Finite Group Databasebeta

← #14925871

Subgroups — #14925871

Order 2816.

1948 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074111C212yesmaximal, complemented
2#13074110C212yesmaximal, complemented
3#13073988C211yesmaximal, characteristic, complemented
4#13073856C211yesmaximal, characteristic, complemented
5#13073620C211yesmaximal, characteristic
6#13073617C211yesmaximal, characteristic
7#13073207C211yesmaximal, characteristic, complemented
8#13073206C212yesmaximal, complemented
9#13072415C211yesmaximal, characteristic, complemented
10#13072414C211yesmaximal, characteristic, complemented
11#13072407C212yesmaximal, complemented
12#13071878C212yesmaximal, complemented
13#13071874C212yesmaximal, complemented
14#13071180C211yesmaximal, characteristic
15#13071163C211yesmaximal, characteristic, complemented
16#13071157C212yesmaximal, complemented
17#13071155C211yesmaximal, characteristic, complemented
18#13071078C211yesmaximal, characteristic, complemented
19#13071076C212yesmaximal, complemented
20#13071074C211yesmaximal, characteristic, complemented
21C4×#66940C211yesmaximal, characteristic, complemented
22C4×#66940C211yesmaximal, characteristic, complemented
23C11×#2513C211yesmaximal, characteristic, complemented
24C2×#66993C2211yescharacteristic
25C2×#66989C2211yescharacteristic
26C2×D4×Dic11C2211yescharacteristic
27C2×#66946C2211yescharacteristic
28C2×#66945C2212yes—
29C2×#66940C2211yescharacteristic
30C2×#66940C2211yescharacteristic
31C2×#66940C2211yescharacteristic
32C2×#66940C2211yescharacteristic
33C2×#66938C2212yes—
34C2×(C22⋊D11)⋊C4C2212yes—
35C2×(C22⋊D11)⋊C4C2212yes—
36C2×#66930C2212yes—
37C2×#66928C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#397C2212yes—
41C11×#397C2212yes—
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#390C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#388C2212yes—
47C11×#388C2212yes—
48C11×#382C2211yescharacteristic
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2211yescharacteristic
51#10622834C2211yescharacteristic
52#10622605C2212yes—
53#10622603C2212yes—
54#10622603C2212yes—
55#10622601C2211yescharacteristic
56#10622601C2211yescharacteristic
57#10622598C2211yescharacteristic
58#10622593C2212yes—
59#10622590C2211yescharacteristic
60#10622589C2211yescharacteristic
61C4⋊C4×Dic11C2211yescharacteristic
62C4⋊C4×Dic11C2211yescharacteristic
63C4⋊C4×Dic11C2211yescharacteristic
64C4⋊C4×Dic11C2211yescharacteristic
65#10622587C2211yescharacteristic
66#10622586C2211yescharacteristic
67#10622585C2212yes—
68#10622574C2212yes—
69#10622572C2212yes—
70#10622572C2212yes—
71#10622572C2212yes—
72#10622570C2212yes—
73#10622570C2212yes—
74#10622570C2212yes—
75#10622570C2212yes—
76#10622570C2212yes—
77#10622565C2212yes—
78#10622564C2212yes—
79#10622562C2212yes—
80#10622558C2212yes—
81#10622558C2212yes—
82#10622557C2212yes—
83#10622557C2212yes—
84#10622557C2212yes—
85C22⋊C4×Dic11C2212yes—
86C22⋊C4×Dic11C2212yes—
87C22⋊C4×Dic11C2212yes—
88#10622553C2212yes—
89#10622553C2212yes—
90#10622552C2211yescharacteristic
91#10622552C2211yescharacteristic
92C4×Dic11⋊C4C2211yescharacteristic
93C4×Dic11⋊C4C2212yes—
94C4×Dic11⋊C4C2211yescharacteristic
95C42×Dic11C2211yescharacteristic
96C42×Dic11C2212yes—
97C42×Dic11C2211yescharacteristic
98C42×Dic11C2211yescharacteristic
99#10622542C2211yescharacteristic
100#10622541C2211yescharacteristic
101#10622288C2212yes—
102#10622288C2212yes—
103#10622288C2212yes—
104#10622283C2212yes—
105#10622282C2212yes—
106#10622282C2212yes—
107#10622282C2212yes—
108#10622279C2212yes—
109#10622279C2212yes—
110#10622279C2212yes—
111#10622272C2212yes—
112#10622271C2212yes—
113#10622270C2212yes—
114#10622263C2212yes—
115#10622262C2212yes—
116#10622262C2211yescharacteristic
117#10622262C2212yes—
118#10622262C2211yescharacteristic
119#10622262C2211yescharacteristic
120#10622262C2211yescharacteristic
121#10622260C2212yes—
122#10622259C2212yes—
123C22×D4×C11C2311yescharacteristic
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2312yes—
126C23×Dic11C2312yes—
127C22×D44C2311yescharacteristic
128C22×C4×D11C2312yes—
129C22×Dic22C2311yescharacteristic
130C22×Dic22C2311yescharacteristic
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C22⋊C4C2312yes—
138C2×C11×C22⋊C4C2312yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C42×C11C2311yescharacteristic
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2312yes—
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2312yes—
152#66993—24no—
153#66989—24no—
154D4×Dic11—24no—
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×C4⋊Dic11C2311yescharacteristic
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2312yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2311yescharacteristic
172C2×Dic11⋊C4C2311yescharacteristic
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2311yescharacteristic
175C2×Dic11⋊C4C2311yescharacteristic
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2311yescharacteristic
179C2×Dic11⋊C4C2311yescharacteristic
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×C4×Dic11C2312yes—
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204#66946—24no—
205#66945—44no—
206#66940—24no—
207#66940—24no—
208#66940—24no—
209#66940—24no—
210#66938—28no—
211(C22⋊D11)⋊C4—28no—
212(C22⋊D11)⋊C4—44no—
213#66930—44no—
214#66928—24no—
215C4×Dic22—24no—
216C4×Dic22—24no—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2311yescharacteristic
220C11×#95C2312yes—
221C11×#95C2311yescharacteristic
222C11×#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2312yes—
229C11⋊#95C2311yescharacteristic
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238#34954—111nomaximal, Sylow
239C24×C11C2412yes—
240C23×D11C2412yes—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C22×C4×C11C2412yes—
245C22×C4×C11C2411yescharacteristic
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—42no—
259C2×C22⋊D11—42no—
260C22×Dic11—24no—
261C22×Dic11—24no—
262C22×Dic11—24no—
263C22×Dic11C2411yescharacteristic
264C22×Dic11C2412yes—
265C22×Dic11C2411yescharacteristic
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2412yes—
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2412yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2411yescharacteristic
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2411yescharacteristic
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—22no—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×C4×D11—24no—
280C2×Dic22—22no—
281C2×Dic22—22no—
282C2×Dic22—22no—
283C2×Dic22—22no—
284C2×Dic22#4114yes—
285C2×Dic22#4114yes—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—42no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—42no—
295C11×C22⋊C4—42no—
296C11×C22⋊C4—42no—
297C11×C22⋊C4—42no—
298C42×C11—22no—
299C42×C11—22no—
300C42×C11—22no—
301C42×C11—42no—
302C22⋊Dic11—24no—
303C22⋊Dic11—24no—
304C22⋊Dic11—24no—
305C22⋊Dic11—24no—
306C22⋊Dic11—42no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—42no—
314(C2×D11)⋊C4—42no—
315(C2×D11)⋊C4—42no—
316(C2×D11)⋊C4—42no—
317(C2×D11)⋊C4—42no—
318C4⋊Dic11—22no—
319C4⋊Dic11—22no—
320C4⋊Dic11—22no—
321C4⋊Dic11—42no—
322Dic11⋊C4—22no—
323Dic11⋊C4—24no—
324Dic11⋊C4—22no—
325Dic11⋊C4—24no—
326Dic11⋊C4—24no—
327Dic11⋊C4—24no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—42no—
333Dic11⋊C4—42no—
334Dic11⋊C4—42no—
335C4×Dic11—24no—
336C4×Dic11—24no—
337C4×Dic11—22no—
338C4×Dic11—22no—
339C4×Dic11—22no—
340C4×Dic11—24no—
341C4×Dic11—24no—
342C4×Dic11—22no—
343C4×Dic11—22no—
344C4×Dic11—24no—
345C4×Dic11—22no—
346C4×Dic11—22no—
347C4×Dic11—22no—
348C4×Dic11—22no—
349C4×Dic11—22no—
350C4×Dic11—41no—
351C4×Dic11—41no—
352C4×Dic11—41no—
353C4×Dic11#4114yes—
354C4×Dic11#4114yes—
355C4×Dic11#4114yes—
356#2593—112no—
357#2593—112no—
358#2582—111no—
359#2571—111no—
360#2548—111no—
361#2548—111no—
362#2513—112no—
363#2513—111no—
364#2513D1111yescharacteristic, complemented
365#2448—112no—
366#2448—111no—
367#2448—111no—
368#2395—112no—
369#2395—112no—
370C4×#127—111no—
371C4×#124—111no—
372C4×#124—112no—
373C4×#124—111no—
374#2293—111no—
375#2293—111no—
376#2293—112no—
377C42×Q8—111no—
378C42×Q8—111no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11C2511yescharacteristic
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394D4×C11—44no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—22no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—22no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—22no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—22no—
411C2×C4×C11—21no—
412C2×C4×C11—22no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
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—
425C22⋊D11—48no—
426C22⋊D11—48no—
427C2×Dic11—21no—
428C2×Dic11—22no—
429C2×Dic11—21no—
430C2×Dic11—22no—
431C2×Dic11—21no—
432C2×Dic11—21no—
433C2×Dic11—21no—
434C2×Dic11—21no—
435C2×Dic11—21no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—21no—
445C2×Dic11—22no—
446C2×Dic11—21no—
447C2×Dic11—22no—
448C2×Dic11—21no—
449C2×Dic11—21no—
450C2×Dic11—48no—
451C2×Dic11C2×#4114yes—
452C2×Dic11C2×#4112yes—
453C2×Dic11C2×#4112yes—
454C2×Dic11C2×#4112yes—
455C2×Dic11C2×#4112yes—
456C2×Dic11C2×#4112yes—
457C2×Dic11C2×#4112yes—
458C2×Dic11C2×#4112yes—
459C2×Dic11C2×#4112yes—
460C2×Dic11H(5,𝔽2)12yes—
461D44—44no—
462C4×D11—48no—
463Dic22—28no—
464Dic22—28no—
465C2×#127—111no—
466C2×#124—111no—
467C2×#124—112no—
468C2×#124—111no—
469C2×C4×Q8—111no—
470C2×C4×Q8—111no—
471C2×C4×Q8—111no—
472C2×C4×Q8—111no—
473C2×C4×Q8—111no—
474C2×C4×Q8—111no—
475C2×C4×D4—111no—
476C2×C4×D4—111no—
477C2×C4×D4—112no—
478C2×C4×D4—112no—
479C2×#117—112no—
480C2×#117—112no—
481#400—112no—
482#400—112no—
483#399—112no—
484#399—112no—
485#398—112no—
486#398—112no—
487#397—112no—
488#397—112no—
489#397—112no—
490#397—112no—
491#397C2×D1112yes—
492#397C2×D1112yes—
493#394—112no—
494#394—112no—
495#394—112no—
496#394—112no—
497#391—111no—
498#391—111no—
499#391—112no—
500#390—111no—
501#390—111no—
502#390—111no—
503#390—112no—
504#390—112no—
505#390—112no—
506#390—112no—
507#390—112no—
508#390—111no—
509#390—111no—
510#390C2×D1111yescharacteristic
511#390C2×D1111yescharacteristic
512#390C2×D1111yescharacteristic
513#389—111no—
514#389—112no—
515#389—111no—
516#389—111no—
517#389—112no—
518#389C2×D1111yescharacteristic
519#388—112no—
520#388—112no—
521#388—112no—
522#388—112no—
523#388—112no—
524#388—112no—
525#388—112no—
526#388—112no—
527#388—112no—
528#388—112no—
529#388—112no—
530#388—112no—
531#388—112no—
532#388—112no—
533#388C2×D1112yes—
534#388C2×D1112yes—
535#384—111no—
536#382—111no—
537#382—112no—
538#382C2×D1111yescharacteristic
539C4×C4⋊C4—111no—
540C4×C4⋊C4—111no—
541C4×C4⋊C4—111no—
542C4×C4⋊C4—111no—
543C4×C4⋊C4—111no—
544C4×C4⋊C4—112no—
545C4×C4⋊C4—111no—
546C4×C4⋊C4—111no—
547C4×C4⋊C4—112no—
548C4×C4⋊C4—111no—
549C4×C4⋊C4—112no—
550C4×C4⋊C4—111no—
551C4×C4⋊C4—111no—
552C4×C4⋊C4C2×D1111yescharacteristic
553C4×C4⋊C4C2×D1111yescharacteristic
554C4×C22⋊C4—112no—
555C4×C22⋊C4—112no—
556C4×C22⋊C4—112no—
557C4×C22⋊C4—112no—
558C4×C22⋊C4—112no—
559C4×C22⋊C4—112no—
560C43—111no—
561C43—112no—
562C43—111no—
563C43—111no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11C22×#4111yescharacteristic
572C22×C11C22×#4111yescharacteristic
573C22×C11C22×#4111yescharacteristic
574C22×C11C22×#4111yescharacteristic
575C22×C11C22×#4111yescharacteristic
576C22×C11C2×H(5,𝔽2)11yescharacteristic
577C22×C11#58511yescharacteristic
578C2×D11—42no—
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C2×D11—42no—
583C2×D11—42no—
584C2×D11—42no—
585C4×C11—22no—
586C4×C11—22no—
587C4×C11—42no—
588C4×C11—41no—
589C4×C11—42no—
590C4×C11—41no—
591C4×C11—42no—
592C4×C11—41no—
593C4×C11—41no—
594C4×C11#52914yes—
595Dic11—22no—
596Dic11—24no—
597Dic11—22no—
598Dic11—22no—
599Dic11—41no—
600Dic11—42no—
601Dic11—41no—
602Dic11—41no—
603Dic11—42no—
604Dic11#52914yes—
605Dic11#55914yes—
606C22×Q8—111no—
607C22×Q8—111no—
608C22×D4—112no—
609C22×D4—112no—
610C22×D4—111no—
611C22×D4C22×D1111yescharacteristic
612C23×C4—112no—
613C23×C4—112no—
614#127—224no—
615#124—224no—
616#124—228no—
617#124—224no—
618C4×Q8—224no—
619C4×Q8—224no—
620C4×Q8—224no—
621C4×Q8—224no—
622C4×Q8—224no—
623C4×Q8—224no—
624C4×D4—228no—
625C4×D4—224no—
626C4×D4—224no—
627C4×D4—444no—
628#117—444no—
629#117—444no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—111no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—111no—
636C2×C4⋊C4—111no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—112no—
639C2×C4⋊C4—111no—
640C2×C4⋊C4—111no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—112no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—112no—
646C2×C4⋊C4—112no—
647C2×C4⋊C4C22×D1111yescharacteristic
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C4⋊C4C22×D1111yescharacteristic
651C2×C4⋊C4C22×D1111yescharacteristic
652C2×C4⋊C4C22×D1112yes—
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×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4C22×D1112yes—
670C2×C22⋊C4C22×D1112yes—
671C2×C22⋊C4C22×D1112yes—
672C2×C22⋊C4C22×D1112yes—
673C2×C22⋊C4C22×D1112yes—
674C2×C22⋊C4C22×D1112yes—
675C2×C42—111no—
676C2×C42—111no—
677C2×C42—111no—
678C2×C42—111no—
679C2×C42—112no—
680C2×C42—111no—
681C2×C42—111no—
682C2×C42—111no—
683C2×C42—112no—
684C2×C42—111no—
685C2×C42—111no—
686C2×C42—111no—
687C2×C42—112no—
688C2×C42—111no—
689C2×C42—112no—
690C2×C42—111no—
691C2×C42—112no—
692C2×C42—111no—
693C2×C42—111no—
694C2×C42—111no—
695C2×C42—111no—
696C2×C42C22×D1111yescharacteristic
697C2×C42C22×D1111yescharacteristic
698C2×C42C22×D1111yescharacteristic
699C2×C42C22×D1112yes—
700#95—112no—
701#95—112no—
702#95—112no—
703#95—112no—
704#95—112no—
705#95—112no—
706#95—112no—
707#95—112no—
708#95—112no—
709#95—112no—
710#95—111no—
711#95—111no—
712#95—112no—
713#95—111no—
714#95—111no—
715#95C22×D1112yes—
716#95C22×D1112yes—
717#95C22×D1112yes—
718#95C22×D1111yescharacteristic
719#95C22×D1112yes—
720#95C22×D1111yescharacteristic
721C2×C11—82no—
722C2×C11C2×#52911yescharacteristic
723C2×C11C2×#52911yescharacteristic
724C2×C11#346011yescharacteristic
725C2×C11C2×#55911yescharacteristic
726C2×C11#348011yescharacteristic
727C2×C11#348011yescharacteristic
728C2×C11#348311yescharacteristic
729D11—82no—
730C24—112no—
731C24C23×D1112yes—
732C2×Q8—114no—
733C2×Q8—114no—
734C2×Q8—222no—
735C2×Q8—222no—
736C2×Q8—222no—
737C2×Q8—222no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—224no—
742C2×D4—224no—
743C2×D4—224no—
744C2×D4—224no—
745C2×D4—222no—
746C2×D4—222no—
747C2×D4—222no—
748C2×D4—442no—
749C2×D4—442no—
750C22×C4—111no—
751C22×C4—111no—
752C22×C4—112no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—111no—
756C22×C4—111no—
757C22×C4—112no—
758C22×C4—111no—
759C22×C4—112no—
760C22×C4—111no—
761C22×C4—224no—
762C22×C4—224no—
763C22×C4—224no—
764C22×C4—224no—
765C22×C4—224no—
766C22×C4—224no—
767C22×C4C23×D1111yescharacteristic
768C22×C4C23×D1112yes—
769C22×C4C23×D1112yes—
770C22×C4C23×D1111yescharacteristic
771C22×C4C23×D1112yes—
772C22×C4C23×D1111yescharacteristic
773C22×C4C23×D1111yescharacteristic
774C22×C4C23×D1111yescharacteristic
775C22×C4C23×D1111yescharacteristic
776C22×C4C23×D1111yescharacteristic
777C4⋊C4—22no—
778C4⋊C4—22no—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—42no—
783C4⋊C4—224no—
784C4⋊C4—222no—
785C4⋊C4—222no—
786C4⋊C4—224no—
787C4⋊C4—222no—
788C4⋊C4—222no—
789C4⋊C4—224no—
790C4⋊C4—224no—
791C4⋊C4—222no—
792C4⋊C4—222no—
793C4⋊C4—222no—
794C4⋊C4—222no—
795C4⋊C4—222no—
796C4⋊C4—442no—
797C4⋊C4—442no—
798C4⋊C4—442no—
799C4⋊C4—442no—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—224no—
807C22⋊C4—224no—
808C22⋊C4—224no—
809C22⋊C4—224no—
810C22⋊C4—224no—
811C22⋊C4—224no—
812C22⋊C4—224no—
813C22⋊C4—224no—
814C22⋊C4—224no—
815C22⋊C4—224no—
816C22⋊C4—442no—
817C22⋊C4—442no—
818C22⋊C4—442no—
819C22⋊C4—442no—
820C22⋊C4—442no—
821C22⋊C4—442no—
822C42—22no—
823C42—22no—
824C42—22no—
825C42—42no—
826C42—114no—
827C42—114no—
828C42—114no—
829C42—222no—
830C42—224no—
831C42—222no—
832C42—222no—
833C42—224no—
834C42—222no—
835C42—224no—
836C42—222no—
837C42—224no—
838C42—222no—
839C42—222no—
840C42—224no—
841C42—222no—
842C42—222no—
843C42—222no—
844C42—441no—
845C42—441no—
846C42—441no—
847C11#3495411yescharacteristic, complemented, Sylow
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23C24×D1111yescharacteristic
863Q8—228no—
864Q8—228no—
865D4—44no—
866D4—448no—
867D4—448no—
868D4—444no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—112no—
895C2×C4—112no—
896C2×C4—112no—
897C2×C4—112no—
898C2×C4—112no—
899C2×C4—112no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—114no—
904C2×C4—221no—
905C2×C4—221no—
906C2×C4—221no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—221no—
910C2×C4—221no—
911C2×C4—221no—
912C2×C4—221no—
913C2×C4—222no—
914C2×C4—221no—
915C2×C4—221no—
916C2×C4—221no—
917C2×C4—222no—
918C2×C4—221no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—221no—
922C2×C4—222no—
923C2×C4—221no—
924C2×C4—222no—
925C2×C4—221no—
926C2×C4—221no—
927C2×C4—448no—
928C2×C4—448no—
929C2×C4#41×D1112yes—
930C2×C4#41×D1112yes—
931C2×C4#41×D1112yes—
932C2×C4#41×D1112yes—
933C2×C4#41×D1112yes—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22C2×#41×D1111yescharacteristic
949C22C2×#41×D1111yescharacteristic
950C22C2×#41×D1111yescharacteristic
951C22C2×#41×D1111yescharacteristic
952C22C2×#41×D1111yescharacteristic
953C22D11×H(5,𝔽2)11yescharacteristic
954C22#1062345511yescharacteristic
955C4—22no—
956C4—22no—
957C4—42no—
958C4—41no—
959C4—42no—
960C4—41no—
961C4—41no—
962C4—41no—
963C4—42no—
964C4—114no—
965C4—114no—
966C4—222no—
967C4—224no—
968C4—222no—
969C4—222no—
970C4—442no—
971C4—441no—
972C4—442no—
973C4—441no—
974C4—441no—
975C4#1062323714yes—
976C2—82no—
977C2—882no—
978C2D11×#52911yescharacteristic
979C2C2×#1062323711yescharacteristic
980C2#1308203111yescharacteristic
981C2D11×#55911yescharacteristic
982C2#1308221011yescharacteristic
983C2#1308221211yescharacteristic
984C2#1308224111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2513C2
prime radicalC2×#66993C22
hypercenter#2513D11
hypocenterC11#34954
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2513

Complements

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

NH ≅ G/Ntype
1. #13074111C2semidirect
2. #13074110C2semidirect
3. #13073988C2semidirect
4. #13073856C2semidirect
7. #13073207C2semidirect
8. #13073206C2semidirect
9. #13072415C2semidirect
10. #13072414C2semidirect
11. #13072407C2semidirect
12. #13071878C2semidirect
13. #13071874C2semidirect
15. #13071163C2semidirect
16. #13071157C2semidirect
17. #13071155C2semidirect
18. #13071078C2semidirect
19. #13071076C2semidirect
20. #13071074C2semidirect
21. C4×#66940C2semidirect
22. C4×#66940C2semidirect
23. C11×#2513C2semidirect
364. #2513D11semidirect
847. C11#34954semidirect

Maximal subgroups

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

subgroupindex
#130741112
#130741102
#130739882
#130738562
#130736202
#130736172
#130732072
#130732062
#130724152
#130724142
#130724072
#130718782
#130718742
#130711802
#130711632
#130711572
#130711552
#130710782
#130710762
#130710742
C4×#669402
C11×#25132
#3495411