Finite Group Databasebeta

← #14770327

Subgroups — #14770327

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623166C211yesmaximal, characteristic
2#13071495C211yesmaximal, characteristic, complemented
3#13071491C211yesmaximal, characteristic, complemented
4#13069602C211yesmaximal, characteristic, complemented
5#13069599C212yesmaximal, complemented
6#13069599C212yesmaximal, complemented
7#13068603C212yesmaximal
8#13068601C211yesmaximal, characteristic
9C4×#66870C211yesmaximal, characteristic
10#13068403C212yesmaximal
11C11×#1996C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×#66999C411yescharacteristic, complemented
14C2×Q8×Dic11C411yescharacteristic, complemented
15C2×C4×C22⋊D11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17#10623166—22no—
18#10623166—22no—
19#10623166—21no—
20#10623166—21no—
21#10623166—21no—
22#10623166—21no—
23C2×#66950C412yescomplemented
24C2×C4⋊C4×D11C411yescharacteristic, complemented
25C2×#66942C412yescomplemented
26C2×#66941C411yescharacteristic, complemented
27C2×(C22⋊D11)⋊C4C2212yes—
28C2×#66931C2212yes—
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31#10622825C2211yescharacteristic
32C4×C22⋊Dic11C2211yescharacteristic
33C4⋊C4×Dic11—21no—
34#10622586—21no—
35C2×#66870C2212yes—
36C2×#66870C2211yescharacteristic
37C2×#66870C2211yescharacteristic
38#10622555C2212yes—
39#10622555C2212yes—
40C22⋊C4×Dic11C2212yes—
41C22⋊C4×Dic11C2212yes—
42C4×C4⋊Dic11—21no—
43#10622541—21no—
44#10622267—22no—
45#10622266—22no—
46C11×#342C2212yes—
47C11×#342C2212yes—
48#10622165C2212yes—
49#10622165C2211yescharacteristic
50#10622165C2211yescharacteristic
51#10622164C2212yes—
52#10622164C2212yes—
53C22×Q8×C11C2×C411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11C2311yescharacteristic
56C23×Dic11C2312yes—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11C2×C412yes—
59C22×Dic22C2×C412yes—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C4⋊C4C2×C412yes—
67C2×C11×C22⋊C4C2312yes—
68C2×C11×C22⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4C2312yes—
70C2×C11×C22⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C22⋊Dic11C2312yes—
73C2×C22⋊Dic11C2311yescharacteristic
74C2×C22⋊Dic11C2311yescharacteristic
75C2×C22⋊Dic11C2311yescharacteristic
76#66999—22no—
77#66999—21no—
78#66999—21no—
79Q8×Dic11—22no—
80Q8×Dic11—21no—
81Q8×Dic11—21no—
82C4×C22⋊D11—21no—
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85C4×C22⋊D11—21no—
86C2×(C2×D11)⋊C4C2×C412yes—
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2×C412yes—
90C2×C4⋊Dic11C2×C411yescharacteristic
91C2×C4⋊Dic11C2×C412yes—
92C2×C4⋊Dic11C2×C411yescharacteristic
93C2×C4⋊Dic11D412yes—
94C2×C4⋊Dic11D412yes—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11D411yescharacteristic
97C2×C4⋊Dic11D411yescharacteristic
98C2×C4⋊Dic11D411yescharacteristic
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4C2×C412yes—
102C2×Dic11⋊C4C2×C412yes—
103C2×Dic11⋊C4C2×C412yes—
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×C4×Dic11—21no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11C2×C412yes—
109C2×C4×Dic11C2×C411yescharacteristic
110#66950—22no—
111#66950—22no—
112#66950—22no—
113#66950—22no—
114C4⋊C4×D11—22no—
115C4⋊C4×D11—21no—
116C4⋊C4×D11—21no—
117#66942—22no—
118#66942—22no—
119#66942—22no—
120#66942—22no—
121#66941—22no—
122#66941—21no—
123#66941—21no—
124(C22⋊D11)⋊C4—22no—
125(C22⋊D11)⋊C4—22no—
126(C22⋊D11)⋊C4—22no—
127(C22⋊D11)⋊C4—22no—
128#66931—22no—
129#66931—22no—
130#66931—22no—
131#66931—22no—
132C11×#95—21no—
133C11×#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140#66870—24no—
141#66870—22no—
142#66870Q814yescomplemented
143#22513—111nomaximal, Sylow
144C24×C11C2411yescharacteristic
145C23×D11C22×C411yescharacteristic
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—42no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—42no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C2×C22⋊D11—21no—
162C2×C22⋊D11—21no—
163C2×C22⋊D11—21no—
164C2×C22⋊D11—21no—
165C2×C22⋊D11C2×Q812yes—
166C2×C22⋊D11#4112yes—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—82no—
171C22×Dic11C22×C411yescharacteristic
172C22×Dic11C22×C411yescharacteristic
173C22×Dic11C22×C411yescharacteristic
174C22×Dic11C22×C412yes—
175C22×Dic11C22×C412yes—
176C22×Dic11C2×D412yes—
177C22×Dic11C2×D412yes—
178C22×Dic11C2×D412yes—
179C22×Dic11C2×D412yes—
180C2×C4×D11—22no—
181C2×C4×D11—22no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—42no—
185C2×C4×D11—82no—
186C2×Dic22—22no—
187C2×Dic22—22no—
188C2×Dic22—82no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—42no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4C2×Q812yes—
202C42×C11—42no—
203C22⋊Dic11—21no—
204C22⋊Dic11—21no—
205C22⋊Dic11—22no—
206C22⋊Dic11—21no—
207C22⋊Dic11—21no—
208C22⋊Dic11—22no—
209C22⋊Dic11—21no—
210C22⋊Dic11C2×Q812yes—
211(C2×D11)⋊C4—22no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—21no—
214(C2×D11)⋊C4—21no—
215C4⋊Dic11—22no—
216C4⋊Dic11—22no—
217C4⋊Dic11—42no—
218C4⋊Dic11C22⋊C412yes—
219C4⋊Dic11C22⋊C411yescharacteristic
220C4⋊Dic11C22⋊C411yescharacteristic
221C4⋊Dic11C22⋊C412yes—
222C4⋊Dic11C22⋊C412yes—
223C4⋊Dic11C22⋊C412yes—
224C4⋊Dic11C22⋊C412yes—
225C4⋊Dic11C22⋊C412yes—
226C4⋊Dic11C22⋊C411yescharacteristic
227C4⋊Dic11C22⋊C411yescharacteristic
228Dic11⋊C4—22no—
229Dic11⋊C4—22no—
230Dic11⋊C4—22no—
231Dic11⋊C4—22no—
232Dic11⋊C4—22no—
233Dic11⋊C4—22no—
234Dic11⋊C4—21no—
235Dic11⋊C4—21no—
236Dic11⋊C4—82no—
237Dic11⋊C4—82no—
238C4×Dic11—22no—
239C4×Dic11—22no—
240C4×Dic11—21no—
241C4×Dic11—21no—
242C4×Dic11—42no—
243C4×Dic11—82no—
244C4×Dic11—82no—
245C2×#554—111no—
246#2345—111no—
247#2345—111no—
248#1996—112no—
249#1996—112no—
250#1996—111no—
251#1996D1111yescharacteristic, complemented
252#1799—111no—
253#1799—112no—
254C4×#99—111no—
255C4×#99—112no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11C23×C411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C22×Q811yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C112−1+411yescharacteristic
264C23×C112−1+411yescharacteristic
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11C4×Q812yes—
270Q8×C11—42no—
271Q8×C11—42no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—42no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11C2×C22⋊C411yescharacteristic
292C2×C4×C11C2×C22⋊C411yescharacteristic
293C2×C4×C11C2×C22⋊C411yescharacteristic
294C2×C4×C11C2×C22⋊C411yescharacteristic
295C22⋊D11—22no—
296C22⋊D11—22no—
297C22⋊D11—22no—
298C22⋊D11—22no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—22no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—42no—
316C2×Dic11—41no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—41no—
320C2×Dic11C2×C22⋊C412yes—
321C2×Dic11C2×C22⋊C412yes—
322C2×Dic11C2×C22⋊C412yes—
323C2×Dic11C2×C22⋊C412yes—
324C2×Dic11C4×Q812yes—
325C4×D11—42no—
326C4×D11—42no—
327C4×D11—82no—
328C4×D11—82no—
329Dic22—82no—
330Dic22—82no—
331#554—221no—
332#554—221no—
333#554—222no—
334#554—222no—
335#554—221no—
336#554—221no—
337C2×C4⋊Q8—111no—
338C2×#125—112no—
339C2×C22⋊Q8—111no—
340C2×C22⋊Q8—112no—
341C2×C22⋊Q8—112no—
342C2×C22⋊Q8C2×D1111yescharacteristic
343C2×C4×Q8—111no—
344C2×C4×D4—111no—
345C2×C4×D4—112no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C2×#99—111no—
349C2×#99—112no—
350C2×#99—111no—
351#389—221no—
352#389—221no—
353#387—222no—
354#387—222no—
355#380—111no—
356#380—112no—
357#380—112no—
358#380C2×D1111yescharacteristic
359C4×C4⋊C4—221no—
360C4×C4⋊C4—221no—
361C4×C22⋊C4—111no—
362C4×C22⋊C4—112no—
363C4×C22⋊C4—112no—
364C4×C22⋊C4C2×D1111yescharacteristic
365#342—112no—
366#342—112no—
367#342—112no—
368#342—111no—
369#342—111no—
370#342C2×D1112yes—
371#342C2×D1112yes—
372C22×C11—21no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11C22×C22⋊C411yescharacteristic
383C22×C11C2×C4×Q811yescharacteristic
384C22×C11#51911yescharacteristic
385C22×C11#54811yescharacteristic
386C22×C11#54811yescharacteristic
387C22×C11D4×Q811yescharacteristic
388C22×C11D4×Q811yescharacteristic
389C2×D11—22no—
390C2×D11—42no—
391C2×D11—41no—
392C2×D11—41no—
393C2×D11—42no—
394C4×C11—21no—
395C4×C11—21no—
396C4×C11—21no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—81no—
401C4×C11—82no—
402C4×C11#41012yes—
403Dic11—22no—
404Dic11—22no—
405Dic11—22no—
406Dic11—22no—
407Dic11—22no—
408Dic11—42no—
409Dic11—41no—
410Dic11—41no—
411Dic11—82no—
412Dic11—81no—
413C22×Q8—112no—
414C22×Q8C4×D1111yescharacteristic
415C22×D4—111no—
416C23×C4—112no—
417C23×C4—111no—
418C23×C4—112no—
419C23×C4C22×D1111yescharacteristic
420C4⋊Q8—222no—
421C4⋊Q8—221no—
422C4⋊Q8—221no—
423#125—222no—
424#125—222no—
425#125—222no—
426#125—222no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—222no—
432C22⋊Q8—222no—
433C22⋊Q8—222no—
434C22⋊Q8—222no—
435C22⋊Q8—222no—
436C22⋊Q8—222no—
437C22⋊Q8—222no—
438C22⋊Q8—222no—
439C22⋊Q8—222no—
440C22⋊Q8—221no—
441C22⋊Q8—221no—
442C4×Q8—222no—
443C4×Q8—221no—
444C4×Q8—221no—
445C4×D4—222no—
446C4×D4—222no—
447C4×D4—222no—
448C4×D4—222no—
449C4×D4—221no—
450C4×D4—221no—
451C4×D4—221no—
452C4×D4—221no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—112no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—112no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4—112no—
467C2×C4⋊C4—112no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—222no—
474C2×C4⋊C4C4×D1111yescharacteristic
475C2×C4⋊C4C4×D1112yes—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—112no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—112no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4C22×D1112yes—
483C2×C22⋊C4C22×D1111yescharacteristic
484C2×C22⋊C4C22×D1112yes—
485C2×C22⋊C4C22×D1111yescharacteristic
486C2×C42—21no—
487C2×C42—112no—
488C2×C42—111no—
489C2×C42—221no—
490C2×C42—222no—
491C2×C42—222no—
492#99—114no—
493#99—222no—
494#99—224no—
495#95—21no—
496#95—21no—
497#95—222no—
498#95—222no—
499#95—222no—
500#95—222no—
501#95—221no—
502#95—221no—
503C2×C11—21no—
504C2×C11—21no—
505C2×C11—21no—
506C2×C11—21no—
507C2×C11—21no—
508C2×C11—21no—
509C2×C11Q8×C22⋊C411yescharacteristic
510C2×C11C2×#41011yescharacteristic
511C2×C11#288311yescharacteristic
512D11—42no—
513C24—111no—
514C24C23×D1111yescharacteristic
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—42no—
518C2×Q8—222no—
519C2×Q8—222no—
520C2×Q8—882no—
521C2×D4—112no—
522C2×D4—112no—
523C2×D4—221no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4—221no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—42no—
531C22×C4—111no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—111no—
539C22×C4—111no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—221no—
543C22×C4—221no—
544C22×C4—221no—
545C22×C4—221no—
546C22×C4—222no—
547C22×C4—442no—
548C22×C4—882no—
549C22×C4—882no—
550C22×C4C2×C4×D1111yescharacteristic
551C22×C4C2×C4×D1112yes—
552C22×C4C2×C4×D1112yes—
553C22×C4C2×C4×D1111yescharacteristic
554C22×C4D4×D1111yescharacteristic
555C22×C4D4×D1111yescharacteristic
556C22×C4D4×D1111yescharacteristic
557C22×C4D4×D1111yescharacteristic
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—42no—
563C4⋊C4—112no—
564C4⋊C4—111no—
565C4⋊C4—111no—
566C4⋊C4—112no—
567C4⋊C4—112no—
568C4⋊C4—112no—
569C4⋊C4—112no—
570C4⋊C4—112no—
571C4⋊C4—111no—
572C4⋊C4—111no—
573C4⋊C4—222no—
574C4⋊C4—222no—
575C4⋊C4—222no—
576C4⋊C4—222no—
577C4⋊C4—222no—
578C4⋊C4—222no—
579C4⋊C4—222no—
580C4⋊C4—222no—
581C4⋊C4—221no—
582C4⋊C4—221no—
583C4⋊C4—442no—
584C4⋊C4—882no—
585C4⋊C4—882no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—21no—
589C22⋊C4—21no—
590C22⋊C4—21no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—112no—
594C22⋊C4—222no—
595C22⋊C4—222no—
596C22⋊C4—221no—
597C22⋊C4—221no—
598C22⋊C4—221no—
599C22⋊C4—221no—
600C22⋊C4—221no—
601C22⋊C4—222no—
602C22⋊C4—222no—
603C22⋊C4—221no—
604C22⋊C4—221no—
605C22⋊C4Q8×D1112yes—
606C42—42no—
607C42—222no—
608C42—222no—
609C42—221no—
610C42—221no—
611C42—442no—
612C42—882no—
613C42—882no—
614C11#2251311yescharacteristic, complemented, Sylow
615C23—41no—
616C23—41no—
617C23—112no—
618C23—221no—
619C23—221no—
620C23—441no—
621C23—441no—
622C23C22×C4×D1111yescharacteristic
623C23C2×D4×D1111yescharacteristic
624C23C2×D4×D1111yescharacteristic
625C23C2×Q8×D1111yescharacteristic
626C23#6704011yescharacteristic
627C23#41×D1111yescharacteristic
628C23#6704311yescharacteristic
629Q8—42no—
630Q8—42no—
631Q8—882no—
632Q8—882no—
633D4—222no—
634D4—222no—
635D4—222no—
636D4—222no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—112no—
657C2×C4—112no—
658C2×C4—112no—
659C2×C4—112no—
660C2×C4—112no—
661C2×C4—221no—
662C2×C4—221no—
663C2×C4—222no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—442no—
667C2×C4—442no—
668C2×C4—442no—
669C2×C4—442no—
670C2×C4—442no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4—442no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—442no—
680C2×C4—442no—
681C2×C4—441no—
682C2×C4—442no—
683C2×C4—441no—
684C2×C4—882no—
685C2×C4—882no—
686C2×C4C22⋊C4×D1111yescharacteristic
687C2×C4C22⋊C4×D1111yescharacteristic
688C2×C4C22⋊C4×D1111yescharacteristic
689C2×C4C22⋊C4×D1111yescharacteristic
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—222no—
701C22—442no—
702C22—442no—
703C22—441no—
704C22—441no—
705C22C2×C22⋊C4×D1111yescharacteristic
706C22C4×Q8×D1111yescharacteristic
707C22#1062310311yescharacteristic
708C22#1062316311yescharacteristic
709C22#1062316411yescharacteristic
710C22#1062320811yescharacteristic
711C22#1062325811yescharacteristic
712C4—21no—
713C4—21no—
714C4—21no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—82no—
719C4—81no—
720C4—222no—
721C4—222no—
722C4—222no—
723C4—222no—
724C4—222no—
725C4—442no—
726C4—441no—
727C4—441no—
728C4—881no—
729C4—882no—
730C4#1062235312yes—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—442no—
738C2#1307145011yescharacteristic
739C2C2×#1062235311yescharacteristic
740C2#1307707511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1996C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C22⋊D11C23
cosocleC24×C11C24
hypercenter#1996D11
hypocenterC11#22513
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #13071495C2semidirect
3. #13071491C2semidirect
4. #13069602C2semidirect
5. #13069599C2semidirect
6. #13069599C2semidirect
11. C11×#1996C2semidirect
13. C2×#66999C4semidirect
14. C2×Q8×Dic11C4semidirect
23. C2×#66950C4semidirect
24. C2×C4⋊C4×D11C4semidirect
25. C2×#66942C4semidirect
26. C2×#66941C4semidirect
142. #66870Q8semidirect
251. #1996D11semidirect
614. C11#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#106231662
#130714952
#130714912
#130696022
#130695992
#130686032
#130686012
C4×#668702
#130684032
C11×#19962
#2251311