Finite Group Databasebeta

← #14796180

Subgroups — #14796180

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622747C211yesmaximal, characteristic, complemented
2C2×#10622747C211yesmaximal, characteristic, complemented
3C2×#10622734C211yesmaximal, characteristic, complemented
4#13072056C211yesmaximal, characteristic
5#13072045C211yesmaximal, characteristic, complemented
6#13070003C211yesmaximal, characteristic, complemented
7#13069996C211yesmaximal, characteristic, complemented
8#13069820C211yesmaximal, characteristic, complemented
9#13069806C211yesmaximal, characteristic, complemented
10#13069470C211yesmaximal, characteristic, complemented
11#13069349C211yesmaximal, characteristic, complemented
12#13068936C211yesmaximal, characteristic, complemented
13#13068921C211yesmaximal, characteristic, complemented
14#13068649C211yesmaximal, characteristic, complemented
15C2×C11×#436C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66992—21no—
20C2×#66983C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C11×#436—24no—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C4×C8×C11C2211yescharacteristic
32#10622835—21no—
33#10622825C2211yescharacteristic
34#10622825C2211yescharacteristic
35#10622747—24no—
36#10622747—24no—
37#10622734—24no—
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66882C2211yescharacteristic
43C2×#66882C2211yescharacteristic
44C2×#66881C2211yescharacteristic
45C2×#66881C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47C2×#66880C2211yescharacteristic
48C2×#66880C2211yescharacteristic
49#10622607—21no—
50#10622585—21no—
51#10622574—21no—
52#10622571—21no—
53#10622565—21no—
54#10622558—21no—
55#10622552C2211yescharacteristic
56#10622542C2211yescharacteristic
57#10622541C2211yescharacteristic
58#10622541C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622189C2211yescharacteristic
63C22×D4×C11D411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C22×D44C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16D414yescomplemented
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92#66992—44no—
93#66983—22no—
94#66983—22no—
95#66983—22no—
96#66983—41no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101#66979—22no—
102#66979—41no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—41no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112#66977—22no—
113#66977—22no—
114#66977—22no—
115#66977—41no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×#4314—22no—
122C2×#4314—22no—
123C2×#4314—22no—
124C11×C4⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C4×C8×C11—22no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134#66885—22no—
135#66885—22no—
136#66885—41no—
137#66882—22no—
138#66882—22no—
139#66882D414yescomplemented
140#66881—22no—
141#66881—22no—
142#66880—22no—
143#66880—22no—
144#66880—41no—
145#24794—111nomaximal, Sylow
146C24×C11C2×D411yescharacteristic
147C24×C11C2×D411yescharacteristic
148C23×D11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—41no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11#4112yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C2×C22⋊D11—42no—
172C2×C22⋊D11—42no—
173C2×C22⋊D11—42no—
174C2×C22⋊D11—81no—
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—
184C22×Dic11—81no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C11×M16—28no—
198C11×M16—44no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11C2×D412yes—
208C2×C8×C11C2×D412yes—
209C2×C8×C11C2×D412yes—
210C2×C8×C11#4112yes—
211C11×C4⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C42×C11—21no—
215C42×C11—21no—
216C22⋊Dic11—42no—
217C22⋊Dic11—42no—
218C22⋊Dic11—42no—
219C22⋊Dic11—42no—
220C22⋊Dic11—42no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—81no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—42no—
236C4⋊Dic11C2×D412yes—
237C4⋊Dic11C2×D412yes—
238Dic11⋊C4—42no—
239Dic11⋊C4—42no—
240Dic11⋊C4—42no—
241Dic11⋊C4—42no—
242C4×Dic11—42no—
243#4314—44no—
244C2×#468—111no—
245C2×#468—111no—
246C2×#436D1111yescharacteristic, complemented
247C2×#428—111no—
248#2416—111no—
249#2415—111no—
250#2067—111no—
251#2066—111no—
252#2036—111no—
253#2034—111no—
254#1968—111no—
255#1942—111no—
256#1875—111no—
257#1872—111no—
258#1809—111no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11#12112yes—
273C23×C11C22×D411yescharacteristic
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281D4×C11—44no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11#12112yes—
301C2×C4×C11AGL(1,ℤ/8)12yes—
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11H(5,𝔽2)11yescharacteristic
307C2×C4×C112−1+411yescharacteristic
308C22⋊D11—84no—
309C22⋊D11—84no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—84no—
332D44—41no—
333D44—41no—
334D44—41no—
335D44—41no—
336Dic22—41no—
337Dic22—41no—
338Dic22—41no—
339Dic22—41no—
340C8×C11—22no—
341C8×C11—41no—
342C8×C11—41no—
343C8×C11#12114yescomplemented
344C22×SD16—111no—
345C22×M16C2×D1111yescharacteristic
346C22×M16C2×D1111yescharacteristic
347C2×C22⋊Q8—111no—
348C2×C22⋊Q8—111no—
349C2×#121—111no—
350C2×#121—111no—
351C2×#121—221no—
352C2×C4×D4C2×D1111yescharacteristic
353C2×#117—111no—
354C22×C4⋊C4—111no—
355#468—224no—
356#468—224no—
357#436—24no—
358#428—224no—
359C2×#107—111no—
360C2×#107—111no—
361C2×#107—111no—
362C2×#106—111no—
363C2×#106—111no—
364C2×C4⋊C8C2×D1111yescharacteristic
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×C22⋊C8C2×D1111yescharacteristic
372C2×C22⋊C8C2×D1111yescharacteristic
373C2×C4×C8C2×D1111yescharacteristic
374#397—221no—
375#396—221no—
376#394—221no—
377#394—221no—
378#391—111no—
379#390—111no—
380#389—111no—
381#389—111no—
382#389—221no—
383#388—221no—
384#386—221no—
385#380—111no—
386#380—111no—
387#340—111no—
388#340—111no—
389#340—111no—
390#340—111no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11C2×#12111yescharacteristic
406C22×C11D4211yescharacteristic
407C22×C11#54711yescharacteristic
408C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C11#57511yescharacteristic
410C22×C11#57711yescharacteristic
411C22×C11#57811yescharacteristic
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—81no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11C2×#12111yescharacteristic
424C4×C11#53711yescharacteristic
425C4×C11#54811yescharacteristic
426C4×C11#55311yescharacteristic
427Dic11—42no—
428Dic11—42no—
429Dic11—81no—
430Dic11—81no—
431Dic11—81no—
432Dic11—81no—
433Dic11—81no—
434C22×Q8—111no—
435C22×D4—111no—
436C22×D4—221no—
437C22×D4—221no—
438C22×D4D4411yescharacteristic
439C23×C4—221no—
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C2×SD16—222no—
443C2×SD16—222no—
444C2×SD16—222no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—22no—
450C2×M16C22⋊D1114yescomplemented
451C22×C8C22×D1111yescharacteristic
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454C22×C8C22×D1111yescharacteristic
455C22⋊Q8—222no—
456C22⋊Q8—222no—
457C22⋊Q8—222no—
458C22⋊Q8—441no—
459#121—222no—
460#121—222no—
461#121—222no—
462#121—441no—
463#121—444no—
464C4×D4—22no—
465C4×D4—22no—
466#117—222no—
467#117—441no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—222no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—441no—
481C2×C4⋊C4D4411yescharacteristic
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4D4411yescharacteristic
492C2×C22⋊C4D4411yescharacteristic
493C2×C42—221no—
494C2×C42C22×D1111yescharacteristic
495#107—114no—
496#107—222no—
497#107—222no—
498#106—222no—
499#106—222no—
500C4⋊C8—22no—
501#103—222no—
502#103—222no—
503#103—441no—
504#102—222no—
505#102—222no—
506#102—441no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C4×C8—22no—
510#95—221no—
511#95—221no—
512#95—221no—
513#95—221no—
514#95—221no—
515#95—221no—
516C2×C11—42no—
517C2×C11—81no—
518C2×C11#241611yescharacteristic
519C2×C11#305511yescharacteristic
520C2×C11#306311yescharacteristic
521C2×C11#327211yescharacteristic
522C2×C11#327711yescharacteristic
523C2×C11#335111yescharacteristic
524C2×C11#335311yescharacteristic
525D11—161no—
526C24—221no—
527C24C2×D4411yescharacteristic
528C24C2×D4411yescharacteristic
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—221no—
533C2×Q8—221no—
534C2×Q8—221no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—41no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—442no—
545C2×D4—442no—
546C2×D4—442no—
547C2×D4—442no—
548C2×D4—442no—
549C2×D4—881no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—442no—
568C22×C4—442no—
569C22×C4—881no—
570C22×C4C2×D4411yescharacteristic
571C22×C4C2×D4411yescharacteristic
572C22×C4C2×D4411yescharacteristic
573C22×C4C2×D4411yescharacteristic
574C22×C4#433912yes—
575C22×C4C2×C22⋊D1112yes—
576C22×C4C23×D1111yescharacteristic
577SD16—444no—
578M16—28no—
579M16—44no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8D4×D1112yes—
589C2×C8#434112yes—
590C2×C8C2×C22⋊D1112yes—
591C2×C8C2×C22⋊D1112yes—
592C4⋊C4—22no—
593C4⋊C4—112no—
594C4⋊C4—112no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—442no—
606C4⋊C4—442no—
607C4⋊C4—442no—
608C4⋊C4—442no—
609C4⋊C4—442no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—881no—
621C42—21no—
622C42—21no—
623C42—442no—
624C11#2479411yescharacteristic, complemented, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23#6698312yes—
646C23C22×D4411yescharacteristic
647Q8—441no—
648Q8—441no—
649Q8—441no—
650Q8—441no—
651D4—44no—
652D4—441no—
653D4—441no—
654D4—441no—
655D4—441no—
656D4—884no—
657D4—884no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—884no—
698C2×C4#6696112yes—
699C2×C4#6698312yes—
700C2×C4C2×#433911yescharacteristic
701C2×C4C2×D4×D1111yescharacteristic
702C2×C4C2×#434111yescharacteristic
703C2×C4#6704211yescharacteristic
704C2×C4#6704311yescharacteristic
705C2×C4C22×C22⋊D1111yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8#6699214yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—881no—
725C22—881no—
726C22—881no—
727C22—881no—
728C22—881no—
729C22—881no—
730C22—881no—
731C22D4×D4411yescharacteristic
732C22#1062308611yescharacteristic
733C22C2×#6696111yescharacteristic
734C22#1062327911yescharacteristic
735C22#1062328211yescharacteristic
736C22#1062328411yescharacteristic
737C22C2×#6698311yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—442no—
743C4—442no—
744C4—881no—
745C4—881no—
746C4—881no—
747C4—881no—
748C4—881no—
749C4#1062308311yescharacteristic
750C4#1062309611yescharacteristic
751C4C2×#6699211yescharacteristic
752C4#1062336411yescharacteristic
753C2—42no—
754C2—81no—
755C2—1761no—
756C2#1307205611yescharacteristic
757C2#1307823511yescharacteristic
758C2#1307830711yescharacteristic
759C2#1308021811yescharacteristic
760C2#1308027411yescharacteristic
761C2#1308117811yescharacteristic
762C2#1308120111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#436C2
socleC23×C11C22×D4
prime radical#13072056C2
hypercenterC2×#436D11
hypocenterC11#24794
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#10622747C2semidirect
2. C2×#10622747C2semidirect
3. C2×#10622734C2semidirect
5. #13072045C2semidirect
6. #13070003C2semidirect
7. #13069996C2semidirect
8. #13069820C2semidirect
9. #13069806C2semidirect
10. #13069470C2semidirect
11. #13069349C2semidirect
12. #13068936C2semidirect
13. #13068921C2semidirect
14. #13068649C2semidirect
15. C2×C11×#436C2semidirect
76. C2×C11×M16D4semidirect
139. #66882D4semidirect
246. C2×#436D11semidirect
343. C8×C11#121semidirect
450. C2×M16C22⋊D11semidirect
624. C11#24794semidirect
709. C8#66992semidirect

Maximal subgroups

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

subgroupindex
C2×#106227472
C2×#106227342
#130720562
#130720452
#130700032
#130699962
#130698202
#130698062
#130694702
#130693492
#130689362
#130689212
#130686492
C2×C11×#4362
#2479411