Finite Group Databasebeta

← #14921837

Subgroups — #14921837

Order 2816.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic, complemented
2C22×#66940C211yesmaximal, characteristic, complemented
3#13072762C212yesmaximal, complemented
4#13072638C212yesmaximal, complemented
5#13072599C212yesmaximal, complemented
6#13072453C211yesmaximal, characteristic, complemented
7#13072429C212yesmaximal
8#13072395C211yesmaximal, characteristic, complemented
9#13072312C211yesmaximal, characteristic, complemented
10#13072261C211yesmaximal, characteristic, complemented
11#13072211C211yesmaximal, characteristic, complemented
12#13072143C211yesmaximal, characteristic, complemented
13#13071981C211yesmaximal, characteristic
14#13071908C212yesmaximal, complemented
15#13071891C212yesmaximal, complemented
16#13071185C211yesmaximal, characteristic, complemented
17C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
18#13071144C212yesmaximal, complemented
19#13071144C211yesmaximal, characteristic, complemented
20#13071087C211yesmaximal, characteristic, complemented
21#13071056C212yesmaximal
22C4×D4×Dic11C211yesmaximal, characteristic
23C11×#2417C211yesmaximal, characteristic
24C23×Dic22C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C11×C4⋊C4C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30C2×#66997C2211yescharacteristic
31C2×#66997C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66977C2212yes—
36C2×#66977C2211yescharacteristic
37C22×Dic11⋊C4C2212yes—
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2212yes—
40C22×C4×Dic11C2211yescharacteristic
41#10623153—28no—
42C2×#66942C2212yes—
43C2×#66941C2211yescharacteristic
44C2×#66940—28no—
45C2×#66940C2211yescharacteristic
46C2×#66940C2212yes—
47C2×#66940C2212yes—
48C2×#66940C2211yescharacteristic
49C2×#66940C2211yescharacteristic
50C2×#66940C2212yes—
51C2×#66940C2211yescharacteristic
52C2×#66931C2212yes—
53C2×#66930C2212yes—
54C11×#398C2212yes—
55C11×#396C2212yes—
56C11×#391C2211yescharacteristic
57C11×#389C2211yescharacteristic
58C11×#386C2212yes—
59C11×#380C2211yescharacteristic
60C11×#380C2212yes—
61#10622843C2211yescharacteristic
62#10622833C2212yes—
63#10622825C2211yescharacteristic
64#10622823C2212yes—
65C4×C22⋊Dic11C2211yescharacteristic
66C4×C22⋊Dic11C2211yescharacteristic
67#10622598C2211yescharacteristic
68#10622598C2211yescharacteristic
69#10622597C2212yes—
70#10622596C2212yes—
71#10622594C2212yes—
72#10622593C2212yes—
73#10622592C2212yes—
74#10622592C2212yes—
75#10622592C2212yes—
76#10622592C2212yes—
77#10622591C2212yes—
78#10622589C2211yescharacteristic
79C4⋊C4×Dic11C2212yes—
80C4⋊C4×Dic11C2212yes—
81C4⋊C4×Dic11C2211yescharacteristic
82C4⋊C4×Dic11C2211yescharacteristic
83C4⋊C4×Dic11C2211yescharacteristic
84#10622587C2211yescharacteristic
85#10622587C2211yescharacteristic
86#10622587C2212yes—
87#10622586C2211yescharacteristic
88#10622586C2212yes—
89#10622563C2212yes—
90#10622562C2212yes—
91#10622561C2212yes—
92#10622560C2212yes—
93#10622559C2212yes—
94#10622559C2212yes—
95#10622559C2212yes—
96#10622559C2212yes—
97#10622558C2212yes—
98#10622557C2212yes—
99C22⋊C4×Dic11C2211yescharacteristic
100C22⋊C4×Dic11C2212yes—
101C22⋊C4×Dic11C2211yescharacteristic
102C22⋊C4×Dic11C2212yes—
103C22⋊C4×Dic11C2211yescharacteristic
104C22⋊C4×Dic11C2211yescharacteristic
105C4×C4⋊Dic11C2211yescharacteristic
106C42×Dic11C2211yescharacteristic
107#10622542C2211yescharacteristic
108#10622542C2211yescharacteristic
109#10622271C2212yes—
110#10622270C2212yes—
111#10622270C2212yes—
112#10622269C2212yes—
113#10622268C2212yes—
114#10622267C2212yes—
115#10622266C2212yes—
116#10622265C2212yes—
117#10622265C2212yes—
118#10622265C2212yes—
119#10622262C2212yes—
120#10622262C2212yes—
121#10622262C2212yes—
122#10622261C2212yes—
123#10622260C2212yes—
124#10622260C2212yes—
125C22×Q8×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×Dic11C2312yes—
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C22×Dic22—24no—
136C22×Dic22—24no—
137C22×Dic22—24no—
138C22×Dic22C2312yes—
139C22×Dic22C2312yes—
140C22×Dic22C2311yescharacteristic
141C22×Dic22C2311yescharacteristic
142C11×C22⋊Q8—24no—
143C11×C22⋊Q8—24no—
144C4×D4×C11—24no—
145C2×C11×C4⋊C4—24no—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C2311yescharacteristic
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C42×C11C2311yescharacteristic
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2311yescharacteristic
164C2×C22⋊Dic11C2311yescharacteristic
165C2×C22⋊Dic11C2311yescharacteristic
166C2×C22⋊Dic11C2311yescharacteristic
167Q8×Dic11—24no—
168#66997—24no—
169#66997—24no—
170D4×Dic11—24no—
171D4×Dic11Q818yescomplemented
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2311yescharacteristic
179#66977—24no—
180#66977—24no—
181#66977—28no—
182C2×Dic11⋊C4—28no—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×C4×Dic11—28no—
198C2×C4×Dic11—24no—
199C2×C4×Dic11—24no—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218#66942—28no—
219#66941—24no—
220#66940—24no—
221#66940—24no—
222#66940—28no—
223#66940—28no—
224#66940—24no—
225#66940—28no—
226#66940D418yescomplemented
227#66931—28no—
228#66930—28no—
229C11×#95C2312yes—
230C11×#95C2312yes—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2311yescharacteristic
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254#34691—111nomaximal, Sylow
255C24×C11C2411yescharacteristic
256C24×C11C2411yescharacteristic
257C2×Q8×C11—22no—
258C2×Q8×C11—22no—
259C2×Q8×C11—22no—
260C2×D4×C11—22no—
261C2×D4×C11—22no—
262C2×D4×C11C2×Q814yes—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—24no—
266C22×C4×C11—24no—
267C22×C4×C11—22no—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—42no—
271C22×C4×C11#4114yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2412yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2412yes—
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×Dic11—22no—
282C22×Dic11—22no—
283C22×Dic11—24no—
284C22×Dic11—24no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—24no—
291C22×Dic11—22no—
292C22×Dic11—41no—
293C22×Dic11—41no—
294C22×Dic11C2×Q814yes—
295C22×Dic11C2×Q814yescomplemented
296C22×Dic11C2412yes—
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2412yes—
306C22×Dic11C2411yescharacteristic
307C22×Dic11C2411yescharacteristic
308C2×Dic22—232no—
309C2×Dic22—24no—
310C2×Dic22—24no—
311C2×Dic22—24no—
312C2×Dic22—22no—
313C2×Dic22—24no—
314C2×Dic22—24no—
315C2×Dic22—22no—
316C2×Dic22—22no—
317C2×Dic22—22no—
318C2×Dic22—42no—
319C2×Dic22C2×D414yes—
320C2×Dic22#4114yes—
321C11×C4⋊C4—24no—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—24no—
324C11×C4⋊C4—22no—
325C11×C4⋊C4—22no—
326C11×C4⋊C4—24no—
327C11×C4⋊C4—42no—
328C11×C4⋊C4C2×D414yes—
329C11×C22⋊C4—22no—
330C11×C22⋊C4—24no—
331C11×C22⋊C4—24no—
332C11×C22⋊C4—22no—
333C11×C22⋊C4—42no—
334C42×C11—22no—
335C22⋊Dic11—24no—
336C22⋊Dic11—24no—
337C22⋊Dic11—22no—
338C22⋊Dic11—24no—
339C22⋊Dic11C2×Q814yes—
340C22⋊Dic11C2×Q814yescomplemented
341C22⋊Dic11#4114yes—
342C4⋊Dic11—24no—
343C4⋊Dic11—24no—
344C4⋊Dic11—22no—
345C4⋊Dic11—22no—
346C4⋊Dic11—22no—
347C4⋊Dic11—42no—
348C4⋊Dic11C2×Q814yescomplemented
349Dic11⋊C4—24no—
350Dic11⋊C4—24no—
351Dic11⋊C4—24no—
352Dic11⋊C4—24no—
353Dic11⋊C4—24no—
354Dic11⋊C4—24no—
355Dic11⋊C4—24no—
356Dic11⋊C4—24no—
357Dic11⋊C4—24no—
358Dic11⋊C4—24no—
359Dic11⋊C4—24no—
360Dic11⋊C4—24no—
361Dic11⋊C4—42no—
362Dic11⋊C4C2×D418yes—
363C4×Dic11—24no—
364C4×Dic11—22no—
365C4×Dic11—22no—
366C4×Dic11—24no—
367C4×Dic11—24no—
368C4×Dic11—22no—
369C4×Dic11—22no—
370C4×Dic11—22no—
371C4×Dic11—22no—
372C4×Dic11—24no—
373C4×Dic11—24no—
374C4×Dic11—22no—
375C4×Dic11—22no—
376C4×Dic11—22no—
377C4×Dic11—41no—
378C4×Dic11C2×D418yes—
379C4×Dic11C2×D414yes—
380C4×Dic11C2×Q814yescomplemented
381C2×#533—111no—
382C22×C4×Q8—111no—
383#2473—112no—
384#2465—112no—
385#2462—112no—
386#2451—111no—
387#2449—112no—
388#2446—111no—
389#2440—111no—
390#2434—111no—
391#2429—111no—
392#2423—111no—
393#2417D1111yescharacteristic
394#2409—111no—
395#2399—112no—
396#2396—112no—
397C4×C4⋊Q8—111no—
398C4×C22⋊Q8—111no—
399C4×C22⋊Q8—112no—
400C4×C22⋊Q8—111no—
401#2295—111no—
402#2290—112no—
403C42×D4—111no—
404C23×C11—21no—
405C23×C11—21no—
406C23×C11—21no—
407C23×C11—21no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11—21no—
414C23×C11C22×Q812yes—
415C23×C11C22×Q812yes—
416C23×C11C2×#4112yes—
417C23×C11C2×#4112yes—
418C23×C11C2511yescharacteristic
419Q8×C11—44no—
420D4×C11—28no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—22no—
427C2×C4×C11—28no—
428C2×C4×C11—21no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—21no—
435C2×C4×C11—22no—
436C2×C4×C11—21no—
437C2×C4×C11—22no—
438C2×C4×C11—21no—
439C2×C4×C11—22no—
440C2×C4×C11—21no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—48no—
444C2×C4×C11—44no—
445C2×C4×C11C22×D414yes—
446C2×C4×C11C22×D412yes—
447C2×C4×C11C22×Q812yes—
448C2×C4×C11C2×#4112yes—
449C2×C4×C11C2×#4112yes—
450C2×C4×C11C2×#4112yes—
451C2×Dic11—216no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—21no—
456C2×Dic11—21no—
457C2×Dic11—21no—
458C2×Dic11—21no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—21no—
463C2×Dic11—21no—
464C2×Dic11—21no—
465C2×Dic11—21no—
466C2×Dic11—21no—
467C2×Dic11—21no—
468C2×Dic11—28no—
469C2×Dic11—28no—
470C2×Dic11—21no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—21no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—21no—
479C2×Dic11—44no—
480C2×Dic11—44no—
481C2×Dic11C22×D412yes—
482C2×Dic11C22×D414yes—
483C2×Dic11C22×D412yes—
484C2×Dic11C22×Q812yes—
485C2×Dic11C22×Q812yes—
486C2×Dic11C22×Q812yes—
487C2×Dic11C22×Q812yes—
488C2×Dic11C2×#4112yes—
489C2×Dic11C2×#4114yes—
490C2×Dic11C2×#4112yes—
491C2×Dic112−1+412yes—
492Dic22—216no—
493Dic22—28no—
494Dic22—28no—
495Dic22—48no—
496C23×Q8—111no—
497#533—228no—
498C2×C4⋊Q8—111no—
499C2×C4⋊Q8—111no—
500C2×C4⋊Q8—111no—
501C2×#125—112no—
502C2×C22⋊Q8—111no—
503C2×C22⋊Q8—111no—
504C2×C22⋊Q8—112no—
505C2×C22⋊Q8—112no—
506C2×C22⋊Q8C2×D1111yescharacteristic
507C2×C22⋊Q8C2×D1111yescharacteristic
508C2×C4×Q8—111no—
509C2×C4×Q8—111no—
510C2×C4×Q8—111no—
511C2×C4×Q8—112no—
512C2×C4×Q8—112no—
513C2×C4×Q8—111no—
514C2×C4×Q8—111no—
515C2×C4×Q8—112no—
516C2×C4×Q8—228no—
517C2×C4×D4—111no—
518C2×C4×D4—111no—
519C2×C4×D4C2×D1111yescharacteristic
520C2×#117—112no—
521C22×C4⋊C4—112no—
522C22×C4⋊C4C2×D1111yescharacteristic
523C22×C42—111no—
524C22×C42—112no—
525C22×C42—111no—
526#400—112no—
527#399—112no—
528#398—112no—
529#398—112no—
530#398—112no—
531#398—112no—
532#398—112no—
533#398C2×D1112yes—
534#396—112no—
535#396C2×D1112yes—
536#395—112no—
537#395—112no—
538#395—112no—
539#395—112no—
540#395—112no—
541#393—112no—
542#391—111no—
543#391—111no—
544#391—111no—
545#391—112no—
546#391—111no—
547#391—111no—
548#391C2×D1111yescharacteristic
549#389—111no—
550#389—112no—
551#389—111no—
552#389—111no—
553#389—112no—
554#389—112no—
555#389C2×D1111yescharacteristic
556#388—112no—
557#388—112no—
558#387—112no—
559#387—112no—
560#387—112no—
561#387—112no—
562#387—112no—
563#387—112no—
564#387—112no—
565#387—112no—
566#386—112no—
567#386C2×D1112yes—
568#385—112no—
569#385—112no—
570#385—112no—
571#385—112no—
572#385—112no—
573#385—112no—
574#384—111no—
575#380—111no—
576#380C2×D1111yescharacteristic
577#380C2×D1112yes—
578C4×C4⋊C4—112no—
579C4×C4⋊C4—112no—
580C4×C4⋊C4—111no—
581C4×C4⋊C4—111no—
582C4×C4⋊C4—111no—
583C4×C4⋊C4—111no—
584C4×C4⋊C4—112no—
585C4×C4⋊C4—112no—
586C4×C4⋊C4—112no—
587C4×C22⋊C4—111no—
588C4×C22⋊C4—111no—
589C4×C22⋊C4—111no—
590C4×C22⋊C4—112no—
591C4×C22⋊C4—111no—
592C4×C22⋊C4—111no—
593C4×C22⋊C4—111no—
594C4×C22⋊C4—112no—
595#376—112no—
596C43—111no—
597C22×C11—22no—
598C22×C11—22no—
599C22×C11—22no—
600C22×C11—22no—
601C22×C11—22no—
602C22×C11—22no—
603C22×C11—22no—
604C22×C11—22no—
605C22×C11—22no—
606C22×C11—41no—
607C22×C11—41no—
608C22×C11—41no—
609C22×C11—41no—
610C22×C11#53314yescomplemented
611C22×C11C23×D411yescharacteristic
612C22×C11C23×Q811yescharacteristic
613C22×C11C22×#4111yescharacteristic
614C22×C11C22×#4111yescharacteristic
615C22×C11C22×#4111yescharacteristic
616C22×C11C2×2−1+411yescharacteristic
617C22×C11#58511yescharacteristic
618C4×C11—22no—
619C4×C11—22no—
620C4×C11—24no—
621C4×C11—41no—
622C4×C11—42no—
623C4×C11—41no—
624C4×C11—42no—
625C4×C11—42no—
626C4×C11#52514yes—
627Dic11—24no—
628Dic11—24no—
629Dic11—22no—
630Dic11—22no—
631Dic11—22no—
632Dic11—22no—
633Dic11—22no—
634Dic11—22no—
635Dic11—42no—
636Dic11—41no—
637Dic11—42no—
638Dic11D4×Q814yes—
639C22×Q8—111no—
640C22×Q8—111no—
641C22×Q8—112no—
642C22×Q8—112no—
643C22×Q8—224no—
644C22×Q8—224no—
645C22×Q8—224no—
646C22×Q8C22×D1111yescharacteristic
647C22×D4C22×D1111yescharacteristic
648C23×C4—111no—
649C23×C4—111no—
650C23×C4—112no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1112yes—
655C23×C4C22×D1111yescharacteristic
656C4⋊Q8—224no—
657C4⋊Q8—224no—
658C4⋊Q8—224no—
659#125—228no—
660C22⋊Q8—24no—
661C22⋊Q8—24no—
662C22⋊Q8—228no—
663C22⋊Q8—228no—
664C22⋊Q8—224no—
665C22⋊Q8—224no—
666C4×Q8—118no—
667C4×Q8—224no—
668C4×Q8—228no—
669C4×Q8—228no—
670C4×Q8—224no—
671C4×Q8—228no—
672C4×Q8—224no—
673C4×Q8—224no—
674C4×D4—24no—
675C4×D4—118no—
676C4×D4—224no—
677#117—228no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—111no—
681C2×C4⋊C4—112no—
682C2×C4⋊C4—112no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—112no—
685C2×C4⋊C4—112no—
686C2×C4⋊C4—111no—
687C2×C4⋊C4—112no—
688C2×C4⋊C4—112no—
689C2×C4⋊C4—111no—
690C2×C4⋊C4—112no—
691C2×C4⋊C4—111no—
692C2×C4⋊C4—112no—
693C2×C4⋊C4—112no—
694C2×C4⋊C4—112no—
695C2×C4⋊C4—112no—
696C2×C4⋊C4—112no—
697C2×C4⋊C4—112no—
698C2×C4⋊C4—112no—
699C2×C4⋊C4—112no—
700C2×C4⋊C4—228no—
701C2×C4⋊C4C22×D1111yescharacteristic
702C2×C4⋊C4C22×D1112yes—
703C2×C4⋊C4C22×D1111yescharacteristic
704C2×C4⋊C4C22×D1112yes—
705C2×C4⋊C4C22×D1111yescharacteristic
706C2×C4⋊C4C22×D1112yes—
707C2×C4⋊C4C22×D1112yes—
708C2×C4⋊C4C22×D1111yescharacteristic
709C2×C22⋊C4—111no—
710C2×C22⋊C4—111no—
711C2×C22⋊C4—111no—
712C2×C22⋊C4—112no—
713C2×C22⋊C4—111no—
714C2×C22⋊C4—112no—
715C2×C22⋊C4—112no—
716C2×C22⋊C4C22×D1112yes—
717C2×C22⋊C4C22×D1111yescharacteristic
718C2×C22⋊C4C22×D1111yescharacteristic
719C2×C22⋊C4C22×D1112yes—
720C2×C22⋊C4C22×D1112yes—
721C2×C42—112no—
722C2×C42—111no—
723C2×C42—111no—
724C2×C42—112no—
725C2×C42—111no—
726C2×C42—111no—
727C2×C42—112no—
728C2×C42—111no—
729C2×C42—111no—
730C2×C42—111no—
731C2×C42—112no—
732C2×C42—112no—
733C2×C42—111no—
734C2×C42—111no—
735C2×C42—111no—
736C2×C42—111no—
737C2×C42—112no—
738C2×C42—111no—
739C2×C42—224no—
740C2×C42—228no—
741C2×C42—224no—
742C2×C42C22×D1111yescharacteristic
743#95—112no—
744#95—112no—
745#95—112no—
746#95—111no—
747#95—111no—
748#95—111no—
749#95—111no—
750#95—111no—
751#95—111no—
752#95—112no—
753#95—112no—
754#95—112no—
755#95—112no—
756#95—112no—
757#95—112no—
758#95—112no—
759#95—112no—
760#95—112no—
761#95—112no—
762#95—112no—
763#95—112no—
764#95C22×D1112yes—
765#95C22×D1112yes—
766#95C22×D1112yes—
767#95C22×D1112yes—
768C2×C11—24no—
769C2×C11—42no—
770C2×C11C2×#52511yescharacteristic
771C2×C11C2×#53311yescharacteristic
772C2×C11#346111yescharacteristic
773C2×C11C2×D4×Q811yescharacteristic
774C2×C11D4×#4111yescharacteristic
775C2×C11Q8×#4111yescharacteristic
776C2×C11#348211yescharacteristic
777C24C23×D1111yescharacteristic
778C24C23×D1111yescharacteristic
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—114no—
783C2×Q8—114no—
784C2×Q8—224no—
785C2×Q8—224no—
786C2×Q8—224no—
787C2×Q8—2232no—
788C2×Q8—222no—
789C2×Q8—224no—
790C2×Q8—224no—
791C2×Q8—222no—
792C2×Q8—222no—
793C2×Q8—222no—
794C2×Q8—442no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4Q8×D1114yes—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—42no—
806C22×C4—111no—
807C22×C4—114no—
808C22×C4—114no—
809C22×C4—111no—
810C22×C4—111no—
811C22×C4—111no—
812C22×C4—111no—
813C22×C4—112no—
814C22×C4—111no—
815C22×C4—112no—
816C22×C4—111no—
817C22×C4—112no—
818C22×C4—111no—
819C22×C4—112no—
820C22×C4—222no—
821C22×C4—224no—
822C22×C4—222no—
823C22×C4—224no—
824C22×C4—222no—
825C22×C4—222no—
826C22×C4—222no—
827C22×C4—222no—
828C22×C4—222no—
829C22×C4—224no—
830C22×C4—222no—
831C22×C4—441no—
832C22×C4—441no—
833C22×C4#434114yes—
834C22×C4C23×D1111yescharacteristic
835C22×C4C23×D1112yes—
836C22×C4C23×D1111yescharacteristic
837C22×C4C23×D1112yes—
838C22×C4C23×D1112yes—
839C22×C4C23×D1112yes—
840C22×C4C23×D1111yescharacteristic
841C22×C4C23×D1111yescharacteristic
842C22×C4C23×D1111yescharacteristic
843C4⋊C4—24no—
844C4⋊C4—22no—
845C4⋊C4—24no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—42no—
850C4⋊C4—118no—
851C4⋊C4—114no—
852C4⋊C4—224no—
853C4⋊C4—224no—
854C4⋊C4—224no—
855C4⋊C4—222no—
856C4⋊C4—224no—
857C4⋊C4—224no—
858C4⋊C4—224no—
859C4⋊C4—224no—
860C4⋊C4—224no—
861C4⋊C4—224no—
862C4⋊C4—224no—
863C4⋊C4—224no—
864C4⋊C4—224no—
865C4⋊C4—224no—
866C4⋊C4—224no—
867C4⋊C4—222no—
868C4⋊C4—222no—
869C4⋊C4—442no—
870C4⋊C4—442no—
871C4⋊C4D4×D1114yes—
872C22⋊C4—22no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—22no—
876C22⋊C4—42no—
877C22⋊C4—114no—
878C22⋊C4—114no—
879C22⋊C4—114no—
880C22⋊C4—224no—
881C22⋊C4—222no—
882C22⋊C4—224no—
883C22⋊C4—224no—
884C42—22no—
885C42—114no—
886C42—118no—
887C42—114no—
888C42—222no—
889C42—222no—
890C42—224no—
891C42—222no—
892C42—224no—
893C42—222no—
894C42—224no—
895C42—222no—
896C42—222no—
897C42—224no—
898C42—224no—
899C42—222no—
900C42—222no—
901C42—222no—
902C42—441no—
903C11#3469111yescharacteristic, complemented, Sylow
904C23—21no—
905C23—21no—
906C23—21no—
907C23—21no—
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23C2×#434112yes—
915C23C2×Q8×D1112yes—
916C23C2×Q8×D1112yes—
917C23#41×D1112yes—
918C23C24×D1111yescharacteristic
919Q8—44no—
920Q8—2216no—
921Q8—228no—
922Q8—228no—
923Q8—448no—
924D4—28no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—28no—
932C2×C4—21no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—48no—
948C2×C4—44no—
949C2×C4—112no—
950C2×C4—112no—
951C2×C4—112no—
952C2×C4—112no—
953C2×C4—114no—
954C2×C4—112no—
955C2×C4—112no—
956C2×C4—112no—
957C2×C4—112no—
958C2×C4—112no—
959C2×C4—114no—
960C2×C4—228no—
961C2×C4—228no—
962C2×C4—2216no—
963C2×C4—221no—
964C2×C4—221no—
965C2×C4—222no—
966C2×C4—221no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—221no—
970C2×C4—221no—
971C2×C4—221no—
972C2×C4—222no—
973C2×C4—221no—
974C2×C4—221no—
975C2×C4—221no—
976C2×C4—221no—
977C2×C4—221no—
978C2×C4—221no—
979C2×C4—221no—
980C2×C4—222no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—221no—
984C2×C4—222no—
985C2×C4—221no—
986C2×C4—222no—
987C2×C4—222no—
988C2×C4—444no—
989C2×C4—444no—
990C2×C4C2×D4×D1114yes—
991C2×C4C2×D4×D1112yes—
992C2×C4C2×#434112yes—
993C2×C4C2×#434112yes—
994C2×C4C2×Q8×D1112yes—
995C2×C4#41×D1112yes—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22#1062315314yescomplemented
1010C22C22×D4×D1111yescharacteristic
1011C22C22×#434111yescharacteristic
1012C22C22×Q8×D1111yescharacteristic
1013C22C2×#41×D1111yescharacteristic
1014C22C2×#41×D1111yescharacteristic
1015C22#1062345511yescharacteristic
1016C22D11×2−1+411yescharacteristic
1017C4—22no—
1018C4—22no—
1019C4—24no—
1020C4—41no—
1021C4—42no—
1022C4—41no—
1023C4—42no—
1024C4—42no—
1025C4—114no—
1026C4—224no—
1027C4—224no—
1028C4—222no—
1029C4—222no—
1030C4—222no—
1031C4—222no—
1032C4—222no—
1033C4—222no—
1034C4—442no—
1035C4—441no—
1036C4—442no—
1037C4#1062313714yes—
1038C2—24no—
1039C2—42no—
1040C2C2×#1062313711yescharacteristic
1041C2C2×#1062315311yescharacteristic
1042C2#1308204411yescharacteristic
1043C2D4×Q8×D1111yescharacteristic
1044C2#1308210011yescharacteristic
1045C2#1308219511yescharacteristic
1046C2#1308223011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2417C2
prime radicalC22×D4×C11C23
hypercenter#2417D11
hypocenterC11#34691
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#10623153C2semidirect
2. C22×#66940C2semidirect
3. #13072762C2semidirect
4. #13072638C2semidirect
5. #13072599C2semidirect
6. #13072453C2semidirect
8. #13072395C2semidirect
9. #13072312C2semidirect
10. #13072261C2semidirect
11. #13072211C2semidirect
12. #13072143C2semidirect
14. #13071908C2semidirect
15. #13071891C2semidirect
16. #13071185C2semidirect
17. C22⋊Q8×Dic11C2semidirect
18. #13071144C2semidirect
19. #13071144C2semidirect
20. #13071087C2semidirect
171. D4×Dic11Q8semidirect
226. #66940D4semidirect
295. C22×Dic11C2×Q8semidirect
340. C22⋊Dic11C2×Q8semidirect
348. C4⋊Dic11C2×Q8semidirect
380. C4×Dic11C2×Q8semidirect
610. C22×C11#533semidirect
903. C11#34691semidirect
1009. C22#10623153semidirect

Maximal subgroups

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

subgroupindex
C2×#106231532
C22×#669402
#130727622
#130726382
#130725992
#130724532
#130724292
#130723952
#130723122
#130722612
#130722112
#130721432
#130719812
#130719082
#130718912
#130711852
C22⋊Q8×Dic112
#130711442
#130710872
#130710562
C4×D4×Dic112
C11×#24172
#3469111