Finite Group Databasebeta

← #14920724

Subgroups — #14920724

Order 2816.

2294 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623069C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13074530C212yesmaximal, complemented
4#13074528C212yesmaximal, complemented
5#13074496C212yesmaximal, complemented
6#13074480C212yesmaximal, complemented
7#13074435C211yesmaximal, characteristic, complemented
8#13074433C211yesmaximal, characteristic, complemented
9#13074402C211yesmaximal, characteristic, complemented
10#13074400C211yesmaximal, characteristic, complemented
11#13074364C211yesmaximal, characteristic
12#13074362C211yesmaximal, characteristic
13#13074338C211yesmaximal, characteristic, complemented
14#13074337C211yesmaximal, characteristic, complemented
15#13071910C212yesmaximal, complemented
16#13071903C212yesmaximal, complemented
17#13071892C212yesmaximal, complemented
18#13071890C212yesmaximal, complemented
19C4×#66939C211yesmaximal, characteristic, complemented
20C4×#66982C211yesmaximal, characteristic, complemented
21C4×#66988C211yesmaximal, characteristic, complemented
22#13071010C211yesmaximal, characteristic, complemented
23C4×C11×#123C211yesmaximal, characteristic, complemented
24C23×Dic22C2211yescharacteristic
25C2×C11×#123C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C2×#66992C2211yescharacteristic
29C2×#66988C2211yescharacteristic
30C2×#66988C2211yescharacteristic
31C2×#66982C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40#10623069—28no—
41C2×#66951C2211yescharacteristic
42C2×#66942C2211yescharacteristic
43C2×#66939C2211yescharacteristic
44C2×#66939C2211yescharacteristic
45C2×#66938C2211yescharacteristic
46C2×#66932C2211yescharacteristic
47C2×#66931C2211yescharacteristic
48C2×#66925C2211yescharacteristic
49C2×C4×Dic22—28no—
50C2×C4×Dic22C2212yes—
51C2×C4×Dic22C2211yescharacteristic
52C2×C4×Dic22C2212yes—
53C2×C4×Dic22C2212yes—
54C2×C4×Dic22C2212yes—
55C11×#388C2212yes—
56C11×#387C2212yes—
57C11×#386C2211yescharacteristic
58C11×#385C2211yescharacteristic
59C11×#381C2211yescharacteristic
60C4×C11×C4⋊C4C2212yes—
61C4×C11×C22⋊C4C2212yes—
62C4×C11×C22⋊C4C2211yescharacteristic
63#10622833C2211yescharacteristic
64#10622826C2211yescharacteristic
65#10622824C2211yescharacteristic
66#10622823C2211yescharacteristic
67C4×C22⋊Dic11C2212yes—
68C4×C22⋊Dic11C2211yescharacteristic
69#10622607C2212yes—
70#10622605C2212yes—
71#10622597C2212yes—
72#10622597C2212yes—
73#10622593C2212yes—
74#10622592C2212yes—
75#10622592C2212yes—
76#10622592C2212yes—
77#10622591C2212yes—
78#10622574C2212yes—
79#10622572C2212yes—
80#10622571C2211yescharacteristic
81#10622565C2212yes—
82#10622563C2211yescharacteristic
83#10622562C2212yes—
84#10622561C2212yes—
85#10622561C2212yes—
86#10622560C2212yes—
87#10622560C2212yes—
88#10622559C2211yescharacteristic
89#10622557C2212yes—
90#10622556C2211yescharacteristic
91#10622556C2211yescharacteristic
92#10622556C2211yescharacteristic
93#10622556C2211yescharacteristic
94#10622555C2211yescharacteristic
95#10622555C2211yescharacteristic
96#10622553C2212yes—
97C4×(C2×D11)⋊C4C2212yes—
98C4×(C2×D11)⋊C4C2212yes—
99C4×C4⋊Dic11C2212yes—
100#10622546C2212yes—
101#10622545C2212yes—
102C4×Dic11⋊C4C2212yes—
103C4×Dic11⋊C4C2212yes—
104C4×Dic11⋊C4C2212yes—
105#10622289C2212yes—
106#10622288C2212yes—
107#10622286C2212yes—
108#10622286C2212yes—
109#10622283C2212yes—
110#10622274C2212yes—
111#10622273C2212yes—
112#10622273C2212yes—
113#10622271C2212yes—
114#10622271C2212yes—
115#10622270C2212yes—
116#10622270C2212yes—
117#10622270C2212yes—
118#10622270C2212yes—
119#10622269C2212yes—
120#10622269C2212yes—
121#10622269C2212yes—
122#10622266C2212yes—
123#10622264C2212yes—
124#10622263C2212yes—
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C22×Dic22—24no—
138C22×Dic22—24no—
139C22×Dic22—24no—
140C22×Dic22C2312yes—
141C22×Dic22C2312yes—
142C22×Dic22C2311yescharacteristic
143C11×#123—24no—
144C4×D4×C11—24no—
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C22⋊C4C2311yescharacteristic
149C2×C11×C22⋊C4C2311yescharacteristic
150C2×C11×C22⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4C2311yescharacteristic
152C2×C11×C22⋊C4C2312yes—
153C2×C11×C22⋊C4C2312yes—
154C2×C42×C11—24no—
155C2×C42×C11C2312yes—
156C2×C42×C11C2312yes—
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2312yes—
159C2×C22⋊Dic11C2311yescharacteristic
160C2×C22⋊Dic11C2311yescharacteristic
161C2×C22⋊Dic11C2311yescharacteristic
162C2×C22⋊Dic11C2311yescharacteristic
163C2×C22⋊Dic11C2311yescharacteristic
164C2×C22⋊Dic11C2311yescharacteristic
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167#66992—24no—
168#66988—24no—
169#66988—24no—
170#66982—24no—
171C4×C22⋊D11—24no—
172C4×C22⋊D11—24no—
173C2×(C2×D11)⋊C4C2311yescharacteristic
174C2×(C2×D11)⋊C4C2311yescharacteristic
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181#66979—24no—
182C2×C4⋊Dic11—24no—
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2311yescharacteristic
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2312yes—
189C2×C4⋊Dic11C2312yes—
190C2×Dic11⋊C4—24no—
191C2×Dic11⋊C4—24no—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2311yescharacteristic
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2311yescharacteristic
199C2×Dic11⋊C4C2311yescharacteristic
200C2×Dic11⋊C4C2311yescharacteristic
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×C4×Dic11—24no—
209C2×C4×Dic11D418yes—
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218#66951—24no—
219#66942—24no—
220#66939—24no—
221#66939—24no—
222#66938—24no—
223#66932—24no—
224#66931—24no—
225#66925—24no—
226C4×Dic22—28no—
227C4×Dic22—28no—
228C4×Dic22—28no—
229C4×Dic22—28no—
230C4×Dic22—24no—
231C11×#95C2312yes—
232C11×#95C2312yes—
233C11×#95C2312yes—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255#34602—111nomaximal, Sylow
256C24×C11C2411yescharacteristic
257C24×C11C2411yescharacteristic
258C23×D11C2411yescharacteristic
259C2×D4×C11—22no—
260C2×D4×C11—22no—
261C2×D4×C11—22no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—24no—
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11—24no—
268C22×C4×C11—42no—
269C22×C4×C11C2×D414yes—
270C22×C4×C11#4114yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2412yes—
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2412yes—
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C2×C22⋊D11—22no—
281C2×C22⋊D11—22no—
282C2×C22⋊D11—22no—
283C2×C22⋊D11—22no—
284C2×C22⋊D11—42no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—42no—
291C22×Dic11—42no—
292C22×Dic11C2×D414yes—
293C22×Dic11C2×D414yes—
294C22×Dic11#4114yes—
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2412yes—
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2412yes—
306C2×C4×D11—22no—
307C2×C4×D11—24no—
308C2×Dic22—232no—
309C2×Dic22—24no—
310C2×Dic22—24no—
311C2×Dic22—24no—
312C2×Dic22—24no—
313C2×Dic22—22no—
314C2×Dic22—24no—
315C2×Dic22—24no—
316C2×Dic22—42no—
317C11×C4⋊C4—22no—
318C11×C4⋊C4—24no—
319C11×C4⋊C4—42no—
320C11×C22⋊C4—22no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—22no—
323C11×C22⋊C4—22no—
324C11×C22⋊C4—24no—
325C11×C22⋊C4—42no—
326C42×C11—24no—
327C42×C11—24no—
328C42×C11—22no—
329C42×C11—24no—
330C22⋊Dic11—22no—
331C22⋊Dic11—22no—
332C22⋊Dic11—22no—
333C22⋊Dic11—24no—
334C22⋊Dic11—22no—
335C22⋊Dic11—22no—
336C22⋊Dic11—22no—
337C22⋊Dic11—42no—
338(C2×D11)⋊C4—22no—
339(C2×D11)⋊C4—22no—
340(C2×D11)⋊C4—22no—
341(C2×D11)⋊C4—24no—
342(C2×D11)⋊C4—22no—
343(C2×D11)⋊C4—24no—
344(C2×D11)⋊C4—42no—
345(C2×D11)⋊C4—42no—
346C4⋊Dic11—24no—
347C4⋊Dic11—24no—
348C4⋊Dic11—22no—
349C4⋊Dic11—22no—
350C4⋊Dic11—22no—
351C4⋊Dic11—24no—
352C4⋊Dic11—42no—
353Dic11⋊C4—24no—
354Dic11⋊C4—24no—
355Dic11⋊C4—24no—
356Dic11⋊C4—24no—
357Dic11⋊C4—22no—
358Dic11⋊C4—22no—
359Dic11⋊C4—22no—
360Dic11⋊C4—22no—
361Dic11⋊C4—22no—
362Dic11⋊C4—24no—
363Dic11⋊C4—22no—
364Dic11⋊C4—24no—
365Dic11⋊C4—42no—
366Dic11⋊C4—42no—
367Dic11⋊C4—42no—
368Dic11⋊C4—42no—
369C4×Dic11—24no—
370C4×Dic11—24no—
371C4×Dic11—22no—
372C4×Dic11—24no—
373C4×Dic11C2×D414yes—
374C4×Dic11C2×D414yes—
375C4×Dic11C2×D414yes—
376C4×Dic11C2×D414yes—
377C2×#529—111no—
378C22×C4×Q8—111no—
379#2637—112no—
380#2637—112no—
381#2634—112no—
382#2632—112no—
383#2627—111no—
384#2627—111no—
385#2623—111no—
386#2623—111no—
387#2618—111no—
388#2618—111no—
389#2614—111no—
390#2614—111no—
391#2399—112no—
392#2398—112no—
393#2396—112no—
394#2396—112no—
395C4×#123—111no—
396C4×#123—111no—
397C4×#123—111no—
398C4×#123D1111yescharacteristic, complemented
399#2283—111no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—21no—
403C23×C11—21no—
404C23×C11—21no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11C22×D412yes—
408C23×C11C2×#4112yes—
409C23×C11C2×#4112yes—
410C23×C11C2511yescharacteristic
411C22×D11—21no—
412C22×D11—21no—
413C22×D11—21no—
414C22×D11—22no—
415C22×D11—22no—
416D4×C11—44no—
417C2×C4×C11—28no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—28no—
422C2×C4×C11—22no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—21no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—44no—
439C2×C4×C11—44no—
440C2×C4×C11C22×D412yes—
441C2×C4×C11C22×D412yes—
442C2×C4×C11C2×#4114yes—
443C2×C4×C112−1+414yes—
444C22⋊D11—44no—
445C22⋊D11—44no—
446C2×Dic11—28no—
447C2×Dic11—28no—
448C2×Dic11—22no—
449C2×Dic11—21no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—21no—
458C2×Dic11—21no—
459C2×Dic11—21no—
460C2×Dic11—21no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—21no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—44no—
473C2×Dic11—44no—
474C2×Dic11C22×D412yes—
475C2×Dic11C22×D412yes—
476C2×Dic11C22×D412yes—
477C2×Dic11C22×D412yes—
478C2×Dic11C2×#4114yes—
479C4×D11—44no—
480Dic22—216no—
481Dic22—216no—
482Dic22—44no—
483C23×Q8—111no—
484#529—228no—
485C2×#126—111no—
486C2×#126—111no—
487C2×#125—111no—
488C2×#124—111no—
489C2×#123—111no—
490C2×#123—111no—
491C2×#123—111no—
492C2×#123—111no—
493C2×#123—111no—
494C2×#123C2×D1111yescharacteristic
495C2×C22⋊Q8—111no—
496C2×#121—111no—
497C2×C4×Q8—112no—
498C2×C4×Q8—112no—
499C2×C4×Q8—112no—
500C2×C4×Q8—112no—
501C2×C4×Q8—111no—
502C2×C4×Q8—228no—
503C2×C4×D4—111no—
504C2×C4×D4—111no—
505C2×C4×D4C2×D1111yescharacteristic
506C2×#117—111no—
507C2×#117—111no—
508C22×C4⋊C4—111no—
509C22×C4⋊C4—111no—
510C22×C4⋊C4—111no—
511C22×C42—111no—
512C22×C42—111no—
513C22×C42C2×D1111yescharacteristic
514#400—112no—
515#400—112no—
516#400—112no—
517#400—112no—
518#399—112no—
519#399—112no—
520#398—112no—
521#398—112no—
522#398—112no—
523#398—112no—
524#398—112no—
525#398—112no—
526#398—112no—
527#398—112no—
528#397—112no—
529#397—112no—
530#396—112no—
531#396—112no—
532#396—112no—
533#396—112no—
534#395—112no—
535#395—112no—
536#395—112no—
537#395—112no—
538#395—112no—
539#395—112no—
540#394—112no—
541#394—112no—
542#393—112no—
543#393—112no—
544#393—112no—
545#393—112no—
546#388—112no—
547#388—112no—
548#388—112no—
549#388C2×D1112yes—
550#387—112no—
551#387—112no—
552#387—112no—
553#387C2×D1112yes—
554#386—111no—
555#386—111no—
556#386—111no—
557#386C2×D1111yescharacteristic
558#385—111no—
559#385—111no—
560#385—111no—
561#385C2×D1111yescharacteristic
562#383—112no—
563#382—112no—
564#381—111no—
565#381—111no—
566#381—111no—
567#381—111no—
568#381—111no—
569#381C2×D1111yescharacteristic
570#380—111no—
571#380—111no—
572C4×C4⋊C4—112no—
573C4×C4⋊C4—112no—
574C4×C4⋊C4—112no—
575C4×C4⋊C4—112no—
576C4×C4⋊C4C2×D1112yes—
577C4×C22⋊C4—112no—
578C4×C22⋊C4—111no—
579C4×C22⋊C4—112no—
580C4×C22⋊C4—112no—
581C4×C22⋊C4C2×D1112yes—
582C4×C22⋊C4C2×D1111yescharacteristic
583#376—112no—
584C22×C11—22no—
585C22×C11—22no—
586C22×C11—24no—
587C22×C11—24no—
588C22×C11—41no—
589C22×C11—41no—
590C22×C11—41no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11#52514yes—
594C22×C11C23×D411yescharacteristic
595C22×C11C22×#4111yescharacteristic
596C22×C11C22×#4111yescharacteristic
597C22×C11C2×2−1+412yes—
598C22×C11#58512yes—
599C2×D11—41no—
600C2×D11—41no—
601C2×D11—41no—
602C2×D11—42no—
603C2×D11—42no—
604C4×C11—24no—
605C4×C11—22no—
606C4×C11—41no—
607C4×C11—41no—
608C4×C11—42no—
609C4×C11—41no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11#53614yes—
613Dic11—22no—
614Dic11—22no—
615Dic11—24no—
616Dic11—22no—
617Dic11—22no—
618Dic11—41no—
619Dic11—41no—
620Dic11—41no—
621Dic11—42no—
622Dic11—42no—
623Dic11—42no—
624C22×Q8—112no—
625C22×Q8—112no—
626C22×Q8—111no—
627C22×Q8—224no—
628C22×Q8—224no—
629C22×Q8—224no—
630C22×D4—111no—
631C22×D4—111no—
632C22×D4C22×D1111yescharacteristic
633C23×C4—111no—
634C23×C4—111no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—111no—
638C23×C4C22×D1111yescharacteristic
639C23×C4C22×D1111yescharacteristic
640C23×C4C22×D1111yescharacteristic
641C23×C4C22×D1111yescharacteristic
642#126—224no—
643#126—224no—
644#125—224no—
645#124—224no—
646#123—24no—
647#123—224no—
648#123—224no—
649#123—224no—
650#123—224no—
651#123—224no—
652C22⋊Q8—224no—
653#121—224no—
654C4×Q8—228no—
655C4×Q8—228no—
656C4×Q8—228no—
657C4×Q8—228no—
658C4×Q8—224no—
659C4×D4—24no—
660C4×D4—224no—
661C4×D4—224no—
662#117—224no—
663#117—224no—
664C2×C4⋊C4—112no—
665C2×C4⋊C4—112no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4—112no—
668C2×C4⋊C4—112no—
669C2×C4⋊C4—112no—
670C2×C4⋊C4—111no—
671C2×C4⋊C4—111no—
672C2×C4⋊C4—111no—
673C2×C4⋊C4—111no—
674C2×C4⋊C4—111no—
675C2×C4⋊C4—111no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—111no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—112no—
681C2×C4⋊C4—112no—
682C2×C4⋊C4—112no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—112no—
685C2×C4⋊C4—112no—
686C2×C4⋊C4—112no—
687C2×C4⋊C4—224no—
688C2×C4⋊C4—224no—
689C2×C4⋊C4—224no—
690C2×C4⋊C4C22×D1111yescharacteristic
691C2×C4⋊C4C22×D1112yes—
692C2×C4⋊C4C22×D1112yes—
693C2×C22⋊C4—111no—
694C2×C22⋊C4—111no—
695C2×C22⋊C4—111no—
696C2×C22⋊C4—111no—
697C2×C22⋊C4—111no—
698C2×C22⋊C4—111no—
699C2×C22⋊C4—112no—
700C2×C22⋊C4—111no—
701C2×C22⋊C4—111no—
702C2×C22⋊C4—111no—
703C2×C22⋊C4—111no—
704C2×C22⋊C4—112no—
705C2×C22⋊C4—112no—
706C2×C22⋊C4—112no—
707C2×C22⋊C4—112no—
708C2×C22⋊C4—112no—
709C2×C22⋊C4C22×D1111yescharacteristic
710C2×C22⋊C4C22×D1111yescharacteristic
711C2×C22⋊C4C22×D1111yescharacteristic
712C2×C22⋊C4C22×D1111yescharacteristic
713C2×C22⋊C4C22×D1112yes—
714C2×C22⋊C4C22×D1112yes—
715C2×C42—24no—
716C2×C42—118no—
717C2×C42—111no—
718C2×C42—111no—
719C2×C42—111no—
720C2×C42—111no—
721C2×C42—112no—
722C2×C42—111no—
723C2×C42—112no—
724C2×C42—112no—
725C2×C42—224no—
726C2×C42C22×D1112yes—
727C2×C42C22×D1111yescharacteristic
728C2×C42C22×D1112yes—
729C2×C42C22×D1112yes—
730#95—112no—
731#95—112no—
732#95—112no—
733#95—112no—
734#95—112no—
735#95—112no—
736#95—112no—
737#95—112no—
738#95—112no—
739#95—112no—
740#95—112no—
741#95—112no—
742#95—112no—
743#95—112no—
744#95—112no—
745#95—112no—
746#95—112no—
747#95—112no—
748#95—112no—
749#95C22×D1112yes—
750#95C22×D1112yes—
751#95C22×D1112yes—
752#95C22×D1112yes—
753#95C22×D1112yes—
754C2×C11—24no—
755C2×C11—81no—
756C2×C11C2×#52511yescharacteristic
757C2×C11C2×#53611yescharacteristic
758C2×C11#344911yescharacteristic
759C2×C11#346112yes—
760C2×C11#346112yes—
761D11—81no—
762C24—111no—
763C24C23×D1111yescharacteristic
764C24C23×D1111yescharacteristic
765C2×Q8—224no—
766C2×Q8—224no—
767C2×Q8—224no—
768C2×Q8—224no—
769C2×Q8—222no—
770C2×Q8—2232no—
771C2×Q8—224no—
772C2×Q8—224no—
773C2×Q8—442no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—222no—
778C2×D4—222no—
779C2×D4—222no—
780C2×D4—222no—
781C2×D4—442no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—24no—
788C22×C4—42no—
789C22×C4—114no—
790C22×C4—114no—
791C22×C4—111no—
792C22×C4—111no—
793C22×C4—112no—
794C22×C4—111no—
795C22×C4—111no—
796C22×C4—114no—
797C22×C4—112no—
798C22×C4—112no—
799C22×C4—111no—
800C22×C4—112no—
801C22×C4—111no—
802C22×C4—111no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—222no—
806C22×C4—222no—
807C22×C4—222no—
808C22×C4—222no—
809C22×C4—224no—
810C22×C4—442no—
811C22×C4—442no—
812C22×C4#433914yes—
813C22×C4D4×D1114yes—
814C22×C4C23×D1112yes—
815C22×C4C23×D1112yes—
816C22×C4C23×D1111yescharacteristic
817C22×C4C23×D1112yes—
818C22×C4C23×D1111yescharacteristic
819C22×C4C23×D1111yescharacteristic
820C22×C4C23×D1112yes—
821C22×C4C23×D1111yescharacteristic
822C22×C4C23×D1111yescharacteristic
823C4⋊C4—24no—
824C4⋊C4—22no—
825C4⋊C4—42no—
826C4⋊C4—224no—
827C4⋊C4—224no—
828C4⋊C4—224no—
829C4⋊C4—224no—
830C4⋊C4—224no—
831C4⋊C4—224no—
832C4⋊C4—222no—
833C4⋊C4—222no—
834C4⋊C4—222no—
835C4⋊C4—222no—
836C4⋊C4—222no—
837C4⋊C4—222no—
838C4⋊C4—222no—
839C4⋊C4—222no—
840C4⋊C4—224no—
841C4⋊C4—224no—
842C4⋊C4—224no—
843C4⋊C4—222no—
844C4⋊C4—442no—
845C4⋊C4—442no—
846C4⋊C4—442no—
847C4⋊C4—442no—
848C4⋊C4—442no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—22no—
852C22⋊C4—24no—
853C22⋊C4—22no—
854C22⋊C4—42no—
855C22⋊C4—222no—
856C22⋊C4—222no—
857C22⋊C4—222no—
858C22⋊C4—224no—
859C22⋊C4—222no—
860C22⋊C4—222no—
861C22⋊C4—222no—
862C22⋊C4—224no—
863C22⋊C4—222no—
864C22⋊C4—222no—
865C22⋊C4—222no—
866C22⋊C4—224no—
867C22⋊C4—222no—
868C22⋊C4—442no—
869C22⋊C4—442no—
870C22⋊C4—442no—
871C42—24no—
872C42—24no—
873C42—22no—
874C42—24no—
875C42—114no—
876C42—114no—
877C42—114no—
878C42—114no—
879C42—224no—
880C42—224no—
881C42—222no—
882C42—224no—
883C11#3460211yescharacteristic, complemented, Sylow
884C23—22no—
885C23—22no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—22no—
890C23—22no—
891C23—221no—
892C23—221no—
893C23—221no—
894C23—222no—
895C23—222no—
896C23C2×#433912yes—
897C23C2×D4×D1112yes—
898C23#41×D1112yes—
899C23C24×D1111yescharacteristic
900Q8—2216no—
901Q8—2216no—
902Q8—444no—
903D4—44no—
904D4—444no—
905D4—444no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—112no—
930C2×C4—112no—
931C2×C4—112no—
932C2×C4—112no—
933C2×C4—114no—
934C2×C4—228no—
935C2×C4—228no—
936C2×C4—221no—
937C2×C4—221no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—221no—
941C2×C4—221no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—221no—
946C2×C4—222no—
947C2×C4—221no—
948C2×C4—221no—
949C2×C4—221no—
950C2×C4—222no—
951C2×C4—221no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—222no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—444no—
961C2×C4—444no—
962C2×C4—444no—
963C2×C4C2×#433914yes—
964C2×C4C2×D4×D1112yes—
965C2×C4C2×D4×D1112yes—
966C2×C4#6704314yes—
967C22—22no—
968C22—22no—
969C22—24no—
970C22—24no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—42no—
975C22—42no—
976C22—441no—
977C22—441no—
978C22—441no—
979C22—442no—
980C22—442no—
981C22#1062307814yes—
982C22C22×#433911yescharacteristic
983C22C22×D4×D1111yescharacteristic
984C22C2×#41×D1111yescharacteristic
985C22C2×#6704312yes—
986C22#1062345312yes—
987C4—24no—
988C4—22no—
989C4—41no—
990C4—41no—
991C4—42no—
992C4—41no—
993C4—42no—
994C4—42no—
995C4—222no—
996C4—222no—
997C4—224no—
998C4—222no—
999C4—222no—
1000C4—441no—
1001C4—441no—
1002C4—442no—
1003C4—441no—
1004C4—442no—
1005C4—442no—
1006C4#1062317914yes—
1007C2—24no—
1008C2—81no—
1009C2—881no—
1010C2C2×#1062307811yescharacteristic
1011C2C2×#1062317911yescharacteristic
1012C2#1308194611yescharacteristic
1013C2#1308204312yes—
1014C2#1308204512yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#123C2
prime radicalC2×#66992C22
hypercenterC4×#123D11
hypocenterC11#34602
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13074530C2semidirect
4. #13074528C2semidirect
5. #13074496C2semidirect
6. #13074480C2semidirect
7. #13074435C2semidirect
8. #13074433C2semidirect
9. #13074402C2semidirect
10. #13074400C2semidirect
13. #13074338C2semidirect
14. #13074337C2semidirect
15. #13071910C2semidirect
16. #13071903C2semidirect
17. #13071892C2semidirect
18. #13071890C2semidirect
19. C4×#66939C2semidirect
20. C4×#66982C2semidirect
21. C4×#66988C2semidirect
22. #13071010C2semidirect
23. C4×C11×#123C2semidirect
398. C4×#123D11semidirect
883. C11#34602semidirect

Maximal subgroups

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

subgroupindex
C2×#106230692
C22×C4×Dic222
#130745302
#130745282
#130744962
#130744802
#130744352
#130744332
#130744022
#130744002
#130743642
#130743622
#130743382
#130743372
#130719102
#130719032
#130718922
#130718902
C4×#669392
C4×#669822
C4×#669882
#130710102
C4×C11×#1232
#3460211