radicalC24×C61C2×D4
hypercenter#2583D61
hypocenterC61#9945
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
242. C61#9945semidirect

Maximal subgroups

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

subgroupindex
#214557632
#214501062
#214459192
#214443522
#214441492
#214436722
C61×#25832
#994561