Finite Group Databasebeta

← #29583358

Subgroups — #29583358

Order 15616.

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

normal subgroups only

This group has 620 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#21444083C211yesmaximal, characteristic
4#21443662C211yesmaximal, characteristic
5C61×#2659C211yesmaximal, characteristic
6C22×C4⋊Dic61C2211yescharacteristic
7C22×#11758196—21no—
8C2×#14519701—22no—
9C2×C22⋊#92418C2212yes—
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—
25C2×#11758196—42no—
26C2×#11758196—42no—
27C2×#11758196—42no—
28#14519701—44no—
29C22⋊#92418—22no—
30C22⋊#92418—22no—
31#14519684—21no—
32#14519684—42no—
33#14519684D412yes—
34C22×Q8×C61D412yes—
35C23×C4×C61D411yescharacteristic
36C23×C4×C61D411yescharacteristic
37C23×C4×C61C2311yescharacteristic
38C22⋊Q8×C61—22no—
39C22⋊Q8×C61—22no—
40C22⋊Q8×C61—22no—
41C22⋊Q8×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D412yes—
48C2×C22⋊C4×C61—22no—
49#95×C61—22no—
50#95×C61—22no—
51#95×C61—22no—
52C24×C61C2×D411yescharacteristic
53C2×Q8×C61—22no—
54C2×Q8×C61—22no—
55C2×Q8×C61—42no—
56C2×Q8×C61—42no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61SD1612yes—
70C22×C4×C61Q1612yes—
71C22×C4×C61C2×D412yes—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4112yes—
74C22×C4×C61#4111yescharacteristic
75C22×Dic61—22no—
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—22no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61—41no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—42no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—81no—
94C4⋊C4×C61—81no—
95C4⋊C4×C61—81no—
96C4⋊C4×C61—81no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—42no—
99C4⋊Dic61—24no—
100C4⋊Dic61—42no—
101#11758196—48no—
102C2×#92418—42no—
103C2×#92418—42no—
104C2×#92418—42no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61#12011yescharacteristic
110C23×C61#12111yescharacteristic
111C23×C61#12411yescharacteristic
112C23×C61C2×SD1611yescharacteristic
113C23×C61C2×Q1611yescharacteristic
114C23×C61#13711yescharacteristic
115C23×C61#13711yescharacteristic
116Q8×C61—44no—
117Q8×C61—82no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—41no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61#12112yes—
140C2×C4×C61#12312yes—
141C2×Dic61—24no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155#92418—82no—
156#10406—611nomaximal, Sylow
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—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#39411yescharacteristic
170C22×C61#44811yescharacteristic
171C22×C61#45111yescharacteristic
172C22×C61#45311yescharacteristic
173C22×C61#45611yescharacteristic
174C22×C61B(4,𝔽2)11yescharacteristic
175C22×C61#45811yescharacteristic
176C22×C61#46111yescharacteristic
177C22×C61#46211yescharacteristic
178C22×C61#48711yescharacteristic
179C22×C61#49111yescharacteristic
180C4×C61—22no—
181C4×C61—22no—
182C4×C61—42no—
183C4×C61—42no—
184C4×C61—82no—
185C4×C61—82no—
186Dic61—44no—
187Dic61—82no—
188#2659D6111yescharacteristic
189#1872—612no—
190C2×#328—612no—
191#1444—611no—
192#1280—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#159611yescharacteristic
198C2×C61#160511yescharacteristic
199C2×C61#161111yescharacteristic
200C2×C61#161411yescharacteristic
201C2×C61#203911yescharacteristic
202C2×C61#204311yescharacteristic
203C2×C61#204411yescharacteristic
204C2×C22⋊Q8C2×D6112yes—
205C22×C4⋊C4—611no—
206C22×C4⋊C4—1221no—
207C2×#103—1222no—
208C2×C22⋊C8—612no—
209#398—22no—
210#395—22no—
211#380—21no—
212#380—21no—
213C2×#95—611no—
214C2×#95—1221no—
215C2×#95C2×D6111yescharacteristic
216#340—1222no—
217#328—1224no—
218C61#1040611yescharacteristic, complemented, Sylow
219C22×Q8C22⋊D6112yes—
220C23×C4—1221no—
221C23×C4—1221no—
222C23×C4C22⋊D6111yescharacteristic
223C23×C4C22⋊D6111yescharacteristic
224C23×C4C22×D6111yescharacteristic
225C22×C8—1222no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229C22⋊Q8—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—1222no—
236C2×C4⋊C4—2442no—
237C2×C4⋊C4—2442no—
238C2×C4⋊C4—2442no—
239C2×C4⋊C4—2442no—
240C2×C4⋊C4C22⋊D6112yes—
241C2×C22⋊C4—22no—
242#103—2444no—
243C22⋊C8—1222no—
244C22⋊C8—1222no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95—612no—
249#95—1221no—
250#95—2442no—
251C24C2×C22⋊D6111yescharacteristic
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—42no—
255C2×Q8—42no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4#1175820112yes—
283C22×C4#1175820212yes—
284C22×C4D4×D6111yescharacteristic
285C22×C4#1175822412yes—
286C22×C4#1175822411yescharacteristic
287C22×C4C2×C22⋊D6112yes—
288C2×C8—2442no—
289C2×C8—2442no—
290C2×C8—2442no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—81no—
296C4⋊C4—81no—
297C4⋊C4—81no—
298C4⋊C4—81no—
299C4⋊C4—1224no—
300C4⋊C4—2442no—
301C4⋊C4—2448no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#1451974611yescharacteristic
309C23#1451974811yescharacteristic
310C23#1451976411yescharacteristic
311C23C2×#1175820111yescharacteristic
312C23C2×#1175820211yescharacteristic
313C23#1451980811yescharacteristic
314C23#1451980811yescharacteristic
315Q8—44no—
316Q8—82no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—1224no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4#1451974912yes—
353C2×C4#1451975812yes—
354C8—4882no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1683967611yescharacteristic
368C22#1683990111yescharacteristic
369C22#1683991811yescharacteristic
370C22#1683993011yescharacteristic
371C22#1683994511yescharacteristic
372C22#1683994911yescharacteristic
373C22#1683995211yescharacteristic
374C22#1683996411yescharacteristic
375C22#1683996911yescharacteristic
376C22#1684011211yescharacteristic
377C22#1684013011yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—82no—
383C4—82no—
384C4—4882no—
385C4—2444no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#2144474211yescharacteristic
391C2#2144479311yescharacteristic
392C2#2144482711yescharacteristic
393C2#2144484411yescharacteristic
394C2#2144704011yescharacteristic
395C2#2144706211yescharacteristic
396C2#2144706711yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2659C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#2659D61
hypocenterC61#10406
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
218. C61#10406semidirect

Maximal subgroups

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

subgroupindex
#214461272
C2×#168394992
#214440832
#214436622
C61×#26592
#1040661