Finite Group Databasebeta

← #29658291

Subgroups — #29658291

Order 15616.

864 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456967C211yesmaximal, characteristic, complemented
2#21456944C211yesmaximal, characteristic
3#21456201C211yesmaximal, characteristic, complemented
4#21444991C214yesmaximal, complemented
5#21444984C214yesmaximal, complemented
6#21444484C211yesmaximal, characteristic, complemented
7#21444240C211yesmaximal, characteristic, complemented
8#21444236C211yesmaximal, characteristic
9C61×#3550C211yesmaximal, characteristic
10C2×#14519777C2211yescharacteristic
11#16840165—21no—
12#16840158—21no—
13#16840132—22no—
14#16840114C2212yes—
15#16840114C2212yes—
16#16840112—21no—
17#16840108—21no—
18#16840095—22no—
19#16840078—22no—
20#16840057C2214yes—
21#16840052C2214yes—
22#16839815C2211yescharacteristic
23#16839815C2211yescharacteristic
24#16839770—22no—
25C4×#11758194C2211yescharacteristic
26#16839508C2212yes—
27#16839508C2212yes—
28Q8⋊#92418C2214yes—
29D4⋊#92418C2214yes—
30C61×#563—22no—
31C61×#559—21no—
32Q82×C61—21no—
33C61×#556—21no—
34C61×#556C2212yes—
35D4×Q8×C61—21no—
36D4×Q8×C61C2212yes—
37C61×#542—22no—
38C61×#542—22no—
39C61×#536—22no—
40C61×#533C2211yescharacteristic
41C61×#533C2211yescharacteristic
42C61×#532C2211yescharacteristic
43C22×Dic122—21no—
44C2×#11758194—21no—
45#14519777—21no—
46#14519777—21no—
47#14519777—21no—
48#14519777C2312yes—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51#14519710—24no—
52#14519708—24no—
53C4⋊#92418C2312yes—
54C4⋊#92418C2312yes—
55#14519701—24no—
56#14519700—24no—
57#14519700—24no—
58#14519698—24no—
59C22⋊#92418—21no—
60C22⋊#92418—21no—
61#14519688—21no—
62C4×#92418—21no—
63C4×#92418—21no—
64C4×#92418C2312yes—
65C2×#41×C61—21no—
66C22×Q8×C61—22no—
67C4⋊Q8×C61—24no—
68C4⋊Q8×C61—22no—
69C4⋊Q8×C61—22no—
70C4⋊Q8×C61D411yescharacteristic
71C4⋊Q8×C61D411yescharacteristic
72C4⋊Q8×C61D411yescharacteristic
73C4⋊Q8×C61C2311yescharacteristic
74C4⋊Q8×C61C2311yescharacteristic
75#127×C61D411yescharacteristic
76#126×C61—24no—
77#126×C61—24no—
78#125×C61—21no—
79#125×C61D412yes—
80#124×C61—24no—
81#124×C61—22no—
82#124×C61—22no—
83#124×C61—21no—
84#123×C61—24no—
85#123×C61—24no—
86C22⋊Q8×C61—24no—
87C22⋊Q8×C61—22no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61—22no—
92C22⋊Q8×C61—24no—
93C22⋊Q8×C61D412yes—
94#121×C61—21no—
95#121×C61D412yes—
96C4×Q8×C61—22no—
97C4×Q8×C61—22no—
98C4×Q8×C61—21no—
99C4×Q8×C61—21no—
100C4×Q8×C61—21no—
101C4×Q8×C61C2312yes—
102C4×D4×C61—22no—
103C4×D4×C61—22no—
104C4×D4×C61—21no—
105C4×D4×C61C2312yes—
106#117×C61—21no—
107#117×C61—22no—
108#117×C61D412yes—
109C2×C42×C61C2311yescharacteristic
110#41×C61—82no—
111C2×Q8×C61—24no—
112C2×Q8×C61—21no—
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C2×Q8×C61—21no—
116C2×Q8×C61—84no—
117C2×Q8×C61C2×D412yes—
118C2×D4×C61—22no—
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61C2×D412yes—
122C22×C4×C61—24no—
123C22×C4×C61—22no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×Dic61—41no—
128C2×Dic122—22no—
129C2×Dic122—44no—
130C2×Dic122—41no—
131C4⋊C4×C61—24no—
132C4⋊C4×C61—24no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—21no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61C2×D412yes—
144C4⋊C4×C61C2×D412yes—
145C4⋊C4×C61C2×D412yes—
146C4⋊C4×C61C2×D412yes—
147C22⋊C4×C61—24no—
148C22⋊C4×C61—24no—
149C22⋊C4×C61—24no—
150C22⋊C4×C61—22no—
151C22⋊C4×C61—22no—
152C22⋊C4×C61—22no—
153C22⋊C4×C61—22no—
154C42×C61—24no—
155C42×C61—22no—
156C42×C61—22no—
157C42×C61C2×D411yescharacteristic
158C42×C61C2×D411yescharacteristic
159C42×C61C2×D411yescharacteristic
160C42×C61C2411yescharacteristic
161C4⋊Dic61—22no—
162C4⋊Dic61—22no—
163C4⋊Dic61—41no—
164C4⋊Dic61—41no—
165#11758194—42no—
166C2×#92418—22no—
167C2×#92418—22no—
168C2×#92418—22no—
169C23×C61—22no—
170C23×C61#12011yescharacteristic
171Q8×C61—24no—
172Q8×C61—42no—
173Q8×C61—42no—
174Q8×C61—42no—
175Q8×C61—81no—
176Q8×C61—84no—
177D4×C61—24no—
178D4×C61—42no—
179D4×C61—81no—
180D4×C61—82no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—44no—
190C2×C4×C61—84no—
191C2×C4×C61#12011yescharacteristic
192C2×C4×C61#12011yescharacteristic
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C2×C4×C61C22×D411yescharacteristic
197C2×Dic61—42no—
198C2×Dic61—82no—
199Dic122—44no—
200Dic122—82no—
201#92418—42no—
202#92418—42no—
203#92418—42no—
204#18730—611nomaximal, Sylow
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—42no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61C2×#12011yescharacteristic
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—42no—
216C4×C61—42no—
217C4×C61—42no—
218C4×C61—42no—
219C4×C61—42no—
220C4×C61#45412yes—
221C4×C61#57712yes—
222C4×C61#57812yes—
223Dic61—82no—
224#3550D6111yescharacteristic
225#3230—611no—
226#3227—611no—
227#3139—611no—
228#1638—614no—
229#1637—614no—
230#1544—611no—
231#1485—611no—
232#1484—611no—
233C2×C61—41no—
234C2×C61—82no—
235C2×C61#300911yescharacteristic
236C2×C61#301111yescharacteristic
237C2×C61C2×#45411yescharacteristic
238#563—22no—
239#559—21no—
240Q82—21no—
241#556—21no—
242#556C2×D6112yes—
243D4×Q8—21no—
244D4×Q8C2×D6112yes—
245#542—22no—
246#542—22no—
247#536—22no—
248#533C2×D6111yescharacteristic
249#533C2×D6111yescharacteristic
250#532C2×D6111yescharacteristic
251C2×C4⋊Q8—611no—
252#500—1221no—
253#498—1221no—
254#491—1222no—
255#487—612no—
256#487—612no—
257#487—1221no—
258#486—1221no—
259#484—1222no—
260#481—1222no—
261#477—614no—
262#476—614no—
263#431—611no—
264#431—611no—
265#419—1222no—
266C4×M16—611no—
267#332—612no—
268#332—612no—
269Q8⋊C8—614no—
270D4⋊C8—614no—
271C61#1873011yescharacteristic, complemented, Sylow
272C2×#41—21no—
273C22×Q8—22no—
274C22×Q8—1221no—
275C2×M16—1221no—
276C4⋊Q8—24no—
277C4⋊Q8—22no—
278C4⋊Q8—22no—
279C4⋊Q8—612no—
280C4⋊Q8—1221no—
281C4⋊Q8—1221no—
282C4⋊Q8—1221no—
283C4⋊Q8C22⋊D6111yescharacteristic
284C4⋊Q8C22⋊D6111yescharacteristic
285C4⋊Q8C22⋊D6111yescharacteristic
286C4⋊Q8C22×D6111yescharacteristic
287C4⋊Q8C22×D6111yescharacteristic
288#127C22⋊D6111yescharacteristic
289#126—24no—
290#126—24no—
291#125—21no—
292#125C22⋊D6112yes—
293#124—24no—
294#124—22no—
295#124—22no—
296#124—21no—
297#123—24no—
298#123—24no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306C22⋊Q8C22⋊D6112yes—
307#121—21no—
308#121C22⋊D6112yes—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8C22×D6112yes—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—21no—
318C4×D4C22×D6112yes—
319#117—21no—
320#117—22no—
321#117C22⋊D6112yes—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C42C22×D6111yescharacteristic
325#107—1224no—
326#106—1224no—
327C4⋊C8—612no—
328C4⋊C8—612no—
329#103—1224no—
330#103—1224no—
331#103—1224no—
332#102—1224no—
333C22⋊C8—1221no—
334C22⋊C8—1221no—
335#97—1221no—
336C4×C8—612no—
337C4×C8—1221no—
338C4×C8—1221no—
339#41—82no—
340C2×Q8—24no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—84no—
346C2×Q8—1222no—
347C2×Q8—2444no—
348C2×Q8—2441no—
349C2×Q8C2×C22⋊D6112yes—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4C2×C22⋊D6112yes—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—2441no—
357C22×C4C2×C22⋊D6111yescharacteristic
358C22×C4C2×C22⋊D6111yescharacteristic
359C22×C4C2×C22⋊D6111yescharacteristic
360M16—2442no—
361C2×C8—1222no—
362C2×C8—1222no—
363C2×C8—1222no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—1222no—
377C4⋊C4—1222no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4C2×C22⋊D6112yes—
381C4⋊C4C2×C22⋊D6112yes—
382C4⋊C4C2×C22⋊D6112yes—
383C4⋊C4C2×C22⋊D6112yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C42—24no—
392C42—22no—
393C42—22no—
394C42C2×C22⋊D6111yescharacteristic
395C42C2×C22⋊D6111yescharacteristic
396C42C2×C22⋊D6111yescharacteristic
397C42C23×D6111yescharacteristic
398C23—22no—
399C23#1451974611yescharacteristic
400Q8—24no—
401Q8—42no—
402Q8—42no—
403Q8—42no—
404Q8—81no—
405Q8—84no—
406Q8—4882no—
407Q8—2444no—
408D4—24no—
409D4—42no—
410D4—81no—
411D4—82no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—44no—
421C2×C4—84no—
422C2×C4—4882no—
423C2×C4—2442no—
424C2×C4#1451974611yescharacteristic
425C2×C4#1451974611yescharacteristic
426C2×C4#1451974611yescharacteristic
427C2×C4C22×C22⋊D6111yescharacteristic
428C2×C4C22×C22⋊D6111yescharacteristic
429C2×C4C22×C22⋊D6111yescharacteristic
430C8—2442no—
431C8—2442no—
432C8—2442no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22C2×#1451974611yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—4882no—
449C4#1683993512yes—
450C4#1684057312yes—
451C4#1684057712yes—
452C2—41no—
453C2—82no—
454C2#2145509611yescharacteristic
455C2#2145511411yescharacteristic
456C2C2×#1683993511yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3550C2
socleC22×C61C2×#120
prime radicalC61×#532C22
hypercenter#3550D61
hypocenterC61#18730
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #21456967C2semidirect
3. #21456201C2semidirect
4. #21444991C2semidirect
5. #21444984C2semidirect
6. #21444484C2semidirect
7. #21444240C2semidirect
271. C61#18730semidirect

Maximal subgroups

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

subgroupindex
#214569672
#214569442
#214562012
#214449912
#214449842
#214444842
#214442402
#214442362
C61×#35502
#1873061