Finite Group Databasebeta

← #14926288

Subgroups — #14926288

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic
3#13074317C211yesmaximal, characteristic, complemented
4#13074315C211yesmaximal, characteristic, complemented
5#13074309C211yesmaximal, characteristic, complemented
6#13074307C211yesmaximal, characteristic, complemented
7#13073827C211yesmaximal, characteristic, complemented
8#13073607C211yesmaximal, characteristic, complemented
9#13073600C211yesmaximal, characteristic, complemented
10#13073564C211yesmaximal, characteristic, complemented
11#13073064C212yesmaximal, complemented
12#13072239C212yesmaximal
13#13072040C212yesmaximal, complemented
14#13072038C212yesmaximal, complemented
15#13071876C211yesmaximal, characteristic, complemented
16#13071875C211yesmaximal, characteristic, complemented
17#13071873C211yesmaximal, characteristic, complemented
18C4×#66941C212yesmaximal, complemented
19C4×#66938C212yesmaximal, complemented
20C4×#66949C212yesmaximal, complemented
21C4×#66931C212yesmaximal, complemented
22C4×#66930C211yesmaximal, characteristic, complemented
23C11×#2395C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×C4×C22⋊D11C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C4×#4341—28no—
34#10623048—28no—
35C2×#66949C2212yes—
36C2×#66945C2211yescharacteristic
37C2×#66943C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×#66941C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66941C2212yes—
42C2×#66940C2211yescharacteristic
43C2×#66938C2212yes—
44C2×(C22⋊D11)⋊C4C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2211yescharacteristic
46C2×#66931C2212yes—
47C2×#66931C2212yes—
48C2×#66931C2212yes—
49C2×#66930C2212yes—
50C2×#66930C2211yescharacteristic
51C2×#66930C2211yescharacteristic
52C2×C42×D11C2211yescharacteristic
53C2×C4×Dic22C2212yes—
54C2×C4×Dic22C2212yes—
55C2×C4×Dic22C2211yescharacteristic
56C11×#400C2211yescharacteristic
57C11×#399C2211yescharacteristic
58C11×#398C2211yescharacteristic
59C11×#397C2211yescharacteristic
60C11×#397C2212yes—
61C11×#394C2212yes—
62C4×C11×C4⋊C4C2212yes—
63C4×C11×C22⋊C4C2211yescharacteristic
64C4×C11×C22⋊C4C2212yes—
65#10622835C2212yes—
66C4×C22⋊Dic11C2211yescharacteristic
67C4×C22⋊Dic11C2212yes—
68#10622606C2211yescharacteristic
69#10622605C2211yescharacteristic
70#10622602C2212yes—
71#10622599C2211yescharacteristic
72#10622598C2212yes—
73#10622596C2211yescharacteristic
74#10622595C2211yescharacteristic
75#10622594C2212yes—
76#10622593C2211yescharacteristic
77#10622589C2212yes—
78#10622586C2212yes—
79#10622585C2212yes—
80#10622574C2212yes—
81#10622572C2212yes—
82#10622570C2212yes—
83#10622566C2211yescharacteristic
84#10622566C2212yes—
85#10622565C2212yes—
86#10622565C2212yes—
87#10622564C2212yes—
88#10622563C2212yes—
89#10622562C2211yescharacteristic
90#10622559C2212yes—
91#10622557C2212yes—
92#10622555C2212yes—
93C22⋊C4×Dic11C2212yes—
94C4×(C2×D11)⋊C4C2212yes—
95C4×(C2×D11)⋊C4C2212yes—
96C4×C4⋊Dic11C2212yes—
97C4×Dic11⋊C4C2212yes—
98C4×Dic11⋊C4C2212yes—
99C4×Dic11⋊C4C2212yes—
100C42×Dic11C2212yes—
101#10622290C2211yescharacteristic
102#10622287C2211yescharacteristic
103#10622283C2212yes—
104#10622282C2212yes—
105#10622281C2212yes—
106#10622280C2212yes—
107#10622274C2211yescharacteristic
108#10622272C2211yescharacteristic
109#10622268C2212yes—
110#10622267C2212yes—
111#10622265C2212yes—
112#10622263C2212yes—
113#10622262C2211yescharacteristic
114#10622262C2211yescharacteristic
115#10622261C2211yescharacteristic
116#10622261C2211yescharacteristic
117#10622260C2212yes—
118#10622260C2212yes—
119#10622260C2212yes—
120#10622259C2212yes—
121#10622259C2212yes—
122#10622259C2212yes—
123#10622259C2212yes—
124#10622259C2212yes—
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C22×C22⋊D11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C2×#4341—24no—
135C2×#4341—24no—
136C2×#4341—24no—
137C22×C4×D11C2311yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×Dic22C2312yes—
141C22×Dic22C2312yes—
142C22×Dic22C2311yescharacteristic
143C4×D4×C11—24no—
144C11×#117—24no—
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C2312yes—
150C2×C11×C22⋊C4C2311yescharacteristic
151C2×C11×C22⋊C4C2311yescharacteristic
152C2×C11×C22⋊C4C2312yes—
153C2×C11×C22⋊C4C2312yes—
154C2×C11×C22⋊C4C2312yes—
155C2×C11×C22⋊C4C2312yes—
156C2×C42×C11C2312yes—
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2312yes—
159C2×C22⋊Dic11C2311yescharacteristic
160C2×C22⋊Dic11C2311yescharacteristic
161C2×C22⋊Dic11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165D4×Dic11—24no—
166C4×C22⋊D11—24no—
167C4×C22⋊D11—24no—
168C2×(C2×D11)⋊C4C2311yescharacteristic
169C2×(C2×D11)⋊C4C2311yescharacteristic
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174#66979—24no—
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2311yescharacteristic
182C2×Dic11⋊C4C2311yescharacteristic
183C2×Dic11⋊C4C2311yescharacteristic
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2311yescharacteristic
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2311yescharacteristic
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×C4×Dic11—24no—
197C2×C4×Dic11D418yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2311yescharacteristic
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202C2×C4×Dic11C2312yes—
203C2×C4×Dic11C2312yes—
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213#66949—28no—
214#66945—24no—
215#66943—24no—
216#66943—24no—
217#66941—28no—
218#66941—24no—
219#66941—24no—
220#66940—24no—
221#66938—28no—
222(C22⋊D11)⋊C4—24no—
223(C22⋊D11)⋊C4—24no—
224#66931—28no—
225#66931—28no—
226#66931—28no—
227#66930—24no—
228#66930—28no—
229#66930—24no—
230C42×D11—24no—
231C4×Dic22—28no—
232C4×Dic22—28no—
233C4×Dic22—24no—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2311yescharacteristic
239C11×#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256#34979—111nomaximal, Sylow
257C24×C11C2411yescharacteristic
258C24×C11C2411yescharacteristic
259C23×D11C2411yescharacteristic
260C2×D4×C11—22no—
261C2×D4×C11—22no—
262C2×D4×C11—22no—
263C22×C4×C11—24no—
264C22×C4×C11—22no—
265C22×C4×C11—24no—
266C22×C4×C11C2×D414yes—
267C22×C4×C11C2412yes—
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2412yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2412yes—
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C2×C22⋊D11—22no—
277C2×C22⋊D11—22no—
278C2×C22⋊D11—22no—
279C2×C22⋊D11—22no—
280C2×C22⋊D11—22no—
281C2×C22⋊D11#4114yes—
282C22×Dic11—22no—
283C22×Dic11—24no—
284C22×Dic11—22no—
285C22×Dic11—22no—
286C22×Dic11—22no—
287C22×Dic11—22no—
288C22×Dic11—24no—
289C22×Dic11—22no—
290C22×Dic11C2×D414yes—
291C22×Dic11C2×D414yes—
292C22×Dic11C2412yes—
293C22×Dic11C2411yescharacteristic
294C22×Dic11C2411yescharacteristic
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2411yescharacteristic
299C22×Dic11C2412yes—
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303#4341—232no—
304C2×C4×D11—22no—
305C2×C4×D11—22no—
306C2×C4×D11—24no—
307C2×C4×D11—22no—
308C2×C4×D11—22no—
309C2×C4×D11—22no—
310C2×C4×D11—24no—
311C2×Dic22—22no—
312C2×Dic22—22no—
313C2×Dic22—24no—
314C2×Dic22—24no—
315C2×Dic22—24no—
316C2×Dic22—24no—
317C2×Dic22—24no—
318C2×Dic22—24no—
319C2×Dic22#4114yes—
320C11×C4⋊C4—22no—
321C11×C4⋊C4—22no—
322C11×C4⋊C4—22no—
323C11×C4⋊C4—24no—
324C11×C4⋊C4—24no—
325C11×C22⋊C4—22no—
326C11×C22⋊C4—24no—
327C11×C22⋊C4—24no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—24no—
330C11×C22⋊C4—24no—
331C42×C11—24no—
332C42×C11—22no—
333C42×C11—24no—
334C22⋊Dic11—22no—
335C22⋊Dic11—24no—
336C22⋊Dic11—24no—
337C22⋊Dic11—22no—
338C22⋊Dic11—24no—
339C22⋊Dic11—24no—
340(C2×D11)⋊C4—22no—
341(C2×D11)⋊C4—24no—
342(C2×D11)⋊C4—24no—
343(C2×D11)⋊C4—24no—
344(C2×D11)⋊C4—22no—
345(C2×D11)⋊C4—24no—
346C4⋊Dic11—24no—
347C4⋊Dic11—24no—
348C4⋊Dic11—22no—
349C4⋊Dic11—24no—
350C4⋊Dic11—22no—
351C4⋊Dic11—22no—
352C4⋊Dic11—24no—
353Dic11⋊C4—22no—
354Dic11⋊C4—22no—
355Dic11⋊C4—24no—
356Dic11⋊C4—24no—
357Dic11⋊C4—24no—
358Dic11⋊C4—24no—
359Dic11⋊C4—22no—
360Dic11⋊C4—24no—
361Dic11⋊C4—24no—
362Dic11⋊C4—24no—
363Dic11⋊C4—24no—
364Dic11⋊C4—22no—
365Dic11⋊C4—24no—
366Dic11⋊C4#4118yescomplemented
367C4×Dic11—22no—
368C4×Dic11—22no—
369C4×Dic11—22no—
370C4×Dic11—22no—
371C4×Dic11—24no—
372C4×Dic11—24no—
373C4×Dic11—24no—
374C4×Dic11—24no—
375C4×Dic11—22no—
376C4×Dic11—24no—
377C4×Dic11—24no—
378C4×Dic11C2×D414yes—
379C4×Dic11C2×D414yes—
380C4×Dic11C2×D414yes—
381C4×Dic11C2×D414yes—
382C2×#533—111no—
383C2×C4×#41—111no—
384#2611—111no—
385#2611—111no—
386#2611—111no—
387#2611—111no—
388#2568—111no—
389#2547—111no—
390#2546—111no—
391#2542—111no—
392#2499—112no—
393#2432—112no—
394#2415—112no—
395#2415—112no—
396#2395—111no—
397#2395—111no—
398#2395—111no—
399#2395D1111yescharacteristic, complemented
400C4×C4⋊Q8—112no—
401C4×#124—112no—
402C4×C22⋊Q8—112no—
403C4×C22⋊Q8—112no—
404C4×#117—111no—
405C23×C11—21no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—21no—
409C23×C11—21no—
410C23×C11—21no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11C22×D412yes—
414C23×C11C2×#4112yes—
415C23×C11C2511yescharacteristic
416C22×D11—21no—
417C22×D11—22no—
418C22×D11—21no—
419C22×D11—22no—
420C22×D11C2×#4112yes—
421D4×C11—28no—
422C2×C4×C11—21no—
423C2×C4×C11—22no—
424C2×C4×C11—21no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—28no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—44no—
442C2×C4×C11C22×D412yes—
443C2×C4×C11C22×D412yes—
444C2×C4×C11C2×#4114yes—
445C2×C4×C11C2×#4112yes—
446C2×C4×C112−1+414yes—
447C22⋊D11—28no—
448C22⋊D11—28no—
449C2×Dic11—28no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—21no—
454C2×Dic11—21no—
455C2×Dic11—21no—
456C2×Dic11—22no—
457C2×Dic11—28no—
458C2×Dic11—28no—
459C2×Dic11—21no—
460C2×Dic11—21no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—44no—
473C2×Dic11C22×D412yes—
474C2×Dic11C22×D412yes—
475C2×Dic11C22×D412yes—
476C2×Dic11C22×D412yes—
477C2×Dic11C2×#4114yes—
478C2×Dic11C2×#4112yes—
479C2×Dic11C2×#4112yes—
480C2×Dic11C2×#4112yes—
481C2×Dic11C2×#4114yes—
482C4×D11—28no—
483C4×D11—44no—
484C4×D11—44no—
485Dic22—28no—
486Dic22—48no—
487Dic22—48no—
488C22×#41—111no—
489#533—228no—
490C2×C4⋊Q8—112no—
491C2×C4⋊Q8—111no—
492C2×C4⋊Q8—111no—
493C2×#125—111no—
494C2×#125—111no—
495C2×#124—112no—
496C2×C22⋊Q8—112no—
497C2×C22⋊Q8—112no—
498C2×C22⋊Q8—112no—
499C2×C22⋊Q8—112no—
500C4×#41—228no—
501C2×C4×Q8—111no—
502C2×C4×Q8—111no—
503C2×C4×Q8—112no—
504C2×C4×Q8—112no—
505C2×C4×D4—111no—
506C2×C4×D4—111no—
507C2×C4×D4—111no—
508C2×C4×D4—111no—
509C2×C4×D4—111no—
510C2×C4×D4C2×D1111yescharacteristic
511C2×#117—111no—
512C2×#117—111no—
513C2×#117—111no—
514C2×#117—111no—
515C2×#117—112no—
516C2×#117C2×D1111yescharacteristic
517C22×C42—111no—
518C22×C42—111no—
519C22×C42—111no—
520#400—111no—
521#400—111no—
522#400—111no—
523#400C2×D1111yescharacteristic
524#399—111no—
525#399—111no—
526#399—111no—
527#399C2×D1111yescharacteristic
528#398—111no—
529#398—111no—
530#398—111no—
531#398C2×D1111yescharacteristic
532#397—111no—
533#397—111no—
534#397—112no—
535#397—112no—
536#397—112no—
537#397—111no—
538#397C2×D1111yescharacteristic
539#397C2×D1112yes—
540#394—112no—
541#394—112no—
542#394—112no—
543#394C2×D1112yes—
544#391—112no—
545#391—112no—
546#391—112no—
547#391—112no—
548#391—112no—
549#390—112no—
550#389—112no—
551#389—112no—
552#389—112no—
553#389—112no—
554#389—112no—
555#389—112no—
556#388—112no—
557#388—112no—
558#388—112no—
559#388—112no—
560#387—112no—
561#387—112no—
562#387—112no—
563#387—112no—
564#385—112no—
565#385—112no—
566#385—112no—
567#385—112no—
568#384—112no—
569#382—112no—
570#380—112no—
571#380—112no—
572C4×C4⋊C4—112no—
573C4×C4⋊C4—112no—
574C4×C4⋊C4—112no—
575C4×C4⋊C4—112no—
576C4×C4⋊C4—111no—
577C4×C4⋊C4—111no—
578C4×C4⋊C4C2×D1112yes—
579C4×C22⋊C4—111no—
580C4×C22⋊C4—112no—
581C4×C22⋊C4—112no—
582C4×C22⋊C4—112no—
583C4×C22⋊C4—112no—
584C4×C22⋊C4C2×D1111yescharacteristic
585C4×C22⋊C4C2×D1112yes—
586#376—111no—
587#376—111no—
588C43—112no—
589C22×C11—22no—
590C22×C11—22no—
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—24no—
594C22×C11—41no—
595C22×C11—41no—
596C22×C11—42no—
597C22×C11—42no—
598C22×C11—42no—
599C22×C11C23×D411yescharacteristic
600C22×C11C22×#4111yescharacteristic
601C22×C11C22×#4111yescharacteristic
602C22×C11C22×#4112yes—
603C22×C11C2×2−1+412yes—
604C2×D11—22no—
605C2×D11—24no—
606C2×D11—41no—
607C2×D11—41no—
608C2×D11—42no—
609C4×C11—22no—
610C4×C11—22no—
611C4×C11—24no—
612C4×C11—42no—
613C4×C11—42no—
614C4×C11—41no—
615C4×C11—41no—
616C4×C11—42no—
617C4×C11#53614yes—
618Dic11—22no—
619Dic11—22no—
620Dic11—22no—
621Dic11—24no—
622Dic11—42no—
623Dic11—42no—
624Dic11—41no—
625Dic11—41no—
626Dic11—42no—
627Dic11#52514yes—
628Dic11#53214yes—
629C2×#41—224no—
630C2×#41—224no—
631C2×#41—224no—
632C22×Q8—111no—
633C22×Q8—112no—
634C22×Q8—112no—
635C22×D4—111no—
636C22×D4—111no—
637C22×D4C22×D1111yescharacteristic
638C23×C4—111no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4C22×D1111yescharacteristic
646C23×C4C22×D1111yescharacteristic
647C4⋊Q8—224no—
648C4⋊Q8—224no—
649C4⋊Q8—228no—
650#125—224no—
651#125—224no—
652#124—228no—
653C22⋊Q8—228no—
654C22⋊Q8—228no—
655C22⋊Q8—228no—
656C22⋊Q8—228no—
657C4×Q8—224no—
658C4×Q8—228no—
659C4×Q8—228no—
660C4×Q8—224no—
661C4×D4—24no—
662C4×D4—224no—
663C4×D4—224no—
664C4×D4—224no—
665C4×D4—224no—
666C4×D4—224no—
667#117—24no—
668#117—224no—
669#117—224no—
670#117—228no—
671#117—224no—
672#117—224no—
673C2×C4⋊C4—112no—
674C2×C4⋊C4—111no—
675C2×C4⋊C4—111no—
676C2×C4⋊C4—111no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—111no—
679C2×C4⋊C4—111no—
680C2×C4⋊C4—111no—
681C2×C4⋊C4—112no—
682C2×C4⋊C4—112no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—112no—
685C2×C4⋊C4—112no—
686C2×C4⋊C4—112no—
687C2×C4⋊C4—112no—
688C2×C4⋊C4—112no—
689C2×C4⋊C4—112no—
690C2×C4⋊C4—112no—
691C2×C4⋊C4—112no—
692C2×C4⋊C4—112no—
693C2×C4⋊C4—112no—
694C2×C4⋊C4C22×D1111yescharacteristic
695C2×C4⋊C4C22×D1111yescharacteristic
696C2×C4⋊C4C22×D1111yescharacteristic
697C2×C4⋊C4C22×D1112yes—
698C2×C4⋊C4C22×D1112yes—
699C2×C22⋊C4—111no—
700C2×C22⋊C4—111no—
701C2×C22⋊C4—112no—
702C2×C22⋊C4—112no—
703C2×C22⋊C4—112no—
704C2×C22⋊C4—112no—
705C2×C22⋊C4—111no—
706C2×C22⋊C4—111no—
707C2×C22⋊C4—112no—
708C2×C22⋊C4—112no—
709C2×C22⋊C4—112no—
710C2×C22⋊C4—112no—
711C2×C22⋊C4C22×D1111yescharacteristic
712C2×C22⋊C4C22×D1111yescharacteristic
713C2×C22⋊C4C22×D1112yes—
714C2×C22⋊C4C22×D1112yes—
715C2×C22⋊C4C22×D1112yes—
716C2×C22⋊C4C22×D1112yes—
717C2×C42—118no—
718C2×C42—111no—
719C2×C42—111no—
720C2×C42—111no—
721C2×C42—111no—
722C2×C42—111no—
723C2×C42—111no—
724C2×C42—112no—
725C2×C42—112no—
726C2×C42—111no—
727C2×C42—111no—
728C2×C42—112no—
729C2×C42—112no—
730C2×C42—112no—
731C2×C42—111no—
732C2×C42—112no—
733C2×C42—224no—
734C2×C42—224no—
735C2×C42C22×D1112yes—
736C2×C42C22×D1111yescharacteristic
737C2×C42C22×D1112yes—
738#95—112no—
739#95—112no—
740#95—111no—
741#95—111no—
742#95—112no—
743#95—112no—
744#95—112no—
745#95—112no—
746#95—112no—
747#95—112no—
748#95—112no—
749#95—112no—
750#95—112no—
751#95—112no—
752#95—112no—
753#95—112no—
754#95C22×D1111yescharacteristic
755#95C22×D1111yescharacteristic
756#95C22×D1112yes—
757#95C22×D1112yes—
758#95C22×D1112yes—
759#95C22×D1112yes—
760C2×C11—42no—
761C2×C11—42no—
762C2×C11C2×#52511yescharacteristic
763C2×C11C2×#53211yescharacteristic
764C2×C11C2×#53611yescharacteristic
765C2×C11#348212yes—
766C2×C11#348212yes—
767D11—42no—
768C24—111no—
769C24C23×D1111yescharacteristic
770C24C23×D1111yescharacteristic
771#41—2232no—
772C2×Q8—114no—
773C2×Q8—222no—
774C2×Q8—222no—
775C2×Q8—224no—
776C2×Q8—224no—
777C2×Q8—224no—
778C2×Q8—224no—
779C2×Q8—224no—
780C2×Q8—224no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—114no—
785C2×D4—222no—
786C2×D4—222no—
787C2×D4—222no—
788C2×D4—222no—
789C2×D4—222no—
790C22×C4—24no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—111no—
794C22×C4—111no—
795C22×C4—114no—
796C22×C4—114no—
797C22×C4—111no—
798C22×C4—112no—
799C22×C4—111no—
800C22×C4—111no—
801C22×C4—112no—
802C22×C4—111no—
803C22×C4—111no—
804C22×C4—112no—
805C22×C4—112no—
806C22×C4—222no—
807C22×C4—222no—
808C22×C4—224no—
809C22×C4—222no—
810C22×C4—222no—
811C22×C4—224no—
812C22×C4—222no—
813C22×C4—222no—
814C22×C4—222no—
815C22×C4—222no—
816C22×C4—224no—
817C22×C4—222no—
818C22×C4—222no—
819C22×C4—222no—
820C22×C4—224no—
821C22×C4D4×D1114yes—
822C22×C4C23×D1112yes—
823C22×C4C23×D1111yescharacteristic
824C22×C4C23×D1111yescharacteristic
825C22×C4C23×D1112yes—
826C22×C4C23×D1112yes—
827C22×C4C23×D1111yescharacteristic
828C22×C4C23×D1112yes—
829C22×C4C23×D1111yescharacteristic
830C22×C4C23×D1111yescharacteristic
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—118no—
837C4⋊C4—222no—
838C4⋊C4—222no—
839C4⋊C4—222no—
840C4⋊C4—222no—
841C4⋊C4—224no—
842C4⋊C4—224no—
843C4⋊C4—224no—
844C4⋊C4—224no—
845C4⋊C4—224no—
846C4⋊C4—224no—
847C4⋊C4—224no—
848C4⋊C4—224no—
849C4⋊C4—224no—
850C4⋊C4—224no—
851C4⋊C4—224no—
852C4⋊C4—222no—
853C4⋊C4—222no—
854C4⋊C4—222no—
855C4⋊C4—224no—
856C4⋊C4—224no—
857C22⋊C4—24no—
858C22⋊C4—22no—
859C22⋊C4—24no—
860C22⋊C4—22no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—222no—
864C22⋊C4—224no—
865C22⋊C4—224no—
866C22⋊C4—224no—
867C22⋊C4—222no—
868C22⋊C4—224no—
869C22⋊C4—224no—
870C22⋊C4—222no—
871C22⋊C4—224no—
872C22⋊C4—224no—
873C22⋊C4—222no—
874C22⋊C4—224no—
875C42—22no—
876C42—24no—
877C42—24no—
878C42—114no—
879C42—114no—
880C42—114no—
881C42—114no—
882C42—222no—
883C42—222no—
884C42—222no—
885C42—222no—
886C42—224no—
887C42—224no—
888C42—224no—
889C42—222no—
890C42—224no—
891C42—224no—
892C42—224no—
893C11#3497911yescharacteristic, complemented, Sylow
894C23—21no—
895C23—22no—
896C23—22no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—22no—
901C23—22no—
902C23—112no—
903C23—221no—
904C23—222no—
905C23—221no—
906C23—222no—
907C23C2×D4×D1112yes—
908C23#41×D1112yes—
909C23C24×D1111yescharacteristic
910Q8—228no—
911Q8—448no—
912Q8—448no—
913D4—28no—
914D4—228no—
915D4—228no—
916C2×C4—21no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—28no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—44no—
936C2×C4—112no—
937C2×C4—112no—
938C2×C4—112no—
939C2×C4—112no—
940C2×C4—114no—
941C2×C4—112no—
942C2×C4—112no—
943C2×C4—114no—
944C2×C4—112no—
945C2×C4—228no—
946C2×C4—228no—
947C2×C4—228no—
948C2×C4—228no—
949C2×C4—221no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—221no—
953C2×C4—221no—
954C2×C4—221no—
955C2×C4—222no—
956C2×C4—221no—
957C2×C4—221no—
958C2×C4—222no—
959C2×C4—222no—
960C2×C4—222no—
961C2×C4—222no—
962C2×C4—222no—
963C2×C4—222no—
964C2×C4—222no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—222no—
968C2×C4—222no—
969C2×C4—444no—
970C2×C4—444no—
971C2×C4—444no—
972C2×C4C2×D4×D1112yes—
973C2×C4C2×D4×D1112yes—
974C2×C4#41×D1114yes—
975C2×C4#41×D1112yes—
976C2×C4#6704314yes—
977C22—22no—
978C22—22no—
979C22—24no—
980C22—22no—
981C22—22no—
982C22—41no—
983C22—41no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—224no—
988C22—222no—
989C22—441no—
990C22—441no—
991C22—442no—
992C22C22×D4×D1111yescharacteristic
993C22C2×#41×D1112yes—
994C22C2×#41×D1111yescharacteristic
995C22C2×#41×D1111yescharacteristic
996C22C2×#6704312yes—
997C4—22no—
998C4—24no—
999C4—22no—
1000C4—41no—
1001C4—42no—
1002C4—41no—
1003C4—42no—
1004C4—42no—
1005C4—114no—
1006C4—114no—
1007C4—222no—
1008C4—224no—
1009C4—222no—
1010C4—222no—
1011C4—441no—
1012C4—442no—
1013C4—441no—
1014C4—442no—
1015C4—442no—
1016C4#1062317914yes—
1017C2—42no—
1018C2—42no—
1019C2—442no—
1020C2D11×#52511yescharacteristic
1021C2D11×#53211yescharacteristic
1022C2C2×#1062317911yescharacteristic
1023C2#1308222912yes—
1024C2#1308222912yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2395C2
prime radicalC22×#4341C22
hypercenter#2395D11
hypocenterC11#34979
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
3. #13074317C2semidirect
4. #13074315C2semidirect
5. #13074309C2semidirect
6. #13074307C2semidirect
7. #13073827C2semidirect
8. #13073607C2semidirect
9. #13073600C2semidirect
10. #13073564C2semidirect
11. #13073064C2semidirect
13. #13072040C2semidirect
14. #13072038C2semidirect
15. #13071876C2semidirect
16. #13071875C2semidirect
17. #13071873C2semidirect
18. C4×#66941C2semidirect
19. C4×#66938C2semidirect
20. C4×#66949C2semidirect
21. C4×#66931C2semidirect
22. C4×#66930C2semidirect
23. C11×#2395C2semidirect
366. Dic11⋊C4#41semidirect
399. #2395D11semidirect
893. C11#34979semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×C4×#43412
#130743172
#130743152
#130743092
#130743072
#130738272
#130736072
#130736002
#130735642
#130730642
#130722392
#130720402
#130720382
#130718762
#130718752
#130718732
C4×#669412
C4×#669382
C4×#669492
C4×#669312
C4×#669302
C11×#23952
#3497911