Finite Group Databasebeta

← #14801221

Subgroups — #14801221

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622640C211yesmaximal, characteristic, complemented
2C2×#10622840C211yesmaximal, characteristic, complemented
3C2×#10622840C211yesmaximal, characteristic, complemented
4C2×C4×#4325C211yesmaximal, characteristic, complemented
5#13072204C211yesmaximal, characteristic
6#13069997C211yesmaximal, characteristic, complemented
7#13069805C211yesmaximal, characteristic, complemented
8#13069805C211yesmaximal, characteristic, complemented
9#13069703C211yesmaximal, characteristic, complemented
10#13069473C211yesmaximal, characteristic, complemented
11#13069224C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068953C211yesmaximal, characteristic, complemented
14#13068884C211yesmaximal, characteristic, complemented
15Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66937—21no—
26C2×#66927C2211yescharacteristic
27C2×C4×D44C2211yescharacteristic
28C11×#391—21no—
29C11×#391—21no—
30C11×#391C2211yescharacteristic
31C11×#391C2211yescharacteristic
32C11×#380—21no—
33C11×#380C2211yescharacteristic
34C4×C11×C22⋊C4—21no—
35C4×C11×C22⋊C4C2211yescharacteristic
36#10622840—24no—
37#10622840—24no—
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622640—24no—
45C4×#4325—24no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52#10622573—21no—
53#10622552C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622285—21no—
58#10622278—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—21no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11—21no—
75C22×C22⋊D11—21no—
76C22×D44—21no—
77C22×D44—21no—
78C22×D44C2311yescharacteristic
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—41no—
84C4×Q8×C11—41no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×#4325—22no—
97C2×#4325—22no—
98C2×#4325—22no—
99C2×#4325—22no—
100C2×#4325—22no—
101C2×#4325—22no—
102C2×#4325—22no—
103C2×#4325—22no—
104C2×#4325—22no—
105C2×#4325—41no—
106C2×#4325—41no—
107C2×#4325D414yescomplemented
108#66983—22no—
109#66983—22no—
110#66983—41no—
111#66983—41no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124#66937—44no—
125#66927—22no—
126#66927—41no—
127C4×D44—22no—
128C4×D44—41no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95D411yescharacteristic
135C11×#95D411yescharacteristic
136#66899—22no—
137#66899—22no—
138#66899—22no—
139#66899D414yescomplemented
140C11⋊#95—21no—
141C22⋊(C11⋊C8)—22no—
142C22⋊(C11⋊C8)—22no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66873—41no—
147#66872—22no—
148#66872—41no—
149C4⋊(C11⋊C8)—22no—
150C4×C11⋊C8—22no—
151#25153—111nomaximal, Sylow
152C24×C11C2×D411yescharacteristic
153C23×D11—21no—
154C23×D11—21no—
155C2×Q8×C11—24no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—42no—
165C2×Q8×C11—42no—
166C2×Q8×C11—44no—
167C2×Q8×C11—44no—
168C2×Q8×C11—44no—
169C2×Q8×C11—44no—
170C2×Q8×C11C2×D412yes—
171C2×Q8×C11C2×D412yes—
172C2×Q8×C11#4112yes—
173C2×Q8×C11#4112yes—
174C22×C4×C11—21no—
175C22×C4×C11—24no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—81no—
198C2×C22⋊D11—81no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—42no—
213C2×D44—42no—
214C2×D44—42no—
215C2×D44—42no—
216C2×D44—81no—
217C2×D44—81no—
218C2×D44C2×D412yes—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—81no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C22⋊C4—41no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4SD1614yescomplemented
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—42no—
236C42×C11—42no—
237#4325—28no—
238#4325—44no—
239#4325—44no—
240#4325—44no—
241(C2×D11)⋊C4—42no—
242(C2×D11)⋊C4—42no—
243(C2×D11)⋊C4—42no—
244(C2×D11)⋊C4—42no—
245(C2×D11)⋊C4—81no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11C2×D412yes—
250Dic11⋊C4—42no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8C2×D412yes—
262C2×C11⋊C8C2×D412yes—
263C2×#460—111no—
264C2×#448—111no—
265C2×#448—111no—
266C2×C4×SD16—111no—
267#2428—111no—
268Q8×C22⋊C4D1111yescharacteristic, complemented
269#2066—111no—
270#2034—111no—
271#2034—111no—
272#2014—111no—
273#1968—111no—
274#1923—111no—
275#1880—111no—
276#1877—111no—
277#1865—111no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11C2×SD1612yes—
285C23×C11C22×D411yescharacteristic
286C22×D11—22no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300Q8×C11—22no—
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—48no—
306Q8×C11—41no—
307Q8×C11—41no—
308Q8×C11#12114yescomplemented
309C2×C4×C11—22no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—22no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—48no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11C2×SD1612yes—
340C2×C4×C11C2×SD1612yes—
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×C4×C11C2×#4111yescharacteristic
345C2×C4×C11H(5,𝔽2)11yescharacteristic
346C2×C4×C11H(5,𝔽2)11yescharacteristic
347C22⋊D11—84no—
348C22⋊D11—84no—
349C2×Dic11—22no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355D44—22no—
356D44—22no—
357D44—41no—
358D44—41no—
359D44—41no—
360D44—41no—
361D44—41no—
362D44—41no—
363D44—84no—
364D44—84no—
365C4×D11—84no—
366C11⋊C8—22no—
367C11⋊C8—22no—
368C11⋊C8—41no—
369C11⋊C8—41no—
370C23×Q8C2×D1111yescharacteristic
371C22×SD16—111no—
372C22×SD16—111no—
373C22×SD16—111no—
374C22×SD16—111no—
375C2×#127—111no—
376C2×#121—111no—
377C2×#121—111no—
378C2×#121—221no—
379C2×C4×Q8C2×D1111yescharacteristic
380C2×C4×Q8C2×D1111yescharacteristic
381C2×C4×D4—111no—
382#460—224no—
383#448—224no—
384#448—224no—
385C4×SD16—224no—
386C2×#106—111no—
387C2×#106—111no—
388C2×C4⋊C8—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103—111no—
392C2×#103—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×#102—111no—
397C2×C22⋊C8—111no—
398C2×C22⋊C8—111no—
399C2×C4×C8—111no—
400#394—221no—
401#392—221no—
402#391—21no—
403#391—21no—
404#391C2×D1111yescharacteristic
405#391C2×D1111yescharacteristic
406#390—111no—
407#389—111no—
408#386—221no—
409#380—21no—
410#380C2×D1111yescharacteristic
411C4×C22⋊C4—21no—
412C4×C22⋊C4C2×D1111yescharacteristic
413#340—111no—
414#340—111no—
415#336—111no—
416#336—111no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11#52511yescharacteristic
425C22×C11D4211yescharacteristic
426C22×C11D4211yescharacteristic
427C22×C11C22×SD1611yescharacteristic
428C22×C11#57511yescharacteristic
429C22×C11#57711yescharacteristic
430C22×C11#57711yescharacteristic
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—81no—
435C2×D11—81no—
436C2×D11—81no—
437C2×D11—81no—
438C2×D11—81no—
439C2×D11—81no—
440C2×D11—81no—
441C2×D11—81no—
442C2×D11—81no—
443C2×D11—81no—
444C2×D11—81no—
445C4×C11—24no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—41no—
449C4×C11—42no—
450C4×C11—41no—
451C4×C11—41no—
452C4×C11—81no—
453C4×C11—81no—
454C4×C11C2×#12111yescharacteristic
455C4×C11#53811yescharacteristic
456C4×C11#54611yescharacteristic
457C4×C11#54611yescharacteristic
458Dic11—42no—
459Dic11—81no—
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—21no—
463C22×Q8—22no—
464C22×Q8—22no—
465C22×Q8—41no—
466C22×Q8—41no—
467C22×Q8C22×D1111yescharacteristic
468C22×Q8C22×D1111yescharacteristic
469C22×D4—111no—
470C22×D4—111no—
471C22×D4—221no—
472C22×D4—221no—
473C22×D4—221no—
474C22×D4—221no—
475C23×C4—21no—
476C23×C4—221no—
477C23×C4C22×D1111yescharacteristic
478C2×SD16—114no—
479C2×SD16—222no—
480C2×SD16—222no—
481C2×SD16—222no—
482C2×SD16—222no—
483C2×SD16—222no—
484C2×SD16—222no—
485C2×SD16—222no—
486C2×SD16—222no—
487C2×SD16—222no—
488C2×SD16—441no—
489C2×SD16—441no—
490C22×C8—111no—
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—111no—
494#127—222no—
495#127—441no—
496#121—222no—
497#121—222no—
498#121—441no—
499#121—441no—
500#121—444no—
501C4×Q8—22no—
502C4×Q8—22no—
503C4×Q8—41no—
504C4×Q8—41no—
505C4×D4—222no—
506C4×D4—441no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4C22⋊D1111yescharacteristic
521C2×C22⋊C4C22⋊D1111yescharacteristic
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C22×D1111yescharacteristic
525C2×C42C22×D1111yescharacteristic
526#106—222no—
527#106—441no—
528C4⋊C8—222no—
529#103—114no—
530#103—222no—
531#103—222no—
532#103—222no—
533#102—222no—
534#102—222no—
535#102—222no—
536#102—441no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C4×C8—222no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—221no—
546#95C22⋊D1111yescharacteristic
547#95C22⋊D1111yescharacteristic
548C2×C11—42no—
549C2×C11#242411yescharacteristic
550C2×C11#310311yescharacteristic
551C2×C11#312611yescharacteristic
552C2×C11#327111yescharacteristic
553C2×C11#327511yescharacteristic
554C2×C11D4×SD1611yescharacteristic
555C2×C11D4×SD1611yescharacteristic
556D11—82no—
557D11—161no—
558C24—221no—
559C24—221no—
560C24C2×C22⋊D1111yescharacteristic
561C2×Q8—24no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8#433912yes—
577C2×Q8#433912yes—
578C2×Q8D4×D1112yes—
579C2×Q8D4×D1112yes—
580C2×D4—112no—
581C2×D4—221no—
582C2×D4—221no—
583C2×D4—221no—
584C2×D4—221no—
585C2×D4—221no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—221no—
592C2×D4—442no—
593C2×D4—442no—
594C2×D4—442no—
595C2×D4—442no—
596C2×D4—442no—
597C2×D4—442no—
598C2×D4—442no—
599C2×D4—442no—
600C2×D4—881no—
601C2×D4—881no—
602C2×D4—881no—
603C2×D4—881no—
604C22×C4—21no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—442no—
620C22×C4—442no—
621C22×C4—881no—
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C2×C22⋊D1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C23×D1111yescharacteristic
628SD16—228no—
629SD16—444no—
630SD16—444no—
631SD16—444no—
632C2×C8—112no—
633C2×C8—112no—
634C2×C8—221no—
635C2×C8—221no—
636C2×C8—221no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—112no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—442no—
655C22⋊C4—41no—
656C22⋊C4—42no—
657C22⋊C4—442no—
658C22⋊C4—442no—
659C22⋊C4—442no—
660C22⋊C4—442no—
661C22⋊C4—881no—
662C22⋊C4#432514yescomplemented
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—42no—
669C11#2515311yescharacteristic, complemented, Sylow
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—222no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23—441no—
689C23—441no—
690C23C2×#432512yes—
691C23C22×C22⋊D1111yescharacteristic
692Q8—22no—
693Q8—22no—
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—48no—
698Q8—41no—
699Q8—41no—
700Q8#6693714yescomplemented
701D4—222no—
702D4—222no—
703D4—441no—
704D4—441no—
705D4—441no—
706D4—441no—
707D4—441no—
708D4—441no—
709D4—884no—
710D4—884no—
711D4—884no—
712D4—884no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—48no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—222no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—884no—
750C2×C4C2×#432512yes—
751C2×C4C2×#432512yes—
752C2×C4C2×#433911yescharacteristic
753C2×C4C2×#433911yescharacteristic
754C2×C4C2×D4×D1111yescharacteristic
755C2×C4C2×D4×D1111yescharacteristic
756C2×C4#6703711yescharacteristic
757C2×C4#6703711yescharacteristic
758C8—222no—
759C8—222no—
760C8—441no—
761C8—441no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—442no—
770C22—442no—
771C22—442no—
772C22—881no—
773C22—881no—
774C22—881no—
775C22—881no—
776C22—881no—
777C22—881no—
778C22—881no—
779C22—881no—
780C22—881no—
781C22—881no—
782C22—881no—
783C22#1062332211yescharacteristic
784C22D4×C22⋊D1111yescharacteristic
785C22D4×C22⋊D1111yescharacteristic
786C22C22×#432511yescharacteristic
787C22#1062335311yescharacteristic
788C22#1062336811yescharacteristic
789C22#1062336811yescharacteristic
790C4—24no—
791C4—22no—
792C4—22no—
793C4—41no—
794C4—42no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—442no—
800C4—881no—
801C4C2×#6693711yescharacteristic
802C4#1062302111yescharacteristic
803C4#1062302111yescharacteristic
804C4#1062302511yescharacteristic
805C2—42no—
806C2—882no—
807C2—1761no—
808C2#1307215211yescharacteristic
809C2#1307864711yescharacteristic
810C2#1307890711yescharacteristic
811C2#1308020211yescharacteristic
812C2#1308024811yescharacteristic
813C2D4×#432511yescharacteristic
814C2D4×#432511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radical#13072204C2
hypercenterQ8×C22⋊C4D11
hypocenterC11#25153
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622640C2semidirect
2. C2×#10622840C2semidirect
3. C2×#10622840C2semidirect
4. C2×C4×#4325C2semidirect
6. #13069997C2semidirect
7. #13069805C2semidirect
8. #13069805C2semidirect
9. #13069703C2semidirect
10. #13069473C2semidirect
11. #13069224C2semidirect
12. #13068971C2semidirect
13. #13068953C2semidirect
14. #13068884C2semidirect
15. Q8×C11×C22⋊C4C2semidirect
107. C2×#4325D4semidirect
139. #66899D4semidirect
230. C11×C22⋊C4SD16semidirect
268. Q8×C22⋊C4D11semidirect
308. Q8×C11#121semidirect
662. C22⋊C4#4325semidirect
669. C11#25153semidirect
700. Q8#66937semidirect

Maximal subgroups

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

subgroupindex
C2×#106226402
C2×#106228402
C2×C4×#43252
#130722042
#130699972
#130698052
#130697032
#130694732
#130692242
#130689712
#130689532
#130688842
Q8×C11×C22⋊C42
#2515311