Finite Group Databasebeta

← #29574856

Subgroups — #29574856

Order 15616.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455827C211yesmaximal, characteristic
2D4×#11758194C211yesmaximal, characteristic
3#21446762C211yesmaximal, characteristic, complemented
4#21444275C211yesmaximal, characteristic, complemented
5#21443722C211yesmaximal, characteristic, complemented
6#21443656C211yesmaximal, characteristic, complemented
7C4×#102×C61C211yesmaximal, characteristic
8C22×#11758194—21no—
9#16840319C2211yescharacteristic
10#16840092—21no—
11#16840052C411yescharacteristic, complemented
12#16840052C411yescharacteristic, complemented
13#16839967C411yescharacteristic, complemented
14#16839967C411yescharacteristic, complemented
15#16839913—21no—
16C4×#11758200—21no—
17C4×#11758200—21no—
18#16839840—21no—
19#16839834—22no—
20D4×#92418—21no—
21#16839815C2211yescharacteristic
22#16839786C2211yescharacteristic
23#16839726—21no—
24C4×#11758194C2211yescharacteristic
25#16839522—21no—
26#16839522—21no—
27#16839494—22no—
28C2×C4×D4×C61C2211yescharacteristic
29C2×#102×C61—21no—
30C2×C4×C8×C61C2211yescharacteristic
31C4×C4⋊C4×C61C2211yescharacteristic
32C61×#340—21no—
33C2×#11758200—21no—
34C2×#11758200—21no—
35C2×#11758194—22no—
36C2×#11758194—21no—
37C2×#11758194—42no—
38C2×#11758194—42no—
39C2×#11758194D411yescharacteristic
40C2×#11758194D411yescharacteristic
41C22×#92418—22no—
42#14519777C2×C411yescharacteristic
43#14519777C2×C411yescharacteristic
44#14519769—21no—
45#14519756—21no—
46#14519756—21no—
47C4×Dic122—21no—
48C4×Dic122—21no—
49#14519736—21no—
50#14519708—21no—
51#14519708—21no—
52C4⋊#92418—21no—
53C4⋊#92418C2×C411yescharacteristic
54C4⋊#92418C2×C411yescharacteristic
55C4⋊#92418D412yes—
56#14519700—21no—
57#14519700—21no—
58#14519698—21no—
59#14519698—21no—
60C22⋊#92418—22no—
61C22⋊#92418—22no—
62C22⋊#92418—21no—
63#14519688—21no—
64C4×#92418—21no—
65C4×#92418—21no—
66C22×D4×C61D411yescharacteristic
67C23×C4×C61—21no—
68C22×C8×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61C2×C411yescharacteristic
72C4×D4×C61C2×C411yescharacteristic
73C4×D4×C61D411yescharacteristic
74C4×D4×C61D411yescharacteristic
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61D411yescharacteristic
77C2×C22⋊C4×C61—21no—
78C2×C42×C61—21no—
79C2×C42×C61C2311yescharacteristic
80#102×C61—24no—
81C4×C8×C61—21no—
82C4×C8×C61—21no—
83#95×C61—21no—
84C24×C61—21no—
85C2×D4×C61—22no—
86C2×D4×C61—21no—
87C2×D4×C61—41no—
88C2×D4×C61C22⋊C411yescharacteristic
89C2×D4×C61C22⋊C411yescharacteristic
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×C8×C61—22no—
106C2×C8×C61—41no—
107C2×C8×C61—41no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—22no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61C22⋊C411yescharacteristic
112C4⋊C4×C61C22⋊C411yescharacteristic
113C22⋊C4×C61—21no—
114C22⋊C4×C61—21no—
115C22⋊C4×C61—21no—
116C22⋊C4×C61—21no—
117C42×C61—41no—
118C42×C61—41no—
119C42×C61C22×C411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61#4111yescharacteristic
123C22⋊Dic61—41no—
124#11758200—42no—
125#11758200—42no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130#11758196—41no—
131#11758196—41no—
132C4×Dic61—41no—
133#11758194—21no—
134#11758194—21no—
135#11758194—21no—
136#11758194—44no—
137#11758194—41no—
138#11758194—41no—
139#11758194SD1612yescomplemented
140C2×#92418—21no—
141C2×#92418—21no—
142C2×#92418—21no—
143C2×#92418—21no—
144C2×#92418—22no—
145C2×#92418—44no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—42no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—81no—
152C23×C61#12111yescharacteristic
153D4×C61—21no—
154D4×C61—21no—
155D4×C61—21no—
156D4×C61—42no—
157D4×C61#10412yes—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61—81no—
175C2×C4×C61—81no—
176C2×C4×C61C2×C22⋊C411yescharacteristic
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61C4×D411yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12111yescharacteristic
181C2×C4×C61#12311yescharacteristic
182C2×C4×C61C2×SD1611yescharacteristic
183C2×C4×C61#13511yescharacteristic
184C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C61#13711yescharacteristic
186C2×Dic61—41no—
187C2×Dic61—41no—
188Dic122—42no—
189Dic122—41no—
190Dic122—41no—
191C8×C61—42no—
192#92418—22no—
193#92418—41no—
194#92418—41no—
195#92418—42no—
196#92418—41no—
197#8989—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—22no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61—82no—
207C22×C61—82no—
208C22×C61#38611yescharacteristic
209C22×C61#46111yescharacteristic
210C22×C61#46311yescharacteristic
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—41no—
215C4×C61—41no—
216C4×C61—82no—
217C4×C61C2×#10411yescharacteristic
218C4×C61#42111yescharacteristic
219C4×C61C4×SD1611yescharacteristic
220C4×C61#44011yescharacteristic
221C4×C61#45011yescharacteristic
222C4×C61#45211yescharacteristic
223Dic61—81no—
224Dic61—81no—
225#3101—611no—
226D4×M16—611no—
227#1986—611no—
228C4×#102D6111yescharacteristic
229#1493—611no—
230#1303—611no—
231#1278—611no—
232C2×C61—21no—
233C2×C61—21no—
234C2×C61—42no—
235C2×C61—81no—
236C2×C61#187111yescharacteristic
237C2×C61#187711yescharacteristic
238C2×C61#188111yescharacteristic
239C22×M16—1221no—
240#533—611no—
241C2×C4×D4C2×D6111yescharacteristic
242#483—1221no—
243#476—611no—
244#476—611no—
245#461—611no—
246#461—611no—
247#450—1221no—
248C4×SD16—1221no—
249C4×SD16—1221no—
250#436—1221no—
251#435—1222no—
252C8×D4—1221no—
253#431—611no—
254#423—611no—
255C2×#102—21no—
256#407—1221no—
257C4×M16—611no—
258C2×C4×C8C2×D6111yescharacteristic
259C4×C4⋊C4C2×D6111yescharacteristic
260#340—21no—
261#339—1221no—
262#339—1221no—
263Q8⋊C8—1222no—
264C61#898911yescharacteristic, complemented, Sylow
265C22×D4C22⋊D6111yescharacteristic
266C23×C4—21no—
267C2×SD16—1221no—
268C2×SD16—1221no—
269C2×M16—611no—
270C2×M16—611no—
271C2×M16—1222no—
272C2×M16—1221no—
273C2×M16—2442no—
274C2×M16—2442no—
275C22×C8—21no—
276C22×C8—1222no—
277C4⋊Q8—611no—
278C4⋊Q8—611no—
279#125—1221no—
280C22⋊Q8—1221no—
281C22⋊Q8—1221no—
282C4×Q8—1221no—
283C4×Q8—1221no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4C4×D6111yescharacteristic
287C4×D4C4×D6111yescharacteristic
288C4×D4D24411yescharacteristic
289C4×D4D24411yescharacteristic
290#117—1221no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4C22⋊D6111yescharacteristic
293C2×C22⋊C4—21no—
294C2×C42—21no—
295C2×C42C22×D6111yescharacteristic
296#106—1221no—
297#106—1221no—
298C4⋊C8—611no—
299C4⋊C8—611no—
300C4⋊C8—612no—
301C4⋊C8—1221no—
302#103—1221no—
303#103—1221no—
304#102—24no—
305#102—1221no—
306#102—1221no—
307C22⋊C8—1222no—
308C22⋊C8—1222no—
309C22⋊C8—1221no—
310#97—1221no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8—1221no—
314C4×C8—1221no—
315#95—21no—
316C24—21no—
317C2×Q8—1221no—
318C2×Q8—1221no—
319C2×D4—22no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4#1175819811yescharacteristic
323C2×D4#1175819811yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4D4×D6111yescharacteristic
335C22×C4#1175822411yescharacteristic
336C22×C4C2×C22⋊D6111yescharacteristic
337SD16—2442no—
338SD16—2442no—
339M16—612no—
340M16—1221no—
341M16—1221no—
342M16—1221no—
343M16—2444no—
344M16—2441no—
345M16—2441no—
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—1221no—
350C2×C8—1221no—
351C2×C8—1221no—
352C2×C8—1221no—
353C2×C8—1222no—
354C2×C8—2444no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—41no—
358C4⋊C4—1221no—
359C4⋊C4—1221no—
360C4⋊C4—1221no—
361C4⋊C4—1221no—
362C4⋊C4—2441no—
363C4⋊C4—2441no—
364C4⋊C4#1175819811yescharacteristic
365C4⋊C4#1175819811yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—2441no—
371C42—41no—
372C42—41no—
373C42—2441no—
374C42C2×C4×D6111yescharacteristic
375C42C2×D24411yescharacteristic
376C42D4×D6111yescharacteristic
377C42#1175822411yescharacteristic
378C23—21no—
379C23—21no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—81no—
384C23#1451974911yescharacteristic
385Q8—2442no—
386Q8—2441no—
387Q8—2441no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—42no—
392D4#1451970512yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—2441no—
412C2×C4—2441no—
413C2×C4C2×#1175819811yescharacteristic
414C2×C4#1451973711yescharacteristic
415C2×C4#1451973711yescharacteristic
416C2×C4#1451974711yescharacteristic
417C2×C4#1451974911yescharacteristic
418C2×C4#1451976111yescharacteristic
419C2×C4SD16×D6111yescharacteristic
420C2×C4#1451979611yescharacteristic
421C2×C4#1451980111yescharacteristic
422C2×C4#1451980611yescharacteristic
423C8—42no—
424C8—1222no—
425C8—2441no—
426C8—2441no—
427C8—2442no—
428C8—2441no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—82no—
438C22—82no—
439C22#1683963911yescharacteristic
440C22#1683996511yescharacteristic
441C22#1683997511yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4—4881no—
449C4—4881no—
450C4C2×#1451970511yescharacteristic
451C4#1683978011yescharacteristic
452C4#1683985311yescharacteristic
453C4#1683985911yescharacteristic
454C4#1683991411yescharacteristic
455C4#1683992511yescharacteristic
456C2—21no—
457C2—21no—
458C2—42no—
459C2—81no—
460C2#2144611911yescharacteristic
461C2#2144615111yescharacteristic
462C2#2144617911yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC4×#102×C61C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenterC4×#102D61
hypocenterC61#8989
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. #21446762C2semidirect
4. #21444275C2semidirect
5. #21443722C2semidirect
6. #21443656C2semidirect
11. #16840052C4semidirect
12. #16840052C4semidirect
13. #16839967C4semidirect
14. #16839967C4semidirect
139. #11758194SD16semidirect
264. C61#8989semidirect

Maximal subgroups

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

subgroupindex
#214558272
D4×#117581942
#214467622
#214442752
#214437222
#214436562
C4×#102×C612
#898961