Finite Group Databasebeta

← #14926879

Subgroups — #14926879

Order 2816.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076995C211yesmaximal, characteristic, complemented
2#13076993C211yesmaximal, characteristic, complemented
3#13076963C211yesmaximal, characteristic, complemented
4#13076957C211yesmaximal, characteristic, complemented
5#13074802C212yesmaximal, complemented
6#13074791C212yesmaximal, complemented
7#13074023C212yesmaximal, complemented
8#13073885C212yesmaximal, complemented
9#13073193C211yesmaximal, characteristic, complemented
10#13073123C212yesmaximal, complemented
11#13072988C211yesmaximal, characteristic, complemented
12#13072438C212yesmaximal
13#13072388C211yesmaximal, characteristic, complemented
14#13072318C211yesmaximal, characteristic, complemented
15#13072218C211yesmaximal, characteristic, complemented
16#13072068C211yesmaximal, characteristic
17#13071975C211yesmaximal, characteristic
18#13071347C212yesmaximal, complemented
19#13071244C212yesmaximal
20C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
21C2×#10622843C211yesmaximal, characteristic, complemented
22C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic
23C11×#2434C211yesmaximal, characteristic, complemented
24C23×Q8×C11C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×C4⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×#66999C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×Q8×Dic11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×(C22⋊D11)⋊C4C2211yescharacteristic
36C2×(C22⋊D11)⋊C4C2211yescharacteristic
37C2×#66931C2212yes—
38C2×C42×D11C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40C11×#395C2212yes—
41C11×#395C2212yes—
42C11×#391C2211yescharacteristic
43C11×#391C2211yescharacteristic
44C11×#385C2212yes—
45C11×#385C2212yes—
46C4×C11×C22⋊C4C2211yescharacteristic
47#10622844C2212yes—
48#10622843C2211yescharacteristic
49#10622843C2211yescharacteristic
50#10622843C2211yescharacteristic
51#10622843C2211yescharacteristic
52#10622843C2211yescharacteristic
53#10622843C2211yescharacteristic
54#10622843C2211yescharacteristic
55#10622843C2211yescharacteristic
56#10622843C2212yes—
57#10622843C2212yes—
58#10622842C2212yes—
59#10622826C2212yes—
60#10622825C2211yescharacteristic
61#10622823C2212yes—
62C2×C11⋊#95C2212yes—
63C2×C11⋊#95C2212yes—
64#10622607C2212yes—
65#10622607C2212yes—
66#10622603C2212yes—
67#10622600C2212yes—
68#10622600C2211yescharacteristic
69#10622600C2212yes—
70#10622599C2212yes—
71#10622598C2211yescharacteristic
72#10622597C2212yes—
73#10622597C2212yes—
74#10622596C2212yes—
75#10622594C2212yes—
76#10622591C2212yes—
77#10622591C2212yes—
78#10622590C2212yes—
79#10622590C2212yes—
80C4⋊C4×Dic11C2211yescharacteristic
81C4⋊C4×Dic11C2212yes—
82#10622587C2212yes—
83#10622587C2212yes—
84#10622586C2211yescharacteristic
85#10622586C2212yes—
86#10622586C2212yes—
87#10622585C2212yes—
88#10622571C2212yes—
89#10622563C2212yes—
90#10622563C2212yes—
91#10622555C2212yes—
92C22⋊C4×Dic11C2212yes—
93C22⋊C4×Dic11C2211yescharacteristic
94C22⋊C4×Dic11C2211yescharacteristic
95C4×(C2×D11)⋊C4C2211yescharacteristic
96#10622548C2211yescharacteristic
97C4×Dic11⋊C4C2211yescharacteristic
98C42×Dic11C2211yescharacteristic
99#10622541C2211yescharacteristic
100#10622541C2211yescharacteristic
101#10622286C2212yes—
102#10622283C2212yes—
103#10622281C2212yes—
104#10622279C2211yescharacteristic
105#10622279C2211yescharacteristic
106#10622277C2212yes—
107#10622274C2212yes—
108#10622273C2212yes—
109#10622273C2212yes—
110#10622272C2212yes—
111#10622269C2212yes—
112#10622268C2212yes—
113#10622268C2212yes—
114#10622267C2212yes—
115#10622266C2212yes—
116#10622266C2212yes—
117#10622265C2212yes—
118#10622265C2212yes—
119#10622264C2212yes—
120#10622262C2211yescharacteristic
121#10622262C2211yescharacteristic
122#10622259C2212yes—
123C22×Q8×C11—24no—
124C22×Q8×C11—42no—
125C22×Q8×C11—42no—
126C22×Q8×C11C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C22×Q8×C11C2311yescharacteristic
129C22×Q8×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C22×C22⋊D11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2312yes—
135C23×Dic11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×Dic22C2312yes—
140C11×C4⋊Q8—42no—
141C11×C4⋊Q8—42no—
142C11×C22⋊Q8—24no—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4C2311yescharacteristic
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2311yescharacteristic
156#66999—42no—
157#66999—42no—
158#66999—42no—
159Q8×Dic11—42no—
160C4×C22⋊D11—24no—
161C2×(C2×D11)⋊C4C2311yescharacteristic
162C2×(C2×D11)⋊C4C2311yescharacteristic
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2311yescharacteristic
168C2×C4⋊Dic11—42no—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2312yes—
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2312yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2311yescharacteristic
188C2×C4×Dic11—42no—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2311yescharacteristic
202(C22⋊D11)⋊C4—24no—
203(C22⋊D11)⋊C4Q818yescomplemented
204#66931—28no—
205C42×D11—42no—
206#66922—42no—
207C11×#95C2312yes—
208C11×#95C2311yescharacteristic
209C11×#95C2311yescharacteristic
210C11×#95C2312yes—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11⋊#95C2311yescharacteristic
214C11⋊#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2311yescharacteristic
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2311yescharacteristic
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240#35016—111nomaximal, Sylow
241C24×C11C2411yescharacteristic
242C23×D11C2411yescharacteristic
243C2×Q8×C11—22no—
244C2×Q8×C11—24no—
245C2×Q8×C11—22no—
246C2×Q8×C11—22no—
247C2×Q8×C11—22no—
248C2×Q8×C11—22no—
249C2×Q8×C11—22no—
250C2×Q8×C11—22no—
251C2×Q8×C11—22no—
252C2×Q8×C11—22no—
253C2×Q8×C11—42no—
254C2×Q8×C11—42no—
255C2×Q8×C11—416no—
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—24no—
259C22×C4×C11—42no—
260C22×C4×C11—42no—
261C22×C4×C11#4114yes—
262C22×C4×C11C2412yes—
263C22×C4×C11C2412yes—
264C22×C4×C11C2412yes—
265C22×C4×C11C2412yes—
266C22×C4×C11C2411yescharacteristic
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2411yescharacteristic
272C2×C22⋊D11—22no—
273C2×C22⋊D11—22no—
274C2×C22⋊D11C2×Q814yes—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—24no—
278C22×Dic11—41no—
279C22×Dic11—41no—
280C22×Dic11—41no—
281C22×Dic11—42no—
282C22×Dic11—42no—
283C22×Dic11C2×Q814yes—
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2411yescharacteristic
292C22×Dic11C2411yescharacteristic
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2411yescharacteristic
295C2×C4×D11—22no—
296C2×C4×D11—22no—
297C2×C4×D11—22no—
298C2×C4×D11—22no—
299C2×C4×D11—22no—
300C2×C4×D11—41no—
301C2×C4×D11—41no—
302C2×C4×D11—41no—
303C2×C4×D11C2×Q814yescomplemented
304C2×Dic22—24no—
305C2×Dic22—42no—
306C2×Dic22—42no—
307C11×C4⋊C4—22no—
308C11×C4⋊C4—24no—
309C11×C4⋊C4—42no—
310C11×C4⋊C4—42no—
311C11×C4⋊C4—42no—
312C11×C4⋊C4—42no—
313C11×C22⋊C4—24no—
314C11×C22⋊C4C2×Q814yes—
315C11×C22⋊C4#4114yes—
316C42×C11—22no—
317C42×C11—22no—
318C22⋊Dic11—24no—
319C22⋊Dic11—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—42no—
323(C2×D11)⋊C4—42no—
324(C2×D11)⋊C4—42no—
325(C2×D11)⋊C4—42no—
326(C2×D11)⋊C4C2×Q814yescomplemented
327C4⋊Dic11—24no—
328C4⋊Dic11—24no—
329C4⋊Dic11—22no—
330C4⋊Dic11—22no—
331C4⋊Dic11—22no—
332C4⋊Dic11—22no—
333C4⋊Dic11—42no—
334C4⋊Dic11—42no—
335C4⋊Dic11—42no—
336C4⋊Dic11—42no—
337Dic11⋊C4—24no—
338Dic11⋊C4—24no—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4—42no—
342Dic11⋊C4—42no—
343Dic11⋊C4—42no—
344Dic11⋊C4—42no—
345Dic11⋊C4C2×Q814yescomplemented
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—22no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—41no—
352C4×Dic11—41no—
353C4×Dic11—41no—
354C4×Dic11—41no—
355C4×Dic11—41no—
356C4×Dic11—42no—
357C4×Dic11—42no—
358C4×Dic11C2×Q814yescomplemented
359#2863—111no—
360#2862—111no—
361#2857—111no—
362#2855—111no—
363#2666—112no—
364#2665—112no—
365#2586—112no—
366#2574—112no—
367#2511—111no—
368#2505—112no—
369#2492—111no—
370#2450—112no—
371#2446—111no—
372#2440—111no—
373#2434D1111yescharacteristic, complemented
374#2429—111no—
375#2417—111no—
376#2409—111no—
377#2329—112no—
378#2318—112no—
379C4×C22⋊Q8—111no—
380C2×#391—111no—
381C42×D4—111no—
382C23×C11—21no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11C22×Q812yes—
387C23×C11C2×#4112yes—
388C23×C11C2×#4112yes—
389C23×C11C2511yescharacteristic
390C22×D11—21no—
391C22×D11—21no—
392C22×D11—21no—
393C22×D11—21no—
394C22×D11—21no—
395C22×D11—21no—
396C22×D11C22×Q812yes—
397Q8×C11—48no—
398Q8×C11—44no—
399Q8×C11—44no—
400Q8×C11—44no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—28no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—48no—
425C2×C4×C11C22×Q812yes—
426C2×C4×C11C22×Q812yes—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11C2×#4112yes—
429C2×C4×C11C2×#4112yes—
430C2×C4×C11C2×#4112yes—
431C2×C4×C11H(5,𝔽2)12yes—
432C2×C4×C11H(5,𝔽2)12yes—
433C22⋊D11—28no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—21no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—21no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—21no—
457C2×Dic11—22no—
458C2×Dic11—21no—
459C2×Dic11—21no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—44no—
464C2×Dic11—44no—
465C2×Dic11—84no—
466C2×Dic11C22×Q812yes—
467C2×Dic11C22×Q812yes—
468C2×Dic11C22×Q812yes—
469C2×Dic112−1+412yes—
470C4×D11—44no—
471C4×D11—44no—
472C4×D11—44no—
473Dic22—84no—
474C23×Q8C2×D1111yescharacteristic
475C2×C4⋊Q8—111no—
476C2×C4⋊Q8C2×D1111yescharacteristic
477C2×C4⋊Q8C2×D1111yescharacteristic
478C2×C22⋊Q8—111no—
479C2×C22⋊Q8—111no—
480C2×C22⋊Q8—111no—
481C2×C22⋊Q8—112no—
482C2×C22⋊Q8C2×D1111yescharacteristic
483C2×C4×Q8—111no—
484C2×C4×D4—111no—
485C2×C4×D4—111no—
486C2×C4×D4—111no—
487C22×C4⋊C4—111no—
488C22×C42—111no—
489C22×C42—111no—
490#400—112no—
491#400—112no—
492#400—112no—
493#400—112no—
494#398—112no—
495#398—112no—
496#398—112no—
497#398—112no—
498#396—112no—
499#396—112no—
500#395—112no—
501#395—112no—
502#395C2×D1112yes—
503#395C2×D1112yes—
504#393—112no—
505#393—112no—
506#391—112no—
507#391—111no—
508#391—111no—
509#391—111no—
510#391—111no—
511#391—111no—
512#391—111no—
513#391—112no—
514#391—111no—
515#391—111no—
516#391—112no—
517#391—112no—
518#391—112no—
519#391C2×D1111yescharacteristic
520#391C2×D1111yescharacteristic
521#389—112no—
522#389—112no—
523#389—112no—
524#389—111no—
525#389—111no—
526#389—111no—
527#389—111no—
528#388—112no—
529#388—112no—
530#387—112no—
531#387—112no—
532#387—112no—
533#387—112no—
534#387—112no—
535#387—112no—
536#387—112no—
537#387—112no—
538#387—112no—
539#387—112no—
540#386—112no—
541#386—112no—
542#385—112no—
543#385—112no—
544#385—112no—
545#385—112no—
546#385C2×D1112yes—
547#385C2×D1112yes—
548#384—111no—
549#383—112no—
550#382—112no—
551#382—112no—
552#381—112no—
553#380—111no—
554#380—112no—
555#380—112no—
556#380—111no—
557#380—112no—
558C4×C4⋊C4—112no—
559C4×C4⋊C4—111no—
560C4×C4⋊C4—111no—
561C4×C4⋊C4—111no—
562C4×C4⋊C4—111no—
563C4×C22⋊C4—112no—
564C4×C22⋊C4—111no—
565C4×C22⋊C4—111no—
566C4×C22⋊C4—111no—
567C4×C22⋊C4—111no—
568C4×C22⋊C4—111no—
569C4×C22⋊C4C2×D1111yescharacteristic
570C2×#95—112no—
571C2×#95—112no—
572C43—111no—
573C22×C11—22no—
574C22×C11—22no—
575C22×C11—22no—
576C22×C11—22no—
577C22×C11—22no—
578C22×C11—22no—
579C22×C11#53314yes—
580C22×C11C23×Q811yescharacteristic
581C22×C11C22×#4111yescharacteristic
582C22×C11C22×#4111yescharacteristic
583C22×C11C2×H(5,𝔽2)11yescharacteristic
584C22×C11C2×H(5,𝔽2)11yescharacteristic
585C22×C11C2×2−1+411yescharacteristic
586C22×C11#58511yescharacteristic
587C2×D11—22no—
588C2×D11—22no—
589C2×D11—22no—
590C2×D11—41no—
591C2×D11—41no—
592C2×D11—41no—
593C2×D11—41no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11—22no—
598C4×C11—22no—
599C4×C11—42no—
600C4×C11—42no—
601C4×C11—42no—
602C4×C11—42no—
603C4×C11#53814yes—
604Dic11—22no—
605Dic11—22no—
606Dic11—22no—
607Dic11—22no—
608Dic11—41no—
609Dic11—41no—
610Dic11—42no—
611Dic11—42no—
612Dic11—42no—
613Dic11—42no—
614Dic11—41no—
615C22×Q8—24no—
616C22×Q8—42no—
617C22×Q8—42no—
618C22×Q8—112no—
619C22×Q8C22×D1111yescharacteristic
620C22×Q8C22×D1111yescharacteristic
621C22×Q8C22×D1111yescharacteristic
622C22×Q8C22×D1112yes—
623C22×D4—111no—
624C23×C4—111no—
625C23×C4—111no—
626C23×C4—111no—
627C23×C4—112no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4C22×D1111yescharacteristic
631C23×C4C22×D1112yes—
632C4⋊Q8—42no—
633C4⋊Q8—42no—
634C4⋊Q8—442no—
635C22⋊Q8—24no—
636C22⋊Q8—228no—
637C22⋊Q8—442no—
638C22⋊Q8—442no—
639C22⋊Q8—442no—
640C4×Q8—442no—
641C4×D4—118no—
642C4×D4—224no—
643C4×D4—224no—
644C2×C4⋊C4—111no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—111no—
647C2×C4⋊C4—111no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—112no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—112no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—112no—
662C2×C4⋊C4—112no—
663C2×C4⋊C4—442no—
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1112yes—
666C2×C4⋊C4C22×D1112yes—
667C2×C4⋊C4C22×D1112yes—
668C2×C4⋊C4C22×D1112yes—
669C2×C4⋊C4C22×D1112yes—
670C2×C22⋊C4—111no—
671C2×C22⋊C4—111no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—111no—
674C2×C22⋊C4—111no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—112no—
679C2×C22⋊C4C22×D1112yes—
680C2×C22⋊C4C22×D1111yescharacteristic
681C2×C22⋊C4C22×D1111yescharacteristic
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—111no—
685C2×C42—111no—
686C2×C42—111no—
687C2×C42—111no—
688C2×C42—112no—
689C2×C42—111no—
690C2×C42—111no—
691C2×C42—112no—
692C2×C42—111no—
693C2×C42—111no—
694C2×C42—111no—
695C2×C42—442no—
696C2×C42—442no—
697C2×C42C22×D1111yescharacteristic
698C2×C42C22×D1111yescharacteristic
699#95—112no—
700#95—112no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95—112no—
706#95—112no—
707#95—111no—
708#95—111no—
709#95—111no—
710#95—111no—
711#95—112no—
712#95—112no—
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95C22×D1111yescharacteristic
727#95C22×D1111yescharacteristic
728#95C22×D1112yes—
729#95C22×D1112yes—
730#95C22×D1112yes—
731#95C22×D1112yes—
732C2×C11—24no—
733C2×C11C2×#53311yescharacteristic
734C2×C11C2×#53811yescharacteristic
735C2×C11#346111yescharacteristic
736C2×C11#350111yescharacteristic
737C2×C11#350311yescharacteristic
738C2×C11#351411yescharacteristic
739C2×C11#352011yescharacteristic
740D11—42no—
741C24—111no—
742C24C23×D1111yescharacteristic
743C2×Q8—22no—
744C2×Q8—24no—
745C2×Q8—22no—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—22no—
749C2×Q8—22no—
750C2×Q8—22no—
751C2×Q8—22no—
752C2×Q8—22no—
753C2×Q8—42no—
754C2×Q8—42no—
755C2×Q8—416no—
756C2×Q8—224no—
757C2×Q8—442no—
758C2×Q8—442no—
759C2×D4—114no—
760C2×D4—222no—
761C2×D4—222no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—111no—
768C22×C4—111no—
769C22×C4—111no—
770C22×C4—111no—
771C22×C4—114no—
772C22×C4—114no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—111no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—224no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—222no—
787C22×C4—222no—
788C22×C4—441no—
789C22×C4—441no—
790C22×C4—441no—
791C22×C4—441no—
792C22×C4—441no—
793C22×C4—441no—
794C22×C4—442no—
795C22×C4—442no—
796C22×C4#434114yes—
797C22×C4C23×D1112yes—
798C22×C4C23×D1112yes—
799C22×C4C23×D1112yes—
800C22×C4C23×D1112yes—
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803C22×C4C23×D1111yescharacteristic
804C22×C4C23×D1111yescharacteristic
805C22×C4C23×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C4⋊C4—22no—
808C4⋊C4—24no—
809C4⋊C4—42no—
810C4⋊C4—42no—
811C4⋊C4—42no—
812C4⋊C4—42no—
813C4⋊C4—114no—
814C4⋊C4—224no—
815C4⋊C4—222no—
816C4⋊C4—222no—
817C4⋊C4—222no—
818C4⋊C4—222no—
819C4⋊C4—222no—
820C4⋊C4—222no—
821C4⋊C4—224no—
822C4⋊C4—224no—
823C4⋊C4—224no—
824C4⋊C4—442no—
825C4⋊C4—442no—
826C4⋊C4—442no—
827C4⋊C4—442no—
828C4⋊C4—442no—
829C4⋊C4—442no—
830C4⋊C4—442no—
831C4⋊C4—442no—
832C22⋊C4—24no—
833C22⋊C4—114no—
834C22⋊C4—222no—
835C22⋊C4—224no—
836C22⋊C4—222no—
837C22⋊C4—222no—
838C22⋊C4—442no—
839C22⋊C4—442no—
840C22⋊C4—442no—
841C22⋊C4—442no—
842C22⋊C4Q8×D1114yes—
843C22⋊C4#434314yes—
844C42—22no—
845C42—22no—
846C42—114no—
847C42—222no—
848C42—222no—
849C42—222no—
850C42—222no—
851C42—222no—
852C42—441no—
853C42—441no—
854C42—441no—
855C42—441no—
856C42—442no—
857C42—441no—
858C42—442no—
859C11#3501611yescharacteristic, complemented, Sylow
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—112no—
865C23—221no—
866C23—221no—
867C23—221no—
868C23—221no—
869C23—221no—
870C23—221no—
871C23C2×#434112yes—
872C23C2×Q8×D1112yes—
873C23C2×#434312yes—
874C23C24×D1111yescharacteristic
875Q8—48no—
876Q8—44no—
877Q8—44no—
878Q8—44no—
879Q8—884no—
880D4—228no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—28no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—48no—
905C2×C4—112no—
906C2×C4—112no—
907C2×C4—112no—
908C2×C4—112no—
909C2×C4—221no—
910C2×C4—221no—
911C2×C4—221no—
912C2×C4—221no—
913C2×C4—221no—
914C2×C4—221no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—221no—
918C2×C4—221no—
919C2×C4—221no—
920C2×C4—221no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—222no—
925C2×C4—221no—
926C2×C4—222no—
927C2×C4—221no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—221no—
932C2×C4—222no—
933C2×C4—221no—
934C2×C4—221no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—444no—
939C2×C4—444no—
940C2×C4—444no—
941C2×C4—444no—
942C2×C4—444no—
943C2×C4—884no—
944C2×C4C2×#434112yes—
945C2×C4C2×#434112yes—
946C2×C4#6703712yes—
947C2×C4#6703712yes—
948C2×C4C2×Q8×D1112yes—
949C2×C4C2×Q8×D1112yes—
950C2×C4C2×#434312yes—
951C2×C4C2×#434312yes—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—222no—
959C22—222no—
960C22—222no—
961C22—441no—
962C22—441no—
963C22—441no—
964C22—441no—
965C22#1062325914yes—
966C22C22×#434111yescharacteristic
967C22C2×#6703711yescharacteristic
968C22C2×#6703711yescharacteristic
969C22C22×Q8×D1111yescharacteristic
970C22C22×#434311yescharacteristic
971C22D11×2−1+411yescharacteristic
972C22#1062345711yescharacteristic
973C4—22no—
974C4—22no—
975C4—22no—
976C4—22no—
977C4—22no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—222no—
983C4—222no—
984C4—222no—
985C4—222no—
986C4—441no—
987C4—442no—
988C4—441no—
989C4—441no—
990C4—442no—
991C4—442no—
992C4—442no—
993C4#1062312414yes—
994C2—24no—
995C2—442no—
996C2C2×#1062325911yescharacteristic
997C2C2×#1062312411yescharacteristic
998C2#1308204011yescharacteristic
999C2#1308241111yescharacteristic
1000C2#1308242711yescharacteristic
1001C2#1308257811yescharacteristic
1002C2#1308266611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2434C2
prime radicalC22×C22⋊D11C23
hypercenter#2434D11
hypocenterC11#35016
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2434

Complements

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

NH ≅ G/Ntype
1. #13076995C2semidirect
2. #13076993C2semidirect
3. #13076963C2semidirect
4. #13076957C2semidirect
5. #13074802C2semidirect
6. #13074791C2semidirect
7. #13074023C2semidirect
8. #13073885C2semidirect
9. #13073193C2semidirect
10. #13073123C2semidirect
11. #13072988C2semidirect
13. #13072388C2semidirect
14. #13072318C2semidirect
15. #13072218C2semidirect
18. #13071347C2semidirect
20. C22⋊Q8×Dic11C2semidirect
21. C2×#10622843C2semidirect
23. C11×#2434C2semidirect
203. (C22⋊D11)⋊C4Q8semidirect
303. C2×C4×D11C2×Q8semidirect
326. (C2×D11)⋊C4C2×Q8semidirect
345. Dic11⋊C4C2×Q8semidirect
358. C4×Dic11C2×Q8semidirect
373. #2434D11semidirect
859. C11#35016semidirect

Maximal subgroups

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

subgroupindex
#130769952
#130769932
#130769632
#130769572
#130748022
#130747912
#130740232
#130738852
#130731932
#130731232
#130729882
#130724382
#130723882
#130723182
#130722182
#130720682
#130719752
#130713472
#130712442
C22⋊Q8×Dic112
C2×#106228432
C4×(C22⋊D11)⋊C42
C11×#24342
#3501611