Finite Group Databasebeta

← #29580600

Subgroups — #29580600

Order 15616.

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

normal subgroups only

This group has 632 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
1C2×#16840097C211yesmaximal, characteristic
2#21451935C211yesmaximal, characteristic
3C2×#16839500C211yesmaximal, characteristic
4C2×#16839499C211yesmaximal, characteristic
5#21444087C211yesmaximal, characteristic
6#21443661C211yesmaximal, characteristic
7C2×C61×#484C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9#16840097—22no—
10#16840097—22no—
11C2×#14519710—21no—
12C2×#14519700—21no—
13C2×C22⋊#92418C2211yescharacteristic
14#16839693—21no—
15#16839692—21no—
16#16839682—21no—
17#16839681—21no—
18#16839620—22no—
19C2×#14519684—22no—
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2211yescharacteristic
22#16839500—22no—
23#16839499—22no—
24C2×C22⋊Q8×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C61×#484—22no—
27C61×#484—22no—
28C2×#107×C61—21no—
29C2×#103×C61—21no—
30C2×C22⋊C8×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C23×Dic61—21no—
33C23×Dic61D412yes—
34C22×#92418—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756—21no—
38#14519756—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—22no—
42C2×#11758196—22no—
43C2×C22⋊Dic61—21no—
44#14519710—24no—
45#14519700—24no—
46C22⋊#92418—21no—
47C22⋊#92418D412yes—
48#14519684—22no—
49#14519684—22no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—44no—
55C22×Q8×C61D411yescharacteristic
56C23×C4×C61—21no—
57C23×C4×C61C2311yescharacteristic
58C22×C8×C61—21no—
59C22⋊Q8×C61—21no—
60C22⋊Q8×C61—21no—
61C22⋊Q8×C61—21no—
62C22⋊Q8×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C4⋊C4×C61D412yes—
71C2×C22⋊C4×C61—21no—
72#107×C61—24no—
73#103×C61—24no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61D412yes—
76C24×C61C2×D411yescharacteristic
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61—42no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—22no—
83C22×C4×C61—42no—
84C22×C4×C61—42no—
85C22×C4×C61—42no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—42no—
100C22×Dic61—42no—
101C22×Dic61—41no—
102C22×Dic61—42no—
103C22×Dic61—41no—
104C22×Dic61—42no—
105C22×Dic61Q1614yes—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122—42no—
109C2×C8×C61—22no—
110C2×C8×C61—42no—
111C4⋊C4×C61—22no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—22no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊Dic61—41no—
122C22⋊Dic61—41no—
123C4⋊Dic61—21no—
124C4⋊Dic61—21no—
125#11758196—41no—
126#11758196—41no—
127#11758196—82no—
128#11758196—82no—
129C2×#92418—22no—
130C2×#92418—42no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—22no—
134C23×C61#12011yescharacteristic
135C23×C61#12111yescharacteristic
136C23×C61#12711yescharacteristic
137C23×C61C2×Q1612yes—
138C23×C61#13712yes—
139Q8×C61—42no—
140Q8×C61—81no—
141C2×C4×C61—22no—
142C2×C4×C61—22no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—44no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—82no—
155C2×C4×C61—81no—
156C2×C4×C61—81no—
157C2×C4×C61#12011yescharacteristic
158C2×C4×C61#12011yescharacteristic
159C2×C4×C61#12111yescharacteristic
160C2×C4×C61#12111yescharacteristic
161C2×Dic61—24no—
162C2×Dic61—42no—
163C2×Dic61—42no—
164C2×Dic61—44no—
165C2×Dic61—44no—
166C2×Dic61—42no—
167C2×Dic61—41no—
168C2×Dic61—41no—
169C2×Dic61—41no—
170C2×Dic61—41no—
171C2×Dic61—42no—
172C2×Dic61—82no—
173C2×Dic61—82no—
174C2×Dic61—81no—
175C2×Dic61—81no—
176Dic122—42no—
177Dic122—81no—
178C8×C61—42no—
179#92418—42no—
180#9972—611nomaximal, Sylow
181C22×C61—22no—
182C22×C61—22no—
183C22×C61—22no—
184C22×C61—22no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—21no—
188C22×C61—21no—
189C22×C61#39211yescharacteristic
190C22×C61#45112yes—
191C22×C61#45311yescharacteristic
192C22×C61#45411yescharacteristic
193C22×C61#45812yes—
194C22×C61#46212yes—
195C22×C61#49411yescharacteristic
196C22×C61#49711yescharacteristic
197C4×C61—21no—
198C4×C61—21no—
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—81no—
202C4×C61—82no—
203C4×C61—81no—
204Dic61—44no—
205Dic61—82no—
206Dic61—81no—
207Dic61—81no—
208C2×#484—611no—
209C2×#484D6111yescharacteristic
210#2659—611no—
211C2×#328—611no—
212C2×#328—611no—
213#1445—611no—
214#1280—611no—
215C2×C61—21no—
216C2×C61—22no—
217C2×C61—21no—
218C2×C61#161412yes—
219C2×C61#161712yes—
220C2×C61#200611yescharacteristic
221C2×C61#201611yescharacteristic
222C2×C61#202211yescharacteristic
223C2×C22⋊Q8—611no—
224C2×C22⋊Q8C2×D6111yescharacteristic
225C22×C4⋊C4C2×D6111yescharacteristic
226#484—22no—
227#484—22no—
228#484—1222no—
229#484—1222no—
230C2×#107—21no—
231C2×#107—1221no—
232C2×#103—21no—
233C2×#103—1221no—
234C2×C22⋊C8—611no—
235C2×C22⋊C8C2×D6111yescharacteristic
236#398—1221no—
237#398—1221no—
238#395—1221no—
239#395—1221no—
240#380—1222no—
241C2×#95—611no—
242C2×#95—611no—
243C2×#95—1222no—
244#328—1222no—
245#328—1222no—
246C61#997211yescharacteristic, complemented, Sylow
247C22×Q8—611no—
248C22×Q8C22⋊D6111yescharacteristic
249C23×C4—21no—
250C23×C4—612no—
251C23×C4—1221no—
252C23×C4C22×D6111yescharacteristic
253C22×C8—21no—
254C22×C8—1221no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—1221no—
260C22⋊Q8—1221no—
261C22⋊Q8—1221no—
262C22⋊Q8—1221no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—1222no—
271C2×C4⋊C4—1222no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4C22⋊D6112yes—
274C2×C4⋊C4C22⋊D6111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—1221no—
277#107—24no—
278#107—1224no—
279#103—24no—
280#103—1224no—
281C22⋊C8—21no—
282C22⋊C8—612no—
283C22⋊C8—1221no—
284C22⋊C8C22⋊D6112yes—
285#95—1222no—
286#95—1222no—
287#95—1221no—
288#95—1221no—
289#95—1221no—
290#95—1221no—
291#95—2444no—
292C24D4×D6111yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C2×Q8—1221no—
297C2×Q8—1221no—
298C2×Q8—2442no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—614no—
308C22×C4—1222no—
309C22×C4—1222no—
310C22×C4—1222no—
311C22×C4—1221no—
312C22×C4—1221no—
313C22×C4—2442no—
314C22×C4—2441no—
315C22×C4—2442no—
316C22×C4—2441no—
317C22×C4—2442no—
318C22×C4—2442no—
319C22×C4D4×D6111yescharacteristic
320C22×C4D4×D6111yescharacteristic
321C22×C4#1175822411yescharacteristic
322C22×C4C2×C22⋊D6111yescharacteristic
323C22×C4C2×C22⋊D6111yescharacteristic
324C22×C4C2×C22⋊D6111yescharacteristic
325C2×C8—22no—
326C2×C8—42no—
327C2×C8—1222no—
328C2×C8—2442no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—1221no—
338C4⋊C4—1221no—
339C4⋊C4—4882no—
340C4⋊C4—4882no—
341C4⋊C4—2441no—
342C4⋊C4—2441no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C23—22no—
348C23—21no—
349C23—21no—
350C23#1451974511yescharacteristic
351C23#1451974911yescharacteristic
352C23#1451977311yescharacteristic
353C23Q16×D6112yes—
354C23#1451980912yes—
355Q8—42no—
356Q8—81no—
357Q8—4881no—
358Q8—2442no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—44no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—1224no—
376C2×C4—4881no—
377C2×C4—4882no—
378C2×C4—4881no—
379C2×C4—4882no—
380C2×C4—2442no—
381C2×C4—2444no—
382C2×C4—2442no—
383C2×C4—2441no—
384C2×C4—2441no—
385C2×C4—2441no—
386C2×C4—2441no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2444no—
390C2×C4#1451974511yescharacteristic
391C2×C4#1451974611yescharacteristic
392C2×C4#1451974811yescharacteristic
393C2×C4#1451974911yescharacteristic
394C8—42no—
395C8—2442no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22#1683967011yescharacteristic
405C22#1683991612yes—
406C22#1683992811yescharacteristic
407C22#1683993311yescharacteristic
408C22#1683995112yes—
409C22#1683997012yes—
410C22#1684014011yescharacteristic
411C22#1684015511yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—81no—
417C4—81no—
418C4—82no—
419C4—4882no—
420C4—4881no—
421C4—4881no—
422C4—2444no—
423C2—21no—
424C2—22no—
425C2—21no—
426C2#2144484212yes—
427C2#2144485912yes—
428C2#2144685911yescharacteristic
429C2#2144691711yescharacteristic
430C2#2144694711yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#484C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#484D61
hypocenterC61#9972
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
246. C61#9972semidirect

Maximal subgroups

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

subgroupindex
C2×#168400972
#214519352
C2×#168395002
C2×#168394992
#214440872
#214436612
C2×C61×#4842
#997261