Finite Group Databasebeta

← #14769588

Subgroups — #14769588

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66962C211yesmaximal, characteristic
2C2×#10622329C211yesmaximal, characteristic, complemented
3C2×C4×Dic44C211yesmaximal, characteristic, complemented
4#13071456C211yesmaximal, characteristic
5C22⋊C4×Dic22C211yesmaximal, characteristic, complemented
6#13069497C211yesmaximal, characteristic, complemented
7#13069470C211yesmaximal, characteristic, complemented
8#13068970C211yesmaximal, characteristic, complemented
9#13068970C211yesmaximal, characteristic, complemented
10#13068956C211yesmaximal, characteristic, complemented
11#13068956C211yesmaximal, characteristic, complemented
12#13068649C211yesmaximal, characteristic, complemented
13#13068557C211yesmaximal, characteristic
14#13068552C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×#66962—24no—
20C2×#66962—24no—
21C2×#66962C418yescomplemented
22C22×Dic44C2211yescharacteristic
23C22×Dic44C2211yescharacteristic
24C22×#4314C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C2×C4×C8×C11C2211yescharacteristic
33C4×C11×C22⋊C4C2211yescharacteristic
34#10622825C2211yescharacteristic
35#10622825C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×#66881C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×#66880C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46#10622570—21no—
47#10622570—21no—
48#10622555—21no—
49C22⋊C4×Dic11—21no—
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622542C2211yescharacteristic
54#10622329—24no—
55C4×Dic44—24no—
56#10622280—21no—
57#10622279—21no—
58#10622259—21no—
59#10622259—21no—
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62#10622189C2211yescharacteristic
63#10622189C2211yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C23×Dic11—21no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—41no—
71C2×#4339—41no—
72C2×#4339C2×C414yes—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22—22no—
76C22×Dic22—22no—
77C22×Dic22—21no—
78C22×Dic22—22no—
79C22×Dic22—41no—
80C22×Dic22—41no—
81C22×Dic22C2×C414yes—
82C22×Dic22C2311yescharacteristic
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C2×C11×M16—22no—
86C2×C11×M16—22no—
87C2×C11×M16C2×C414yes—
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114#66962—232no—
115C2×Dic44—22no—
116C2×Dic44—22no—
117C2×Dic44C2×C414yes—
118C2×Dic44C2×C414yes—
119C2×Dic44D414yes—
120C2×Dic44D414yes—
121C2×#4314—22no—
122C2×#4314—22no—
123C2×#4314—22no—
124C2×#4314—22no—
125C2×#4314C2×C414yes—
126C2×#4314C2×C414yes—
127C4×Dic22—22no—
128C4×Dic22—22no—
129C4×Dic22—22no—
130C4×Dic22—22no—
131C4×Dic22—41no—
132C4×Dic22—41no—
133C4×Dic22—41no—
134C4×Dic22—41no—
135C11×C22⋊C8—22no—
136C11×#97—22no—
137C4×C8×C11—22no—
138C11×#95D411yescharacteristic
139C11×#95D411yescharacteristic
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146#66885—41no—
147#66885—41no—
148#66882—22no—
149#66881—22no—
150#66880—22no—
151#66880—22no—
152#66880—22no—
153#66880—22no—
154#66880—41no—
155#66880—41no—
156#22445—111nomaximal, Sylow
157C24×C11C2×D411yescharacteristic
158C23×D11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11#4112yes—
170C22×C4×C11C2411yescharacteristic
171C2×C22⋊D11—24no—
172C2×C22⋊D11—42no—
173C2×C22⋊D11—42no—
174C22×Dic11—24no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184#4339—28no—
185#4339—44no—
186#4339—44no—
187#4339—44no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44C22×C412yes—
194C2×C4×D11—24no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×Dic22—28no—
198C2×Dic22—24no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—44no—
211C2×Dic22—44no—
212C2×Dic22—44no—
213C2×Dic22—42no—
214C2×Dic22—42no—
215C2×Dic22C22×C412yes—
216C2×Dic22C22×C412yes—
217C2×Dic22C22×C412yes—
218C2×Dic22C2×D412yes—
219C2×Dic22C2×D412yes—
220C2×Dic22C2×D412yes—
221C2×Dic22C2×D412yes—
222C11×M16—28no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11C22×C412yes—
232C2×C8×C11C22×C412yes—
233C2×C8×C11C2×D412yes—
234C2×C8×C11C2×D412yes—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—41no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11—21no—
241C22⋊Dic11—42no—
242C22⋊Dic11—81no—
243(C2×D11)⋊C4—42no—
244(C2×D11)⋊C4—42no—
245(C2×D11)⋊C4—81no—
246(C2×D11)⋊C4—81no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255Dic11⋊C4—42no—
256Dic11⋊C4—42no—
257Dic11⋊C4—42no—
258Dic11⋊C4—42no—
259C4×Dic11—42no—
260C4×Dic11—42no—
261C4×Dic11—42no—
262C4×Dic11—42no—
263Dic44—28no—
264Dic44C22⋊C4116yescomplemented
265#4314—28no—
266#4314—28no—
267C22×#137—111no—
268C2×#441—111no—
269C2×C4×Q16—111no—
270#2341—111no—
271Q8×C22⋊C4—111no—
272#1973—111no—
273#1968—111no—
274#1880—111no—
275#1880—111no—
276#1878—111no—
277#1878—111no—
278#1809—111no—
279#1788—111no—
280#1787—111no—
281#1753D1111yescharacteristic, complemented
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11C4×D412yes—
289C23×C11C22×D411yescharacteristic
290C22×D11—22no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
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×C11C4×D412yes—
315C2×C4×C11#13712yescomplemented
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C22⋊D11—48no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—48no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345D44—22no—
346D44—22no—
347D44—41no—
348D44—41no—
349C4×D11—48no—
350Dic22—22no—
351Dic22—22no—
352Dic22—22no—
353Dic22—22no—
354Dic22—22no—
355Dic22—22no—
356Dic22—22no—
357Dic22—22no—
358Dic22—48no—
359Dic22—41no—
360Dic22—41no—
361Dic22C2×C22⋊C414yes—
362Dic22C2×C22⋊C414yes—
363C8×C11—22no—
364C8×C11—41no—
365C8×C11—41no—
366C8×C11C2×C22⋊C414yes—
367C22×#41—111no—
368C23×Q8—111no—
369C2×#137—118no—
370C2×#137—224no—
371C2×#137—224no—
372C22×Q16—111no—
373C22×Q16—111no—
374C22×SD16—111no—
375C22×SD16—111no—
376C22×M16C2×D1111yescharacteristic
377C2×C4×Q8—111no—
378C2×C4×Q8—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8—111no—
381#441—224no—
382C4×Q16—224no—
383C2×#107—111no—
384C2×#106—111no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×C22⋊C8C2×D1111yescharacteristic
394C2×#97C2×D1111yescharacteristic
395C2×C4×C8C2×D1111yescharacteristic
396#391—111no—
397#391—111no—
398#391—221no—
399#391—221no—
400#390—111no—
401#390—111no—
402#390—221no—
403#390—221no—
404#380—111no—
405#380—111no—
406#380—221no—
407#380—221no—
408C4×C22⋊C4—221no—
409C4×C22⋊C4—221no—
410C4×C22⋊C4C2×D1111yescharacteristic
411#340—111no—
412#340—111no—
413#336C2×D1111yescharacteristic
414#336C2×D1111yescharacteristic
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11C2×C4×D411yescharacteristic
423C22×C11D4211yescharacteristic
424C22×C11D4211yescharacteristic
425C22×C11C2×#13711yescharacteristic
426C22×C11#57511yescharacteristic
427C22×C11#57711yescharacteristic
428C22×C11#57811yescharacteristic
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—81no—
433C2×D11—81no—
434C2×D11—81no—
435C2×D11—81no—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—41no—
439C4×C11—41no—
440C4×C11—41no—
441C4×C11C22×C22⋊C411yescharacteristic
442C4×C11#51811yescharacteristic
443C4×C11#54611yescharacteristic
444C4×C11#54611yescharacteristic
445Dic11—24no—
446Dic11—24no—
447Dic11—42no—
448Dic11—81no—
449Dic11—81no—
450Dic11—81no—
451Dic11—81no—
452C2×#41—114no—
453C2×#41—222no—
454C2×#41—222no—
455C2×#41—222no—
456C2×#41—441no—
457C2×#41—441no—
458C22×Q8—114no—
459C22×Q8—111no—
460C22×Q8—111no—
461C22×Q8—111no—
462C22×Q8—222no—
463C22×Q8—222no—
464C22×Q8—221no—
465C22×Q8—222no—
466C22×Q8—441no—
467C22×Q8—441no—
468C22×D4—111no—
469C22×D4—221no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4C22×D1111yescharacteristic
473#137—2232no—
474C2×Q16—114no—
475C2×Q16—114no—
476C2×Q16—114no—
477C2×Q16—114no—
478C2×Q16—222no—
479C2×Q16—222no—
480C2×SD16—114no—
481C2×SD16—114no—
482C2×SD16—222no—
483C2×SD16—222no—
484C2×SD16—222no—
485C2×SD16—222no—
486C2×M16—22no—
487C2×M16—22no—
488C2×M16C4×D1114yes—
489C22×C8C22×D1111yescharacteristic
490C22×C8C22×D1111yescharacteristic
491C22×C8C22×D1111yescharacteristic
492C22×C8C22×D1111yescharacteristic
493C4×Q8—222no—
494C4×Q8—222no—
495C4×Q8—222no—
496C4×Q8—222no—
497C4×Q8—441no—
498C4×Q8—441no—
499C4×Q8—441no—
500C4×Q8—441no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4D4411yescharacteristic
516C2×C22⋊C4D4411yescharacteristic
517C2×C42—221no—
518C2×C42—221no—
519C2×C42—221no—
520C2×C42—221no—
521C2×C42C22×D1111yescharacteristic
522C2×C42C22×D1111yescharacteristic
523#107—222no—
524#106—222no—
525#103—222no—
526#103—222no—
527#103—222no—
528#103—222no—
529#103—441no—
530#103—441no—
531#102—441no—
532#102—441no—
533C22⋊C8—22no—
534#97—22no—
535C4×C8—22no—
536#95—221no—
537#95—221no—
538#95—221no—
539#95—221no—
540#95—221no—
541#95—221no—
542#95D4411yescharacteristic
543#95D4411yescharacteristic
544C2×C11—42no—
545C2×C11D4×C22⋊C411yescharacteristic
546C2×C11C4×#13711yescharacteristic
547C2×C11#294711yescharacteristic
548C2×C11#327011yescharacteristic
549C2×C11#327111yescharacteristic
550C2×C11#327711yescharacteristic
551C2×C11#327811yescharacteristic
552D11—82no—
553C24—221no—
554C24C2×D4411yescharacteristic
555#41—228no—
556#41—444no—
557#41—444no—
558#41—444no—
559C2×Q8—112no—
560C2×Q8—112no—
561C2×Q8—112no—
562C2×Q8—112no—
563C2×Q8—112no—
564C2×Q8—112no—
565C2×Q8—112no—
566C2×Q8—228no—
567C2×Q8—224no—
568C2×Q8—221no—
569C2×Q8—221no—
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—221no—
579C2×Q8—442no—
580C2×Q8—442no—
581C2×Q8—444no—
582C2×Q8—444no—
583C2×Q8—444no—
584C2×D4—112no—
585C2×D4—224no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—442no—
592C2×D4—442no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—224no—
600C22×C4—221no—
601C22×C4—224no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—442no—
607C22×C4—442no—
608C22×C4—442no—
609C22×C4—442no—
610C22×C4C2×C4×D1112yes—
611C22×C4C2×D4411yescharacteristic
612C22×C4C2×D4411yescharacteristic
613C22×C4C2×D4411yescharacteristic
614C22×C4C2×D4411yescharacteristic
615C22×C4C2×D4411yescharacteristic
616C22×C4#433912yes—
617C22×C4C23×D1111yescharacteristic
618Q16—1116no—
619Q16—228no—
620SD16—228no—
621SD16—228no—
622M16—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8C2×C4×D1112yes—
632C2×C8C2×C4×D1112yes—
633C2×C8D4×D1112yes—
634C2×C8D4×D1112yes—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—442no—
644C4⋊C4—442no—
645C4⋊C4—442no—
646C4⋊C4—442no—
647C22⋊C4—22no—
648C22⋊C4—41no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—881no—
653C22⋊C4—881no—
654C22⋊C4—881no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—442no—
660C42—442no—
661C42—442no—
662C42—442no—
663C11#2244511yescharacteristic, complemented, Sylow
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—222no—
671C23—441no—
672C23—441no—
673C23—441no—
674C23—441no—
675C23—441no—
676C23—441no—
677C23C4×D4412yes—
678C23C22×D4411yescharacteristic
679Q8—114no—
680Q8—114no—
681Q8—222no—
682Q8—222no—
683Q8—222no—
684Q8—222no—
685Q8—222no—
686Q8—222no—
687Q8—222no—
688Q8—222no—
689Q8—448no—
690Q8—441no—
691Q8—441no—
692D4—222no—
693D4—222no—
694D4—448no—
695D4—441no—
696D4—441no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—448no—
722C2×C4—448no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4C4×D4412yes—
738C2×C4#6696212yescomplemented
739C2×C4C22×C4×D1111yescharacteristic
740C2×C4C2×#433911yescharacteristic
741C2×C4C2×D4×D1111yescharacteristic
742C2×C4C2×D4×D1111yescharacteristic
743C2×C4#6704211yescharacteristic
744C2×C4#6704211yescharacteristic
745C8—22no—
746C8—41no—
747C8—41no—
748C8C22⋊C4×D1114yes—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—442no—
757C22—442no—
758C22—442no—
759C22—881no—
760C22—881no—
761C22—881no—
762C22—881no—
763C22C2×C4×D4411yescharacteristic
764C22D4×D4411yescharacteristic
765C22D4×D4411yescharacteristic
766C22C2×#6696211yescharacteristic
767C22#1062327911yescharacteristic
768C22#1062328211yescharacteristic
769C22#1062328411yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—224no—
776C4—224no—
777C4—442no—
778C4—881no—
779C4—881no—
780C4—881no—
781C4—881no—
782C4C2×C22⋊C4×D1111yescharacteristic
783C4#1062305211yescharacteristic
784C4#1062308111yescharacteristic
785C4#1062308111yescharacteristic
786C2—42no—
787C2—882no—
788C2C22⋊C4×D4411yescharacteristic
789C2C4×#6696211yescharacteristic
790C2#1307746111yescharacteristic
791C2#1308019111yescharacteristic
792C2#1308020611yescharacteristic
793C2#1308027411yescharacteristic
794C2#1308028411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22445
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#10622329C2semidirect
3. C2×C4×Dic44C2semidirect
5. C22⋊C4×Dic22C2semidirect
6. #13069497C2semidirect
7. #13069470C2semidirect
8. #13068970C2semidirect
9. #13068970C2semidirect
10. #13068956C2semidirect
11. #13068956C2semidirect
12. #13068649C2semidirect
14. #13068552C2semidirect
15. C11×#1753C2semidirect
21. C2×#66962C4semidirect
264. Dic44C22⋊C4semidirect
281. #1753D11semidirect
315. C2×C4×C11#137semidirect
663. C11#22445semidirect
738. C2×C4#66962semidirect

Maximal subgroups

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

subgroupindex
C22×#669622
C2×#106223292
C2×C4×Dic442
#130714562
C22⋊C4×Dic222
#130694972
#130694702
#130689702
#130689562
#130686492
#130685572
#130685522
C11×#17532
#2244511