Finite Group Databasebeta

← #14739246

Subgroups — #14739246

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078398C211yesmaximal, characteristic
2#13078099C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic
4#13068043C212yesmaximal, complemented
5#13068036C212yesmaximal, complemented
6#13067995C212yesmaximal, complemented
7#13067988C212yesmaximal, complemented
8#13067387C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10C2×#10622185C211yesmaximal, characteristic, complemented
11C11×#3229C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66995—21no—
15C4×#4339C2211yescharacteristic
16C11×#498C2212yes—
17C11×#487C2212yes—
18C11×#483—22no—
19C11×#475—21no—
20C11×#475—21no—
21C11×#431C2211yescharacteristic
22#10622838—21no—
23#10622707C2211yescharacteristic
24#10622704C2211yescharacteristic
25#10622703—21no—
26#10622703C2212yes—
27#10622700C2211yescharacteristic
28#10622697C2211yescharacteristic
29#10622696—21no—
30#10622696C2212yes—
31#10622679—21no—
32#10622676—21no—
33#10622615—21no—
34#10622611—21no—
35#10622537C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622446—21no—
39D11×C4⋊C8—21no—
40(C22⋊D11)⋊C8—22no—
41C8×D44C2212yes—
42C8×Dic22C2212yes—
43#10622185C2212yes—
44#10622185C2212yes—
45#10622185C2212yes—
46#10622184C2212yes—
47#10622095C2212yes—
48#10622095C2212yes—
49C22×Q8×C11—21no—
50C2×#4339D411yescharacteristic
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2312yes—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C11×#117—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C2×#4326—22no—
67#66995—44no—
68C2×#4325—22no—
69C4×C22⋊D11—21no—
70C4×C22⋊D11—21no—
71#66979D411yescharacteristic
72C2×#4318—21no—
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75C2×C8×D11—22no—
76C4×D44D411yescharacteristic
77C4×D44C2311yescharacteristic
78#66925—21no—
79C42×D11—21no—
80C4×Dic22D411yescharacteristic
81C4×Dic22C2311yescharacteristic
82C11×#106—22no—
83C11×#106—22no—
84C11×C4⋊C8D411yescharacteristic
85C11×C4⋊C8D411yescharacteristic
86C11×#103—22no—
87C11×#103—22no—
88C11×C22⋊C8D412yes—
89C4×C8×C11C2312yes—
90#66899—22no—
91#66899—22no—
92(C2×D11)⋊C8—22no—
93Dic11⋊C8—22no—
94C8×Dic11—22no—
95#66874—21no—
96#66874—21no—
97#66873—21no—
98#66873—21no—
99#66872—21no—
100#66872—21no—
101#66871—21no—
102#66871—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2312yes—
110#19415—111nomaximal, Sylow
111C2×Q8×C11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—41no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C22×C4×C11—41no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C2×C22⋊D11—21no—
122#4339—22no—
123#4339SD1614yes—
124C2×D44C2×D411yescharacteristic
125C2×C4×D11—21no—
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×Dic22C2×D411yescharacteristic
129C2×C8×C11C2×D412yes—
130C2×C8×C11C2×D412yes—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147C22⋊Dic11—21no—
148#4326—44no—
149#4325—44no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152C4⋊Dic11C2×D411yescharacteristic
153C4⋊Dic11C2×D411yescharacteristic
154Dic11⋊C4—21no—
155Dic11⋊C4—21no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C4×Dic11—21no—
159#4318—42no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—42no—
165C2×C11⋊C8—81no—
166C8×D11—82no—
167#3229D1111yescharacteristic, complemented
168#3076—111no—
169#3039—111no—
170#2988—111no—
171#1680—112no—
172#1679—112no—
173#1672—112no—
174#1671—112no—
175#1570—111no—
176#1550—111no—
177C2×#332—111no—
178C23×C11#12111yescharacteristic
179C22×D11—21no—
180Q8×C11—42no—
181Q8×C11—42no—
182Q8×C11—41no—
183Q8×C11—41no—
184Q8×C11—81no—
185Q8×C11—82no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—82no—
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11C2×SD1612yes—
197C2×C4×C11#13512yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C22⋊D11—24no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205D44—21no—
206D44C2×SD1612yes—
207C4×D11—24no—
208C4×D11—41no—
209C4×D11—41no—
210C4×D11—81no—
211Dic22—21no—
212Dic22C2×SD1612yes—
213C8×C11—22no—
214C8×C11—22no—
215C11⋊C8—42no—
216C11⋊C8—41no—
217C11⋊C8—41no—
218C11⋊C8—42no—
219C2×#137—221no—
220#533C2×D1111yescharacteristic
221C2×C4⋊Q8C2×D1111yescharacteristic
222C4×#41—111no—
223#498C2×D1112yes—
224#487C2×D1112yes—
225#483—22no—
226#479—221no—
227#478—221no—
228#477—111no—
229#476—111no—
230#475—21no—
231#475—21no—
232#475—111no—
233#474—111no—
234#462—112no—
235#462—221no—
236#461—112no—
237#461—221no—
238C8×Q8—112no—
239C8×D4—112no—
240C8×D4—222no—
241#431—221no—
242#431C2×D1111yescharacteristic
243#427—221no—
244#423—111no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8—111no—
247C2×C4⋊C8—221no—
248#419—221no—
249#416—221no—
250#334—112no—
251#334—112no—
252#333—112no—
253#332—112no—
254#332—112no—
255#332—112no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11#46512yes—
259C22×C11C2×#12111yescharacteristic
260C2×D11—22no—
261C2×D11—41no—
262C2×D11—41no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—81no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11#46512yes—
270C4×C11C22×SD1611yescharacteristic
271C4×C11C2×#13511yescharacteristic
272C4×C11#57711yescharacteristic
273C4×C11#57811yescharacteristic
274Dic11—22no—
275Dic11—41no—
276Dic11—41no—
277C2×#41—111no—
278C22×Q8—21no—
279#137—444no—
280C2×Q16—222no—
281C2×SD16—222no—
282C2×M16—221no—
283C22×C8—221no—
284C22×C8—221no—
285C22×C8—222no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8C22×D1112yes—
290C4⋊Q8C22×D1111yescharacteristic
291C4⋊Q8C22×D1111yescharacteristic
292#125—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—111no—
298C4×Q8—111no—
299C4×D4—111no—
300C4×D4—111no—
301C4×D4—221no—
302C4×D4—221no—
303#117—21no—
304#117—111no—
305#117—221no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C42—221no—
309C2×C42C22×D1111yescharacteristic
310#107—221no—
311#107—221no—
312#106—22no—
313#106—22no—
314#106—221no—
315#106—221no—
316C4⋊C8—112no—
317C4⋊C8—111no—
318C4⋊C8—111no—
319C4⋊C8—112no—
320C4⋊C8—222no—
321C4⋊C8—221no—
322C4⋊C8—221no—
323C4⋊C8—221no—
324C4⋊C8C22⋊D1111yescharacteristic
325C4⋊C8C22⋊D1111yescharacteristic
326#103—22no—
327#103—22no—
328#103—221no—
329#103—221no—
330#103—222no—
331#103—222no—
332#102—221no—
333#102—221no—
334C22⋊C8—222no—
335C22⋊C8C22⋊D1112yes—
336C4×C8—222no—
337C4×C8C22×D1112yes—
338C2×C11—22no—
339C2×C11#304611yescharacteristic
340C2×C11C2×#46511yescharacteristic
341C2×C11#306911yescharacteristic
342D11—42no—
343#41—114no—
344#41—222no—
345C2×Q8—22no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—41no—
349C2×Q8—42no—
350C2×Q8—42no—
351C2×Q8—111no—
352C2×D4—111no—
353C2×D4—221no—
354C22×C4—41no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4D4×D1111yescharacteristic
359C22×C4#434111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361Q16—444no—
362SD16—444no—
363M16—442no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—442no—
369C2×C8—882no—
370C2×C8—881no—
371C2×C8C2×C22⋊D1112yes—
372C2×C8C2×C22⋊D1112yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—111no—
384C4⋊C4—111no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C22⋊C4—41no—
388C22⋊C4—221no—
389C22⋊C4—221no—
390C22⋊C4—221no—
391C42—41no—
392C42—221no—
393C42—221no—
394C42—221no—
395C42D4×D1111yescharacteristic
396C42#434111yescharacteristic
397C42C2×C22⋊D1111yescharacteristic
398C42C23×D1111yescharacteristic
399C11#1941511yescharacteristic, complemented, Sylow
400C23—221no—
401C23#6699111yescharacteristic
402Q8—42no—
403Q8—42no—
404Q8—41no—
405Q8—41no—
406Q8—81no—
407Q8—82no—
408Q8—112no—
409Q8—221no—
410D4—112no—
411D4—224no—
412D4—221no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—82no—
420C2×C4—221no—
421C2×C4—224no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—881no—
427C2×C4SD16×D1112yes—
428C2×C4#6696912yes—
429C2×C4#6699111yescharacteristic
430C2×C4#6699111yescharacteristic
431C2×C4#6699111yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C2×#434111yescharacteristic
434C2×C4C22×C22⋊D1111yescharacteristic
435C8—22no—
436C8—22no—
437C8—442no—
438C8—441no—
439C8—441no—
440C8—442no—
441C22—21no—
442C22—21no—
443C22—222no—
444C22—441no—
445C22—441no—
446C22#1062278412yes—
447C22C2×#6699111yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—81no—
452C4—81no—
453C4—82no—
454C4—222no—
455C4—441no—
456C4—441no—
457C4#1062278412yes—
458C4C2×SD16×D1111yescharacteristic
459C4C2×#6696911yescharacteristic
460C4#1062336811yescharacteristic
461C4#1062336911yescharacteristic
462C2—22no—
463C2—442no—
464C2#1307816211yescharacteristic
465C2C2×#1062278411yescharacteristic
466C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3229C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#3229D11
hypocenterC11#19415
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
4. #13068043C2semidirect
5. #13068036C2semidirect
6. #13067995C2semidirect
7. #13067988C2semidirect
8. #13067387C2semidirect
9. #13067306C2semidirect
10. C2×#10622185C2semidirect
11. C11×#3229C2semidirect
167. #3229D11semidirect
399. C11#19415semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130780992
#130777242
#130680432
#130680362
#130679952
#130679882
#130673872
#130673062
C2×#106221852
C11×#32292
#1941511