Finite Group Databasebeta

← #29580971

Subgroups — #29580971

Order 15616.

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

normal subgroups only

This group has 468 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#21457161C211yesmaximal, characteristic
2#21455949C211yesmaximal, characteristic
3#21446760C211yesmaximal, characteristic
4#21444435C211yesmaximal, characteristic
5#21444434C211yesmaximal, characteristic
6#21443688C211yesmaximal, characteristic
7C61×#3113C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840092—21no—
10#16840057—21no—
11#16840054—21no—
12#16840047—21no—
13#16840001—22no—
14#16839972—21no—
15#16839972—21no—
16#16839969—21no—
17#16839918—21no—
18#16839867—22no—
19#16839819C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519688C2211yescharacteristic
22#16839517—22no—
23#16839504—22no—
24#16839503—22no—
25C61×#533C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C61×#483—21no—
28C61×#475—21no—
29C61×#462—21no—
30C61×#451—21no—
31C61×#441—22no—
32C61×#432C2211yescharacteristic
33C2×#11758202—22no—
34C2×#11758202—22no—
35C22×#92418—21no—
36C22×#92418D412yes—
37#14519777D411yescharacteristic
38#14519777D411yescharacteristic
39#14519769—21no—
40#14519756—21no—
41#14519756—21no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44#14519736—21no—
45#14519710—22no—
46#14519708—22no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519701—22no—
51#14519701—22no—
52#14519700—22no—
53#14519700—22no—
54C22⋊#92418—21no—
55#14519688—21no—
56#14519688—21no—
57#14519688D412yes—
58C22×Q8×C61D411yescharacteristic
59C2×Q16×C61—22no—
60C4⋊Q8×C61D411yescharacteristic
61C4⋊Q8×C61D411yescharacteristic
62#125×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71#117×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C42×C61—21no—
75C2×C42×C61C2311yescharacteristic
76#106×C61—22no—
77C4⋊C8×C61—21no—
78#103×C61—22no—
79#103×C61—22no—
80C22⋊C8×C61—21no—
81#97×C61D412yes—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—42no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61#4111yescharacteristic
92C2×Dic122—21no—
93C2×Dic122—21no—
94Q16×C61—44no—
95C2×C8×C61—22no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C22⋊C4×C61—41no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61—41no—
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C22⋊Dic61—41no—
115#11758202—44no—
116#11758202—82no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121#11758196—41no—
122#11758196—41no—
123C4×Dic61—41no—
124C2×#92418—22no—
125C2×#92418—22no—
126C2×#92418—22no—
127C2×#92418—41no—
128C2×#92418—41no—
129C2×#92418—42no—
130C23×C61#12111yescharacteristic
131Q8×C61—22no—
132Q8×C61—22no—
133Q8×C61—41no—
134Q8×C61—41no—
135Q8×C61—42no—
136Q8×C61—41no—
137Q8×C61—41no—
138C2×C4×C61—22no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12011yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12711yescharacteristic
155C2×Dic61—41no—
156C2×Dic61—41no—
157Dic122—42no—
158Dic122—41no—
159Dic122—41no—
160C8×C61—42no—
161#92418—42no—
162#92418—42no—
163#92418—42no—
164#10031—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#39211yescharacteristic
168C22×C61#47312yes—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—42no—
175C4×C61—81no—
176C4×C61—81no—
177C4×C61—81no—
178C4×C61#45511yescharacteristic
179C4×C61#45611yescharacteristic
180Dic61—81no—
181Dic61—81no—
182#3249—611no—
183#3113—611no—
184#3113D6111yescharacteristic
185#1985—611no—
186#1531—611no—
187#1531—611no—
188#1290—611no—
189C2×C61—22no—
190C2×C61#200711yescharacteristic
191C2×C61#201011yescharacteristic
192C2×C61#202011yescharacteristic
193#533—611no—
194#533C2×D6111yescharacteristic
195C2×C4×Q8C2×D6111yescharacteristic
196#483—21no—
197#483—1221no—
198#477—1221no—
199#477—1221no—
200#475—21no—
201#475—1221no—
202#467—1222no—
203#462—21no—
204#462—1221no—
205#462—1221no—
206#462—1221no—
207#451—21no—
208#451—1221no—
209#441—22no—
210#441—1222no—
211#432—611no—
212#432C2×D6111yescharacteristic
213C2×C4⋊C8—611no—
214C2×#97—611no—
215#336—1222no—
216#330—1222no—
217#330—1222no—
218C61#1003111yescharacteristic, complemented, Sylow
219C22×Q8C22⋊D6111yescharacteristic
220C2×Q16—22no—
221C2×Q16—1222no—
222C2×Q16—1222no—
223C22×C8—612no—
224C22×C8—1221no—
225C4⋊Q8—611no—
226C4⋊Q8—611no—
227C4⋊Q8C22⋊D6111yescharacteristic
228C4⋊Q8C22⋊D6111yescharacteristic
229#125—21no—
230#125—1221no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—1221no—
234C22⋊Q8—1221no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—1221no—
242C4×Q8—1221no—
243#117—21no—
244#117—1221no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4C22⋊D6111yescharacteristic
247C2×C42—21no—
248C2×C42C22×D6111yescharacteristic
249#107—1222no—
250#106—22no—
251#106—1222no—
252C4⋊C8—21no—
253C4⋊C8—1221no—
254C4⋊C8—1221no—
255C4⋊C8—1221no—
256#103—22no—
257#103—22no—
258#103—1222no—
259#103—1222no—
260#103—1222no—
261#103—1222no—
262C22⋊C8—21no—
263C22⋊C8—1221no—
264#97—612no—
265#97—1221no—
266#97—1221no—
267#97C22⋊D6112yes—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—42no—
273C2×Q8—1221no—
274C2×Q8—1221no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4D4×D6111yescharacteristic
278C22×C4#1175822411yescharacteristic
279C22×C4C2×C22⋊D6111yescharacteristic
280Q16—44no—
281Q16—4882no—
282Q16—2444no—
283C2×C8—22no—
284C2×C8—1222no—
285C2×C8—1222no—
286C2×C8—1222no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2442no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—41no—
307C22⋊C4—2441no—
308C42—41no—
309C42—41no—
310C42—41no—
311C42—2441no—
312C42D4×D6111yescharacteristic
313C42D4×D6111yescharacteristic
314C42C2×C22⋊D6111yescharacteristic
315C42C2×C22⋊D6111yescharacteristic
316C23#1451974911yescharacteristic
317Q8—22no—
318Q8—22no—
319Q8—41no—
320Q8—41no—
321Q8—42no—
322Q8—41no—
323Q8—41no—
324Q8—2442no—
325Q8—2441no—
326Q8—2441no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4#1451974511yescharacteristic
341C2×C4#1451974511yescharacteristic
342C2×C4#1451974611yescharacteristic
343C2×C4#1451974811yescharacteristic
344C2×C4#1451974911yescharacteristic
345C2×C4#1451977311yescharacteristic
346C8—42no—
347C8—2442no—
348C8—2442no—
349C8—2442no—
350C22—21no—
351C22—21no—
352C22#1683967011yescharacteristic
353C22#1684003512yes—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—42no—
360C4—81no—
361C4—81no—
362C4—81no—
363C4—4881no—
364C4—4881no—
365C4#1683993811yescharacteristic
366C4#1683994311yescharacteristic
367C2—22no—
368C2#2144686411yescharacteristic
369C2#2144688411yescharacteristic
370C2#2144693711yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3113C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#3113D61
hypocenterC61#10031
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
218. C61#10031semidirect

Maximal subgroups

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

subgroupindex
#214571612
#214559492
#214467602
#214444352
#214444342
#214436882
C61×#31132
#1003161