Finite Group Databasebeta

← #29578006

Subgroups — #29578006

Order 15616.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454454C211yesmaximal, characteristic
2#21450108C211yesmaximal, characteristic
3#21445900C211yesmaximal, characteristic
4#21444148C211yesmaximal, characteristic
5#21444148C211yesmaximal, characteristic
6#21443727C211yesmaximal, characteristic
7C61×#1306C211yesmaximal, characteristic
8C2×#14519736C2211yescharacteristic
9C22×#11758196C2211yescharacteristic
10#16839820—22no—
11#16839820—22no—
12#16839785—21no—
13#16839726C2211yescharacteristic
14#16839726C2211yescharacteristic
15M16×Dic61—21no—
16#16839702—21no—
17#16839694—21no—
18#16839647—21no—
19#16839647—21no—
20#16839637C411yescharacteristic
21#16839637C411yescharacteristic
22#16839623C411yescharacteristic
23#16839623C411yescharacteristic
24#16839530—21no—
25#16839530—21no—
26#16839487—22no—
27#16839487—22no—
28C61×#407C2211yescharacteristic
29C61×#407C2211yescharacteristic
30C61×#381C2211yescharacteristic
31C23×Dic61C2×C411yescharacteristic
32C23×Dic61C2×C411yescharacteristic
33C2×#11758194—21no—
34C2×#11758194—21no—
35#14519736—21no—
36#14519736—21no—
37#14519736—21no—
38#14519736—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×C22⋊Dic61C2×C411yescharacteristic
50C2×C22⋊Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53#14519706—24no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418D412yes—
58#14519687—22no—
59C8×Dic61—22no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66C23×C4×C61C2311yescharacteristic
67C2×M16×C61—21no—
68C2×M16×C61—21no—
69C2×C22⋊C4×C61C2×C411yescharacteristic
70C2×C22⋊C4×C61C2×C411yescharacteristic
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yes—
75#95×C61—21no—
76#95×C61—21no—
77C24×C61C22×C411yescharacteristic
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—42no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101M16×C61—41no—
102M16×C61—41no—
103M16×C61—41no—
104M16×C61—41no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C22⋊C4×C61—41no—
108C22⋊C4×C61—41no—
109C22⋊Dic61—21no—
110C22⋊Dic61—21no—
111C22⋊Dic61—21no—
112C22⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—42no—
118C4⋊Dic61—42no—
119#11758196—41no—
120#11758196—41no—
121#11758196—41no—
122#11758196—41no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127#11758194—41no—
128#11758194—41no—
129#11758194—41no—
130#11758194—41no—
131C2×#92418—22no—
132C2×#92418—41no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61C2×C22⋊C411yescharacteristic
138C23×C61C4×D411yescharacteristic
139C23×C61C4×D411yescharacteristic
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
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#12011yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12311yescharacteristic
158C2×Dic61—22no—
159C2×Dic61—22no—
160C2×Dic61—22no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—41no—
176C2×Dic61—81no—
177C2×Dic61—81no—
178C8×C61—42no—
179C8×C61—81no—
180#92418—42no—
181#92418—81no—
182#9514—611nomaximal, Sylow
183C22×C61—21no—
184C22×C61—21no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—42no—
192C22×C61—42no—
193C22×C61#38611yescharacteristic
194C22×C61#41011yescharacteristic
195C22×C61#41011yescharacteristic
196C4×C61—21no—
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—81no—
201C4×C61—81no—
202Dic61—42no—
203Dic61—41no—
204Dic61—41no—
205Dic61—41no—
206Dic61—41no—
207Dic61—81no—
208#2921—611no—
209#2484—611no—
210#1822—611no—
211#1463—611no—
212#1463—611no—
213#1306—611no—
214#1306D6111yescharacteristic
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—41no—
218C2×C61—41no—
219C2×C61#189111yescharacteristic
220C2×C61#189911yescharacteristic
221C2×C61#191511yescharacteristic
222C2×#117—611no—
223C22×C4⋊C4—611no—
224#433—1222no—
225#433—1222no—
226#423—1221no—
227#407—611no—
228#407—611no—
229#407C2×D6111yescharacteristic
230#407C2×D6111yescharacteristic
231C4×M16—1221no—
232#400—1221no—
233#398—1221no—
234#387—1221no—
235#387—1221no—
236#385—611no—
237#385—611no—
238#381—611no—
239#381—611no—
240#381C2×D6111yescharacteristic
241#343—1221no—
242#343—1221no—
243#324—1222no—
244#324—1222no—
245C61#951411yescharacteristic, complemented, Sylow
246C23×C4—611no—
247C23×C4—611no—
248C23×C4C22×D6111yescharacteristic
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—1221no—
252C2×M16—1221no—
253#117—1221no—
254#117—1221no—
255#117—1221no—
256#117—1221no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—1221no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1221no—
265C2×C4⋊C4—1221no—
266C2×C4⋊C4—1221no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4C4×D6111yescharacteristic
270C2×C22⋊C4C4×D6111yescharacteristic
271C2×C42—611no—
272C2×C42—611no—
273C4⋊C8—1224no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—612no—
278C22⋊C8—1221no—
279C22⋊C8—1221no—
280C22⋊C8—1221no—
281C22⋊C8D24412yes—
282#97—1222no—
283C4×C8—1222no—
284#95—21no—
285#95—21no—
286#95—1221no—
287#95—1221no—
288#95—1221no—
289#95—1221no—
290#95—1221no—
291#95—1221no—
292C24C2×C4×D6111yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4—1221no—
307C22×C4—2442no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4C2×D24411yescharacteristic
311C22×C4#1175822211yescharacteristic
312C22×C4D4×D6111yescharacteristic
313C22×C4D4×D6111yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C22×C4#1175822611yescharacteristic
316M16—41no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—2441no—
321M16—2441no—
322M16—2441no—
323M16—2441no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—1222no—
327C2×C8—2441no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—2442no—
333C4⋊C4—2442no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C4⋊C4—2441no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—1221no—
344C42—1221no—
345C42—1221no—
346C42—1221no—
347C42—1221no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23C22⋊C4×D6111yescharacteristic
353C23#1451973911yescharacteristic
354C23C4×D24411yescharacteristic
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—1222no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—1221no—
373C2×C4—1221no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—4881no—
377C2×C4—4881no—
378C2×C4—2441no—
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—2441no—
388C2×C4—2441no—
389C2×C4#1451974711yescharacteristic
390C2×C4#1451975011yescharacteristic
391C2×C4#1451975211yescharacteristic
392C2×C4#1451976211yescharacteristic
393C8—42no—
394C8—81no—
395C8—4881no—
396C8—2442no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—42no—
406C22—42no—
407C22#1683964011yescharacteristic
408C22#1683973411yescharacteristic
409C22#1683973411yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—81no—
415C4—81no—
416C4—4881no—
417C4—2442no—
418C4—2441no—
419C4—2441no—
420C4—2441no—
421C4—2441no—
422C2—21no—
423C2—21no—
424C2—41no—
425C2—41no—
426C2#2144623611yescharacteristic
427C2#2144627611yescharacteristic
428C2#2144637011yescharacteristic
subgroupG/H
centerC22#16839640
commutator, prime radicalC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1306C2
socleC22×C61#386
cosocleC23×C4×C61C23
hypercenter#1306D61
hypocenterC61#9514
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
245. C61#9514semidirect

Maximal subgroups

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

subgroupindex
#214544542
#214501082
#214459002
#214441482
#214437272
C61×#13062
#951461