Finite Group Databasebeta

← #29580778

Subgroups — #29580778

Order 15616.

568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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#21455827C211yesmaximal, characteristic
2#21455624C211yesmaximal, characteristic, complemented
3#21444382C211yesmaximal, characteristic, complemented
4#21444244C211yesmaximal, characteristic
5#21444214C211yesmaximal, characteristic, complemented
6#21443677C211yesmaximal, characteristic, complemented
7C61×#2536C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840092—21no—
10#16840069—22no—
11#16840057—21no—
12#16840052—21no—
13#16840047—21no—
14#16839967—21no—
15#16839913—21no—
16C4×#11758200—22no—
17#16839815C2211yescharacteristic
18#16839815C2211yescharacteristic
19#16839802—21no—
20#16839786C2211yescharacteristic
21#16839771—21no—
22#16839498—22no—
23Q8⋊#92418—22no—
24D4⋊#92418—22no—
25C2×C22⋊Q8×C61—21no—
26C2×C4×Q8×C61C2211yescharacteristic
27C2×C4×D4×C61C2211yescharacteristic
28C61×#398—21no—
29C61×#394—21no—
30C61×#388—22no—
31C61×#382C2211yescharacteristic
32C61×#380—21no—
33C2×#11758200—22no—
34C2×#11758194—21no—
35#14519777D411yescharacteristic
36#14519777D411yescharacteristic
37#14519769—21no—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519736—21no—
43#14519710—22no—
44#14519708—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418D412yes—
50#14519701—22no—
51#14519701—22no—
52#14519700—22no—
53#14519698—22no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C4×#92418—21no—
57C4×#92418D412yes—
58C22×Q8×C61D411yescharacteristic
59C22×D4×C61D411yescharacteristic
60C23×C4×C61—21no—
61C22⋊Q8×C61—42no—
62C22⋊Q8×C61—42no—
63C4×Q8×C61—21no—
64C4×Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×D4×C61—21no—
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C2×C4⋊C4×C61—22no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61—21no—
79C2×C42×C61—21no—
80C2×C42×C61C2311yescharacteristic
81#95×C61—22no—
82#95×C61—21no—
83#95×C61D412yes—
84C24×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61—21no—
89C2×Q8×C61—21no—
90C2×Q8×C61SD1612yescomplemented
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—42no—
94C22×C4×C61—21no—
95C22×C4×C61—22no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C2×Dic122—21no—
108C2×Dic122—21no—
109C4⋊C4×C61—21no—
110C4⋊C4×C61—21no—
111C4⋊C4×C61—21no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—44no—
114C4⋊C4×C61—41no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C22⋊C4×C61—44no—
119C22⋊C4×C61—44no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C42×C61—41no—
123C42×C61—41no—
124C42×C61C2×D411yescharacteristic
125C42×C61C2×D411yescharacteristic
126C42×C61C2×D411yescharacteristic
127C42×C61#4111yescharacteristic
128C22⋊Dic61—41no—
129#11758200—44no—
130C4⋊Dic61—21no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133C4⋊Dic61—21no—
134#11758196—41no—
135#11758196—41no—
136C4×Dic61—41no—
137#11758194—41no—
138#11758194—41no—
139C2×#92418—22no—
140C2×#92418—22no—
141C2×#92418—41no—
142C23×C61—22no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61#12011yescharacteristic
150Q8×C61—22no—
151Q8×C61—22no—
152Q8×C61—41no—
153Q8×C61—41no—
154D4×C61—22no—
155D4×C61—22no—
156D4×C61—41no—
157D4×C61—41no—
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—42no—
165C2×C4×C61—42no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—42no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—81no—
172C2×C4×C61—81no—
173C2×C4×C61—81no—
174C2×C4×C61—81no—
175C2×C4×C61#12011yescharacteristic
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61#12111yescharacteristic
178C2×C4×C61#12111yescharacteristic
179C2×C4×C61#12111yescharacteristic
180C2×C4×C61#12711yescharacteristic
181C2×C4×C61C2×SD1611yescharacteristic
182C2×C4×C61#13511yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61#13711yescharacteristic
185C2×Dic61—41no—
186C2×Dic61—41no—
187Dic122—42no—
188Dic122—81no—
189#92418—42no—
190#92418—42no—
191#92418—81no—
192#10001—611nomaximal, Sylow
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—42no—
196C22×C61—42no—
197C22×C61—42no—
198C22×C61—81no—
199C22×C61—81no—
200C22×C61—81no—
201C22×C61—81no—
202C22×C61#39211yescharacteristic
203C22×C61#45011yescharacteristic
204C22×C61#45211yescharacteristic
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—42no—
210C4×C61—82no—
211C4×C61—81no—
212C4×C61—81no—
213C4×C61#44811yescharacteristic
214C4×C61#44911yescharacteristic
215C4×C61#46511yescharacteristic
216C4×C61#46811yescharacteristic
217Dic61—81no—
218Dic61—81no—
219#3101—611no—
220#3078—611no—
221#2536D6111yescharacteristic
222#1518—611no—
223#1486—611no—
224#1479—611no—
225#1286—611no—
226C2×C61—21no—
227C2×C61—21no—
228C2×C61—82no—
229C2×C61#200011yescharacteristic
230C2×C61#200911yescharacteristic
231C2×C61#201011yescharacteristic
232#533—611no—
233C2×C22⋊Q8—21no—
234C2×C4×Q8C2×D6111yescharacteristic
235C2×C4×D4C2×D6111yescharacteristic
236#483—1221no—
237#479—1222no—
238#477—1221no—
239#476—1221no—
240#475—1221no—
241#461—1221no—
242#450—1221no—
243C4×SD16—1222no—
244#431—611no—
245#431—611no—
246#428—1221no—
247#423—611no—
248#419—1221no—
249#398—21no—
250#394—21no—
251#388—22no—
252#382C2×D6111yescharacteristic
253#380—21no—
254#328—1222no—
255Q8⋊C8—1222no—
256D4⋊C8—1222no—
257C61#1000111yescharacteristic, complemented, Sylow
258C22×Q8C22⋊D6111yescharacteristic
259C22×D4C22⋊D6111yescharacteristic
260C23×C4—21no—
261C2×SD16—1222no—
262C2×M16—1221no—
263C4⋊Q8—611no—
264C4⋊Q8—611no—
265#125—1221no—
266C22⋊Q8—42no—
267C22⋊Q8—42no—
268C22⋊Q8—1221no—
269C22⋊Q8—1221no—
270C4×Q8—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8—1221no—
275C4×Q8—1221no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280#117—1221no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4C22⋊D6111yescharacteristic
285C2×C4⋊C4C22⋊D6111yescharacteristic
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C42—21no—
290C2×C42C22×D6111yescharacteristic
291#107—1222no—
292#106—1222no—
293#106—1222no—
294C4⋊C8—612no—
295C4⋊C8—1221no—
296C4⋊C8—1221no—
297C4⋊C8—1221no—
298#103—1222no—
299#103—1222no—
300#103—1222no—
301#102—1222no—
302C22⋊C8—1221no—
303C22⋊C8—1221no—
304C4×C8—612no—
305C4×C8—1221no—
306#95—22no—
307#95—21no—
308#95C22⋊D6112yes—
309C24—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—1221no—
316C2×Q8—1221no—
317C2×Q8#1175820012yescomplemented
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—42no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4C2×C22⋊D6111yescharacteristic
332C22×C4C2×C22⋊D6111yescharacteristic
333C22×C4C2×C22⋊D6111yescharacteristic
334SD16—2444no—
335M16—2441no—
336M16—2441no—
337C2×C8—1222no—
338C2×C8—1222no—
339C2×C8—2441no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—44no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—1221no—
353C4⋊C4—2441no—
354C4⋊C4—2441no—
355C22⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—2441no—
360C42—41no—
361C42—41no—
362C42—2441no—
363C42D4×D6111yescharacteristic
364C42D4×D6111yescharacteristic
365C42D4×D6111yescharacteristic
366C42#1175822411yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#1451974611yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—4881no—
380Q8—2442no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4#1451974511yescharacteristic
405C2×C4#1451974511yescharacteristic
406C2×C4#1451974811yescharacteristic
407C2×C4#1451974911yescharacteristic
408C2×C4#1451974911yescharacteristic
409C2×C4#1451977311yescharacteristic
410C2×C4C2×#1175820011yescharacteristic
411C2×C4#1451979711yescharacteristic
412C2×C4#1451980311yescharacteristic
413C2×C4#1451980711yescharacteristic
414C8—4881no—
415C8—2442no—
416C8—2442no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1683967011yescharacteristic
427C22#1683991311yescharacteristic
428C22#1683992411yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—81no—
437C4—4881no—
438C4—4881no—
439C4#1683990011yescharacteristic
440C4#1683990511yescharacteristic
441C4#1683998911yescharacteristic
442C4#1684000611yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2#2144682211yescharacteristic
447C2#2144687911yescharacteristic
448C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2536C2
socleC22×C61#392
prime radicalC22×D4×C61D4
hypercenter#2536D61
hypocenterC61#10001
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. #21455624C2semidirect
3. #21444382C2semidirect
5. #21444214C2semidirect
6. #21443677C2semidirect
90. C2×Q8×C61SD16semidirect
257. C61#10001semidirect
317. C2×Q8#11758200semidirect

Maximal subgroups

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

subgroupindex
#214558272
#214556242
#214443822
#214442442
#214442142
#214436772
C61×#25362
#1000161