Finite Group Databasebeta

← #29577686

Subgroups — #29577686

Order 15616.

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

normal subgroups only

This group has 424 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#21454903C211yesmaximal, characteristic
2#21451010C211yesmaximal, characteristic
3#21444445C211yesmaximal, characteristic
4#21444445C211yesmaximal, characteristic
5#21444162C211yesmaximal, characteristic
6#21443675C211yesmaximal, characteristic
7C61×#1285C211yesmaximal, characteristic
8C2×#14519769C2211yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10#16839891—22no—
11#16839890—22no—
12#16839819C2211yescharacteristic
13#16839819C2211yescharacteristic
14#16839816—21no—
15#16839812—21no—
16#16839692—21no—
17#16839692—21no—
18#16839668C411yescharacteristic
19#16839668C411yescharacteristic
20#16839647—21no—
21#16839647—21no—
22#16839632C411yescharacteristic
23#16839628C411yescharacteristic
24#16839503—22no—
25#16839503—22no—
26#16839487—21no—
27#16839487—21no—
28C61×#432C2211yescharacteristic
29C61×#432C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32#14519769—21no—
33#14519769—21no—
34#14519769—21no—
35#14519769—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196D411yescharacteristic
48C2×#11758196D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519706—22no—
54#14519706—22no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57#14519688—21no—
58#14519688D412yes—
59#14519687—22no—
60C8×Dic61—22no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—21no—
67C2×C4⋊C4×C61—21no—
68C2×C42×C61C2×C411yescharacteristic
69C2×C42×C61C2×C411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75#97×C61—21no—
76#97×C61D412yes—
77#95×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61C22×C411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×Dic122—22no—
92C2×Dic122—41no—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C4⋊C4×C61—42no—
96C42×C61—41no—
97C42×C61—41no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—42no—
109C4⋊Dic61—42no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196—41no—
115#11758196—41no—
116#11758196—41no—
117#11758196—41no—
118C4×Dic61—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C2×#92418—22no—
123C2×#92418—41no—
124C23×C61C2×C22⋊C411yescharacteristic
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61#10112yes—
156Dic122—42no—
157Dic122—42no—
158C8×C61—42no—
159C8×C61—81no—
160#92418—42no—
161#92418—81no—
162#9450—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#38611yescharacteristic
166C22×C61C2×#10111yescharacteristic
167C22×C61#41311yescharacteristic
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—42no—
175C4×C61—81no—
176Dic61—22no—
177Dic61—41no—
178Dic61—41no—
179Dic61—41no—
180Dic61—81no—
181Dic61—81no—
182#2983—611no—
183#2565—611no—
184#1534—611no—
185#1534—611no—
186#1467—611no—
187#1285—611no—
188#1285D6111yescharacteristic
189C2×C61—21no—
190C2×C61—21no—
191C2×C61#188411yescharacteristic
192C2×C61#190111yescharacteristic
193C2×C61#191211yescharacteristic
194C2×#125—611no—
195C2×C4×Q8—611no—
196#446—1222no—
197#446—1222no—
198#432—611no—
199#432—611no—
200#432—1221no—
201#432C2×D6111yescharacteristic
202#432C2×D6111yescharacteristic
203#431—1221no—
204#398—1221no—
205#398—1221no—
206#391—611no—
207#391—611no—
208#387—1221no—
209#387—1221no—
210#384—611no—
211#382—611no—
212C4×C4⋊C4C2×D6111yescharacteristic
213#330—1222no—
214#330—1222no—
215#324—1221no—
216#324—1221no—
217C61#945011yescharacteristic, complemented, Sylow
218C22×Q8—611no—
219#125—1221no—
220#125—1221no—
221#125—1221no—
222#125—1221no—
223C4×Q8—1221no—
224C4×Q8—1221no—
225C4×Q8—1221no—
226C4×Q8—1221no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—611no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42C4×D6111yescharacteristic
240C2×C42C4×D6111yescharacteristic
241C2×C42C22×D6111yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—1222no—
245C4⋊C8—1222no—
246C4⋊C8—1221no—
247C4⋊C8—1221no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—1221no—
251C22⋊C8—1221no—
252#97—21no—
253#97—612no—
254#97—1222no—
255#97—1221no—
256#97D24412yes—
257C4×C8—1222no—
258#95—21no—
259#95—1221no—
260#95—1221no—
261#95—1221no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265C2×Q8—1222no—
266C2×Q8—1221no—
267C2×Q8—1221no—
268C2×Q8—2441no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4C2×C4×D6111yescharacteristic
278C22×C4D4×D6111yescharacteristic
279C22×C4D4×D6111yescharacteristic
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—1222no—
283C2×C8—2441no—
284C4⋊C4—42no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—2442no—
296C4⋊C4—2442no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C42—41no—
302C42—41no—
303C42—1221no—
304C42—1221no—
305C42—1221no—
306C42—1221no—
307C42C2×D24411yescharacteristic
308C42#1175822211yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822611yescharacteristic
311C23C22⋊C4×D6111yescharacteristic
312Q8—2442no—
313Q8—2442no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—612no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2442no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4#1451973911yescharacteristic
340C2×C4C4×D24411yescharacteristic
341C2×C4#1451974711yescharacteristic
342C2×C4#1451975011yescharacteristic
343C2×C4#1451975211yescharacteristic
344C2×C4#1451976211yescharacteristic
345C8—42no—
346C8—81no—
347C8—4881no—
348C8—2442no—
349C22—21no—
350C22—21no—
351C22#1683964011yescharacteristic
352C22#101×D6111yescharacteristic
353C22#1683974311yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—81no—
362C4—1222no—
363C4—4881no—
364C4—4881no—
365C4—2441no—
366C4—2441no—
367C4—2441no—
368C2—21no—
369C2—21no—
370C2#2144620111yescharacteristic
371C2#2144628611yescharacteristic
372C2#2144635511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1285C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1285D61
hypocenterC61#9450
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
217. C61#9450semidirect

Maximal subgroups

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

subgroupindex
#214549032
#214510102
#214444452
#214441622
#214436752
C61×#12852
#945061