Finite Group Databasebeta

← #14914182

Subgroups — #14914182

Order 2816.

3102 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3C2×#10623017C211yesmaximal, characteristic
4#13071690C212yesmaximal, complemented
5#13071688C212yesmaximal, complemented
6#13071684C212yesmaximal, complemented
7#13071682C212yesmaximal, complemented
8#13071468C211yesmaximal, characteristic, complemented
9#13071467C211yesmaximal, characteristic, complemented
10#13071466C211yesmaximal, characteristic, complemented
11#13071465C211yesmaximal, characteristic, complemented
12#13071462C211yesmaximal, characteristic, complemented
13#13071461C211yesmaximal, characteristic, complemented
14#13071458C211yesmaximal, characteristic, complemented
15#13071325C212yesmaximal, complemented
16#13071322C212yesmaximal, complemented
17#13071201C211yesmaximal, characteristic, complemented
18#13071197C211yesmaximal, characteristic
19#13071157C212yesmaximal, complemented
20C4×#66938C212yesmaximal, complemented
21#13071018C211yesmaximal, characteristic, complemented
22C4×#66930C211yesmaximal, characteristic, complemented
23C11×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D11C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2212yes—
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C2×#66979C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37#10623047—28no—
38C2×#66940C2212yescomplemented
39C2×#66940C2212yescomplemented
40C2×#66938C4116yescomplemented
41C2×#66938C2211yescharacteristic
42C2×#66938C2211yescharacteristic
43C2×#66938C2211yescharacteristic
44C2×#66938C2211yescharacteristic
45C2×#66938C2211yescharacteristic
46C2×#66938C2211yescharacteristic
47C2×#66938C2211yescharacteristic
48C2×#66938C2211yescharacteristic
49#10623017—28no—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yes—
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×C22⋊C4×D11C2211yescharacteristic
54C2×#66930C2211yescharacteristic
55C2×#66930C2211yescharacteristic
56C2×#66930C2211yescharacteristic
57C2×#66930C2211yescharacteristic
58C2×#66930C2211yescharacteristic
59C2×#66930C2211yescharacteristic
60C2×C4×Dic22C2212yescomplemented
61C2×C4×Dic22C2212yescomplemented
62C11×#388C2212yescomplemented
63C11×#388C2212yescomplemented
64C11×#385C2212yescomplemented
65C11×#381C2211yescharacteristic
66C11×#380C2211yescharacteristic
67C11×#379C2211yescharacteristic
68C4×C11×C22⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2212yescomplemented
70#10622860C2211yescharacteristic
71#10622825C2211yescharacteristic
72#10622824C2211yescharacteristic
73#10622823C2212yescomplemented
74C4×C22⋊Dic11C2211yescharacteristic
75C4×C22⋊Dic11C2212yescomplemented
76#10622603C2212yescomplemented
77#10622603C2212yescomplemented
78#10622602C2212yescomplemented
79#10622602C2212yescomplemented
80#10622589C2212yescomplemented
81C4⋊C4×Dic11C2212yescomplemented
82#10622570C2212yes—
83#10622570C2212yes—
84#10622570C2212yes—
85#10622570C2212yes—
86#10622568C2211yescharacteristic
87#10622568C2211yescharacteristic
88#10622564C2212yescomplemented
89#10622564C2212yescomplemented
90#10622563C2212yescomplemented
91#10622559C2212yescomplemented
92#10622558C2212yescomplemented
93#10622558C2212yescomplemented
94#10622557C2212yescomplemented
95#10622557C2212yescomplemented
96#10622556C2211yescharacteristic
97#10622556C2211yescharacteristic
98#10622555C2211yescharacteristic
99#10622555C2211yescharacteristic
100C22⋊C4×Dic11C2211yescharacteristic
101C22⋊C4×Dic11C2211yescharacteristic
102C22⋊C4×Dic11C2212yescomplemented
103C22⋊C4×Dic11C2212yescomplemented
104#10622553C2212yescomplemented
105#10622553C2212yescomplemented
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×(C2×D11)⋊C4C2212yescomplemented
108C4×Dic11⋊C4C2212yescomplemented
109C42×Dic11C2212yescomplemented
110#10622283C2212yescomplemented
111#10622283C2212yescomplemented
112#10622282C2212yescomplemented
113#10622282C2212yescomplemented
114#10622281C2212yescomplemented
115#10622281C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622263C2212yescomplemented
119#10622262C2212yescomplemented
120#10622262C2212yescomplemented
121#10622261C2212yescomplemented
122#10622259C2212yescomplemented
123#10622259C2212yescomplemented
124#10622259C2212yescomplemented
125#10622259C2212yescomplemented
126C25×C11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11—24no—
132C22×C22⋊D11—24no—
133C22×C22⋊D11C2×C418yes—
134C22×C22⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2311yescharacteristic
137C22×C22⋊D11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C23×Dic11C2312yes—
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2311yescharacteristic
142C22×C4×D11C2312yes—
143C22×C4×D11C2312yes—
144C22×Dic22—24no—
145C22×Dic22—24no—
146C22×Dic22C2×C418yescomplemented
147C22×Dic22C2311yescharacteristic
148C22×Dic22C2311yescharacteristic
149C22×Dic22C2311yescharacteristic
150C22×Dic22C2311yescharacteristic
151C11×#117—24no—
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C22⋊C4—24no—
155C2×C11×C22⋊C4C2×C418yescomplemented
156C2×C11×C22⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C42×C11C2312yes—
168C2×C42×C11C2312yes—
169C2×C22⋊Dic11—24no—
170C2×C22⋊Dic11C2×C418yescomplemented
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C4×C22⋊D11—28no—
183C4×C22⋊D11—28no—
184C2×(C2×D11)⋊C4C2×C418yescomplemented
185C2×(C2×D11)⋊C4C2×C418yescomplemented
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2311yescharacteristic
195C2×(C2×D11)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200#66979—24no—
201C2×C4⋊Dic11C2312yes—
202C2×C4⋊Dic11C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×Dic11⋊C4C2312yes—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×C4×Dic11C2×C418yescomplemented
212C2×C4×Dic11C2312yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2312yes—
216C2×C4×Dic11C2312yes—
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2312yes—
220C2×C4×Dic11C2312yes—
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2312yes—
226#66940—28no—
227#66940—28no—
228#66938C2×C418yescomplemented
229#66938C2×C418yescomplemented
230#66938C2×C418yescomplemented
231#66938C2×C418yescomplemented
232#66938C2×C418yescomplemented
233#66938C2×C418yescomplemented
234#66938C2×C418yescomplemented
235#66938C2×C418yescomplemented
236(C22⋊D11)⋊C4—28no—
237(C22⋊D11)⋊C4—28no—
238C22⋊C4×D11—24no—
239C22⋊C4×D11—24no—
240#66930—24no—
241#66930—24no—
242#66930—24no—
243#66930—24no—
244#66930—24no—
245#66930D418yes—
246C4×Dic22—28no—
247C4×Dic22—28no—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
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—
264#34211—111nomaximal, Sylow
265C24×C11—22no—
266C24×C11—22no—
267C24×C11—42no—
268C24×C11—42no—
269C24×C11C22×C414yes—
270C24×C11C2411yescharacteristic
271C24×C11C2411yescharacteristic
272C24×C11C2411yescharacteristic
273C23×D11—22no—
274C23×D11—22no—
275C23×D11—42no—
276C23×D11—42no—
277C23×D11C22×C414yes—
278C23×D11C2411yescharacteristic
279C23×D11C2411yescharacteristic
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—24no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11C22×C414yes—
287C22×C4×C11C22×C414yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C2×C22⋊D11—232no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11C22×C414yes—
306C2×C22⋊D11C22×C414yes—
307C2×C22⋊D11C22×C414yes—
308C2×C22⋊D11C22×C414yes—
309C22×Dic11—24no—
310C22×Dic11—22no—
311C22×Dic11—22no—
312C22×Dic11—42no—
313C22×Dic11—42no—
314C22×Dic11—42no—
315C22×Dic11C22×C414yes—
316C22×Dic11C22×C414yes—
317C22×Dic11C22×C414yes—
318C22×Dic11C2×D414yes—
319C22×Dic11#4114yes—
320C22×Dic11C2412yes—
321C22×Dic11C2412yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2412yes—
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2411yescharacteristic
330C2×C4×D11—24no—
331C2×C4×D11—24no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×Dic22—232no—
337C2×Dic22—22no—
338C2×Dic22—22no—
339C2×Dic22—22no—
340C2×Dic22—22no—
341C2×Dic22—22no—
342C2×Dic22—22no—
343C2×Dic22—22no—
344C2×Dic22—22no—
345C2×Dic22C22×C414yes—
346C2×Dic22C22×C414yes—
347C2×Dic22C22×C414yes—
348C2×Dic22C22×C414yes—
349C11×C4⋊C4—24no—
350C11×C4⋊C4—42no—
351C11×C22⋊C4—22no—
352C11×C22⋊C4—22no—
353C11×C22⋊C4—22no—
354C11×C22⋊C4—24no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—42no—
357C11×C22⋊C4C22×C414yes—
358C11×C22⋊C4C22×C414yes—
359C11×C22⋊C4C22×C414yes—
360C11×C22⋊C4C22×C414yes—
361C11×C22⋊C4C2×D414yes—
362C42×C11—24no—
363C42×C11—42no—
364C22⋊Dic11—24no—
365C22⋊Dic11—22no—
366C22⋊Dic11—22no—
367C22⋊Dic11—22no—
368C22⋊Dic11—42no—
369C22⋊Dic11—42no—
370C22⋊Dic11C22×C414yes—
371C22⋊Dic11C22×C414yes—
372C22⋊Dic11C22×C414yes—
373C22⋊Dic11C22×C414yes—
374C22⋊Dic11C2×D414yes—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4C22×C414yes—
382(C2×D11)⋊C4C22×C414yes—
383(C2×D11)⋊C4C22×C414yes—
384(C2×D11)⋊C4C22×C414yes—
385(C2×D11)⋊C4C22×C414yes—
386(C2×D11)⋊C4C22×C414yes—
387(C2×D11)⋊C4C22×C414yes—
388(C2×D11)⋊C4C22×C414yes—
389C4⋊Dic11—24no—
390C4⋊Dic11—42no—
391Dic11⋊C4—24no—
392Dic11⋊C4—24no—
393Dic11⋊C4—24no—
394Dic11⋊C4—24no—
395Dic11⋊C4—24no—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398Dic11⋊C4C2×D418yes—
399C4×Dic11—24no—
400C4×Dic11—24no—
401C4×Dic11—24no—
402C4×Dic11—24no—
403C4×Dic11—24no—
404C4×Dic11—24no—
405C4×Dic11—42no—
406C4×Dic11—42no—
407C4×Dic11—42no—
408C4×Dic11C22×C414yes—
409C4×Dic11C22×C414yes—
410C4×Dic11C22×C414yes—
411C4×Dic11C22×C414yes—
412C4×Dic11C2×D418yes—
413C22×#124—111no—
414C2×#519—111no—
415C2×#518—111no—
416#2367—112no—
417#2367—112no—
418#2367—112no—
419#2367—112no—
420#2342—111no—
421#2342—111no—
422#2342—111no—
423#2342—111no—
424#2342—111no—
425#2342—111no—
426#2342—111no—
427#2342D1111yescharacteristic, complemented
428#2326—112no—
429#2326—112no—
430#2310—111no—
431#2309—111no—
432C4×#124—112no—
433C4×#124—112no—
434#2285—111no—
435C4×#117—111no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—28no—
447C23×C11—44no—
448C23×C11—44no—
449C23×C11—84no—
450C23×C11—84no—
451C23×C11C23×C412yes—
452C23×C11C23×C412yes—
453C23×C11C23×C412yes—
454C23×C11C22×D412yes—
455C23×C11C2×#4112yes—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—28no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—84no—
469C22×D11—84no—
470C22×D11C23×C412yes—
471C22×D11C23×C412yes—
472C2×C4×C11—28no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—44no—
491C2×C4×C11—84no—
492C2×C4×C11C23×C412yes—
493C2×C4×C11C23×C412yes—
494C2×C4×C11C23×C412yes—
495C2×C4×C11C23×C412yes—
496C2×C4×C11C22×D414yes—
497C22⋊D11—28no—
498C22⋊D11—28no—
499C22⋊D11—28no—
500C22⋊D11—28no—
501C2×Dic11—28no—
502C2×Dic11—21no—
503C2×Dic11—21no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—44no—
520C2×Dic11—84no—
521C2×Dic11C4×D4116yes—
522C2×Dic11C23×C412yes—
523C2×Dic11C23×C412yes—
524C2×Dic11C23×C412yes—
525C2×Dic11C23×C412yes—
526C2×Dic11C23×C412yes—
527C2×Dic11C23×C412yes—
528C2×Dic11C22×D414yes—
529C2×Dic11C22×D412yes—
530C2×Dic11C22×D412yes—
531C2×Dic11C2×#4112yes—
532C2×Dic11C2×#4112yes—
533C4×D11—84no—
534C4×D11—84no—
535Dic22—28no—
536Dic22—28no—
537Dic22—28no—
538Dic22—28no—
539C23×Q8—111no—
540C23×D4—111no—
541C2×#124—111no—
542C2×#124—111no—
543C2×#124—111no—
544C2×#124—111no—
545C2×#124—111no—
546C2×#124—111no—
547C2×#124—111no—
548C2×#124—111no—
549C2×#124—1116no—
550#519—228no—
551#518—228no—
552C2×C4×Q8—112no—
553C2×C4×Q8—112no—
554C2×C4×Q8—112no—
555C2×C4×Q8—112no—
556C2×C4×D4—112no—
557C2×C4×D4—112no—
558C2×C4×D4—112no—
559C2×C4×D4—112no—
560C2×#117—111no—
561C2×#117—111no—
562C2×#117—111no—
563C2×#117—111no—
564C2×#117—111no—
565C2×#117—111no—
566C2×#117—111no—
567C2×#117C2×D1111yescharacteristic
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4—111no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—111no—
574C22×C22⋊C4C2×D1111yescharacteristic
575C22×C22⋊C4C2×D1111yescharacteristic
576C22×C42—111no—
577#391—112no—
578#391—112no—
579#391—112no—
580#391—112no—
581#390—112no—
582#390—112no—
583#390—112no—
584#390—112no—
585#388—112no—
586#388—112no—
587#388—112no—
588#388—112no—
589#388—112no—
590#388—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388—112no—
599#388C2×D1112yescomplemented
600#388C2×D1112yescomplemented
601#385—112no—
602#385—112no—
603#385—112no—
604#385—112no—
605#385—112no—
606#385—112no—
607#385—112no—
608#385C2×D1112yescomplemented
609#384—112no—
610#382—112no—
611#381—111no—
612#381—111no—
613#381—111no—
614#381C2×D1111yescharacteristic
615#380—111no—
616#380—111no—
617#380—111no—
618#380C2×D1111yescharacteristic
619#379—111no—
620#379—111no—
621#379—111no—
622#379C2×D1111yescharacteristic
623C4×C4⋊C4—112no—
624C4×C4⋊C4—112no—
625C4×C4⋊C4—112no—
626C4×C4⋊C4—112no—
627C4×C22⋊C4—111no—
628C4×C22⋊C4—112no—
629C4×C22⋊C4—111no—
630C4×C22⋊C4—111no—
631C4×C22⋊C4—112no—
632C4×C22⋊C4—112no—
633C4×C22⋊C4—112no—
634C4×C22⋊C4—112no—
635C4×C22⋊C4—112no—
636C4×C22⋊C4—112no—
637C4×C22⋊C4C2×D1111yescharacteristic
638C4×C22⋊C4C2×D1112yescomplemented
639#376—112no—
640C43—112no—
641C22×C11—22no—
642C22×C11—22no—
643C22×C11—24no—
644C22×C11—24no—
645C22×C11—22no—
646C22×C11—22no—
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—88no—
656C22×C11C2×C4×D414yes—
657C22×C11C24×C411yescharacteristic
658C22×C11C23×D411yescharacteristic
659C22×C11C22×#4111yescharacteristic
660C22×C11#58512yes—
661C22×C11#58512yes—
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—88no—
673C4×C11—22no—
674C4×C11—22no—
675C4×C11—22no—
676C4×C11—22no—
677C4×C11—24no—
678C4×C11—42no—
679C4×C11—42no—
680C4×C11—42no—
681Dic11—22no—
682Dic11—22no—
683Dic11—22no—
684Dic11—22no—
685Dic11—24no—
686Dic11—42no—
687Dic11—42no—
688Dic11—42no—
689Dic11C2×C4×D414yes—
690Dic11C2×C4×D414yes—
691C25—111no—
692C25C22×D1111yescharacteristic
693C22×Q8—118no—
694C22×Q8—111no—
695C22×Q8—111no—
696C22×Q8—111no—
697C22×Q8—111no—
698C22×Q8—224no—
699C22×Q8—224no—
700C22×D4—118no—
701C22×D4—111no—
702C22×D4—111no—
703C22×D4—111no—
704C22×D4—111no—
705C22×D4—224no—
706C22×D4—224no—
707C23×C4—111no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—112no—
711C23×C4—112no—
712C23×C4—112no—
713C23×C4C22×D1111yescharacteristic
714C23×C4C22×D1112yes—
715C23×C4C22×D1111yescharacteristic
716#124—118no—
717#124—118no—
718#124—118no—
719#124—118no—
720#124—118no—
721#124—118no—
722#124—118no—
723#124—118no—
724C4×Q8—228no—
725C4×Q8—228no—
726C4×Q8—228no—
727C4×Q8—228no—
728C4×D4—228no—
729C4×D4—228no—
730C4×D4—228no—
731C4×D4—228no—
732#117—24no—
733#117—118no—
734#117—224no—
735#117—224no—
736#117—224no—
737#117—224no—
738#117—224no—
739#117—224no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—112no—
747C2×C4⋊C4—112no—
748C2×C4⋊C4—112no—
749C2×C4⋊C4—112no—
750C2×C4⋊C4C22×D1112yes—
751C2×C4⋊C4C22×D1112yes—
752C2×C22⋊C4—24no—
753C2×C22⋊C4—118no—
754C2×C22⋊C4—111no—
755C2×C22⋊C4—111no—
756C2×C22⋊C4—111no—
757C2×C22⋊C4—111no—
758C2×C22⋊C4—111no—
759C2×C22⋊C4—118no—
760C2×C22⋊C4—118no—
761C2×C22⋊C4—111no—
762C2×C22⋊C4—111no—
763C2×C22⋊C4—111no—
764C2×C22⋊C4—111no—
765C2×C22⋊C4—111no—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—111no—
768C2×C22⋊C4—111no—
769C2×C22⋊C4—111no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—111no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—112no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—224no—
782C2×C22⋊C4—224no—
783C2×C22⋊C4—224no—
784C2×C22⋊C4C4×D1118yescomplemented
785C2×C22⋊C4C22×D1111yescharacteristic
786C2×C22⋊C4C22×D1112yes—
787C2×C22⋊C4C22×D1111yescharacteristic
788C2×C22⋊C4C22×D1111yescharacteristic
789C2×C22⋊C4C22×D1112yes—
790C2×C22⋊C4C22×D1112yes—
791C2×C22⋊C4C22×D1111yescharacteristic
792C2×C22⋊C4C22×D1111yescharacteristic
793C2×C22⋊C4C22×D1111yescharacteristic
794C2×C22⋊C4C22×D1111yescharacteristic
795C2×C22⋊C4C22×D1111yescharacteristic
796C2×C42—118no—
797C2×C42—112no—
798C2×C42—111no—
799C2×C42—111no—
800C2×C42—111no—
801C2×C42—111no—
802C2×C42—112no—
803C2×C42—112no—
804C2×C42—112no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—112no—
808C2×C42—112no—
809C2×C42—112no—
810C2×C42—112no—
811C2×C42C22×D1112yes—
812C2×C42C22×D1112yes—
813#95—112no—
814#95—112no—
815#95—112no—
816#95—112no—
817#95—112no—
818#95—112no—
819#95—112no—
820#95—112no—
821#95—112no—
822#95—112no—
823#95—112no—
824#95—112no—
825#95C22×D1112yes—
826#95C22×D1112yes—
827#95C22×D1112yes—
828#95C22×D1112yes—
829C2×C11—24no—
830C2×C11—42no—
831C2×C11—42no—
832C2×C11C22×C4×D411yescharacteristic
833C2×C11#342811yescharacteristic
834C2×C11#342811yescharacteristic
835C2×C11#350012yes—
836C2×C11#351012yes—
837D11—42no—
838D11—42no—
839C24—22no—
840C24—22no—
841C24—42no—
842C24—42no—
843C24—111no—
844C24—111no—
845C24—114no—
846C24—222no—
847C24—222no—
848C24—442no—
849C24—442no—
850C24C2×C4×D1114yes—
851C24C23×D1111yescharacteristic
852C24C23×D1111yescharacteristic
853C24C23×D1111yescharacteristic
854C2×Q8—114no—
855C2×Q8—114no—
856C2×Q8—114no—
857C2×Q8—114no—
858C2×Q8—222no—
859C2×Q8—222no—
860C2×Q8—222no—
861C2×Q8—222no—
862C2×Q8—2232no—
863C2×Q8—222no—
864C2×Q8—222no—
865C2×Q8—222no—
866C2×Q8—222no—
867C2×D4—114no—
868C2×D4—114no—
869C2×D4—114no—
870C2×D4—114no—
871C2×D4—222no—
872C2×D4—222no—
873C2×D4—222no—
874C2×D4—222no—
875C2×D4—2232no—
876C2×D4—222no—
877C2×D4—222no—
878C2×D4—222no—
879C2×D4—222no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—24no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—114no—
887C22×C4—114no—
888C22×C4—114no—
889C22×C4—111no—
890C22×C4—111no—
891C22×C4—114no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—112no—
897C22×C4—114no—
898C22×C4—112no—
899C22×C4—112no—
900C22×C4—112no—
901C22×C4—224no—
902C22×C4—224no—
903C22×C4—222no—
904C22×C4—222no—
905C22×C4—224no—
906C22×C4—442no—
907C22×C4—442no—
908C22×C4—442no—
909C22×C4—442no—
910C22×C4—442no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4C2×C4×D1114yes—
914C22×C4C2×C4×D1114yes—
915C22×C4C23×D1112yes—
916C22×C4C23×D1112yes—
917C22×C4C23×D1112yes—
918C22×C4C23×D1111yescharacteristic
919C22×C4C23×D1111yescharacteristic
920C22×C4C23×D1111yescharacteristic
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1112yes—
923C4⋊C4—24no—
924C4⋊C4—42no—
925C4⋊C4—118no—
926C4⋊C4—224no—
927C4⋊C4—224no—
928C4⋊C4—224no—
929C4⋊C4—224no—
930C4⋊C4—224no—
931C4⋊C4—224no—
932C4⋊C4—442no—
933C4⋊C4—442no—
934C4⋊C4—442no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—24no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—114no—
942C22⋊C4—114no—
943C22⋊C4—114no—
944C22⋊C4—114no—
945C22⋊C4—114no—
946C22⋊C4—114no—
947C22⋊C4—114no—
948C22⋊C4—114no—
949C22⋊C4—114no—
950C22⋊C4—114no—
951C22⋊C4—114no—
952C22⋊C4—114no—
953C22⋊C4—114no—
954C22⋊C4—224no—
955C22⋊C4—224no—
956C22⋊C4—222no—
957C22⋊C4—222no—
958C22⋊C4—222no—
959C22⋊C4—224no—
960C22⋊C4—442no—
961C22⋊C4—442no—
962C22⋊C4—442no—
963C22⋊C4—442no—
964C22⋊C4—442no—
965C22⋊C4—442no—
966C22⋊C4C2×C4×D1114yes—
967C22⋊C4C2×C4×D1114yes—
968C22⋊C4C2×C4×D1114yes—
969C22⋊C4C2×C4×D1114yes—
970C22⋊C4D4×D1114yes—
971C42—24no—
972C42—42no—
973C42—114no—
974C42—114no—
975C42—114no—
976C42—114no—
977C42—118no—
978C42—224no—
979C42—224no—
980C42—224no—
981C42—224no—
982C42—224no—
983C42—224no—
984C42—442no—
985C42—442no—
986C42—442no—
987C11#3421111yescharacteristic, complemented, Sylow
988C23—22no—
989C23—22no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—28no—
999C23—44no—
1000C23—44no—
1001C23—84no—
1002C23—84no—
1003C23—112no—
1004C23—112no—
1005C23—221no—
1006C23—221no—
1007C23—221no—
1008C23—221no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—228no—
1014C23—444no—
1015C23—444no—
1016C23—884no—
1017C23—884no—
1018C23C22×C4×D1112yes—
1019C23C22×C4×D1112yes—
1020C23C22×C4×D1112yes—
1021C23C2×D4×D1112yes—
1022C23#41×D1112yes—
1023C23C24×D1111yescharacteristic
1024Q8—228no—
1025Q8—228no—
1026Q8—228no—
1027Q8—228no—
1028D4—228no—
1029D4—228no—
1030D4—228no—
1031D4—228no—
1032C2×C4—28no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—44no—
1051C2×C4—84no—
1052C2×C4—1116no—
1053C2×C4—112no—
1054C2×C4—112no—
1055C2×C4—112no—
1056C2×C4—112no—
1057C2×C4—112no—
1058C2×C4—112no—
1059C2×C4—112no—
1060C2×C4—112no—
1061C2×C4—112no—
1062C2×C4—112no—
1063C2×C4—114no—
1064C2×C4—228no—
1065C2×C4—221no—
1066C2×C4—221no—
1067C2×C4—221no—
1068C2×C4—221no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—444no—
1083C2×C4—884no—
1084C2×C4—884no—
1085C2×C4—884no—
1086C2×C4C22×C4×D1112yes—
1087C2×C4C22×C4×D1112yes—
1088C2×C4C22×C4×D1112yes—
1089C2×C4C22×C4×D1112yes—
1090C2×C4C2×D4×D1114yes—
1091C22—24no—
1092C22—24no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—88no—
1106C22—222no—
1107C22—222no—
1108C22—222no—
1109C22—222no—
1110C22—222no—
1111C22—222no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—888no—
1117C22C4×D4×D1114yes—
1118C22C23×C4×D1111yescharacteristic
1119C22C22×D4×D1111yescharacteristic
1120C22C2×#41×D1111yescharacteristic
1121C22#1062345312yes—
1122C22#1062345512yes—
1123C4—24no—
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—114no—
1132C4—114no—
1133C4—224no—
1134C4—222no—
1135C4—222no—
1136C4—222no—
1137C4—222no—
1138C4—442no—
1139C4—442no—
1140C4—442no—
1141C2—24no—
1142C2—42no—
1143C2—42no—
1144C2—442no—
1145C2—442no—
1146C2C2×C4×D4×D1111yescharacteristic
1147C2#1308181411yescharacteristic
1148C2#1308181711yescharacteristic
1149C2#1308240212yes—
1150C2#1308250412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2342C2
socle, cosocleC23×C11C25
prime radicalC23×C22⋊D11C22
hypercenter#2342D11
hypocenterC11#34211
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
4. #13071690C2semidirect
5. #13071688C2semidirect
6. #13071684C2semidirect
7. #13071682C2semidirect
8. #13071468C2semidirect
9. #13071467C2semidirect
10. #13071466C2semidirect
11. #13071465C2semidirect
12. #13071462C2semidirect
13. #13071461C2semidirect
14. #13071458C2semidirect
15. #13071325C2semidirect
16. #13071322C2semidirect
17. #13071201C2semidirect
19. #13071157C2semidirect
20. C4×#66938C2semidirect
21. #13071018C2semidirect
22. C4×#66930C2semidirect
23. C11×#2342C2semidirect
38. C2×#66940C22semidirect
39. C2×#66940C22semidirect
40. C2×#66938C4semidirect
60. C2×C4×Dic22C22semidirect
61. C2×C4×Dic22C22semidirect
62. C11×#388C22semidirect
63. C11×#388C22semidirect
64. C11×#385C22semidirect
69. C4×C11×C22⋊C4C22semidirect
73. #10622823C22semidirect
75. C4×C22⋊Dic11C22semidirect
76. #10622603C22semidirect
77. #10622603C22semidirect
78. #10622602C22semidirect
79. #10622602C22semidirect
80. #10622589C22semidirect
81. C4⋊C4×Dic11C22semidirect
88. #10622564C22semidirect
89. #10622564C22semidirect
90. #10622563C22semidirect
91. #10622559C22semidirect
92. #10622558C22semidirect
93. #10622558C22semidirect
94. #10622557C22semidirect
95. #10622557C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. C22⋊C4×Dic11C22semidirect
104. #10622553C22semidirect
105. #10622553C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. C42×Dic11C22semidirect
110. #10622283C22semidirect
111. #10622283C22semidirect
112. #10622282C22semidirect
113. #10622282C22semidirect
114. #10622281C22semidirect
115. #10622281C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622263C22semidirect
119. #10622262C22semidirect
120. #10622262C22semidirect
121. #10622261C22semidirect
122. #10622259C22semidirect
123. #10622259C22semidirect
124. #10622259C22semidirect
125. #10622259C22semidirect
146. C22×Dic22C2×C4semidirect
155. C2×C11×C22⋊C4C2×C4semidirect
170. C2×C22⋊Dic11C2×C4semidirect
184. C2×(C2×D11)⋊C4C2×C4semidirect
185. C2×(C2×D11)⋊C4C2×C4semidirect
211. C2×C4×Dic11C2×C4semidirect
228. #66938C2×C4semidirect
229. #66938C2×C4semidirect
230. #66938C2×C4semidirect
231. #66938C2×C4semidirect
232. #66938C2×C4semidirect
233. #66938C2×C4semidirect
234. #66938C2×C4semidirect
235. #66938C2×C4semidirect
427. #2342D11semidirect
599. #388C2×D11semidirect
600. #388C2×D11semidirect
608. #385C2×D11semidirect
638. C4×C22⋊C4C2×D11semidirect
784. C2×C22⋊C4C4×D11semidirect
987. C11#34211semidirect

Maximal subgroups

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

subgroupindex
C22×#669382
C2×#106230472
C2×#106230172
#130716902
#130716882
#130716842
#130716822
#130714682
#130714672
#130714662
#130714652
#130714622
#130714612
#130714582
#130713252
#130713222
#130712012
#130711972
#130711572
C4×#669382
#130710182
C4×#669302
C11×#23422
#3421111