Finite Group Databasebeta

← #14914248

Subgroups — #14914248

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic
2#13071715C212yesmaximal, complemented
3#13071713C212yesmaximal, complemented
4#13071709C212yesmaximal, complemented
5#13071707C212yesmaximal, complemented
6#13071495C211yesmaximal, characteristic
7#13071494C211yesmaximal, characteristic
8#13071494C211yesmaximal, characteristic
9#13071493C211yesmaximal, characteristic
10#13071491C211yesmaximal, characteristic
11#13071488C211yesmaximal, characteristic
12#13071488C211yesmaximal, characteristic
13#13071354C212yesmaximal, complemented
14#13071352C212yesmaximal, complemented
15#13071233C211yesmaximal, characteristic
16#13071233C211yesmaximal, characteristic
17#13071173C212yesmaximal, complemented
18C4×#66942C212yesmaximal, complemented
19#13071018C211yesmaximal, characteristic
20#13070971C211yesmaximal, characteristic
21#13070971C211yesmaximal, characteristic
22C4×#66930C211yesmaximal, characteristic
23C11×#2345C211yesmaximal, characteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66942C4116yescomplemented
32C2×#66942C2211yescharacteristic
33C2×#66942C2211yescharacteristic
34C2×#66942C2211yescharacteristic
35C2×#66942C2211yescharacteristic
36C2×#66942C2211yescharacteristic
37C2×#66942C2211yescharacteristic
38C2×#66942C2211yescharacteristic
39C2×#66942C2211yescharacteristic
40C2×#66930C2211yescharacteristic
41C2×#66930C2211yescharacteristic
42C2×#66930C2211yescharacteristic
43C2×#66930C2211yescharacteristic
44C11×#389C2212yes—
45C11×#387C2212yes—
46C11×#387C2212yes—
47C11×#380C2211yescharacteristic
48C11×#380C2211yescharacteristic
49C11×#380C2211yescharacteristic
50C4×C11×C4⋊C4C2212yes—
51C4×C11×C22⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4C2211yescharacteristic
54#10622825C2211yescharacteristic
55#10622825C2211yescharacteristic
56#10622825C2211yescharacteristic
57C4×C22⋊Dic11C2211yescharacteristic
58C4×C22⋊Dic11C2211yescharacteristic
59C4×C22⋊Dic11C2211yescharacteristic
60#10622598C2212yes—
61#10622594C2212yes—
62#10622594C2212yes—
63#10622591C2212yes—
64#10622591C2212yes—
65#10622589C2212yes—
66C4⋊C4×Dic11C2212yes—
67C4⋊C4×Dic11C2212yes—
68C4⋊C4×Dic11C2212yes—
69#10622586C2212yes—
70#10622585C2212yes—
71#10622585C2212yes—
72#10622585C2212yes—
73#10622585C2212yes—
74#10622585C2212yes—
75#10622585C2212yes—
76#10622555C2211yescharacteristic
77#10622555C2211yescharacteristic
78#10622555C2211yescharacteristic
79#10622555C2211yescharacteristic
80#10622555C2211yescharacteristic
81#10622555C2211yescharacteristic
82C22⋊C4×Dic11C2211yescharacteristic
83C22⋊C4×Dic11C2211yescharacteristic
84C22⋊C4×Dic11C2211yescharacteristic
85C22⋊C4×Dic11C2211yescharacteristic
86C22⋊C4×Dic11C2211yescharacteristic
87C22⋊C4×Dic11C2211yescharacteristic
88C4×C4⋊Dic11C2212yes—
89#10622546C2212yes—
90#10622546C2212yes—
91C4×Dic11⋊C4C2212yes—
92C4×Dic11⋊C4C2212yes—
93C4×Dic11⋊C4C2212yes—
94C4×Dic11⋊C4C2212yes—
95C4×Dic11⋊C4C2212yes—
96C4×Dic11⋊C4C2212yes—
97C4×Dic11⋊C4C2212yes—
98C42×Dic11C2212yes—
99#10622541C2212yes—
100#10622268C2212yes—
101#10622268C2212yes—
102#10622267C2212yes—
103#10622267C2212yes—
104#10622266C2212yes—
105#10622266C2212yes—
106#10622265C2212yes—
107#10622265C2212yes—
108#10622263C2212yes—
109#10622262C2212yes—
110#10622262C2212yes—
111#10622262C2212yes—
112#10622262C2212yes—
113#10622262C2212yes—
114#10622262C2212yes—
115#10622262C2212yes—
116#10622262C2212yes—
117#10622261C2212yes—
118#10622260C2212yes—
119#10622260C2212yes—
120#10622260C2212yes—
121#10622260C2212yes—
122#10622260C2212yes—
123#10622260C2212yes—
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×Dic11C2311yescharacteristic
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C2×C11×C4⋊C4C2×C418yes—
132C2×C11×C4⋊C4C2312yes—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2312yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C22⋊C4C2311yescharacteristic
140C2×C11×C22⋊C4C2311yescharacteristic
141C2×C11×C22⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C42×C11C2312yes—
144C2×C42×C11C2312yes—
145C2×C42×C11C2312yes—
146C2×C22⋊Dic11C2311yescharacteristic
147C2×C22⋊Dic11C2311yescharacteristic
148C2×C22⋊Dic11C2311yescharacteristic
149C2×C22⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2×C418yes—
151C2×C4⋊Dic11C2312yes—
152C2×C4⋊Dic11C2312yes—
153C2×C4⋊Dic11C2312yes—
154C2×C4⋊Dic11C2311yescharacteristic
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2311yescharacteristic
157C2×C4⋊Dic11C2311yescharacteristic
158C2×Dic11⋊C4C2×C418yes—
159C2×Dic11⋊C4C2×C418yes—
160C2×Dic11⋊C4C2×C418yes—
161C2×Dic11⋊C4C2×C418yes—
162C2×Dic11⋊C4C2312yes—
163C2×Dic11⋊C4C2312yes—
164C2×Dic11⋊C4C2312yes—
165C2×Dic11⋊C4C2312yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2312yes—
168C2×Dic11⋊C4C2312yes—
169C2×Dic11⋊C4C2312yes—
170C2×Dic11⋊C4C2312yes—
171C2×Dic11⋊C4C2311yescharacteristic
172C2×Dic11⋊C4C2311yescharacteristic
173C2×Dic11⋊C4C2311yescharacteristic
174C2×Dic11⋊C4C2311yescharacteristic
175C2×Dic11⋊C4C2311yescharacteristic
176C2×Dic11⋊C4C2311yescharacteristic
177C2×Dic11⋊C4C2311yescharacteristic
178C2×Dic11⋊C4C2311yescharacteristic
179C2×Dic11⋊C4C2311yescharacteristic
180C2×Dic11⋊C4C2311yescharacteristic
181C2×Dic11⋊C4C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2311yescharacteristic
184C2×Dic11⋊C4C2311yescharacteristic
185C2×Dic11⋊C4C2311yescharacteristic
186C2×Dic11⋊C4C2311yescharacteristic
187C2×Dic11⋊C4C2312yes—
188C2×C4×Dic11C2×C418yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2311yescharacteristic
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2312yes—
206#66942C2×C418yes—
207#66942C2×C418yes—
208#66942C2×C418yes—
209#66942C2×C418yes—
210#66942C2×C418yes—
211#66942C2×C418yes—
212#66942C2×C418yes—
213#66942C2×C418yes—
214#66930—24no—
215#66930—24no—
216#66930—24no—
217#66930Q818yes—
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—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242#34217—111nomaximal, Sylow
243C24×C11C2411yescharacteristic
244C22×C4×C11—42no—
245C22×C4×C11—42no—
246C22×C4×C11—42no—
247C22×C4×C11C22×C414yes—
248C22×C4×C11C22×C414yes—
249C22×C4×C11C22×C414yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2412yes—
260C22×Dic11—42no—
261C22×Dic11—42no—
262C22×Dic11—42no—
263C22×Dic11C22×C414yes—
264C22×Dic11C22×C414yes—
265C22×Dic11C22×C414yes—
266C22×Dic11C22×C414yes—
267C22×Dic11C2×Q814yes—
268C22×Dic11#4114yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2411yescharacteristic
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2411yescharacteristic
278C22×Dic11C2412yes—
279C22×Dic11C2411yescharacteristic
280C22×Dic11C2411yescharacteristic
281C11×C4⋊C4—42no—
282C11×C4⋊C4—42no—
283C11×C4⋊C4—42no—
284C11×C4⋊C4C22×C414yes—
285C11×C4⋊C4C22×C414yes—
286C11×C4⋊C4C22×C414yes—
287C11×C4⋊C4C22×C414yes—
288C11×C22⋊C4—22no—
289C11×C22⋊C4—22no—
290C11×C22⋊C4—22no—
291C11×C22⋊C4C2×Q814yes—
292C42×C11—42no—
293C42×C11—42no—
294C42×C11—42no—
295C22⋊Dic11—22no—
296C22⋊Dic11—22no—
297C22⋊Dic11—22no—
298C22⋊Dic11C2×Q814yes—
299C4⋊Dic11—42no—
300C4⋊Dic11—42no—
301C4⋊Dic11—42no—
302C4⋊Dic11C22×C414yes—
303C4⋊Dic11C22×C414yes—
304C4⋊Dic11C22×C414yes—
305C4⋊Dic11C22×C414yes—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4—24no—
309Dic11⋊C4—42no—
310Dic11⋊C4—42no—
311Dic11⋊C4—42no—
312Dic11⋊C4—42no—
313Dic11⋊C4—42no—
314Dic11⋊C4—42no—
315Dic11⋊C4C22×C414yes—
316Dic11⋊C4C22×C414yes—
317Dic11⋊C4C22×C414yes—
318Dic11⋊C4C22×C414yes—
319Dic11⋊C4C22×C414yes—
320Dic11⋊C4C22×C414yes—
321Dic11⋊C4C22×C414yes—
322Dic11⋊C4C22×C414yes—
323Dic11⋊C4C22×C414yes—
324Dic11⋊C4C22×C414yes—
325Dic11⋊C4C22×C414yes—
326Dic11⋊C4C22×C414yes—
327Dic11⋊C4C22×C414yes—
328Dic11⋊C4C22×C414yes—
329Dic11⋊C4C22×C414yes—
330Dic11⋊C4C22×C414yes—
331Dic11⋊C4C2×Q818yes—
332C4×Dic11—24no—
333C4×Dic11—24no—
334C4×Dic11—24no—
335C4×Dic11—42no—
336C4×Dic11—42no—
337C4×Dic11—42no—
338C4×Dic11—42no—
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×Dic11C2×Q818yes—
349C22×#125—111no—
350#2370—112no—
351#2370—112no—
352#2370—112no—
353#2370—112no—
354#2345—111no—
355#2345—111no—
356#2345—111no—
357#2345—111no—
358#2345—111no—
359#2345—111no—
360#2345—111no—
361#2345D1111yescharacteristic
362#2330—112no—
363#2330—112no—
364#2316—111no—
365#2316—111no—
366C4×#125—112no—
367C4×#125—112no—
368#2285—111no—
369#2274—111no—
370#2274—111no—
371C4×#117—111no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11C23×C412yes—
375C23×C11C22×Q812yes—
376C23×C11C2×#4112yes—
377C23×C11C2511yescharacteristic
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—44no—
396C2×C4×C11—44no—
397C2×C4×C11—44no—
398C2×C4×C11C23×C412yes—
399C2×C4×C11C23×C412yes—
400C2×C4×C11C23×C412yes—
401C2×C4×C11C23×C412yes—
402C2×C4×C11C23×C412yes—
403C2×C4×C11C23×C412yes—
404C2×C4×C11C22×Q814yes—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—44no—
423C2×Dic11—44no—
424C2×Dic11—44no—
425C2×Dic11C4×Q8116yes—
426C2×Dic11C23×C412yes—
427C2×Dic11C23×C412yes—
428C2×Dic11C23×C412yes—
429C2×Dic11C23×C412yes—
430C2×Dic11C23×C412yes—
431C2×Dic11C23×C412yes—
432C2×Dic11C23×C412yes—
433C2×Dic11C23×C412yes—
434C2×Dic11C22×Q814yes—
435C2×Dic11C22×Q812yes—
436C2×Dic11C22×Q812yes—
437C2×Dic11C2×#4112yes—
438C2×Dic11C2×#4112yes—
439C2×#125—111no—
440C2×#125—111no—
441C2×#125—111no—
442C2×#125—111no—
443C2×#125—111no—
444C2×#125—111no—
445C2×#125—111no—
446C2×#125—111no—
447C2×#125—1116no—
448C2×#117—111no—
449C2×#117—111no—
450C2×#117—111no—
451C2×#117—111no—
452C22×C4⋊C4—111no—
453C22×C4⋊C4—111no—
454C22×C4⋊C4—111no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4C2×D1111yescharacteristic
458C22×C42—111no—
459#389—112no—
460#389—112no—
461#389—112no—
462#389—112no—
463#389—112no—
464#389—112no—
465#389—112no—
466#389—112no—
467#389—112no—
468#389—112no—
469#389—112no—
470#389—112no—
471#389—112no—
472#389—112no—
473#389—112no—
474#389C2×D1112yes—
475#387—112no—
476#387—112no—
477#387—112no—
478#387—112no—
479#387—112no—
480#387—112no—
481#387—112no—
482#387—112no—
483#387—112no—
484#387—112no—
485#387—112no—
486#387—112no—
487#387—112no—
488#387—112no—
489#387C2×D1112yes—
490#387C2×D1112yes—
491#384—112no—
492#382—112no—
493#380—111no—
494#380—111no—
495#380—111no—
496#380—111no—
497#380—111no—
498#380—111no—
499#380—111no—
500#380—111no—
501#380—111no—
502#380C2×D1111yescharacteristic
503#380C2×D1111yescharacteristic
504#380C2×D1111yescharacteristic
505C4×C4⋊C4—112no—
506C4×C4⋊C4—112no—
507C4×C4⋊C4—112no—
508C4×C4⋊C4—112no—
509C4×C4⋊C4—112no—
510C4×C4⋊C4—112no—
511C4×C4⋊C4—112no—
512C4×C4⋊C4—112no—
513C4×C4⋊C4—112no—
514C4×C4⋊C4—112no—
515C4×C4⋊C4—112no—
516C4×C4⋊C4—112no—
517C4×C4⋊C4—112no—
518C4×C4⋊C4—112no—
519C4×C4⋊C4—112no—
520C4×C4⋊C4—112no—
521C4×C4⋊C4—112no—
522C4×C4⋊C4—112no—
523C4×C4⋊C4—112no—
524C4×C4⋊C4C2×D1112yes—
525C4×C22⋊C4—111no—
526C4×C22⋊C4—111no—
527C4×C22⋊C4—111no—
528C4×C22⋊C4—111no—
529C4×C22⋊C4—111no—
530C4×C22⋊C4—111no—
531C4×C22⋊C4—111no—
532C4×C22⋊C4—111no—
533C4×C22⋊C4—111no—
534C4×C22⋊C4C2×D1111yescharacteristic
535C4×C22⋊C4C2×D1111yescharacteristic
536C4×C22⋊C4C2×D1111yescharacteristic
537#376—112no—
538C43—112no—
539C22×C11—22no—
540C22×C11—22no—
541C22×C11—24no—
542C22×C11—24no—
543C22×C11C2×C4×Q814yes—
544C22×C11C24×C411yescharacteristic
545C22×C11C23×Q811yescharacteristic
546C22×C11C22×#4111yescharacteristic
547C22×C11#58512yes—
548C22×C11#58512yes—
549C4×C11—22no—
550C4×C11—22no—
551C4×C11—22no—
552C4×C11—22no—
553C4×C11—22no—
554C4×C11—22no—
555C4×C11—24no—
556C4×C11—42no—
557C4×C11—42no—
558C4×C11—42no—
559Dic11—22no—
560Dic11—22no—
561Dic11—22no—
562Dic11—22no—
563Dic11—22no—
564Dic11—22no—
565Dic11—24no—
566Dic11—42no—
567Dic11—42no—
568Dic11—42no—
569Dic11C2×C4×Q814yes—
570Dic11C2×C4×Q814yes—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578#125—118no—
579#125—118no—
580#125—118no—
581#125—118no—
582#125—118no—
583#125—118no—
584#125—118no—
585#125—118no—
586#117—118no—
587#117—224no—
588#117—224no—
589#117—224no—
590C2×C4⋊C4—118no—
591C2×C4⋊C4—118no—
592C2×C4⋊C4—118no—
593C2×C4⋊C4—118no—
594C2×C4⋊C4—118no—
595C2×C4⋊C4—111no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—111no—
600C2×C4⋊C4—111no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—111no—
604C2×C4⋊C4—111no—
605C2×C4⋊C4—111no—
606C2×C4⋊C4—111no—
607C2×C4⋊C4—111no—
608C2×C4⋊C4—111no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—111no—
613C2×C4⋊C4—111no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—112no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4C4×D1118yes—
629C2×C4⋊C4C22×D1112yes—
630C2×C4⋊C4C22×D1112yes—
631C2×C4⋊C4C22×D1112yes—
632C2×C4⋊C4C22×D1111yescharacteristic
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C4⋊C4C22×D1111yescharacteristic
635C2×C4⋊C4C22×D1111yescharacteristic
636C2×C22⋊C4—111no—
637C2×C22⋊C4—111no—
638C2×C22⋊C4—111no—
639C2×C22⋊C4—111no—
640C2×C22⋊C4C22×D1111yescharacteristic
641C2×C22⋊C4C22×D1111yescharacteristic
642C2×C22⋊C4C22×D1111yescharacteristic
643C2×C22⋊C4C22×D1111yescharacteristic
644C2×C42—118no—
645C2×C42—112no—
646C2×C42—111no—
647C2×C42—111no—
648C2×C42—111no—
649C2×C42—111no—
650C2×C42—112no—
651C2×C42—112no—
652C2×C42—112no—
653C2×C42—112no—
654C2×C42—112no—
655C2×C42—112no—
656C2×C42—112no—
657C2×C42—112no—
658C2×C42—112no—
659C2×C42—112no—
660C2×C42—112no—
661C2×C42—112no—
662C2×C42C22×D1112yes—
663C2×C42C22×D1112yes—
664C2×C42C22×D1112yes—
665#95—112no—
666#95—112no—
667#95—112no—
668#95—112no—
669#95—112no—
670#95—112no—
671#95—112no—
672#95—112no—
673#95—112no—
674#95—112no—
675#95—112no—
676#95—112no—
677#95—112no—
678#95—112no—
679#95—112no—
680#95—112no—
681#95—112no—
682#95—112no—
683#95C22×D1112yes—
684#95C22×D1112yes—
685#95C22×D1112yes—
686#95C22×D1112yes—
687#95C22×D1112yes—
688#95C22×D1112yes—
689C2×C11—24no—
690C2×C11C22×C4×Q811yescharacteristic
691C2×C11#342811yescharacteristic
692C2×C11#342811yescharacteristic
693C2×C11#350412yes—
694C2×C11#351212yes—
695C24C23×D1111yescharacteristic
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—114no—
700C22×C4—114no—
701C22×C4—114no—
702C22×C4—111no—
703C22×C4—111no—
704C22×C4—112no—
705C22×C4—111no—
706C22×C4—111no—
707C22×C4—111no—
708C22×C4—111no—
709C22×C4—111no—
710C22×C4—111no—
711C22×C4—114no—
712C22×C4—114no—
713C22×C4—114no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—442no—
718C22×C4—442no—
719C22×C4—442no—
720C22×C4C2×C4×D1114yes—
721C22×C4C2×C4×D1114yes—
722C22×C4C2×C4×D1114yes—
723C22×C4C23×D1112yes—
724C22×C4C23×D1112yes—
725C22×C4C23×D1112yes—
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1111yescharacteristic
728C22×C4C23×D1111yescharacteristic
729C22×C4C23×D1111yescharacteristic
730C22×C4C23×D1111yescharacteristic
731C22×C4C23×D1111yescharacteristic
732C22×C4C23×D1112yes—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—114no—
737C4⋊C4—114no—
738C4⋊C4—114no—
739C4⋊C4—114no—
740C4⋊C4—114no—
741C4⋊C4—114no—
742C4⋊C4—114no—
743C4⋊C4—114no—
744C4⋊C4—114no—
745C4⋊C4—114no—
746C4⋊C4—114no—
747C4⋊C4—114no—
748C4⋊C4—114no—
749C4⋊C4—114no—
750C4⋊C4—114no—
751C4⋊C4—114no—
752C4⋊C4—114no—
753C4⋊C4—114no—
754C4⋊C4—114no—
755C4⋊C4—114no—
756C4⋊C4—118no—
757C4⋊C4—224no—
758C4⋊C4—224no—
759C4⋊C4—224no—
760C4⋊C4—442no—
761C4⋊C4—442no—
762C4⋊C4—442no—
763C4⋊C4—442no—
764C4⋊C4—442no—
765C4⋊C4—442no—
766C4⋊C4—442no—
767C4⋊C4—442no—
768C4⋊C4—442no—
769C4⋊C4C2×C4×D1114yes—
770C4⋊C4C2×C4×D1114yes—
771C4⋊C4C2×C4×D1114yes—
772C4⋊C4C2×C4×D1114yes—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—114no—
777C22⋊C4—222no—
778C22⋊C4—222no—
779C22⋊C4—222no—
780C22⋊C4Q8×D1114yes—
781C42—42no—
782C42—42no—
783C42—42no—
784C42—114no—
785C42—114no—
786C42—114no—
787C42—114no—
788C42—118no—
789C42—224no—
790C42—224no—
791C42—224no—
792C42—442no—
793C42—442no—
794C42—442no—
795C42—442no—
796C42—442no—
797C42—442no—
798C42—442no—
799C42—442no—
800C42—442no—
801C11#3421711yescharacteristic, complemented, Sylow
802C23—22no—
803C23—22no—
804C23C22×C4×D1112yes—
805C23C2×Q8×D1112yes—
806C23#41×D1112yes—
807C23C24×D1111yescharacteristic
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—1116no—
829C2×C4—112no—
830C2×C4—112no—
831C2×C4—112no—
832C2×C4—112no—
833C2×C4—112no—
834C2×C4—112no—
835C2×C4—112no—
836C2×C4—112no—
837C2×C4—112no—
838C2×C4—112no—
839C2×C4—112no—
840C2×C4—112no—
841C2×C4—114no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—444no—
860C2×C4—444no—
861C2×C4—444no—
862C2×C4C22×C4×D1112yes—
863C2×C4C22×C4×D1112yes—
864C2×C4C22×C4×D1112yes—
865C2×C4C22×C4×D1112yes—
866C2×C4C22×C4×D1112yes—
867C2×C4C22×C4×D1112yes—
868C2×C4C2×Q8×D1114yes—
869C22—24no—
870C22—24no—
871C22—22no—
872C22—22no—
873C22C4×Q8×D1114yes—
874C22C23×C4×D1111yescharacteristic
875C22C22×Q8×D1111yescharacteristic
876C22C2×#41×D1111yescharacteristic
877C22#1062345312yes—
878C22#1062345512yes—
879C4—24no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—114no—
890C4—114no—
891C4—224no—
892C4—222no—
893C4—222no—
894C4—222no—
895C4—222no—
896C4—222no—
897C4—222no—
898C4—442no—
899C4—442no—
900C4—442no—
901C2—24no—
902C2C2×C4×Q8×D1111yescharacteristic
903C2#1308181411yescharacteristic
904C2#1308181711yescharacteristic
905C2#1308243612yes—
906C2#1308253212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2345C2
socle, cosocleC23×C11C25
prime radicalC24×C11C24
hypercenter#2345D11
hypocenterC11#34217
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #13071715C2semidirect
3. #13071713C2semidirect
4. #13071709C2semidirect
5. #13071707C2semidirect
13. #13071354C2semidirect
14. #13071352C2semidirect
17. #13071173C2semidirect
18. C4×#66942C2semidirect
31. C2×#66942C4semidirect
801. C11#34217semidirect

Maximal subgroups

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

subgroupindex
C22×#669422
#130717152
#130717132
#130717092
#130717072
#130714952
#130714942
#130714932
#130714912
#130714882
#130713542
#130713522
#130712332
#130711732
C4×#669422
#130710182
#130709712
C4×#669302
C11×#23452
#3421711