Finite Group Databasebeta

← #29583363

Subgroups — #29583363

Order 15616.

576 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 117 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#21446127C212yesmaximal
2C2×#16839499C212yesmaximal
3#21444075C211yesmaximal, characteristic
4#21443662C211yesmaximal, characteristic
5C61×#2659C211yesmaximal, characteristic
6C22×C4⋊Dic61C2211yescharacteristic
7C2×#14519701—22no—
8C2×C22⋊#92418C2212yes—
9C2×#14519684—21no—
10C2×#14519684—21no—
11C2×#14519684C2211yescharacteristic
12#16839524—22no—
13#16839499—24no—
14C2×C22⋊Q8×C61C2212yes—
15C61×#398—22no—
16C61×#395—22no—
17C61×#380—21no—
18C61×#380—21no—
19C2×#95×C61C2211yescharacteristic
20C23×Dic61—21no—
21C23×Dic61—21no—
22C22×#92418—22no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61—42no—
25#14519701—44no—
26C22⋊#92418—22no—
27C22⋊#92418—22no—
28#14519684—21no—
29#14519684—42no—
30#14519684—42no—
31#14519684D412yes—
32C22×Q8×C61D412yes—
33C23×C4×C61D411yescharacteristic
34C23×C4×C61D411yescharacteristic
35C23×C4×C61C2311yescharacteristic
36C22⋊Q8×C61—22no—
37C22⋊Q8×C61—22no—
38C22⋊Q8×C61—22no—
39C22⋊Q8×C61—22no—
40C2×C4⋊C4×C61—22no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61D412yes—
46C2×C22⋊C4×C61—22no—
47#95×C61—22no—
48#95×C61—22no—
49#95×C61—22no—
50C24×C61C2×D411yescharacteristic
51C2×Q8×C61—22no—
52C2×Q8×C61—22no—
53C2×Q8×C61—42no—
54C2×Q8×C61—42no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61SD1612yes—
68C22×C4×C61Q1612yes—
69C22×C4×C61C2×D412yes—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61#4112yes—
72C22×C4×C61#4111yescharacteristic
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—42no—
91C4⋊C4×C61—81no—
92C4⋊C4×C61—81no—
93C4⋊C4×C61—81no—
94C4⋊C4×C61—81no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C4⋊Dic61—24no—
98C4⋊Dic61—42no—
99C2×#92418—42no—
100C2×#92418—42no—
101C2×#92418—42no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61#12011yescharacteristic
107C23×C61#12111yescharacteristic
108C23×C61#12411yescharacteristic
109C23×C61C2×SD1611yescharacteristic
110C23×C61C2×Q1611yescharacteristic
111C23×C61#13711yescharacteristic
112C23×C61#13711yescharacteristic
113Q8×C61—44no—
114Q8×C61—82no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—41no—
120C2×C4×C61—42no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61#12112yes—
137C2×C4×C61#12312yes—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C2×Dic61—81no—
152#92418—82no—
153#10407—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61#39411yescharacteristic
167C22×C61#44811yescharacteristic
168C22×C61#45111yescharacteristic
169C22×C61#45411yescharacteristic
170C22×C61#45511yescharacteristic
171C22×C61B(4,𝔽2)11yescharacteristic
172C22×C61#45811yescharacteristic
173C22×C61#46111yescharacteristic
174C22×C61#46211yescharacteristic
175C22×C61#48711yescharacteristic
176C22×C61#49111yescharacteristic
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—42no—
180C4×C61—42no—
181C4×C61—82no—
182C4×C61—82no—
183Dic61—82no—
184Dic61—82no—
185#2659D6111yescharacteristic
186#1872—612no—
187C2×#328—612no—
188#1442—611no—
189#1280—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61—21no—
194C2×C61#159911yescharacteristic
195C2×C61#160211yescharacteristic
196C2×C61#160811yescharacteristic
197C2×C61#161711yescharacteristic
198C2×C61#204011yescharacteristic
199C2×C61#204311yescharacteristic
200C2×C61#204411yescharacteristic
201C2×C22⋊Q8C2×D6112yes—
202C22×C4⋊C4—611no—
203C2×#103—1222no—
204C2×C22⋊C8—612no—
205#398—22no—
206#395—22no—
207#380—21no—
208#380—21no—
209C2×#95—611no—
210C2×#95—1221no—
211C2×#95—1221no—
212C2×#95C2×D6111yescharacteristic
213#340—1222no—
214#328—1224no—
215C61#1040711yescharacteristic, complemented, Sylow
216C22×Q8C22⋊D6112yes—
217C23×C4—1221no—
218C23×C4—1221no—
219C23×C4C22⋊D6111yescharacteristic
220C23×C4C22⋊D6111yescharacteristic
221C23×C4C22×D6111yescharacteristic
222C22×C8—1222no—
223C22⋊Q8—22no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C22⋊Q8—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—1222no—
233C2×C4⋊C4—2442no—
234C2×C4⋊C4C22⋊D6112yes—
235C2×C22⋊C4—22no—
236#103—2444no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239#95—22no—
240#95—22no—
241#95—22no—
242#95—612no—
243#95—1221no—
244#95—2442no—
245#95—2442no—
246C24C2×C22⋊D6111yescharacteristic
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—42no—
250C2×Q8—42no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4#1175820112yes—
278C22×C4#1175820212yes—
279C22×C4D4×D6111yescharacteristic
280C22×C4#1175822412yes—
281C22×C4#1175822411yescharacteristic
282C22×C4C2×C22⋊D6112yes—
283C2×C8—2442no—
284C2×C8—2442no—
285C2×C8—2442no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—81no—
293C4⋊C4—81no—
294C4⋊C4—1224no—
295C4⋊C4—2442no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#1451974611yescharacteristic
303C23#1451974811yescharacteristic
304C23#1451976411yescharacteristic
305C23C2×#1175820111yescharacteristic
306C23C2×#1175820211yescharacteristic
307C23#1451980811yescharacteristic
308C23#1451980811yescharacteristic
309Q8—44no—
310Q8—82no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4#1451974912yes—
347C2×C4#1451975812yes—
348C8—4882no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22#1683967611yescharacteristic
362C22#1683990111yescharacteristic
363C22#1683991811yescharacteristic
364C22#1683993511yescharacteristic
365C22#1683994011yescharacteristic
366C22#1683994911yescharacteristic
367C22#1683995211yescharacteristic
368C22#1683996411yescharacteristic
369C22#1683996911yescharacteristic
370C22#1684011211yescharacteristic
371C22#1684013011yescharacteristic
372C4—22no—
373C4—22no—
374C4—42no—
375C4—42no—
376C4—82no—
377C4—82no—
378C4—4882no—
379C4—4882no—
380C2—21no—
381C2—21no—
382C2—21no—
383C2—21no—
384C2#2144475911yescharacteristic
385C2#2144477611yescharacteristic
386C2#2144481011yescharacteristic
387C2#2144486111yescharacteristic
388C2#2144704511yescharacteristic
389C2#2144706211yescharacteristic
390C2#2144706711yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2659C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#2659D61
hypocenterC61#10407
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2659

Complements

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

NH ≅ G/Ntype
215. C61#10407semidirect

Maximal subgroups

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

subgroupindex
#214461272
C2×#168394992
#214440752
#214436622
C61×#26592
#1040761