Finite Group Databasebeta

← #14927319

Subgroups — #14927319

Order 2816.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077002C211yesmaximal, characteristic, complemented
2#13076984C211yesmaximal, characteristic, complemented
3#13076969C211yesmaximal, characteristic, complemented
4#13076949C211yesmaximal, characteristic, complemented
5#13074678C212yesmaximal, complemented
6#13074466C212yesmaximal, complemented
7#13074123C212yesmaximal, complemented
8#13073755C212yesmaximal, complemented
9#13073075C211yesmaximal, characteristic, complemented
10#13073010C211yesmaximal, characteristic, complemented
11#13072916C211yesmaximal, characteristic, complemented
12#13072657C212yesmaximal, complemented
13#13072611C212yesmaximal, complemented
14#13072466C211yesmaximal, characteristic, complemented
15#13072309C211yesmaximal, characteristic, complemented
16#13072109C211yesmaximal, characteristic, complemented
17#13072032C211yesmaximal, characteristic
18#13071409C212yesmaximal, complemented
19#13071370C212yesmaximal, complemented
20C4×#66948C211yesmaximal, characteristic, complemented
21#13071097C211yesmaximal, characteristic, complemented
22C4×#66946C211yesmaximal, characteristic, complemented
23C11×#2507C211yesmaximal, characteristic, complemented
24C2×#66951C2212yes—
25C2×#66950C2212yes—
26C2×#66949C2212yes—
27C2×#66948C2211yescharacteristic
28C2×#66948C2211yescharacteristic
29C2×#66947C2212yes—
30C2×#66946C2211yescharacteristic
31C2×#66946C2211yescharacteristic
32C2×#66945C2211yescharacteristic
33C2×#66945C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C2×C4×D44C2212yes—
36C2×C4×D44C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40C11×#398C2212yes—
41C11×#398C2212yes—
42C11×#389C2211yescharacteristic
43C11×#389C2212yes—
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#387C2212yes—
48C11×#384C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51#10622607C2212yes—
52#10622607C2212yes—
53#10622606C2212yes—
54#10622606C2212yes—
55#10622604C2212yes—
56#10622604C2212yes—
57#10622604C2212yes—
58#10622604C2212yes—
59#10622603C2212yes—
60#10622603C2212yes—
61#10622603C2212yes—
62#10622603C2212yes—
63#10622603C2212yes—
64#10622602C2212yes—
65#10622601C2211yescharacteristic
66#10622601C2212yes—
67#10622601C2211yescharacteristic
68#10622600C2211yescharacteristic
69#10622600C2211yescharacteristic
70#10622600C2211yescharacteristic
71#10622600C2212yes—
72#10622600C2211yescharacteristic
73#10622598C2211yescharacteristic
74#10622598C2212yes—
75#10622598C2211yescharacteristic
76#10622594C2212yes—
77#10622594C2212yes—
78#10622591C2212yes—
79#10622590C2211yescharacteristic
80#10622590C2211yescharacteristic
81C4⋊C4×Dic11C2211yescharacteristic
82C4⋊C4×Dic11C2212yes—
83C4⋊C4×Dic11C2211yescharacteristic
84#10622587C2212yes—
85#10622586C2211yescharacteristic
86#10622586C2211yescharacteristic
87#10622553C2212yes—
88#10622552C2211yescharacteristic
89#10622552C2211yescharacteristic
90C4×(C2×D11)⋊C4C2212yes—
91C4×(C2×D11)⋊C4C2211yescharacteristic
92C4×(C2×D11)⋊C4C2211yescharacteristic
93#10622546C2212yes—
94C42×Dic11C2211yescharacteristic
95#10622541C2211yescharacteristic
96#10622541C2211yescharacteristic
97#10622288C2212yes—
98#10622286C2212yes—
99#10622286C2212yes—
100#10622285C2212yes—
101#10622284C2212yes—
102#10622283C2212yes—
103#10622283C2212yes—
104#10622283C2212yes—
105#10622282C2212yes—
106#10622282C2212yes—
107#10622281C2212yes—
108#10622281C2212yes—
109#10622279C2211yescharacteristic
110#10622279C2211yescharacteristic
111#10622279C2211yescharacteristic
112#10622279C2211yescharacteristic
113#10622278C2212yes—
114#10622278C2212yes—
115#10622278C2212yes—
116#10622277C2212yes—
117C11⋊#401C2212yes—
118#10622268C2212yes—
119#10622266C2212yes—
120#10622265C2212yes—
121#10622262C2212yes—
122#10622259C2212yes—
123C22×D44C2311yescharacteristic
124C22×D44C2311yescharacteristic
125C22×D44C2312yes—
126C22×D44C2312yes—
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2312yes—
133C22×C4×D11C2311yescharacteristic
134C22×Dic22C2312yes—
135C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2312yes—
151C2×(C2×D11)⋊C4C2312yes—
152C2×(C2×D11)⋊C4C2311yescharacteristic
153C2×(C2×D11)⋊C4C2311yescharacteristic
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2311yescharacteristic
156C2×(C2×D11)⋊C4C2311yescharacteristic
157C2×(C2×D11)⋊C4C2311yescharacteristic
158C2×(C2×D11)⋊C4C2311yescharacteristic
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×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×C4×Dic11C2311yescharacteristic
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×Dic11C2312yes—
196C2×C4×Dic11C2311yescharacteristic
197#66951—44no—
198#66950—44no—
199#66949—28no—
200#66948—24no—
201#66948—42no—
202#66947—28no—
203#66946—24no—
204#66946—24no—
205#66945—24no—
206#66945—42no—
207C4×D44—24no—
208C4×D44—44no—
209C4×D44—42no—
210C42×D11—42no—
211C42×D11—42no—
212#66922—42no—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11×#95C2312yes—
218C11×#95C2311yescharacteristic
219C11×#95C2311yescharacteristic
220C11⋊#95C2311yescharacteristic
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2312yes—
238#35037—111nomaximal, Sylow
239C23×D11C2412yes—
240C23×D11C2411yescharacteristic
241C23×D11C2411yescharacteristic
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×Dic11C2411yescharacteristic
254C22×Dic11C2411yescharacteristic
255C22×Dic11C2411yescharacteristic
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2411yescharacteristic
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2411yescharacteristic
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—24no—
265C2×D44—24no—
266C2×D44—22no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44—22no—
270C2×D44—42no—
271C2×D44—42no—
272C2×D44—42no—
273C2×D44—42no—
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—24no—
281C2×C4×D11—22no—
282C2×C4×D11—22no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—41no—
286C2×C4×D11—41no—
287C2×C4×D11—41no—
288C2×C4×D11—41no—
289C2×C4×D11—41no—
290C2×C4×D11—41no—
291C2×C4×D11—42no—
292C2×C4×D11—42no—
293C2×C4×D11#4114yes—
294C2×C4×D11#4114yes—
295C2×Dic22—24no—
296C2×Dic22—42no—
297C2×Dic22—42no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—24no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—22no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—42no—
305C11×C4⋊C4—42no—
306C11×C4⋊C4—42no—
307C11×C4⋊C4—42no—
308C11×C4⋊C4—42no—
309C11×C4⋊C4#4114yes—
310C42×C11—22no—
311C42×C11—22no—
312C42×C11—22no—
313C42×C11—42no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—42no—
329(C2×D11)⋊C4—42no—
330(C2×D11)⋊C4—42no—
331(C2×D11)⋊C4—42no—
332(C2×D11)⋊C4—42no—
333(C2×D11)⋊C4—42no—
334(C2×D11)⋊C4—42no—
335(C2×D11)⋊C4—42no—
336(C2×D11)⋊C4—42no—
337C4⋊Dic11—22no—
338C4⋊Dic11—24no—
339C4⋊Dic11—24no—
340C4⋊Dic11—22no—
341C4⋊Dic11—22no—
342C4⋊Dic11—22no—
343C4⋊Dic11—42no—
344Dic11⋊C4—24no—
345Dic11⋊C4—24no—
346Dic11⋊C4—24no—
347Dic11⋊C4—42no—
348C4×Dic11—24no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—22no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354C4×Dic11—41no—
355C4×Dic11—41no—
356C4×Dic11—41no—
357C4×Dic11—41no—
358C4×Dic11—42no—
359C4×Dic11—41no—
360#2864—111no—
361#2860—111no—
362#2857—111no—
363#2854—111no—
364#2653—112no—
365#2630—112no—
366#2594—112no—
367#2560—112no—
368#2507D1111yescharacteristic, complemented
369#2500—111no—
370#2494—111no—
371#2485—111no—
372#2466—112no—
373#2463—112no—
374#2452—111no—
375#2439—111no—
376#2420—111no—
377#2414—111no—
378#2335—112no—
379#2332—112no—
380C4×#121—111no—
381#2296—111no—
382C42×D4—111no—
383C23×C11C2511yescharacteristic
384C22×D11—21no—
385C22×D11—21no—
386C22×D11—21no—
387C22×D11—21no—
388C22×D11—21no—
389C22×D11—21no—
390C22×D11—21no—
391C22×D11—21no—
392C22×D11—21no—
393C22×D11—21no—
394C22×D11—21no—
395C22×D11—21no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11C2×#4112yes—
404C22×D11C2×#4112yes—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—22no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—21no—
427C2×C4×C11—22no—
428C2×C4×C11—21no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11C2×#4112yes—
432C2×C4×C11C2×#4112yes—
433C2×C4×C11C2×#4112yes—
434C2×C4×C11C2×#4112yes—
435C2×C4×C11C2×#4112yes—
436C2×C4×C11H(5,𝔽2)12yes—
437C2×C4×C112−1+412yes—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—22no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—21no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—21no—
459C2×Dic11—21no—
460C2×Dic11—21no—
461C2×Dic11—21no—
462C2×Dic11C2×#4112yes—
463C2×Dic11C2×#4112yes—
464C2×Dic11H(5,𝔽2)12yes—
465D44—28no—
466D44—48no—
467D44—44no—
468D44—84no—
469C4×D11—28no—
470C4×D11—44no—
471C4×D11—44no—
472C4×D11—44no—
473C4×D11—44no—
474C4×D11—44no—
475C4×D11—84no—
476Dic22—84no—
477C2×C4⋊Q8—111no—
478C2×#126—112no—
479C2×#123—112no—
480C2×C22⋊Q8—112no—
481C2×C22⋊Q8—112no—
482C2×#121—111no—
483C2×#121—111no—
484C2×C4×D4—111no—
485C2×C4×D4—111no—
486C2×C4×D4—111no—
487C2×C4×D4—111no—
488C2×C4×D4—112no—
489C2×#117—111no—
490C2×#117—111no—
491C22×C42—111no—
492C22×C42—111no—
493#401—112no—
494#398C2×D1112yes—
495#398C2×D1112yes—
496#397—112no—
497#397—112no—
498#397—112no—
499#396—112no—
500#396—112no—
501#394—112no—
502#394—112no—
503#394—112no—
504#394—112no—
505#394—112no—
506#393—112no—
507#393—112no—
508#392—112no—
509#391—112no—
510#391—112no—
511#390—112no—
512#390—111no—
513#390—111no—
514#390—111no—
515#390—111no—
516#389—112no—
517#389—111no—
518#389—111no—
519#389—111no—
520#389—111no—
521#389—111no—
522#389—111no—
523#389C2×D1112yes—
524#389C2×D1111yescharacteristic
525#389C2×D1111yescharacteristic
526#389C2×D1111yescharacteristic
527#389C2×D1111yescharacteristic
528#388—112no—
529#388—112no—
530#388—112no—
531#388—112no—
532#388—112no—
533#388—112no—
534#388—112no—
535#388—112no—
536#388—112no—
537#388—112no—
538#388—112no—
539#387—112no—
540#387—112no—
541#387—112no—
542#387—112no—
543#387—112no—
544#387—112no—
545#387—112no—
546#387C2×D1112yes—
547#386—112no—
548#386—112no—
549#386—112no—
550#385—112no—
551#385—112no—
552#385—112no—
553#384C2×D1111yescharacteristic
554#382—111no—
555#382—111no—
556#381—112no—
557#380—112no—
558#380—111no—
559#380—111no—
560#380—111no—
561#380—111no—
562C4×C4⋊C4—112no—
563C4×C4⋊C4—111no—
564C4×C4⋊C4—111no—
565C4×C4⋊C4—112no—
566C4×C4⋊C4C2×D1111yescharacteristic
567C4×C4⋊C4C2×D1111yescharacteristic
568C4×C22⋊C4—112no—
569C4×C22⋊C4—111no—
570C4×C22⋊C4—111no—
571C4×C22⋊C4—111no—
572C4×C22⋊C4—111no—
573C4×C22⋊C4—111no—
574C4×C22⋊C4—111no—
575C43—111no—
576C22×C11C22×#4111yescharacteristic
577C22×C11C22×#4111yescharacteristic
578C22×C11C22×#4111yescharacteristic
579C22×C11C2×H(5,𝔽2)11yescharacteristic
580C22×C11C2×H(5,𝔽2)11yescharacteristic
581C22×C11C2×2−1+411yescharacteristic
582C22×C11#58511yescharacteristic
583C2×D11—22no—
584C2×D11—22no—
585C2×D11—22no—
586C2×D11—22no—
587C2×D11—22no—
588C2×D11—22no—
589C2×D11—41no—
590C2×D11—41no—
591C2×D11—41no—
592C2×D11—41no—
593C2×D11—41no—
594C2×D11—41no—
595C2×D11—41no—
596C2×D11—41no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C4×C11—22no—
605C4×C11—22no—
606C4×C11—22no—
607C4×C11—22no—
608C4×C11—42no—
609C4×C11—41no—
610C4×C11—42no—
611C4×C11—41no—
612C4×C11—42no—
613C4×C11—42no—
614C4×C11#53914yes—
615Dic11—22no—
616Dic11—22no—
617Dic11—22no—
618Dic11—42no—
619Dic11—41no—
620Dic11—41no—
621Dic11—41no—
622Dic11—42no—
623Dic11—42no—
624C22×Q8—112no—
625C22×D4—111no—
626C22×D4—111no—
627C22×D4—112no—
628C22×D4—112no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—112no—
635C23×C4—111no—
636C4⋊Q8—442no—
637#126—444no—
638#123—228no—
639C22⋊Q8—228no—
640C22⋊Q8—444no—
641#121—224no—
642#121—442no—
643C4×D4—224no—
644C4×D4—224no—
645C4×D4—224no—
646C4×D4—442no—
647C4×D4—444no—
648#117—224no—
649#117—442no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—112no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4C22×D1111yescharacteristic
662C2×C4⋊C4C22×D1111yescharacteristic
663C2×C4⋊C4C22×D1111yescharacteristic
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1112yes—
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C4⋊C4C22×D1112yes—
668C2×C4⋊C4C22×D1112yes—
669C2×C4⋊C4C22×D1112yes—
670C2×C4⋊C4C22×D1112yes—
671C2×C4⋊C4C22×D1112yes—
672C2×C4⋊C4C22×D1111yescharacteristic
673C2×C22⋊C4—112no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—111no—
676C2×C22⋊C4—111no—
677C2×C22⋊C4—111no—
678C2×C22⋊C4—111no—
679C2×C22⋊C4—111no—
680C2×C22⋊C4—111no—
681C2×C22⋊C4—112no—
682C2×C22⋊C4—112no—
683C2×C22⋊C4—112no—
684C2×C22⋊C4—112no—
685C2×C22⋊C4—112no—
686C2×C22⋊C4—112no—
687C2×C22⋊C4—112no—
688C2×C22⋊C4—112no—
689C2×C22⋊C4—112no—
690C2×C22⋊C4—112no—
691C2×C22⋊C4—112no—
692C2×C22⋊C4—112no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—112no—
695C2×C22⋊C4—112no—
696C2×C42—112no—
697C2×C42—111no—
698C2×C42—111no—
699C2×C42—111no—
700C2×C42—111no—
701C2×C42—111no—
702C2×C42—112no—
703C2×C42—111no—
704C2×C42—111no—
705C2×C42—111no—
706C2×C42—111no—
707C2×C42—111no—
708C2×C42—442no—
709C2×C42—442no—
710C2×C42C22×D1111yescharacteristic
711C2×C42C22×D1111yescharacteristic
712C2×C42C22×D1111yescharacteristic
713C2×C42C22×D1112yes—
714#95—111no—
715#95—111no—
716#95—111no—
717#95—111no—
718#95—112no—
719#95—112no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95—112no—
730#95—112no—
731#95—112no—
732#95C22×D1111yescharacteristic
733#95C22×D1111yescharacteristic
734#95C22×D1112yes—
735#95C22×D1112yes—
736#95C22×D1112yes—
737#95C22×D1112yes—
738#95C22×D1112yes—
739C2×C11#344411yescharacteristic
740C2×C11C2×#53911yescharacteristic
741C2×C11#346011yescharacteristic
742C2×C11#350511yescharacteristic
743C2×C11#351111yescharacteristic
744C2×C11#351811yescharacteristic
745C2×C11#351911yescharacteristic
746D11—42no—
747D11—42no—
748D11—82no—
749C24—111no—
750C24—111no—
751C24—112no—
752C2×Q8—224no—
753C2×Q8—442no—
754C2×Q8—442no—
755C2×D4—222no—
756C2×D4—222no—
757C2×D4—224no—
758C2×D4—224no—
759C2×D4—222no—
760C2×D4—222no—
761C2×D4—222no—
762C2×D4—222no—
763C2×D4—442no—
764C2×D4—442no—
765C2×D4—442no—
766C2×D4—442no—
767C22×C4—111no—
768C22×C4—111no—
769C22×C4—111no—
770C22×C4—114no—
771C22×C4—114no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—222no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—222no—
787C22×C4—222no—
788C22×C4—224no—
789C22×C4—441no—
790C22×C4—441no—
791C22×C4—441no—
792C22×C4—441no—
793C22×C4—441no—
794C22×C4—441no—
795C22×C4—442no—
796C22×C4—442no—
797C22×C4C23×D1112yes—
798C22×C4C23×D1111yescharacteristic
799C22×C4C23×D1112yes—
800C22×C4C23×D1112yes—
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1112yes—
803C22×C4C23×D1111yescharacteristic
804C22×C4C23×D1111yescharacteristic
805C22×C4C23×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1111yescharacteristic
808C4⋊C4—22no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—24no—
813C4⋊C4—22no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—222no—
820C4⋊C4—224no—
821C4⋊C4—224no—
822C4⋊C4—224no—
823C4⋊C4—224no—
824C4⋊C4—224no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4—222no—
828C4⋊C4—442no—
829C4⋊C4—442no—
830C4⋊C4#434314yes—
831C22⋊C4—222no—
832C22⋊C4—224no—
833C22⋊C4—224no—
834C22⋊C4—224no—
835C22⋊C4—224no—
836C22⋊C4—222no—
837C22⋊C4—222no—
838C22⋊C4—224no—
839C22⋊C4—222no—
840C22⋊C4—222no—
841C22⋊C4—224no—
842C22⋊C4—224no—
843C22⋊C4—222no—
844C22⋊C4—224no—
845C22⋊C4—442no—
846C22⋊C4—442no—
847C22⋊C4—442no—
848C22⋊C4—442no—
849C22⋊C4—442no—
850C22⋊C4—442no—
851C22⋊C4—442no—
852C22⋊C4—442no—
853C22⋊C4—442no—
854C42—22no—
855C42—22no—
856C42—22no—
857C42—42no—
858C42—224no—
859C42—222no—
860C42—222no—
861C42—222no—
862C42—222no—
863C42—222no—
864C42—441no—
865C42—441no—
866C42—441no—
867C42—441no—
868C42—442no—
869C42—441no—
870C11#3503711yescharacteristic, complemented, Sylow
871C23—112no—
872C23—112no—
873C23—221no—
874C23—221no—
875C23—221no—
876C23—221no—
877C23—221no—
878C23—221no—
879C23—221no—
880C23—221no—
881C23—221no—
882C23—221no—
883C23—221no—
884C23—221no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23C24×D1111yescharacteristic
893Q8—884no—
894D4—228no—
895D4—448no—
896D4—444no—
897D4—884no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—112no—
925C2×C4—112no—
926C2×C4—112no—
927C2×C4—221no—
928C2×C4—221no—
929C2×C4—221no—
930C2×C4—221no—
931C2×C4—221no—
932C2×C4—221no—
933C2×C4—228no—
934C2×C4—221no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—221no—
939C2×C4—221no—
940C2×C4—221no—
941C2×C4—221no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—221no—
945C2×C4—221no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—221no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—221no—
952C2×C4—444no—
953C2×C4—444no—
954C2×C4—444no—
955C2×C4—444no—
956C2×C4—444no—
957C2×C4—884no—
958C2×C4C2×#434312yes—
959C2×C4C2×#434312yes—
960C2×C4C2×#434312yes—
961C2×C4#6704012yes—
962C2×C4#41×D1112yes—
963C2×C4#41×D1112yes—
964C2×C4#6704212yes—
965C22—222no—
966C22—222no—
967C22—222no—
968C22—222no—
969C22—222no—
970C22—222no—
971C22—441no—
972C22—441no—
973C22—441no—
974C22—441no—
975C22—441no—
976C22—441no—
977C22—441no—
978C22—441no—
979C22—442no—
980C22—442no—
981C22—442no—
982C22—442no—
983C22—442no—
984C22—442no—
985C22—442no—
986C22C22×#434311yescharacteristic
987C22C2×#6704011yescharacteristic
988C22C2×#41×D1111yescharacteristic
989C22C2×#41×D1111yescharacteristic
990C22C2×#6704211yescharacteristic
991C22D11×H(5,𝔽2)11yescharacteristic
992C22#1062345511yescharacteristic
993C4—22no—
994C4—22no—
995C4—22no—
996C4—22no—
997C4—41no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—41no—
1002C4—42no—
1003C4—222no—
1004C4—222no—
1005C4—222no—
1006C4—441no—
1007C4—442no—
1008C4—442no—
1009C4—442no—
1010C4—441no—
1011C4—441no—
1012C4#1062322314yes—
1013C2—442no—
1014C2—442no—
1015C2—882no—
1016C2#1308191311yescharacteristic
1017C2C2×#1062322311yescharacteristic
1018C2#1308203111yescharacteristic
1019C2#1308244511yescharacteristic
1020C2#1308252411yescharacteristic
1021C2#1308263411yescharacteristic
1022C2#1308264911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2507C2
prime radical#13072032C2
hypercenter#2507D11
hypocenterC11#35037
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2507

Complements

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

NH ≅ G/Ntype
1. #13077002C2semidirect
2. #13076984C2semidirect
3. #13076969C2semidirect
4. #13076949C2semidirect
5. #13074678C2semidirect
6. #13074466C2semidirect
7. #13074123C2semidirect
8. #13073755C2semidirect
9. #13073075C2semidirect
10. #13073010C2semidirect
11. #13072916C2semidirect
12. #13072657C2semidirect
13. #13072611C2semidirect
14. #13072466C2semidirect
15. #13072309C2semidirect
16. #13072109C2semidirect
18. #13071409C2semidirect
19. #13071370C2semidirect
20. C4×#66948C2semidirect
21. #13071097C2semidirect
22. C4×#66946C2semidirect
23. C11×#2507C2semidirect
368. #2507D11semidirect
870. C11#35037semidirect

Maximal subgroups

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

subgroupindex
#130770022
#130769842
#130769692
#130769492
#130746782
#130744662
#130741232
#130737552
#130730752
#130730102
#130729162
#130726572
#130726112
#130724662
#130723092
#130721092
#130720322
#130714092
#130713702
C4×#669482
#130710972
C4×#669462
C11×#25072
#3503711