Finite Group Databasebeta

← #30601655

Subgroups — #30601655

Order 15616.

704 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 118 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#21461673C211yesmaximal, characteristic, complemented
2#21461545C211yesmaximal, characteristic, complemented
3C2×#16840608C212yesmaximal, complemented
4C2×#16840605C212yesmaximal
5C2×#16839650C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420C2212yes—
8C2×C22⋊#92420C2212yes—
9C2×#14519832—21no—
10#16840628—21no—
11#16840628—21no—
12#16840608—24no—
13#16840605—24no—
14C22×#11758196C2211yescharacteristic
15C22×C22⋊Dic61C411yescharacteristic
16C22×C22⋊Dic61C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18#16839650—21no—
19#16839650—21no—
20#16839650—21no—
21#16839650—21no—
22C2×#14519684C411yescharacteristic
23C2×#14519684C411yescharacteristic
24C22×C22⋊C4×C61C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27C4⋊#92420—42no—
28C22⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31C22⋊#92420D414yes—
32#14519832—42no—
33C23×Dic61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61C2311yescharacteristic
37C2×#11758196—22no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—22no—
41C2×C22⋊Dic61—22no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—22no—
45C2×C22⋊Dic61—22no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—22no—
49C2×C4×Dic61—42no—
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C25×C61C2×C411yescharacteristic
59C23×C4×C61C2×C411yescharacteristic
60C23×C4×C61C2×C411yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61—42no—
64C24×C61—21no—
65C24×C61—21no—
66C24×C61—22no—
67C24×C61—22no—
68C24×C61—41no—
69C24×C61—41no—
70C24×C61—41no—
71C24×C61—41no—
72C24×C61M1612yes—
73C24×C61C22×C411yescharacteristic
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22⋊C411yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—22no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—22no—
89C22×Dic61—21no—
90C22×Dic61—22no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61M1612yes—
100C22×Dic61C2×D411yescharacteristic
101C22×Dic61C2×D411yescharacteristic
102C22×Dic61C2×D412yes—
103C22×Dic61#4112yes—
104C2×#92420—24no—
105C2×#92420—42no—
106C2×#92420—42no—
107C2×#92420—42no—
108C2×#92420—42no—
109C2×#92420—42no—
110C22⋊C4×C61—42no—
111C22⋊C4×C61—42no—
112C22⋊Dic61—24no—
113C22⋊Dic61—24no—
114C22⋊Dic61—42no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117#11758196—42no—
118#11758196—41no—
119#11758196—41no—
120C4×Dic61—22no—
121C4×Dic61—22no—
122C4×Dic61—41no—
123C4×Dic61—41no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—22no—
129C23×C61—24no—
130C23×C61—42no—
131C23×C61—42no—
132C23×C61—42no—
133C23×C61—42no—
134C23×C61—41no—
135C23×C61—41no—
136C23×C61—41no—
137C23×C61—41no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—42no—
141C23×C61—82no—
142C23×C61—82no—
143C23×C61—82no—
144C23×C61—82no—
145C23×C61C2×C22⋊C411yescharacteristic
146C23×C61C4×D412yes—
147C23×C61C2×M1611yescharacteristic
148C23×C61C2×M1611yescharacteristic
149C23×C61#13112yes—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—44no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—82no—
160C2×C4×C61#9912yes—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—22no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—24no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—42no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—82no—
184C2×Dic61#12112yes—
185C2×Dic61#12411yescharacteristic
186C2×Dic61#12711yescharacteristic
187#92420—44no—
188#92420—82no—
189#9652—611nomaximal, Sylow
190C22×C61—22no—
191C22×C61—22no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—42no—
199C22×C61—42no—
200C22×C61—42no—
201C22×C61—84no—
202C22×C61—84no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61#39011yescharacteristic
208C22×C61#40711yescharacteristic
209C22×C61#40811yescharacteristic
210C22×C61C2×#9911yescharacteristic
211C22×C61#41011yescharacteristic
212C22×C61#41311yescharacteristic
213C22×C61#41311yescharacteristic
214C22×C61#43512yes—
215C22×C61#43512yes—
216C4×C61—22no—
217C4×C61—41no—
218C4×C61—81no—
219Dic61—22no—
220Dic61—21no—
221Dic61—21no—
222Dic61—42no—
223Dic61—41no—
224Dic61—41no—
225Dic61—81no—
226C2×#388—611no—
227#1797—611no—
228#1749—611no—
229C2×#324—612no—
230C2×#323—612no—
231C2×C61—22no—
232C2×C61—22no—
233C2×C61—82no—
234C2×C61#146411yescharacteristic
235C2×C61#146511yescharacteristic
236C2×C61#146811yescharacteristic
237C2×C61#147311yescharacteristic
238C2×C61#195511yescharacteristic
239C2×C61#196411yescharacteristic
240C2×C61#196711yescharacteristic
241C22×C4⋊C4—611no—
242C22×C22⋊C4—611no—
243C22×C22⋊C4—611no—
244C22×C22⋊C4#692311yescharacteristic
245C22×C42—611no—
246C2×C4⋊C8—1221no—
247C2×C22⋊C8—612no—
248C2×C22⋊C8—612no—
249C2×#97—1221no—
250#388—1221no—
251#388—1221no—
252#388—1221no—
253#388—1221no—
254C2×#95—611no—
255C2×#95—611no—
256#336—1221no—
257#336—1221no—
258#324—1224no—
259#323—1224no—
260C61#965211yescharacteristic, complemented, Sylow
261C25C2×#692311yescharacteristic
262C23×C4—611no—
263C23×C4—611no—
264C23×C4—611no—
265C23×C4—611no—
266C23×C4C2×#692311yescharacteristic
267C23×C4C2×#692311yescharacteristic
268C22×C8—1222no—
269C22×C8—1222no—
270C2×C4⋊C4—1222no—
271C2×C4⋊C4—1221no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1222no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1222no—
280C2×C22⋊C4—1222no—
281C2×C22⋊C4—1222no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1222no—
285C2×C42—611no—
286C2×C42—611no—
287C2×C42—611no—
288C2×C42—611no—
289C2×C42—2442no—
290C4⋊C8—2442no—
291C22⋊C8—614no—
292C22⋊C8—1222no—
293C22⋊C8—1222no—
294C22⋊C8—1222no—
295#97—2442no—
296#95—1221no—
297#95—1221no—
298#95—1221no—
299#95—1221no—
300C24—21no—
301C24—21no—
302C24—22no—
303C24—22no—
304C24—41no—
305C24—41no—
306C24—41no—
307C24—41no—
308C24#1175821312yes—
309C24C22×#692311yescharacteristic
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—612no—
320C22×C4—612no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—612no—
324C22×C4—1221no—
325C22×C4—1222no—
326C22×C4—1221no—
327C22×C4—1221no—
328C22×C4—1221no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—1221no—
332C22×C4—2441no—
333C22×C4—2441no—
334C22×C4—2441no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4C22⋊#692311yescharacteristic
339C22×C4C22⋊#692311yescharacteristic
340C2×C8—1224no—
341C2×C8—2442no—
342C2×C8—2442no—
343C2×C8—2442no—
344C2×C8—2442no—
345C2×C8—2442no—
346C4⋊C4—2442no—
347C4⋊C4—2441no—
348C4⋊C4—2441no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—1224no—
352C22⋊C4—1224no—
353C22⋊C4—2442no—
354C22⋊C4—2441no—
355C22⋊C4—2441no—
356C42—1222no—
357C42—1222no—
358C42—2441no—
359C42—2441no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—22no—
365C23—24no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—82no—
378C23—82no—
379C23—82no—
380C23—82no—
381C23C2×C22⋊#692311yescharacteristic
382C23D4×#692312yes—
383C23D61⋊M1611yescharacteristic
384C23C2×#1175821311yescharacteristic
385C23#1451986412yes—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—44no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—82no—
396C2×C4—612no—
397C2×C4—611no—
398C2×C4—611no—
399C2×C4—1221no—
400C2×C4—1221no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1222no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1224no—
411C2×C4—4882no—
412C2×C4—2442no—
413C2×C4—2442no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2442no—
418C2×C4—2442no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2442no—
422C2×C4#1451983512yes—
423C8—4882no—
424C8—2444no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—84no—
437C22—84no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22#1684071411yescharacteristic
443C22#1684073311yescharacteristic
444C22#1684073511yescharacteristic
445C22C2×#1451983511yescharacteristic
446C22#1684074211yescharacteristic
447C22#1684074811yescharacteristic
448C22#1684074911yescharacteristic
449C22#1684079112yes—
450C22#1684079412yes—
451C4—22no—
452C4—41no—
453C4—81no—
454C4—1221no—
455C4—1222no—
456C4—1221no—
457C4—4881no—
458C4—2441no—
459C4—2441no—
460C4—2442no—
461C2—22no—
462C2—22no—
463C2—82no—
464C2#2146107111yescharacteristic
465C2#2146107411yescharacteristic
466C2#2146108411yescharacteristic
467C2#2146110111yescharacteristic
468C2#2146194411yescharacteristic
469C2#2146195811yescharacteristic
470C2#2146196311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#9652
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461673C2semidirect
2. #21461545C2semidirect
3. C2×#16840608C2semidirect
260. C61#9652semidirect

Maximal subgroups

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

subgroupindex
#214616732
#214615452
C2×#168406082
C2×#168406052
C2×#168396502
#965261