Finite Group Databasebeta

← #14796191

Subgroups — #14796191

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622787C211yesmaximal, characteristic, complemented
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622494C211yesmaximal, characteristic, complemented
4#13072063C211yesmaximal, characteristic, complemented
5#13072030C211yesmaximal, characteristic
6#13070007C211yesmaximal, characteristic, complemented
7#13069986C211yesmaximal, characteristic, complemented
8#13069809C211yesmaximal, characteristic, complemented
9#13069795C211yesmaximal, characteristic, complemented
10#13069472C211yesmaximal, characteristic, complemented
11#13069350C211yesmaximal, characteristic, complemented
12#13068930C211yesmaximal, characteristic, complemented
13#13068925C211yesmaximal, characteristic, complemented
14#13068649C211yesmaximal, characteristic, complemented
15C2×C11×#468C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C2×#66945C2211yescharacteristic
25C2×C4⋊C4×D11C2211yescharacteristic
26C11×#468—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30#10622843C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622836—21no—
34#10622834—21no—
35#10622834C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622825C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622787—24no—
42#10622741—24no—
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×#66882C2211yescharacteristic
45C2×#66881C2211yescharacteristic
46C2×Dic11⋊C8C2211yescharacteristic
47C2×C8×Dic11C2211yescharacteristic
48#10622600—21no—
49#10622598C2211yescharacteristic
50#10622598C2211yescharacteristic
51#10622593—21no—
52C2×#66872C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54#10622574—21no—
55#10622569—21no—
56#10622561—21no—
57#10622557—21no—
58#10622494—24no—
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11D411yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C2×C11×SD16—22no—
72C2×C11×SD16—22no—
73C2×C11×SD16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—41no—
81C11×#121—22no—
82C11×#121—41no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11D411yescharacteristic
94#66999—22no—
95#66999—22no—
96#66991—22no—
97#66991—22no—
98C4×C22⋊D11—22no—
99C4×C22⋊D11—22no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4D411yescharacteristic
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4D411yescharacteristic
112C2×C4×Dic11—21no—
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C2×#4313—22no—
117C2×#4313—22no—
118C2×#4313D414yescomplemented
119#66945—22no—
120#66945—41no—
121C4⋊C4×D11—22no—
122C4⋊C4×D11—41no—
123C11×#107D414yescomplemented
124C11×#103—22no—
125C11×#102—22no—
126#66899—22no—
127#66899—41no—
128#66896—22no—
129#66896—41no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C22⋊(C11⋊C8)—22no—
137(C2×D11)⋊C8—22no—
138#66882—22no—
139#66881—22no—
140Dic11⋊C8—22no—
141C8×Dic11—22no—
142#66872—22no—
143#66871—22no—
144#24795—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C23×D11C2×D411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—81no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C2×C22⋊D11—22no—
175C2×C22⋊D11—22no—
176C2×C22⋊D11—41no—
177C2×C22⋊D11—42no—
178C2×C22⋊D11—81no—
179C2×C22⋊D11—81no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11C2×D411yescharacteristic
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—81no—
194C2×C4×D11C2×D412yes—
195C2×C4×D11#4112yes—
196C11×SD16—44no—
197C11×M16—44no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11C2×D412yes—
202C2×C8×C11C2×D412yes—
203C2×C8×C11#4112yes—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—42no—
207C11×C4⋊C4C2×D412yes—
208C11×C4⋊C4C2×D412yes—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C22⋊Dic11—22no—
212C22⋊Dic11—42no—
213C22⋊Dic11—42no—
214C22⋊Dic11—81no—
215C22⋊Dic11—81no—
216C22⋊Dic11—81no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—42no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—81no—
229C4⋊Dic11—81no—
230Dic11⋊C4—22no—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—42no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8C2×D412yes—
242#4313—28no—
243C2×#468—111no—
244C2×#468D1111yescharacteristic, complemented
245C2×#436—111no—
246C2×#428—111no—
247#2417—111no—
248#2414—111no—
249#2068—111no—
250#2065—111no—
251#2035—111no—
252#2033—111no—
253#1968—111no—
254#1942—111no—
255#1874—111no—
256#1873—111no—
257#1809—111no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11C22×D411yescharacteristic
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11#12112yes—
280Q8×C11—41no—
281Q8×C11—41no—
282Q8×C11—41no—
283Q8×C11—41no—
284D4×C11—41no—
285D4×C11—41no—
286D4×C11—41no—
287D4×C11—41no—
288D4×C11—84no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C22⋊D11—44no—
312C22⋊D11—84no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
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—41no—
332C2×Dic11#12112yes—
333C2×Dic11#13712yes—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—22no—
338C4×D11—84no—
339C8×C11—41no—
340C8×C11#12114yes—
341C11⋊C8—22no—
342C11⋊C8—41no—
343C22×SD16C2×D1111yescharacteristic
344C22×M16—111no—
345C22×M16C2×D1111yescharacteristic
346C2×C22⋊Q8—111no—
347C2×C22⋊Q8C2×D1111yescharacteristic
348C2×#121—111no—
349C2×#121C2×D1111yescharacteristic
350C2×C4×D4—111no—
351C2×#117—111no—
352C22×C4⋊C4—111no—
353#468—24no—
354#468—224no—
355#436—224no—
356#428—224no—
357C2×#107—111no—
358C2×#107—111no—
359C2×#107C2×D1111yescharacteristic
360C2×#106—111no—
361C2×#106—111no—
362C2×C4⋊C8—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103C2×D1111yescharacteristic
366C2×#102—111no—
367C2×#102—111no—
368C2×#102C2×D1111yescharacteristic
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C4×C8—111no—
372#398—221no—
373#396—221no—
374#394—221no—
375#392—221no—
376#391—111no—
377#390—111no—
378#390—221no—
379#389—111no—
380#389—111no—
381#388—221no—
382#386—221no—
383#380—111no—
384#380—111no—
385#380—221no—
386#340—111no—
387#340—111no—
388#340—111no—
389#340—111no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11C2×#12111yescharacteristic
405C22×C11D4211yescharacteristic
406C22×C11#54711yescharacteristic
407C22×C11C2×#13711yescharacteristic
408C22×C11#57511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57711yescharacteristic
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C4×C11—41no—
419C4×C11—42no—
420C4×C11—42no—
421C4×C11—81no—
422C4×C11C2×#12111yescharacteristic
423C4×C11#53711yescharacteristic
424C4×C11#54811yescharacteristic
425C4×C11#55311yescharacteristic
426Dic11—22no—
427Dic11—22no—
428Dic11—41no—
429Dic11—81no—
430Dic11—81no—
431Dic11—81no—
432Dic11—81no—
433C22×Q8C22×D1111yescharacteristic
434C22×D4—21no—
435C22×D4—111no—
436C22×D4—221no—
437C22×D4C22×D1111yescharacteristic
438C23×C4—111no—
439C23×C4—221no—
440C23×C4C22×D1111yescharacteristic
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×M16—22no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—114no—
448C2×M16—222no—
449C2×M16—222no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454C22⋊Q8—22no—
455C22⋊Q8—41no—
456C22⋊Q8—222no—
457C22⋊Q8—222no—
458#121—22no—
459#121—41no—
460#121—222no—
461#121—222no—
462C4×D4—222no—
463C4×D4—222no—
464#117—222no—
465#117—441no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—441no—
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
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×C42—111no—
492C2×C42—221no—
493#107—222no—
494#107—222no—
495#107C22⋊D1114yescomplemented
496#106—222no—
497#106—222no—
498C4⋊C8—222no—
499#103—22no—
500#103—222no—
501#103—441no—
502#102—22no—
503#102—222no—
504#102—441no—
505C22⋊C8—222no—
506C22⋊C8—222no—
507C4×C8—222no—
508#95—221no—
509#95—221no—
510#95—221no—
511#95—221no—
512#95—221no—
513#95—221no—
514C2×C11—81no—
515C2×C11—161no—
516C2×C11#241611yescharacteristic
517C2×C11#305611yescharacteristic
518C2×C11#306211yescharacteristic
519C2×C11#327311yescharacteristic
520C2×C11#327811yescharacteristic
521C2×C11#335111yescharacteristic
522C2×C11#335711yescharacteristic
523D11—42no—
524C24—21no—
525C24—111no—
526C24D4×D1111yescharacteristic
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—81no—
542C2×D4—222no—
543C2×D4—222no—
544C2×D4—441no—
545C2×D4—442no—
546C2×D4—881no—
547C2×D4—881no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—111no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—442no—
571C22×C4—442no—
572C22×C4—881no—
573C22×C4D4×D1111yescharacteristic
574C22×C4C23×D1111yescharacteristic
575SD16—44no—
576M16—44no—
577M16—228no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—112no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8D4×D1112yes—
588C2×C8#434112yes—
589C2×C8C2×C22⋊D1112yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—222no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—442no—
603C4⋊C4—442no—
604C4⋊C4—881no—
605C4⋊C4—881no—
606C4⋊C4C2×C22⋊D1112yes—
607C4⋊C4C2×C22⋊D1112yes—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—222no—
611C22⋊C4—222no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—881no—
617C22⋊C4—881no—
618C22⋊C4—881no—
619C42—221no—
620C42—221no—
621C42—442no—
622C11#2479511yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—112no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23C2×D4×D1111yescharacteristic
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654D4—444no—
655D4—884no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—112no—
673C2×C4—112no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
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×C4C2×D4×D1111yescharacteristic
699C2×C4C2×#434111yescharacteristic
700C2×C4#6703711yescharacteristic
701C2×C4#41×D1111yescharacteristic
702C2×C4#6704311yescharacteristic
703C2×C4C22×C22⋊D1111yescharacteristic
704C8—41no—
705C8—222no—
706C8—441no—
707C8#6699114yes—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—222no—
723C22—222no—
724C22—222no—
725C22—441no—
726C22—441no—
727C22—441no—
728C22—441no—
729C22D11×#12111yescharacteristic
730C22#1062314211yescharacteristic
731C22#1062330411yescharacteristic
732C22#1062330511yescharacteristic
733C22D11×#13711yescharacteristic
734C22#1062330911yescharacteristic
735C22D4×C22⋊D1111yescharacteristic
736C4—42no—
737C4—42no—
738C4—41no—
739C4—81no—
740C4—222no—
741C4—222no—
742C4—441no—
743C4—881no—
744C4—881no—
745C4—881no—
746C4—881no—
747C4#1062313911yescharacteristic
748C4#1062314511yescharacteristic
749C4C2×#6699111yescharacteristic
750C4#1062336211yescharacteristic
751C2—81no—
752C2—161no—
753C2—442no—
754C2#1307205211yescharacteristic
755C2#1307824111yescharacteristic
756C2#1307829111yescharacteristic
757C2#1308022111yescharacteristic
758C2#1308027611yescharacteristic
759C2#1308117111yescharacteristic
760C2#1308123711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
prime radical#13072030C2
hypercenterC2×#468D11
hypocenterC11#24795
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10622787C2semidirect
2. C2×#10622741C2semidirect
3. C2×#10622494C2semidirect
4. #13072063C2semidirect
6. #13070007C2semidirect
7. #13069986C2semidirect
8. #13069809C2semidirect
9. #13069795C2semidirect
10. #13069472C2semidirect
11. #13069350C2semidirect
12. #13068930C2semidirect
13. #13068925C2semidirect
14. #13068649C2semidirect
15. C2×C11×#468C2semidirect
118. C2×#4313D4semidirect
123. C11×#107D4semidirect
244. C2×#468D11semidirect
495. #107C22⋊D11semidirect
622. C11#24795semidirect

Maximal subgroups

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

subgroupindex
C2×#106227872
C2×#106227412
C2×#106224942
#130720632
#130720302
#130700072
#130699862
#130698092
#130697952
#130694722
#130693502
#130689302
#130689252
#130686492
C2×C11×#4682
#2479511