Finite Group Databasebeta

← #14801146

Subgroups — #14801146

Order 2816.

1402 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622628C211yesmaximal, characteristic, complemented
2C2×#10622830C211yesmaximal, characteristic, complemented
3C2×#10622830C211yesmaximal, characteristic, complemented
4C2×C4×#4323C211yesmaximal, characteristic, complemented
5#13072204C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069798C211yesmaximal, characteristic, complemented
8#13069798C211yesmaximal, characteristic, complemented
9#13069686C211yesmaximal, characteristic, complemented
10#13069481C211yesmaximal, characteristic, complemented
11#13069224C211yesmaximal, characteristic, complemented
12#13068967C211yesmaximal, characteristic, complemented
13#13068964C211yesmaximal, characteristic, complemented
14#13068863C211yesmaximal, characteristic, complemented
15D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×#4323C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66937—21no—
27C2×#66927C2211yescharacteristic, complemented
28C2×C4×D44C2211yescharacteristic, complemented
29C11×#390C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#386—21no—
32C11×#386—21no—
33C11×#380C2211yescharacteristic
34C11×#379—21no—
35C4×C11×C22⋊C4C2211yescharacteristic
36#10622830—24no—
37#10622830—24no—
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622628—24no—
45C4×#4323—24no—
46C2×#66873C2211yescharacteristic, complemented
47C2×#66873C2211yescharacteristic, complemented
48C2×#66873C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51C2×#66871C2211yescharacteristic, complemented
52#10622573—21no—
53#10622552C2211yescharacteristic, complemented
54#10622541C2211yescharacteristic, complemented
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622285—21no—
58#10622278—21no—
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63C25×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—21no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2311yescharacteristic
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×D44—21no—
79C22×D44—21no—
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C22×C4×D11—21no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—41no—
86C4×D4×C11—41no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—44no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×#4323—22no—
102C2×#4323—22no—
103C2×#4323—22no—
104C2×#4323—22no—
105C2×#4323—22no—
106C2×#4323—22no—
107C2×#4323—22no—
108C2×#4323—22no—
109C2×#4323—22no—
110C2×#4323—41no—
111C2×#4323—41no—
112C2×#4323D414yescomplemented
113#66983—22no—
114#66983—22no—
115#66983—41no—
116#66983—41no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×Dic11⋊C4—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129#66937—44no—
130#66927—22no—
131#66927—41no—
132C4×D44—22no—
133C4×D44—41no—
134C11×#95—21no—
135C11×#95D411yescharacteristic
136C11×#95D411yescharacteristic
137#66896—22no—
138#66896—22no—
139#66896—22no—
140#66896D414yescomplemented
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)—22no—
144#66873—22no—
145#66873—22no—
146#66873—22no—
147#66873—41no—
148#66871—22no—
149#66871—41no—
150C4⋊(C11⋊C8)—22no—
151C4×C11⋊C8—22no—
152#25148—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—24no—
155C24×C11—21no—
156C24×C11—42no—
157C24×C11—42no—
158C24×C11—42no—
159C24×C11—42no—
160C24×C11—81no—
161C24×C11—81no—
162C24×C11C2×D411yescharacteristic
163C23×D11—21no—
164C23×D11—21no—
165C2×D4×C11—24no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—44no—
177C2×D4×C11—44no—
178C2×D4×C11—44no—
179C2×D4×C11—44no—
180C2×D4×C11C2×D412yes—
181C2×D4×C11C2×D412yes—
182C2×D4×C11#4112yes—
183C2×D4×C11#4112yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11—81no—
197C22×C4×C11—81no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—42no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—81no—
209C2×C22⋊D11—81no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—42no—
224C2×D44—42no—
225C2×D44—42no—
226C2×D44—42no—
227C2×D44—81no—
228C2×D44—81no—
229C2×D44C2×D412yes—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
232C2×C4×D11—81no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C22⋊C4—41no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—42no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—81no—
244C11×C22⋊C4—81no—
245C11×C22⋊C4D814yescomplemented
246C42×C11—21no—
247C42×C11—21no—
248C42×C11—21no—
249C42×C11—21no—
250#4323—28no—
251#4323—44no—
252#4323—44no—
253#4323—44no—
254(C2×D11)⋊C4—42no—
255(C2×D11)⋊C4—42no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—81no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11C2×D412yes—
263Dic11⋊C4—42no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8C2×D412yes—
275C2×C11⋊C8C2×D412yes—
276C2×#459—111no—
277C2×#447—111no—
278C2×#447—111no—
279C2×C4×D8—111no—
280#2428—111no—
281D4×C22⋊C4D1111yescharacteristic, complemented
282#2067—111no—
283#2033—111no—
284#2033—111no—
285#2011—111no—
286#1970—111no—
287#1923—111no—
288#1879—111no—
289#1879—111no—
290#1862—111no—
291C23×C11—21no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—22no—
301C23×C11—48no—
302C23×C11—48no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—84no—
314C23×C11—84no—
315C23×C11—84no—
316C23×C11—84no—
317C23×C11—84no—
318C23×C11C2×D812yes—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—48no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11#12114yescomplemented
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—84no—
367C2×C4×C11—84no—
368C2×C4×C11C2×D812yes—
369C2×C4×C11C2×D812yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C2×#4111yescharacteristic
373C2×C4×C11C2×#4111yescharacteristic
374C2×C4×C11H(5,𝔽2)11yescharacteristic
375C2×C4×C11H(5,𝔽2)11yescharacteristic
376C22⋊D11—84no—
377C22⋊D11—84no—
378C2×Dic11—22no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384D44—22no—
385D44—22no—
386D44—41no—
387D44—41no—
388D44—41no—
389D44—41no—
390D44—41no—
391D44—41no—
392D44—84no—
393D44—84no—
394C4×D11—84no—
395C11⋊C8—22no—
396C11⋊C8—22no—
397C11⋊C8—41no—
398C11⋊C8—41no—
399C23×D4C2×D1111yescharacteristic
400C22×D8—111no—
401C22×D8—111no—
402C22×D8—111no—
403C22×D8—111no—
404C2×#127—111no—
405C2×#121—111no—
406C2×#121—111no—
407C2×#121—221no—
408C2×C4×D4—111no—
409C2×C4×D4C2×D1111yescharacteristic
410C2×C4×D4C2×D1111yescharacteristic
411C22×C22⋊C4—21no—
412#459—224no—
413#447—224no—
414#447—224no—
415C4×D8—224no—
416C2×#107—111no—
417C2×#107—111no—
418C2×C4⋊C8—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×C22⋊C8—111no—
428C2×C22⋊C8—111no—
429C2×C4×C8—111no—
430#394—221no—
431#392—221no—
432#390—111no—
433#390C2×D1111yescharacteristic
434#390C2×D1111yescharacteristic
435#389—111no—
436#386—21no—
437#386—21no—
438#386—221no—
439#380C2×D1111yescharacteristic
440#379—21no—
441C4×C22⋊C4C2×D1111yescharacteristic
442#340—111no—
443#340—111no—
444#336—111no—
445#336—111no—
446C22×C11—22no—
447C22×C11—24no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—42no—
451C22×C11—41no—
452C22×C11—42no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—816no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11#52511yescharacteristic
469C22×C11D4211yescharacteristic
470C22×C11D4211yescharacteristic
471C22×C11C22×D811yescharacteristic
472C22×C11#57511yescharacteristic
473C22×C11#57611yescharacteristic
474C22×C11#57611yescharacteristic
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—81no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C2×D11—81no—
485C2×D11—81no—
486C2×D11—81no—
487C2×D11—81no—
488C2×D11—81no—
489C4×C11—22no—
490C4×C11—22no—
491C4×C11—41no—
492C4×C11—41no—
493C4×C11—41no—
494C4×C11—81no—
495C4×C11—81no—
496C4×C11C2×#12111yescharacteristic
497C4×C11#53811yescharacteristic
498C4×C11#54611yescharacteristic
499C4×C11#54611yescharacteristic
500Dic11—42no—
501Dic11—81no—
502C25—21no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—111no—
511C22×D4—111no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4—221no—
516C22×D4C22×D1111yescharacteristic
517C22×D4C22×D1111yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C2×D8—114no—
523C2×D8—222no—
524C2×D8—222no—
525C2×D8—222no—
526C2×D8—222no—
527C2×D8—222no—
528C2×D8—222no—
529C2×D8—222no—
530C2×D8—222no—
531C2×D8—222no—
532C2×D8—441no—
533C2×D8—441no—
534C22×C8—111no—
535C22×C8—111no—
536C22×C8—111no—
537C22×C8—111no—
538#127—222no—
539#127—441no—
540#121—222no—
541#121—222no—
542#121—441no—
543#121—441no—
544#121—444no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—222no—
550C4×D4—441no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—44no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4C22⋊D1111yescharacteristic
570C2×C22⋊C4C22⋊D1111yescharacteristic
571C2×C42C22×D1111yescharacteristic
572C2×C42C22×D1111yescharacteristic
573#107—222no—
574#107—441no—
575C4⋊C8—222no—
576#102—114no—
577#102—222no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—441no—
584C22⋊C8—222no—
585C22⋊C8—222no—
586C4×C8—222no—
587#95—21no—
588#95—221no—
589#95C22⋊D1111yescharacteristic
590#95C22⋊D1111yescharacteristic
591C2×C11—42no—
592C2×C11—44no—
593C2×C11—82no—
594C2×C11#242411yescharacteristic
595C2×C11#310011yescharacteristic
596C2×C11#312211yescharacteristic
597C2×C11#326811yescharacteristic
598C2×C11#327311yescharacteristic
599C2×C11D4×D811yescharacteristic
600C2×C11D4×D811yescharacteristic
601D11—82no—
602D11—161no—
603C24—21no—
604C24—24no—
605C24—21no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—81no—
611C24—81no—
612C24—221no—
613C24—221no—
614C24C2×C22⋊D1111yescharacteristic
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—112no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—442no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—881no—
651C2×D4—881no—
652C2×D4—881no—
653C2×D4—881no—
654C2×D4#433912yes—
655C2×D4#433912yes—
656C2×D4D4×D1112yes—
657C2×D4D4×D1112yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—81no—
671C22×C4—81no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—442no—
675C22×C4—442no—
676C22×C4—881no—
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C23×D1111yescharacteristic
683D8—228no—
684D8—444no—
685D8—444no—
686D8—444no—
687C2×C8—112no—
688C2×C8—112no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8—221no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—112no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—442no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4—81no—
716C22⋊C4—442no—
717C22⋊C4—442no—
718C22⋊C4—442no—
719C22⋊C4—442no—
720C22⋊C4—881no—
721C22⋊C4#432314yescomplemented
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C11#2514811yescharacteristic, complemented, Sylow
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—48no—
738C23—48no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—222no—
755C23—441no—
756C23—441no—
757C23—441no—
758C23—441no—
759C23—441no—
760C23—441no—
761C23—441no—
762C23—441no—
763C23—441no—
764C23—441no—
765C23—441no—
766C23—441no—
767C23—441no—
768C23C2×#432312yes—
769C23C22×C22⋊D1111yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—48no—
776D4—41no—
777D4—41no—
778D4—222no—
779D4—222no—
780D4—441no—
781D4—441no—
782D4—441no—
783D4—441no—
784D4—441no—
785D4—441no—
786D4—884no—
787D4—884no—
788D4—884no—
789D4—884no—
790D4#6693714yescomplemented
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4—222no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—441no—
822C2×C4—884no—
823C2×C4C2×#432312yes—
824C2×C4C2×#432312yes—
825C2×C4C2×#433911yescharacteristic
826C2×C4C2×#433911yescharacteristic
827C2×C4C2×D4×D1111yescharacteristic
828C2×C4C2×D4×D1111yescharacteristic
829C2×C4#6703711yescharacteristic
830C2×C4#6703711yescharacteristic
831C8—222no—
832C8—222no—
833C8—441no—
834C8—441no—
835C22—24no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—881no—
861C22—881no—
862C22—881no—
863C22—881no—
864C22—881no—
865C22—881no—
866C22—881no—
867C22—881no—
868C22—881no—
869C22—881no—
870C22—881no—
871C22#1062332211yescharacteristic
872C22C22×#432311yescharacteristic
873C22D4×C22⋊D1111yescharacteristic
874C22D4×C22⋊D1111yescharacteristic
875C22#1062335311yescharacteristic
876C22#1062336611yescharacteristic
877C22#1062336611yescharacteristic
878C4—22no—
879C4—22no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—442no—
886C4—881no—
887C4C2×#6693711yescharacteristic
888C4#1062302111yescharacteristic
889C4#1062302111yescharacteristic
890C4#1062302511yescharacteristic
891C2—42no—
892C2—44no—
893C2—82no—
894C2—882no—
895C2—1761no—
896C2#1307215211yescharacteristic
897C2#1307861611yescharacteristic
898C2#1307885911yescharacteristic
899C2#1308015211yescharacteristic
900C2#1308022311yescharacteristic
901C2D4×#432311yescharacteristic
902C2D4×#432311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
hypercenterD4×C22⋊C4D11
hypocenterC11#25148
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622628C2semidirect
2. C2×#10622830C2semidirect
3. C2×#10622830C2semidirect
4. C2×C4×#4323C2semidirect
5. #13072204C2semidirect
6. #13070004C2semidirect
7. #13069798C2semidirect
8. #13069798C2semidirect
9. #13069686C2semidirect
10. #13069481C2semidirect
11. #13069224C2semidirect
12. #13068967C2semidirect
13. #13068964C2semidirect
14. #13068863C2semidirect
15. D4×C11×C22⋊C4C2semidirect
27. C2×#66927C22semidirect
28. C2×C4×D44C22semidirect
46. C2×#66873C22semidirect
47. C2×#66873C22semidirect
48. C2×#66873C22semidirect
49. C2×#66873C22semidirect
50. C2×#66871C22semidirect
51. C2×#66871C22semidirect
53. #10622552C22semidirect
54. #10622541C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×C4×C11⋊C8C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
62. #10622162C22semidirect
112. C2×#4323D4semidirect
140. #66896D4semidirect
245. C11×C22⋊C4D8semidirect
281. D4×C22⋊C4D11semidirect
342. D4×C11#121semidirect
721. C22⋊C4#4323semidirect
726. C11#25148semidirect
790. D4#66937semidirect

Maximal subgroups

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

subgroupindex
C2×#106226282
C2×#106228302
C2×C4×#43232
#130722042
#130700042
#130697982
#130696862
#130694812
#130692242
#130689672
#130689642
#130688632
D4×C11×C22⋊C42
#2514811