Finite Group Databasebeta

← #15638488

Subgroups — #15638488

Order 2816.

2370 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082374C211yesmaximal, characteristic
2D4×Q8×D11C211yesmaximal, characteristic, complemented
3#13080480C211yesmaximal, characteristic, complemented
4#13080479C212yesmaximal, complemented
5#13080478C211yesmaximal, characteristic, complemented
6#13080477C212yesmaximal, complemented
7#13080475C211yesmaximal, characteristic, complemented
8#13080315C211yesmaximal, characteristic, complemented
9D4×#4314C211yesmaximal, characteristic, complemented
10SD16×D44C211yesmaximal, characteristic, complemented
11D4×#4325C211yesmaximal, characteristic, complemented
12#13080309C212yesmaximal, complemented
13#13080305C212yesmaximal, complemented
14#13079542C211yesmaximal, characteristic, complemented
15#13079540C211yesmaximal, characteristic, complemented
16#13079372C212yesmaximal, complemented
17#13079368C212yesmaximal, complemented
18#13078649C211yesmaximal, characteristic, complemented
19#13078645C211yesmaximal, characteristic, complemented
20C2×#10622419C212yesmaximal, complemented
21D11×#448C212yesmaximal, complemented
22#13077637C211yesmaximal, characteristic, complemented
23C11×#3298C211yesmaximal, characteristic, complemented
24C2×#67042—21no—
25C22×Q8×D11C2212yescomplemented
26D4×Q8×C11C2211yescharacteristic, complemented
27C11×#547C2211yescharacteristic
28#10623360—21no—
29Q8×C22⋊D11C2212yescomplemented
30C22×#4325C2212yescomplemented
31C2×SD16×D11C2212yescomplemented
32C2×SD16×D11C2212yescomplemented
33C22×#4314C2212yescomplemented
34#10623258—21no—
35#10623258C2211yescharacteristic, complemented
36#10623257C2211yescharacteristic
37#10623256C2211yescharacteristic
38D11×C4⋊Q8—21no—
39D11×C4⋊Q8C2211yescharacteristic, complemented
40#10623185—22no—
41#10623184—22no—
42#10623163—22no—
43#10623163C2212yescomplemented
44#10623161—21no—
45#10623160—21no—
46D11×C22⋊Q8—22no—
47D11×C22⋊Q8C2212yescomplemented
48#10623140C2212yes—
49D11×#121C2212yes—
50Q8×D44C2211yescharacteristic, complemented
51C4×Q8×D11C2211yescharacteristic, complemented
52D4×D44C2211yescharacteristic
53D4×D44C2211yescharacteristic
54#10623079C2211yescharacteristic
55C4×D4×D11—21no—
56C4×D4×D11C2211yescharacteristic
57D4×Dic22—21no—
58D4×Dic22C2211yescharacteristic, complemented
59#10623038C2212yes—
60C2×#66948C2212yes—
61C11×#487C2211yescharacteristic, complemented
62C11×#483C2212yescomplemented
63C11×#475C2211yescharacteristic, complemented
64C11×#465C2212yescomplemented
65C11×#461C2211yescharacteristic, complemented
66C11×#448C2212yescomplemented
67C4×C11×SD16C2211yescharacteristic, complemented
68C8×D4×C11C2211yescharacteristic, complemented
69C2×C11×#103C2212yescomplemented
70#10622840C2212yescomplemented
71#10622788C2212yescomplemented
72#10622783C2211yescharacteristic, complemented
73#10622783C2212yescomplemented
74#10622782C2212yescomplemented
75#10622776C2211yescharacteristic, complemented
76#10622727C2212yescomplemented
77C8×C22⋊D11C2212yescomplemented
78C2×(C2×D11)⋊C8C2212yescomplemented
79#10622707C2211yescharacteristic, complemented
80#10622706C2211yescharacteristic, complemented
81#10622698C2211yescharacteristic, complemented
82#10622696C2211yescharacteristic, complemented
83#10622661C2212yescomplemented
84#10622659C2212yescomplemented
85#10622654C2212yescomplemented
86#10622653C2212yescomplemented
87#10622640C2211yescharacteristic, complemented
88C4×#4325C2211yescharacteristic, complemented
89#10622632C2211yescharacteristic, complemented
90C4×#4324C2211yescharacteristic, complemented
91D4×C11⋊C8C2211yescharacteristic, complemented
92#10622584C2212yescomplemented
93C2×#66874C2212yescomplemented
94#10622477C2212yescomplemented
95#10622477C2212yescomplemented
96#10622476C2212yescomplemented
97#10622476C2211yescharacteristic, complemented
98#10622475C2212yescomplemented
99#10622467C2211yescharacteristic, complemented
100#10622465C2212yescomplemented
101#10622461C2211yescharacteristic, complemented
102#10622454C2211yescharacteristic, complemented
103#10622447C2211yescharacteristic, complemented
104#10622446C2211yescharacteristic, complemented
105#10622431C2212yescomplemented
106#10622431C2212yescomplemented
107#10622420C2212yescomplemented
108#10622420C2212yescomplemented
109#10622419C2212yescomplemented
110#10622419C2212yescomplemented
111#10622419C2211yescharacteristic, complemented
112#10622419C2212yescomplemented
113#10622419C2212yescomplemented
114#10622419C2212yescomplemented
115#10622419C2212yescomplemented
116#10622419C2212yescomplemented
117#10622419C2212yescomplemented
118#10622418C2212yescomplemented
119D11×#103C2212yescomplemented
120D11×#103C2212yescomplemented
121#10622405C2212yescomplemented
122#10622404C2211yescharacteristic, complemented
123#10622401C2212yescomplemented
124#10622390C2211yescharacteristic, complemented
125#10622389C2212yescomplemented
126#10622375C2211yescharacteristic, complemented
127#10622351C2212yescomplemented
128#10622344C2212yescomplemented
129(C22⋊D11)⋊C8C2212yescomplemented
130D11×C22⋊C8C2212yescomplemented
131#10622306C2211yescharacteristic, complemented
132C4×#4314C2211yescharacteristic, complemented
133C8×D44C2211yescharacteristic, complemented
134#10622298C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C22×Q8×C11C2312yes—
137#67042—48no—
138C2×#4343—21no—
139C2×#4343—21no—
140C2×Q8×D11—22no—
141C2×Q8×D11—22no—
142C2×Q8×D11—44no—
143C2×Q8×D11—44no—
144C2×Q8×D11C2311yescharacteristic
145C2×Q8×D11C2312yes—
146C2×Q8×D11C2312yes—
147C2×Q8×D11C2312yes—
148C2×D4×D11—22no—
149C2×D4×D11—21no—
150C2×D4×D11—22no—
151C2×D4×D11D411yescharacteristic
152C2×D4×D11C2312yes—
153C2×#4339—22no—
154C2×#4339—21no—
155C22×D44—22no—
156C22×D44—21no—
157C22×D44C2312yes—
158C22×C4×D11—22no—
159C22×C4×D11C2312yes—
160C22×Dic22—22no—
161C22×Dic22C2312yes—
162C2×C11×SD16C2311yescharacteristic
163C2×C11×SD16C2312yes—
164C22×C8×C11C2312yes—
165C11×C4⋊Q8—21no—
166C11×C4⋊Q8C2311yescharacteristic
167C11×C4⋊Q8C2311yescharacteristic
168C11×#123—22no—
169C11×C22⋊Q8—21no—
170C11×C22⋊Q8—22no—
171C11×C22⋊Q8C2312yes—
172C11×#121C2312yes—
173C4×Q8×C11C2311yescharacteristic
174C4×D4×C11—21no—
175C4×D4×C11C2311yescharacteristic
176C4×D4×C11C2311yescharacteristic
177C2×C11×C4⋊C4C2312yes—
178#67000—21no—
179#66999—22no—
180#66999—21no—
181#66999C2312yes—
182Q8×Dic11C2311yescharacteristic
183#66997—22no—
184#66997C2312yes—
185C2×#4325—44no—
186C2×#4325C2311yescharacteristic
187C2×#4325C2312yes—
188C2×#4325C2312yes—
189C2×#4325C2312yes—
190C2×#4325C2312yes—
191#66993C2311yescharacteristic
192#66992—22no—
193#66991C2311yescharacteristic
194#66990—22no—
195D4×Dic11—21no—
196D4×Dic11D411yescharacteristic
197C2×#4324C2311yescharacteristic
198C2×#4324C2312yes—
199#66983—21no—
200#66983C2312yes—
201#66982—22no—
202C4×C22⋊D11—22no—
203C4×C22⋊D11—21no—
204C4×C22⋊D11C2312yes—
205C2×(C2×D11)⋊C4—22no—
206#66977—22no—
207#66977C2312yes—
208C22×C11⋊C8C2312yes—
209SD16×D11—44no—
210SD16×D11—44no—
211C2×#4314—44no—
212C2×#4314C2312yes—
213C2×#4314C2311yescharacteristic
214C2×#4314C2312yes—
215C2×#4314C2312yes—
216C2×#4314C2312yes—
217C2×C8×D11C2312yes—
218C2×C8×D11C2312yes—
219#66950—22no—
220#66950C2312yes—
221#66949—22no—
222#66949—22no—
223#66949—22no—
224#66949—22no—
225#66948—21no—
226#66948—22no—
227#66948—22no—
228#66948—21no—
229#66948C2312yes—
230#66948C2311yescharacteristic
231#66948C2312yes—
232#66948C2312yes—
233#66947—22no—
234#66947—22no—
235#66946—21no—
236#66946—21no—
237#66946D411yescharacteristic
238#66946C2312yes—
239C4⋊C4×D11—21no—
240C4⋊C4×D11—22no—
241C4⋊C4×D11—21no—
242C4⋊C4×D11—21no—
243C4⋊C4×D11D411yescharacteristic
244C4⋊C4×D11C2312yes—
245C4⋊C4×D11C2311yescharacteristic
246#66941—21no—
247#66941—21no—
248#66941—22no—
249#66941—21no—
250#66941—21no—
251#66941C2311yescharacteristic
252#66940—21no—
253#66940C2311yescharacteristic
254#66938—21no—
255#66937—21no—
256#66937—22no—
257#66937—22no—
258#66935—22no—
259#66935—22no—
260#66935—22no—
261(C22⋊D11)⋊C4—22no—
262(C22⋊D11)⋊C4D412yes—
263C22⋊C4×D11—22no—
264C22⋊C4×D11—22no—
265C22⋊C4×D11D412yes—
266#66931—22no—
267#66931—22no—
268#66931—22no—
269#66927C2311yescharacteristic
270C4×D44—21no—
271C4×D44C2311yescharacteristic
272C4×D44C2311yescharacteristic
273C42×D11—21no—
274C42×D11C2311yescharacteristic
275#66922—21no—
276#66922C2311yescharacteristic
277C4×Dic22—21no—
278C4×Dic22C2311yescharacteristic
279C11×#106C2312yes—
280C11×#106C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×#103C2311yescharacteristic
283C11×#103C2312yes—
284C11×#103C2312yes—
285C11×#103C2312yes—
286C11×#103C2312yes—
287C11×#102C2311yescharacteristic
288C11×C22⋊C8C2312yes—
289C4×C8×C11C2311yescharacteristic
290#66899C2311yescharacteristic
291#66899C2312yes—
292#66896C2311yescharacteristic
293C22⋊(C11⋊C8)C2312yes—
294#66885C2312yes—
295#66885C2311yescharacteristic
296(C2×D11)⋊C8C2311yescharacteristic
297(C2×D11)⋊C8C2312yes—
298(C2×D11)⋊C8C2312yes—
299(C2×D11)⋊C8C2312yes—
300(C2×D11)⋊C8C2311yescharacteristic
301#66881C2311yescharacteristic
302#66880C2311yescharacteristic
303#66880C2312yes—
304Dic11⋊C8C2311yescharacteristic
305Dic11⋊C8C2311yescharacteristic
306C8×Dic11C2312yes—
307#66874C2312yes—
308#66874C2311yescharacteristic
309#66874C2312yes—
310#66874C2312yes—
311#66874C2312yes—
312#66873C2312yes—
313#66873C2311yescharacteristic
314#66872C2311yescharacteristic
315#66872C2311yescharacteristic
316#66872C2312yes—
317C4⋊(C11⋊C8)C2311yescharacteristic
318C4×C11⋊C8C2311yescharacteristic
319#61562—111nomaximal, Sylow
320C23×D11—22no—
321C23×D11—22no—
322C23×D11C2×D412yes—
323C11×#41—44no—
324C2×Q8×C11—22no—
325C2×Q8×C11—21no—
326C2×Q8×C11—24no—
327C2×Q8×C11—42no—
328C2×Q8×C11C2412yes—
329C2×Q8×C11C2411yescharacteristic
330C2×D4×C11—22no—
331C2×D4×C11C2×D411yescharacteristic
332C2×D4×C11C2411yescharacteristic
333C22×C4×C11—22no—
334C22×C4×C11—22no—
335C22×C4×C11—21no—
336C22×C4×C11C2412yes—
337C2×C22⋊D11—21no—
338C2×C22⋊D11—21no—
339C2×C22⋊D11—22no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11—21no—
342C2×C22⋊D11C2×D412yes—
343C22×Dic11—22no—
344C22×Dic11C2×D412yes—
345#4343—44no—
346#4343—44no—
347Q8×D11—22no—
348Q8×D11—24no—
349Q8×D11—22no—
350Q8×D11—24no—
351Q8×D11—42no—
352Q8×D11—42no—
353Q8×D11—42no—
354Q8×D11—42no—
355Q8×D11—48no—
356Q8×D11—48no—
357D4×D11—42no—
358D4×D11—42no—
359D4×D11—48no—
360D4×D11—48no—
361D4×D11—44no—
362D4×D11SD1618yescomplemented
363#4339—48no—
364#4339—44no—
365C2×D44—22no—
366C2×D44—22no—
367C2×D44—21no—
368C2×D44—22no—
369C2×D44—21no—
370C2×D44—21no—
371C2×D44—22no—
372C2×D44—42no—
373C2×D44—42no—
374C2×D44—44no—
375C2×D44—48no—
376C2×D44C2×D411yescharacteristic
377C2×D44C2411yescharacteristic
378C2×D44C2412yes—
379C2×C4×D11—22no—
380C2×C4×D11—21no—
381C2×C4×D11—21no—
382C2×C4×D11—22no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11—21no—
387C2×C4×D11—42no—
388C2×C4×D11—42no—
389C2×C4×D11—48no—
390C2×C4×D11C2×D411yescharacteristic
391C2×C4×D11C2×D412yes—
392C2×C4×D11C2×D412yes—
393C2×C4×D11C2×D411yescharacteristic
394C2×C4×D11C2411yescharacteristic
395C2×C4×D11C2412yes—
396C2×Dic22—21no—
397C2×Dic22—24no—
398C2×Dic22—22no—
399C2×Dic22—22no—
400C2×Dic22—22no—
401C2×Dic22—21no—
402C2×Dic22—22no—
403C2×Dic22—42no—
404C2×Dic22—48no—
405C2×Dic22C2412yes—
406C2×Dic22C2411yescharacteristic
407C11×SD16—22no—
408C11×SD16—42no—
409C2×C8×C11—42no—
410C2×C8×C11C2412yes—
411C2×C8×C11C2411yescharacteristic
412C2×C8×C11C2411yescharacteristic
413C11×C4⋊C4—21no—
414C11×C4⋊C4—21no—
415C11×C4⋊C4—21no—
416C11×C4⋊C4—22no—
417C11×C4⋊C4—21no—
418C11×C4⋊C4—22no—
419C11×C4⋊C4C2×D411yescharacteristic
420C11×C4⋊C4C2411yescharacteristic
421C11×C4⋊C4C2411yescharacteristic
422C11×C4⋊C4C2412yes—
423C11×C22⋊C4—22no—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4C2×D412yes—
427C42×C11—21no—
428C42×C11C2411yescharacteristic
429C22⋊Dic11—21no—
430C22⋊Dic11—22no—
431C22⋊Dic11C2×D412yes—
432#4325—24no—
433#4325—22no—
434#4325—42no—
435#4325—42no—
436#4325—42no—
437#4324—22no—
438#4324—42no—
439(C2×D11)⋊C4—22no—
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—21no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—21no—
447(C2×D11)⋊C4—22no—
448(C2×D11)⋊C4C2×D412yes—
449(C2×D11)⋊C4C2×D412yes—
450C4⋊Dic11—21no—
451C4⋊Dic11—22no—
452C4⋊Dic11—21no—
453C4⋊Dic11—21no—
454C4⋊Dic11C2×D411yescharacteristic
455C4⋊Dic11C2411yescharacteristic
456C4⋊Dic11C2411yescharacteristic
457Dic11⋊C4—21no—
458Dic11⋊C4—21no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—21no—
463Dic11⋊C4—22no—
464Dic11⋊C4—21no—
465Dic11⋊C4—22no—
466Dic11⋊C4C2×D412yes—
467C4×Dic11—21no—
468C4×Dic11—21no—
469C4×Dic11—21no—
470C4×Dic11C2×D411yescharacteristic
471C4×Dic11C2×D411yescharacteristic
472C4×Dic11C2411yescharacteristic
473C2×C11⋊C8—42no—
474C2×C11⋊C8C2411yescharacteristic
475C2×C11⋊C8C2411yescharacteristic
476C2×C11⋊C8C2412yes—
477#4314—22no—
478#4314—24no—
479#4314—42no—
480#4314—42no—
481#4314—42no—
482C8×D11—42no—
483C8×D11—42no—
484#3496—111no—
485C2×D4×Q8—111no—
486#3298—111no—
487#3298—112no—
488#3298—111no—
489#3298—112no—
490#3298—111no—
491#3298D1111yescharacteristic, complemented
492D4×SD16—112no—
493D4×SD16—111no—
494D4×SD16—112no—
495D4×SD16—111no—
496D4×SD16—111no—
497D4×SD16—111no—
498#3206—111no—
499#3206—111no—
500#3187—112no—
501#3187—112no—
502#3103—111no—
503#3103—111no—
504C2×#448—112no—
505C2×#448—112no—
506#2972—111no—
507C23×C11—21no—
508C23×C11C22×D412yes—
509C22×D11—22no—
510C22×D11—21no—
511C22×D11—42no—
512C22×D11—42no—
513C22×D11—44no—
514C22×D11—44no—
515C22×D11—82no—
516C22×D11—82no—
517C22×D11—82no—
518C22×D11—82no—
519C22×D11C2×SD1618yescomplemented
520C22×D11C22×D412yes—
521C22×D11C22×D411yescharacteristic
522Q8×C11—21no—
523Q8×C11—22no—
524Q8×C11—22no—
525Q8×C11—44no—
526Q8×C11—42no—
527Q8×C11H(5,𝔽2)12yescomplemented
528D4×C11—21no—
529D4×C11—21no—
530D4×C11—44no—
531D4×C11C2×SD1614yescomplemented
532C2×C4×C11—21no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—21no—
536C2×C4×C11—22no—
537C2×C4×C11—21no—
538C2×C4×C11—22no—
539C2×C4×C11—44no—
540C2×C4×C11—44no—
541C2×C4×C11—42no—
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D412yes—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C2511yescharacteristic
546C22⋊D11—44no—
547C22⋊D11—42no—
548C22⋊D11—42no—
549C22⋊D11—82no—
550C22⋊D11—81no—
551C22⋊D11C2×SD1618yescomplemented
552C2×Dic11—21no—
553C2×Dic11—21no—
554C2×Dic11—22no—
555C2×Dic11—21no—
556C2×Dic11—42no—
557C2×Dic11—44no—
558C2×Dic11C22×D411yescharacteristic
559C2×Dic11C22×D411yescharacteristic
560C2×Dic11C22×D412yes—
561C2×Dic11C22×D411yescharacteristic
562D44—21no—
563D44—22no—
564D44—22no—
565D44—21no—
566D44—44no—
567D44—42no—
568D44—44no—
569D44—44no—
570D44—42no—
571D44—81no—
572D44—82no—
573D44C2×SD1614yescomplemented
574C4×D11—24no—
575C4×D11—22no—
576C4×D11—22no—
577C4×D11—21no—
578C4×D11—21no—
579C4×D11—42no—
580C4×D11—42no—
581C4×D11—41no—
582C4×D11—44no—
583C4×D11—44no—
584C4×D11—42no—
585C4×D11—44no—
586C4×D11—44no—
587C4×D11—42no—
588C4×D11—44no—
589C4×D11C2×SD1614yescomplemented
590Dic22—24no—
591Dic22—21no—
592Dic22—22no—
593Dic22—22no—
594Dic22—44no—
595Dic22—44no—
596Dic22—44no—
597Dic22—44no—
598Dic22—42no—
599Dic22H(5,𝔽2)12yescomplemented
600C8×C11—21no—
601C8×C11—22no—
602C8×C11—21no—
603C11⋊C8—21no—
604C11⋊C8—22no—
605C11⋊C8—21no—
606C2×H(5,𝔽2)—221no—
607C23×Q8—112no—
608C22×SD16—112no—
609C22×SD16—112no—
610C22×SD16—112no—
611C22×SD16—112no—
612D4×Q8—112no—
613D4×Q8—111no—
614D4×Q8—112no—
615D4×Q8—111no—
616D4×Q8—111no—
617D4×Q8—221no—
618D4×Q8—222no—
619D4×Q8—221no—
620D4×Q8C2×D1111yescharacteristic, complemented
621#547—111no—
622#547—112no—
623#547C2×D1111yescharacteristic
624#546—221no—
625#546—222no—
626#546—221no—
627D42—112no—
628D42—111no—
629D42—111no—
630#537—221no—
631#534—222no—
632#532—111no—
633#532—111no—
634C2×C4⋊Q8—111no—
635C2×C4⋊Q8—221no—
636C2×C22⋊Q8—112no—
637C2×C22⋊Q8—222no—
638C2×#121—112no—
639C2×#121—112no—
640C2×C4×Q8—111no—
641C2×C4×D4—111no—
642C2×C4×D4—221no—
643#492—112no—
644#492—111no—
645#492—111no—
646#487—111no—
647#487—112no—
648#487C2×D1111yescharacteristic, complemented
649#483—112no—
650#483—112no—
651#483—112no—
652#483C2×D1112yescomplemented
653#481—112no—
654#481—111no—
655#481—111no—
656#475—111no—
657#475—111no—
658#475—111no—
659#475C2×D1111yescharacteristic, complemented
660#465—112no—
661#465—112no—
662#465—112no—
663#465—112no—
664#465—112no—
665#465—112no—
666#465—112no—
667#465C2×D1112yescomplemented
668#461—111no—
669#461—111no—
670#461—111no—
671#461—112no—
672#461—112no—
673#461C2×D1111yescharacteristic, complemented
674#460—111no—
675#460—111no—
676#460—111no—
677#460—111no—
678#450—112no—
679#450—112no—
680#450—112no—
681#450—112no—
682#448—112no—
683#448—111no—
684#448—112no—
685#448—112no—
686#448—112no—
687#448—111no—
688#448—112no—
689#448—112no—
690#448—112no—
691#448—112no—
692#448—112no—
693#448—112no—
694#448—112no—
695#448—112no—
696#448C2×D1112yescomplemented
697C4×SD16—111no—
698C4×SD16—111no—
699C4×SD16—112no—
700C4×SD16—112no—
701C4×SD16—111no—
702C4×SD16C2×D1111yescharacteristic, complemented
703C8×D4—112no—
704C8×D4—111no—
705C8×D4—111no—
706C8×D4—112no—
707C8×D4—111no—
708C8×D4C2×D1111yescharacteristic, complemented
709#431—111no—
710#431—111no—
711C2×#103—112no—
712C2×#103—112no—
713C2×#103—112no—
714C2×#103C2×D1112yescomplemented
715C2×C22⋊C8—112no—
716C2×C22⋊C8—112no—
717C22×C11—22no—
718C22×C11—22no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11—41no—
722C22×C11C22×SD1614yes—
723C22×C11C23×D411yescharacteristic
724C2×D11—21no—
725C2×D11—22no—
726C2×D11—21no—
727C2×D11—22no—
728C2×D11—48no—
729C2×D11—42no—
730C2×D11—41no—
731C2×D11—41no—
732C2×D11—42no—
733C2×D11—41no—
734C2×D11—42no—
735C2×D11—164no—
736C2×D11—164no—
737C2×D11C22×SD1614yes—
738C2×D11C22×SD1612yes—
739C4×C11—21no—
740C4×C11—22no—
741C4×C11—22no—
742C4×C11—41no—
743C4×C11—42no—
744C4×C11—41no—
745C4×C11—42no—
746C4×C11C22×SD1612yes—
747C4×C11C2×H(5,𝔽2)11yescharacteristic
748C4×C11C2×H(5,𝔽2)11yescharacteristic
749Dic11—21no—
750Dic11—21no—
751Dic11—22no—
752Dic11—22no—
753Dic11—41no—
754Dic11—42no—
755Dic11—41no—
756Dic11C22×SD1612yes—
757H(5,𝔽2)—448no—
758C2×#41—21no—
759C2×#41—221no—
760C2×#41—222no—
761C2×#41—221no—
762C2×#41—221no—
763C22×Q8—111no—
764C22×Q8—112no—
765C22×Q8—112no—
766C22×Q8—112no—
767C22×Q8—112no—
768C22×Q8—222no—
769C22×Q8—222no—
770C22×Q8—222no—
771C22×Q8—444no—
772C22×Q8—444no—
773C22×Q8C22×D1112yes—
774C22×D4—111no—
775C22×D4—112no—
776C22×D4—112no—
777C22×D4—221no—
778C22×D4—222no—
779C22×D4—222no—
780C22×D4—222no—
781C22×D4—221no—
782C23×C4—112no—
783C23×C4—222no—
784C2×SD16—111no—
785C2×SD16—112no—
786C2×SD16—111no—
787C2×SD16—112no—
788C2×SD16—112no—
789C2×SD16—112no—
790C2×SD16—112no—
791C2×SD16—112no—
792C2×SD16—111no—
793C2×SD16—112no—
794C2×SD16—112no—
795C2×SD16—112no—
796C2×SD16—444no—
797C2×SD16—444no—
798C2×SD16—444no—
799C2×SD16—444no—
800C2×SD16C22×D1111yescharacteristic
801C2×SD16C22×D1112yes—
802C22×C8—112no—
803C22×C8—112no—
804C22×C8—112no—
805C22×C8C22×D1112yes—
806C4⋊Q8—21no—
807C4⋊Q8—111no—
808C4⋊Q8—112no—
809C4⋊Q8—111no—
810C4⋊Q8—221no—
811C4⋊Q8—221no—
812C4⋊Q8—221no—
813C4⋊Q8—222no—
814C4⋊Q8—221no—
815C4⋊Q8—222no—
816C4⋊Q8—221no—
817C4⋊Q8C22×D1111yescharacteristic
818C4⋊Q8C22×D1111yescharacteristic
819#127—111no—
820#127—111no—
821#124—221no—
822#124—221no—
823#123—22no—
824#123—222no—
825#123—222no—
826#123—222no—
827C22⋊Q8—21no—
828C22⋊Q8—22no—
829C22⋊Q8—112no—
830C22⋊Q8—112no—
831C22⋊Q8—112no—
832C22⋊Q8—222no—
833C22⋊Q8—222no—
834C22⋊Q8—222no—
835C22⋊Q8—222no—
836C22⋊Q8—222no—
837C22⋊Q8—222no—
838C22⋊Q8—222no—
839C22⋊Q8—222no—
840C22⋊Q8—222no—
841C22⋊Q8—221no—
842C22⋊Q8—222no—
843C22⋊Q8C22×D1112yes—
844#121—111no—
845#121—112no—
846#121—112no—
847#121—111no—
848#121—112no—
849#121—112no—
850#121—222no—
851#121—222no—
852#121—221no—
853#121—222no—
854#121—222no—
855#121—221no—
856#121—221no—
857#121—222no—
858#121—221no—
859#121C22×D1112yes—
860#120—222no—
861#120—222no—
862#120—222no—
863#120—222no—
864C4×Q8—111no—
865C4×Q8—111no—
866C4×Q8—111no—
867C4×Q8—221no—
868C4×Q8—221no—
869C4×Q8C22×D1111yescharacteristic
870C4×D4—21no—
871C4×D4—111no—
872C4×D4—112no—
873C4×D4—111no—
874C4×D4—112no—
875C4×D4—112no—
876C4×D4—111no—
877C4×D4—111no—
878C4×D4—221no—
879C4×D4—221no—
880C4×D4—221no—
881C4×D4—222no—
882C4×D4—221no—
883C4×D4—222no—
884C4×D4—221no—
885C4×D4C22×D1111yescharacteristic
886C4×D4C22×D1111yescharacteristic
887C2×C4⋊C4—111no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—112no—
890C2×C4⋊C4—221no—
891C2×C4⋊C4—221no—
892C2×C4⋊C4—222no—
893C2×C4⋊C4—221no—
894C2×C4⋊C4C22×D1112yes—
895C2×C22⋊C4—112no—
896C2×C22⋊C4—222no—
897C2×C22⋊C4—222no—
898C2×C22⋊C4—222no—
899C2×C42—111no—
900C2×C42—221no—
901#106—111no—
902#106—112no—
903#106—111no—
904#106—111no—
905#106C22×D1112yes—
906#106C22×D1111yescharacteristic
907C4⋊C8—111no—
908C4⋊C8—111no—
909C4⋊C8—111no—
910C4⋊C8C22×D1111yescharacteristic
911#103—111no—
912#103—112no—
913#103—111no—
914#103—112no—
915#103—112no—
916#103—111no—
917#103—112no—
918#103—112no—
919#103—112no—
920#103C22×D1112yes—
921#103C22×D1112yes—
922#103C22×D1111yescharacteristic
923#103C22×D1112yes—
924#103C22×D1112yes—
925#102—111no—
926#102—112no—
927#102—111no—
928#102—112no—
929#102—111no—
930#102C22×D1111yescharacteristic
931C22⋊C8—112no—
932C22⋊C8—112no—
933C22⋊C8—111no—
934C22⋊C8—111no—
935C22⋊C8—112no—
936C22⋊C8—112no—
937C22⋊C8C22×D1112yes—
938C4×C8—112no—
939C4×C8—111no—
940C4×C8C22×D1111yescharacteristic
941C2×C11—24no—
942C2×C11—81no—
943C2×C11#348411yescharacteristic
944C2×C11C23×SD1611yescharacteristic
945C2×C11#358611yescharacteristic
946D11—22no—
947D11—24no—
948D11—82no—
949D11—81no—
950C24—112no—
951C24—222no—
952C24—222no—
953#41—44no—
954#41—444no—
955#41—448no—
956#41—444no—
957#41—444no—
958C2×Q8—21no—
959C2×Q8—22no—
960C2×Q8—24no—
961C2×Q8—42no—
962C2×Q8—111no—
963C2×Q8—112no—
964C2×Q8—221no—
965C2×Q8—221no—
966C2×Q8—222no—
967C2×Q8—222no—
968C2×Q8—222no—
969C2×Q8—224no—
970C2×Q8—222no—
971C2×Q8—222no—
972C2×Q8—222no—
973C2×Q8—224no—
974C2×Q8—224no—
975C2×Q8—442no—
976C2×Q8—448no—
977C2×Q8—442no—
978C2×Q8—442no—
979C2×Q8—442no—
980C2×Q8—442no—
981C2×Q8—448no—
982C2×Q8—448no—
983C2×Q8C23×D1112yes—
984C2×Q8C23×D1111yescharacteristic
985C2×D4—22no—
986C2×D4—112no—
987C2×D4—118no—
988C2×D4—111no—
989C2×D4—112no—
990C2×D4—111no—
991C2×D4—222no—
992C2×D4—222no—
993C2×D4—221no—
994C2×D4—222no—
995C2×D4—221no—
996C2×D4—221no—
997C2×D4—222no—
998C2×D4—221no—
999C2×D4—222no—
1000C2×D4—221no—
1001C2×D4—221no—
1002C2×D4—222no—
1003C2×D4—442no—
1004C2×D4—442no—
1005C2×D4—444no—
1006C2×D4—448no—
1007C2×D4—442no—
1008C2×D4—442no—
1009C2×D4—448no—
1010C2×D4—448no—
1011C2×D4—444no—
1012C2×D4D4×D1111yescharacteristic
1013C2×D4C23×D1111yescharacteristic
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—21no—
1017C22×C4—111no—
1018C22×C4—112no—
1019C22×C4—111no—
1020C22×C4—112no—
1021C22×C4—111no—
1022C22×C4—112no—
1023C22×C4—112no—
1024C22×C4—222no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—222no—
1028C22×C4—222no—
1029C22×C4—222no—
1030C22×C4—222no—
1031C22×C4—222no—
1032C22×C4—221no—
1033C22×C4—442no—
1034C22×C4—442no—
1035C22×C4—448no—
1036C22×C4C23×D1112yes—
1037SD16—22no—
1038SD16—42no—
1039SD16—222no—
1040SD16—224no—
1041SD16—222no—
1042SD16—224no—
1043SD16—222no—
1044SD16—442no—
1045SD16—442no—
1046SD16—442no—
1047SD16—442no—
1048SD16—442no—
1049SD16—442no—
1050SD16—442no—
1051C2×C8—42no—
1052C2×C8—112no—
1053C2×C8—111no—
1054C2×C8—111no—
1055C2×C8—442no—
1056C2×C8—442no—
1057C2×C8—442no—
1058C2×C8C23×D1112yes—
1059C2×C8C23×D1111yescharacteristic
1060C2×C8C23×D1111yescharacteristic
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—21no—
1067C4⋊C4—112no—
1068C4⋊C4—111no—
1069C4⋊C4—111no—
1070C4⋊C4—111no—
1071C4⋊C4—221no—
1072C4⋊C4—222no—
1073C4⋊C4—222no—
1074C4⋊C4—221no—
1075C4⋊C4—221no—
1076C4⋊C4—222no—
1077C4⋊C4—222no—
1078C4⋊C4—222no—
1079C4⋊C4—221no—
1080C4⋊C4—221no—
1081C4⋊C4—221no—
1082C4⋊C4—222no—
1083C4⋊C4—221no—
1084C4⋊C4D4×D1111yescharacteristic
1085C4⋊C4C23×D1111yescharacteristic
1086C4⋊C4C23×D1112yes—
1087C4⋊C4C23×D1111yescharacteristic
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—21no—
1091C22⋊C4—112no—
1092C22⋊C4—112no—
1093C22⋊C4—112no—
1094C22⋊C4—221no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C22⋊C4—222no—
1100C22⋊C4—222no—
1101C22⋊C4—221no—
1102C22⋊C4—222no—
1103C22⋊C4—222no—
1104C22⋊C4—221no—
1105C22⋊C4D4×D1112yes—
1106C42—21no—
1107C42—111no—
1108C42—111no—
1109C42—111no—
1110C42—221no—
1111C42—221no—
1112C42—221no—
1113C42C23×D1111yescharacteristic
1114C11#6156211yescharacteristic, complemented, Sylow
1115C23—21no—
1116C23—112no—
1117C23—111no—
1118C23—118no—
1119C23—221no—
1120C23—222no—
1121C23—442no—
1122C23—442no—
1123C23—444no—
1124C23—444no—
1125C23—882no—
1126C23—882no—
1127C23—882no—
1128C23—882no—
1129C23C2×D4×D1112yes—
1130Q8—21no—
1131Q8—22no—
1132Q8—22no—
1133Q8—44no—
1134Q8—42no—
1135Q8—112no—
1136Q8—224no—
1137Q8—221no—
1138Q8—222no—
1139Q8—222no—
1140Q8—444no—
1141Q8—444no—
1142Q8—442no—
1143Q8—444no—
1144Q8—444no—
1145Q8#6704212yescomplemented
1146D4—21no—
1147D4—21no—
1148D4—44no—
1149D4—118no—
1150D4—114no—
1151D4—222no—
1152D4—221no—
1153D4—221no—
1154D4—222no—
1155D4—442no—
1156D4—444no—
1157D4—444no—
1158D4—444no—
1159D4—442no—
1160D4—442no—
1161D4—444no—
1162D4—442no—
1163D4—882no—
1164D4—881no—
1165D4—882no—
1166D4—881no—
1167D4SD16×D1114yescomplemented
1168C2×C4—21no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—44no—
1176C2×C4—44no—
1177C2×C4—42no—
1178C2×C4—111no—
1179C2×C4—114no—
1180C2×C4—111no—
1181C2×C4—111no—
1182C2×C4—112no—
1183C2×C4—224no—
1184C2×C4—221no—
1185C2×C4—222no—
1186C2×C4—221no—
1187C2×C4—222no—
1188C2×C4—221no—
1189C2×C4—221no—
1190C2×C4—221no—
1191C2×C4—222no—
1192C2×C4—442no—
1193C2×C4—442no—
1194C2×C4—441no—
1195C2×C4—444no—
1196C2×C4—444no—
1197C2×C4—444no—
1198C2×C4—444no—
1199C2×C4—444no—
1200C2×C4—442no—
1201C2×C4—442no—
1202C2×C4—444no—
1203C2×C4—442no—
1204C2×C4C2×D4×D1111yescharacteristic
1205C2×C4C2×D4×D1112yes—
1206C2×C4C2×D4×D1111yescharacteristic
1207C2×C4C24×D1111yescharacteristic
1208C8—21no—
1209C8—21no—
1210C8—22no—
1211C8—222no—
1212C8—221no—
1213C8—221no—
1214C22—22no—
1215C22—22no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—112no—
1220C22—114no—
1221C22—221no—
1222C22—222no—
1223C22—221no—
1224C22—222no—
1225C22—448no—
1226C22—442no—
1227C22—441no—
1228C22—441no—
1229C22—442no—
1230C22—442no—
1231C22—441no—
1232C22—1764no—
1233C22—1764no—
1234C22C2×SD16×D1114yes—
1235C22C22×D4×D1111yescharacteristic
1236C4—21no—
1237C4—22no—
1238C4—22no—
1239C4—41no—
1240C4—42no—
1241C4—41no—
1242C4—42no—
1243C4—112no—
1244C4—221no—
1245C4—221no—
1246C4—222no—
1247C4—222no—
1248C4—441no—
1249C4—442no—
1250C4—441no—
1251C4C2×SD16×D1112yes—
1252C4C2×#6704211yescharacteristic
1253C4D11×H(5,𝔽2)11yescharacteristic
1254C2—24no—
1255C2—81no—
1256C2—222no—
1257C2—224no—
1258C2—881no—
1259C2—882no—
1260C2#1308224611yescharacteristic
1261C2C22×SD16×D1111yescharacteristic
1262C2#1308340111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3298C2
socleC22×C11C23×D4
prime radical#13082374C2
hypercenter#3298D11
hypocenterC11#61562
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3298

Complements

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

NH ≅ G/Ntype
2. D4×Q8×D11C2semidirect
3. #13080480C2semidirect
4. #13080479C2semidirect
5. #13080478C2semidirect
6. #13080477C2semidirect
7. #13080475C2semidirect
8. #13080315C2semidirect
9. D4×#4314C2semidirect
10. SD16×D44C2semidirect
11. D4×#4325C2semidirect
12. #13080309C2semidirect
13. #13080305C2semidirect
14. #13079542C2semidirect
15. #13079540C2semidirect
16. #13079372C2semidirect
17. #13079368C2semidirect
18. #13078649C2semidirect
19. #13078645C2semidirect
20. C2×#10622419C2semidirect
21. D11×#448C2semidirect
22. #13077637C2semidirect
23. C11×#3298C2semidirect
25. C22×Q8×D11C22semidirect
26. D4×Q8×C11C22semidirect
29. Q8×C22⋊D11C22semidirect
30. C22×#4325C22semidirect
31. C2×SD16×D11C22semidirect
32. C2×SD16×D11C22semidirect
33. C22×#4314C22semidirect
35. #10623258C22semidirect
39. D11×C4⋊Q8C22semidirect
43. #10623163C22semidirect
47. D11×C22⋊Q8C22semidirect
50. Q8×D44C22semidirect
51. C4×Q8×D11C22semidirect
58. D4×Dic22C22semidirect
61. C11×#487C22semidirect
62. C11×#483C22semidirect
63. C11×#475C22semidirect
64. C11×#465C22semidirect
65. C11×#461C22semidirect
66. C11×#448C22semidirect
67. C4×C11×SD16C22semidirect
68. C8×D4×C11C22semidirect
69. C2×C11×#103C22semidirect
70. #10622840C22semidirect
71. #10622788C22semidirect
72. #10622783C22semidirect
73. #10622783C22semidirect
74. #10622782C22semidirect
75. #10622776C22semidirect
76. #10622727C22semidirect
77. C8×C22⋊D11C22semidirect
78. C2×(C2×D11)⋊C8C22semidirect
79. #10622707C22semidirect
80. #10622706C22semidirect
81. #10622698C22semidirect
82. #10622696C22semidirect
83. #10622661C22semidirect
84. #10622659C22semidirect
85. #10622654C22semidirect
86. #10622653C22semidirect
87. #10622640C22semidirect
88. C4×#4325C22semidirect
89. #10622632C22semidirect
90. C4×#4324C22semidirect
91. D4×C11⋊C8C22semidirect
92. #10622584C22semidirect
93. C2×#66874C22semidirect
94. #10622477C22semidirect
95. #10622477C22semidirect
96. #10622476C22semidirect
97. #10622476C22semidirect
98. #10622475C22semidirect
99. #10622467C22semidirect
100. #10622465C22semidirect
101. #10622461C22semidirect
102. #10622454C22semidirect
103. #10622447C22semidirect
104. #10622446C22semidirect
105. #10622431C22semidirect
106. #10622431C22semidirect
107. #10622420C22semidirect
108. #10622420C22semidirect
109. #10622419C22semidirect
110. #10622419C22semidirect
111. #10622419C22semidirect
112. #10622419C22semidirect
113. #10622419C22semidirect
114. #10622419C22semidirect
115. #10622419C22semidirect
116. #10622419C22semidirect
117. #10622419C22semidirect
118. #10622418C22semidirect
119. D11×#103C22semidirect
120. D11×#103C22semidirect
121. #10622405C22semidirect
122. #10622404C22semidirect
123. #10622401C22semidirect
124. #10622390C22semidirect
125. #10622389C22semidirect
126. #10622375C22semidirect
127. #10622351C22semidirect
128. #10622344C22semidirect
129. (C22⋊D11)⋊C8C22semidirect
130. D11×C22⋊C8C22semidirect
131. #10622306C22semidirect
132. C4×#4314C22semidirect
133. C8×D44C22semidirect
134. #10622298C22semidirect
362. D4×D11SD16semidirect
491. #3298D11semidirect
519. C22×D11C2×SD16semidirect
527. Q8×C11H(5,𝔽2)semidirect
531. D4×C11C2×SD16semidirect
551. C22⋊D11C2×SD16semidirect
573. D44C2×SD16semidirect
589. C4×D11C2×SD16semidirect
599. Dic22H(5,𝔽2)semidirect
620. D4×Q8C2×D11semidirect
648. #487C2×D11semidirect
652. #483C2×D11semidirect
659. #475C2×D11semidirect
667. #465C2×D11semidirect
673. #461C2×D11semidirect
696. #448C2×D11semidirect
702. C4×SD16C2×D11semidirect
708. C8×D4C2×D11semidirect
714. C2×#103C2×D11semidirect
1114. C11#61562semidirect
1145. Q8#67042semidirect
1167. D4SD16×D11semidirect

Maximal subgroups

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

subgroupindex
#130823742
D4×Q8×D112
#130804802
#130804792
#130804782
#130804772
#130804752
#130803152
D4×#43142
SD16×D442
D4×#43252
#130803092
#130803052
#130795422
#130795402
#130793722
#130793682
#130786492
#130786452
C2×#106224192
D11×#4482
#130776372
C11×#32982
#6156211