Finite Group Databasebeta

← #14769653

Subgroups — #14769653

Order 2816.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C2×#10622436C211yesmaximal, characteristic, complemented
3C2×#10622437C211yesmaximal, characteristic, complemented
4#13077066C211yesmaximal, characteristic, complemented
5#13077065C211yesmaximal, characteristic, complemented
6#13069506C211yesmaximal, characteristic, complemented
7#13069501C211yesmaximal, characteristic, complemented
8#13068941C211yesmaximal, characteristic, complemented
9#13068941C211yesmaximal, characteristic, complemented
10#13068940C211yesmaximal, characteristic, complemented
11#13068940C211yesmaximal, characteristic, complemented
12#13068656C211yesmaximal, characteristic, complemented
13#13068561C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#1789C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×#67004C411yescharacteristic, complemented
19C2×#67004C411yescharacteristic, complemented
20#10623353—24no—
21#10623353—24no—
22C2×#67003C2211yescharacteristic
23C2×#67003C2211yescharacteristic
24C2×#67003C2211yescharacteristic
25C2×#67003C2211yescharacteristic
26C2×#67002C411yescharacteristic, complemented
27C2×#67002C411yescharacteristic, complemented
28C2×#67001C2211yescharacteristic, complemented
29C2×#67001C2211yescharacteristic, complemented
30C2×#66995C411yescharacteristic, complemented
31C2×#66995C411yescharacteristic, complemented
32C2×#66985C411yescharacteristic, complemented
33C2×#66985C411yescharacteristic, complemented
34C22×#4318C2211yescharacteristic
35C2×#66960C2211yescharacteristic, complemented
36C2×#66960C2211yescharacteristic, complemented
37C2×C11×#104C2211yescharacteristic, complemented
38C2×C11×#104C2211yescharacteristic, complemented
39C2×C11×#104C2211yescharacteristic, complemented
40C2×C11×#104C2211yescharacteristic, complemented
41C11×#407C2211yescharacteristic
42C4×C11×C22⋊C4C2211yescharacteristic
43#10622847—21no—
44#10622847—21no—
45#10622847C2211yescharacteristic, complemented
46#10622847C2211yescharacteristic, complemented
47#10622820—21no—
48#10622820C2211yescharacteristic
49C2×C22⋊(C11⋊C8)—21no—
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51#10622742C2211yescharacteristic, complemented
52#10622742C2211yescharacteristic, complemented
53C2×#66886C2211yescharacteristic, complemented
54C2×#66886C2211yescharacteristic, complemented
55C2×#66869C2211yescharacteristic, complemented
56C2×#66869C2211yescharacteristic, complemented
57C2×#66869C2211yescharacteristic, complemented
58C2×#66869C2211yescharacteristic, complemented
59C2×#66867C2211yescharacteristic, complemented
60C2×C4×C11⋊C8C2211yescharacteristic, complemented
61#10622437—24no—
62#10622436—24no—
63#10622340—21no—
64#10622340—21no—
65#10622339—21no—
66D11×C22⋊C8—21no—
67#10622196C2211yescharacteristic, complemented
68#10622196C2211yescharacteristic, complemented
69#10622162C2211yescharacteristic, complemented
70#10622162C2211yescharacteristic, complemented
71C2×C11×#41—21no—
72C2×C11×#41—21no—
73C2×C11×#41—22no—
74C2×C11×#41—22no—
75C2×C11×#41—41no—
76C2×C11×#41—41no—
77C2×C11×#41C2×C411yescharacteristic
78C2×C11×#41C2×C411yescharacteristic
79C2×C11×#41C2311yescharacteristic
80C2×C11×#41C2311yescharacteristic
81C22×Q8×C11C2×C411yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2×C411yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C2×#4339—21no—
88C2×#4339—21no—
89C2×#4339—22no—
90C2×#4339—22no—
91C2×#4339—41no—
92C2×#4339—41no—
93C2×#4339C2×C411yescharacteristic
94C2×#4339C2×C411yescharacteristic
95C2×#4339C2311yescharacteristic
96C2×#4339C2311yescharacteristic
97C22×D44C2×C411yescharacteristic
98C22×C4×D11—21no—
99C22×Dic22C2×C411yescharacteristic
100C2×C11×M16C2311yescharacteristic
101C2×C11×M16C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105#67004—24no—
106#67004—24no—
107#67003—22no—
108#67003—22no—
109#67003—22no—
110#67003—22no—
111#67003—22no—
112#67003—22no—
113#67003D414yes—
114#67003D414yes—
115#67002—24no—
116#67002—24no—
117#67001—22no—
118#67001—22no—
119#67001—41no—
120#67001—41no—
121C2×#4326C2×C411yescharacteristic
122C2×#4326C2×C411yescharacteristic
123C2×#4326C2×C411yescharacteristic
124C2×#4326C2×C411yescharacteristic
125#66995—24no—
126#66995—24no—
127C2×#4325C2×C411yescharacteristic
128C2×#4325C2×C411yescharacteristic
129C2×#4325C2×C411yescharacteristic
130C2×#4325C2×C411yescharacteristic
131C2×#4324C2×C411yescharacteristic
132C2×#4324C2×C411yescharacteristic
133C2×#4324C2×C411yescharacteristic
134C2×#4324C2×C411yescharacteristic
135#66985—24no—
136#66985—24no—
137C2×#4323C2×C411yescharacteristic
138C2×#4323C2×C411yescharacteristic
139C2×#4323C2×C411yescharacteristic
140C2×#4323C2×C411yescharacteristic
141C2×#4318—22no—
142C2×#4318—22no—
143C2×#4318—21no—
144C2×#4318—21no—
145C2×#4318C2×C411yescharacteristic
146C2×#4318C2×C411yescharacteristic
147C2×#4318C2×C411yescharacteristic
148C2×#4318C2×C411yescharacteristic
149C2×#4318C2311yescharacteristic
150C2×#4318C2311yescharacteristic
151C22×C11⋊C8—21no—
152C22×C11⋊C8—21no—
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157#66960—22no—
158#66960—22no—
159#66960—41no—
160#66960—41no—
161C2×#4313—21no—
162C2×#4313—21no—
163C2×C8×D11—21no—
164C2×C8×D11—21no—
165C11×#104—22no—
166C11×#104—22no—
167C11×#104—41no—
168C11×#104—41no—
169C11×C22⋊C8—21no—
170C11×C22⋊C8—21no—
171C11×#95—21no—
172C22⋊(C11⋊C8)—21no—
173C22⋊(C11⋊C8)—21no—
174C22⋊(C11⋊C8)—21no—
175C22⋊(C11⋊C8)—21no—
176C22⋊(C11⋊C8)—21no—
177C22⋊(C11⋊C8)—21no—
178C22⋊(C11⋊C8)D411yescharacteristic
179C22⋊(C11⋊C8)D411yescharacteristic
180C22⋊(C11⋊C8)D411yescharacteristic
181C22⋊(C11⋊C8)D411yescharacteristic
182#66886—22no—
183#66886—22no—
184(C2×D11)⋊C8—21no—
185(C2×D11)⋊C8—21no—
186(C2×D11)⋊C8—21no—
187(C2×D11)⋊C8—21no—
188#66869—22no—
189#66869—22no—
190#66869—41no—
191#66869—41no—
192#66867—22no—
193C4×C11⋊C8—22no—
194#22453—111nomaximal, Sylow
195C24×C11—21no—
196C24×C11#4111yescharacteristic
197C23×D11—21no—
198C11×#41—21no—
199C11×#41—21no—
200C11×#41—22no—
201C11×#41—22no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41—21no—
205C11×#41—21no—
206C11×#41—42no—
207C11×#41—42no—
208C11×#41—41no—
209C11×#41—41no—
210C11×#41—42no—
211C11×#41—42no—
212C11×#41C2×D412yes—
213C11×#41C2×D412yes—
214C2×Q8×C11—21no—
215C2×Q8×C11—22no—
216C2×Q8×C11—41no—
217C2×Q8×C11C22×C411yescharacteristic
218C2×Q8×C11C22×C411yescharacteristic
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—41no—
226C2×D4×C11—42no—
227C2×D4×C11—42no—
228C2×D4×C11C22×C411yescharacteristic
229C2×D4×C11C22×C411yescharacteristic
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—42no—
242C22×C4×C11—42no—
243C22×C4×C11C22×C411yescharacteristic
244C22×C4×C11C22×C411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11#4111yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C2×C22⋊D11—21no—
250C2×C22⋊D11—21no—
251C2×C22⋊D11—21no—
252C2×C22⋊D11—21no—
253C2×C22⋊D11—42no—
254C2×C22⋊D11—42no—
255C22×Dic11—21no—
256#4339—22no—
257#4339—22no—
258#4339—21no—
259#4339—21no—
260#4339—21no—
261#4339—21no—
262#4339—21no—
263#4339—21no—
264#4339—41no—
265#4339—41no—
266#4339—42no—
267#4339—42no—
268#4339—42no—
269#4339—42no—
270#4339C2×D412yes—
271#4339C2×D412yes—
272C2×D44—22no—
273C2×D44—21no—
274C2×D44—41no—
275C2×D44C22×C411yescharacteristic
276C2×D44C22×C411yescharacteristic
277C2×C4×D11—21no—
278C2×C4×D11—21no—
279C2×C4×D11—21no—
280C2×C4×D11—21no—
281C2×C4×D11—42no—
282C2×C4×D11—42no—
283C2×Dic22—22no—
284C2×Dic22—21no—
285C2×Dic22—41no—
286C2×Dic22C22×C411yescharacteristic
287C2×Dic22C22×C411yescharacteristic
288C11×M16—21no—
289C11×M16—21no—
290C11×M16—21no—
291C11×M16—21no—
292C2×C8×C11—21no—
293C2×C8×C11—21no—
294C11×C22⋊C4—42no—
295C42×C11—21no—
296C42×C11—21no—
297C42×C11—21no—
298C42×C11—21no—
299#4326—22no—
300#4326—22no—
301#4326—22no—
302#4326C22⋊C414yescomplemented
303#4325—22no—
304#4325—22no—
305#4325—22no—
306#4325C22⋊C414yescomplemented
307#4324—22no—
308#4324—22no—
309#4324—22no—
310#4324C22⋊C414yescomplemented
311#4323—22no—
312#4323—22no—
313#4323—22no—
314#4323C22⋊C414yescomplemented
315#4318—22no—
316#4318—22no—
317#4318—22no—
318#4318—22no—
319#4318—21no—
320#4318—21no—
321#4318—21no—
322#4318—21no—
323#4318—42no—
324#4318—42no—
325C2×C11⋊C8—21no—
326C2×C11⋊C8—21no—
327C2×C11⋊C8—21no—
328C2×C11⋊C8—21no—
329C2×C11⋊C8—21no—
330C2×C11⋊C8—21no—
331C2×C11⋊C8—21no—
332C2×C11⋊C8—21no—
333C2×C11⋊C8—42no—
334C2×C11⋊C8—42no—
335C2×C11⋊C8C22×C411yescharacteristic
336C2×C11⋊C8C22×C411yescharacteristic
337C2×C11⋊C8C22×C411yescharacteristic
338C2×C11⋊C8C22×C411yescharacteristic
339C2×C11⋊C8C2×D411yescharacteristic
340C2×C11⋊C8C2×D411yescharacteristic
341C2×C11⋊C8C2×D411yescharacteristic
342C2×C11⋊C8C2×D411yescharacteristic
343C2×C11⋊C8C2×D412yes—
344C2×C11⋊C8C2×D412yes—
345#4313—42no—
346#4313—42no—
347C8×D11—42no—
348C8×D11—42no—
349C2×#575—111no—
350C2×#444—111no—
351C2×#443—111no—
352#2880—111no—
353#2880—111no—
354#1975—111no—
355#1974—111no—
356#1876—111no—
357#1876—111no—
358#1876—111no—
359#1876—111no—
360#1811—111no—
361#1789—111no—
362#1789D1111yescharacteristic, complemented
363#1753—111no—
364C23×C11—21no—
365C23×C11—21no—
366C23×C11—21no—
367C23×C11—21no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—81no—
373C23×C11C4×D411yescharacteristic
374C23×C11C4×D411yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C22×D11—21no—
377C22×D11—21no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—81no—
381Q8×C11—21no—
382Q8×C11—21no—
383Q8×C11—21no—
384Q8×C11—42no—
385Q8×C11C2×C22⋊C412yes—
386D4×C11—22no—
387D4×C11—22no—
388D4×C11—21no—
389D4×C11—21no—
390D4×C11—21no—
391D4×C11—42no—
392D4×C11—42no—
393D4×C11—42no—
394D4×C11—41no—
395D4×C11—41no—
396D4×C11C2×C22⋊C412yes—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—22no—
411C2×C4×C11—21no—
412C2×C4×C11—42no—
413C2×C4×C11—42no—
414C2×C4×C11—42no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11C4×D411yescharacteristic
423C2×C4×C11C4×D411yescharacteristic
424C2×C4×C11C23×C411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C22×D411yescharacteristic
427C2×C4×C11C22×D411yescharacteristic
428C2×C4×C11H(5,𝔽2)11yescharacteristic
429C2×C4×C11H(5,𝔽2)11yescharacteristic
430C22⋊D11—22no—
431C22⋊D11—22no—
432C22⋊D11—42no—
433C22⋊D11—42no—
434C22⋊D11—41no—
435C22⋊D11—41no—
436C2×Dic11—21no—
437C2×Dic11—21no—
438C2×Dic11—42no—
439D44—21no—
440D44—21no—
441D44—21no—
442D44—42no—
443D44C2×C22⋊C412yes—
444C4×D11—22no—
445C4×D11—22no—
446C4×D11—42no—
447C4×D11—42no—
448C4×D11—41no—
449C4×D11—41no—
450Dic22—21no—
451Dic22—21no—
452Dic22—21no—
453Dic22—42no—
454Dic22C2×C22⋊C412yes—
455C8×C11—41no—
456C8×C11—41no—
457C11⋊C8—21no—
458C11⋊C8—21no—
459C11⋊C8—21no—
460C11⋊C8—21no—
461C11⋊C8—21no—
462C11⋊C8—21no—
463C11⋊C8—41no—
464C11⋊C8—41no—
465C11⋊C8C2×C22⋊C412yes—
466C11⋊C8C2×C22⋊C412yes—
467C22×#41—111no—
468C22×#41C2×D1111yescharacteristic
469#575—224no—
470#575—224no—
471C2×#137—111no—
472C2×#137—111no—
473C2×#137—111no—
474C2×#137—111no—
475C2×AGL(1,ℤ/8)—111no—
476C2×AGL(1,ℤ/8)—111no—
477C2×AGL(1,ℤ/8)—111no—
478C2×AGL(1,ℤ/8)—111no—
479C2×#135—111no—
480C2×#135—111no—
481C2×#135—111no—
482C2×#135—111no—
483C2×#131—111no—
484C2×#131—111no—
485C2×#131—111no—
486C2×#131—111no—
487C22×M16—111no—
488#444—224no—
489#443—224no—
490C2×#108—111no—
491C2×#108—111no—
492C2×#104—111no—
493C2×#104—111no—
494C2×#104—111no—
495C2×#104—111no—
496C2×#104C2×D1111yescharacteristic, complemented
497C2×#104C2×D1111yescharacteristic, complemented
498C2×#104C2×D1111yescharacteristic, complemented
499C2×#104C2×D1111yescharacteristic, complemented
500#408—111no—
501#408—111no—
502#408—111no—
503#408—111no—
504#408—221no—
505#408—221no—
506#408—221no—
507#408—221no—
508#407—111no—
509#407—221no—
510#407—221no—
511#407C2×D1111yescharacteristic
512C2×C22⋊C8—111no—
513C2×C22⋊C8—221no—
514C2×C22⋊C8—221no—
515C2×#97—111no—
516C2×C4×C8—111no—
517C4×C22⋊C4C2×D1111yescharacteristic
518#341—111no—
519#341—111no—
520#336—111no—
521#336—111no—
522C22×C11—21no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—22no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—41no—
532C22×C11—41no—
533C22×C11—41no—
534C22×C11—41no—
535C22×C11—41no—
536C22×C11—81no—
537C22×C11—81no—
538C22×C11—84no—
539C22×C11C2×C4×D411yescharacteristic
540C22×C11#54611yescharacteristic
541C22×C11#54611yescharacteristic
542C2×D11—22no—
543C2×D11—41no—
544C2×D11—41no—
545C2×D11—41no—
546C2×D11—41no—
547C2×D11—41no—
548C2×D11—84no—
549C4×C11—21no—
550C4×C11—21no—
551C4×C11—22no—
552C4×C11—42no—
553C4×C11—41no—
554C4×C11—81no—
555C4×C11C22×C22⋊C411yescharacteristic
556C4×C11#51811yescharacteristic
557C4×C11D4211yescharacteristic
558C4×C11D4211yescharacteristic
559Dic11—22no—
560Dic11—41no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—111no—
568C2×#41—111no—
569C2×#41—111no—
570C2×#41—111no—
571C2×#41—222no—
572C2×#41—222no—
573C2×#41—221no—
574C2×#41—221no—
575C2×#41—441no—
576C2×#41—441no—
577C2×#41C4×D1111yescharacteristic
578C2×#41C4×D1111yescharacteristic
579C2×#41C22×D1111yescharacteristic
580C2×#41C22×D1111yescharacteristic
581C22×Q8—111no—
582C22×Q8C4×D1111yescharacteristic
583C22×D4—21no—
584C22×D4—111no—
585C22×D4—221no—
586C22×D4C4×D1111yescharacteristic
587C23×C4—21no—
588C23×C4—221no—
589C23×C4C22×D1111yescharacteristic
590#137—224no—
591#137—224no—
592#137—224no—
593#137—224no—
594AGL(1,ℤ/8)—224no—
595AGL(1,ℤ/8)—224no—
596AGL(1,ℤ/8)—224no—
597AGL(1,ℤ/8)—224no—
598#135—114no—
599#135—114no—
600#135—222no—
601#135—222no—
602#135—222no—
603#135—222no—
604#135—222no—
605#135—222no—
606C2×Q16—111no—
607C2×Q16—111no—
608C2×Q16—111no—
609C2×Q16—111no—
610C2×SD16—111no—
611C2×SD16—111no—
612C2×SD16—111no—
613C2×SD16—111no—
614C2×SD16—111no—
615C2×SD16—111no—
616C2×SD16—111no—
617C2×SD16—111no—
618C2×D8—111no—
619C2×D8—111no—
620C2×D8—111no—
621C2×D8—111no—
622#131—222no—
623#131—222no—
624#131—222no—
625#131—222no—
626#131—441no—
627#131—441no—
628#131—441no—
629#131—441no—
630C2×M16—111no—
631C2×M16—111no—
632C2×M16—111no—
633C2×M16—111no—
634C2×M16—111no—
635C2×M16—111no—
636C2×M16—221no—
637C2×M16—221no—
638C2×M16—222no—
639C2×M16—222no—
640C2×M16—221no—
641C2×M16—221no—
642C2×M16C22×D1111yescharacteristic
643C2×M16C22×D1111yescharacteristic
644C22×C8—111no—
645C22×C8—111no—
646C22×C8—111no—
647C22×C8—111no—
648C22×C8—221no—
649C22×C8—221no—
650C22×C8—221no—
651C22×C8—221no—
652C2×C22⋊C4—21no—
653C2×C42C22×D1111yescharacteristic
654C2×C42C22×D1111yescharacteristic
655#108—222no—
656#108—222no—
657#104—22no—
658#104—22no—
659#104—41no—
660#104—41no—
661#104—222no—
662#104—222no—
663#104—441no—
664#104—441no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—111no—
668C22⋊C8—111no—
669C22⋊C8—111no—
670C22⋊C8—111no—
671C22⋊C8—221no—
672C22⋊C8—221no—
673C22⋊C8—221no—
674C22⋊C8—221no—
675C22⋊C8—221no—
676C22⋊C8—221no—
677C22⋊C8—221no—
678C22⋊C8—221no—
679C22⋊C8—221no—
680C22⋊C8—221no—
681#97—222no—
682C4×C8—222no—
683#95—21no—
684C2×C11—21no—
685C2×C11—21no—
686C2×C11—41no—
687C2×C11—41no—
688C2×C11—42no—
689C2×C11—81no—
690C2×C11D4×C22⋊C411yescharacteristic
691C2×C11#295511yescharacteristic
692C2×C11#295611yescharacteristic
693D11—42no—
694D11—81no—
695C24—21no—
696C24—221no—
697C24#434111yescharacteristic
698#41—21no—
699#41—21no—
700#41—22no—
701#41—22no—
702#41—21no—
703#41—21no—
704#41—21no—
705#41—21no—
706#41—42no—
707#41—42no—
708#41—41no—
709#41—41no—
710#41—42no—
711#41—42no—
712#41—112no—
713#41—112no—
714#41—222no—
715#41—222no—
716#41—221no—
717#41—221no—
718#41—221no—
719#41—221no—
720#41—221no—
721#41—221no—
722#41—442no—
723#41—442no—
724#41—441no—
725#41—441no—
726#41—442no—
727#41—442no—
728#41D4×D1112yes—
729#41D4×D1112yes—
730C2×Q8—21no—
731C2×Q8—22no—
732C2×Q8—41no—
733C2×Q8—111no—
734C2×Q8—111no—
735C2×Q8—222no—
736C2×Q8—221no—
737C2×Q8—441no—
738C2×Q8C2×C4×D1111yescharacteristic
739C2×Q8C2×C4×D1111yescharacteristic
740C2×D4—21no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—41no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—111no—
750C2×D4—111no—
751C2×D4—222no—
752C2×D4—221no—
753C2×D4—221no—
754C2×D4—221no—
755C2×D4—221no—
756C2×D4—221no—
757C2×D4—441no—
758C2×D4—442no—
759C2×D4—442no—
760C2×D4C2×C4×D1111yescharacteristic
761C2×D4C2×C4×D1111yescharacteristic
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—221no—
776C22×C4—221no—
777C22×C4—221no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—442no—
781C22×C4—442no—
782C22×C4C2×C4×D1111yescharacteristic
783C22×C4C2×C4×D1111yescharacteristic
784C22×C4D4×D1111yescharacteristic
785C22×C4D4×D1111yescharacteristic
786C22×C4#434111yescharacteristic
787C22×C4C23×D1111yescharacteristic
788Q16—114no—
789Q16—222no—
790Q16—222no—
791Q16—222no—
792SD16—114no—
793SD16—114no—
794SD16—222no—
795SD16—222no—
796SD16—222no—
797SD16—222no—
798SD16—222no—
799SD16—222no—
800D8—114no—
801D8—222no—
802D8—222no—
803D8—222no—
804M16—21no—
805M16—21no—
806M16—21no—
807M16—21no—
808M16—222no—
809M16—222no—
810M16—222no—
811M16—222no—
812M16—221no—
813M16—221no—
814M16—221no—
815M16—221no—
816M16—442no—
817M16—442no—
818M16—442no—
819M16—442no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—111no—
823C2×C8—111no—
824C2×C8—112no—
825C2×C8—112no—
826C2×C8—111no—
827C2×C8—111no—
828C2×C8—111no—
829C2×C8—111no—
830C2×C8—111no—
831C2×C8—111no—
832C2×C8—221no—
833C2×C8—221no—
834C2×C8—221no—
835C2×C8—221no—
836C2×C8—221no—
837C2×C8—221no—
838C2×C8—221no—
839C2×C8—221no—
840C2×C8—442no—
841C2×C8—442no—
842C2×C8—442no—
843C2×C8—442no—
844C22⋊C4—42no—
845C42—21no—
846C42—21no—
847C42—21no—
848C42—21no—
849C11#2245311yescharacteristic, complemented, Sylow
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—81no—
859C23—221no—
860C23—221no—
861C23—442no—
862C23—442no—
863C23—881no—
864C23(C22⋊D11)⋊C411yescharacteristic
865C23(C22⋊D11)⋊C411yescharacteristic
866C23C2×#434111yescharacteristic
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—42no—
871Q8—112no—
872Q8—221no—
873Q8—221no—
874Q8—221no—
875Q8—442no—
876Q8C22⋊C4×D1112yes—
877D4—22no—
878D4—22no—
879D4—21no—
880D4—21no—
881D4—21no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—41no—
886D4—41no—
887D4—112no—
888D4—222no—
889D4—222no—
890D4—221no—
891D4—221no—
892D4—221no—
893D4—442no—
894D4—442no—
895D4—442no—
896D4—441no—
897D4—441no—
898D4C22⋊C4×D1112yes—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—221no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—221no—
928C2×C4—442no—
929C2×C4—442no—
930C2×C4—442no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4(C22⋊D11)⋊C411yescharacteristic
934C2×C4(C22⋊D11)⋊C411yescharacteristic
935C2×C4C22×C4×D1111yescharacteristic
936C2×C4C2×D4×D1111yescharacteristic
937C2×C4C2×D4×D1111yescharacteristic
938C2×C4C2×D4×D1111yescharacteristic
939C2×C4#6703711yescharacteristic
940C2×C4#6703711yescharacteristic
941C8—41no—
942C8—41no—
943C8—112no—
944C8—112no—
945C8—221no—
946C8—221no—
947C8—221no—
948C8—221no—
949C8—221no—
950C8—221no—
951C8—441no—
952C8—441no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—81no—
968C22—81no—
969C22—84no—
970C22—222no—
971C22—441no—
972C22—441no—
973C22—441no—
974C22—441no—
975C22—441no—
976C22—884no—
977C22C2×(C22⋊D11)⋊C411yescharacteristic
978C22#1062312211yescharacteristic
979C22#1062312211yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—81no—
986C4—222no—
987C4—441no—
988C4C2×C22⋊C4×D1111yescharacteristic
989C4#1062301711yescharacteristic
990C4#1062312111yescharacteristic
991C4#1062312111yescharacteristic
992C2—21no—
993C2—21no—
994C2—41no—
995C2—41no—
996C2—42no—
997C2—81no—
998C2—442no—
999C2—881no—
1000C2#1307143211yescharacteristic
1001C2#1307751511yescharacteristic
1002C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1789C2
socleC22×C11C2×C4×D4
prime radicalC2×#10623353C2
cosocleC22×C4×C11C24
hypercenter#1789D11
hypocenterC11#22453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. C2×#10622436C2semidirect
3. C2×#10622437C2semidirect
4. #13077066C2semidirect
5. #13077065C2semidirect
6. #13069506C2semidirect
7. #13069501C2semidirect
8. #13068941C2semidirect
9. #13068941C2semidirect
10. #13068940C2semidirect
11. #13068940C2semidirect
12. #13068656C2semidirect
13. #13068561C2semidirect
14. #13068400C2semidirect
15. C11×#1789C2semidirect
18. C2×#67004C4semidirect
19. C2×#67004C4semidirect
26. C2×#67002C4semidirect
27. C2×#67002C4semidirect
28. C2×#67001C22semidirect
29. C2×#67001C22semidirect
30. C2×#66995C4semidirect
31. C2×#66995C4semidirect
32. C2×#66985C4semidirect
33. C2×#66985C4semidirect
35. C2×#66960C22semidirect
36. C2×#66960C22semidirect
37. C2×C11×#104C22semidirect
38. C2×C11×#104C22semidirect
39. C2×C11×#104C22semidirect
40. C2×C11×#104C22semidirect
45. #10622847C22semidirect
46. #10622847C22semidirect
51. #10622742C22semidirect
52. #10622742C22semidirect
53. C2×#66886C22semidirect
54. C2×#66886C22semidirect
55. C2×#66869C22semidirect
56. C2×#66869C22semidirect
57. C2×#66869C22semidirect
58. C2×#66869C22semidirect
59. C2×#66867C22semidirect
60. C2×C4×C11⋊C8C22semidirect
67. #10622196C22semidirect
68. #10622196C22semidirect
69. #10622162C22semidirect
70. #10622162C22semidirect
302. #4326C22⋊C4semidirect
306. #4325C22⋊C4semidirect
310. #4324C22⋊C4semidirect
314. #4323C22⋊C4semidirect
362. #1789D11semidirect
496. C2×#104C2×D11semidirect
497. C2×#104C2×D11semidirect
498. C2×#104C2×D11semidirect
499. C2×#104C2×D11semidirect
849. C11#22453semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106224362
C2×#106224372
#130770662
#130770652
#130695062
#130695012
#130689412
#130689402
#130686562
#130685612
#130684002
C11×#17892
#2245311