Finite Group Databasebeta

← #14920925

Subgroups — #14920925

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074644C212yesmaximal, complemented
2#13074642C212yesmaximal, complemented
3#13074599C212yesmaximal, complemented
4#13074597C212yesmaximal, complemented
5#13074593C211yesmaximal, characteristic, complemented
6#13074579C211yesmaximal, characteristic, complemented
7#13074577C211yesmaximal, characteristic, complemented
8#13074560C211yesmaximal, characteristic, complemented
9#13074450C211yesmaximal, characteristic, complemented
10#13074405C211yesmaximal, characteristic, complemented
11#13074370C211yesmaximal, characteristic
12#13071881C212yesmaximal, complemented
13#13071874C212yesmaximal, complemented
14#13071859C212yesmaximal, complemented
15#13071855C212yesmaximal, complemented
16#13071180C211yesmaximal, characteristic, complemented
17#13071175C211yesmaximal, characteristic, complemented
18#121×Dic11C211yesmaximal, characteristic, complemented
19#13071122C211yesmaximal, characteristic, complemented
20#13071078C211yesmaximal, characteristic, complemented
21#13071074C211yesmaximal, characteristic, complemented
22#117×Dic11C211yesmaximal, characteristic, complemented
23C11×#2624C211yesmaximal, characteristic, complemented
24C2×C11×#121C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C2×#66993C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2212yes—
29C2×#66983C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×#66946C2211yescharacteristic
33C2×#66945C2212yes—
34C2×#66943C2211yescharacteristic
35C2×(C22⋊D11)⋊C4C2212yes—
36C2×(C22⋊D11)⋊C4C2212yes—
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×#66930C2212yes—
39C11×#399C2212yes—
40C11×#397C2212yes—
41C11×#394C2212yes—
42C11×#394C2212yes—
43C11×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#389C2211yescharacteristic
47C11×#380C2211yescharacteristic
48#10622836C2212yes—
49#10622836C2212yes—
50#10622834C2211yescharacteristic
51#10622834C2211yescharacteristic
52#10622833C2212yes—
53#10622825C2211yescharacteristic
54#10622607C2212yes—
55#10622606C2212yes—
56#10622606C2212yes—
57#10622605C2212yes—
58#10622603C2212yes—
59#10622601C2211yescharacteristic
60#10622601C2211yescharacteristic
61#10622598C2211yescharacteristic
62#10622598C2211yescharacteristic
63#10622596C2212yes—
64#10622595C2212yes—
65#10622591C2212yes—
66#10622590C2211yescharacteristic
67#10622589C2211yescharacteristic
68C4⋊C4×Dic11C2211yescharacteristic
69C4⋊C4×Dic11C2211yescharacteristic
70C4⋊C4×Dic11C2212yes—
71C4⋊C4×Dic11C2211yescharacteristic
72C4⋊C4×Dic11C2211yescharacteristic
73C4⋊C4×Dic11C2211yescharacteristic
74C4⋊C4×Dic11C2211yescharacteristic
75#10622586C2211yescharacteristic
76#10622586C2211yescharacteristic
77#10622574C2212yes—
78#10622574C2212yes—
79#10622574C2212yes—
80#10622574C2212yes—
81#10622572C2212yes—
82#10622572C2212yes—
83#10622572C2212yes—
84#10622572C2212yes—
85#10622571C2212yes—
86#10622570C2212yes—
87#10622570C2212yes—
88#10622566C2212yes—
89#10622565C2212yes—
90#10622565C2212yes—
91#10622564C2212yes—
92#10622561C2212yes—
93#10622561C2212yes—
94#10622561C2212yes—
95#10622558C2212yes—
96#10622557C2212yes—
97C22⋊C4×Dic11C2212yes—
98C22⋊C4×Dic11C2212yes—
99C22⋊C4×Dic11C2211yescharacteristic
100C22⋊C4×Dic11C2211yescharacteristic
101C22⋊C4×Dic11C2211yescharacteristic
102C22⋊C4×Dic11C2211yescharacteristic
103#10622552C2211yescharacteristic
104#10622552C2211yescharacteristic
105#10622545C2211yescharacteristic
106#10622545C2211yescharacteristic
107C42×Dic11C2211yescharacteristic
108C42×Dic11C2211yescharacteristic
109#10622541C2211yescharacteristic
110#10622541C2211yescharacteristic
111#10622288C2212yes—
112#10622287C2212yes—
113#10622283C2212yes—
114#10622282C2212yes—
115#10622279C2212yes—
116#10622279C2212yes—
117#10622274C2212yes—
118#10622271C2212yes—
119#10622270C2212yes—
120#10622270C2212yes—
121#10622266C2212yes—
122#10622262C2212yes—
123C22×D4×C11C2311yescharacteristic
124C22×D4×C11C2312yes—
125C23×C4×C11C2311yescharacteristic
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2312yes—
129C23×Dic11C2312yes—
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×D44C2311yescharacteristic
133C22×C4×D11C2312yes—
134C11×#121—24no—
135C11×#117—24no—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C22⋊C4C2311yescharacteristic
144C2×C11×C22⋊C4C2311yescharacteristic
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2311yescharacteristic
153C2×C22⋊Dic11C2311yescharacteristic
154C2×C22⋊Dic11C2311yescharacteristic
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161#66993—24no—
162D4×Dic11—24no—
163D4×Dic11—44no—
164#66983—24no—
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×(C2×D11)⋊C4C2312yes—
175#66979—24no—
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C2312yes—
183C2×C4⋊Dic11C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×C4×Dic11—24no—
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208#66946—24no—
209#66945—44no—
210#66943—24no—
211(C22⋊D11)⋊C4—44no—
212(C22⋊D11)⋊C4—44no—
213(C22⋊D11)⋊C4—44no—
214#66930—44no—
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⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237#34621—111nomaximal, Sylow
238C24×C11C2412yes—
239C24×C11C2411yescharacteristic
240C23×D11C2412yes—
241C2×D4×C11—24no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11#4114yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2412yes—
256C22×C4×C11C2412yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C2×C22⋊D11—24no—
260C2×C22⋊D11—24no—
261C2×C22⋊D11—24no—
262C2×C22⋊D11—42no—
263C2×C22⋊D11—42no—
264C2×C22⋊D11—42no—
265C2×C22⋊D11—42no—
266C2×C22⋊D11—42no—
267C2×C22⋊D11—42no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—24no—
271C22×Dic11—24no—
272C22×Dic11—22no—
273C22×Dic11—24no—
274C22×Dic11—22no—
275C22×Dic11—41no—
276C22×Dic11—41no—
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2412yes—
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2411yescharacteristic
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2411yescharacteristic
288C2×D44—22no—
289C2×D44—22no—
290C2×D44—22no—
291C2×C4×D11—24no—
292C2×C4×D11—24no—
293C2×C4×D11—24no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—22no—
298C11×C4⋊C4—22no—
299C11×C4⋊C4—42no—
300C11×C4⋊C4—42no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—24no—
304C11×C22⋊C4—42no—
305C11×C22⋊C4—42no—
306C11×C22⋊C4—42no—
307C11×C22⋊C4—42no—
308C11×C22⋊C4—42no—
309C42×C11—22no—
310C42×C11—22no—
311C22⋊Dic11—22no—
312C22⋊Dic11—22no—
313C22⋊Dic11—24no—
314C22⋊Dic11—42no—
315C22⋊Dic11—42no—
316C22⋊Dic11—42no—
317C22⋊Dic11—42no—
318C22⋊Dic11—42no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—42no—
322(C2×D11)⋊C4—42no—
323(C2×D11)⋊C4—42no—
324(C2×D11)⋊C4—42no—
325(C2×D11)⋊C4—42no—
326(C2×D11)⋊C4—42no—
327(C2×D11)⋊C4—42no—
328(C2×D11)⋊C4—42no—
329C4⋊Dic11—24no—
330C4⋊Dic11—22no—
331C4⋊Dic11—22no—
332C4⋊Dic11—22no—
333C4⋊Dic11—22no—
334C4⋊Dic11—22no—
335C4⋊Dic11—42no—
336C4⋊Dic11—42no—
337Dic11⋊C4—24no—
338Dic11⋊C4—42no—
339Dic11⋊C4—42no—
340Dic11⋊C4—42no—
341Dic11⋊C4—42no—
342Dic11⋊C4—42no—
343Dic11⋊C4—42no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346C4×Dic11—22no—
347C4×Dic11—24no—
348C4×Dic11—22no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—24no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354C4×Dic11—41no—
355C4×Dic11—41no—
356C4×Dic11—41no—
357C4×Dic11—41no—
358C4×Dic11#4114yes—
359C4×Dic11#4114yes—
360#2651—112no—
361#2651—112no—
362#2648—112no—
363#2648—112no—
364#2647—111no—
365#2644—111no—
366#2644—111no—
367#2641—111no—
368#2629—111no—
369#2624—111no—
370#2624D1111yescharacteristic, complemented
371#2619—111no—
372#2395—112no—
373#2395—112no—
374#2392—112no—
375#2392—112no—
376C4×#127—111no—
377C4×#125—111no—
378C4×#121—111no—
379C4×#121—111no—
380#2293—111no—
381#2293—111no—
382C4×#117—111no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—21no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11C2×#4112yes—
397C23×C11C2511yescharacteristic
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405D4×C11—48no—
406D4×C11—44no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—28no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—21no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—21no—
426C2×C4×C11—21no—
427C2×C4×C11—21no—
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—
435C22⋊D11—48no—
436C22⋊D11—48no—
437C22⋊D11—48no—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—21no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—21no—
457C2×Dic11—22no—
458C2×Dic11—21no—
459C2×Dic11—21no—
460C2×Dic11—21no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—21no—
464C2×Dic11—21no—
465C2×Dic11—44no—
466C2×Dic11—44no—
467C2×Dic11—48no—
468C2×Dic11C2×#4112yes—
469C2×Dic11C2×#4112yes—
470C2×Dic11C2×#4112yes—
471C2×Dic11C2×#4112yes—
472C2×Dic11H(5,𝔽2)12yes—
473C2×Dic11H(5,𝔽2)12yes—
474D44—44no—
475C4×D11—48no—
476C2×#127—111no—
477C2×#125—111no—
478C2×#121—111no—
479C2×#121C2×D1111yescharacteristic
480C2×C4×D4—111no—
481C2×C4×D4—112no—
482C2×C4×D4—111no—
483C2×C4×D4—112no—
484C2×C4×D4—112no—
485C2×C4×D4—112no—
486C2×#117—111no—
487C2×#117—112no—
488C2×#117—112no—
489C2×#117C2×D1111yescharacteristic
490C22×C42—111no—
491#400—112no—
492#400—112no—
493#399—112no—
494#399C2×D1112yes—
495#398—112no—
496#398—112no—
497#398—112no—
498#398—112no—
499#397—112no—
500#397—112no—
501#397—112no—
502#397—112no—
503#397—112no—
504#397—112no—
505#397—112no—
506#397C2×D1112yes—
507#396—112no—
508#396—112no—
509#396—112no—
510#396—112no—
511#394—112no—
512#394—112no—
513#394—112no—
514#394—112no—
515#394—112no—
516#394—112no—
517#394—112no—
518#394—112no—
519#394C2×D1112yes—
520#394C2×D1112yes—
521#392—112no—
522#392—112no—
523#390—111no—
524#390—111no—
525#390—111no—
526#390—111no—
527#390—112no—
528#390—112no—
529#390—111no—
530#390—111no—
531#390C2×D1111yescharacteristic
532#390C2×D1111yescharacteristic
533#389—111no—
534#389—111no—
535#389—111no—
536#389—111no—
537#389—111no—
538#389—111no—
539#389C2×D1111yescharacteristic
540#389C2×D1111yescharacteristic
541#388—112no—
542#388—112no—
543#388—112no—
544#388—112no—
545#388—112no—
546#388—112no—
547#387—112no—
548#387—112no—
549#386—112no—
550#386—112no—
551#384—111no—
552#382—111no—
553#380—111no—
554#380C2×D1111yescharacteristic
555C4×C4⋊C4—112no—
556C4×C4⋊C4—111no—
557C4×C4⋊C4—111no—
558C4×C4⋊C4—111no—
559C4×C4⋊C4—111no—
560C4×C4⋊C4—111no—
561C4×C4⋊C4—111no—
562C4×C4⋊C4—112no—
563C4×C22⋊C4—111no—
564C4×C22⋊C4—111no—
565C4×C22⋊C4—112no—
566C4×C22⋊C4—111no—
567C4×C22⋊C4—111no—
568C4×C22⋊C4—112no—
569C4×C22⋊C4—112no—
570C4×C22⋊C4—112no—
571#376—111no—
572#376—111no—
573C43—111no—
574C43—111no—
575C22×C11—22no—
576C22×C11—22no—
577C22×C11—22no—
578C22×C11—41no—
579C22×C11—41no—
580C22×C11—41no—
581C22×C11—41no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11C22×#4111yescharacteristic
590C22×C11C22×#4111yescharacteristic
591C22×C11C22×#4111yescharacteristic
592C22×C11C2×H(5,𝔽2)11yescharacteristic
593C22×C11C2×H(5,𝔽2)11yescharacteristic
594C22×C11#58511yescharacteristic
595C22×C11#58511yescharacteristic
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C4×C11—22no—
604C4×C11—42no—
605C4×C11—41no—
606C4×C11—41no—
607C4×C11—42no—
608C4×C11—41no—
609C4×C11—41no—
610C4×C11—42no—
611C4×C11#52914yes—
612Dic11—22no—
613Dic11—22no—
614Dic11—22no—
615Dic11—41no—
616Dic11—42no—
617Dic11—41no—
618Dic11—41no—
619Dic11—41no—
620Dic11—42no—
621Dic11—42no—
622Dic11#54014yes—
623C22×D4—112no—
624C22×D4—112no—
625C22×D4—112no—
626C22×D4—111no—
627C22×D4C22×D1111yescharacteristic
628C22×D4C22×D1112yes—
629C23×C4—112no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—112no—
633C23×C4C22×D1111yescharacteristic
634#127—224no—
635#125—224no—
636#121—24no—
637#121—224no—
638C4×D4—224no—
639C4×D4—224no—
640C4×D4—444no—
641C4×D4—444no—
642C4×D4—444no—
643C4×D4—444no—
644#117—24no—
645#117—224no—
646#117—444no—
647#117—444no—
648C2×C4⋊C4—111no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—112no—
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⋊C4—112no—
662C2×C4⋊C4—112no—
663C2×C4⋊C4C22×D1111yescharacteristic
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1111yescharacteristic
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C4⋊C4C22×D1111yescharacteristic
668C2×C4⋊C4C22×D1112yes—
669C2×C4⋊C4C22×D1112yes—
670C2×C22⋊C4—111no—
671C2×C22⋊C4—111no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—112no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—112no—
679C2×C22⋊C4—112no—
680C2×C22⋊C4—112no—
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⋊C4C22×D1111yescharacteristic
689C2×C22⋊C4C22×D1111yescharacteristic
690C2×C22⋊C4C22×D1112yes—
691C2×C22⋊C4C22×D1112yes—
692C2×C22⋊C4C22×D1112yes—
693C2×C22⋊C4C22×D1112yes—
694C2×C22⋊C4C22×D1112yes—
695C2×C22⋊C4C22×D1112yes—
696C2×C42—111no—
697C2×C42—111no—
698C2×C42—111no—
699C2×C42—111no—
700C2×C42—112no—
701C2×C42—112no—
702C2×C42—111no—
703C2×C42—111no—
704C2×C42—111no—
705C2×C42—111no—
706C2×C42—111no—
707C2×C42—111no—
708C2×C42—111no—
709C2×C42—111no—
710C2×C42—111no—
711C2×C42—111no—
712C2×C42—224no—
713C2×C42C22×D1111yescharacteristic
714C2×C42C22×D1111yescharacteristic
715#95—111no—
716#95—111no—
717#95—111no—
718#95—111no—
719#95—111no—
720#95—111no—
721#95—111no—
722#95—111no—
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#95—112no—
733#95—112no—
734#95C22×D1112yes—
735#95C22×D1112yes—
736#95C22×D1112yes—
737C2×C11—42no—
738C2×C11—82no—
739C2×C11C2×#52911yescharacteristic
740C2×C11C2×#54011yescharacteristic
741C2×C11#345511yescharacteristic
742C2×C11#346011yescharacteristic
743C2×C11#346011yescharacteristic
744C2×C11#346011yescharacteristic
745C2×C11#346011yescharacteristic
746D11—82no—
747C24—112no—
748C24C23×D1112yes—
749C24C23×D1111yescharacteristic
750C2×D4—24no—
751C2×D4—22no—
752C2×D4—22no—
753C2×D4—22no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—224no—
757C2×D4—224no—
758C2×D4—224no—
759C2×D4—222no—
760C2×D4—222no—
761C2×D4—222no—
762C2×D4—442no—
763C2×D4—442no—
764C2×D4—442no—
765C2×D4—442no—
766C2×D4—442no—
767C2×D4—442no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—111no—
771C22×C4—111no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—112no—
776C22×C4—111no—
777C22×C4—111no—
778C22×C4—111no—
779C22×C4—112no—
780C22×C4—112no—
781C22×C4—224no—
782C22×C4—224no—
783C22×C4—224no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—224no—
787C22×C4—224no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—224no—
791C22×C4—441no—
792C22×C4—441no—
793C22×C4#434114yes—
794C22×C4C23×D1112yes—
795C22×C4C23×D1111yescharacteristic
796C22×C4C23×D1111yescharacteristic
797C22×C4C23×D1111yescharacteristic
798C22×C4C23×D1111yescharacteristic
799C22×C4C23×D1112yes—
800C22×C4C23×D1112yes—
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—42no—
809C4⋊C4—42no—
810C4⋊C4—222no—
811C4⋊C4—222no—
812C4⋊C4—224no—
813C4⋊C4—224no—
814C4⋊C4—222no—
815C4⋊C4—222no—
816C4⋊C4—222no—
817C4⋊C4—442no—
818C4⋊C4—442no—
819C4⋊C4—442no—
820C4⋊C4—442no—
821C4⋊C4—442no—
822C4⋊C4—442no—
823C4⋊C4—442no—
824C4⋊C4—442no—
825C22⋊C4—22no—
826C22⋊C4—22no—
827C22⋊C4—24no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—42no—
831C22⋊C4—42no—
832C22⋊C4—42no—
833C22⋊C4—224no—
834C22⋊C4—222no—
835C22⋊C4—222no—
836C22⋊C4—224no—
837C22⋊C4—224no—
838C22⋊C4—442no—
839C22⋊C4—442no—
840C22⋊C4—442no—
841C22⋊C4—442no—
842C22⋊C4—442no—
843C22⋊C4—442no—
844C22⋊C4—442no—
845C22⋊C4—442no—
846C22⋊C4—442no—
847C22⋊C4—442no—
848C22⋊C4—442no—
849C22⋊C4—442no—
850C22⋊C4—442no—
851C42—22no—
852C42—22no—
853C42—114no—
854C42—114no—
855C42—222no—
856C42—222no—
857C42—222no—
858C42—222no—
859C42—224no—
860C42—224no—
861C42—222no—
862C42—222no—
863C42—222no—
864C42—222no—
865C42—441no—
866C42—441no—
867C42—441no—
868C42—441no—
869C11#3462111yescharacteristic, complemented, Sylow
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—222no—
884C23—222no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23C2×#434112yes—
891C23C24×D1111yescharacteristic
892D4—48no—
893D4—44no—
894D4—448no—
895D4—448no—
896D4—448no—
897D4—444no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—28no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—112no—
923C2×C4—112no—
924C2×C4—112no—
925C2×C4—112no—
926C2×C4—112no—
927C2×C4—112no—
928C2×C4—221no—
929C2×C4—221no—
930C2×C4—221no—
931C2×C4—221no—
932C2×C4—221no—
933C2×C4—221no—
934C2×C4—222no—
935C2×C4—221no—
936C2×C4—221no—
937C2×C4—221no—
938C2×C4—221no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—221no—
943C2×C4—221no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—221no—
947C2×C4—221no—
948C2×C4—222no—
949C2×C4—221no—
950C2×C4—221no—
951C2×C4—221no—
952C2×C4—222no—
953C2×C4—221no—
954C2×C4—222no—
955C2×C4—448no—
956C2×C4—444no—
957C2×C4—448no—
958C2×C4—444no—
959C2×C4C2×#434112yes—
960C2×C4C2×#434112yes—
961C2×C4#41×D1112yes—
962C2×C4#41×D1112yes—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—442no—
978C22—442no—
979C22—442no—
980C22—442no—
981C22—442no—
982C22—442no—
983C22—442no—
984C22C22×#434111yescharacteristic
985C22C2×#41×D1111yescharacteristic
986C22C2×#41×D1111yescharacteristic
987C22D11×H(5,𝔽2)11yescharacteristic
988C22D11×H(5,𝔽2)11yescharacteristic
989C22#1062345511yescharacteristic
990C22#1062345711yescharacteristic
991C4—22no—
992C4—42no—
993C4—42no—
994C4—41no—
995C4—41no—
996C4—42no—
997C4—41no—
998C4—41no—
999C4—114no—
1000C4—222no—
1001C4—222no—
1002C4—222no—
1003C4—441no—
1004C4—442no—
1005C4—441no—
1006C4—441no—
1007C4—442no—
1008C4—441no—
1009C4—442no—
1010C4#1062318014yes—
1011C2—42no—
1012C2—82no—
1013C2—882no—
1014C2C2×#1062318011yescharacteristic
1015C2D11×#54011yescharacteristic
1016C2#1308200311yescharacteristic
1017C2#1308202911yescharacteristic
1018C2#1308203111yescharacteristic
1019C2#1308203311yescharacteristic
1020C2#1308203611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2624C2
prime radical#13074370C2
hypercenter#2624D11
hypocenterC11#34621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2624

Complements

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

NH ≅ G/Ntype
1. #13074644C2semidirect
2. #13074642C2semidirect
3. #13074599C2semidirect
4. #13074597C2semidirect
5. #13074593C2semidirect
6. #13074579C2semidirect
7. #13074577C2semidirect
8. #13074560C2semidirect
9. #13074450C2semidirect
10. #13074405C2semidirect
12. #13071881C2semidirect
13. #13071874C2semidirect
14. #13071859C2semidirect
15. #13071855C2semidirect
16. #13071180C2semidirect
17. #13071175C2semidirect
18. #121×Dic11C2semidirect
19. #13071122C2semidirect
20. #13071078C2semidirect
21. #13071074C2semidirect
22. #117×Dic11C2semidirect
23. C11×#2624C2semidirect
370. #2624D11semidirect
869. C11#34621semidirect

Maximal subgroups

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

subgroupindex
#130746442
#130746422
#130745992
#130745972
#130745932
#130745792
#130745772
#130745602
#130744502
#130744052
#130743702
#130718812
#130718742
#130718592
#130718552
#130711802
#130711752
#121×Dic112
#130711222
#130710782
#130710742
#117×Dic112
C11×#26242
#3462111