Finite Group Databasebeta

← #30601659

Subgroups — #30601659

Order 15616.

920 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 920 conjugacy classes of subgroups — too many to draw. Only its 126 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#21461675C211yesmaximal, characteristic, complemented
2#21461545C211yesmaximal, characteristic, complemented
3C2×#16840605C214yesmaximal, complemented
4C2×#16839665C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×C22⋊#92420C2212yes—
7C2×C22⋊#92420C2212yes—
8C2×#14519832—21no—
9#16840628—21no—
10#16840628—21no—
11#16840605—28no—
12C22×C4⋊Dic61C411yescharacteristic
13C22×C22⋊Dic61C412yes—
14C22×C22⋊Dic61C2212yes—
15C22×C4×Dic61C2211yescharacteristic
16#16839665—21no—
17#16839665—21no—
18#16839665—21no—
19#16839665—21no—
20C23×D4×C61C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23#14519844—42no—
24C22⋊#92420—22no—
25C22⋊#92420—24no—
26C22⋊#92420D414yescomplemented
27#14519832—42no—
28C23×Dic61C2×C411yescharacteristic
29C23×Dic61C2×C412yes—
30C23×Dic61C2311yescharacteristic
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—42no—
34C2×C22⋊Dic61—22no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—24no—
37C2×C22⋊Dic61—22no—
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61—24no—
40C2×C22⋊Dic61—44no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C25×C61C2×C412yes—
47C22×D4×C61—24no—
48C22×D4×C61—21no—
49C22×D4×C61—21no—
50C22×D4×C61—42no—
51C22×D4×C61—42no—
52C23×C4×C61C2×C411yescharacteristic
53C24×C61—22no—
54C24×C61—22no—
55C24×C61—24no—
56C24×C61—24no—
57C24×C61—42no—
58C24×C61—42no—
59C24×C61—42no—
60C24×C61—42no—
61C24×C61M1614yes—
62C24×C61C22×C411yescharacteristic
63C2×D4×C61—24no—
64C2×D4×C61—24no—
65C2×D4×C61—416no—
66C2×D4×C61—42no—
67C2×D4×C61—42no—
68C2×D4×C61—42no—
69C2×D4×C61—42no—
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×Dic61—22no—
76C22×Dic61—22no—
77C22×Dic61—22no—
78C22×Dic61—24no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—42no—
83C22×Dic61—42no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C2×D411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C22×Dic61C2×D412yes—
89C22×Dic61#4112yes—
90C2×#92420—24no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C22⋊Dic61—44no—
97C22⋊Dic61—44no—
98C22⋊Dic61—44no—
99C22⋊Dic61—42no—
100C22⋊Dic61—42no—
101C4⋊Dic61—42no—
102C4⋊Dic61—42no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—24no—
112C23×C61—28no—
113C23×C61—44no—
114C23×C61—44no—
115C23×C61—44no—
116C23×C61—44no—
117C23×C61—42no—
118C23×C61—42no—
119C23×C61—42no—
120C23×C61—42no—
121C23×C61—42no—
122C23×C61—42no—
123C23×C61—44no—
124C23×C61—84no—
125C23×C61—84no—
126C23×C61—84no—
127C23×C61—84no—
128C23×C61C2×C22⋊C411yescharacteristic
129C23×C61C4×D412yes—
130C23×C61C2×M1612yes—
131C23×C61#13112yes—
132D4×C61—48no—
133D4×C61—48no—
134C2×C4×C61—28no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61#9912yes—
140C2×C4×C61#10012yes—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—44no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—84no—
157C2×Dic61#10012yes—
158C2×Dic61#12112yes—
159C2×Dic61#12411yescharacteristic
160C2×Dic61#12711yescharacteristic
161#92420—44no—
162#92420—82no—
163#9653—611nomaximal, Sylow
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—22no—
170C22×C61—44no—
171C22×C61—44no—
172C22×C61—44no—
173C22×C61—88no—
174C22×C61—88no—
175C22×C61—82no—
176C22×C61—82no—
177C22×C61—82no—
178C22×C61—82no—
179C22×C61#39011yescharacteristic
180C22×C61#40711yescharacteristic
181C22×C61#40811yescharacteristic
182C22×C61C2×#9911yescharacteristic
183C22×C61#41011yescharacteristic
184C22×C61C2×#10011yescharacteristic
185C22×C61C2×#10011yescharacteristic
186C22×C61#43514yes—
187C4×C61—22no—
188C4×C61—22no—
189Dic61—22no—
190Dic61—21no—
191Dic61—21no—
192Dic61—22no—
193Dic61—41no—
194Dic61—82no—
195C2×#390—611no—
196#1797—611no—
197#1749—611no—
198C2×#323—614no—
199C2×C61—24no—
200C2×C61—84no—
201C2×C61#146211yescharacteristic
202C2×C61#146611yescharacteristic
203C2×C61#146911yescharacteristic
204C2×C61#147111yescharacteristic
205C2×C61#195511yescharacteristic
206C2×C61#196411yescharacteristic
207C2×C61#196511yescharacteristic
208C23×D4#692311yescharacteristic
209C22×C4⋊C4—611no—
210C22×C22⋊C4—612no—
211C22×C22⋊C4—612no—
212C22×C42—611no—
213C2×C4⋊C8—1221no—
214C2×C22⋊C8—612no—
215C2×C22⋊C8—612no—
216C2×#97—1221no—
217#390—1221no—
218#390—1221no—
219#390—1221no—
220#390—1221no—
221#336—1221no—
222#336—1221no—
223#323—1228no—
224C61#965311yescharacteristic, complemented, Sylow
225C25C2×#692312yes—
226C22×D4—24no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—42no—
230C22×D4—42no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—612no—
234C23×C4C2×#692311yescharacteristic
235C22×C8—1222no—
236C22×C8—1222no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—2442no—
240C2×C22⋊C4—1224no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1222no—
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—1224no—
246C2×C22⋊C4—2444no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—2442no—
252C4⋊C8—2442no—
253C22⋊C8—614no—
254C22⋊C8—1222no—
255C22⋊C8—1224no—
256#97—2442no—
257C24—22no—
258C24—22no—
259C24—24no—
260C24—24no—
261C24—42no—
262C24—42no—
263C24—42no—
264C24—42no—
265C24#1175821714yes—
266C24C22×#692311yescharacteristic
267C2×D4—24no—
268C2×D4—24no—
269C2×D4—416no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—42no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—612no—
281C22×C4—612no—
282C22×C4—611no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1224no—
286C22×C4—1222no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4C22⋊#692311yescharacteristic
293C22×C4C22⋊#692311yescharacteristic
294C2×C8—1224no—
295C2×C8—2442no—
296C2×C8—2442no—
297C2×C8—2442no—
298C2×C8—2442no—
299C2×C8—2442no—
300C4⋊C4—2442no—
301C4⋊C4—2442no—
302C22⋊C4—2444no—
303C22⋊C4—2442no—
304C22⋊C4—2442no—
305C22⋊C4—2444no—
306C22⋊C4—2444no—
307C42—1222no—
308C42—1222no—
309C42—2441no—
310C42—2441no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—24no—
316C23—28no—
317C23—44no—
318C23—44no—
319C23—44no—
320C23—44no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—44no—
328C23—84no—
329C23—84no—
330C23—84no—
331C23—84no—
332C23C2×C22⋊#692311yescharacteristic
333C23D4×#692312yes—
334C23C2×#1175821712yes—
335C23#1451986412yes—
336D4—48no—
337D4—48no—
338C2×C4—28no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—612no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—4884no—
357C2×C4—2442no—
358C2×C4—2442no—
359C2×C4—2444no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4#1451983512yes—
364C2×C4#1451983712yes—
365C8—4882no—
366C8—2444no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—44no—
374C22—44no—
375C22—44no—
376C22—88no—
377C22—88no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22#1684071411yescharacteristic
383C22#1684073211yescharacteristic
384C22#1684073611yescharacteristic
385C22C2×#1451983511yescharacteristic
386C22#1684074211yescharacteristic
387C22C2×#1451983711yescharacteristic
388C22D61⋊#10011yescharacteristic
389C22#1684079314yes—
390C4—22no—
391C4—22no—
392C4—1222no—
393C4—1221no—
394C4—1222no—
395C4—1221no—
396C4—4882no—
397C4—2441no—
398C2—24no—
399C2—84no—
400C2#2146106411yescharacteristic
401C2#2146107911yescharacteristic
402C2#2146108911yescharacteristic
403C2#2146109411yescharacteristic
404C2#2146194311yescharacteristic
405C2#2146195811yescharacteristic
406C2#2146196111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
Fitting, prime radicalC23×D4×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC23×D4#6923
hypocenterC61#9653
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #21461675C2semidirect
2. #21461545C2semidirect
3. C2×#16840605C2semidirect
26. C22⋊#92420D4semidirect
224. C61#9653semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214615452
C2×#168406052
C2×#168396652
#965361