Finite Group Databasebeta

← #14913996

Subgroups — #14913996

Order 2816.

2370 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2#13071578C212yesmaximal, complemented
3#13071554C212yesmaximal, complemented
4#13071551C212yesmaximal, complemented
5#13071522C212yesmaximal, complemented
6#13071506C212yesmaximal, complemented
7#13071475C212yesmaximal, complemented
8#13071474C212yesmaximal, complemented
9#13071442C212yesmaximal
10#13071266C211yesmaximal, characteristic, complemented
11#13071264C211yesmaximal, characteristic, complemented
12#13071251C211yesmaximal, characteristic, complemented
13#13071249C211yesmaximal, characteristic, complemented
14#13071245C211yesmaximal, characteristic, complemented
15#13071011C211yesmaximal, characteristic, complemented
16#13071010C211yesmaximal, characteristic, complemented
17#13071009C211yesmaximal, characteristic, complemented
18#13071007C211yesmaximal, characteristic, complemented
19C2×#10622264C211yesmaximal, characteristic, complemented
20D11×#383C211yesmaximal, characteristic, complemented
21#13070975C211yesmaximal, characteristic, complemented
22#13070974C211yesmaximal, characteristic, complemented
23C11×#2318C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×D4×Dic11C2211yescharacteristic
27C2×C4×C22⋊D11C2212yes—
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×C4×C22⋊D11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C4×#4341C4116yescomplemented
33C2×#66945C2211yescharacteristic
34C2×#66940C2211yescharacteristic
35C2×(C22⋊D11)⋊C4C2212yes—
36C2×(C22⋊D11)⋊C4C2211yescharacteristic
37C2×(C22⋊D11)⋊C4C2211yescharacteristic
38C2×#66930C2211yescharacteristic
39C2×#66930C2211yescharacteristic
40C2×C42×D11C2211yescharacteristic
41C2×C4×Dic22C2211yescharacteristic
42C11×#388C2212yes—
43C11×#387C2212yes—
44C11×#386C2212yes—
45C11×#385C2212yes—
46C11×#383C2211yescharacteristic
47C11×#382C2211yescharacteristic
48C11×#381C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52#10622833C2212yes—
53#10622825C2211yescharacteristic
54#10622824C2211yescharacteristic
55C4×C22⋊Dic11C2212yes—
56C4×C22⋊Dic11C2211yescharacteristic
57C2×C11⋊#95C2212yes—
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2212yes—
60#10622602C2212yes—
61#10622600C2212yes—
62#10622594C2212yes—
63#10622591C2212yes—
64#10622591C2212yes—
65#10622590C2212yes—
66C4⋊C4×Dic11C2212yes—
67C4⋊C4×Dic11C2212yes—
68#10622585C2212yes—
69#10622569C2212yes—
70#10622569C2212yes—
71#10622564C2212yes—
72#10622563C2212yes—
73#10622558C2212yes—
74#10622557C2212yes—
75#10622556C2212yes—
76#10622556C2212yes—
77#10622555C2212yes—
78#10622555C2212yes—
79C22⋊C4×Dic11C2212yes—
80C22⋊C4×Dic11C2212yes—
81C22⋊C4×Dic11C2212yes—
82C4×(C2×D11)⋊C4C2212yes—
83#10622550C2211yescharacteristic
84#10622549C2211yescharacteristic
85#10622545C2212yes—
86C4×Dic11⋊C4C2212yes—
87C4×Dic11⋊C4C2212yes—
88#10622281C2212yes—
89#10622279C2212yes—
90#10622279C2211yescharacteristic
91#10622279C2211yescharacteristic
92#10622277C2212yes—
93D11×#95C2212yes—
94D11×#95C2211yescharacteristic
95D11×#95C2211yescharacteristic
96D11×#95C2212yes—
97#10622268C2212yes—
98#10622268C2212yes—
99#10622267C2212yes—
100#10622266C2212yes—
101#10622264C2212yes—
102#10622264C2212yes—
103#10622264C2211yescharacteristic
104#10622264C2211yescharacteristic
105#10622264C2211yescharacteristic
106#10622264C2211yescharacteristic
107#10622264C2212yes—
108#10622264C2211yescharacteristic
109#10622264C2212yes—
110#10622264C2211yescharacteristic
111#10622263C2211yescharacteristic
112#10622263C2211yescharacteristic
113#10622263C2212yes—
114#10622262C2212yes—
115#10622262C2211yescharacteristic
116#10622262C2211yescharacteristic
117#10622261C2212yes—
118#10622261C2211yescharacteristic
119#10622261C2211yescharacteristic
120#10622261C2212yes—
121#10622260C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124C22×D4×C11C2311yescharacteristic
125C23×C4×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C22×C22⋊D11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2312yes—
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C2×#4341—28no—
136C2×#4341C2×C418yes—
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2312yes—
139C22×C4×D11C2312yes—
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2311yescharacteristic
142C22×Dic22C2311yescharacteristic
143C4×D4×C11C2×C418yescomplemented
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4C2311yescharacteristic
152C2×C42×C11C2312yes—
153C2×C42×C11C2311yescharacteristic
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2311yescharacteristic
158C2×C22⋊Dic11C2311yescharacteristic
159D4×Dic11C2×C418yescomplemented
160C4×C22⋊D11—28no—
161C4×C22⋊D11C2×C418yes—
162C4×C22⋊D11C2×C418yescomplemented
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2311yescharacteristic
167C2×C4⋊Dic11C2312yes—
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2311yescharacteristic
175C2×Dic11⋊C4C2311yescharacteristic
176C2×Dic11⋊C4C2311yescharacteristic
177C2×Dic11⋊C4C2311yescharacteristic
178C2×C4×Dic11C2×C418yescomplemented
179C2×C4×Dic11C2×C418yescomplemented
180C2×C4×Dic11C2312yes—
181C2×C4×Dic11C2312yes—
182C2×C4×Dic11C2312yes—
183C2×C4×Dic11C2312yes—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196#66945C2×C418yescomplemented
197#66940C2×C418yescomplemented
198(C22⋊D11)⋊C4—28no—
199(C22⋊D11)⋊C4C2×C418yes—
200(C22⋊D11)⋊C4C2×C418yescomplemented
201#66930C2×C418yescomplemented
202#66930C2×C418yescomplemented
203C42×D11C2×C418yescomplemented
204C4×Dic22C2×C418yescomplemented
205C11×#95C2312yes—
206C11×#95C2312yes—
207C11×#95C2312yes—
208C11×#95C2311yescharacteristic
209C11×#95C2312yes—
210C11×#95C2311yescharacteristic
211C11×#95C2311yescharacteristic
212C11×#95C2311yescharacteristic
213C11×#95C2312yes—
214C11⋊#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2311yescharacteristic
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2311yescharacteristic
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2311yescharacteristic
231C11⋊#95C2312yes—
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241#34195—111nomaximal, Sylow
242C24×C11C2411yescharacteristic
243C24×C11C2411yescharacteristic
244C23×D11C2411yescharacteristic
245C2×D4×C11—24no—
246C2×D4×C11C22×C414yes—
247C22×C4×C11—24no—
248C22×C4×C11—42no—
249C22×C4×C11—42no—
250C22×C4×C11—42no—
251C22×C4×C11—42no—
252C22×C4×C11C22×C414yes—
253C22×C4×C11C22×C414yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C22×C4×C11C2411yescharacteristic
262C22×C4×C11C2411yescharacteristic
263C2×C22⋊D11—24no—
264C2×C22⋊D11C22×C414yes—
265C2×C22⋊D11C22×C414yes—
266C2×C22⋊D11#4118yes—
267C22×Dic11—24no—
268C22×Dic11—24no—
269C22×Dic11—24no—
270C22×Dic11—41no—
271C22×Dic11—41no—
272C22×Dic11—41no—
273C22×Dic11—41no—
274C22×Dic11—42no—
275C22×Dic11—42no—
276C22×Dic11C22×C414yes—
277C22×Dic11C22×C414yes—
278C22×Dic11C22×C414yes—
279C22×Dic11C22×C414yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291#4341—232no—
292C2×C4×D11—24no—
293C2×C4×D11—24no—
294C2×C4×D11—24no—
295C2×C4×D11—41no—
296C2×C4×D11—41no—
297C2×C4×D11—42no—
298C2×C4×D11—42no—
299C2×C4×D11—42no—
300C2×C4×D11—42no—
301C2×C4×D11—42no—
302C2×C4×D11C22×C414yes—
303C2×C4×D11C22×C414yes—
304C2×C4×D11C22×C414yes—
305C2×Dic22—24no—
306C2×Dic22C22×C414yes—
307C11×C4⋊C4—42no—
308C11×C4⋊C4—42no—
309C11×C4⋊C4C22×C414yes—
310C11×C22⋊C4—24no—
311C11×C22⋊C4—42no—
312C11×C22⋊C4—42no—
313C11×C22⋊C4C22×C414yes—
314C11×C22⋊C4C22×C414yes—
315C42×C11—42no—
316C42×C11C22×C414yes—
317C22⋊Dic11—24no—
318C22⋊Dic11—42no—
319C22⋊Dic11—42no—
320C22⋊Dic11C22×C414yes—
321C22⋊Dic11C22×C414yes—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4C22×C414yes—
325(C2×D11)⋊C4C22×C414yes—
326C4⋊Dic11—42no—
327C4⋊Dic11—42no—
328C4⋊Dic11C22×C414yes—
329Dic11⋊C4—24no—
330Dic11⋊C4—24no—
331Dic11⋊C4—42no—
332Dic11⋊C4—42no—
333Dic11⋊C4C22×C414yes—
334Dic11⋊C4C22×C414yes—
335Dic11⋊C4C22×C414yes—
336Dic11⋊C4C22×C414yes—
337C4×Dic11—24no—
338C4×Dic11—24no—
339C4×Dic11—42no—
340C4×Dic11—42no—
341C4×Dic11—42no—
342C4×Dic11—42no—
343C4×Dic11—42no—
344C4×Dic11C22×C414yes—
345C4×Dic11C22×C414yes—
346C4×Dic11C22×C414yes—
347C4×Dic11C22×C414yes—
348C4×Dic11C22×C414yes—
349C4×Dic11C22×C414yes—
350C4×Dic11C22×C414yes—
351C4×Dic11C22×C414yes—
352C4×Dic11C22×C414yes—
353C2×C4×#41—111no—
354#2356—112no—
355#2353—112no—
356#2353—112no—
357#2349—112no—
358#2347—112no—
359#2343—112no—
360#2343—112no—
361#2339—112no—
362#2320—111no—
363#2320—111no—
364#2318—111no—
365#2318—111no—
366#2318—111no—
367#2318D1111yescharacteristic, complemented
368#2283—111no—
369#2283—111no—
370#2283—111no—
371#2283—111no—
372C2×#383—111no—
373C2×#383—111no—
374#2275—111no—
375#2275—111no—
376C23×C11—21no—
377C23×C11—22no—
378C23×C11—21no—
379C23×C11—22no—
380C23×C11—21no—
381C23×C11—22no—
382C23×C11—21no—
383C23×C11C23×C412yes—
384C23×C11C23×C412yes—
385C23×C11C2×#4114yes—
386C23×C11C2511yescharacteristic
387C22×D11—22no—
388C22×D11—21no—
389C22×D11—21no—
390C22×D11C23×C412yes—
391C22×D11C2×#4114yes—
392D4×C11—28no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—21no—
396C2×C4×C11—22no—
397C2×C4×C11—21no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—44no—
412C2×C4×C11—44no—
413C2×C4×C11—84no—
414C2×C4×C11C23×C412yes—
415C2×C4×C11C23×C412yes—
416C2×C4×C11C23×C412yes—
417C2×C4×C11C23×C412yes—
418C2×C4×C11C23×C412yes—
419C22⋊D11—28no—
420C22⋊D11#117116yes—
421C2×Dic11—28no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—21no—
426C2×Dic11—21no—
427C2×Dic11—21no—
428C2×Dic11—21no—
429C2×Dic11—21no—
430C2×Dic11—21no—
431C2×Dic11—28no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—44no—
445C2×Dic11—44no—
446C2×Dic11—84no—
447C2×Dic11C23×C412yes—
448C2×Dic11C23×C412yes—
449C2×Dic11C23×C412yes—
450C2×Dic11C23×C412yes—
451C2×Dic11C23×C412yes—
452C2×Dic11C23×C412yes—
453C2×Dic11C23×C412yes—
454C2×Dic11C2×#4114yes—
455C4×D11—28no—
456C4×D11—44no—
457C4×D11—44no—
458C4×D11—84no—
459C4×D11—84no—
460Dic22—28no—
461C22×#41—111no—
462C4×#41—1116no—
463C2×C4×Q8—111no—
464C2×C4×Q8—111no—
465C2×C4×D4—111no—
466C2×C4×D4—111no—
467C2×C4×D4—111no—
468C2×C4×D4—112no—
469C2×C4×D4—111no—
470C2×C4×D4—111no—
471C2×C4×D4—112no—
472C2×C4×D4C2×D1111yescharacteristic
473C2×#117—111no—
474C2×#117—111no—
475C2×#117—111no—
476C22×C42—111no—
477C22×C42—111no—
478C22×C42—111no—
479#391—112no—
480#391—112no—
481#389—112no—
482#389—112no—
483#388—112no—
484#388—112no—
485#388—112no—
486#388C2×D1112yes—
487#387—112no—
488#387—112no—
489#387—112no—
490#387—112no—
491#387—112no—
492#387—112no—
493#387—112no—
494#387C2×D1112yes—
495#386—112no—
496#386—112no—
497#386—112no—
498#386C2×D1112yes—
499#385—112no—
500#385—112no—
501#385—112no—
502#385C2×D1112yes—
503#383—111no—
504#383—111no—
505#383—111no—
506#383—112no—
507#383—112no—
508#383—112no—
509#383—112no—
510#383—111no—
511#383—111no—
512#383—111no—
513#383—111no—
514#383C2×D1111yescharacteristic
515#382—112no—
516#382—111no—
517#382—111no—
518#382—111no—
519#382—112no—
520#382C2×D1111yescharacteristic
521#381—111no—
522#381—112no—
523#381—112no—
524#381—112no—
525#381C2×D1111yescharacteristic
526#380—111no—
527#380—112no—
528#380—112no—
529#380—112no—
530#380C2×D1111yescharacteristic
531C4×C4⋊C4—112no—
532C4×C4⋊C4—112no—
533C4×C4⋊C4—112no—
534C4×C4⋊C4—112no—
535C4×C4⋊C4—111no—
536C4×C4⋊C4—111no—
537C4×C4⋊C4—112no—
538C4×C22⋊C4—111no—
539C4×C22⋊C4—112no—
540C4×C22⋊C4—112no—
541C4×C22⋊C4—112no—
542C4×C22⋊C4—112no—
543C4×C22⋊C4—112no—
544C4×C22⋊C4—111no—
545C4×C22⋊C4—111no—
546C4×C22⋊C4—112no—
547C4×C22⋊C4C2×D1111yescharacteristic
548#376—112no—
549#376—111no—
550#376—111no—
551#376—112no—
552#376—112no—
553C2×#95—111no—
554C2×#95—112no—
555C2×#95—112no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—112no—
559C2×#95—112no—
560C2×#95C2×D1111yescharacteristic
561C22×C11—22no—
562C22×C11—22no—
563C22×C11—24no—
564C22×C11—24no—
565C22×C11—22no—
566C22×C11—22no—
567C22×C11—22no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11C2×#11714yes—
571C22×C11C24×C411yescharacteristic
572C22×C11C22×#4112yes—
573C22×C11#58512yes—
574C22×C11#58511yescharacteristic
575C22×C11#58511yescharacteristic
576C2×D11—22no—
577C2×D11—22no—
578C2×D11—24no—
579C2×D11—24no—
580C2×D11C2×#11714yes—
581C4×C11—22no—
582C4×C11—22no—
583C4×C11—22no—
584C4×C11—22no—
585C4×C11—22no—
586C4×C11—42no—
587C4×C11—42no—
588C4×C11—42no—
589C4×C11—42no—
590Dic11—22no—
591Dic11—22no—
592Dic11—22no—
593Dic11—22no—
594Dic11—22no—
595Dic11—22no—
596Dic11—42no—
597Dic11—42no—
598Dic11—42no—
599Dic11—42no—
600Dic11C2×#11714yes—
601C2×#41—118no—
602C2×#41—228no—
603C22×Q8—111no—
604C22×D4—111no—
605C22×D4—111no—
606C22×D4C22×D1111yescharacteristic
607C23×C4—111no—
608C23×C4—111no—
609C23×C4—111no—
610C23×C4—111no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—112no—
615C23×C4—112no—
616C23×C4—112no—
617C23×C4C22×D1112yes—
618C23×C4C22×D1111yescharacteristic
619C23×C4C22×D1111yescharacteristic
620C4×Q8—118no—
621C4×Q8—118no—
622C4×D4—118no—
623C4×D4—118no—
624C4×D4—118no—
625C4×D4—118no—
626C4×D4—118no—
627C4×D4—228no—
628C4×D4—228no—
629C4×D4C4×D1118yescomplemented
630#117—118no—
631#117—118no—
632#117—118no—
633C2×C4⋊C4—111no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—112no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4C22×D1112yes—
645C2×C4⋊C4C22×D1112yes—
646C2×C4⋊C4C22×D1111yescharacteristic
647C2×C22⋊C4—111no—
648C2×C22⋊C4—111no—
649C2×C22⋊C4—111no—
650C2×C22⋊C4—111no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4C22×D1112yes—
657C2×C22⋊C4C22×D1112yes—
658C2×C22⋊C4C22×D1112yes—
659C2×C22⋊C4C22×D1111yescharacteristic
660C2×C22⋊C4C22×D1111yescharacteristic
661C2×C42—118no—
662C2×C42—118no—
663C2×C42—111no—
664C2×C42—111no—
665C2×C42—111no—
666C2×C42—111no—
667C2×C42—111no—
668C2×C42—111no—
669C2×C42—111no—
670C2×C42—111no—
671C2×C42—111no—
672C2×C42—118no—
673C2×C42—112no—
674C2×C42—112no—
675C2×C42—112no—
676C2×C42—112no—
677C2×C42—112no—
678C2×C42—112no—
679C2×C42—112no—
680C2×C42C22×D1112yes—
681C2×C42C22×D1111yescharacteristic
682#95—111no—
683#95—112no—
684#95—112no—
685#95—112no—
686#95—112no—
687#95—112no—
688#95—112no—
689#95—111no—
690#95—111no—
691#95—112no—
692#95—112no—
693#95—112no—
694#95—112no—
695#95—112no—
696#95—112no—
697#95—112no—
698#95—112no—
699#95—112no—
700#95—112no—
701#95—111no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95—112no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95C22×D1111yescharacteristic
710#95C22×D1111yescharacteristic
711#95C22×D1112yes—
712#95C22×D1112yes—
713#95C22×D1111yescharacteristic
714#95C22×D1112yes—
715#95C22×D1111yescharacteristic
716#95C22×D1112yes—
717#95C22×D1112yes—
718C2×C11—24no—
719C2×C11—42no—
720C2×C11C22×#11711yescharacteristic
721C2×C11#342811yescharacteristic
722C2×C11#342811yescharacteristic
723C2×C11#352112yes—
724C2×C11#352112yes—
725D11—24no—
726C24—111no—
727C24C23×D1111yescharacteristic
728C24C23×D1111yescharacteristic
729#41—2232no—
730C2×Q8—114no—
731C2×Q8—224no—
732C2×D4—24no—
733C2×D4—114no—
734C2×D4—118no—
735C2×D4—114no—
736C2×D4—224no—
737C2×D4C2×C4×D1114yes—
738C22×C4—24no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—111no—
744C22×C4—114no—
745C22×C4—114no—
746C22×C4—111no—
747C22×C4—111no—
748C22×C4—111no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—114no—
753C22×C4—114no—
754C22×C4—114no—
755C22×C4—114no—
756C22×C4—114no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—224no—
762C22×C4—224no—
763C22×C4—224no—
764C22×C4—224no—
765C22×C4—224no—
766C22×C4—224no—
767C22×C4—441no—
768C22×C4—442no—
769C22×C4—441no—
770C22×C4—442no—
771C22×C4—442no—
772C22×C4—442no—
773C22×C4—442no—
774C22×C4—441no—
775C22×C4—441no—
776C22×C4—441no—
777C22×C4—441no—
778C22×C4—442no—
779C22×C4—442no—
780C22×C4C2×C4×D1114yes—
781C22×C4C2×C4×D1114yes—
782C22×C4C23×D1112yes—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1111yescharacteristic
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—114no—
794C4⋊C4—114no—
795C4⋊C4—114no—
796C4⋊C4—114no—
797C4⋊C4—114no—
798C4⋊C4—224no—
799C4⋊C4—224no—
800C4⋊C4—442no—
801C4⋊C4—442no—
802C4⋊C4—442no—
803C4⋊C4—442no—
804C4⋊C4C2×C4×D1114yes—
805C22⋊C4—24no—
806C22⋊C4—42no—
807C22⋊C4—42no—
808C22⋊C4—114no—
809C22⋊C4—114no—
810C22⋊C4—114no—
811C22⋊C4—114no—
812C22⋊C4—224no—
813C22⋊C4—224no—
814C22⋊C4—224no—
815C22⋊C4—442no—
816C22⋊C4—442no—
817C22⋊C4C2×C4×D1114yes—
818C22⋊C4C2×C4×D1114yes—
819C42—42no—
820C42—114no—
821C42—114no—
822C42—114no—
823C42—114no—
824C42—114no—
825C42—114no—
826C42—114no—
827C42—114no—
828C42—114no—
829C42—224no—
830C42—224no—
831C42—442no—
832C42—442no—
833C42—442no—
834C42—442no—
835C42—442no—
836C42C2×C4×D1114yes—
837C11#3419511yescharacteristic, complemented, Sylow
838C23—22no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—112no—
846C23—114no—
847C23—222no—
848C23—221no—
849C23—221no—
850C23C22×C4×D1112yes—
851C23C22×C4×D1112yes—
852C23#41×D1114yes—
853C23C24×D1111yescharacteristic
854Q8—228no—
855D4—28no—
856D4—1116no—
857D4—228no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—84no—
879C2×C4—112no—
880C2×C4—114no—
881C2×C4—112no—
882C2×C4—112no—
883C2×C4—112no—
884C2×C4—112no—
885C2×C4—112no—
886C2×C4—112no—
887C2×C4—228no—
888C2×C4—228no—
889C2×C4—228no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—221no—
894C2×C4—221no—
895C2×C4—221no—
896C2×C4—221no—
897C2×C4—221no—
898C2×C4—221no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—444no—
912C2×C4—444no—
913C2×C4—444no—
914C2×C4—444no—
915C2×C4—884no—
916C2×C4—884no—
917C2×C4—884no—
918C2×C4C22×C4×D1112yes—
919C2×C4C22×C4×D1112yes—
920C2×C4C22×C4×D1112yes—
921C2×C4C22×C4×D1112yes—
922C2×C4C22×C4×D1112yes—
923C22—24no—
924C22—24no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—42no—
931C22—42no—
932C22—114no—
933C22—224no—
934C22—224no—
935C22—222no—
936C22—222no—
937C22D11×#11714yes—
938C22C23×C4×D1111yescharacteristic
939C22C2×#41×D1112yes—
940C22#1062345512yes—
941C22#1062345511yescharacteristic
942C22#1062345711yescharacteristic
943C4—22no—
944C4—22no—
945C4—22no—
946C4—22no—
947C4—22no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—114no—
953C4—222no—
954C4—222no—
955C4—222no—
956C4—222no—
957C4—222no—
958C4—222no—
959C4—442no—
960C4—442no—
961C4—442no—
962C4—442no—
963C2—24no—
964C2—42no—
965C2—224no—
966C2C2×D11×#11711yescharacteristic
967C2#1308181411yescharacteristic
968C2#1308181611yescharacteristic
969C2#1308267412yes—
970C2#1308268012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2318C2
socle, cosocleC23×C11C25
prime radicalC22×#4341C22
hypercenter#2318D11
hypocenterC11#34195
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #13071578C2semidirect
3. #13071554C2semidirect
4. #13071551C2semidirect
5. #13071522C2semidirect
6. #13071506C2semidirect
7. #13071475C2semidirect
8. #13071474C2semidirect
10. #13071266C2semidirect
11. #13071264C2semidirect
12. #13071251C2semidirect
13. #13071249C2semidirect
14. #13071245C2semidirect
15. #13071011C2semidirect
16. #13071010C2semidirect
17. #13071009C2semidirect
18. #13071007C2semidirect
19. C2×#10622264C2semidirect
20. D11×#383C2semidirect
21. #13070975C2semidirect
22. #13070974C2semidirect
23. C11×#2318C2semidirect
32. C4×#4341C4semidirect
143. C4×D4×C11C2×C4semidirect
159. D4×Dic11C2×C4semidirect
162. C4×C22⋊D11C2×C4semidirect
178. C2×C4×Dic11C2×C4semidirect
179. C2×C4×Dic11C2×C4semidirect
196. #66945C2×C4semidirect
197. #66940C2×C4semidirect
200. (C22⋊D11)⋊C4C2×C4semidirect
201. #66930C2×C4semidirect
202. #66930C2×C4semidirect
203. C42×D11C2×C4semidirect
204. C4×Dic22C2×C4semidirect
367. #2318D11semidirect
629. C4×D4C4×D11semidirect
837. C11#34195semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
#130715782
#130715542
#130715512
#130715222
#130715062
#130714752
#130714742
#130714422
#130712662
#130712642
#130712512
#130712492
#130712452
#130710112
#130710102
#130710092
#130710072
C2×#106222642
D11×#3832
#130709752
#130709742
C11×#23182
#3419511