Finite Group Databasebeta

← #14914816

Subgroups — #14914816

Order 2816.

5682 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67042C211yesmaximal, characteristic
2C2×#10623105C211yesmaximal, characteristic, complemented
3C2×C4×#4343C211yesmaximal, characteristic, complemented
4#13071457C211yesmaximal, characteristic, complemented
5#13071454C211yesmaximal, characteristic, complemented
6#13071454C211yesmaximal, characteristic, complemented
7C22⋊C4×D44C213yesmaximal, complemented
8#13071437C213yesmaximal, complemented
9#13071437C213yesmaximal, complemented
10#13071436C213yesmaximal, complemented
11#13071205C213yesmaximal, complemented
12#13071195C213yesmaximal, complemented
13#13071102C213yesmaximal, complemented
14D11×#390C213yesmaximal, complemented
15C11×#2341C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×#67042—28no—
18C2×#67042—28no—
19C2×#67042C4116yescomplemented
20C22×#4343C2211yescharacteristic
21C22×#4343C2211yescharacteristic
22C22×D4×D11C2213yes—
23C22×D4×D11C2213yes—
24C22×#4339C2213yes—
25C23×D44C2213yes—
26C2×C4×Q8×C11C2211yescharacteristic, complemented
27C2×C4×Q8×C11C2211yescharacteristic, complemented
28C2×Q8×Dic11C2211yescharacteristic, complemented
29C2×Q8×Dic11C2211yescharacteristic, complemented
30#10623105—28no—
31C4×#4343—28no—
32C2×#66946C2213yescomplemented
33C2×#66946C2213yescomplemented
34C2×#66945C2213yescomplemented
35C2×C4⋊C4×D11C2213yescomplemented
36C2×C22⋊C4×D11C2216yescomplemented
37C2×C22⋊C4×D11C2216yescomplemented
38C2×C4×D44C2213yescomplemented
39C2×C4×D44C2213yescomplemented
40C2×#66925C2213yescomplemented
41C2×C42×D11C2213yescomplemented
42C11×#390C2213yescomplemented
43C11×#390C2213yescomplemented
44C11×#380C2213yescomplemented
45C4×C11×C22⋊C4C2213yescomplemented
46#10622834C2213yescomplemented
47#10622834C2213yescomplemented
48#10622825C2213yescomplemented
49C4×C22⋊Dic11C2213yescomplemented
50#10622601C2213yescomplemented
51#10622601C2213yescomplemented
52#10622600C2213yescomplemented
53#10622600C2213yescomplemented
54#10622570C2213yescomplemented
55#10622570C2216yescomplemented
56#10622570C2213yescomplemented
57#10622569C2216yescomplemented
58#10622569C2213yescomplemented
59#10622569C2213yescomplemented
60#10622568C2216yescomplemented
61#10622568C2216yescomplemented
62#10622552C2213yescomplemented
63#10622552C2213yescomplemented
64C4×(C2×D11)⋊C4C2213yescomplemented
65C4×(C2×D11)⋊C4C2213yescomplemented
66#10622278C2213yescomplemented
67#10622278C2216yescomplemented
68#10622278C2213yescomplemented
69#10622259C2213yescomplemented
70#10622259C2211yescharacteristic, complemented
71C24×D11C2316yes—
72C2×C11×#41—24no—
73C2×C11×#41—24no—
74C2×C11×#41C2×C418yescomplemented
75C22×Q8×C11C2311yescharacteristic
76C22×D4×C11C2313yes—
77C23×C4×C11C2313yes—
78C22×C22⋊D11C2313yes—
79C22×C22⋊D11C2313yes—
80#67042—2128no—
81C2×#4343—24no—
82C2×#4343—24no—
83C2×#4343C2×C418yes—
84C2×#4343C2×C418yescomplemented
85C2×#4343D418yes—
86C2×#4343D418yes—
87C2×D4×D11—212no—
88C2×D4×D11—212no—
89C2×D4×D11—212no—
90C2×D4×D11—212no—
91C2×D4×D11C2×C4124yescomplemented
92C2×D4×D11C2×C4124yescomplemented
93C2×#4339—212no—
94C2×#4339—212no—
95C2×#4339C2×C4124yescomplemented
96C22×D44—212no—
97C22×D44—212no—
98C22×D44C2×C4124yescomplemented
99C22×D44C2313yes—
100C22×D44C2313yes—
101C22×D44C2313yes—
102C22×C4×D11C2313yes—
103C22×C4×D11C2313yes—
104C22×C4×D11C2313yes—
105C22×C4×D11C2316yes—
106C22×C4×D11C2313yes—
107C22×Dic22C2311yescharacteristic
108C4×Q8×C11—24no—
109C4×Q8×C11—24no—
110C2×C11×C4⋊C4C2313yes—
111C2×C11×C4⋊C4C2313yes—
112C2×C11×C22⋊C4C2313yes—
113C2×C11×C22⋊C4C2316yes—
114C2×C11×C22⋊C4C2313yes—
115C2×C42×C11C2313yes—
116C2×C42×C11C2313yes—
117C2×C22⋊Dic11C2313yes—
118C2×C22⋊Dic11C2316yes—
119C2×C22⋊Dic11C2313yes—
120Q8×Dic11—24no—
121Q8×Dic11—24no—
122C2×(C2×D11)⋊C4C2313yes—
123C2×(C2×D11)⋊C4C2313yes—
124C2×(C2×D11)⋊C4C2316yes—
125C2×(C2×D11)⋊C4C2313yes—
126C2×(C2×D11)⋊C4C2313yes—
127C2×(C2×D11)⋊C4C2316yes—
128C2×(C2×D11)⋊C4C2316yes—
129C2×(C2×D11)⋊C4C2313yes—
130C2×(C2×D11)⋊C4C2313yes—
131C2×C4⋊Dic11C2313yes—
132C2×C4⋊Dic11C2313yes—
133C2×Dic11⋊C4C2311yescharacteristic
134C2×Dic11⋊C4C2313yes—
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2313yes—
137C2×C4×Dic11C2313yes—
138C2×C4×Dic11C2313yes—
139#66946—212no—
140#66946—212no—
141#66945—212no—
142C4⋊C4×D11—212no—
143C22⋊C4×D11—412no—
144C22⋊C4×D11—412no—
145C4×D44—212no—
146C4×D44—212no—
147#66925—212no—
148C42×D11—212no—
149C11×#95C2311yescharacteristic
150C11×#95C2313yes—
151C11⋊#95C2311yescharacteristic
152C11⋊#95C2313yes—
153C11⋊#95C2311yescharacteristic
154C11⋊#95C2311yescharacteristic
155C11⋊#95C2313yes—
156C11⋊#95C2313yes—
157#34258—111nomaximal, Sylow
158C24×C11C2413yes—
159C23×D11—212no—
160C23×D11—212no—
161C23×D11—46no—
162C23×D11—46no—
163C23×D11—46no—
164C23×D11—46no—
165C23×D11C22×C4124yes—
166C23×D11C2413yes—
167C23×D11C2413yes—
168C11×#41—232no—
169C2×Q8×C11C22×C414yes—
170C2×Q8×C11C2×D414yes—
171C2×Q8×C11C2×D414yes—
172C2×D4×C11—26no—
173C2×D4×C11—26no—
174C2×D4×C11C22×C4112yes—
175C22×C4×C11—26no—
176C22×C4×C11—26no—
177C22×C4×C11C22×C4112yes—
178C22×C4×C11C2413yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2413yes—
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×C4×C11C2413yes—
184C2×C22⋊D11—26no—
185C2×C22⋊D11—26no—
186C2×C22⋊D11—26no—
187C2×C22⋊D11—26no—
188C2×C22⋊D11C22×C4112yes—
189C2×C22⋊D11C22×C4112yes—
190C22×Dic11C2411yescharacteristic
191C22×Dic11C2413yes—
192C22×Dic11C2413yes—
193C22×Dic11C2411yescharacteristic
194C22×Dic11C2411yescharacteristic
195C22×Dic11C2411yescharacteristic
196#4343—232no—
197#4343C22⋊C4164yescomplemented
198D4×D11—296no—
199D4×D11—296no—
200#4339—296no—
201C2×D44—296no—
202C2×D44—26no—
203C2×D44—26no—
204C2×D44—26no—
205C2×D44—26no—
206C2×D44C22×C4112yes—
207C2×D44C22×C4112yes—
208C2×D44C22×C4112yes—
209C2×D44C2×D4112yes—
210C2×D44C2×D4112yes—
211C2×C4×D11—26no—
212C2×C4×D11—26no—
213C2×C4×D11—26no—
214C2×C4×D11—212no—
215C2×C4×D11—26no—
216C2×C4×D11—26no—
217C2×C4×D11—26no—
218C2×C4×D11—43no—
219C2×C4×D11—43no—
220C2×C4×D11—46no—
221C2×C4×D11—46no—
222C2×C4×D11C22×C4112yes—
223C2×C4×D11C22×C4112yes—
224C2×C4×D11C2×D4112yes—
225C2×C4×D11C2×D4112yes—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22C22×C414yes—
229C11×C4⋊C4—26no—
230C11×C4⋊C4—26no—
231C11×C22⋊C4—26no—
232C11×C22⋊C4—46no—
233C11×C22⋊C4—43no—
234C42×C11—26no—
235C42×C11—26no—
236C22⋊Dic11—26no—
237C22⋊Dic11—46no—
238C22⋊Dic11—43no—
239(C2×D11)⋊C4—26no—
240(C2×D11)⋊C4—26no—
241(C2×D11)⋊C4—26no—
242(C2×D11)⋊C4—212no—
243(C2×D11)⋊C4—26no—
244(C2×D11)⋊C4—46no—
245(C2×D11)⋊C4—46no—
246(C2×D11)⋊C4—43no—
247(C2×D11)⋊C4—43no—
248C4⋊Dic11—26no—
249C4⋊Dic11—26no—
250Dic11⋊C4—22no—
251Dic11⋊C4—26no—
252C4×Dic11—22no—
253C4×Dic11—26no—
254C4×Dic11—26no—
255C4×Dic11—26no—
256C22×H(5,𝔽2)—111no—
257C2×#520—111no—
258C2×C4×#41—111no—
259#2341—111no—
260#2341—111no—
261#2341—111no—
262#2341D1111yescharacteristic, complemented
263D4×C22⋊C4—113no—
264D4×C22⋊C4—113no—
265D4×C22⋊C4—113no—
266D4×C22⋊C4—113no—
267#2311—113no—
268#2309—113no—
269#2297—113no—
270C2×#390—113no—
271C23×C11—23no—
272C23×C11—23no—
273C23×C11—23no—
274C23×C11—23no—
275C23×C11—23no—
276C23×C11—23no—
277C23×C11C23×C416yes—
278C23×C11C2511yescharacteristic
279C22×D11—23no—
280C22×D11—23no—
281C22×D11—23no—
282C22×D11—23no—
283C22×D11—23no—
284C22×D11—23no—
285C22×D11—23no—
286C22×D11—23no—
287C22×D11—23no—
288C22×D11—23no—
289C22×D11—248no—
290C22×D11—424no—
291C22×D11—424no—
292C22×D11—812no—
293C22×D11—812no—
294C22×D11—812no—
295C22×D11—812no—
296C22×D11C23×C416yes—
297C22×D11C23×C416yes—
298C22×D11C22×D416yes—
299C22×D11C22×D416yes—
300Q8×C11C2×C22⋊C4116yescomplemented
301D4×C11—224no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—224no—
307C2×C4×C11—23no—
308C2×C4×C11—21no—
309C2×C4×C11—23no—
310C2×C4×C11—23no—
311C2×C4×C11—23no—
312C2×C4×C11—23no—
313C2×C4×C11—21no—
314C2×C4×C11—23no—
315C2×C4×C11—21no—
316C2×C4×C11C23×C412yes—
317C2×C4×C11C23×C416yes—
318C2×C4×C11C22×D416yes—
319C2×C4×C11C22×D416yes—
320C2×C4×C11H(5,𝔽2)12yescomplemented
321C22⋊D11—224no—
322C22⋊D11—224no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—23no—
329C2×Dic11—23no—
330C2×Dic11—23no—
331C2×Dic11—23no—
332C2×Dic11—23no—
333C2×Dic11—21no—
334C2×Dic11—23no—
335C2×Dic11—21no—
336C2×Dic11C23×C412yes—
337C2×Dic11C23×C412yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C2×Dic11H(5,𝔽2)12yescomplemented
341D44—224no—
342D44—224no—
343D44C2×C22⋊C4148yescomplemented
344C4×D11—224no—
345C4×D11—412no—
346C4×D11—412no—
347C4×D11—812no—
348C4×D11C2×C22⋊C4148yescomplemented
349Dic22—28no—
350C2×H(5,𝔽2)—1116no—
351C2×H(5,𝔽2)—228no—
352C2×H(5,𝔽2)—228no—
353C22×#41—111no—
354C22×#41—111no—
355C22×#41—113no—
356C22×#41C2×D1111yescharacteristic
357C23×D4—113no—
358C23×D4—113no—
359C23×D4—113no—
360#520—228no—
361C4×#41—228no—
362C2×C4×Q8—111no—
363C2×C4×Q8—111no—
364C2×C4×Q8C2×D1111yescharacteristic, complemented
365C2×C4×Q8C2×D1111yescharacteristic, complemented
366C2×C4×D4—113no—
367C2×C4×D4—113no—
368C2×C4×D4—113no—
369C2×C4×D4—113no—
370C2×#117—113no—
371C2×#117—113no—
372C22×C4⋊C4—113no—
373C22×C22⋊C4—116no—
374C22×C22⋊C4—116no—
375C22×C42—113no—
376#391—113no—
377#391—111no—
378#390—113no—
379#390—113no—
380#390—113no—
381#390—113no—
382#390—113no—
383#390—116no—
384#390—113no—
385#390—113no—
386#390—113no—
387#390C2×D1113yescomplemented
388#390C2×D1113yescomplemented
389#386—116no—
390#386—113no—
391#386—113no—
392#386—116no—
393#386—113no—
394#386—113no—
395#380—113no—
396#380—113no—
397#380—113no—
398#380C2×D1113yescomplemented
399#379—116no—
400#379—116no—
401C4×C22⋊C4—113no—
402C4×C22⋊C4—113no—
403C4×C22⋊C4—113no—
404C4×C22⋊C4C2×D1113yescomplemented
405C22×C11—26no—
406C22×C11—26no—
407C22×C11—26no—
408C22×C11—43no—
409C22×C11—43no—
410C22×C11—43no—
411C22×C11—43no—
412C22×C11C24×C411yescharacteristic
413C22×C11C23×D411yescharacteristic
414C22×C11C23×D411yescharacteristic
415C22×C11C2×H(5,𝔽2)11yescharacteristic
416C22×C11C2×H(5,𝔽2)11yescharacteristic
417C22×C11#58511yescharacteristic
418C22×C11#58511yescharacteristic
419C2×D11—26no—
420C2×D11—26no—
421C2×D11—26no—
422C2×D11—26no—
423C2×D11—26no—
424C2×D11—26no—
425C2×D11—26no—
426C2×D11—26no—
427C2×D11—26no—
428C2×D11—43no—
429C2×D11—43no—
430C2×D11—43no—
431C2×D11—43no—
432C2×D11—848no—
433C2×D11C22×C22⋊C4112yes—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11—43no—
437C4×C11—43no—
438C4×C11—41no—
439C4×C11C22×C22⋊C4112yes—
440Dic11—22no—
441Dic11—22no—
442Dic11—43no—
443Dic11—43no—
444Dic11—41no—
445Dic11C22×C22⋊C414yes—
446C25—116no—
447H(5,𝔽2)—22128no—
448C2×#41—24no—
449C2×#41—24no—
450C2×#41—118no—
451C2×#41—118no—
452C2×#41—118no—
453C2×#41—118no—
454C2×#41—1124no—
455C2×#41—2212no—
456C2×#41—2212no—
457C2×#41—224no—
458C2×#41—224no—
459C2×#41C4×D1118yescomplemented
460C22×Q8—111no—
461C22×Q8C22×D1111yescharacteristic
462C22×D4—113no—
463C22×D4—113no—
464C22×D4—1124no—
465C22×D4—1124no—
466C22×D4—1124no—
467C22×D4—113no—
468C22×D4—113no—
469C22×D4—113no—
470C22×D4—2212no—
471C22×D4—2212no—
472C22×D4—2212no—
473C22×D4—2212no—
474C22×D4—2212no—
475C22×D4—2212no—
476C22×D4C22×D1113yes—
477C23×C4—113no—
478C23×C4—113no—
479C23×C4—113no—
480C23×C4—113no—
481C23×C4—116no—
482C23×C4C22×D1113yes—
483C4×Q8—24no—
484C4×Q8—24no—
485C4×Q8—224no—
486C4×Q8—224no—
487C4×D4—2212no—
488C4×D4—2212no—
489C4×D4—2212no—
490C4×D4—2212no—
491#117—2212no—
492#117—2212no—
493C2×C4⋊C4—113no—
494C2×C4⋊C4—113no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—113no—
497C2×C4⋊C4—2212no—
498C2×C4⋊C4C22×D1113yes—
499C2×C4⋊C4C22×D1113yes—
500C2×C22⋊C4—113no—
501C2×C22⋊C4—113no—
502C2×C22⋊C4—113no—
503C2×C22⋊C4—113no—
504C2×C22⋊C4—116no—
505C2×C22⋊C4—113no—
506C2×C22⋊C4—116no—
507C2×C22⋊C4—113no—
508C2×C22⋊C4—116no—
509C2×C22⋊C4—116no—
510C2×C22⋊C4—113no—
511C2×C22⋊C4—113no—
512C2×C22⋊C4—4412no—
513C2×C22⋊C4—4412no—
514C2×C22⋊C4C22×D1113yes—
515C2×C22⋊C4C22×D1116yes—
516C2×C22⋊C4C22×D1113yes—
517C2×C42—113no—
518C2×C42—113no—
519C2×C42—113no—
520C2×C42—111no—
521C2×C42—2212no—
522C2×C42C22×D1113yes—
523C2×C42C22×D1113yes—
524#95—111no—
525#95—111no—
526#95—111no—
527#95—113no—
528#95—113no—
529#95—113no—
530#95C22×D1111yescharacteristic
531#95C22×D1113yes—
532C2×C11—46no—
533C2×C11C23×C22⋊C411yescharacteristic
534C2×C11C4×H(5,𝔽2)11yescharacteristic
535C2×C11C4×H(5,𝔽2)11yescharacteristic
536C2×C11#348811yescharacteristic
537C2×C11#348811yescharacteristic
538C2×C11#349811yescharacteristic
539C2×C11#350011yescharacteristic
540D11—212no—
541D11—46no—
542C24—113no—
543C24—113no—
544C24—1124no—
545C24—2212no—
546C24—2212no—
547C24—446no—
548C24—446no—
549C24—446no—
550C24—446no—
551C24C23×D1113yes—
552#41—232no—
553#41—1164no—
554#41—2296no—
555#41—2232no—
556C2×Q8—114no—
557C2×Q8—222no—
558C2×Q8—222no—
559C2×Q8C2×C4×D1114yes—
560C2×Q8D4×D1114yes—
561C2×Q8D4×D1114yes—
562C2×D4—26no—
563C2×D4—26no—
564C2×D4—1112no—
565C2×D4—1112no—
566C2×D4—1112no—
567C2×D4—1112no—
568C2×D4—1112no—
569C2×D4—1112no—
570C2×D4—1112no—
571C2×D4—2296no—
572C2×D4—226no—
573C2×D4—226no—
574C2×D4—2296no—
575C2×D4—226no—
576C2×D4—226no—
577C2×D4—2296no—
578C2×D4—226no—
579C2×D4—226no—
580C2×D4—226no—
581C2×D4—226no—
582C2×D4C2×C4×D11112yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—111no—
586C22×C4—1112no—
587C22×C4—1112no—
588C22×C4—1112no—
589C22×C4—111no—
590C22×C4—111no—
591C22×C4—1112no—
592C22×C4—111no—
593C22×C4—113no—
594C22×C4—113no—
595C22×C4—226no—
596C22×C4—226no—
597C22×C4—226no—
598C22×C4—2212no—
599C22×C4—226no—
600C22×C4—226no—
601C22×C4—226no—
602C22×C4—443no—
603C22×C4—443no—
604C22×C4—446no—
605C22×C4—446no—
606C22×C4C2×C4×D11112yes—
607C22×C4C23×D1113yes—
608C22×C4C23×D1111yescharacteristic
609C22×C4C23×D1113yes—
610C22×C4C23×D1111yescharacteristic
611C22×C4C23×D1111yescharacteristic
612C22×C4C23×D1113yes—
613C4⋊C4—26no—
614C4⋊C4—26no—
615C4⋊C4—226no—
616C4⋊C4—222no—
617C4⋊C4—226no—
618C4⋊C4—226no—
619C22⋊C4—26no—
620C22⋊C4—46no—
621C22⋊C4—43no—
622C22⋊C4—226no—
623C22⋊C4—226no—
624C22⋊C4—2212no—
625C22⋊C4—226no—
626C22⋊C4—226no—
627C22⋊C4—226no—
628C22⋊C4—446no—
629C22⋊C4—446no—
630C22⋊C4—443no—
631C22⋊C4—443no—
632C22⋊C4—446no—
633C22⋊C4—443no—
634C42—26no—
635C42—26no—
636C42—222no—
637C42—226no—
638C42—226no—
639C42—226no—
640C11#3425811yescharacteristic, complemented, Sylow
641C23—23no—
642C23—23no—
643C23—23no—
644C23—23no—
645C23—23no—
646C23—23no—
647C23—116no—
648C23—116no—
649C23—116no—
650C23—116no—
651C23—2248no—
652C23—223no—
653C23—223no—
654C23—223no—
655C23—223no—
656C23—223no—
657C23—223no—
658C23—223no—
659C23—223no—
660C23—223no—
661C23—223no—
662C23—4424no—
663C23—4424no—
664C23—8812no—
665C23—8812no—
666C23—8812no—
667C23—8812no—
668C23C22×C4×D1116yes—
669C23C24×D1111yescharacteristic
670Q8—228no—
671Q8C22⋊C4×D11116yescomplemented
672D4—224no—
673D4—1148no—
674D4—2224no—
675D4—2224no—
676D4—2224no—
677D4—2224no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—224no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—23no—
687C2×C4—21no—
688C2×C4—23no—
689C2×C4—23no—
690C2×C4—23no—
691C2×C4—21no—
692C2×C4—112no—
693C2×C4—112no—
694C2×C4—112no—
695C2×C4—1148no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—221no—
701C2×C4—221no—
702C2×C4—2224no—
703C2×C4—221no—
704C2×C4—223no—
705C2×C4—223no—
706C2×C4—223no—
707C2×C4—223no—
708C2×C4—221no—
709C2×C4—223no—
710C2×C4—221no—
711C2×C4—223no—
712C2×C4—4412no—
713C2×C4—4412no—
714C2×C4—8812no—
715C2×C4C22×C4×D1112yes—
716C2×C4C22×C4×D1116yes—
717C2×C4C2×D4×D1116yes—
718C2×C4C2×D4×D1116yes—
719C2×C4#6704212yescomplemented
720C22—26no—
721C22—26no—
722C22—26no—
723C22—43no—
724C22—43no—
725C22—43no—
726C22—43no—
727C22—1112no—
728C22—226no—
729C22—226no—
730C22—226no—
731C22—226no—
732C22—226no—
733C22—226no—
734C22—226no—
735C22—226no—
736C22—226no—
737C22—443no—
738C22—443no—
739C22—443no—
740C22—443no—
741C22—8848no—
742C22C23×C4×D1111yescharacteristic
743C22C22×D4×D1111yescharacteristic
744C22C22×D4×D1111yescharacteristic
745C22C2×#6704211yescharacteristic
746C22#1062345311yescharacteristic
747C22D11×H(5,𝔽2)11yescharacteristic
748C22#1062345711yescharacteristic
749C4—22no—
750C4—22no—
751C4—43no—
752C4—41no—
753C4—43no—
754C4—114no—
755C4—222no—
756C4—222no—
757C4—443no—
758C4—441no—
759C4—443no—
760C4C2×C22⋊C4×D11112yes—
761C2—46no—
762C2—2212no—
763C2—446no—
764C2C22×C22⋊C4×D1111yescharacteristic
765C2#1308182211yescharacteristic
766C2C4×#6704211yescharacteristic
767C2#1308228211yescharacteristic
768C2#1308228411yescharacteristic
769C2#1308239311yescharacteristic
770C2#1308240711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2341C2
socle, cosocleC23×C11C25
prime radicalC22×#67042C2
hypercenter#2341D11
hypocenterC11#34258
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#10623105C2semidirect
3. C2×C4×#4343C2semidirect
4. #13071457C2semidirect
5. #13071454C2semidirect
6. #13071454C2semidirect
7. C22⋊C4×D44C2semidirect
8. #13071437C2semidirect
9. #13071437C2semidirect
10. #13071436C2semidirect
11. #13071205C2semidirect
12. #13071195C2semidirect
13. #13071102C2semidirect
14. D11×#390C2semidirect
15. C11×#2341C2semidirect
19. C2×#67042C4semidirect
26. C2×C4×Q8×C11C22semidirect
27. C2×C4×Q8×C11C22semidirect
28. C2×Q8×Dic11C22semidirect
29. C2×Q8×Dic11C22semidirect
32. C2×#66946C22semidirect
33. C2×#66946C22semidirect
34. C2×#66945C22semidirect
35. C2×C4⋊C4×D11C22semidirect
36. C2×C22⋊C4×D11C22semidirect
37. C2×C22⋊C4×D11C22semidirect
38. C2×C4×D44C22semidirect
39. C2×C4×D44C22semidirect
40. C2×#66925C22semidirect
41. C2×C42×D11C22semidirect
42. C11×#390C22semidirect
43. C11×#390C22semidirect
44. C11×#380C22semidirect
45. C4×C11×C22⋊C4C22semidirect
46. #10622834C22semidirect
47. #10622834C22semidirect
48. #10622825C22semidirect
49. C4×C22⋊Dic11C22semidirect
50. #10622601C22semidirect
51. #10622601C22semidirect
52. #10622600C22semidirect
53. #10622600C22semidirect
54. #10622570C22semidirect
55. #10622570C22semidirect
56. #10622570C22semidirect
57. #10622569C22semidirect
58. #10622569C22semidirect
59. #10622569C22semidirect
60. #10622568C22semidirect
61. #10622568C22semidirect
62. #10622552C22semidirect
63. #10622552C22semidirect
64. C4×(C2×D11)⋊C4C22semidirect
65. C4×(C2×D11)⋊C4C22semidirect
66. #10622278C22semidirect
67. #10622278C22semidirect
68. #10622278C22semidirect
69. #10622259C22semidirect
70. #10622259C22semidirect
74. C2×C11×#41C2×C4semidirect
84. C2×#4343C2×C4semidirect
91. C2×D4×D11C2×C4semidirect
92. C2×D4×D11C2×C4semidirect
95. C2×#4339C2×C4semidirect
98. C22×D44C2×C4semidirect
197. #4343C22⋊C4semidirect
262. #2341D11semidirect
300. Q8×C11C2×C22⋊C4semidirect
320. C2×C4×C11H(5,𝔽2)semidirect
340. C2×Dic11H(5,𝔽2)semidirect
343. D44C2×C22⋊C4semidirect
348. C4×D11C2×C22⋊C4semidirect
364. C2×C4×Q8C2×D11semidirect
365. C2×C4×Q8C2×D11semidirect
387. #390C2×D11semidirect
388. #390C2×D11semidirect
398. #380C2×D11semidirect
404. C4×C22⋊C4C2×D11semidirect
459. C2×#41C4×D11semidirect
640. C11#34258semidirect
671. Q8C22⋊C4×D11semidirect
719. C2×C4#67042semidirect

Maximal subgroups

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

subgroupindex
C22×#670422
C2×#106231052
C2×C4×#43432
#130714572
#130714542
C22⋊C4×D442
#130714372
#130714362
#130712052
#130711952
#130711022
D11×#3902
C11×#23412
#3425811