Finite Group Databasebeta

← #29576440

Subgroups — #29576440

Order 15616.

552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#16840093C211yesmaximal, characteristic
2#21448690C211yesmaximal, characteristic
3#21446803C211yesmaximal, characteristic
4#21445903C211yesmaximal, characteristic
5#21444390C211yesmaximal, characteristic
6#21443666C211yesmaximal, characteristic
7C61×#1289C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C2×#14519733—21no—
10C22×C4⋊Dic61C2211yescharacteristic
11#16840093—22no—
12#16840093—21no—
13#16840093—21no—
14C2×#14519709C412yescomplemented
15C2×#14519702C412yescomplemented
16C2×C22⋊#92418C2211yescharacteristic
17#16839658—21no—
18#16839645—22no—
19#16839623—21no—
20C4⋊C4×Dic61—21no—
21C4×C22⋊Dic61C2211yescharacteristic
22#16839528—21no—
23#16839528—21no—
24#16839524—22no—
25#16839498—22no—
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#380C2211yescharacteristic
29C22×Dic122C2×C411yescharacteristic
30C23×Dic61—21no—
31C22×#92418—21no—
32#14519756—21no—
33#14519756—21no—
34#14519756—21no—
35#14519756—21no—
36#14519733—42no—
37#14519733—42no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61C2×C412yes—
43C2×C4⋊Dic61D412yes—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—22no—
47C2×#11758196—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61D411yescharacteristic
50C2×C22⋊Dic61D411yescharacteristic
51C2×C4×Dic61—22no—
52C2×C4×Dic61—21no—
53#14519709—22no—
54#14519709—22no—
55#14519702—22no—
56#14519702—22no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59#14519684—22no—
60#14519684—22no—
61#14519684—21no—
62C23×C4×C61C2311yescharacteristic
63C22×C8×C61C2×C412yes—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70#95×C61—21no—
71#95×C61D412yes—
72C24×C61C2×D411yescharacteristic
73C22×C4×C61—22no—
74C22×C4×C61—42no—
75C22×C4×C61—41no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C22×Dic61—22no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—41no—
91C22×Dic61—41no—
92C22×Dic61—41no—
93C22×Dic61—41no—
94C2×Dic122—21no—
95C2×Dic122—21no—
96C2×Dic122—42no—
97C2×C8×C61—22no—
98C2×C8×C61—42no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61—42no—
101C22⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C22⋊C4×C61—41no—
105C22⋊Dic61—21no—
106C22⋊Dic61—21no—
107C22⋊Dic61—21no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110C22⋊Dic61SD1612yes—
111C4⋊Dic61—22no—
112C4⋊Dic61—22no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61C22⋊C412yes—
118C4⋊Dic61C22⋊C412yes—
119#11758196—44no—
120#11758196—41no—
121#11758196—41no—
122C4×Dic61—44no—
123C4×Dic61—42no—
124C2×#92418—42no—
125C2×#92418—41no—
126C23×C61—41no—
127C23×C61—41no—
128C23×C61C4×D411yescharacteristic
129C23×C61#12011yescharacteristic
130C23×C61#12111yescharacteristic
131C23×C61C2×SD1611yescharacteristic
132C23×C61#13511yescharacteristic
133C23×C61AGL(1,ℤ/8)11yescharacteristic
134C23×C61#13711yescharacteristic
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—81no—
145C2×C4×C61—81no—
146C2×C4×C61—81no—
147C2×C4×C61C2×C22⋊C411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12311yescharacteristic
151C2×Dic61—22no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—41no—
165C2×Dic61—41no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—81no—
170C2×Dic61—81no—
171Dic122—42no—
172Dic122—81no—
173C8×C61—42no—
174#92418—81no—
175#9256—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61#38611yescharacteristic
187C22×C61C4×SD1611yescharacteristic
188C22×C61#44011yescharacteristic
189C22×C61#45011yescharacteristic
190C22×C61#45211yescharacteristic
191C22×C61#46111yescharacteristic
192C22×C61#46311yescharacteristic
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—21no—
196C4×C61—82no—
197C4×C61—161no—
198C4×C61#41012yes—
199Dic61—42no—
200Dic61—42no—
201Dic61—42no—
202Dic61—81no—
203Dic61—81no—
204Dic61—81no—
205C2×#483—611no—
206#2344—611no—
207#1996—611no—
208#1823—611no—
209#1520—611no—
210#1289D6111yescharacteristic
211#1282—611no—
212C2×C61—21no—
213C2×C61—21no—
214C2×C61—21no—
215C2×C61—21no—
216C2×C61—21no—
217C2×C61—21no—
218C2×C61#187711yescharacteristic
219C2×C61#189911yescharacteristic
220C2×C61#190511yescharacteristic
221C2×C22⋊Q8—611no—
222C2×#117—1221no—
223C22×C4⋊C4—611no—
224#483—1222no—
225#483—1221no—
226#483—1221no—
227C2×#106—612no—
228C2×#103—612no—
229C2×C22⋊C8—611no—
230C2×C22⋊C8C2×D6111yescharacteristic
231#389—1221no—
232#387—1222no—
233#381—1221no—
234#380C2×D6111yescharacteristic
235#380C2×D6111yescharacteristic
236C4×C4⋊C4—1221no—
237C4×C22⋊C4—611no—
238#342—1221no—
239#342—1221no—
240#340—1222no—
241#328—1222no—
242C61#925611yescharacteristic, complemented, Sylow
243C22×Q8—611no—
244C23×C4—1221no—
245C23×C4C22×D6111yescharacteristic
246C22×C8—1221no—
247C22×C8C4×D6112yes—
248C22⋊Q8—1221no—
249C22⋊Q8—1221no—
250C22⋊Q8—1221no—
251C22⋊Q8—1221no—
252#117—2442no—
253#117—2442no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—612no—
257C2×C4⋊C4—612no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—1221no—
262C2×C4⋊C4—1221no—
263C2×C4⋊C4—1221no—
264C2×C4⋊C4—1222no—
265C2×C4⋊C4—1221no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—1221no—
271C2×C42—1222no—
272C2×C42—1221no—
273#106—1222no—
274#106—1222no—
275#103—1222no—
276#103—1222no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—1221no—
280C22⋊C8—1221no—
281#95—21no—
282#95—1222no—
283#95—1222no—
284#95—1221no—
285#95D24412yes—
286C24D4×D6111yescharacteristic
287C2×Q8—1221no—
288C2×Q8—1221no—
289C2×Q8—2442no—
290C22×C4—22no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—1222no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1222no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—2441no—
302C22×C4—2441no—
303C22×C4—2441no—
304C22×C4—2441no—
305C22×C4C2×C4×D6111yescharacteristic
306C22×C4C2×D24411yescharacteristic
307C22×C4#1175822211yescharacteristic
308C22×C4D4×D6111yescharacteristic
309C22×C4D4×D6111yescharacteristic
310C22×C4#1175822611yescharacteristic
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—2442no—
314C2×C8—2441no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—612no—
318C4⋊C4—612no—
319C4⋊C4—1222no—
320C4⋊C4—1222no—
321C4⋊C4—1221no—
322C4⋊C4—1221no—
323C4⋊C4—1221no—
324C4⋊C4—1221no—
325C4⋊C4—2444no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—612no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—2441no—
337C22⋊C4—2441no—
338C42—2442no—
339C42—2444no—
340C23—41no—
341C23—41no—
342C23#1451973911yescharacteristic
343C23#1451974711yescharacteristic
344C23#1451975011yescharacteristic
345C23SD16×D6111yescharacteristic
346C23#1451979811yescharacteristic
347C23#1451980111yescharacteristic
348C23#1451980911yescharacteristic
349Q8—4881no—
350Q8—2442no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—1222no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—4881no—
367C2×C4—4881no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4—2441no—
375C2×C4—2442no—
376C2×C4—2442no—
377C2×C4—2442no—
378C2×C4—2442no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4C22⋊C4×D6111yescharacteristic
384C2×C4C4×D24411yescharacteristic
385C2×C4#1451975211yescharacteristic
386C2×C4#1451976211yescharacteristic
387C8—42no—
388C8—4881no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22#1683964011yescharacteristic
400C22#1683984911yescharacteristic
401C22#1683986111yescharacteristic
402C22#1683991411yescharacteristic
403C22#1683992711yescharacteristic
404C22#1683996611yescharacteristic
405C22#1683997611yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—82no—
410C4—161no—
411C4—4881no—
412C4—4881no—
413C4—4881no—
414C4—2442no—
415C4—2442no—
416C4—2442no—
417C4#1683973412yes—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—21no—
424C2#2144615411yescharacteristic
425C2#2144627611yescharacteristic
426C2#2144631411yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1289C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1289D61
hypocenterC61#9256
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
14. C2×#14519709C4semidirect
15. C2×#14519702C4semidirect
242. C61#9256semidirect

Maximal subgroups

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

subgroupindex
C2×#168400932
#214486902
#214468032
#214459032
#214443902
#214436662
C61×#12892
#925661