Finite Group Databasebeta

← #14677170

Subgroups — #14677170

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622552C211yesmaximal, characteristic
4C2×#10622541C211yesmaximal, characteristic, complemented
5C2×#10622602C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066846C211yesmaximal, characteristic, complemented
9#13066846C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C2×C4×D44—24no—
29C2×C4×D44—24no—
30C2×C4×D44—24no—
31C4×C11×C4⋊C4—24no—
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622602—28no—
40#10622552—24no—
41#10622552C418yescomplemented
42#10622541—24no—
43C24×D11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44C2×C414yes—
59C22×D44D414yes—
60C22×D44Q814yes—
61C22×C4×D11—24no—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—42no—
67C22×C4×D11—42no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4D414yescomplemented
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×C42×C11—22no—
81C2×C42×C11C2×C414yescomplemented
82C2×C42×C11D414yes—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—42no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4C2×C418yescomplemented
97C2×(C2×D11)⋊C4C2×C418yescomplemented
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11C2×C414yescomplemented
106C2×C4⋊Dic11D414yes—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—42no—
110C4×D44—232no—
111C11×#95—22no—
112C11×#95—22no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—42no—
117C11⋊#95—42no—
118#14018—111nomaximal, Sylow
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11C22×C414yes—
133C23×D11C2×D414yes—
134C23×D11C2×Q814yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11C22×C412yes—
168C22×C4×C11C22×C412yes—
169C22×C4×C11C22×C412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×Q812yes—
179C22×C4×C11#4112yes—
180C22×C4×C11#4112yes—
181C22×C4×C11#4112yes—
182C22×C4×C11#4112yes—
183C22×C4×C11#4112yes—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11C22×C414yes—
204C22×Dic11C2×D414yes—
205C2×D44—28no—
206C2×D44—28no—
207C2×D44—28no—
208C2×D44—28no—
209C2×D44—28no—
210C2×D44—28no—
211C2×D44C4⋊C4116yescomplemented
212C2×C4×D11—216no—
213C2×C4×D11—48no—
214C2×C4×D11—48no—
215C2×C4×D11—48no—
216C2×C4×D11—48no—
217C2×C4×D11—48no—
218C2×C4×D11—48no—
219C11×C4⋊C4—28no—
220C11×C4⋊C4—28no—
221C42×C11—28no—
222C42×C11—28no—
223C42×C11—44no—
224(C2×D11)⋊C4—216no—
225(C2×D11)⋊C4—216no—
226(C2×D11)⋊C4—48no—
227(C2×D11)⋊C4—48no—
228(C2×D11)⋊C4—48no—
229C4⋊Dic11—28no—
230C4⋊Dic11—28no—
231C4⋊Dic11—44no—
232Dic11⋊C4—48no—
233C22×C4×D4—111no—
234C2×#390—111no—
235C2×#390—111no—
236C2×#389—111no—
237C2×#385—112no—
238C2×C4×C4⋊C4D1111yescharacteristic, complemented
239#1439—112no—
240#1439—112no—
241C4⋊#95—111no—
242C4⋊#95—111no—
243C22⋊#95—112no—
244C23×C11C23×C411yescharacteristic
245C23×C11C22×D411yescharacteristic
246C23×C11C22×D411yescharacteristic
247C23×C11C22×D411yescharacteristic
248C23×C11C22×D411yescharacteristic
249C23×C11C22×Q811yescharacteristic
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4111yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11C2×#4111yescharacteristic
255C23×C11H(5,𝔽2)11yescharacteristic
256C23×C11H(5,𝔽2)11yescharacteristic
257C23×C11H(5,𝔽2)11yescharacteristic
258C23×C112−1+411yescharacteristic
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—24no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—24no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—24no—
275C22×D11—24no—
276C22×D11—24no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11C2×C4⋊C418yes—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11C2×C4⋊C414yes—
335C2×C4×C11C4×D414yes—
336C2×C4×C11C4×D414yes—
337C2×C4×C11C4×D414yescomplemented
338C2×C4×C11#12014yes—
339C2×C4×C11#12114yes—
340C2×C4×C11C22⋊Q814yes—
341C2×C4×C11C22⋊Q814yes—
342C2×C4×C11#12314yes—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364D44—232no—
365C4×D11—432no—
366C23×D4—111no—
367C24×C4—112no—
368C2×C4×D4—224no—
369C2×C4×D4—224no—
370C2×C4×D4—224no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—112no—
375C22×C4⋊C4C2×D1111yescharacteristic
376C22×C4⋊C4C2×D1111yescharacteristic
377C22×C22⋊C4—112no—
378C22×C22⋊C4—112no—
379C22×C22⋊C4—112no—
380C22×C22⋊C4—112no—
381C22×C22⋊C4—112no—
382C22×C42C2×D1111yescharacteristic
383C22×C42C2×D1111yescharacteristic
384C22×C42C2×D1111yescharacteristic
385#390—118no—
386#390—224no—
387#389—224no—
388#385—228no—
389C4×C4⋊C4—24no—
390C2×#95—112no—
391C2×#95—112no—
392C2×#95—112no—
393C2×#95—112no—
394C2×#95—112no—
395C2×#95C2×D1111yescharacteristic
396C2×#95C2×D1111yescharacteristic
397C22×C11C22×C4⋊C411yescharacteristic
398C22×C11C2×C4×D411yescharacteristic
399C22×C11C2×C4×D411yescharacteristic
400C22×C11C2×C4×D411yescharacteristic
401C22×C11C4×#4111yescharacteristic
402C22×C11#51811yescharacteristic
403C22×C11#52011yescharacteristic
404C22×C11C2×#12011yescharacteristic
405C22×C11C2×#12111yescharacteristic
406C22×C11C2×C22⋊Q811yescharacteristic
407C22×C11C2×C22⋊Q811yescharacteristic
408C22×C11C2×#12311yescharacteristic
409C22×C11#52511yescharacteristic
410C22×C11#52911yescharacteristic
411C22×C11#53211yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11#53711yescharacteristic
414C22×C11#54011yescharacteristic
415C22×C11#54211yescharacteristic
416C22×C11D4211yescharacteristic
417C22×C11D4211yescharacteristic
418C22×C11#54611yescharacteristic
419C22×C11#54611yescharacteristic
420C22×C11#54611yescharacteristic
421C22×C11#54711yescharacteristic
422C22×C11#54811yescharacteristic
423C22×C11D4×Q811yescharacteristic
424C22×C11#55011yescharacteristic
425C22×C11#55011yescharacteristic
426C22×C11#55411yescharacteristic
427C22×C11#55411yescharacteristic
428C22×C11#55411yescharacteristic
429C22×C11#55611yescharacteristic
430C22×C11#55911yescharacteristic
431C22×C11#55911yescharacteristic
432C2×D11—28no—
433C2×D11—28no—
434C2×D11—28no—
435C2×D11—44no—
436C2×D11—44no—
437C2×D11—44no—
438C2×D11—44no—
439C2×D11—44no—
440C2×D11—44no—
441C2×D11—44no—
442C2×D11—44no—
443C2×D11—44no—
444C2×D11—44no—
445C2×D11—44no—
446C2×D11—44no—
447C4×C11—24no—
448C4×C11—24no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11#38518yescomplemented
454Dic11—44no—
455Dic11—44no—
456Dic11—82no—
457C25—112no—
458C22×D4—114no—
459C22×D4—114no—
460C22×D4—114no—
461C22×D4—222no—
462C22×D4—222no—
463C22×D4—222no—
464C22×D4—222no—
465C23×C4—112no—
466C23×C4—112no—
467C23×C4—112no—
468C23×C4—224no—
469C23×C4—224no—
470C23×C4—224no—
471C23×C4—224no—
472C23×C4—224no—
473C23×C4—442no—
474C23×C4—442no—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1111yescharacteristic
482C4×D4—2232no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—222no—
494C2×C4⋊C4—224no—
495C2×C4⋊C4—224no—
496C2×C4⋊C4—222no—
497C2×C4⋊C4—222no—
498C2×C4⋊C4—222no—
499C2×C4⋊C4—442no—
500C2×C4⋊C4D4414yescomplemented
501C2×C22⋊C4—118no—
502C2×C22⋊C4—118no—
503C2×C22⋊C4—224no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—224no—
506C2×C22⋊C4—224no—
507C2×C22⋊C4—224no—
508C2×C22⋊C4—224no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—224no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—442no—
513C2×C22⋊C4—442no—
514C2×C22⋊C4—442no—
515C2×C22⋊C4—442no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42C4×D1114yescomplemented
524C2×C42C22⋊D1114yes—
525#95—22no—
526#95—22no—
527#95—224no—
528#95—224no—
529#95—224no—
530#95—442no—
531#95—442no—
532C2×C11C2×#38511yescharacteristic
533C2×C11C4×#12111yescharacteristic
534C2×C11#232411yescharacteristic
535C2×C11D4×C4⋊C411yescharacteristic
536C2×C11#234911yescharacteristic
537C2×C11#236611yescharacteristic
538C2×C11#236711yescharacteristic
539C2×C11#240711yescharacteristic
540C2×C11#240811yescharacteristic
541C2×C11#244511yescharacteristic
542C2×C11#244711yescharacteristic
543C2×C11#245211yescharacteristic
544C2×C11#245411yescharacteristic
545C2×C11#253811yescharacteristic
546C2×C11#258011yescharacteristic
547D11—48no—
548C24—114no—
549C24—114no—
550C24—114no—
551C24—222no—
552C24—222no—
553C24—222no—
554C24—222no—
555C24—222no—
556C24—222no—
557C24—222no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24—222no—
562C24—222no—
563C24C23×D1111yescharacteristic
564C2×D4—1116no—
565C2×D4—228no—
566C2×D4—228no—
567C2×D4—228no—
568C2×D4—228no—
569C2×D4—228no—
570C2×D4—228no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—114no—
604C22×C4—114no—
605C22×C4—2216no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—448no—
626C22×C4—448no—
627C22×C4—448no—
628C22×C4—448no—
629C22×C4—448no—
630C22×C4—448no—
631C22×C4C2×C4×D1112yes—
632C22×C4C2×C4×D1112yes—
633C22×C4C2×C4×D1112yes—
634C22×C4C2×D4412yes—
635C22×C4C2×D4412yes—
636C22×C4C2×D4412yes—
637C22×C4#433912yes—
638C22×C4#433912yes—
639C22×C4#433912yes—
640C22×C4#433912yes—
641C22×C4D4×D1112yes—
642C22×C4D4×D1112yes—
643C22×C4Q8×D1112yes—
644C22×C4#434312yes—
645C22×C4C2×C22⋊D1112yes—
646C22×C4C2×C22⋊D1112yes—
647C22×C4C2×C22⋊D1112yes—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—228no—
651C4⋊C4—228no—
652C4⋊C4—448no—
653C4⋊C4—444no—
654C22⋊C4—2216no—
655C22⋊C4—2216no—
656C22⋊C4—448no—
657C22⋊C4—448no—
658C22⋊C4—448no—
659C42—28no—
660C42—28no—
661C42—44no—
662C11#1401811yescharacteristic, complemented, Sylow
663C23—118no—
664C23—224no—
665C23—224no—
666C23—224no—
667C23—224no—
668C23—224no—
669C23—224no—
670C23—224no—
671C23—224no—
672C23—224no—
673C23—224no—
674C23—224no—
675C23—224no—
676C23—224no—
677C23—224no—
678C23—224no—
679C23—224no—
680C23—224no—
681C23—224no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23—442no—
688C23—442no—
689C23—442no—
690C23—442no—
691C23—442no—
692C23—442no—
693C23—442no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23—442no—
698C23C22×C4×D1111yescharacteristic
699C23C22×D4411yescharacteristic
700C23C2×#433911yescharacteristic
701C23C2×#433911yescharacteristic
702C23C2×#433911yescharacteristic
703C23C2×#433911yescharacteristic
704C23C2×D4×D1111yescharacteristic
705C23C2×D4×D1111yescharacteristic
706C23C2×Q8×D1111yescharacteristic
707C23C2×#434311yescharacteristic
708C23#6704211yescharacteristic
709C23#6704211yescharacteristic
710C23#6704211yescharacteristic
711C23#6704311yescharacteristic
712C23C22×C22⋊D1111yescharacteristic
713D4—2232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—4432no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4C4×D4414yescomplemented
777C2×C4C4⋊C4×D1114yes—
778C2×C4#6694614yes—
779C2×C4#6694714yes—
780C2×C4#6694914yes—
781C2×C4C4×C22⋊D1114yes—
782C2×C4#6698314yes—
783C2×C4#6699014yes—
784C2×C4#6699914yes—
785C22—228no—
786C22—228no—
787C22—228no—
788C22—444no—
789C22—444no—
790C22—444no—
791C22—444no—
792C22—444no—
793C22—444no—
794C22—444no—
795C22—444no—
796C22—444no—
797C22—444no—
798C22—444no—
799C22—444no—
800C22C2×C4×D4411yescharacteristic
801C22C4×#433911yescharacteristic
802C22#1062300811yescharacteristic
803C22#1062301011yescharacteristic
804C22C2×C4⋊C4×D1111yescharacteristic
805C22C2×#6694611yescharacteristic
806C22C2×#6694711yescharacteristic
807C22C2×#6694911yescharacteristic
808C22#1062305211yescharacteristic
809C22#1062305411yescharacteristic
810C22#1062306511yescharacteristic
811C22#1062306611yescharacteristic
812C22D4×D4411yescharacteristic
813C22D4×D4411yescharacteristic
814C22#1062308111yescharacteristic
815C22#1062308111yescharacteristic
816C22#1062308111yescharacteristic
817C22#1062308211yescharacteristic
818C22#1062308311yescharacteristic
819C22#1062308411yescharacteristic
820C22Q8×D4411yescharacteristic
821C22#1062310811yescharacteristic
822C22#1062311011yescharacteristic
823C22#1062311011yescharacteristic
824C22#1062311011yescharacteristic
825C22#1062311511yescharacteristic
826C22#1062311611yescharacteristic
827C22#1062311611yescharacteristic
828C22C2×C4×C22⋊D1111yescharacteristic
829C22C2×#6698311yescharacteristic
830C22#1062332211yescharacteristic
831C22C2×#6699011yescharacteristic
832C22C2×#6699911yescharacteristic
833C22#1062336111yescharacteristic
834C22#1062336411yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—444no—
842C4—444no—
843C4—882no—
844C4#1062260218yescomplemented
845C2—448no—
846C2C2×#1062260211yescharacteristic
847C2C4×#6698311yescharacteristic
848C2#1307130911yescharacteristic
849C2C4⋊C4×D4411yescharacteristic
850C2#1307152711yescharacteristic
851C2#1307168011yescharacteristic
852C2#1307168511yescharacteristic
853C2#1307196111yescharacteristic
854C2#1307197211yescharacteristic
855C2#1307238111yescharacteristic
856C2#1307240311yescharacteristic
857C2#1307246611yescharacteristic
858C2#1307248811yescharacteristic
859C2#1307353411yescharacteristic
860C2#1307397411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#14018
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#10622541C2semidirect
5. C2×#10622602C2semidirect
6. #13066860C2semidirect
7. #13066858C2semidirect
8. #13066846C2semidirect
9. #13066846C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
41. #10622552C4semidirect
73. C2×C11×C4⋊C4D4semidirect
81. C2×C42×C11C2×C4semidirect
96. C2×(C2×D11)⋊C4C2×C4semidirect
97. C2×(C2×D11)⋊C4C2×C4semidirect
105. C2×C4⋊Dic11C2×C4semidirect
211. C2×D44C4⋊C4semidirect
238. C2×C4×C4⋊C4D11semidirect
337. C2×C4×C11C4×D4semidirect
453. C4×C11#385semidirect
500. C2×C4⋊C4D44semidirect
523. C2×C42C4×D11semidirect
662. C11#14018semidirect
776. C2×C4C4×D44semidirect
844. C4#10622602semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×#106225522
C2×#106225412
C2×#106226022
#130668602
#130668582
#130668462
(C2×D11)⋊#952
C2×C4×C11×C4⋊C42
#1401811