Finite Group Databasebeta

← #14725167

Subgroups — #14725167

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078655C211yesmaximal, characteristic
2#13077717C211yesmaximal, characteristic
3#13067523C211yesmaximal, characteristic, complemented
4#13067511C211yesmaximal, characteristic, complemented
5#13067487C211yesmaximal, characteristic, complemented
6#13067485C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067464C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10C8×#4326C211yesmaximal, characteristic, complemented
11#13067397C211yesmaximal, characteristic
12#13067088C211yesmaximal, characteristic
13#13067011C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic
15C11×#2984C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#446—21no—
19C11×#446—21no—
20C11×#446C2211yescharacteristic
21C11×#446C2211yescharacteristic
22C8×Q8×C11C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C11×#432—21no—
25C11×#432C2211yescharacteristic
26C11×#431—21no—
27C11×#431C2211yescharacteristic
28#10622841C411yescharacteristic
29#10622841C411yescharacteristic
30#10622644C411yescharacteristic
31#10622644C411yescharacteristic
32C4×#4326C2211yescharacteristic
33C4×#4326C2211yescharacteristic
34C4×#4326C2211yescharacteristic
35C4×#4326C2211yescharacteristic
36#10622634C411yescharacteristic
37#10622634C411yescharacteristic
38#10622583C411yescharacteristic
39#10622583C411yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622444—21no—
44#10622443—21no—
45#10622333—21no—
46#10622333—21no—
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11C2×C411yescharacteristic
68C4×Q8×C11—21no—
69C4×Q8×C11—21no—
70C4×Q8×C11C2×C411yescharacteristic
71C4×Q8×C11C2×C411yescharacteristic
72C4×Q8×C11C2311yescharacteristic
73C4×Q8×C11C2311yescharacteristic
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×#4326C2×C411yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4326C2×C411yescharacteristic
82#66979—21no—
83#66977—21no—
84#66977C2×C411yescharacteristic
85#66977C2×C411yescharacteristic
86#66923—21no—
87#66922C2×C411yescharacteristic
88#66922C2×C411yescharacteristic
89C4×Dic22—21no—
90C4×Dic22C2311yescharacteristic
91C4×Dic22C2311yescharacteristic
92C11×C4⋊C8—21no—
93C11×C4⋊C8—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8D411yescharacteristic
97C11×C4⋊C8D411yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C22⋊C8—21no—
101C11×C22⋊C8D411yescharacteristic
102C11×C22⋊C8D411yescharacteristic
103C11×#97—21no—
104C11×#97—21no—
105C11×#97—21no—
106C4×C8×C11—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66899C2×C411yescharacteristic
112#66899C2×C411yescharacteristic
113#66899C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66871C2×C411yescharacteristic
131#66871C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18032—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—41no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×Q8×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C2×Dic22—21no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11C22×C411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11#4111yescharacteristic
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180C22⋊Dic11—21no—
181#4326—22no—
182#4326—22no—
183#4326—41no—
184#4326—41no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204#3104—111no—
205#2986—111no—
206#2984D1111yescharacteristic
207#1593—111no—
208#1591—111no—
209#1587—111no—
210#1587—111no—
211#1584—111no—
212#1584—111no—
213#1579—111no—
214C8×Q16—111no—
215#1572—111no—
216#1497—111no—
217#1479—111no—
218#1454—111no—
219C23×C11C4×D411yescharacteristic
220Q8×C11—21no—
221Q8×C11—21no—
222Q8×C11—21no—
223Q8×C11—42no—
224Q8×C11#13112yes—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246Dic22—21no—
247Dic22—21no—
248Dic22—21no—
249Dic22—21no—
250Dic22—42no—
251C8×C11—21no—
252C8×C11—21no—
253C8×C11—21no—
254C8×C11—21no—
255C8×C11—41no—
256C8×C11—41no—
257C11⋊C8—21no—
258C11⋊C8—21no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—41no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265#533—111no—
266C2×C4×Q8C2×D1111yescharacteristic
267#484—111no—
268#484—111no—
269#477—111no—
270#477—111no—
271#462—111no—
272#462—111no—
273#451—111no—
274#451—111no—
275#446—21no—
276#446—21no—
277#446—111no—
278#446—111no—
279#446—221no—
280#446C2×D1111yescharacteristic
281#446C2×D1111yescharacteristic
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—221no—
285C8×Q8C2×D1111yescharacteristic
286C8×Q8C2×D1111yescharacteristic
287C4×Q16—111no—
288C4×Q16—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291#433—221no—
292#433—221no—
293#432—21no—
294#432C2×D1111yescharacteristic
295#431—21no—
296#431—111no—
297#431—111no—
298#431—111no—
299#431C2×D1111yescharacteristic
300#335—111no—
301#335—111no—
302#334—111no—
303#334—111no—
304Q8⋊C8—111no—
305Q8⋊C8—111no—
306Q8⋊C8—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312#322—111no—
313#322—111no—
314#322—111no—
315C82—111no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11C2×C4×D411yescharacteristic
320C4×C11—21no—
321C4×C11—22no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11C2×#13111yescharacteristic
329C4×C11#56811yescharacteristic
330C4×C11#57811yescharacteristic
331C4×C11#57811yescharacteristic
332Dic11—41no—
333Dic11—41no—
334Dic11—41no—
335Dic11—41no—
336C22×Q8C4×D1111yescharacteristic
337C2×Q16—111no—
338C2×Q16—111no—
339C2×Q16—111no—
340C2×Q16—111no—
341C4⋊Q8—111no—
342C4⋊Q8—111no—
343#125—221no—
344C22⋊Q8—111no—
345C22⋊Q8—111no—
346C22⋊Q8—221no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—111no—
350C4×Q8—111no—
351C4×Q8—221no—
352C4×Q8C4×D1111yescharacteristic
353C4×Q8C4×D1111yescharacteristic
354C4×Q8C22×D1111yescharacteristic
355C4×Q8C22×D1111yescharacteristic
356#117—221no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C4×D1111yescharacteristic
359C2×C42—21no—
360C2×C42C22×D1111yescharacteristic
361#107—111no—
362#107—111no—
363#107—111no—
364#107—111no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—111no—
370C4⋊C8—111no—
371C4⋊C8—111no—
372C4⋊C8—111no—
373C4⋊C8—221no—
374C4⋊C8—221no—
375C4⋊C8—221no—
376C4⋊C8—221no—
377C4⋊C8—221no—
378C4⋊C8C22⋊D1111yescharacteristic
379C4⋊C8C22⋊D1111yescharacteristic
380C4⋊C8C22×D1111yescharacteristic
381C4⋊C8C22×D1111yescharacteristic
382#103—111no—
383#103—111no—
384#103—111no—
385#103—111no—
386#103—111no—
387#103—111no—
388#103—111no—
389#103—111no—
390C22⋊C8—21no—
391C22⋊C8—111no—
392C22⋊C8—111no—
393C22⋊C8—221no—
394C22⋊C8—221no—
395C22⋊C8C22⋊D1111yescharacteristic
396C22⋊C8C22⋊D1111yescharacteristic
397#97—21no—
398#97—21no—
399#97—21no—
400#97—221no—
401#97—221no—
402C4×C8—21no—
403C4×C8—21no—
404C4×C8—111no—
405C4×C8—111no—
406C4×C8—111no—
407C4×C8—111no—
408C4×C8—221no—
409C4×C8—221no—
410C4×C8—221no—
411C4×C8C22×D1111yescharacteristic
412C4×C8C22×D1111yescharacteristic
413C2×C11—41no—
414C2×C11#293311yescharacteristic
415C2×C11#295011yescharacteristic
416C2×C11#295511yescharacteristic
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—41no—
420C2×Q8—111no—
421C2×Q8—111no—
422C2×Q8—221no—
423C2×Q8C2×C4×D1111yescharacteristic
424C2×Q8C2×C4×D1111yescharacteristic
425C22×C4—21no—
426C22×C4—21no—
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4#433911yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430Q16—222no—
431Q16—222no—
432Q16—441no—
433Q16—441no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—111no—
437C2×C8—111no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8C2×C22⋊D1111yescharacteristic
445C2×C8C2×C22⋊D1111yescharacteristic
446C2×C8C2×C22⋊D1111yescharacteristic
447C2×C8C2×C22⋊D1111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—111no—
454C4⋊C4—111no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4C2×C4×D1111yescharacteristic
463C4⋊C4C2×C4×D1111yescharacteristic
464C22⋊C4—221no—
465C22⋊C4—221no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—221no—
471C42—221no—
472C42C2×C4×D1111yescharacteristic
473C42#433911yescharacteristic
474C42C2×C22⋊D1111yescharacteristic
475C42C23×D1111yescharacteristic
476C11#1803211yescharacteristic, complemented, Sylow
477C23C4×C22⋊D1111yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—42no—
482Q8—221no—
483Q8—221no—
484Q8—221no—
485Q8—221no—
486Q8—442no—
487Q8#6696012yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4C4×C22⋊D1111yescharacteristic
504C2×C4C4×C22⋊D1111yescharacteristic
505C2×C4C4×C22⋊D1111yescharacteristic
506C2×C4C22×C4×D1111yescharacteristic
507C2×C4C2×#433911yescharacteristic
508C2×C4C22×C22⋊D1111yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—221no—
516C8—221no—
517C8—221no—
518C8—221no—
519C8—441no—
520C8—441no—
521C8—441no—
522C8—441no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×C4×C22⋊D1111yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—22no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—441no—
536C4—441no—
537C4—441no—
538C4—441no—
539C4C2×#6696011yescharacteristic
540C4#1062327611yescharacteristic
541C4#1062336911yescharacteristic
542C4#1062336911yescharacteristic
543C2—41no—
544C2#1307734111yescharacteristic
545C2#1307748211yescharacteristic
546C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2984C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#2984D11
hypocenterC11#18032
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #13067523C2semidirect
4. #13067511C2semidirect
5. #13067487C2semidirect
6. #13067485C2semidirect
7. #13067466C2semidirect
8. #13067464C2semidirect
9. #13067433C2semidirect
10. C8×#4326C2semidirect
476. C11#18032semidirect

Maximal subgroups

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

subgroupindex
#130786552
#130777172
#130675232
#130675112
#130674872
#130674852
#130674662
#130674642
#130674332
C8×#43262
#130673972
#130670882
#130670112
#130669162
C11×#29842
#1803211