Finite Group Databasebeta

← #14769562

Subgroups — #14769562

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66968C211yesmaximal, characteristic
2C2×SD16×Dic11C211yesmaximal, characteristic, complemented
3Q8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#13071441C211yesmaximal, characteristic
5#13069487C211yesmaximal, characteristic, complemented
6#13069475C211yesmaximal, characteristic, complemented
7#13068957C211yesmaximal, characteristic, complemented
8#13068955C211yesmaximal, characteristic, complemented
9#13068950C211yesmaximal, characteristic, complemented
10#13068948C211yesmaximal, characteristic, complemented
11#13068650C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic
13#13068549C211yesmaximal, characteristic, complemented
14#13068401C211yesmaximal, characteristic, complemented
15C2×C11×#440C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×#4341C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C22×#4324C2211yescharacteristic
25C2×#66968—24no—
26C2×#66968—24no—
27C2×#66968C418yescomplemented
28C22×Dic44C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C11×#440—24no—
31C2×C11×#107C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622826—21no—
38C2×C11⋊#95—21no—
39SD16×Dic11—24no—
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×#66881C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45#10622600—21no—
46#10622600C2211yescharacteristic
47#10622600C2211yescharacteristic
48#10622587—21no—
49#10622587C2211yescharacteristic
50#10622587C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66874C2211yescharacteristic
53#10622571—21no—
54#10622556—21no—
55C4×(C2×D11)⋊C4—21no—
56C4×(C2×D11)⋊C4C2211yescharacteristic
57#10622542—21no—
58#10622542C2211yescharacteristic
59#10622542C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622162C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C23×Dic11—21no—
70C2×Q8×D11—22no—
71C2×Q8×D11—22no—
72C2×Q8×D11—22no—
73C2×Q8×D11—41no—
74C2×Q8×D11—41no—
75C2×Q8×D11C2×C414yescomplemented
76C2×#4341—22no—
77C2×#4341—22no—
78C2×#4341—22no—
79C2×#4341—41no—
80C2×#4341—41no—
81C2×#4341C2×C414yes—
82C22×C4×D11—21no—
83C22×C4×D11C2311yescharacteristic
84C22×Dic22—21no—
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C2×C11×SD16C2×C414yes—
88C2×C11×SD16D414yes—
89C2×C11×SD16D414yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×Q8×C11—22no—
93C4×Q8×C11—41no—
94C4×D4×C11—22no—
95C4×D4×C11—41no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103Q8×Dic11—22no—
104Q8×Dic11—41no—
105C2×#4326—22no—
106C2×#4326—22no—
107C2×#4326C2×C414yescomplemented
108D4×Dic11—22no—
109D4×Dic11—41no—
110C2×#4324—22no—
111C2×#4324—22no—
112C2×#4324C2×C414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4D411yescharacteristic
116C2×(C2×D11)⋊C4D411yescharacteristic
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4×Dic11—21no—
121C2×C4×Dic11C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124#66968—232no—
125C2×Dic44—22no—
126C2×Dic44—22no—
127C2×Dic44C2×C414yescomplemented
128C2×#4313—22no—
129C2×#4313—22no—
130C2×#4313C2×C414yescomplemented
131C11×#107—22no—
132C11×#103—22no—
133C11×#102—22no—
134C11×#97—22no—
135#66899—22no—
136#66896—22no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95D411yescharacteristic
148C11⋊#95D411yescharacteristic
149(C2×D11)⋊C8—22no—
150#66881—22no—
151#66880—41no—
152#66880—41no—
153C8×Dic11—22no—
154#66874—41no—
155#66874—41no—
156#22444—111nomaximal, Sylow
157C24×C11—21no—
158C23×D11C2×D411yescharacteristic
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11C22×C412yes—
163C2×Q8×C11C2×D412yes—
164C2×Q8×C11C2×D412yes—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11C22×C412yes—
169C2×D4×C11C2×D412yes—
170C2×D4×C11C2×D412yes—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—81no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C2×C22⋊D11—24no—
181C2×C22⋊D11—42no—
182C2×C22⋊D11—42no—
183C22×Dic11—24no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—42no—
189C22×Dic11—42no—
190C22×Dic11—42no—
191C22×Dic11—42no—
192C22×Dic11—81no—
193C22×Dic11C2×D411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195C22×Dic11C2×D411yescharacteristic
196Q8×D11—28no—
197Q8×D11—44no—
198Q8×D11—44no—
199Q8×D11—44no—
200#4341—28no—
201#4341—44no—
202#4341—44no—
203#4341—44no—
204C2×C4×D11—24no—
205C2×C4×D11—21no—
206C2×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11C22×C412yes—
212C2×C4×D11#4112yes—
213C2×Dic22—24no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—42no—
225C2×Dic22—42no—
226C2×Dic22C22×C412yes—
227C2×Dic22C22×C412yes—
228C11×SD16C22⋊C4116yescomplemented
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11C22×C412yes—
233C2×C8×C11C2×D412yes—
234C2×C8×C11C2×D412yes—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—42no—
240C11×C22⋊C4—42no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—42no—
244C22⋊Dic11—42no—
245#4326—28no—
246#4324—28no—
247(C2×D11)⋊C4—22no—
248(C2×D11)⋊C4—41no—
249(C2×D11)⋊C4—42no—
250(C2×D11)⋊C4—81no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—42no—
256C4×Dic11—21no—
257C4×Dic11—21no—
258C4×Dic11—42no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8C22×C412yes—
265Dic44—28no—
266#4313—28no—
267C22×#137—111no—
268C2×#440D1111yescharacteristic, complemented
269C2×C4×SD16—111no—
270Q8×C22⋊C4—111no—
271#2339—111no—
272#1971—111no—
273#1969—111no—
274#1878—111no—
275#1878—111no—
276#1877—111no—
277#1877—111no—
278#1809—111no—
279#1788—111no—
280#1787—111no—
281#1753—111no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11C22×D411yescharacteristic
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11C4×D412yes—
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11C2×C22⋊C414yes—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11C2×C22⋊C414yes—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—84no—
321C2×C4×C11C23×C411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C22⋊D11—48no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—48no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—84no—
349C2×Dic11C4×D412yes—
350C2×Dic11#13712yescomplemented
351C4×D11—22no—
352C4×D11—22no—
353C4×D11—22no—
354C4×D11—22no—
355C4×D11—48no—
356Dic22—22no—
357Dic22—22no—
358Dic22—22no—
359Dic22—22no—
360Dic22—48no—
361Dic22—41no—
362Dic22—41no—
363Dic22—41no—
364Dic22—41no—
365C8×C11—41no—
366C8×C11C2×C22⋊C414yes—
367C11⋊C8—22no—
368C11⋊C8—41no—
369C22×#41—111no—
370C23×Q8—111no—
371C2×#137—118no—
372C2×#137—224no—
373C2×#137—224no—
374C22×Q16—111no—
375C22×Q16—111no—
376C22×SD16—111no—
377C22×SD16C2×D1111yescharacteristic
378C22×M16—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8C2×D1111yescharacteristic
381C2×C4×D4—111no—
382C2×C4×D4C2×D1111yescharacteristic
383#440—24no—
384C4×SD16—224no—
385C2×#107C2×D1111yescharacteristic
386C2×#106—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#103C2×D1111yescharacteristic
393C2×#102—111no—
394C2×#102C2×D1111yescharacteristic
395C2×C22⋊C8—111no—
396C2×#97C2×D1111yescharacteristic
397C2×C4×C8—111no—
398#391—111no—
399#391—111no—
400#391—111no—
401#391—111no—
402#391—221no—
403#391—221no—
404#386—221no—
405#386—221no—
406#381—221no—
407#380—111no—
408#380—111no—
409#380—221no—
410C4×C22⋊C4—111no—
411C4×C22⋊C4—221no—
412C2×#95—221no—
413#340—111no—
414#340—111no—
415#336—111no—
416#336—111no—
417C22×C11—24no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11C2×C4×D411yescharacteristic
425C22×C11D4211yescharacteristic
426C22×C11D4211yescharacteristic
427C22×C11C2×#13711yescharacteristic
428C22×C11#57511yescharacteristic
429C22×C11#57711yescharacteristic
430C22×C11#57811yescharacteristic
431C2×D11—22no—
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—41no—
435C2×D11—41no—
436C2×D11—41no—
437C2×D11—41no—
438C4×C11—24no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11—81no—
442C4×C11—81no—
443C4×C11C22×C22⋊C411yescharacteristic
444C4×C11#51811yescharacteristic
445C4×C11#54611yescharacteristic
446C4×C11#54611yescharacteristic
447Dic11—22no—
448Dic11—22no—
449Dic11—42no—
450Dic11—42no—
451Dic11—41no—
452Dic11—81no—
453Dic11—81no—
454C2×#41—114no—
455C2×#41—222no—
456C2×#41—222no—
457C2×#41—222no—
458C2×#41—441no—
459C2×#41—441no—
460C22×Q8—114no—
461C22×Q8—111no—
462C22×Q8—111no—
463C22×Q8—221no—
464C22×Q8—222no—
465C22×Q8—222no—
466C22×Q8—222no—
467C22×Q8—441no—
468C22×Q8—441no—
469C22×Q8C22×D1111yescharacteristic
470C22×D4—221no—
471C22×D4C22×D1111yescharacteristic
472C23×C4—21no—
473C23×C4—111no—
474C23×C4—221no—
475C23×C4—221no—
476C23×C4—221no—
477#137—2232no—
478C2×Q16—114no—
479C2×Q16—114no—
480C2×Q16—222no—
481C2×Q16—222no—
482C2×Q16—222no—
483C2×Q16—222no—
484C2×SD16—114no—
485C2×SD16—222no—
486C2×SD16—222no—
487C2×SD16C4×D1114yes—
488C2×SD16D4414yes—
489C2×SD16C22⋊D1114yes—
490C2×M16—114no—
491C2×M16—222no—
492C2×M16—222no—
493C22×C8—111no—
494C22×C8—111no—
495C22×C8C22×D1111yescharacteristic
496C22×C8C22×D1111yescharacteristic
497C4×Q8—22no—
498C4×Q8—41no—
499C4×Q8—222no—
500C4×Q8—441no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—222no—
504C4×D4—441no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—111no—
513C2×C22⋊C4—111no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C42—21no—
518C2×C42—111no—
519C2×C42—221no—
520C2×C42C22×D1111yescharacteristic
521#107—22no—
522#106—222no—
523#103—22no—
524#103—222no—
525#103—441no—
526#103—441no—
527#103—441no—
528#103—441no—
529#102—22no—
530#102—222no—
531C22⋊C8—222no—
532#97—22no—
533C4×C8—222no—
534#95—111no—
535#95—111no—
536#95—221no—
537#95—221no—
538#95—221no—
539#95—221no—
540#95—221no—
541#95—221no—
542#95—221no—
543#95—221no—
544#95—221no—
545#95—221no—
546C2×C11—44no—
547C2×C11D4×C22⋊C411yescharacteristic
548C2×C11C4×#13711yescharacteristic
549C2×C11#294711yescharacteristic
550C2×C11#326611yescharacteristic
551C2×C11#326911yescharacteristic
552C2×C11#327511yescharacteristic
553C2×C11#327611yescharacteristic
554D11—42no—
555C24—21no—
556C24—111no—
557#41—228no—
558#41—444no—
559#41—444no—
560#41—444no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—112no—
565C2×Q8—112no—
566C2×Q8—224no—
567C2×Q8—221no—
568C2×Q8—221no—
569C2×Q8—228no—
570C2×Q8—221no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×Q8—221no—
574C2×Q8—221no—
575C2×Q8—221no—
576C2×Q8—221no—
577C2×Q8—221no—
578C2×Q8—442no—
579C2×Q8—442no—
580C2×Q8—444no—
581C2×Q8—444no—
582C2×Q8—444no—
583C2×Q8C2×C4×D1112yes—
584C2×Q8C2×D4412yes—
585C2×Q8C2×C22⋊D1112yes—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—224no—
590C2×D4—442no—
591C2×D4—442no—
592C2×D4C2×C4×D1112yes—
593C2×D4C2×D4412yes—
594C2×D4C2×C22⋊D1112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—81no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—111no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4—442no—
619C22×C4—442no—
620C22×C4—442no—
621C22×C4—442no—
622C22×C4—881no—
623C22×C4D4×D1111yescharacteristic
624C22×C4D4×D1111yescharacteristic
625C22×C4C23×D1111yescharacteristic
626Q16—228no—
627Q16—228no—
628SD16—228no—
629SD16(C2×D11)⋊C4116yescomplemented
630M16—228no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—112no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8C2×C4×D1112yes—
641C2×C8C2×D4412yes—
642C2×C8C2×C22⋊D1112yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—42no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4—442no—
653C22⋊C4—42no—
654C22⋊C4—222no—
655C22⋊C4—441no—
656C22⋊C4—442no—
657C22⋊C4—442no—
658C22⋊C4—881no—
659C42—21no—
660C42—21no—
661C42—42no—
662C42—221no—
663C42—221no—
664C42—442no—
665C11#2244411yescharacteristic, complemented, Sylow
666C23—22no—
667C23—22no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—112no—
674C23—221no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23C2×D4×D1111yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—222no—
685Q8—222no—
686Q8—222no—
687Q8—222no—
688Q8—448no—
689Q8—441no—
690Q8—441no—
691Q8—441no—
692Q8—441no—
693Q8C2×(C2×D11)⋊C414yes—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—448no—
698D4C2×(C2×D11)⋊C414yes—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—84no—
715C2×C4—112no—
716C2×C4—112no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—221no—
730C2×C4—448no—
731C2×C4—448no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—884no—
743C2×C4C22×C4×D1111yescharacteristic
744C2×C4C22×D4411yescharacteristic
745C2×C4#6703711yescharacteristic
746C2×C4#41×D1111yescharacteristic
747C2×C4#6704211yescharacteristic
748C2×C4C22×C22⋊D1111yescharacteristic
749C8—41no—
750C8—222no—
751C8—441no—
752C8C2×(C2×D11)⋊C414yes—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—222no—
761C22—222no—
762C22—222no—
763C22—441no—
764C22—441no—
765C22—441no—
766C22—441no—
767C22C4×D4×D1111yescharacteristic
768C22D4×D4411yescharacteristic
769C22#1062330411yescharacteristic
770C22#1062330611yescharacteristic
771C22D11×#13711yescharacteristic
772C22#1062331011yescharacteristic
773C22D4×C22⋊D1111yescharacteristic
774C4—24no—
775C4—41no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—222no—
780C4—222no—
781C4—442no—
782C4—442no—
783C4—441no—
784C4—881no—
785C4—881no—
786C4#1062307611yescharacteristic
787C4#1062308511yescharacteristic
788C4C22×(C2×D11)⋊C411yescharacteristic
789C4#1062336011yescharacteristic
790C2—44no—
791C2—442no—
792C2D4×(C2×D11)⋊C411yescharacteristic
793C2#1307743811yescharacteristic
794C2#1307745611yescharacteristic
795C2#1308012811yescharacteristic
796C2#1308017311yescharacteristic
797C2#1308024711yescharacteristic
798C2#1308025611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
cosocleC22×C4×C11C24
hypercenterC2×#440D11
hypocenterC11#22444
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic11C2semidirect
3. Q8×(C2×D11)⋊C4C2semidirect
5. #13069487C2semidirect
6. #13069475C2semidirect
7. #13068957C2semidirect
8. #13068955C2semidirect
9. #13068950C2semidirect
10. #13068948C2semidirect
11. #13068650C2semidirect
13. #13068549C2semidirect
14. #13068401C2semidirect
15. C2×C11×#440C2semidirect
27. C2×#66968C4semidirect
75. C2×Q8×D11C2×C4semidirect
107. C2×#4326C2×C4semidirect
127. C2×Dic44C2×C4semidirect
130. C2×#4313C2×C4semidirect
228. C11×SD16C22⋊C4semidirect
268. C2×#440D11semidirect
350. C2×Dic11#137semidirect
629. SD16(C2×D11)⋊C4semidirect
665. C11#22444semidirect

Maximal subgroups

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

subgroupindex
C22×#669682
C2×SD16×Dic112
Q8×(C2×D11)⋊C42
#130714412
#130694872
#130694752
#130689572
#130689552
#130689502
#130689482
#130686502
#130685532
#130685492
#130684012
C2×C11×#4402
#2244411