Finite Group Databasebeta

← #14912829

Subgroups — #14912829

Order 2816.

3186 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623139C211yesmaximal, characteristic
2C2×#10623053C211yesmaximal, characteristic, complemented
3C2×C4×#4341C211yesmaximal, characteristic, complemented
4#13071318C212yesmaximal, complemented
5#13071313C212yesmaximal, complemented
6#13071303C211yesmaximal, characteristic, complemented
7#13071302C212yesmaximal, complemented
8#13071299C211yesmaximal, characteristic, complemented
9#13071298C211yesmaximal, characteristic, complemented
10#13071291C212yesmaximal, complemented
11#13071231C211yesmaximal, characteristic, complemented
12#13071206C211yesmaximal, characteristic, complemented
13#13071205C211yesmaximal, characteristic, complemented
14#13071148C212yesmaximal, complemented
15#13071146C211yesmaximal, characteristic, complemented
16#13071144C211yesmaximal, characteristic, complemented
17#13071132C211yesmaximal, characteristic, complemented
18#13071132C212yesmaximal, complemented
19#121×Dic11C211yesmaximal, characteristic, complemented
20#13071128C212yesmaximal, complemented
21#13071126C212yesmaximal, complemented
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C11×#2324C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C2×#66992C2212yes—
30C2×#66991C2211yescharacteristic
31C2×#66991C2212yes—
32C2×D4×Dic11C2211yescharacteristic
33C2×D4×Dic11C2212yes—
34C2×C4×C22⋊D11C2212yes—
35C2×#66977C2211yescharacteristic
36C22×C4×Dic11C2212yes—
37C22×C4×Dic11C2211yescharacteristic
38#10623139C4116yescomplemented
39C4×#4341—28no—
40#10623053—28no—
41C2×#66950C2211yescharacteristic
42C2×#66946C2211yescharacteristic
43C2×#66946C2211yescharacteristic
44C2×#66945C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C4⋊C4×D11C2211yescharacteristic
47C2×#66940C2211yescharacteristic
48C2×#66940C2211yescharacteristic
49C2×#66940C2211yescharacteristic
50C2×#66937C2212yes—
51C2×(C22⋊D11)⋊C4C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2212yes—
53C2×(C22⋊D11)⋊C4C2211yescharacteristic
54C2×(C22⋊D11)⋊C4C2211yescharacteristic
55C2×(C22⋊D11)⋊C4C2211yescharacteristic
56C2×(C22⋊D11)⋊C4C2212yes—
57C2×#66931C2212yes—
58C2×#66930C2212yes—
59C2×#66925C2211yescharacteristic
60C2×#66925C2211yescharacteristic
61C2×C42×D11C2211yescharacteristic
62C2×C42×D11C2212yes—
63C2×C42×D11C2211yescharacteristic
64C2×C4×Dic22C2211yescharacteristic
65C11×#390C2211yescharacteristic
66C11×#390C2212yes—
67C11×#389C2211yescharacteristic
68C11×#388C2212yes—
69C11×#386C2212yes—
70C11×#385C2212yes—
71C11×#380C2211yescharacteristic
72C4×C11×C4⋊C4C2211yescharacteristic
73#10622834C2211yescharacteristic
74#10622833C2212yes—
75#10622826C2212yes—
76#10622825C2211yescharacteristic
77#10622823C2212yes—
78#10622602C2212yes—
79#10622600C2211yescharacteristic
80#10622600C2212yes—
81#10622600C2211yescharacteristic
82#10622598C2211yescharacteristic
83#10622591C2212yes—
84C4⋊C4×Dic11C2211yescharacteristic
85C4⋊C4×Dic11C2211yescharacteristic
86C4⋊C4×Dic11C2212yes—
87#10622587C2211yescharacteristic
88#10622586C2211yescharacteristic
89#10622585C2212yes—
90#10622585C2212yes—
91#10622570C2212yes—
92#10622570C2212yes—
93#10622569C2212yes—
94#10622569C2212yes—
95#10622569C2212yes—
96#10622569C2212yes—
97#10622564C2212yes—
98#10622559C2212yes—
99#10622558C2212yes—
100#10622558C2212yes—
101#10622558C2212yes—
102#10622557C2212yes—
103#10622555C2212yes—
104#10622555C2212yes—
105C22⋊C4×Dic11C2212yes—
106C22⋊C4×Dic11C2212yes—
107C22⋊C4×Dic11C2212yes—
108#10622553C2212yes—
109C4×C4⋊Dic11C2211yescharacteristic
110C4×Dic11⋊C4C2212yes—
111#10622542C2211yescharacteristic
112#10622541C2211yescharacteristic
113#10622541C2212yes—
114#10622283C2212yes—
115#10622280C2212yes—
116#10622279C2212yes—
117#10622278C2212yes—
118D11×#95C2212yes—
119#10622267C2212yes—
120#10622266C2212yes—
121#10622265C2212yes—
122#10622262C2212yes—
123#10622262C2212yes—
124#10622260C2212yes—
125#10622259C2212yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2312yes—
136C23×Dic11C2312yes—
137C23×Dic11C2311yescharacteristic
138C2×#4341—24no—
139C2×#4341—24no—
140C2×#4341C2×C418yescomplemented
141C2×#4339—24no—
142C2×#4339—24no—
143C2×#4339C2×C418yescomplemented
144C22×D44C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2311yescharacteristic
152C22×C4×D11C2311yescharacteristic
153C22×Dic22C2311yescharacteristic
154C22×Dic22C2311yescharacteristic
155C11×#121C2×C418yescomplemented
156C4×D4×C11—24no—
157C11×#117—24no—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2311yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2312yes—
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2312yes—
173C2×C42×C11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180#66992C2×C4116yescomplemented
181#66991C2×C4116yescomplemented
182#66991C2×C418yescomplemented
183D4×Dic11—24no—
184D4×Dic11—44no—
185C4×C22⋊D11—28no—
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×C4⋊Dic11C2311yescharacteristic
195C2×C4⋊Dic11C2311yescharacteristic
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2312yes—
198C2×C4⋊Dic11C2311yescharacteristic
199#66977C2×C418yescomplemented
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2311yescharacteristic
203C2×Dic11⋊C4C2311yescharacteristic
204C2×Dic11⋊C4C2311yescharacteristic
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×C4×Dic11—24no—
212C2×C4×Dic11—28no—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227#66950C2×C418yescomplemented
228#66946—24no—
229#66946—24no—
230#66945—24no—
231C4⋊C4×D11—24no—
232C4⋊C4×D11C2×C418yescomplemented
233#66940—24no—
234#66940—24no—
235#66940—24no—
236#66937C2×C4116yescomplemented
237(C22⋊D11)⋊C4—24no—
238(C22⋊D11)⋊C4—24no—
239(C22⋊D11)⋊C4—28no—
240(C22⋊D11)⋊C4—24no—
241(C22⋊D11)⋊C4—24no—
242(C22⋊D11)⋊C4—44no—
243#66931C2×C4116yescomplemented
244#66930—28no—
245#66925—24no—
246#66925—24no—
247C42×D11—24no—
248C42×D11—44no—
249C42×D11D418yescomplemented
250C4×Dic22—24no—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267C4×#537—111nomaximal, Sylow
268C24×C11C2412yes—
269C24×C11C2411yescharacteristic
270C23×D11C2411yescharacteristic
271C23×D11C2411yescharacteristic
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—42no—
275C2×D4×C11—42no—
276C2×D4×C11C22×C414yes—
277C2×D4×C11C22×C418yes—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—24no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11C22×C414yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C2×C22⋊D11—22no—
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11C22×C418yes—
302C2×C22⋊D11C22×C414yes—
303C2×C22⋊D11C22×C414yes—
304C2×C22⋊D11C22×C418yes—
305C22×Dic11—24no—
306C22×Dic11—24no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—24no—
310C22×Dic11—24no—
311C22×Dic11—22no—
312C22×Dic11—22no—
313C22×Dic11—24no—
314C22×Dic11—41no—
315C22×Dic11—41no—
316C22×Dic11C22×C418yes—
317C22×Dic11C2412yes—
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327#4341—232no—
328#4339—232no—
329C2×D44—22no—
330C2×D44—22no—
331C2×D44C22×C414yes—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11—42no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—42no—
347C2×C4×D11—41no—
348C2×C4×D11—41no—
349C2×C4×D11C22×C414yes—
350C2×C4×D11C22×C418yes—
351C2×C4×D11C22×C414yes—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11#4114yes—
356C2×Dic22—22no—
357C2×Dic22—22no—
358C2×Dic22—22no—
359C2×Dic22—22no—
360C2×Dic22C22×C414yes—
361C2×Dic22C22×C414yes—
362C11×C4⋊C4—22no—
363C11×C4⋊C4—22no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—22no—
366C11×C4⋊C4—42no—
367C11×C4⋊C4C22×C414yes—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—42no—
372C11×C22⋊C4—42no—
373C11×C22⋊C4—42no—
374C11×C22⋊C4C22×C418yes—
375C42×C11—22no—
376C42×C11—42no—
377C42×C11C2×D414yes—
378C22⋊Dic11—24no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11C22×C418yes—
383C22⋊Dic11C22×C418yes—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4C22×C418yes—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394C4⋊Dic11—42no—
395C4⋊Dic11C22×C418yes—
396C4⋊Dic11C22×C414yes—
397Dic11⋊C4—22no—
398Dic11⋊C4—22no—
399Dic11⋊C4—24no—
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406Dic11⋊C4C22×C418yes—
407Dic11⋊C4C22×C418yes—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—24no—
411C4×Dic11—24no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—24no—
415C4×Dic11—24no—
416C4×Dic11—24no—
417C4×Dic11—22no—
418C4×Dic11—42no—
419C4×Dic11C2×D414yes—
420C4×Dic11C2×D414yes—
421C4×Dic11C2×D414yes—
422C2×#537—111no—
423C2×C4×#41—111no—
424C2×C4×#41—111no—
425#2325—112no—
426#2325—112no—
427#2324—112no—
428#2324—111no—
429#2324D1111yescharacteristic, complemented
430#2323—112no—
431#2323—111no—
432#2323—111no—
433#2316—111no—
434#2311—111no—
435#2311—111no—
436C4×C22⋊Q8—111no—
437C4×C22⋊Q8—112no—
438C4×C22⋊Q8—111no—
439C4×#121—111no—
440C4×#121—112no—
441C4×#121—112no—
442C4×#121—112no—
443C4×#121—111no—
444C2×C4×C4⋊C4—111no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—21no—
453C23×C11—22no—
454C23×C11—21no—
455C23×C11—21no—
456C23×C11—22no—
457C23×C11C23×C412yes—
458C23×C11C23×C414yes—
459C23×C11C2511yescharacteristic
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—21no—
469C22×D11—21no—
470C22×D11C23×C412yes—
471C22×D11C23×C412yes—
472C22×D11C22×D412yes—
473C22×D11C2×#4112yes—
474D4×C11—28no—
475D4×C11—48no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—22no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—28no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—21no—
495C2×C4×C11—22no—
496C2×C4×C11—21no—
497C2×C4×C11—48no—
498C2×C4×C11C23×C412yes—
499C2×C4×C11C23×C414yes—
500C2×C4×C11C23×C412yes—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C22×D412yes—
503C2×C4×C11C22×D412yes—
504C2×C4×C11C2×#4112yes—
505C22⋊D11—28no—
506C22⋊D11—216no—
507C22⋊D11—28no—
508C22⋊D11—48no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—21no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—216no—
518C2×Dic11—21no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—21no—
530C2×Dic11—44no—
531C2×Dic11—44no—
532C2×Dic11—48no—
533C2×Dic11C23×C414yes—
534C2×Dic11C23×C414yes—
535C2×Dic11C23×C412yes—
536C2×Dic11C23×C412yes—
537C2×Dic11C22×D412yes—
538C2×Dic11C22×D412yes—
539C2×Dic11C22×D412yes—
540C2×Dic11C2×#4112yes—
541C2×Dic11H(5,𝔽2)12yes—
542C2×Dic112−1+412yes—
543D44—28no—
544C4×D11—28no—
545C4×D11—28no—
546C4×D11—48no—
547C4×D11—44no—
548C4×D11—44no—
549C4×D11—48no—
550C4×D11—44no—
551C4×D11C4×D4116yescomplemented
552Dic22—28no—
553Dic22—28no—
554C22×#41—111no—
555C22×#41—111no—
556#537—1116no—
557C2×C22⋊Q8—111no—
558C2×C22⋊Q8—111no—
559C2×C22⋊Q8—112no—
560C2×#121—111no—
561C2×#121—112no—
562C2×#121—112no—
563C2×#121—112no—
564C2×#121C2×D1111yescharacteristic
565C4×#41—228no—
566C4×#41—228no—
567C2×C4×Q8—111no—
568C2×C4×Q8—111no—
569C2×C4×Q8—111no—
570C2×C4×Q8—111no—
571C2×C4×D4—111no—
572C2×C4×D4—112no—
573C2×C4×D4—112no—
574C2×C4×D4—111no—
575C2×C4×D4—111no—
576C2×C4×D4—111no—
577C2×C4×D4—111no—
578C2×C4×D4—111no—
579C2×C4×D4—112no—
580C2×C4×D4—111no—
581C2×C4×D4—112no—
582C2×C4×D4C2×D1111yescharacteristic
583C2×#117—111no—
584C2×#117—112no—
585C2×#117—111no—
586C2×#117—111no—
587C2×#117C2×D1111yescharacteristic
588C22×C4⋊C4—111no—
589C22×C4⋊C4—111no—
590C22×C42—111no—
591C22×C42—112no—
592C22×C42—111no—
593C22×C42—111no—
594C22×C42—112no—
595#391—111no—
596#391—111no—
597#391—112no—
598#390—111no—
599#390—112no—
600#390—112no—
601#390C2×D1111yescharacteristic
602#390C2×D1112yes—
603#389—111no—
604#389—112no—
605#389—111no—
606#389—112no—
607#389—111no—
608#389—112no—
609#389—112no—
610#389C2×D1111yescharacteristic
611#388—112no—
612#388—112no—
613#388—112no—
614#388—112no—
615#388—112no—
616#388—112no—
617#388—112no—
618#388C2×D1112yes—
619#387—112no—
620#387—112no—
621#387—112no—
622#387—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386C2×D1112yes—
631#385—112no—
632#385—112no—
633#385—112no—
634#385C2×D1112yes—
635#380—111no—
636#380—111no—
637#380—111no—
638#380—112no—
639#380—112no—
640#380—112no—
641#380—112no—
642#380C2×D1111yescharacteristic
643C4×C4⋊C4—111no—
644C4×C4⋊C4—111no—
645C4×C4⋊C4—112no—
646C4×C4⋊C4—112no—
647C4×C4⋊C4—111no—
648C4×C4⋊C4—112no—
649C4×C4⋊C4—112no—
650C4×C4⋊C4C2×D1111yescharacteristic
651C4×C22⋊C4—112no—
652C4×C22⋊C4—112no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4—112no—
655C2×#95—112no—
656C22×C11—22no—
657C22×C11—24no—
658C22×C11—22no—
659C22×C11—24no—
660C22×C11—24no—
661C22×C11—22no—
662C22×C11—42no—
663C22×C11—41no—
664C22×C11—42no—
665C22×C11—41no—
666C22×C11—42no—
667C22×C11—41no—
668C22×C11—42no—
669C22×C11—41no—
670C22×C11C24×C411yescharacteristic
671C22×C11C23×D411yescharacteristic
672C22×C11C22×#4111yescharacteristic
673C22×C11C2×H(5,𝔽2)11yescharacteristic
674C22×C11C2×2−1+411yescharacteristic
675C22×C11#58511yescharacteristic
676C22×C11#58511yescharacteristic
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11—41no—
689C2×D11—41no—
690C2×D11C2×C4×D414yes—
691C4×C11—22no—
692C4×C11—24no—
693C4×C11—22no—
694C4×C11—22no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11—41no—
698C4×C11—42no—
699C4×C11C2×C4×D414yes—
700Dic11—22no—
701Dic11—24no—
702Dic11—24no—
703Dic11—22no—
704Dic11—41no—
705Dic11—42no—
706Dic11—41no—
707Dic11—42no—
708Dic11C2×C4×D414yes—
709Dic11#53714yescomplemented
710C2×#41—118no—
711C2×#41—118no—
712C2×#41—224no—
713C2×#41—224no—
714C2×#41—224no—
715C2×#41—224no—
716C22×Q8—111no—
717C22×Q8—111no—
718C22×D4—112no—
719C22×D4—111no—
720C22×D4—111no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4C22×D1111yescharacteristic
724C22×D4C22×D1112yes—
725C23×C4—111no—
726C23×C4—112no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—112no—
730C23×C4—111no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—112no—
736C23×C4—111no—
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1112yes—
739C22⋊Q8—118no—
740C22⋊Q8—118no—
741C22⋊Q8—1116no—
742#121—118no—
743#121—1116no—
744#121—1116no—
745#121—1116no—
746#121C4×D1118yescomplemented
747C4×Q8—224no—
748C4×Q8—224no—
749C4×Q8—224no—
750C4×Q8—224no—
751C4×D4—24no—
752C4×D4—224no—
753C4×D4—224no—
754C4×D4—224no—
755C4×D4—224no—
756C4×D4—224no—
757C4×D4—228no—
758C4×D4—224no—
759C4×D4—224no—
760C4×D4—228no—
761C4×D4—444no—
762C4×D4—444no—
763#117—24no—
764#117—224no—
765#117—228no—
766#117—224no—
767#117—224no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—118no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—111no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—224no—
786C2×C4⋊C4C22×D1111yescharacteristic
787C2×C4⋊C4C22×D1111yescharacteristic
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1112yes—
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4C22×D1112yes—
807C2×C22⋊C4C22×D1111yescharacteristic
808C2×C22⋊C4C22×D1111yescharacteristic
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C22⋊C4C22×D1112yes—
812C2×C22⋊C4C22×D1112yes—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—118no—
817C2×C42—112no—
818C2×C42—111no—
819C2×C42—111no—
820C2×C42—112no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42—111no—
824C2×C42—112no—
825C2×C42—112no—
826C2×C42—112no—
827C2×C42—112no—
828C2×C42—224no—
829C2×C42—228no—
830C2×C42—224no—
831C2×C42—444no—
832C2×C42C22×D1111yescharacteristic
833C2×C42C22×D1112yes—
834C2×C42C22×D1111yescharacteristic
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95C22×D1112yes—
849#95C22×D1112yes—
850#95C22×D1112yes—
851C2×C11—42no—
852C2×C11—44no—
853C2×C11C22×C4×D411yescharacteristic
854C2×C11C4×H(5,𝔽2)11yescharacteristic
855C2×C11C4×2−1+411yescharacteristic
856C2×C11C2×#53711yescharacteristic
857C2×C11#344911yescharacteristic
858C2×C11#346011yescharacteristic
859C2×C11#346111yescharacteristic
860D11—24no—
861D11—42no—
862C24—111no—
863C24—111no—
864C24C23×D1111yescharacteristic
865C24C23×D1112yes—
866#41—2232no—
867#41—2232no—
868C2×Q8—114no—
869C2×Q8—114no—
870C2×Q8—222no—
871C2×Q8—222no—
872C2×Q8—222no—
873C2×Q8—222no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—114no—
879C2×D4—114no—
880C2×D4—118no—
881C2×D4—118no—
882C2×D4—114no—
883C2×D4—222no—
884C2×D4—222no—
885C2×D4—222no—
886C2×D4—222no—
887C2×D4—222no—
888C2×D4—224no—
889C2×D4—222no—
890C2×D4—224no—
891C2×D4—442no—
892C2×D4—442no—
893C2×D4C2×C4×D1114yes—
894C2×D4C2×C4×D1118yes—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—24no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—111no—
901C22×C4—111no—
902C22×C4—114no—
903C22×C4—114no—
904C22×C4—114no—
905C22×C4—118no—
906C22×C4—111no—
907C22×C4—112no—
908C22×C4—111no—
909C22×C4—112no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—118no—
913C22×C4—114no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—111no—
917C22×C4—111no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—222no—
921C22×C4—222no—
922C22×C4—222no—
923C22×C4—222no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—224no—
929C22×C4—222no—
930C22×C4—224no—
931C22×C4—222no—
932C22×C4—224no—
933C22×C4—222no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4—441no—
940C22×C4—441no—
941C22×C4—441no—
942C22×C4—442no—
943C22×C4—441no—
944C22×C4—441no—
945C22×C4—441no—
946C22×C4C2×C4×D1114yes—
947C22×C4C23×D1112yes—
948C22×C4C23×D1111yescharacteristic
949C22×C4C23×D1112yes—
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1111yescharacteristic
952C22×C4C23×D1112yes—
953C22×C4C23×D1111yescharacteristic
954C22×C4C23×D1111yescharacteristic
955C22×C4C23×D1111yescharacteristic
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—42no—
961C4⋊C4—118no—
962C4⋊C4—114no—
963C4⋊C4—118no—
964C4⋊C4—118no—
965C4⋊C4—224no—
966C4⋊C4—222no—
967C4⋊C4—222no—
968C4⋊C4—224no—
969C4⋊C4—222no—
970C4⋊C4—224no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—442no—
975C4⋊C4—442no—
976C4⋊C4—442no—
977C4⋊C4C2×C4×D1114yes—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—24no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—118no—
985C22⋊C4—118no—
986C22⋊C4—118no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—222no—
992C22⋊C4—222no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C22⋊C4C2×C4×D1118yes—
999C42—22no—
1000C42—42no—
1001C42—114no—
1002C42—114no—
1003C42—114no—
1004C42—224no—
1005C42—222no—
1006C42—222no—
1007C42—222no—
1008C42—222no—
1009C42—224no—
1010C42—224no—
1011C42—224no—
1012C42—222no—
1013C42—224no—
1014C42—442no—
1015C42D4×D1114yes—
1016C11C4×#53711yescharacteristic, complemented, Sylow
1017C23—21no—
1018C23—22no—
1019C23—21no—
1020C23—22no—
1021C23—22no—
1022C23—21no—
1023C23—21no—
1024C23—22no—
1025C23—22no—
1026C23—21no—
1027C23—21no—
1028C23—22no—
1029C23—112no—
1030C23—112no—
1031C23—112no—
1032C23—112no—
1033C23—221no—
1034C23—221no—
1035C23—221no—
1036C23—221no—
1037C23—221no—
1038C23—221no—
1039C23—221no—
1040C23—221no—
1041C23—221no—
1042C23—221no—
1043C23C22×C4×D1112yes—
1044C23C22×C4×D1114yes—
1045C23C24×D1111yescharacteristic
1046Q8—228no—
1047Q8—228no—
1048D4—28no—
1049D4—48no—
1050D4—228no—
1051D4—228no—
1052D4—228no—
1053D4—2216no—
1054D4—448no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—28no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—48no—
1077C2×C4—112no—
1078C2×C4—112no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—112no—
1082C2×C4—112no—
1083C2×C4—1116no—
1084C2×C4—114no—
1085C2×C4—112no—
1086C2×C4—114no—
1087C2×C4—112no—
1088C2×C4—228no—
1089C2×C4—2216no—
1090C2×C4—221no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—228no—
1099C2×C4—222no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—222no—
1108C2×C4—221no—
1109C2×C4—222no—
1110C2×C4—221no—
1111C2×C4—444no—
1112C2×C4—448no—
1113C2×C4—444no—
1114C2×C4—444no—
1115C2×C4—448no—
1116C2×C4—444no—
1117C2×C4—448no—
1118C2×C4—444no—
1119C2×C4C22×C4×D1114yes—
1120C2×C4C22×C4×D1112yes—
1121C2×C4C22×C4×D1112yes—
1122C2×C4C2×D4×D1112yes—
1123C2×C4C2×D4×D1112yes—
1124C2×C4C2×D4×D1112yes—
1125C2×C4#41×D1112yes—
1126C22—22no—
1127C22—24no—
1128C22—22no—
1129C22—24no—
1130C22—22no—
1131C22—24no—
1132C22—41no—
1133C22—42no—
1134C22—42no—
1135C22—41no—
1136C22—41no—
1137C22—42no—
1138C22—41no—
1139C22—42no—
1140C22—114no—
1141C22—222no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22—222no—
1146C22—222no—
1147C22—222no—
1148C22—222no—
1149C22—222no—
1150C22—441no—
1151C22—441no—
1152C22—441no—
1153C22—441no—
1154C22C23×C4×D1111yescharacteristic
1155C22C22×D4×D1111yescharacteristic
1156C22C2×#41×D1111yescharacteristic
1157C22D11×H(5,𝔽2)11yescharacteristic
1158C22#1062345511yescharacteristic
1159C22#1062345511yescharacteristic
1160C22D11×2−1+411yescharacteristic
1161C4—22no—
1162C4—22no—
1163C4—22no—
1164C4—24no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—42no—
1169C4—114no—
1170C4—114no—
1171C4—222no—
1172C4—224no—
1173C4—222no—
1174C4—224no—
1175C4—442no—
1176C4—441no—
1177C4—441no—
1178C4—442no—
1179C4C4×D4×D1114yes—
1180C2—42no—
1181C2—44no—
1182C2—224no—
1183C2—442no—
1184C2C2×C4×D4×D1111yescharacteristic
1185C2#1308182011yescharacteristic
1186C2#1308182711yescharacteristic
1187C2D11×#53711yescharacteristic
1188C2#1308194711yescharacteristic
1189C2#1308203111yescharacteristic
1190C2#1308204211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2324C2
socle, cosocleC23×C11C25
prime radicalC2×#10623139C2
hypercenter#2324D11
hypocenterC11C4×#537
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×#10623053C2semidirect
3. C2×C4×#4341C2semidirect
4. #13071318C2semidirect
5. #13071313C2semidirect
6. #13071303C2semidirect
7. #13071302C2semidirect
8. #13071299C2semidirect
9. #13071298C2semidirect
10. #13071291C2semidirect
11. #13071231C2semidirect
12. #13071206C2semidirect
13. #13071205C2semidirect
14. #13071148C2semidirect
15. #13071146C2semidirect
16. #13071144C2semidirect
17. #13071132C2semidirect
18. #13071132C2semidirect
19. #121×Dic11C2semidirect
20. #13071128C2semidirect
21. #13071126C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C11×#2324C2semidirect
38. #10623139C4semidirect
140. C2×#4341C2×C4semidirect
143. C2×#4339C2×C4semidirect
155. C11×#121C2×C4semidirect
180. #66992C2×C4semidirect
181. #66991C2×C4semidirect
182. #66991C2×C4semidirect
199. #66977C2×C4semidirect
227. #66950C2×C4semidirect
232. C4⋊C4×D11C2×C4semidirect
236. #66937C2×C4semidirect
243. #66931C2×C4semidirect
249. C42×D11D4semidirect
429. #2324D11semidirect
551. C4×D11C4×D4semidirect
709. Dic11#537semidirect
746. #121C4×D11semidirect
1016. C11C4×#537semidirect

Maximal subgroups

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

subgroupindex
C2×#106231392
C2×#106230532
C2×C4×#43412
#130713182
#130713132
#130713032
#130713022
#130712992
#130712982
#130712912
#130712312
#130712062
#130712052
#130711482
#130711462
#130711442
#130711322
#121×Dic112
#130711282
#130711262
C4×C4⋊C4×D112
C11×#23242
C4×#53711