Finite Group Databasebeta

← #14959840

Subgroups — #14959840

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077009C212yesmaximal, complemented
2#13077006C212yesmaximal, complemented
3#13077001C211yesmaximal, characteristic, complemented
4#13076999C211yesmaximal, characteristic, complemented
5#13076989C211yesmaximal, characteristic, complemented
6#13076984C211yesmaximal, characteristic, complemented
7#13076954C211yesmaximal, characteristic, complemented
8#13076949C211yesmaximal, characteristic
9#13076940C212yesmaximal, complemented
10#13076934C212yesmaximal, complemented
11#13076921C211yesmaximal, characteristic, complemented
12#13076918C211yesmaximal, characteristic
13C4×#66951C212yesmaximal, complemented
14C4×#66928C211yesmaximal, characteristic, complemented
15C4×#66950C211yesmaximal, characteristic, complemented
16C4×#66947C212yesmaximal, complemented
17C4×#66948C211yesmaximal, characteristic
18#13071109C212yesmaximal, complemented
19#13071090C211yesmaximal, characteristic, complemented
20#13071077C211yesmaximal, characteristic, complemented
21#13071057C212yesmaximal, complemented
22C43×D11C211yesmaximal, characteristic, complemented
23C4×C11×#125C211yesmaximal, characteristic, complemented
24C2×C11×#125C2211yescharacteristic
25C2×#66951C2212yes—
26C2×#66950C2211yescharacteristic
27C2×#66948C2211yescharacteristic
28C2×#66947C2212yes—
29C2×#66928C2211yescharacteristic
30C2×C4×D44C2212yes—
31C2×C4×D44C2211yescharacteristic
32C2×#66925C2212yes—
33C2×C42×D11C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C42×D11C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C42×D11C2211yescharacteristic
40C2×C4×Dic22C2211yescharacteristic
41C11×#389C2211yescharacteristic
42C11×#389C2211yescharacteristic
43C11×#387C2212yes—
44C11×#387C2212yes—
45C11×#382C2211yescharacteristic
46C4×C11×C4⋊C4C2212yes—
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C4⋊C4C2212yes—
50C43×C11C2211yescharacteristic
51#10622603C2212yes—
52#10622603C2212yes—
53#10622603C2212yes—
54#10622603C2212yes—
55#10622603C2212yes—
56#10622603C2212yes—
57#10622602C2212yes—
58#10622602C2212yes—
59#10622602C2212yes—
60#10622601C2211yescharacteristic
61#10622601C2211yescharacteristic
62#10622601C2211yescharacteristic
63#10622600C2211yescharacteristic
64#10622600C2211yescharacteristic
65#10622598C2211yescharacteristic
66#10622598C2211yescharacteristic
67#10622594C2212yes—
68#10622594C2212yes—
69#10622591C2212yes—
70#10622591C2212yes—
71#10622591C2212yes—
72#10622587C2211yescharacteristic
73#10622587C2211yescharacteristic
74#10622587C2211yescharacteristic
75#10622586C2211yescharacteristic
76#10622586C2211yescharacteristic
77#10622586C2211yescharacteristic
78#10622586C2211yescharacteristic
79#10622553C2212yes—
80#10622553C2212yes—
81#10622552C2211yescharacteristic
82C4×(C2×D11)⋊C4C2212yes—
83C4×(C2×D11)⋊C4C2212yes—
84C4×(C2×D11)⋊C4C2212yes—
85C4×(C2×D11)⋊C4C2212yes—
86C4×(C2×D11)⋊C4C2212yes—
87#10622549C2211yescharacteristic
88C4×C4⋊Dic11C2212yes—
89#10622545C2212yes—
90C4×Dic11⋊C4C2212yes—
91C42×Dic11C2211yescharacteristic
92C42×Dic11C2211yescharacteristic
93C42×Dic11C2211yescharacteristic
94C42×Dic11C2211yescharacteristic
95C42×Dic11C2211yescharacteristic
96C42×Dic11C2211yescharacteristic
97C42×Dic11C2211yescharacteristic
98#10622542C2211yescharacteristic
99#10622283C2212yes—
100#10622283C2212yes—
101#10622283C2212yes—
102#10622283C2212yes—
103#10622282C2212yes—
104#10622282C2212yes—
105#10622282C2212yes—
106#10622282C2212yes—
107#10622281C2212yes—
108#10622278C2212yes—
109#10622278C2212yes—
110#10622278C2212yes—
111#10622278C2212yes—
112#10622277C2212yes—
113#10622268C2212yes—
114#10622268C2212yes—
115#10622268C2212yes—
116#10622267C2212yes—
117#10622267C2212yes—
118#10622267C2212yes—
119#10622266C2212yes—
120#10622265C2212yes—
121#10622265C2212yes—
122#10622264C2212yes—
123C22×D44C2311yescharacteristic
124C22×D44C2312yes—
125C22×C4×D11C2311yescharacteristic
126C22×C4×D11C2311yescharacteristic
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2312yes—
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×Dic22C2311yescharacteristic
134C11×#125—24no—
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2312yes—
149C2×C42×C11C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2312yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×C4×Dic11C2312yes—
178C2×C4×Dic11C2311yescharacteristic
179C2×C4×Dic11C2311yescharacteristic
180C2×C4×Dic11C2311yescharacteristic
181C2×C4×Dic11C2311yescharacteristic
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2311yescharacteristic
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
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199#66951—28no—
200#66950—24no—
201#66948—24no—
202#66947—28no—
203#66928—24no—
204C4×D44—28no—
205C4×D44—24no—
206#66925—28no—
207C42×D11—24no—
208C42×D11—24no—
209C42×D11—24no—
210C42×D11—24no—
211C42×D11—24no—
212C42×D11—24no—
213C42×D11—24no—
214C4×Dic22—24no—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239#36638—111nomaximal, Sylow
240C23×D11C2412yes—
241C23×D11C2411yescharacteristic
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2411yescharacteristic
257C22×Dic11C2411yescharacteristic
258C22×Dic11C2411yescharacteristic
259C22×Dic11C2411yescharacteristic
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2411yescharacteristic
262C22×Dic11C2411yescharacteristic
263C2×D44—24no—
264C2×D44—24no—
265C2×D44—24no—
266C2×D44—22no—
267C2×D44—22no—
268C2×D44—22no—
269C2×C4×D11—22no—
270C2×C4×D11—22no—
271C2×C4×D11—22no—
272C2×C4×D11—22no—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—22no—
276C2×C4×D11—22no—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—22no—
280C2×C4×D11—22no—
281C2×C4×D11—22no—
282C2×C4×D11—22no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—22no—
287C2×C4×D11—24no—
288C2×C4×D11—24no—
289C2×C4×D11—24no—
290C2×C4×D11#4114yes—
291C2×C4×D11#4114yes—
292C2×C4×D11#4114yes—
293C2×Dic22—22no—
294C2×Dic22—22no—
295C2×Dic22—22no—
296C11×C4⋊C4—24no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—24no—
300C11×C4⋊C4—24no—
301C11×C4⋊C4—24no—
302C11×C4⋊C4—22no—
303C11×C4⋊C4—22no—
304C42×C11—22no—
305C42×C11—22no—
306C42×C11—22no—
307C42×C11—22no—
308C42×C11—22no—
309C42×C11—24no—
310C42×C11—24no—
311C42×C11#4114yes—
312C42×C11#4114yes—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—24no—
328C4⋊Dic11—24no—
329C4⋊Dic11—24no—
330C4⋊Dic11—24no—
331C4⋊Dic11—22no—
332C4⋊Dic11—22no—
333Dic11⋊C4—24no—
334Dic11⋊C4—24no—
335Dic11⋊C4—24no—
336Dic11⋊C4—24no—
337Dic11⋊C4—24no—
338C4×Dic11—22no—
339C4×Dic11—22no—
340C4×Dic11—22no—
341C4×Dic11—22no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—24no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—22no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354C4×Dic11—22no—
355C4×Dic11—22no—
356C4×Dic11—22no—
357C4×Dic11—22no—
358C4×Dic11#4114yes—
359C4×Dic11#4114yes—
360#2866—112no—
361#2865—112no—
362#2864—111no—
363#2863—111no—
364#2861—111no—
365#2860—111no—
366#2855—111no—
367#2854—111no—
368#2853—112no—
369#2852—112no—
370#2851—111no—
371#2850—111no—
372C4×#125D1111yescharacteristic, complemented
373C4×#126—112no—
374C4×#124—111no—
375C4×C22⋊Q8—111no—
376C4×#123—112no—
377C4×#121—111no—
378#2298—112no—
379#2295—111no—
380#2293—111no—
381#2290—112no—
382C2×C43—111no—
383C23×C11C2511yescharacteristic
384C22×D11—21no—
385C22×D11—21no—
386C22×D11—21no—
387C22×D11—21no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11C2×#4112yes—
396C22×D11C2×#4112yes—
397C22×D11C2×#4112yes—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
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—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
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×C11C2×#4112yes—
421C2×C4×C11C2×#4112yes—
422C2×C4×C11C2×#4112yes—
423C2×C4×C11C2×#4112yes—
424C2×C4×C11C2×#4112yes—
425C2×C4×C11C2×#4112yes—
426C2×C4×C11C2×#4112yes—
427C2×C4×C11C2×#4112yes—
428C2×C4×C11C2×#4112yes—
429C2×C4×C11C2×#4112yes—
430C2×C4×C11C2×#4112yes—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—21no—
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—21no—
444C2×Dic11—21no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11C2×#4112yes—
455C2×Dic11C2×#4112yes—
456C2×Dic11C2×#4112yes—
457C2×Dic11C2×#4112yes—
458C2×Dic11C2×#4112yes—
459C2×Dic11C2×#4112yes—
460C2×Dic11C2×#4112yes—
461D44—48no—
462D44—44no—
463C4×D11—28no—
464C4×D11—28no—
465C4×D11—28no—
466C4×D11—28no—
467C4×D11—28no—
468C4×D11—28no—
469C4×D11—28no—
470C4×D11—48no—
471Dic22—44no—
472C2×#126—112no—
473C2×#125C2×D1111yescharacteristic
474C2×#124—111no—
475C2×#123—112no—
476C2×C22⋊Q8—111no—
477C2×#121—111no—
478C2×C4×Q8—111no—
479C2×C4×D4—112no—
480C2×C4×D4—111no—
481C2×#117—112no—
482C22×C42—111no—
483C22×C42—111no—
484C22×C42—111no—
485C22×C42—111no—
486C22×C42—111no—
487C22×C42—111no—
488C22×C42—111no—
489#391—111no—
490#391—111no—
491#391—111no—
492#391—111no—
493#390—111no—
494#390—111no—
495#390—111no—
496#390—111no—
497#389—111no—
498#389—111no—
499#389—111no—
500#389—111no—
501#389—111no—
502#389—111no—
503#389C2×D1111yescharacteristic
504#389C2×D1111yescharacteristic
505#388—112no—
506#388—112no—
507#388—112no—
508#388—112no—
509#388—112no—
510#388—112no—
511#388—112no—
512#388—112no—
513#388—112no—
514#388—112no—
515#388—112no—
516#388—112no—
517#388—112no—
518#388—112no—
519#388—112no—
520#388—112no—
521#387—112no—
522#387—112no—
523#387—112no—
524#387—112no—
525#387—112no—
526#387—112no—
527#387—112no—
528#387—112no—
529#387—112no—
530#387—112no—
531#387—112no—
532#387—112no—
533#387—112no—
534#387—112no—
535#387C2×D1112yes—
536#387C2×D1112yes—
537#386—112no—
538#386—112no—
539#386—112no—
540#386—112no—
541#385—112no—
542#385—112no—
543#385—112no—
544#385—112no—
545#383—112no—
546#382—111no—
547#382C2×D1111yescharacteristic
548#381—112no—
549#380—111no—
550#380—111no—
551C4×C4⋊C4—112no—
552C4×C4⋊C4—112no—
553C4×C4⋊C4C2×D1112yes—
554C4×C4⋊C4C2×D1111yescharacteristic
555C4×C4⋊C4C2×D1111yescharacteristic
556C4×C4⋊C4C2×D1112yes—
557C4×C22⋊C4—112no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—112no—
560C4×C22⋊C4—112no—
561C4×C22⋊C4—112no—
562#376—112no—
563C43—111no—
564C43—111no—
565C43—111no—
566C43—111no—
567C43—111no—
568C43—111no—
569C43—111no—
570C43C2×D1111yescharacteristic
571C22×C11C22×#4111yescharacteristic
572C22×C11C22×#4111yescharacteristic
573C22×C11C22×#4111yescharacteristic
574C22×C11C22×#4111yescharacteristic
575C22×C11C22×#4111yescharacteristic
576C22×C11C22×#4111yescharacteristic
577C22×C11C22×#4111yescharacteristic
578C2×D11—22no—
579C2×D11—22no—
580C2×D11—22no—
581C2×D11—22no—
582C2×D11—22no—
583C2×D11—22no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11#52914yes—
592C4×C11—22no—
593C4×C11—22no—
594C4×C11—22no—
595C4×C11—22no—
596C4×C11—22no—
597C4×C11—42no—
598C4×C11—42no—
599C4×C11—42no—
600C4×C11—42no—
601C4×C11#52914yes—
602C4×C11#52914yes—
603Dic11—22no—
604Dic11—22no—
605Dic11—22no—
606Dic11—22no—
607Dic11—22no—
608Dic11—22no—
609Dic11—22no—
610Dic11—42no—
611Dic11—42no—
612Dic11—42no—
613C22×Q8—111no—
614C22×D4—112no—
615C22×D4—111no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—111no—
620C23×C4—111no—
621C23×C4—111no—
622C23×C4—111no—
623C23×C4—112no—
624#126—228no—
625#125—24no—
626#124—224no—
627#123—228no—
628C22⋊Q8—224no—
629#121—224no—
630C4×Q8—224no—
631C4×D4—228no—
632C4×D4—224no—
633#117—228no—
634C2×C4⋊C4—112no—
635C2×C4⋊C4—112no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—112no—
640C2×C4⋊C4—112no—
641C2×C4⋊C4—112no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C4⋊C4C22×D1111yescharacteristic
646C2×C4⋊C4C22×D1112yes—
647C2×C4⋊C4C22×D1111yescharacteristic
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1112yes—
650C2×C4⋊C4C22×D1112yes—
651C2×C4⋊C4C22×D1112yes—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—112no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—112no—
661C2×C22⋊C4—112no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—112no—
665C2×C22⋊C4—112no—
666C2×C22⋊C4—112no—
667C2×C42—111no—
668C2×C42—111no—
669C2×C42—111no—
670C2×C42—111no—
671C2×C42—111no—
672C2×C42—111no—
673C2×C42—111no—
674C2×C42—111no—
675C2×C42—111no—
676C2×C42—111no—
677C2×C42—111no—
678C2×C42—111no—
679C2×C42—111no—
680C2×C42—111no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—111no—
684C2×C42—111no—
685C2×C42—111no—
686C2×C42—112no—
687C2×C42—111no—
688C2×C42—111no—
689C2×C42—224no—
690C2×C42—224no—
691C2×C42—224no—
692C2×C42—224no—
693C2×C42—224no—
694C2×C42—224no—
695C2×C42—224no—
696C2×C42C22×D1111yescharacteristic
697C2×C42C22×D1111yescharacteristic
698C2×C42C22×D1111yescharacteristic
699C2×C42C22×D1112yes—
700C2×C42C22×D1112yes—
701C2×C42C22×D1111yescharacteristic
702C2×C42C22×D1111yescharacteristic
703C2×C42C22×D1111yescharacteristic
704C2×C42C22×D1111yescharacteristic
705#95—112no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95—112no—
710#95—112no—
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#95C22×D1112yes—
724#95C22×D1112yes—
725#95C22×D1112yes—
726#95C22×D1112yes—
727#95C22×D1112yes—
728#95C22×D1112yes—
729C2×C11C2×#52911yescharacteristic
730C2×C11C2×#52911yescharacteristic
731C2×C11C2×#52911yescharacteristic
732C2×C11#344411yescharacteristic
733C2×C11#344411yescharacteristic
734C2×C11#344411yescharacteristic
735C2×C11#344411yescharacteristic
736D11—24no—
737D11—82no—
738C24—111no—
739C24—112no—
740C2×Q8—222no—
741C2×Q8—222no—
742C2×Q8—222no—
743C2×D4—224no—
744C2×D4—224no—
745C2×D4—224no—
746C2×D4—222no—
747C2×D4—222no—
748C2×D4—222no—
749C22×C4—111no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—111no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—111no—
756C22×C4—114no—
757C22×C4—114no—
758C22×C4—114no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—222no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—224no—
781C22×C4—224no—
782C22×C4—224no—
783C22×C4C23×D1112yes—
784C22×C4C23×D1112yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791C22×C4C23×D1111yescharacteristic
792C22×C4C23×D1111yescharacteristic
793C22×C4C23×D1111yescharacteristic
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—22no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—224no—
803C4⋊C4—224no—
804C4⋊C4—224no—
805C4⋊C4—224no—
806C4⋊C4—224no—
807C4⋊C4—224no—
808C4⋊C4—224no—
809C4⋊C4—222no—
810C4⋊C4—224no—
811C4⋊C4—222no—
812C22⋊C4—224no—
813C22⋊C4—224no—
814C22⋊C4—224no—
815C22⋊C4—224no—
816C22⋊C4—224no—
817C22⋊C4—224no—
818C22⋊C4—224no—
819C22⋊C4—224no—
820C22⋊C4—224no—
821C22⋊C4—224no—
822C22⋊C4—224no—
823C22⋊C4—224no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—224no—
827C42—22no—
828C42—22no—
829C42—22no—
830C42—22no—
831C42—22no—
832C42—24no—
833C42—24no—
834C42—114no—
835C42—114no—
836C42—222no—
837C42—222no—
838C42—222no—
839C42—222no—
840C42—222no—
841C42—222no—
842C42—222no—
843C42—222no—
844C42—222no—
845C42—222no—
846C42—222no—
847C42—222no—
848C42—222no—
849C42—222no—
850C42—222no—
851C42—222no—
852C42—224no—
853C42—222no—
854C42—222no—
855C42—222no—
856C42#433914yes—
857C42#434314yes—
858C11#3663811yescharacteristic, complemented, Sylow
859C23—112no—
860C23—112no—
861C23—112no—
862C23—221no—
863C23—221no—
864C23—221no—
865C23—221no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23C24×D1111yescharacteristic
874Q8—444no—
875D4—448no—
876D4—444no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—112no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—112no—
905C2×C4—112no—
906C2×C4—228no—
907C2×C4—228no—
908C2×C4—228no—
909C2×C4—228no—
910C2×C4—228no—
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—221no—
922C2×C4—221no—
923C2×C4—221no—
924C2×C4—221no—
925C2×C4—228no—
926C2×C4—228no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—448no—
937C2×C4C2×#433912yes—
938C2×C4C2×#433912yes—
939C2×C4C2×#433912yes—
940C2×C4C2×#434312yes—
941C2×C4C2×#434312yes—
942C2×C4C2×#434312yes—
943C2×C4#41×D1112yes—
944C2×C4#41×D1112yes—
945C2×C4#41×D1112yes—
946C2×C4#41×D1112yes—
947C2×C4#41×D1112yes—
948C22—114no—
949C22—222no—
950C22—222no—
951C22—222no—
952C22—222no—
953C22—222no—
954C22—222no—
955C22—442no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22C22×#433911yescharacteristic
963C22C22×#434311yescharacteristic
964C22C2×#41×D1111yescharacteristic
965C22C2×#41×D1111yescharacteristic
966C22C2×#41×D1111yescharacteristic
967C22C2×#41×D1111yescharacteristic
968C22C2×#41×D1111yescharacteristic
969C4—22no—
970C4—22no—
971C4—22no—
972C4—22no—
973C4—22no—
974C4—42no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—222no—
979C4—222no—
980C4—222no—
981C4—222no—
982C4—222no—
983C4—222no—
984C4—222no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4#1062311114yes—
989C4#1062322214yes—
990C2—224no—
991C2—882no—
992C2D11×#52911yescharacteristic
993C2C2×#1062322211yescharacteristic
994C2C2×#1062311111yescharacteristic
995C2#1308190911yescharacteristic
996C2#1308190911yescharacteristic
997C2#1308191011yescharacteristic
998C2#1308191311yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#125C2
prime radicalC2×#66948C22
hypercenterC4×#125D11
hypocenterC11#36638
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
1. #13077009C2semidirect
2. #13077006C2semidirect
3. #13077001C2semidirect
4. #13076999C2semidirect
5. #13076989C2semidirect
6. #13076984C2semidirect
7. #13076954C2semidirect
9. #13076940C2semidirect
10. #13076934C2semidirect
11. #13076921C2semidirect
13. C4×#66951C2semidirect
14. C4×#66928C2semidirect
15. C4×#66950C2semidirect
16. C4×#66947C2semidirect
18. #13071109C2semidirect
19. #13071090C2semidirect
20. #13071077C2semidirect
21. #13071057C2semidirect
22. C43×D11C2semidirect
23. C4×C11×#125C2semidirect
372. C4×#125D11semidirect
858. C11#36638semidirect

Maximal subgroups

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

subgroupindex
#130770092
#130770062
#130770012
#130769992
#130769892
#130769842
#130769542
#130769492
#130769402
#130769342
#130769212
#130769182
C4×#669512
C4×#669282
C4×#669502
C4×#669472
C4×#669482
#130711092
#130710902
#130710772
#130710572
C43×D112
C4×C11×#1252
#3663811