Finite Group Databasebeta

← #14676179

Subgroups — #14676179

Order 2816.

1710 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic
2C2×#10622590C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4#13066886C212yesmaximal
5#13066882C212yesmaximal
6#13066850C212yesmaximal
7#13066847C212yesmaximal
8#13066846C211yesmaximal, characteristic
9#13066845C211yesmaximal, characteristic
10#13066845C211yesmaximal, characteristic
11C11×C4⋊#95C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C2×C4×Dic22—24no—
25C2×C4×Dic22—24no—
26C2×C4×Dic22C418yescomplemented
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622590—24no—
39C4⋊C4×Dic11—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22C2×C414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4Q814yescomplemented
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11C2×C414yes—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11C2×C414yes—
75C2×C4⋊Dic11Q814yescomplemented
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4C2×C414yes—
81C2×Dic11⋊C4C2×C414yes—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—42no—
86C2×C4×Dic11—42no—
87C2×C4×Dic11C2×C414yes—
88C2×C4×Dic11C2×C414yes—
89C2×C4×Dic11D414yes—
90C2×C4×Dic11D414yes—
91C4×Dic22—232no—
92C11×#95—24no—
93C11×#95—42no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103#13925—111nomaximal, Sylow
104C24×C11C2411yescharacteristic
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×Q814yes—
134C22×C4×C11C2×Q812yes—
135C22×C4×C11C2×Q812yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11#4112yes—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11C22×C412yes—
172C22×Dic11C22×C412yes—
173C22×Dic11C22×C412yes—
174C22×Dic11C22×C412yes—
175C22×Dic11C2×D412yes—
176C22×Dic11C2×D412yes—
177C22×Dic11C2×D412yes—
178C22×Dic11C2×D412yes—
179C22×Dic11C2×Q814yes—
180C22×Dic11#4112yes—
181C22×Dic11#4112yes—
182C2×Dic22—28no—
183C2×Dic22—28no—
184C2×Dic22—28no—
185C2×Dic22—28no—
186C2×Dic22—28no—
187C2×Dic22—28no—
188C2×Dic22—28no—
189C11×C4⋊C4—28no—
190C11×C4⋊C4—44no—
191C42×C11—28no—
192C4⋊Dic11—28no—
193C4⋊Dic11—28no—
194C4⋊Dic11—44no—
195Dic11⋊C4—28no—
196Dic11⋊C4—28no—
197C4×Dic11—28no—
198C4×Dic11—48no—
199C4×Dic11C22⋊C4116yes—
200C22×C4×Q8—111no—
201C2×#382—111no—
202C2×C4×C4⋊C4—111no—
203#1446—112no—
204#1445—112no—
205#1436—112no—
206#1436—112no—
207C4⋊#95—111no—
208C4⋊#95—111no—
209C4⋊#95—111no—
210C4⋊#95D1111yescharacteristic
211C23×C11C23×C411yescharacteristic
212C23×C11C22×D411yescharacteristic
213C23×C11C22×D411yescharacteristic
214C23×C11C22×Q811yescharacteristic
215C23×C11C22×Q811yescharacteristic
216C23×C11C2×#4111yescharacteristic
217C23×C11C2×#4111yescharacteristic
218C23×C11C2×#4111yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11C2×#4111yescharacteristic
221C23×C11C2×#4111yescharacteristic
222C23×C11H(5,𝔽2)11yescharacteristic
223C23×C11H(5,𝔽2)11yescharacteristic
224C23×C112−1+411yescharacteristic
225C23×C112−1+411yescharacteristic
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11C2×C22⋊C414yes—
254C2×C4×C11#11714yes—
255C2×C4×C11C4×Q814yes—
256C2×C4×C11C4×Q814yes—
257C2×C4×C11C22⋊Q814yes—
258C2×C4×C11C22⋊Q814yes—
259C2×C4×C11#12414yes—
260C2×C4×C11C4⋊Q814yes—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11C2×C22⋊C414yes—
301C2×Dic11C2×C22⋊C414yes—
302C2×Dic11#11714yes—
303Dic22—232no—
304C23×Q8—111no—
305C2×C4×Q8—118no—
306C2×C4×Q8—224no—
307C2×C4×Q8—224no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—111no—
310C22×C4⋊C4—111no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4C2×D1111yescharacteristic
314C22×C4⋊C4C2×D1111yescharacteristic
315C22×C42—111no—
316C22×C42—111no—
317C22×C42—112no—
318C22×C42C2×D1111yescharacteristic
319#382—224no—
320C4×C4⋊C4—224no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95—112no—
329C2×#95—112no—
330C2×#95C2×D1112yes—
331C2×#95C2×D1112yes—
332C22×C11C22×C22⋊C411yescharacteristic
333C22×C11C2×#11711yescharacteristic
334C22×C11C2×#11711yescharacteristic
335C22×C11C2×C4×Q811yescharacteristic
336C22×C11C2×C4×Q811yescharacteristic
337C22×C11#52011yescharacteristic
338C22×C11#52011yescharacteristic
339C22×C11C2×C22⋊Q811yescharacteristic
340C22×C11C2×C22⋊Q811yescharacteristic
341C22×C11#52511yescharacteristic
342C22×C11#52511yescharacteristic
343C22×C11#52511yescharacteristic
344C22×C11#52511yescharacteristic
345C22×C11C2×#12411yescharacteristic
346C22×C11C2×C4⋊Q811yescharacteristic
347C22×C11#53511yescharacteristic
348C22×C11#53611yescharacteristic
349C22×C11#53711yescharacteristic
350C22×C11#53711yescharacteristic
351C22×C11#55411yescharacteristic
352C22×C11#55411yescharacteristic
353C22×C11#55411yescharacteristic
354C22×C11#55411yescharacteristic
355C22×C11#55611yescharacteristic
356C22×C11#55611yescharacteristic
357C22×C11#55611yescharacteristic
358C22×C11#55611yescharacteristic
359C22×C11#55711yescharacteristic
360C22×C11#55711yescharacteristic
361C22×C11#55711yescharacteristic
362C22×C11#55711yescharacteristic
363C22×C11#55911yescharacteristic
364C22×C11#55911yescharacteristic
365C22×C11#55911yescharacteristic
366C22×C11#55911yescharacteristic
367C4×C11—24no—
368C4×C11—42no—
369C4×C11—44no—
370C4×C11—82no—
371C4×C11#39118yes—
372Dic11—24no—
373Dic11—24no—
374Dic11—24no—
375Dic11—42no—
376Dic11—44no—
377Dic11—82no—
378C22×Q8—114no—
379C22×Q8—222no—
380C22×Q8—222no—
381C22×Q8—222no—
382C22×Q8—222no—
383C22×Q8—222no—
384C22×Q8—222no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—112no—
390C23×C4—112no—
391C23×C4C22×D1112yes—
392C23×C4C22×D1112yes—
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C23×C4C22×D1111yescharacteristic
396C4×Q8—2232no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4Dic2214yescomplemented
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—114no—
421C2×C42—114no—
422C2×C42—114no—
423C2×C42—114no—
424C2×C42—222no—
425C2×C42—222no—
426C2×C42—224no—
427C2×C42—442no—
428C2×C42—442no—
429C2×C42C4×D1114yes—
430#95—24no—
431#95—42no—
432#95—224no—
433#95—224no—
434#95—224no—
435#95—224no—
436#95—224no—
437#95—224no—
438#95—442no—
439#95—442no—
440#95—442no—
441C2×C11#228011yescharacteristic
442C2×C11C2×#39111yescharacteristic
443C2×C11#231111yescharacteristic
444C2×C11#235511yescharacteristic
445C2×C11#235511yescharacteristic
446C2×C11#235511yescharacteristic
447C2×C11#235511yescharacteristic
448C2×C11#258011yescharacteristic
449C2×C11#258011yescharacteristic
450C2×C11#258111yescharacteristic
451C2×C11#258111yescharacteristic
452C2×C11#258411yescharacteristic
453C2×C11#258411yescharacteristic
454C2×C11#259211yescharacteristic
455C2×C11#259211yescharacteristic
456C24C23×D1111yescharacteristic
457C2×Q8—228no—
458C2×Q8—228no—
459C2×Q8—228no—
460C2×Q8—228no—
461C2×Q8—228no—
462C2×Q8—228no—
463C2×Q8—228no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—112no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—114no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—221no—
518C22×C4—222no—
519C22×C4—221no—
520C22×C4—222no—
521C22×C4—221no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4C2×Dic2214yes—
530C22×C4C2×Dic2212yes—
531C22×C4C2×C4×D1112yes—
532C22×C4C2×C4×D1112yes—
533C22×C4C2×C4×D1112yes—
534C22×C4#433912yes—
535C22×C4D4×D1112yes—
536C22×C4D4×D1112yes—
537C22×C4#434112yes—
538C22×C4#434112yes—
539C22×C4Q8×D1112yes—
540C22×C4#434312yes—
541C4⋊C4—28no—
542C4⋊C4—44no—
543C4⋊C4—228no—
544C4⋊C4—228no—
545C4⋊C4—228no—
546C4⋊C4—228no—
547C4⋊C4—444no—
548C42—28no—
549C42—1116no—
550C42—228no—
551C42—448no—
552C11#1392511yescharacteristic, complemented, Sylow
553C23C22×Dic2211yescharacteristic
554C23C22×C4×D1111yescharacteristic
555C23C2×#433911yescharacteristic
556C23C2×D4×D1111yescharacteristic
557C23C2×D4×D1111yescharacteristic
558C23C2×#434111yescharacteristic
559C23C2×#434111yescharacteristic
560C23#6703711yescharacteristic
561C23C2×Q8×D1111yescharacteristic
562C23C2×#434311yescharacteristic
563C23#6704011yescharacteristic
564C23#41×D1111yescharacteristic
565C23#41×D1111yescharacteristic
566C23#6704211yescharacteristic
567C23#6704311yescharacteristic
568Q8—2232no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—114no—
597C2×C4—114no—
598C2×C4—114no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—224no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—224no—
621C2×C4—222no—
622C2×C4—224no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—442no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4C4×Dic2214yes—
639C2×C4#6693114yes—
640C2×C4C22⋊C4×D1114yes—
641C2×C4#6693814yes—
642C2×C4#6694014yes—
643C2×C4#6694114yes—
644C2×C4#6694514yes—
645C2×C4#6694914yes—
646C22C2×C4×Dic2211yescharacteristic
647C22C2×#6693111yescharacteristic
648C22C2×C22⋊C4×D1111yescharacteristic
649C22C2×#6693811yescharacteristic
650C22C2×#6694011yescharacteristic
651C22C2×#6694111yescharacteristic
652C22C2×#6694511yescharacteristic
653C22#1062303511yescharacteristic
654C22C2×#6694911yescharacteristic
655C22D11×#11711yescharacteristic
656C22#1062305411yescharacteristic
657C22#1062307011yescharacteristic
658C22#1062307311yescharacteristic
659C22#1062307411yescharacteristic
660C22#1062309011yescharacteristic
661C22#1062309911yescharacteristic
662C22#1062310011yescharacteristic
663C22#1062310111yescharacteristic
664C22#1062311611yescharacteristic
665C22#1062313711yescharacteristic
666C22#1062313711yescharacteristic
667C22#1062313811yescharacteristic
668C22#1062313911yescharacteristic
669C22#1062315811yescharacteristic
670C22#1062315811yescharacteristic
671C22#1062315911yescharacteristic
672C22#1062316011yescharacteristic
673C22#1062320211yescharacteristic
674C22#1062321211yescharacteristic
675C22#1062321611yescharacteristic
676C22#1062322111yescharacteristic
677C22#1062324411yescharacteristic
678C22#1062325211yescharacteristic
679C22#1062326111yescharacteristic
680C22#1062326311yescharacteristic
681C4—24no—
682C4—44no—
683C4—42no—
684C4—82no—
685C4—224no—
686C4—224no—
687C4—224no—
688C4—444no—
689C4—442no—
690C4—882no—
691C4#1062225918yes—
692C2#1307099811yescharacteristic
693C2C2×#1062225911yescharacteristic
694C2#1307120511yescharacteristic
695C2#1307156811yescharacteristic
696C2#1307157111yescharacteristic
697C2#1307157411yescharacteristic
698C2#1307157511yescharacteristic
699C2#1307397211yescharacteristic
700C2#1307397611yescharacteristic
701C2#1307398011yescharacteristic
702C2#1307398411yescharacteristic
703C2#1307400111yescharacteristic
704C2#1307400311yescharacteristic
705C2#1307410111yescharacteristic
706C2#1307410311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#13925
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
26. C2×C4×Dic22C4semidirect
63. C2×C11×C4⋊C4Q8semidirect
75. C2×C4⋊Dic11Q8semidirect
417. C2×C4⋊C4Dic22semidirect
552. C11#13925semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×#106225902
C2×C4⋊C4×Dic112
#130668862
#130668822
#130668502
#130668472
#130668462
#130668452
C11×C4⋊#952
#1392511