Finite Group Databasebeta

← #14914192

Subgroups — #14914192

Order 2816.

2634 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2#13071700C212yesmaximal, complemented
3#13071693C212yesmaximal, complemented
4#13071626C211yesmaximal, characteristic, complemented
5#13071623C211yesmaximal, characteristic, complemented
6#13071620C211yesmaximal, characteristic, complemented
7#13071617C211yesmaximal, characteristic, complemented
8#13071492C211yesmaximal, characteristic, complemented
9#13071490C212yesmaximal, complemented
10#13071489C212yesmaximal, complemented
11#13071489C211yesmaximal, characteristic, complemented
12#13071450C211yesmaximal, characteristic, complemented
13Q8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14#13071347C212yesmaximal, complemented
15#13071344C212yesmaximal, complemented
16#13071227C212yesmaximal
17C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
18C4×#66977C211yesmaximal, characteristic, complemented
19#13071144C211yesmaximal, characteristic, complemented
20D11×#380C211yesmaximal, characteristic
21#13070968C212yesmaximal
22C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
23C4×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
24C22×Q8×D11C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic, complemented
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C2×#66977C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35D11×C22⋊Q8C4116yescomplemented
36C2×#66950C2211yescharacteristic
37C2×#66949C2212yes—
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2212yes—
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66940C2211yescharacteristic, complemented
43C2×C22⋊C4×D11C2212yes—
44C2×C22⋊C4×D11C2212yes—
45C2×#66931C2212yes—
46C2×C4×Dic22C2211yescharacteristic, complemented
47C11×#391C2211yescharacteristic, complemented
48C11×#389C2211yescharacteristic, complemented
49C11×#387C2212yescomplemented
50C11×#385C2212yes—
51C11×#380C2211yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic, complemented
53C4×C11×C4⋊C4C2212yescomplemented
54C4×C11×C22⋊C4C2212yes—
55#10622843C2211yescharacteristic, complemented
56#10622825C2211yescharacteristic
57#10622823C2212yes—
58C4×C22⋊Dic11C2212yes—
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622602C2212yes—
62#10622602C2212yes—
63#10622600C2212yes—
64#10622600C2211yescharacteristic
65#10622600C2211yescharacteristic
66#10622600C2212yes—
67#10622598C2211yescharacteristic, complemented
68#10622594C2212yescomplemented
69#10622591C2212yescomplemented
70C4⋊C4×Dic11C2211yescharacteristic, complemented
71C4⋊C4×Dic11C2211yescharacteristic, complemented
72C4⋊C4×Dic11C2212yescomplemented
73#10622587C2211yescharacteristic, complemented
74#10622587C2212yescomplemented
75#10622586C2212yescomplemented
76#10622586C2211yescharacteristic, complemented
77#10622585C2212yescomplemented
78#10622563C2212yes—
79#10622559C2212yes—
80#10622555C2212yes—
81C22⋊C4×Dic11C2212yes—
82C22⋊C4×Dic11C2212yes—
83C4×(C2×D11)⋊C4C2211yescharacteristic
84C4×(C2×D11)⋊C4C2212yes—
85C4×(C2×D11)⋊C4C2211yescharacteristic
86C4×(C2×D11)⋊C4C2212yes—
87C4×(C2×D11)⋊C4C2211yescharacteristic
88C4×(C2×D11)⋊C4C2211yescharacteristic
89C4×(C2×D11)⋊C4C2211yescharacteristic
90C4×(C2×D11)⋊C4C2212yes—
91C4×(C2×D11)⋊C4C2211yescharacteristic
92C4×(C2×D11)⋊C4C2211yescharacteristic
93C4×(C2×D11)⋊C4C2211yescharacteristic
94C4×(C2×D11)⋊C4C2212yes—
95C4×C4⋊Dic11C2211yescharacteristic, complemented
96#10622546C2212yescomplemented
97#10622546C2212yescomplemented
98#10622546C2212yescomplemented
99C4×Dic11⋊C4C2212yescomplemented
100#10622542C2211yescharacteristic, complemented
101#10622542C2212yescomplemented
102#10622541C2211yescharacteristic, complemented
103#10622541C2212yescomplemented
104#10622281C2212yes—
105#10622281C2212yes—
106#10622280C2212yes—
107#10622280C2212yes—
108#10622280C2212yes—
109#10622279C2212yes—
110#10622279C2212yes—
111#10622279C2212yes—
112#10622279C2212yes—
113D11×#95C2212yes—
114#10622268C2212yescomplemented
115#10622267C2212yescomplemented
116#10622266C2212yescomplemented
117#10622265C2212yescomplemented
118#10622265C2212yescomplemented
119#10622265C2212yescomplemented
120#10622262C2212yescomplemented
121#10622260C2212yescomplemented
122#10622259C2212yescomplemented
123#10622259C2212yescomplemented
124C24×D11C2311yescharacteristic
125C22×Q8×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C2×Q8×D11—42no—
133C2×Q8×D11—42no—
134C2×Q8×D11C2×C418yescomplemented
135C22×C4×D11—42no—
136C22×C4×D11—42no—
137C22×C4×D11C2×C418yes—
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2312yes—
141C22×C4×D11C2312yes—
142C22×C4×D11C2312yes—
143C22×C4×D11C2312yes—
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×Dic22C2311yescharacteristic
147C22×Dic22C2312yes—
148C11×C22⋊Q8C2×C418yescomplemented
149C4×Q8×C11—42no—
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C42×C11—42no—
159C2×C42×C11C2311yescharacteristic
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2312yes—
162C2×C42×C11C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C22⋊Dic11C2312yes—
166C2×C22⋊Dic11C2312yes—
167#66999C2×C418yescomplemented
168Q8×Dic11—42no—
169C2×(C2×D11)⋊C4—24no—
170C2×(C2×D11)⋊C4Q818yescomplemented
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2311yescharacteristic
174C2×(C2×D11)⋊C4C2311yescharacteristic
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2311yescharacteristic
180C2×(C2×D11)⋊C4C2311yescharacteristic
181C2×(C2×D11)⋊C4C2311yescharacteristic
182C2×(C2×D11)⋊C4C2311yescharacteristic
183C2×C4⋊Dic11C2311yescharacteristic
184C2×C4⋊Dic11C2311yescharacteristic
185C2×C4⋊Dic11C2312yes—
186C2×C4⋊Dic11C2312yes—
187C2×C4⋊Dic11C2312yes—
188C2×C4⋊Dic11C2311yescharacteristic
189#66977C2×C418yescomplemented
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C2312yes—
198C2×Dic11⋊C4C2312yes—
199C2×C4×Dic11—42no—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210#66950C2×C418yescomplemented
211#66949C2×C4116yescomplemented
212C4⋊C4×D11—42no—
213C4⋊C4×D11—42no—
214C4⋊C4×D11C2×C418yescomplemented
215C4⋊C4×D11C2×C4116yescomplemented
216#66940—42no—
217C22⋊C4×D11—28no—
218C22⋊C4×D11C2×C4116yes—
219#66931C2×C4116yescomplemented
220C4×Dic22—42no—
221C11×#95C2312yes—
222C11×#95C2312yes—
223C11×#95C2312yes—
224C11×#95C2312yes—
225C11×#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2311yescharacteristic
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2311yescharacteristic
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2312yes—
237C11⋊#95C2312yes—
238C11⋊#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2311yescharacteristic
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249#34212—111nomaximal, Sylow
250C24×C11C2411yescharacteristic
251C23×D11—41no—
252C23×D11—41no—
253C23×D11—41no—
254C23×D11—41no—
255C23×D11C22×C414yes—
256C23×D11C2×Q814yes—
257C23×D11#4114yes—
258C23×D11C2411yescharacteristic
259C23×D11C2411yescharacteristic
260C2×Q8×C11—22no—
261C2×Q8×C11—22no—
262C2×Q8×C11C22×C414yes—
263C22×C4×C11—22no—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11—41no—
267C22×C4×C11—41no—
268C22×C4×C11—41no—
269C22×C4×C11—41no—
270C22×C4×C11C22×C414yes—
271C22×C4×C11C2×Q814yescomplemented
272C22×C4×C11C2412yes—
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2412yes—
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×Dic11—22no—
283C22×Dic11—41no—
284C22×Dic11—41no—
285C22×Dic11—41no—
286C22×Dic11—41no—
287C22×Dic11—41no—
288C22×Dic11—41no—
289C22×Dic11C22×C414yes—
290C22×Dic11C2×Q814yescomplemented
291C22×Dic11C2412yes—
292C22×Dic11C2411yescharacteristic
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2412yes—
295C22×Dic11C2411yescharacteristic
296C22×Dic11C2412yes—
297C22×Dic11C2412yes—
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301Q8×D11—416no—
302C2×C4×D11—24no—
303C2×C4×D11—24no—
304C2×C4×D11—22no—
305C2×C4×D11—22no—
306C2×C4×D11—22no—
307C2×C4×D11—22no—
308C2×C4×D11—41no—
309C2×C4×D11—41no—
310C2×C4×D11—41no—
311C2×C4×D11—41no—
312C2×C4×D11—42no—
313C2×C4×D11—42no—
314C2×C4×D11—42no—
315C2×C4×D11—42no—
316C2×C4×D11—42no—
317C2×C4×D11—42no—
318C2×C4×D11—42no—
319C2×C4×D11—42no—
320C2×C4×D11—416no—
321C2×C4×D11C22×C414yes—
322C2×C4×D11C22×C414yes—
323C2×C4×D11C22×C418yes—
324C2×C4×D11C22×C418yes—
325C2×C4×D11C22×C414yes—
326C2×C4×D11C22×C414yes—
327C2×Dic22—22no—
328C2×Dic22—22no—
329C2×Dic22—42no—
330C2×Dic22—42no—
331C2×Dic22C22×C414yes—
332C2×Dic22C22×C418yes—
333C11×C4⋊C4—22no—
334C11×C4⋊C4—22no—
335C11×C4⋊C4—42no—
336C11×C4⋊C4—42no—
337C11×C4⋊C4C22×C418yes—
338C11×C4⋊C4C22×C414yes—
339C11×C22⋊C4—24no—
340C11×C22⋊C4C22×C418yes—
341C42×C11—22no—
342C42×C11—22no—
343C42×C11—41no—
344C42×C11—41no—
345C42×C11—42no—
346C42×C11—42no—
347C22⋊Dic11—24no—
348C22⋊Dic11C22×C418yes—
349(C2×D11)⋊C4—24no—
350(C2×D11)⋊C4—24no—
351(C2×D11)⋊C4—22no—
352(C2×D11)⋊C4—22no—
353(C2×D11)⋊C4—22no—
354(C2×D11)⋊C4—22no—
355(C2×D11)⋊C4C22×C418yes—
356(C2×D11)⋊C4C22×C418yes—
357(C2×D11)⋊C4C2×Q814yes—
358(C2×D11)⋊C4C2×Q814yes—
359(C2×D11)⋊C4C2×Q814yescomplemented
360(C2×D11)⋊C4C2×Q814yescomplemented
361C4⋊Dic11—22no—
362C4⋊Dic11—22no—
363C4⋊Dic11—42no—
364C4⋊Dic11—42no—
365C4⋊Dic11C22×C418yes—
366C4⋊Dic11C22×C414yes—
367Dic11⋊C4—42no—
368Dic11⋊C4—42no—
369Dic11⋊C4—42no—
370Dic11⋊C4—42no—
371Dic11⋊C4—42no—
372Dic11⋊C4—42no—
373Dic11⋊C4C22×C418yes—
374Dic11⋊C4C22×C418yes—
375Dic11⋊C4C22×C418yes—
376C4×Dic11—22no—
377C4×Dic11—22no—
378C4×Dic11—42no—
379C4×Dic11—42no—
380C4×Dic11—41no—
381C4×Dic11—41no—
382C4×Dic11—42no—
383C4×Dic11—42no—
384C4×Dic11—42no—
385C4×Dic11—42no—
386C22×C22⋊Q8—111no—
387#2368—112no—
388#2368—112no—
389#2360—111no—
390#2360—111no—
391#2360—111no—
392#2360—111no—
393#2345—111no—
394#2345—112no—
395#2345—111no—
396#2345—112no—
397Q8×C22⋊C4—111no—
398Q8×C22⋊C4—111no—
399#2329—112no—
400#2329—112no—
401#2315—112no—
402C4×C22⋊Q8—111no—
403C4×C22⋊Q8—111no—
404C4×C22⋊Q8—111no—
405C4×C22⋊Q8D1111yescharacteristic, complemented
406C2×#380—111no—
407#2273—112no—
408C2×C4×C22⋊C4—111no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—21no—
412C23×C11—21no—
413C23×C11C23×C412yes—
414C23×C11C22×Q812yes—
415C23×C11C2×#4112yes—
416C23×C11C2511yescharacteristic
417C22×D11—21no—
418C22×D11—21no—
419C22×D11—21no—
420C22×D11—21no—
421C22×D11—21no—
422C22×D11—21no—
423C22×D11—21no—
424C22×D11—21no—
425C22×D11—44no—
426C22×D11—44no—
427C22×D11—44no—
428C22×D11—44no—
429C22×D11—44no—
430C22×D11—44no—
431C22×D11C4×Q8116yescomplemented
432C22×D11C23×C412yes—
433C22×D11C23×C412yes—
434C22×D11C22×Q812yes—
435C22×D11C22×Q812yes—
436C22×D11C2×#4112yes—
437C22×D11C2×#4112yes—
438Q8×C11—28no—
439C2×C4×C11—21no—
440C2×C4×C11—21no—
441C2×C4×C11—22no—
442C2×C4×C11—21no—
443C2×C4×C11—21no—
444C2×C4×C11—22no—
445C2×C4×C11—21no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—21no—
449C2×C4×C11—28no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—21no—
456C2×C4×C11—22no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—21no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—44no—
463C2×C4×C11—44no—
464C2×C4×C11C23×C412yes—
465C2×C4×C11C23×C414yes—
466C2×C4×C11C23×C414yes—
467C2×C4×C11C23×C412yes—
468C2×C4×C11C22×Q812yes—
469C2×C4×C11C22×Q812yes—
470C2×C4×C11H(5,𝔽2)12yes—
471C2×C4×C11H(5,𝔽2)12yes—
472C2×Dic11—21no—
473C2×Dic11—21no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—21no—
477C2×Dic11—21no—
478C2×Dic11—21no—
479C2×Dic11—21no—
480C2×Dic11—21no—
481C2×Dic11—21no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—21no—
485C2×Dic11—21no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—21no—
489C2×Dic11—21no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—21no—
495C2×Dic11—21no—
496C2×Dic11—44no—
497C2×Dic11—44no—
498C2×Dic11—44no—
499C2×Dic11C23×C414yes—
500C2×Dic11C23×C412yes—
501C2×Dic11C23×C412yes—
502C2×Dic11C23×C414yes—
503C2×Dic11C22×Q812yes—
504C2×Dic11C22×Q812yes—
505C4×D11—28no—
506C4×D11—28no—
507C4×D11—44no—
508C4×D11—44no—
509C4×D11—48no—
510C4×D11—48no—
511C4×D11—84no—
512C4×D11—84no—
513Dic22—28no—
514Dic22—48no—
515C23×Q8—111no—
516C24×C4—111no—
517C2×C22⋊Q8—111no—
518C2×C22⋊Q8—111no—
519C2×C22⋊Q8—1116no—
520C2×C22⋊Q8—111no—
521C2×C22⋊Q8—112no—
522C2×C22⋊Q8—112no—
523C2×C22⋊Q8C2×D1111yescharacteristic
524C2×C4×Q8—111no—
525C2×C4×Q8—111no—
526C2×C4×Q8—111no—
527C2×C4×Q8C2×D1111yescharacteristic, complemented
528C22×C4⋊C4—112no—
529C22×C4⋊C4—111no—
530C22×C4⋊C4—111no—
531C22×C4⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—112no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—112no—
536C22×C42—111no—
537C22×C42C2×D1111yescharacteristic
538#391—111no—
539#391—112no—
540#391—111no—
541#391—112no—
542#391—111no—
543#391—112no—
544#391—112no—
545#391C2×D1111yescharacteristic, complemented
546#389—112no—
547#389—112no—
548#389—111no—
549#389—111no—
550#389—112no—
551#389—111no—
552#389—112no—
553#389C2×D1111yescharacteristic, complemented
554#387—112no—
555#387—112no—
556#387—112no—
557#387—112no—
558#387—112no—
559#387—112no—
560#387—112no—
561#387—112no—
562#387—112no—
563#387—112no—
564#387—112no—
565#387C2×D1112yescomplemented
566#385—112no—
567#385—112no—
568#385—112no—
569#385—112no—
570#385—112no—
571#385—112no—
572#385—112no—
573#385C2×D1112yes—
574#380—111no—
575#380—112no—
576#380—112no—
577#380—111no—
578#380—111no—
579#380—112no—
580#380—112no—
581#380—112no—
582#380—112no—
583#380C2×D1111yescharacteristic
584C4×C4⋊C4—111no—
585C4×C4⋊C4—111no—
586C4×C4⋊C4—112no—
587C4×C4⋊C4—111no—
588C4×C4⋊C4—112no—
589C4×C4⋊C4—112no—
590C4×C4⋊C4C2×D1111yescharacteristic, complemented
591C4×C4⋊C4C2×D1112yescomplemented
592C4×C22⋊C4—112no—
593C4×C22⋊C4—112no—
594C4×C22⋊C4—112no—
595C4×C22⋊C4—111no—
596C4×C22⋊C4—111no—
597C4×C22⋊C4—112no—
598C4×C22⋊C4—111no—
599C4×C22⋊C4—111no—
600C4×C22⋊C4—112no—
601C4×C22⋊C4—111no—
602C4×C22⋊C4—111no—
603C4×C22⋊C4—112no—
604C4×C22⋊C4—112no—
605C4×C22⋊C4—111no—
606C4×C22⋊C4—111no—
607C4×C22⋊C4—112no—
608C4×C22⋊C4—112no—
609C4×C22⋊C4—112no—
610C4×C22⋊C4—112no—
611C4×C22⋊C4C2×D1112yes—
612C2×#95—111no—
613C2×#95—111no—
614C2×#95—112no—
615C22×C11—22no—
616C22×C11—22no—
617C22×C11—22no—
618C22×C11—22no—
619C22×C11—22no—
620C22×C11—22no—
621C22×C11C2×C4×Q814yes—
622C22×C11C24×C411yescharacteristic
623C22×C11C23×Q811yescharacteristic
624C22×C11C22×#4111yescharacteristic
625C22×C11C2×H(5,𝔽2)11yescharacteristic
626C22×C11C2×H(5,𝔽2)11yescharacteristic
627C22×C11#58511yescharacteristic
628C22×C11#58511yescharacteristic
629C2×D11—22no—
630C2×D11—22no—
631C2×D11—22no—
632C2×D11—22no—
633C2×D11—22no—
634C2×D11—22no—
635C2×D11—22no—
636C2×D11—22no—
637C2×D11—22no—
638C2×D11—22no—
639C2×D11—22no—
640C2×D11—22no—
641C2×D11—416no—
642C2×D11C2×C4×Q814yes—
643C2×D11C2×C4×Q814yes—
644C4×C11—22no—
645C4×C11—24no—
646C4×C11—24no—
647C4×C11—22no—
648C4×C11—22no—
649C4×C11—41no—
650C4×C11—41no—
651C4×C11—42no—
652C4×C11—42no—
653C4×C11#51814yes—
654Dic11—24no—
655Dic11—22no—
656Dic11—22no—
657Dic11—24no—
658Dic11—22no—
659Dic11—22no—
660Dic11—42no—
661Dic11—42no—
662Dic11—41no—
663Dic11—41no—
664C25—111no—
665C22×Q8—118no—
666C22×Q8—111no—
667C22×Q8—112no—
668C22×Q8—442no—
669C22×Q8—442no—
670C22×Q8C22×D1111yescharacteristic
671C23×C4—111no—
672C23×C4—111no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—118no—
676C23×C4—112no—
677C23×C4—112no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—112no—
682C23×C4—112no—
683C23×C4—442no—
684C23×C4—442no—
685C23×C4C22×D1111yescharacteristic
686C23×C4C22×D1111yescharacteristic
687C23×C4C22×D1111yescharacteristic
688C22⋊Q8—118no—
689C22⋊Q8—118no—
690C22⋊Q8—1116no—
691C22⋊Q8—118no—
692C22⋊Q8—1116no—
693C22⋊Q8C4×D1118yescomplemented
694C4×Q8—42no—
695C4×Q8—442no—
696C4×Q8—442no—
697C4×Q8—442no—
698C2×C4⋊C4—112no—
699C2×C4⋊C4—111no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—112no—
702C2×C4⋊C4—112no—
703C2×C4⋊C4—118no—
704C2×C4⋊C4—1116no—
705C2×C4⋊C4—111no—
706C2×C4⋊C4—111no—
707C2×C4⋊C4—112no—
708C2×C4⋊C4—112no—
709C2×C4⋊C4—112no—
710C2×C4⋊C4—112no—
711C2×C4⋊C4—112no—
712C2×C4⋊C4—112no—
713C2×C4⋊C4—112no—
714C2×C4⋊C4—112no—
715C2×C4⋊C4—442no—
716C2×C4⋊C4—442no—
717C2×C4⋊C4C22×D1111yescharacteristic
718C2×C4⋊C4C22×D1111yescharacteristic
719C2×C4⋊C4C22×D1112yes—
720C2×C4⋊C4C22×D1112yes—
721C2×C4⋊C4C22×D1112yes—
722C2×C4⋊C4C22×D1111yescharacteristic
723C2×C22⋊C4—112no—
724C2×C22⋊C4—118no—
725C2×C22⋊C4—112no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—111no—
728C2×C22⋊C4—111no—
729C2×C22⋊C4—111no—
730C2×C22⋊C4—111no—
731C2×C22⋊C4—1116no—
732C2×C22⋊C4—112no—
733C2×C22⋊C4—112no—
734C2×C22⋊C4—111no—
735C2×C22⋊C4—111no—
736C2×C22⋊C4—112no—
737C2×C22⋊C4—111no—
738C2×C22⋊C4—111no—
739C2×C22⋊C4—228no—
740C2×C22⋊C4—224no—
741C2×C22⋊C4C22×D1112yes—
742C2×C22⋊C4C22×D1112yes—
743C2×C42—42no—
744C2×C42—111no—
745C2×C42—111no—
746C2×C42—112no—
747C2×C42—112no—
748C2×C42—112no—
749C2×C42—112no—
750C2×C42—112no—
751C2×C42—112no—
752C2×C42—111no—
753C2×C42—111no—
754C2×C42—442no—
755C2×C42C22×D1111yescharacteristic
756C2×C42C22×D1111yescharacteristic
757C2×C42C22×D1112yes—
758C2×C42C22×D1112yes—
759C2×C42C22×D1111yescharacteristic
760C2×C42C22×D1111yescharacteristic
761#95—111no—
762#95—111no—
763#95—111no—
764#95—111no—
765#95—111no—
766#95—111no—
767#95—111no—
768#95—111no—
769#95—112no—
770#95—112no—
771#95—112no—
772#95—112no—
773#95—112no—
774#95—112no—
775#95—112no—
776#95—112no—
777#95—112no—
778#95—112no—
779#95—112no—
780#95—112no—
781#95—112no—
782#95—112no—
783#95—112no—
784#95C22×D1112yes—
785#95C22×D1112yes—
786#95C22×D1112yes—
787#95C22×D1112yes—
788#95C22×D1112yes—
789C2×C11—24no—
790C2×C11C22×C4×Q811yescharacteristic
791C2×C11C2×#51811yescharacteristic
792C2×C11#342811yescharacteristic
793C2×C11#350111yescharacteristic
794C2×C11#350111yescharacteristic
795C2×C11#350511yescharacteristic
796C2×C11#350511yescharacteristic
797D11—24no—
798D11—24no—
799C24—111no—
800C24—111no—
801C24—114no—
802C24—114no—
803C24—114no—
804C24—441no—
805C24—441no—
806C24—441no—
807C24—441no—
808C24C23×D1111yescharacteristic
809C2×Q8—22no—
810C2×Q8—22no—
811C2×Q8—114no—
812C2×Q8—118no—
813C2×Q8—222no—
814C2×Q8—222no—
815C2×Q8—442no—
816C2×Q8—442no—
817C2×Q8—4416no—
818C2×Q8C2×C4×D1114yes—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—111no—
827C22×C4—111no—
828C22×C4—111no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—111no—
832C22×C4—114no—
833C22×C4—114no—
834C22×C4—114no—
835C22×C4—114no—
836C22×C4—118no—
837C22×C4—118no—
838C22×C4—114no—
839C22×C4—114no—
840C22×C4—112no—
841C22×C4—111no—
842C22×C4—111no—
843C22×C4—112no—
844C22×C4—224no—
845C22×C4—224no—
846C22×C4—222no—
847C22×C4—222no—
848C22×C4—222no—
849C22×C4—222no—
850C22×C4—222no—
851C22×C4—4416no—
852C22×C4—441no—
853C22×C4—441no—
854C22×C4—441no—
855C22×C4—441no—
856C22×C4—442no—
857C22×C4—442no—
858C22×C4—442no—
859C22×C4—442no—
860C22×C4—442no—
861C22×C4—442no—
862C22×C4—442no—
863C22×C4—442no—
864C22×C4—441no—
865C22×C4—441no—
866C22×C4—441no—
867C22×C4—441no—
868C22×C4—441no—
869C22×C4—441no—
870C22×C4C2×C4×D1114yes—
871C22×C4Q8×D1114yescomplemented
872C22×C4C23×D1112yes—
873C22×C4C23×D1111yescharacteristic
874C22×C4C23×D1111yescharacteristic
875C22×C4C23×D1112yes—
876C22×C4C23×D1111yescharacteristic
877C22×C4C23×D1112yes—
878C22×C4C23×D1112yes—
879C22×C4C23×D1111yescharacteristic
880C22×C4C23×D1111yescharacteristic
881C22×C4C23×D1111yescharacteristic
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—118no—
887C4⋊C4—118no—
888C4⋊C4—118no—
889C4⋊C4—114no—
890C4⋊C4—118no—
891C4⋊C4—222no—
892C4⋊C4—222no—
893C4⋊C4—442no—
894C4⋊C4—442no—
895C4⋊C4—442no—
896C4⋊C4—442no—
897C4⋊C4—442no—
898C4⋊C4—442no—
899C4⋊C4—442no—
900C4⋊C4—442no—
901C4⋊C4C2×C4×D1114yes—
902C4⋊C4C2×C4×D1118yes—
903C22⋊C4—24no—
904C22⋊C4—118no—
905C22⋊C4—118no—
906C22⋊C4—118no—
907C22⋊C4—114no—
908C22⋊C4—114no—
909C22⋊C4—114no—
910C22⋊C4—114no—
911C22⋊C4—224no—
912C22⋊C4—224no—
913C22⋊C4—222no—
914C22⋊C4—222no—
915C22⋊C4—222no—
916C22⋊C4—222no—
917C22⋊C4—224no—
918C22⋊C4C2×C4×D1118yes—
919C42—22no—
920C42—22no—
921C42—41no—
922C42—41no—
923C42—42no—
924C42—42no—
925C42—222no—
926C42—222no—
927C42—441no—
928C42—441no—
929C42—442no—
930C42—442no—
931C42—442no—
932C42—442no—
933C42—442no—
934C42—442no—
935C11#3421211yescharacteristic, complemented, Sylow
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—112no—
941C23—112no—
942C23—112no—
943C23—112no—
944C23—112no—
945C23—112no—
946C23—1116no—
947C23—221no—
948C23—221no—
949C23—221no—
950C23—221no—
951C23—221no—
952C23—221no—
953C23—221no—
954C23—221no—
955C23—444no—
956C23—444no—
957C23—444no—
958C23—444no—
959C23—444no—
960C23—444no—
961C23C22×C4×D1112yes—
962C23C2×Q8×D1112yes—
963C23#41×D1112yes—
964C23C24×D1111yescharacteristic
965Q8—28no—
966Q8—228no—
967Q8—448no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—28no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—44no—
992C2×C4—44no—
993C2×C4—114no—
994C2×C4—114no—
995C2×C4—112no—
996C2×C4—112no—
997C2×C4—112no—
998C2×C4—112no—
999C2×C4—222no—
1000C2×C4—221no—
1001C2×C4—221no—
1002C2×C4—221no—
1003C2×C4—221no—
1004C2×C4—222no—
1005C2×C4—221no—
1006C2×C4—221no—
1007C2×C4—221no—
1008C2×C4—221no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—228no—
1012C2×C4—228no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—221no—
1016C2×C4—221no—
1017C2×C4—222no—
1018C2×C4—221no—
1019C2×C4—221no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—221no—
1024C2×C4—221no—
1025C2×C4—444no—
1026C2×C4—444no—
1027C2×C4—448no—
1028C2×C4—448no—
1029C2×C4—444no—
1030C2×C4—444no—
1031C2×C4—444no—
1032C2×C4—884no—
1033C2×C4—884no—
1034C2×C4C22×C4×D1114yes—
1035C2×C4C22×C4×D1114yes—
1036C2×C4C22×C4×D1112yes—
1037C2×C4C22×C4×D1112yes—
1038C2×C4#6703712yes—
1039C2×C4C2×Q8×D1112yes—
1040C2×C4C2×Q8×D1112yes—
1041C2×C4#6704212yes—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—114no—
1049C22—114no—
1050C22—222no—
1051C22—222no—
1052C22—222no—
1053C22—222no—
1054C22—222no—
1055C22—222no—
1056C22—222no—
1057C22—222no—
1058C22—222no—
1059C22—222no—
1060C22—222no—
1061C22—222no—
1062C22—4416no—
1063C22C4×Q8×D1114yes—
1064C22C23×C4×D1111yescharacteristic
1065C22C2×#6703711yescharacteristic
1066C22C22×Q8×D1111yescharacteristic
1067C22C2×#41×D1111yescharacteristic
1068C22C2×#6704211yescharacteristic
1069C22#1062345311yescharacteristic
1070C22#1062345311yescharacteristic
1071C4—22no—
1072C4—22no—
1073C4—22no—
1074C4—24no—
1075C4—24no—
1076C4—41no—
1077C4—41no—
1078C4—42no—
1079C4—42no—
1080C4—222no—
1081C4—222no—
1082C4—222no—
1083C4—222no—
1084C4—224no—
1085C4—224no—
1086C4—442no—
1087C4—441no—
1088C4—441no—
1089C4—442no—
1090C4#1062307614yes—
1091C2—24no—
1092C2—224no—
1093C2—224no—
1094C2C2×C4×Q8×D1111yescharacteristic
1095C2C2×#1062307611yescharacteristic
1096C2#1308181511yescharacteristic
1097C2#1308241211yescharacteristic
1098C2#1308241711yescharacteristic
1099C2#1308244411yescharacteristic
1100C2#1308245111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×C22⋊Q8C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenterC4×C22⋊Q8D11
hypocenterC11#34212
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13071700C2semidirect
3. #13071693C2semidirect
4. #13071626C2semidirect
5. #13071623C2semidirect
6. #13071620C2semidirect
7. #13071617C2semidirect
8. #13071492C2semidirect
9. #13071490C2semidirect
10. #13071489C2semidirect
11. #13071489C2semidirect
12. #13071450C2semidirect
13. Q8×(C2×D11)⋊C4C2semidirect
14. #13071347C2semidirect
15. #13071344C2semidirect
17. C22⋊Q8×Dic11C2semidirect
18. C4×#66977C2semidirect
19. #13071144C2semidirect
23. C4×C11×C22⋊Q8C2semidirect
27. C2×C4×Q8×C11C22semidirect
30. C2×Q8×Dic11C22semidirect
35. D11×C22⋊Q8C4semidirect
42. C2×#66940C22semidirect
46. C2×C4×Dic22C22semidirect
47. C11×#391C22semidirect
48. C11×#389C22semidirect
49. C11×#387C22semidirect
52. C4×C11×C4⋊C4C22semidirect
53. C4×C11×C4⋊C4C22semidirect
55. #10622843C22semidirect
67. #10622598C22semidirect
68. #10622594C22semidirect
69. #10622591C22semidirect
70. C4⋊C4×Dic11C22semidirect
71. C4⋊C4×Dic11C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. #10622587C22semidirect
74. #10622587C22semidirect
75. #10622586C22semidirect
76. #10622586C22semidirect
77. #10622585C22semidirect
95. C4×C4⋊Dic11C22semidirect
96. #10622546C22semidirect
97. #10622546C22semidirect
98. #10622546C22semidirect
99. C4×Dic11⋊C4C22semidirect
100. #10622542C22semidirect
101. #10622542C22semidirect
102. #10622541C22semidirect
103. #10622541C22semidirect
114. #10622268C22semidirect
115. #10622267C22semidirect
116. #10622266C22semidirect
117. #10622265C22semidirect
118. #10622265C22semidirect
119. #10622265C22semidirect
120. #10622262C22semidirect
121. #10622260C22semidirect
122. #10622259C22semidirect
123. #10622259C22semidirect
134. C2×Q8×D11C2×C4semidirect
148. C11×C22⋊Q8C2×C4semidirect
167. #66999C2×C4semidirect
170. C2×(C2×D11)⋊C4Q8semidirect
189. #66977C2×C4semidirect
210. #66950C2×C4semidirect
211. #66949C2×C4semidirect
214. C4⋊C4×D11C2×C4semidirect
215. C4⋊C4×D11C2×C4semidirect
219. #66931C2×C4semidirect
271. C22×C4×C11C2×Q8semidirect
290. C22×Dic11C2×Q8semidirect
359. (C2×D11)⋊C4C2×Q8semidirect
360. (C2×D11)⋊C4C2×Q8semidirect
405. C4×C22⋊Q8D11semidirect
431. C22×D11C4×Q8semidirect
527. C2×C4×Q8C2×D11semidirect
545. #391C2×D11semidirect
553. #389C2×D11semidirect
565. #387C2×D11semidirect
590. C4×C4⋊C4C2×D11semidirect
591. C4×C4⋊C4C2×D11semidirect
693. C22⋊Q8C4×D11semidirect
871. C22×C4Q8×D11semidirect
935. C11#34212semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
#130717002
#130716932
#130716262
#130716232
#130716202
#130716172
#130714922
#130714902
#130714892
#130714502
Q8×(C2×D11)⋊C42
#130713472
#130713442
#130712272
C22⋊Q8×Dic112
C4×#669772
#130711442
D11×#3802
#130709682
C2×C4×(C2×D11)⋊C42
C4×C11×C22⋊Q82
#3421211