Finite Group Databasebeta

← #30597470

Subgroups — #30597470

Order 15616.

710 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 136 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#21461545C211yesmaximal, characteristic, complemented
2C4×C22⋊#92420C211yesmaximal, characteristic, complemented
3C2×#16840605C212yesmaximal
4#21460657C212yesmaximal, complemented
5C2×#16839650C211yesmaximal, characteristic
6C2×C22⋊#92420C2212yes—
7C2×C22⋊#92420C2212yes—
8C2×#14519832—21no—
9C2×C4×#92420—21no—
10#16840628—21no—
11#16840628—21no—
12#16840605C418yescomplemented
13C22×#11758196C411yescharacteristic
14C22×C22⋊Dic61C411yescharacteristic
15C22×C22⋊Dic61C2211yescharacteristic
16C22×C4×Dic61C2211yescharacteristic
17#16839650—21no—
18#16839650—21no—
19#16839650—21no—
20#16839650—21no—
21C2×#14519684C411yescharacteristic
22C2×#14519684C2211yescharacteristic
23C22×C22⋊C4×C61C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—22no—
28C22⋊#92420C2×C414yes—
29C22⋊#92420C2×C414yes—
30#14519832—42no—
31C4×#92420—42no—
32C23×Dic61C2×C411yescharacteristic
33C23×Dic61C2×C411yescharacteristic
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2311yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—42no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—22no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—42no—
45C2×C22⋊Dic61C2×C414yes—
46C2×C4×Dic61—42no—
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C25×C61C2×C411yescharacteristic
56C23×C4×C61C2×C411yescharacteristic
57C23×C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—42no—
61C24×C61—21no—
62C24×C61—21no—
63C24×C61—22no—
64C24×C61—22no—
65C24×C61—41no—
66C24×C61—41no—
67C24×C61—41no—
68C24×C61—41no—
69C24×C61C4212yes—
70C24×C61C22×C411yescharacteristic
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—21no—
74C22×C4×C61—22no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22⋊C411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—22no—
84C22×Dic61—21no—
85C22×Dic61—22no—
86C22×Dic61—41no—
87C22×Dic61—41no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61C4212yes—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22×C412yes—
97C22×Dic61C2×D411yescharacteristic
98C22×Dic61C2×D411yescharacteristic
99C22×Dic61#4112yes—
100C2×#92420—24no—
101C2×#92420—24no—
102C2×#92420—42no—
103C2×#92420—42no—
104C2×#92420—42no—
105C2×#92420—42no—
106C22⋊C4×C61—42no—
107C22⋊C4×C61—42no—
108C22⋊Dic61—24no—
109C22⋊Dic61—24no—
110C22⋊Dic61—42no—
111C22⋊Dic61—42no—
112#11758196—42no—
113#11758196—42no—
114C4×Dic61—22no—
115C4×Dic61—22no—
116C4×Dic61—41no—
117C4×Dic61—41no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—22no—
123C23×C61—24no—
124C23×C61—42no—
125C23×C61—42no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61—41no—
131C23×C61—41no—
132C23×C61—41no—
133C23×C61—41no—
134C23×C61—42no—
135C23×C61—82no—
136C23×C61—82no—
137C23×C61—82no—
138C23×C61—82no—
139C23×C61C2×C4211yescharacteristic
140C23×C61C2×C22⋊C411yescharacteristic
141C23×C61#11711yescharacteristic
142C23×C61#13112yes—
143C23×C61#13112yes—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—44no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—82no—
154C2×C4×C61#9912yes—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—22no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—42no—
166C2×Dic61—42no—
167C2×Dic61—44no—
168C2×Dic61—42no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—82no—
176C2×Dic61#10012yes—
177C2×Dic61C4×D412yes—
178C2×Dic61C4×D412yes—
179#92420—44no—
180#92420—44no—
181#8155—611nomaximal, Sylow
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—21no—
190C22×C61—42no—
191C22×C61—42no—
192C22×C61—42no—
193C22×C61—84no—
194C22×C61—84no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61—81no—
198C22×C61—81no—
199C22×C61C4×C22⋊C411yescharacteristic
200C22×C61#40512yes—
201C22×C61#40811yescharacteristic
202C22×C61#40811yescharacteristic
203C22×C61C2×#9911yescharacteristic
204C22×C61#41011yescharacteristic
205C22×C61C2×#10011yescharacteristic
206C22×C61#41311yescharacteristic
207C22×C61#43312yes—
208C4×C61—22no—
209C4×C61—41no—
210C4×C61—81no—
211Dic61—22no—
212Dic61—22no—
213Dic61—22no—
214Dic61—41no—
215Dic61—42no—
216Dic61—81no—
217C2×#388—611no—
218#1749—611no—
219C4×C22⋊C8—611no—
220C2×#323—612no—
221#1280—612no—
222C2×C61—22no—
223C2×C61—22no—
224C2×C61—82no—
225C2×C61#146811yescharacteristic
226C2×C61#146911yescharacteristic
227C2×C61#147111yescharacteristic
228C2×C61#147311yescharacteristic
229C2×C61#175011yescharacteristic
230C2×C61C4×#9911yescharacteristic
231C2×C61C4×#10011yescharacteristic
232C22×C4⋊C4—611no—
233C22×C22⋊C4—611no—
234C22×C22⋊C4—611no—
235C22×C22⋊C4#692311yescharacteristic
236C22×C42—611no—
237C2×C22⋊C8—612no—
238C2×C22⋊C8—612no—
239C2×#97—1221no—
240C2×C4×C8—1221no—
241#388—1221no—
242#388—1221no—
243#388—1221no—
244#388—1221no—
245C2×#95—611no—
246C2×#95—611no—
247#336—1221no—
248#336—1221no—
249#323—618no—
250C61#815511yescharacteristic, complemented, Sylow
251C25C2×#692311yescharacteristic
252C23×C4—611no—
253C23×C4—611no—
254C23×C4—611no—
255C23×C4—611no—
256C23×C4C2×#692311yescharacteristic
257C23×C4C2×#692311yescharacteristic
258C22×C8—1222no—
259C22×C8—1222no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—2442no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—42no—
266C2×C22⋊C4—614no—
267C2×C22⋊C4—1221no—
268C2×C22⋊C4—1221no—
269C2×C22⋊C4—1222no—
270C2×C22⋊C4—1221no—
271C2×C22⋊C4—1221no—
272C2×C22⋊C4—2442no—
273C2×C42—611no—
274C2×C42—611no—
275C2×C42—611no—
276C2×C42—611no—
277C2×C42—2442no—
278C22⋊C8—614no—
279C22⋊C8—614no—
280C22⋊C8—1222no—
281C22⋊C8—1222no—
282#97—2442no—
283C4×C8—2442no—
284#95—1221no—
285#95—1221no—
286#95—1221no—
287#95—1221no—
288C24—21no—
289C24—21no—
290C24—22no—
291C24—22no—
292C24—41no—
293C24—41no—
294C24—41no—
295C24—41no—
296C24C4×#692312yes—
297C24C22×#692311yescharacteristic
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—611no—
306C22×C4—611no—
307C22×C4—611no—
308C22×C4—612no—
309C22×C4—612no—
310C22×C4—611no—
311C22×C4—612no—
312C22×C4—1222no—
313C22×C4—1221no—
314C22×C4—1221no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1221no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4—2441no—
325C22×C4C22⋊#692311yescharacteristic
326C22×C4C22⋊#692311yescharacteristic
327C2×C8—1224no—
328C2×C8—1224no—
329C2×C8—2442no—
330C2×C8—2442no—
331C2×C8—2442no—
332C2×C8—2442no—
333C4⋊C4—2442no—
334C4⋊C4—2442no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—1224no—
338C22⋊C4—1224no—
339C22⋊C4—2442no—
340C22⋊C4—2442no—
341C42—1222no—
342C42—1222no—
343C42—2441no—
344C42—2441no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—22no—
350C23—24no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—82no—
363C23—82no—
364C23—82no—
365C23—82no—
366C23C2×C4×#692311yescharacteristic
367C23C2×C22⋊#692311yescharacteristic
368C23#1451985611yescharacteristic
369C23#1451986412yes—
370C23#1451986412yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—44no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—82no—
381C2×C4—612no—
382C2×C4—612no—
383C2×C4—612no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1222no—
394C2×C4—4882no—
395C2×C4—2442no—
396C2×C4—2442no—
397C2×C4—2444no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2441no—
401C2×C4—2442no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2442no—
405C2×C4#1451983512yes—
406C8—2444no—
407C8—2444no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—84no—
420C22—84no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22C4×C22⋊#692311yescharacteristic
426C22#1684072612yes—
427C22#1684073511yescharacteristic
428C22#1684073611yescharacteristic
429C22C2×#1451983511yescharacteristic
430C22#1684074111yescharacteristic
431C22D61⋊#10011yescharacteristic
432C22#1684074911yescharacteristic
433C22#1684078612yes—
434C4—22no—
435C4—41no—
436C4—81no—
437C4—1222no—
438C4—1222no—
439C4—1222no—
440C4—4881no—
441C4—2442no—
442C4—2441no—
443C2—22no—
444C2—22no—
445C2—82no—
446C2#2146108411yescharacteristic
447C2#2146108811yescharacteristic
448C2#2146109411yescharacteristic
449C2#2146110011yescharacteristic
450C2#2146154911yescharacteristic
451C2C4×#1451983511yescharacteristic
452C2#2146156911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenterC22×C22⋊C4#6923
hypocenterC61#8155
LCSG ▷ C23×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. #21461545C2semidirect
2. C4×C22⋊#92420C2semidirect
4. #21460657C2semidirect
12. #16840605C4semidirect
250. C61#8155semidirect

Maximal subgroups

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

subgroupindex
#214615452
C4×C22⋊#924202
C2×#168406052
#214606572
C2×#168396502
#815561