Finite Group Databasebeta

← #14660581

Subgroups — #14660581

Order 2816.

1390 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4326C211yesmaximal, characteristic
2C22×#66880C211yesmaximal, characteristic
3C2×#10622843C211yesmaximal, characteristic
4C2×#10622587C211yesmaximal, characteristic
5C2×#10622167C211yesmaximal, characteristic
6C2×#10622188C211yesmaximal, characteristic
7C22×C11×#103C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×#4326—22no—
13C22×#4326—22no—
14C22×#4326—22no—
15C22×#4326—22no—
16C22×#4326—22no—
17C22×#4326—22no—
18C22×#4326C414yescomplemented
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×C11×#103—22no—
23C2×C11×#103—22no—
24C2×C11×#103—22no—
25#10622843—22no—
26#10622843—22no—
27C2×C11⋊#95—22no—
28C2×C11⋊#95—22no—
29C2×#66880—22no—
30C2×#66880—22no—
31C2×#66880—22no—
32#10622587—22no—
33#10622587—22no—
34#10622188—22no—
35#10622167—22no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11C2×C412yes—
48C22×Q8×C11D412yes—
49C22×Q8×C11D412yes—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C23×Dic11—21no—
55C23×Dic11D412yes—
56C22×Dic22—21no—
57C22×Dic22—21no—
58C22×Dic22—21no—
59C22×Dic22—21no—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C22×Dic22—21no—
63C22×Dic22—21no—
64C22×Dic22—21no—
65C22×Dic22—21no—
66C22×Dic22—21no—
67C22×Dic22C2×C412yes—
68C22×Dic22D412yes—
69C22×Dic22D412yes—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11D412yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D412yes—
83C2×#4326—28no—
84C2×#4326—28no—
85C2×#4326—28no—
86C2×#4326—28no—
87C2×#4326—28no—
88C2×#4326—28no—
89C2×#4326—28no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11D412yes—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8C2×C412yes—
107C22×C11⋊C8D412yes—
108C22×C11⋊C8D412yes—
109C11×#103—28no—
110C11⋊#95—28no—
111C11⋊#95—28no—
112#66880—28no—
113#11024—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—41no—
131C2×Q8×C11—41no—
132C2×Q8×C11—41no—
133C2×Q8×C11—41no—
134C2×Q8×C11—41no—
135C2×Q8×C11—41no—
136C2×Q8×C11—41no—
137C2×Q8×C11—41no—
138C2×Q8×C11—41no—
139C2×Q8×C11—41no—
140C2×Q8×C11—41no—
141C2×Q8×C11—41no—
142C2×Q8×C11C22⋊C414yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—41no—
180C22×Dic11—41no—
181C22×Dic11—41no—
182C22×Dic11—41no—
183C22×Dic11—41no—
184C22×Dic11—41no—
185C22×Dic11—42no—
186C22×Dic11—42no—
187C22×Dic11Q1614yescomplemented
188C2×Dic22—22no—
189C2×Dic22—22no—
190C2×Dic22—22no—
191C2×Dic22—22no—
192C2×Dic22—22no—
193C2×Dic22—22no—
194C2×Dic22—22no—
195C2×Dic22—22no—
196C2×Dic22—22no—
197C2×Dic22—22no—
198C2×Dic22—22no—
199C2×Dic22—22no—
200C2×Dic22—22no—
201C2×Dic22—22no—
202C2×Dic22—22no—
203C2×Dic22—41no—
204C2×Dic22—41no—
205C2×Dic22—41no—
206C2×Dic22—41no—
207C2×Dic22—41no—
208C2×Dic22—41no—
209C2×Dic22—41no—
210C2×Dic22—41no—
211C2×Dic22—41no—
212C2×Dic22—41no—
213C2×Dic22—41no—
214C2×Dic22—41no—
215C2×Dic22C22⋊C414yes—
216C2×C8×C11—22no—
217C2×C8×C11—22no—
218C2×C8×C11—22no—
219C2×C8×C11—41no—
220C2×C8×C11—41no—
221C2×C8×C11—41no—
222C2×C8×C11—41no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—41no—
226C11×C4⋊C4—41no—
227#4326—232no—
228C4⋊Dic11—22no—
229C4⋊Dic11—22no—
230C4⋊Dic11—41no—
231C4⋊Dic11—41no—
232C4×Dic11—41no—
233C4×Dic11—41no—
234C4×Dic11—41no—
235C4×Dic11—41no—
236C2×C11⋊C8—22no—
237C2×C11⋊C8—22no—
238C2×C11⋊C8—22no—
239C2×C11⋊C8—22no—
240C2×C11⋊C8—22no—
241C2×C11⋊C8—22no—
242C2×C11⋊C8C22⋊C414yes—
243C23×Q16—111no—
244C22×#103—111no—
245C22×#103D1111yescharacteristic
246C2×#391—111no—
247C2×#391—111no—
248C2×#340—111no—
249C2×#336—111no—
250C23×C11C4×D411yescharacteristic
251C23×C11#12011yescharacteristic
252C23×C11#12011yescharacteristic
253C23×C11#12111yescharacteristic
254C23×C11#12111yescharacteristic
255C23×C11#12111yescharacteristic
256C23×C11#12711yescharacteristic
257C23×C11C2×Q1612yes—
258C23×C11#13512yes—
259C23×C11#13712yes—
260C23×C11#13712yes—
261Q8×C11—24no—
262Q8×C11—24no—
263Q8×C11—42no—
264Q8×C11—42no—
265Q8×C11—42no—
266Q8×C11—42no—
267Q8×C11—42no—
268Q8×C11—42no—
269C2×C4×C11—24no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—44no—
278C2×C4×C11—82no—
279C2×C4×C11—81no—
280C2×C4×C11—81no—
281C2×C4×C11C2×C22⋊C411yescharacteristic
282C2×C4×C11C2×C22⋊C411yescharacteristic
283C2×C4×C11C2×C22⋊C411yescharacteristic
284C2×C4×C11C4×D411yescharacteristic
285C2×C4×C11C4×D411yescharacteristic
286C2×C4×C11C4×D411yescharacteristic
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11#12011yescharacteristic
293C2×C4×C11#12111yescharacteristic
294C2×C4×C11#12111yescharacteristic
295C2×C4×C11#12111yescharacteristic
296C2×C4×C11#12111yescharacteristic
297C2×C4×C11#12111yescharacteristic
298C2×C4×C11#12111yescharacteristic
299C2×C4×C11#12111yescharacteristic
300C2×C4×C11#12111yescharacteristic
301C2×C4×C11#12111yescharacteristic
302C2×C4×C11#12311yescharacteristic
303C2×C4×C11#12311yescharacteristic
304C2×C4×C11#12311yescharacteristic
305C2×C4×C11#12311yescharacteristic
306C2×C4×C11#12411yescharacteristic
307C2×C4×C11#12411yescharacteristic
308C2×C4×C11#12711yescharacteristic
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—42no—
314C2×Dic11—42no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—44no—
325C2×Dic11—82no—
326C2×Dic11—81no—
327C2×Dic11—81no—
328Dic22—24no—
329Dic22—24no—
330Dic22—42no—
331Dic22—42no—
332Dic22—42no—
333Dic22—42no—
334Dic22—42no—
335Dic22—42no—
336C8×C11—42no—
337C11⋊C8—24no—
338C23×Q8—111no—
339C23×Q8C2×D1111yescharacteristic
340C22×Q16—114no—
341C22×Q16—222no—
342C22×Q16—222no—
343C22×Q16—222no—
344C22×Q16—222no—
345C22×Q16—222no—
346C22×Q16—222no—
347C23×C8—111no—
348C23×C8C2×D1111yescharacteristic
349C22×C4⋊C4—111no—
350C22×C4⋊C4C2×D1111yescharacteristic
351C22×C42—111no—
352C2×#103—22no—
353C2×#103—22no—
354C2×#103—22no—
355C2×#103—222no—
356C2×#103—222no—
357C2×#103—222no—
358#391—222no—
359#391—222no—
360#391—222no—
361#391—222no—
362C2×#95—222no—
363C2×#95—222no—
364#340—222no—
365#336—222no—
366C22×C11#38611yescharacteristic
367C22×C11#38611yescharacteristic
368C22×C11#39011yescharacteristic
369C22×C11#39211yescharacteristic
370C22×C11#39211yescharacteristic
371C22×C11#39211yescharacteristic
372C22×C11#39411yescharacteristic
373C22×C11C4×Q1612yes—
374C22×C11#44112yes—
375C22×C11#45112yes—
376C22×C11#45112yes—
377C22×C11#45212yes—
378C22×C11#45212yes—
379C22×C11#46212yes—
380C22×C11#46212yes—
381C22×C11#46412yes—
382C22×C11#46412yes—
383C22×C11#46712yes—
384C22×C11#47012yes—
385C22×C11#49411yescharacteristic
386C22×C11#49511yescharacteristic
387C22×C11#49711yescharacteristic
388C22×C11#49711yescharacteristic
389C4×C11—44no—
390C4×C11—82no—
391C4×C11#37911yescharacteristic
392C4×C11#38611yescharacteristic
393C4×C11#38611yescharacteristic
394C4×C11#39011yescharacteristic
395C4×C11#39211yescharacteristic
396C4×C11#39411yescharacteristic
397C4×C11#39411yescharacteristic
398C4×C11#39411yescharacteristic
399Dic11—44no—
400Dic11—44no—
401Dic11—82no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8—21no—
405C22×Q8—21no—
406C22×Q8—21no—
407C22×Q8—21no—
408C22×Q8—21no—
409C22×Q8—21no—
410C22×Q8—21no—
411C22×Q8—21no—
412C22×Q8—21no—
413C22×Q8—112no—
414C22×Q8—112no—
415C22×Q8—112no—
416C22×Q8—221no—
417C22×Q8—221no—
418C22×Q8—221no—
419C22×Q8—221no—
420C22×Q8—221no—
421C22×Q8—221no—
422C22×Q8—221no—
423C22×Q8—221no—
424C22×Q8—221no—
425C22×Q8—221no—
426C22×Q8—221no—
427C22×Q8C4×D1112yes—
428C22×Q8D4412yes—
429C22×Q8C22⋊D1112yes—
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—112no—
433C23×C4—221no—
434C23×C4—221no—
435C23×C4C22×D1111yescharacteristic
436C2×Q16—228no—
437C2×Q16—228no—
438C2×Q16—228no—
439C2×Q16—228no—
440C2×Q16—228no—
441C2×Q16—228no—
442C2×Q16—228no—
443C22×C8—21no—
444C22×C8—21no—
445C22×C8—21no—
446C22×C8—21no—
447C22×C8—21no—
448C22×C8—21no—
449C22×C8—112no—
450C22×C8—112no—
451C22×C8—112no—
452C22×C8—221no—
453C22×C8—221no—
454C22×C8—221no—
455C22×C8—221no—
456C22×C8C22⋊D1112yes—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—112no—
463C2×C4⋊C4—221no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4C22⋊D1112yes—
469C2×C42—221no—
470C2×C42—221no—
471C2×C42—221no—
472C2×C42—221no—
473C2×C42—221no—
474C2×C42—221no—
475#103—28no—
476#103—228no—
477#95—228no—
478#95—228no—
479C2×C11#143811yescharacteristic
480C2×C11#187812yes—
481C2×C11#187812yes—
482C2×C11#196911yescharacteristic
483C2×C11#197111yescharacteristic
484C2×C11#200112yes—
485C2×C11#201511yescharacteristic
486C2×C11#201511yescharacteristic
487C2×C11#201611yescharacteristic
488C2×C11#201611yescharacteristic
489C2×C11#205612yes—
490C24D4×D1111yescharacteristic
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8—41no—
510C2×Q8—41no—
511C2×Q8—41no—
512C2×Q8—41no—
513C2×Q8—41no—
514C2×Q8—41no—
515C2×Q8—41no—
516C2×Q8—41no—
517C2×Q8—41no—
518C2×Q8—114no—
519C2×Q8—222no—
520C2×Q8—222no—
521C2×Q8—222no—
522C2×Q8—222no—
523C2×Q8—222no—
524C2×Q8—222no—
525C2×Q8—222no—
526C2×Q8—222no—
527C2×Q8—222no—
528C2×Q8—222no—
529C2×Q8—222no—
530C2×Q8—222no—
531C2×Q8—222no—
532C2×Q8—222no—
533C2×Q8—222no—
534C2×Q8—441no—
535C2×Q8—441no—
536C2×Q8—441no—
537C2×Q8—441no—
538C2×Q8—441no—
539C2×Q8—441no—
540C2×Q8—441no—
541C2×Q8—441no—
542C2×Q8—441no—
543C2×Q8—441no—
544C2×Q8—441no—
545C2×Q8—441no—
546C2×Q8(C2×D11)⋊C414yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—114no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—441no—
571C22×C4—441no—
572C22×C4—441no—
573C22×C4—441no—
574C22×C4—441no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4—441no—
578C22×C4C2×C4×D1111yescharacteristic
579C22×C4C2×D4411yescharacteristic
580C22×C4#433911yescharacteristic
581C22×C4#433911yescharacteristic
582C22×C4D4×D1111yescharacteristic
583C22×C4D4×D1111yescharacteristic
584C22×C4D4×D1111yescharacteristic
585C22×C4D4×D1111yescharacteristic
586C22×C4D4×D1111yescharacteristic
587C22×C4#434111yescharacteristic
588C22×C4#434111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1111yescharacteristic
592Q16—2232no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—114no—
601C2×C8—222no—
602C2×C8—222no—
603C2×C8—222no—
604C2×C8—222no—
605C2×C8—222no—
606C2×C8—222no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—222no—
612C4⋊C4—222no—
613C4⋊C4—441no—
614C4⋊C4—441no—
615C42—441no—
616C42—441no—
617C42—441no—
618C42—441no—
619C11#1102411yescharacteristic, complemented, Sylow
620C23(C22⋊D11)⋊C411yescharacteristic
621C23#6693511yescharacteristic
622C23#6693711yescharacteristic
623C23#6693711yescharacteristic
624C23#6696812yes—
625C23#6696912yes—
626C23Q16×D1112yes—
627C23#6697112yes—
628C23#6699011yescharacteristic
629C23#6699211yescharacteristic
630C23#6699311yescharacteristic
631Q8—24no—
632Q8—24no—
633Q8—42no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—224no—
640Q8—224no—
641Q8—442no—
642Q8—442no—
643Q8—442no—
644Q8—442no—
645Q8—442no—
646Q8—442no—
647C2×C4—24no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—44no—
655C2×C4—42no—
656C2×C4—82no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—224no—
660C2×C4—224no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—442no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—442no—
668C2×C4—442no—
669C2×C4—442no—
670C2×C4—442no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—444no—
675C2×C4—881no—
676C2×C4—881no—
677C2×C4—882no—
678C2×C4C22⋊C4×D1111yescharacteristic
679C2×C4C22⋊C4×D1111yescharacteristic
680C2×C4(C22⋊D11)⋊C411yescharacteristic
681C2×C4#6693511yescharacteristic
682C2×C4#6693511yescharacteristic
683C2×C4#6693611yescharacteristic
684C2×C4#6693611yescharacteristic
685C2×C4#6693711yescharacteristic
686C2×C4#6693711yescharacteristic
687C2×C4#6693811yescharacteristic
688C2×C4#6693811yescharacteristic
689C2×C4#6693911yescharacteristic
690C2×C4C2×(C2×D11)⋊C411yescharacteristic
691C2×C4C4×C22⋊D1111yescharacteristic
692C2×C4C4×C22⋊D1111yescharacteristic
693C2×C4#6698211yescharacteristic
694C2×C4#6698311yescharacteristic
695C2×C4#6698311yescharacteristic
696C2×C4#6699011yescharacteristic
697C2×C4#6699011yescharacteristic
698C2×C4#6699011yescharacteristic
699C2×C4#6699111yescharacteristic
700C2×C4#6699111yescharacteristic
701C2×C4#6699211yescharacteristic
702C2×C4#6699211yescharacteristic
703C2×C4#6699211yescharacteristic
704C2×C4#6699311yescharacteristic
705C2×C4#6700611yescharacteristic
706C8—42no—
707C8—224no—
708C22#1062240212yes—
709C22#1062240312yes—
710C22#1062240612yes—
711C22#1062241112yes—
712C22#1062242112yes—
713C22#1062242312yes—
714C22#1062242612yes—
715C22#1062242912yes—
716C22#1062256911yescharacteristic
717C22#1062257011yescharacteristic
718C22#1062257111yescharacteristic
719C22#1062257211yescharacteristic
720C22#1062257311yescharacteristic
721C22#1062257311yescharacteristic
722C22#1062277912yes—
723C22#1062278011yescharacteristic
724C22#1062278111yescharacteristic
725C22#1062278612yes—
726C22#1062279411yescharacteristic
727C22#1062279512yes—
728C22#1062279912yes—
729C22#1062280311yescharacteristic
730C22#1062283611yescharacteristic
731C4—44no—
732C4—82no—
733C4—444no—
734C4—444no—
735C4—882no—
736C4#1062256811yescharacteristic
737C4#1062256911yescharacteristic
738C4#1062257011yescharacteristic
739C4#1062257211yescharacteristic
740C4#1062257411yescharacteristic
741C4#1062257411yescharacteristic
742C4#1062282611yescharacteristic
743C4#1062283611yescharacteristic
744C2#1306685511yescharacteristic
745C2#1306895412yes—
746C2#1306895512yes—
747C2#1306947411yescharacteristic
748C2#1306948411yescharacteristic
749C2#1306962512yes—
750C2#1306970811yescharacteristic
751C2#1306971111yescharacteristic
752C2#1306971411yescharacteristic
753C2#1306971711yescharacteristic
754C2#1306993712yes—
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#103C2
socle, prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC22×#103D11
hypocenterC11#11024
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
18. C22×#4326C4semidirect
187. C22×Dic11Q16semidirect
619. C11#11024semidirect

Maximal subgroups

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

subgroupindex
C23×#43262
C22×#668802
C2×#106228432
C2×#106225872
C2×#106221672
C2×#106221882
C22×C11×#1032
#1102411