Finite Group Databasebeta

← #29580661

Subgroups — #29580661

Order 15616.

602 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 81 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#21455759C211yesmaximal, characteristic, complemented
2#21453841C211yesmaximal, characteristic
3#21445896C211yesmaximal, characteristic, complemented
4#21444349C211yesmaximal, characteristic, complemented
5#21444348C211yesmaximal, characteristic, complemented
6#21443728C211yesmaximal, characteristic, complemented
7C61×#3094C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9#16840086—22no—
10#16840080—21no—
11#16840075—21no—
12#16839805—21no—
13#16839766—21no—
14#16839726C2211yescharacteristic
15#16839688—21no—
16#16839687—21no—
17#16839671—21no—
18#16839670—22no—
19#16839670—21no—
20#16839625C2211yescharacteristic
21#16839625C2211yescharacteristic
22#16839529—22no—
23#16839497—22no—
24#16839496—22no—
25C2×#121×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#482—22no—
28C61×#481—21no—
29C61×#480—21no—
30C61×#428—21no—
31C61×#418—21no—
32C61×#407C2211yescharacteristic
33C22×D244D411yescharacteristic
34C22×C22⋊D61—21no—
35C22×C22⋊D61—22no—
36C2×#11758194—21no—
37#14519751—21no—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—22no—
44C2×C22⋊Dic61D412yes—
45C2×#11758198—21no—
46C2×#11758198—22no—
47#14519710—22no—
48#14519708—22no—
49#14519697—22no—
50#14519697—22no—
51C22⋊#92418—21no—
52C22⋊#92418D412yescomplemented
53#14519684—22no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58C22×D4×C61—21no—
59C22×D4×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C2×M16×C61—21no—
62#121×C61—21no—
63#121×C61—21no—
64#121×C61—21no—
65#121×C61—21no—
66#117×C61—21no—
67#117×C61—21no—
68#117×C61—21no—
69#117×C61—21no—
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C4⋊C4×C61D411yescharacteristic, complemented
72C2×C4⋊C4×C61D411yescharacteristic, complemented
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C42×C61—21no—
76#107×C61—22no—
77#106×C61—22no—
78#102×C61—22no—
79#102×C61—22no—
80C22⋊C8×C61—21no—
81C22⋊C8×C61D412yescomplemented
82C24×C61—21no—
83C24×C61C2×D411yescharacteristic
84C23×D61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61—42no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—82no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—42no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—82no—
104C2×C22⋊D61—82no—
105C2×C22⋊D61—82no—
106C2×C22⋊D61—82no—
107C22×Dic61—22no—
108C22×Dic61—21no—
109C22×Dic61—41no—
110C2×D244—21no—
111C2×D244—21no—
112C2×D244—42no—
113M16×C61—42no—
114C2×C8×C61—22no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—21no—
117C4⋊C4×C61—21no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C42×C61—41no—
126C42×C61—41no—
127C22⋊Dic61—42no—
128C22⋊Dic61—42no—
129C22⋊Dic61—82no—
130#11758198—41no—
131#11758198—41no—
132#11758198—82no—
133C4⋊Dic61—21no—
134C4⋊Dic61—21no—
135#11758194—42no—
136C2×#92418—22no—
137C23×C61—22no—
138C23×C61—41no—
139C23×C61—41no—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—42no—
143C23×C61—41no—
144C23×C61—42no—
145C23×C61#12011yescharacteristic
146C23×C61#12111yescharacteristic
147C23×C61#12711yescharacteristic
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—42no—
151C22×D61—41no—
152C22×D61—42no—
153D4×C61—42no—
154D4×C61—81no—
155D4×C61—82no—
156D4×C61—82no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—42no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—81no—
168C2×C4×C61—81no—
169C2×C4×C61#12011yescharacteristic
170C2×C4×C61#12011yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C22⋊D61—82no—
174C22⋊D61—82no—
175C22⋊D61—88no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—41no—
180C2×Dic61—42no—
181C2×Dic61—81no—
182C2×Dic61—81no—
183C2×Dic61—81no—
184D244—42no—
185D244—81no—
186C8×C61—42no—
187#92418—42no—
188#9983—611nomaximal, Sylow
189C22×C61—21no—
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—82no—
198C22×C61—82no—
199C22×C61—82no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61—81no—
203C22×C61#39211yescharacteristic
204C22×C61#45812yes—
205C2×D61—82no—
206C2×D61—82no—
207C2×D61—81no—
208C2×D61—81no—
209C2×D61—81no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—81no—
215C4×C61—81no—
216C4×C61—81no—
217Dic61—82no—
218Dic61—81no—
219Dic61—161no—
220#3094—611no—
221#3094D6111yescharacteristic, complemented
222#2815—611no—
223#1820—611no—
224#1510—611no—
225#1510—611no—
226#1306—611no—
227C2×C61—22no—
228C2×C61—41no—
229C2×C61—41no—
230C2×C61—161no—
231C2×C61#200811yescharacteristic
232C2×C61#200811yescharacteristic
233C2×C61#202211yescharacteristic
234D61—161no—
235C2×#121—611no—
236C2×#121C2×D6111yescharacteristic
237C2×#117C2×D6111yescharacteristic
238#482—22no—
239#482—1222no—
240#481—21no—
241#481—1221no—
242#480—21no—
243#480—1221no—
244#428—21no—
245#428—1221no—
246#418—21no—
247#418—1221no—
248#407—611no—
249#407C2×D6111yescharacteristic
250#397—1221no—
251#397—1221no—
252#392—1221no—
253#392—1222no—
254#392—1221no—
255#381—611no—
256#381—611no—
257#342—1222no—
258#327—1222no—
259#327—1222no—
260C61#998311yescharacteristic, complemented, Sylow
261C22×D4—21no—
262C22×D4—611no—
263C22×D4—1222no—
264C22×D4—1221no—
265C22×D4C22⋊D6111yescharacteristic
266C23×C4C22×D6111yescharacteristic
267C2×M16—21no—
268C2×M16—1221no—
269#121—21no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—1221no—
274#121—1221no—
275#121—1221no—
276#121—1221no—
277#117—21no—
278#117—21no—
279#117—21no—
280#117—21no—
281C2×C4⋊C4—611no—
282C2×C4⋊C4C22⋊D6111yescharacteristic
283C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
284C2×C4⋊C4C22⋊D6111yescharacteristic, complemented
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—612no—
288C2×C22⋊C4—1222no—
289C2×C22⋊C4—1222no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C42—21no—
293#107—22no—
294#107—1222no—
295#106—22no—
296#106—1222no—
297#102—22no—
298#102—22no—
299#102—1222no—
300#102—1222no—
301C22⋊C8—21no—
302C22⋊C8—612no—
303C22⋊C8—1221no—
304C22⋊C8C22⋊D6112yescomplemented
305#95—1222no—
306#95—1221no—
307#95—1221no—
308#95—1221no—
309#95—1221no—
310C24—21no—
311C24—1221no—
312C24D4×D6111yescharacteristic
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—82no—
319C2×D4—1221no—
320C2×D4—1221no—
321C2×D4—4882no—
322C2×D4—4882no—
323C2×D4—4882no—
324C2×D4—4882no—
325C2×D4—2442no—
326C2×D4—2441no—
327C2×D4—2441no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—42no—
332C22×C4—1222no—
333C22×C4—1221no—
334C22×C4—2441no—
335C22×C4D4×D6111yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4#1175822411yescharacteristic
338C22×C4C2×C22⋊D6111yescharacteristic
339C22×C4C2×C22⋊D6111yescharacteristic
340C22×C4C2×C22⋊D6111yescharacteristic
341M16—42no—
342M16—2442no—
343C2×C8—22no—
344C2×C8—1222no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—4882no—
358C22⋊C4—4882no—
359C22⋊C4—2442no—
360C22⋊C4—2441no—
361C22⋊C4—2441no—
362C22⋊C4—2442no—
363C42—41no—
364C42—41no—
365C23—22no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—41no—
371C23—42no—
372C23—41no—
373C23—2441no—
374C23—2442no—
375C23—2441no—
376C23—2442no—
377C23—2441no—
378C23#1451974511yescharacteristic
379C23#1451974911yescharacteristic
380C23#1451977311yescharacteristic
381D4—42no—
382D4—81no—
383D4—82no—
384D4—82no—
385D4—4881no—
386D4—4882no—
387D4—4882no—
388D4—4888no—
389D4—2442no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—4881no—
403C2×C4—4881no—
404C2×C4—4881no—
405C2×C4—2442no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2441no—
410C2×C4#1451974511yescharacteristic
411C2×C4#1451974611yescharacteristic
412C2×C4#1451974811yescharacteristic
413C2×C4#1451974911yescharacteristic
414C8—42no—
415C8—2442no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—4882no—
431C22—4882no—
432C22—4881no—
433C22—4881no—
434C22—4881no—
435C22#1683967011yescharacteristic
436C22#1683995112yes—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—9761no—
445C4—4882no—
446C4—4881no—
447C2—22no—
448C2—41no—
449C2—41no—
450C2—161no—
451C2—9761no—
452C2#2144686911yescharacteristic
453C2#2144687011yescharacteristic
454C2#2144694711yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#3094C2
socleC22×C61#392
prime radical#21453841C2
hypercenter#3094D61
hypocenterC61#9983
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #21455759C2semidirect
3. #21445896C2semidirect
4. #21444349C2semidirect
5. #21444348C2semidirect
6. #21443728C2semidirect
7. C61×#3094C2semidirect
52. C22⋊#92418D4semidirect
71. C2×C4⋊C4×C61D4semidirect
72. C2×C4⋊C4×C61D4semidirect
81. C22⋊C8×C61D4semidirect
221. #3094D61semidirect
260. C61#9983semidirect
283. C2×C4⋊C4C22⋊D61semidirect
284. C2×C4⋊C4C22⋊D61semidirect
304. C22⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214557592
#214538412
#214458962
#214443492
#214443482
#214437282
C61×#30942
#998361