Finite Group Databasebeta

← #14914825

Subgroups — #14914825

Order 2816.

5106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67040C211yesmaximal, characteristic
2C2×#10623105C211yesmaximal, characteristic, complemented
3C2×C4×#4343C211yesmaximal, characteristic, complemented
4Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
5Q8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6Q8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#13071447C213yesmaximal, complemented
8#13071445C213yesmaximal, complemented
9#13071445C213yesmaximal, complemented
10#13071444C213yesmaximal, complemented
11#13071205C213yesmaximal, complemented
12#13071199C213yesmaximal, complemented
13#13071102C213yesmaximal, complemented
14D11×#391C213yesmaximal, complemented
15Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C2×#67040—28no—
18C2×#67040—28no—
19C2×#67040C4116yescomplemented
20C22×#4343C2213yes—
21C22×#4343C2211yescharacteristic
22C22×Q8×D11C2211yescharacteristic
23C22×Q8×D11C2213yes—
24C22×#4339C2213yes—
25C22×#4339C2213yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30#10623105—28no—
31C4×#4343—28no—
32C2×#66946C2213yes—
33C2×#66946C2213yes—
34C2×#66945C2213yes—
35C2×C4⋊C4×D11C2213yes—
36C2×C4×D44C2213yes—
37C2×C4×D44C2213yes—
38C2×#66925C2213yes—
39C2×C42×D11C2213yes—
40C11×#391C2213yes—
41C11×#391C2213yes—
42C11×#380C2213yes—
43C4×C11×C22⋊C4C2213yes—
44#10622843C2213yes—
45#10622843C2213yes—
46#10622825C2213yes—
47C4×C22⋊Dic11C2213yes—
48#10622600C2213yes—
49#10622600C2213yes—
50#10622587C2213yes—
51#10622587C2213yes—
52#10622570C2213yes—
53#10622570C2211yescharacteristic
54#10622569C2213yes—
55#10622569C2216yes—
56#10622569C2213yes—
57C4×(C2×D11)⋊C4C2213yes—
58C4×(C2×D11)⋊C4C2213yes—
59#10622542C2213yes—
60#10622542C2213yes—
61#10622278C2216yes—
62#10622278C2213yes—
63#10622278C2213yes—
64#10622277C2216yes—
65#10622277C2216yes—
66D11×#95C2216yes—
67D11×#95C2216yes—
68#10622259C2213yes—
69#10622259C2216yes—
70#10622259C2213yes—
71C22×Q8×C11—24no—
72C22×Q8×C11—24no—
73C22×Q8×C11C2×C418yescomplemented
74C22×Q8×C11C2313yes—
75C22×Q8×C11C2311yescharacteristic
76C23×C4×C11C2313yes—
77C22×C22⋊D11C2313yes—
78C22×C22⋊D11C2311yescharacteristic
79#67040—2128no—
80C2×#4343—212no—
81C2×#4343—212no—
82C2×#4343C2×C418yes—
83C2×#4343C2×C4124yescomplemented
84C2×#4343D418yes—
85C2×#4343D418yes—
86C2×Q8×D11—24no—
87C2×Q8×D11—24no—
88C2×Q8×D11—212no—
89C2×Q8×D11—212no—
90C2×Q8×D11C2×C418yescomplemented
91C2×Q8×D11C2×C4124yescomplemented
92C2×#4339—212no—
93C2×#4339—212no—
94C2×#4339—212no—
95C2×#4339—212no—
96C2×#4339C2×C4124yescomplemented
97C2×#4339C2×C4124yescomplemented
98C22×D44C2313yes—
99C22×D44C2313yes—
100C22×C4×D11C2313yes—
101C22×C4×D11C2313yes—
102C22×C4×D11C2316yes—
103C22×C4×D11C2313yes—
104C22×C4×D11C2316yes—
105C22×C4×D11C2313yes—
106C22×Dic22C2313yes—
107C22×Dic22C2313yes—
108C4×Q8×C11—24no—
109C4×Q8×C11—24no—
110C2×C11×C4⋊C4C2313yes—
111C2×C11×C4⋊C4C2313yes—
112C2×C11×C22⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4C2313yes—
114C2×C42×C11C2313yes—
115C2×C42×C11C2313yes—
116C2×C22⋊Dic11C2311yescharacteristic
117C2×C22⋊Dic11C2313yes—
118Q8×Dic11—24no—
119Q8×Dic11—24no—
120C2×(C2×D11)⋊C4C2313yes—
121C2×(C2×D11)⋊C4C2313yes—
122C2×(C2×D11)⋊C4C2316yes—
123C2×(C2×D11)⋊C4C2311yescharacteristic
124C2×(C2×D11)⋊C4C2311yescharacteristic
125C2×(C2×D11)⋊C4C2313yes—
126C2×(C2×D11)⋊C4C2313yes—
127C2×C4⋊Dic11C2313yes—
128C2×C4⋊Dic11C2313yes—
129C2×Dic11⋊C4C2311yescharacteristic
130C2×Dic11⋊C4C2313yes—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2313yes—
133C2×C4×Dic11C2313yes—
134C2×C4×Dic11C2313yes—
135#66946—212no—
136#66946—212no—
137#66945—212no—
138C4⋊C4×D11—212no—
139C4×D44—212no—
140C4×D44—212no—
141#66925—212no—
142C42×D11—212no—
143C11×#95C2313yes—
144C11×#95C2316yes—
145C11×#95C2313yes—
146C11⋊#95C2313yes—
147C11⋊#95C2313yes—
148C11⋊#95C2313yes—
149C11⋊#95C2316yes—
150C11⋊#95C2316yes—
151C11⋊#95C2316yes—
152C11⋊#95C2313yes—
153C11⋊#95C2313yes—
154C11⋊#95C2313yes—
155#34259—111nomaximal, Sylow
156C24×C11C2411yescharacteristic
157C23×D11C2411yescharacteristic
158C23×D11C2413yes—
159C2×Q8×C11—232no—
160C2×Q8×C11—26no—
161C2×Q8×C11—26no—
162C2×Q8×C11C22×C4112yes—
163C2×Q8×C11C22×C414yes—
164C2×Q8×C11C2×D414yes—
165C2×Q8×C11C2×D414yes—
166C22×C4×C11—26no—
167C22×C4×C11—26no—
168C22×C4×C11C22×C4112yes—
169C22×C4×C11C2413yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2413yes—
172C22×C4×C11C2413yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2413yes—
175C2×C22⋊D11—22no—
176C2×C22⋊D11—22no—
177C2×C22⋊D11—26no—
178C2×C22⋊D11—26no—
179C2×C22⋊D11C22×C414yes—
180C2×C22⋊D11C22×C4112yes—
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2413yes—
183C22×Dic11C2413yes—
184C22×Dic11C2413yes—
185C22×Dic11C2411yescharacteristic
186C22×Dic11C2411yescharacteristic
187#4343—296no—
188#4343C22⋊C4164yescomplemented
189Q8×D11—296no—
190Q8×D11—232no—
191#4339—296no—
192#4339—296no—
193C2×D44—26no—
194C2×D44—26no—
195C2×D44C22×C4112yes—
196C2×D44C22×C4112yes—
197C2×D44C2×D4112yes—
198C2×D44C2×D4112yes—
199C2×C4×D11—26no—
200C2×C4×D11—212no—
201C2×C4×D11—212no—
202C2×C4×D11—26no—
203C2×C4×D11—26no—
204C2×C4×D11—212no—
205C2×C4×D11—26no—
206C2×C4×D11—26no—
207C2×C4×D11—26no—
208C2×C4×D11—43no—
209C2×C4×D11—43no—
210C2×C4×D11—46no—
211C2×C4×D11—46no—
212C2×C4×D11C22×C4124yes—
213C2×C4×D11C22×C4112yes—
214C2×C4×D11C22×C4112yes—
215C2×C4×D11C2×D4112yes—
216C2×C4×D11C2×D4112yes—
217C2×Dic22—26no—
218C2×Dic22—26no—
219C2×Dic22—26no—
220C2×Dic22—26no—
221C2×Dic22C22×C4112yes—
222C2×Dic22C22×C4112yes—
223C11×C4⋊C4—26no—
224C11×C4⋊C4—26no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—43no—
227C42×C11—26no—
228C42×C11—26no—
229C22⋊Dic11—22no—
230C22⋊Dic11—43no—
231(C2×D11)⋊C4—22no—
232(C2×D11)⋊C4—26no—
233(C2×D11)⋊C4—26no—
234(C2×D11)⋊C4—212no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—43no—
237(C2×D11)⋊C4—43no—
238C4⋊Dic11—26no—
239C4⋊Dic11—26no—
240Dic11⋊C4—22no—
241Dic11⋊C4—26no—
242C4×Dic11—22no—
243C4×Dic11—26no—
244C4×Dic11—26no—
245C4×Dic11—26no—
246C22×2−1+4—111no—
247C2×#520—111no—
248C2×C4×#41—111no—
249Q8×C22⋊C4—111no—
250Q8×C22⋊C4—111no—
251Q8×C22⋊C4—111no—
252Q8×C22⋊C4D1111yescharacteristic, complemented
253#2339—113no—
254#2339—113no—
255#2339—113no—
256#2339—113no—
257#2311—113no—
258#2310—113no—
259#2297—113no—
260C2×#391—113no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11C23×C412yes—
268C23×C11C2511yescharacteristic
269C22×D11—23no—
270C22×D11—23no—
271C22×D11—23no—
272C22×D11—23no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11C23×C412yes—
280C22×D11C23×C416yes—
281C22×D11C22×D416yes—
282C22×D11C22×D416yes—
283Q8×C11—224no—
284Q8×C11C2×C22⋊C4116yes—
285C2×C4×C11—21no—
286C2×C4×C11—23no—
287C2×C4×C11—23no—
288C2×C4×C11—21no—
289C2×C4×C11—224no—
290C2×C4×C11—23no—
291C2×C4×C11—21no—
292C2×C4×C11—23no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—23no—
296C2×C4×C11—23no—
297C2×C4×C11—23no—
298C2×C4×C11—23no—
299C2×C4×C11C23×C416yes—
300C2×C4×C11C23×C416yes—
301C2×C4×C11C22×D416yes—
302C2×C4×C11C22×D416yes—
303C2×C4×C112−1+412yescomplemented
304C22⋊D11—224no—
305C22⋊D11—28no—
306C2×Dic11—21no—
307C2×Dic11—23no—
308C2×Dic11—23no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—23no—
312C2×Dic11—23no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—23no—
316C2×Dic11—23no—
317C2×Dic11—23no—
318C2×Dic11—23no—
319C2×Dic11C23×C416yes—
320C2×Dic11C23×C412yes—
321C2×Dic11C22×D412yes—
322C2×Dic11C22×D412yes—
323C2×Dic112−1+412yescomplemented
324D44—224no—
325D44C2×C22⋊C4148yes—
326C4×D11—248no—
327C4×D11—224no—
328C4×D11—412no—
329C4×D11—412no—
330C4×D11—812no—
331C4×D11C2×C22⋊C4148yes—
332Dic22—224no—
333Dic22—224no—
334C2×2−1+4—1116no—
335C2×2−1+4—228no—
336C2×2−1+4—228no—
337C22×#41—111no—
338C22×#41—113no—
339C22×#41—113no—
340C22×#41—113no—
341C23×Q8—113no—
342C23×Q8—111no—
343C23×Q8C2×D1111yescharacteristic
344#520—228no—
345C4×#41—228no—
346C2×C4×Q8—111no—
347C2×C4×Q8—111no—
348C2×C4×Q8C2×D1111yescharacteristic
349C2×C4×Q8C2×D1111yescharacteristic
350C2×C4×D4—113no—
351C2×C4×D4—113no—
352C2×C4×D4—113no—
353C2×C4×D4—113no—
354C2×#117—113no—
355C2×#117—113no—
356C22×C4⋊C4—113no—
357C22×C42—113no—
358#391—113no—
359#391—113no—
360#391—113no—
361#391—113no—
362#391—113no—
363#391—113no—
364#391—113no—
365#391—116no—
366#391—113no—
367#391C2×D1113yes—
368#391C2×D1113yes—
369#390—113no—
370#390—111no—
371#386—116no—
372#386—113no—
373#386—113no—
374#386—116no—
375#386—113no—
376#386—113no—
377#381—116no—
378#381—116no—
379#380—113no—
380#380—113no—
381#380—113no—
382#380C2×D1113yes—
383C4×C22⋊C4—113no—
384C4×C22⋊C4—113no—
385C4×C22⋊C4—113no—
386C4×C22⋊C4C2×D1113yes—
387C2×#95—116no—
388C2×#95—116no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11C24×C411yescharacteristic
397C22×C11C23×D411yescharacteristic
398C22×C11C23×D411yescharacteristic
399C22×C11C2×2−1+411yescharacteristic
400C22×C11C2×2−1+411yescharacteristic
401C22×C11#58511yescharacteristic
402C22×C11#58511yescharacteristic
403C2×D11—26no—
404C2×D11—26no—
405C2×D11—26no—
406C2×D11—26no—
407C2×D11—26no—
408C2×D11—26no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C2×D11C22×C22⋊C4112yes—
417C4×C11—26no—
418C4×C11—22no—
419C4×C11—43no—
420C4×C11—41no—
421C4×C11—43no—
422C4×C11C22×C22⋊C4112yes—
423Dic11—26no—
424Dic11—22no—
425Dic11—43no—
426Dic11—41no—
427Dic11—43no—
428Dic11C22×C22⋊C414yes—
4292−1+4—22128no—
430C2×#41—118no—
431C2×#41—1124no—
432C2×#41—118no—
433C2×#41—118no—
434C2×#41—1124no—
435C2×#41—1124no—
436C2×#41—2212no—
437C2×#41—2212no—
438C2×#41—2212no—
439C2×#41—2212no—
440C2×#41—2212no—
441C2×#41—2212no—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—1124no—
445C22×Q8—118no—
446C22×Q8—113no—
447C22×Q8—113no—
448C22×Q8—2212no—
449C22×Q8—2212no—
450C22×Q8—224no—
451C22×Q8—224no—
452C22×Q8C4×D1118yescomplemented
453C22×Q8C22×D1113yes—
454C22×Q8C22×D1111yescharacteristic
455C22×D4—113no—
456C22×D4—111no—
457C22×D4—113no—
458C22×D4—113no—
459C23×C4—113no—
460C23×C4—116no—
461C23×C4—113no—
462C23×C4—113no—
463C23×C4—113no—
464C23×C4—116no—
465C23×C4C22×D1113yes—
466C4×Q8—24no—
467C4×Q8—24no—
468C4×Q8—224no—
469C4×Q8—224no—
470C4×D4—2212no—
471C4×D4—2212no—
472C4×D4—2212no—
473C4×D4—2212no—
474#117—2212no—
475#117—2212no—
476C2×C4⋊C4—113no—
477C2×C4⋊C4—113no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—113no—
480C2×C4⋊C4—2212no—
481C2×C4⋊C4C22×D1113yes—
482C2×C4⋊C4C22×D1113yes—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—113no—
485C2×C22⋊C4—116no—
486C2×C22⋊C4—113no—
487C2×C22⋊C4—111no—
488C2×C22⋊C4—111no—
489C2×C22⋊C4—113no—
490C2×C22⋊C4—113no—
491C2×C22⋊C4—113no—
492C2×C22⋊C4C22×D1111yescharacteristic
493C2×C22⋊C4C22×D1113yes—
494C2×C42—113no—
495C2×C42—113no—
496C2×C42—113no—
497C2×C42—111no—
498C2×C42—2212no—
499C2×C42C22×D1113yes—
500C2×C42C22×D1113yes—
501#95—113no—
502#95—113no—
503#95—113no—
504#95—116no—
505#95—116no—
506#95—116no—
507#95—113no—
508#95—113no—
509#95—113no—
510#95C22×D1113yes—
511#95C22×D1116yes—
512#95C22×D1113yes—
513C2×C11—42no—
514C2×C11C23×C22⋊C411yescharacteristic
515C2×C11C4×2−1+411yescharacteristic
516C2×C11C4×2−1+411yescharacteristic
517C2×C11#348911yescharacteristic
518C2×C11#348911yescharacteristic
519C2×C11#349911yescharacteristic
520C2×C11#350011yescharacteristic
521D11—212no—
522D11—42no—
523C24—113no—
524C24—111no—
525C24C23×D1111yescharacteristic
526#41—1164no—
527#41—2296no—
528#41—2296no—
529#41—2296no—
530C2×Q8—232no—
531C2×Q8—26no—
532C2×Q8—26no—
533C2×Q8—1112no—
534C2×Q8—1112no—
535C2×Q8—226no—
536C2×Q8—226no—
537C2×Q8—2296no—
538C2×Q8—2232no—
539C2×Q8—226no—
540C2×Q8—226no—
541C2×Q8C2×C4×D11112yes—
542C2×Q8C2×C4×D1114yes—
543C2×Q8D4×D1114yes—
544C2×Q8D4×D1114yes—
545C2×D4—114no—
546C2×D4—1112no—
547C2×D4—1112no—
548C2×D4—1112no—
549C2×D4—1112no—
550C2×D4—1112no—
551C2×D4—226no—
552C2×D4—226no—
553C2×D4—222no—
554C2×D4—222no—
555C2×D4—226no—
556C2×D4—226no—
557C22×C4—26no—
558C22×C4—26no—
559C22×C4—111no—
560C22×C4—1112no—
561C22×C4—1112no—
562C22×C4—1112no—
563C22×C4—113no—
564C22×C4—111no—
565C22×C4—1124no—
566C22×C4—1112no—
567C22×C4—111no—
568C22×C4—113no—
569C22×C4—113no—
570C22×C4—226no—
571C22×C4—2212no—
572C22×C4—2212no—
573C22×C4—226no—
574C22×C4—226no—
575C22×C4—2212no—
576C22×C4—226no—
577C22×C4—226no—
578C22×C4—226no—
579C22×C4—443no—
580C22×C4—443no—
581C22×C4—446no—
582C22×C4—446no—
583C22×C4C2×C4×D11112yes—
584C22×C4C23×D1113yes—
585C22×C4C23×D1111yescharacteristic
586C22×C4C23×D1113yes—
587C22×C4C23×D1113yes—
588C22×C4C23×D1111yescharacteristic
589C22×C4C23×D1113yes—
590C4⋊C4—26no—
591C4⋊C4—26no—
592C4⋊C4—226no—
593C4⋊C4—222no—
594C4⋊C4—226no—
595C4⋊C4—226no—
596C22⋊C4—22no—
597C22⋊C4—43no—
598C22⋊C4—222no—
599C22⋊C4—226no—
600C22⋊C4—2212no—
601C22⋊C4—226no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—443no—
605C22⋊C4—443no—
606C22⋊C4—443no—
607C42—26no—
608C42—26no—
609C42—222no—
610C42—226no—
611C42—226no—
612C42—226no—
613C11#3425911yescharacteristic, complemented, Sylow
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—116no—
621C23—116no—
622C23—116no—
623C23—112no—
624C23—223no—
625C23—223no—
626C23—223no—
627C23—223no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23C22×C4×D1112yes—
635C23C24×D1111yescharacteristic
636Q8—224no—
637Q8—2224no—
638Q8—2224no—
639Q8C22⋊C4×D11116yes—
640D4—1148no—
641D4—2224no—
642D4—228no—
643D4—2224no—
644C2×C4—21no—
645C2×C4—23no—
646C2×C4—23no—
647C2×C4—21no—
648C2×C4—224no—
649C2×C4—21no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—23no—
655C2×C4—21no—
656C2×C4—23no—
657C2×C4—23no—
658C2×C4—112no—
659C2×C4—112no—
660C2×C4—112no—
661C2×C4—1148no—
662C2×C4—116no—
663C2×C4—112no—
664C2×C4—2248no—
665C2×C4—221no—
666C2×C4—223no—
667C2×C4—223no—
668C2×C4—221no—
669C2×C4—2224no—
670C2×C4—221no—
671C2×C4—223no—
672C2×C4—223no—
673C2×C4—221no—
674C2×C4—223no—
675C2×C4—223no—
676C2×C4—221no—
677C2×C4—223no—
678C2×C4—223no—
679C2×C4—4412no—
680C2×C4—4412no—
681C2×C4—8812no—
682C2×C4C22×C4×D1116yes—
683C2×C4C22×C4×D1116yes—
684C2×C4C2×D4×D1116yes—
685C2×C4C2×D4×D1116yes—
686C2×C4#6704012yescomplemented
687C22—22no—
688C22—22no—
689C22—22no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—1112no—
695C22—226no—
696C22—226no—
697C22—226no—
698C22—226no—
699C22—226no—
700C22—226no—
701C22—222no—
702C22—222no—
703C22—222no—
704C22—441no—
705C22—441no—
706C22—441no—
707C22—441no—
708C22C23×C4×D1111yescharacteristic
709C22C22×D4×D1111yescharacteristic
710C22C22×D4×D1111yescharacteristic
711C22C2×#6704011yescharacteristic
712C22#1062345311yescharacteristic
713C22D11×2−1+411yescharacteristic
714C22#1062345711yescharacteristic
715C4—26no—
716C4—22no—
717C4—41no—
718C4—43no—
719C4—43no—
720C4—114no—
721C4—226no—
722C4—222no—
723C4—441no—
724C4—443no—
725C4—443no—
726C4C2×C22⋊C4×D11112yes—
727C2—42no—
728C2—2212no—
729C2—442no—
730C2C22×C22⋊C4×D1111yescharacteristic
731C2#1308182511yescharacteristic
732C2C4×#6704011yescharacteristic
733C2#1308229311yescharacteristic
734C2#1308229511yescharacteristic
735C2#1308240011yescharacteristic
736C2#1308240711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC22×#67040C2
hypercenterQ8×C22⋊C4D11
hypocenterC11#34259
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10623105C2semidirect
3. C2×C4×#4343C2semidirect
4. Q8×C22⋊Dic11C2semidirect
5. Q8×(C2×D11)⋊C4C2semidirect
6. Q8×(C2×D11)⋊C4C2semidirect
7. #13071447C2semidirect
8. #13071445C2semidirect
9. #13071445C2semidirect
10. #13071444C2semidirect
11. #13071205C2semidirect
12. #13071199C2semidirect
13. #13071102C2semidirect
14. D11×#391C2semidirect
15. Q8×C11×C22⋊C4C2semidirect
19. C2×#67040C4semidirect
73. C22×Q8×C11C2×C4semidirect
83. C2×#4343C2×C4semidirect
90. C2×Q8×D11C2×C4semidirect
91. C2×Q8×D11C2×C4semidirect
96. C2×#4339C2×C4semidirect
97. C2×#4339C2×C4semidirect
188. #4343C22⋊C4semidirect
252. Q8×C22⋊C4D11semidirect
303. C2×C4×C112−1+4semidirect
323. C2×Dic112−1+4semidirect
452. C22×Q8C4×D11semidirect
613. C11#34259semidirect
686. C2×C4#67040semidirect

Maximal subgroups

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

subgroupindex
C22×#670402
C2×#106231052
C2×C4×#43432
Q8×C22⋊Dic112
Q8×(C2×D11)⋊C42
#130714472
#130714452
#130714442
#130712052
#130711992
#130711022
D11×#3912
Q8×C11×C22⋊C42
#3425911