Finite Group Databasebeta

← C2×#13080267 #15628925

Subgroups — C2×#13080267 #15628925

Order 2816.

2762 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C211yesmaximal, characteristic, complemented
2C2×#10623348C211yesmaximal, characteristic, complemented
3C2×#10623362C211yesmaximal, characteristic, complemented
4#13080267C2116yesmaximal, direct product factor
5C2×#10622781C211yesmaximal, characteristic, complemented
6C2×#10622747C211yesmaximal, characteristic, complemented
7C2×#10622787C211yesmaximal, characteristic, complemented
8C2×#10622798C211yesmaximal, characteristic, complemented
9C2×#10622779C211yesmaximal, characteristic, complemented
10C2×#10622851C211yesmaximal, characteristic, complemented
11C2×#10622785C211yesmaximal, characteristic, complemented
12C2×#10622841C211yesmaximal, characteristic, complemented
13C2×#10622799C211yesmaximal, characteristic, complemented
14C2×Q16×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622741C211yesmaximal, characteristic, complemented
16C22×C11×#137C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C22×#4343C2211yescharacteristic
20C22×Q8×D11C2211yescharacteristic
21C2×C11×#137—28no—
22C2×C11×#137C2218yescomplemented
23C22×C11×Q16C2211yescharacteristic
24C22×C11×Q16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic
26C22×C11×SD16C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28#10623362—24no—
29#10623362C2218yescomplemented
30#10623348—24no—
31#10623348C2218yescomplemented
32C2×#67000—21no—
33C2×#67000C2211yescharacteristic
34C2×#66999—21no—
35C2×#66999C2211yescharacteristic
36C2×Q8×Dic11C2211yescharacteristic
37C2×Q8×Dic11C2211yescharacteristic
38C22×#4326C2211yescharacteristic
39C22×#4326C2211yescharacteristic
40C22×#4325C2211yescharacteristic
41C2×#66991—21no—
42C2×#66991C2211yescharacteristic
43C2×#66989—21no—
44C2×#66989C2211yescharacteristic
45C22×#4323C2211yescharacteristic
46C2×#66983—21no—
47C2×#66983C2211yescharacteristic
48C2×C4×C22⋊D11—21no—
49C2×C4×C22⋊D11—21no—
50C2×C4×C22⋊D11C2211yescharacteristic
51C2×#66977—21no—
52C2×#66977C2211yescharacteristic
53C2×#66971—28no—
54C2×#66971C2218yescomplemented
55C22×#4314C2211yescharacteristic
56C22×#4313C2211yescharacteristic
57#10622851C2218yescomplemented
58#10622841C2218yescomplemented
59C2×#66899C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66899C2211yescharacteristic
62C2×#66896C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622799C2218yescomplemented
65#10622798C2218yescomplemented
66Q16×Dic11C2218yescomplemented
67#10622787C2218yescomplemented
68#10622785C2218yescomplemented
69#10622781C2218yescomplemented
70#10622779C2218yescomplemented
71#10622747C2218yescomplemented
72#10622741C2218yescomplemented
73C2×#66885C2211yescharacteristic
74C2×(C2×D11)⋊C8C2211yescharacteristic
75C2×#66882C2211yescharacteristic
76C2×#66880C2211yescharacteristic
77C2×Dic11⋊C8C2211yescharacteristic
78C2×C8×Dic11C2211yescharacteristic
79C2×C11×#41—22no—
80C2×C11×#41—24no—
81C2×C11×#41—42no—
82C2×C11×#41C2314yes—
83C22×Q8×C11—21no—
84C22×Q8×C11—22no—
85C22×Q8×C11—24no—
86C22×Q8×C11—42no—
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2314yes—
89C22×Q8×C11C2311yescharacteristic
90C22×Q8×C11C2311yescharacteristic
91C22×D4×C11—21no—
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11—21no—
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C22×C22⋊D11D411yescharacteristic
99C2×#4343—22no—
100C2×#4343—24no—
101C2×#4343—42no—
102C2×#4343C2314yes—
103C2×Q8×D11—22no—
104C2×Q8×D11—24no—
105C2×Q8×D11—42no—
106C2×Q8×D11C2314yes—
107C22×D44—21no—
108C22×D44C2311yescharacteristic
109C22×C4×D11—21no—
110C22×C4×D11—21no—
111C22×C4×D11C2311yescharacteristic
112C22×Dic22—21no—
113C22×Dic22C2311yescharacteristic
114C11×#137—232no—
115C2×C11×Q16—24no—
116C2×C11×Q16D418yescomplemented
117C2×C11×Q16C2314yes—
118C2×C11×Q16C2314yes—
119C2×C11×SD16—24no—
120C2×C11×SD16—24no—
121C2×C11×SD16C2314yes—
122C2×C11×SD16C2314yes—
123C2×C11×M16—24no—
124C2×C11×M16C2314yes—
125C22×C8×C11C2311yescharacteristic
126C22×C8×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11D411yescharacteristic
132#67000—28no—
133#67000—22no—
134#67000C2314yes—
135#66999—22no—
136#66999—28no—
137#66999C2314yes—
138Q8×Dic11—22no—
139Q8×Dic11—22no—
140Q8×Dic11C2314yes—
141Q8×Dic11C2314yes—
142C2×#4326—24no—
143C2×#4326—42no—
144C2×#4326C2314yes—
145C2×#4326C2314yes—
146C2×#4325—24no—
147C2×#4325C2314yes—
148#66991—28no—
149#66991—22no—
150#66991C2314yes—
151#66989—28no—
152#66989—22no—
153#66989C2314yes—
154C2×#4323—42no—
155C2×#4323C2314yes—
156#66983—22no—
157#66983—28no—
158#66983C2314yes—
159C4×C22⋊D11—28no—
160C4×C22⋊D11—28no—
161C4×C22⋊D11D414yes—
162C4×C22⋊D11C2314yes—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×(C2×D11)⋊C4D411yescharacteristic
168C2×C4⋊Dic11—21no—
169C2×C4⋊Dic11—21no—
170C2×C4⋊Dic11C2311yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172#66977—22no—
173#66977—28no—
174#66977C2314yes—
175C2×Dic11⋊C4—21no—
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4D411yescharacteristic
178C2×C4×Dic11—21no—
179C2×C4×Dic11—21no—
180C2×C4×Dic11C2311yescharacteristic
181C22×C11⋊C8C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183#66971—232no—
184C2×#4314—24no—
185C2×#4314C2314yes—
186C2×#4313—24no—
187C2×#4313C2314yes—
188#66899C2314yes—
189#66899C2314yes—
190#66899C2314yes—
191#66896C2314yes—
192C22⋊(C11⋊C8)C2314yes—
193#66885C2314yes—
194(C2×D11)⋊C8C2314yes—
195#66882C2314yes—
196#66880C2314yes—
197Dic11⋊C8C2314yes—
198C8×Dic11C2314yes—
199C2×#3277—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11C2×D411yescharacteristic
204C11×#41—28no—
205C11×#41—44no—
206C11×#41—48no—
207C2×Q8×C11—21no—
208C2×Q8×C11—21no—
209C2×Q8×C11—24no—
210C2×Q8×C11—21no—
211C2×Q8×C11—22no—
212C2×Q8×C11—22no—
213C2×Q8×C11—28no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11—44no—
217C2×Q8×C11—44no—
218C2×Q8×C11—48no—
219C2×Q8×C11C2×D414yes—
220C2×Q8×C11C2×D414yes—
221C2×Q8×C11C2412yes—
222C2×Q8×C11C2412yes—
223C2×Q8×C11C2412yes—
224C2×D4×C11—24no—
225C2×D4×C11—22no—
226C2×D4×C11—21no—
227C2×D4×C11—22no—
228C2×D4×C11—44no—
229C2×D4×C11C2412yes—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—21no—
235C22×C4×C11—24no—
236C22×C4×C11—24no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2411yescharacteristic
243C2×C22⋊D11—24no—
244C2×C22⋊D11—24no—
245C2×C22⋊D11—42no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—44no—
248C2×C22⋊D11C2×D414yes—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11C2×D411yescharacteristic
253C22×Dic11C2×D411yescharacteristic
254C22×Dic11C2×D411yescharacteristic
255#4343—28no—
256#4343—44no—
257#4343—48no—
258Q8×D11—28no—
259Q8×D11—44no—
260Q8×D11—48no—
261C2×D44—24no—
262C2×D44—21no—
263C2×D44—22no—
264C2×D44—22no—
265C2×D44—44no—
266C2×D44C2412yes—
267C2×C4×D11—24no—
268C2×C4×D11—24no—
269C2×C4×D11—22no—
270C2×C4×D11—22no—
271C2×C4×D11—44no—
272C2×C4×D11—44no—
273C2×C4×D11C2×D412yes—
274C2×C4×D11C2412yes—
275C2×Dic22—24no—
276C2×Dic22—22no—
277C2×Dic22—21no—
278C2×Dic22—22no—
279C2×Dic22—44no—
280C2×Dic22C2412yes—
281C11×Q16—28no—
282C11×Q16C2×D4116yescomplemented
283C11×SD16—28no—
284C11×SD16—28no—
285C11×M16—28no—
286C2×C8×C11—22no—
287C2×C8×C11C2×D414yes—
288C2×C8×C11C2412yes—
289C2×C8×C11C2412yes—
290C22⋊Dic11—24no—
291C22⋊Dic11—24no—
292C22⋊Dic11—24no—
293C22⋊Dic11—24no—
294C22⋊Dic11C2×D414yes—
295#4326—28no—
296#4326—44no—
297#4325—28no—
298#4323—44no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4C2×D414yes—
304C4⋊Dic11—24no—
305C4⋊Dic11—24no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11C2412yes—
309C4⋊Dic11C2412yes—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4C2×D414yes—
313C4×Dic11—24no—
314C4×Dic11—24no—
315C4×Dic11C2×D412yes—
316C4×Dic11C2412yes—
317C2×C11⋊C8—22no—
318C2×C11⋊C8—22no—
319C2×C11⋊C8C2412yes—
320C2×C11⋊C8C2412yes—
321#4314—28no—
322#4313—28no—
323C22×#137—111no—
324C22×#137D1111yescharacteristic, complemented
325C2×#548—111no—
326C2×#548—111no—
327#3277—1116no—
328C2×#495—111no—
329C2×#468—111no—
330C2×#468—111no—
331C2×#464—111no—
332C2×#464—111no—
333C2×#449—111no—
334C2×#449—111no—
335C2×#451—111no—
336C2×#451—111no—
337C2×C4×Q16—111no—
338C2×#436—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11—42no—
346C23×C11C22×D412yes—
347C23×C11C22×D411yescharacteristic
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11C22×D412yes—
356Q8×C11—24no—
357Q8×C11—24no—
358Q8×C11—22no—
359Q8×C11—22no—
360Q8×C11—22no—
361Q8×C11—22no—
362Q8×C11—48no—
363Q8×C11—42no—
364Q8×C11C22×D414yes—
365Q8×C11C22×D414yes—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—48no—
369D4×C11—42no—
370C2×C4×C11—24no—
371C2×C4×C11—24no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—24no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—48no—
380C2×C4×C11—48no—
381C2×C4×C11—42no—
382C2×C4×C11C22×D412yes—
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C22×D412yes—
385C2×C4×C11H(5,𝔽2)12yes—
386C2×C4×C11C2511yescharacteristic
387C22⋊D11—44no—
388C22⋊D11—48no—
389C22⋊D11—48no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—42no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11C22×D412yes—
400C2×Dic11C22×D412yes—
401C2×Dic11C22×D412yes—
402D44—22no—
403D44—22no—
404D44—48no—
405D44—42no—
406C4×D11—24no—
407C4×D11—22no—
408C4×D11—22no—
409C4×D11—48no—
410C4×D11—48no—
411Dic22—22no—
412Dic22—22no—
413Dic22—48no—
414Dic22—42no—
415C8×C11—22no—
416C8×C11C22×D414yes—
417C11⋊C8—22no—
418C11⋊C8—22no—
419C22×#41—111no—
420C22×#41C2×D1111yescharacteristic
421C23×Q8—111no—
422C23×Q8C2×D1111yescharacteristic
423C2×#137—28no—
424C2×#137—118no—
425C2×#137—228no—
426C2×#137C2×D1118yescomplemented
427C22×Q16—111no—
428C22×Q16—111no—
429C22×Q16C2×D1111yescharacteristic
430C22×Q16C2×D1111yescharacteristic
431C22×SD16—111no—
432C22×SD16—111no—
433C22×SD16C2×D1111yescharacteristic
434C22×SD16C2×D1111yescharacteristic
435C22×D8—111no—
436C22×M16—111no—
437C22×M16C2×D1111yescharacteristic
438#548—118no—
439#548—118no—
440#548—224no—
441#548—224no—
442C2×#124—111no—
443C2×#124—111no—
444C2×#124—221no—
445C2×#124—221no—
446C2×C22⋊Q8—111no—
447C2×C22⋊Q8—111no—
448C2×C22⋊Q8—221no—
449C2×C22⋊Q8—221no—
450C2×#121—111no—
451C2×#121—111no—
452C2×#121—221no—
453C2×#121—221no—
454C2×C4×Q8—111no—
455C2×C4×Q8—111no—
456C2×C4×D4—111no—
457C2×C4×D4—221no—
458C2×C4×D4—221no—
459#495—118no—
460#468—118no—
461#468—118no—
462#464—118no—
463#464—118no—
464#451—118no—
465#451—118no—
466#449—118no—
467#449—118no—
468C4×Q16—118no—
469#436—118no—
470C2×#107—111no—
471C2×C4⋊C8—111no—
472C2×#103—111no—
473C2×#103—111no—
474C2×#103—111no—
475C2×#103—111no—
476C2×#102—111no—
477C2×#102—111no—
478C2×C22⋊C8—111no—
479C2×C22⋊C8—111no—
480C2×C4×C8—111no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—44no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—84no—
489C22×C11D4212yes—
490C22×C11#57512yes—
491C22×C11#57812yes—
492C22×C11C23×D411yescharacteristic
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—44no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—24no—
503C4×C11—24no—
504C4×C11—42no—
505C4×C11D4212yes—
506C4×C11C23×D411yescharacteristic
507C4×C11C2×H(5,𝔽2)11yescharacteristic
508Dic11—22no—
509Dic11—22no—
510Dic11—22no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514C2×#41—22no—
515C2×#41—24no—
516C2×#41—42no—
517C2×#41—114no—
518C2×#41—222no—
519C2×#41—224no—
520C2×#41—442no—
521C2×#41C22×D1114yes—
522C22×Q8—21no—
523C22×Q8—22no—
524C22×Q8—24no—
525C22×Q8—42no—
526C22×Q8—114no—
527C22×Q8—111no—
528C22×Q8—221no—
529C22×Q8—222no—
530C22×Q8—224no—
531C22×Q8—442no—
532C22×Q8C22×D1111yescharacteristic
533C22×Q8C22×D1114yes—
534C22×Q8C22×D1111yescharacteristic
535C22×Q8C22×D1111yescharacteristic
536C22×D4—21no—
537C22×D4—111no—
538C22×D4—111no—
539C22×D4—221no—
540C22×D4—221no—
541C22×D4—221no—
542C22×D4C22×D1111yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—111no—
546C23×C4—221no—
547C23×C4—221no—
548C23×C4C22×D1111yescharacteristic
549#137—232no—
550#137—2232no—
551C2×Q16—24no—
552C2×Q16—114no—
553C2×Q16—114no—
554C2×Q16—224no—
555C2×Q16—442no—
556C2×Q16C22⋊D1118yescomplemented
557C2×Q16C22×D1114yes—
558C2×Q16C22×D1114yes—
559C2×SD16—24no—
560C2×SD16—24no—
561C2×SD16—114no—
562C2×SD16—114no—
563C2×SD16—224no—
564C2×SD16—224no—
565C2×SD16C22×D1114yes—
566C2×SD16C22×D1114yes—
567C2×D8—114no—
568C2×D8—442no—
569C2×M16—24no—
570C2×M16—114no—
571C2×M16—224no—
572C2×M16C22×D1114yes—
573C22×C8—111no—
574C22×C8—111no—
575C22×C8C22×D1111yescharacteristic
576C22×C8C22×D1111yescharacteristic
577#124—114no—
578#124—114no—
579#124—222no—
580#124—222no—
581#124—228no—
582#124—228no—
583C22⋊Q8—114no—
584C22⋊Q8—114no—
585C22⋊Q8—228no—
586C22⋊Q8—228no—
587C22⋊Q8—222no—
588C22⋊Q8—222no—
589#121—114no—
590#121—114no—
591#121—228no—
592#121—222no—
593#121—228no—
594#121—222no—
595C4×Q8—114no—
596C4×Q8—114no—
597C4×Q8—222no—
598C4×Q8—222no—
599C4×D4—114no—
600C4×D4—114no—
601C4×D4—228no—
602C4×D4—228no—
603C2×C4⋊C4—111no—
604C2×C4⋊C4—111no—
605C2×C4⋊C4—111no—
606C2×C4⋊C4—221no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4—221no—
609C2×C4⋊C4—221no—
610C2×C22⋊C4—111no—
611C2×C22⋊C4—111no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C22⋊C4—221no—
618C2×C22⋊C4—221no—
619C2×C22⋊C4—221no—
620C2×C42—111no—
621C2×C42—221no—
622C2×C42—221no—
623#107—114no—
624C4⋊C8—114no—
625#103—114no—
626#103—114no—
627#103—114no—
628#103—114no—
629#102—114no—
630#102—114no—
631C22⋊C8—114no—
632C22⋊C8—114no—
633C4×C8—114no—
634C2×C11—42no—
635C2×C11—82no—
636C2×C11#327714yescomplemented
637C2×C11C2×D4211yescharacteristic
638C2×C11C2×#57511yescharacteristic
639C2×C11C2×#57811yescharacteristic
640D11—42no—
641D11—82no—
642C24—21no—
643C24—111no—
644C24—221no—
645C24D4×D1111yescharacteristic
646#41—28no—
647#41—44no—
648#41—48no—
649#41—228no—
650#41—444no—
651#41—448no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—24no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—28no—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—48no—
664C2×Q8—112no—
665C2×Q8—224no—
666C2×Q8—221no—
667C2×Q8—228no—
668C2×Q8—222no—
669C2×Q8—222no—
670C2×Q8—444no—
671C2×Q8—444no—
672C2×Q8—448no—
673C2×Q8C2×C22⋊D1114yes—
674C2×Q8C2×C22⋊D1114yes—
675C2×Q8C23×D1112yes—
676C2×Q8C23×D1112yes—
677C2×Q8C23×D1112yes—
678C2×D4—24no—
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—22no—
682C2×D4—44no—
683C2×D4—114no—
684C2×D4—112no—
685C2×D4—224no—
686C2×D4—224no—
687C2×D4—224no—
688C2×D4—221no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—444no—
692C2×D4—442no—
693C2×D4—444no—
694C2×D4—444no—
695C2×D4C23×D1112yes—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—24no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—111no—
706C22×C4—111no—
707C22×C4—111no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—224no—
711C22×C4—224no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—444no—
718C22×C4—444no—
719C22×C4D4×D1112yes—
720C22×C4D4×D1111yescharacteristic
721C22×C4C23×D1112yes—
722C22×C4C23×D1111yescharacteristic
723Q16—28no—
724Q16—228no—
725Q16—444no—
726Q16C2×C22⋊D11116yescomplemented
727SD16—28no—
728SD16—28no—
729SD16—228no—
730SD16—228no—
731D8—444no—
732M16—28no—
733M16—228no—
734C2×C8—22no—
735C2×C8—112no—
736C2×C8—112no—
737C2×C8—222no—
738C2×C8—222no—
739C2×C8C2×C22⋊D1114yes—
740C2×C8C23×D1112yes—
741C2×C8C23×D1112yes—
742C4⋊C4—114no—
743C4⋊C4—112no—
744C4⋊C4—112no—
745C4⋊C4—224no—
746C4⋊C4—224no—
747C4⋊C4—224no—
748C4⋊C4—221no—
749C4⋊C4—221no—
750C4⋊C4—224no—
751C22⋊C4—114no—
752C22⋊C4—114no—
753C22⋊C4—224no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C42—112no—
762C42—112no—
763C42—224no—
764C42—224no—
765C11C2×#327711yescharacteristic, complemented, Sylow
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—112no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—442no—
779C23—442no—
780C23—442no—
781C23C2×D4×D1112yes—
782C23C2×D4×D1111yescharacteristic
783Q8—24no—
784Q8—24no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—22no—
789Q8—48no—
790Q8—42no—
791Q8—222no—
792Q8—222no—
793Q8—448no—
794Q8—442no—
795Q8C22×C22⋊D1114yes—
796Q8C22×C22⋊D1114yes—
797D4—22no—
798D4—22no—
799D4—48no—
800D4—42no—
801D4—222no—
802D4—222no—
803D4—448no—
804D4—444no—
805D4—448no—
806D4—448no—
807D4—442no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—48no—
818C2×C4—48no—
819C2×C4—42no—
820C2×C4—112no—
821C2×C4—112no—
822C2×C4—112no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—224no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—448no—
833C2×C4—448no—
834C2×C4—442no—
835C2×C4—442no—
836C2×C4—442no—
837C2×C4C2×D4×D1112yes—
838C2×C4C2×D4×D1111yescharacteristic
839C2×C4#6703712yes—
840C2×C4C22×C22⋊D1112yes—
841C2×C4C24×D1111yescharacteristic
842C8—22no—
843C8—222no—
844C8—222no—
845C8C22×C22⋊D1114yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—84no—
854C22—222no—
855C22—222no—
856C22—222no—
857C22—444no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—884no—
862C22#1062330812yes—
863C22#1062331012yes—
864C22D4×C22⋊D1112yes—
865C22C22×D4×D1111yescharacteristic
866C4—22no—
867C4—24no—
868C4—24no—
869C4—42no—
870C4—222no—
871C4—222no—
872C4—222no—
873C4—442no—
874C4—442no—
875C4—442no—
876C4D4×C22⋊D1112yes—
877C4C2×#6703711yescharacteristic
878C4C23×C22⋊D1111yescharacteristic
879C2—42no—
880C2—82no—
881C2—442no—
882C2—882no—
883C2#1308026714yesdirect product factor
884C2C2×D4×C22⋊D1111yescharacteristic
885C2C2×#1062330811yescharacteristic
886C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
hypercenterC22×#137D11
hypocenterC11C2×#3277
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
2. C2×#10623348C2semidirect
3. C2×#10623362C2semidirect
4. #13080267C2direct (N × H)
5. C2×#10622781C2semidirect
6. C2×#10622747C2semidirect
7. C2×#10622787C2semidirect
8. C2×#10622798C2semidirect
9. C2×#10622779C2semidirect
10. C2×#10622851C2semidirect
11. C2×#10622785C2semidirect
12. C2×#10622841C2semidirect
13. C2×#10622799C2semidirect
14. C2×Q16×Dic11C2semidirect
15. C2×#10622741C2semidirect
16. C22×C11×#137C2semidirect
22. C2×C11×#137C22semidirect
29. #10623362C22semidirect
31. #10623348C22semidirect
54. C2×#66971C22semidirect
57. #10622851C22semidirect
58. #10622841C22semidirect
64. #10622799C22semidirect
65. #10622798C22semidirect
66. Q16×Dic11C22semidirect
67. #10622787C22semidirect
68. #10622785C22semidirect
69. #10622781C22semidirect
70. #10622779C22semidirect
71. #10622747C22semidirect
72. #10622741C22semidirect
116. C2×C11×Q16D4semidirect
282. C11×Q16C2×D4semidirect
324. C22×#137D11semidirect
426. C2×#137C2×D11semidirect
556. C2×Q16C22⋊D11semidirect
636. C2×C11#3277semidirect
726. Q16C2×C22⋊D11semidirect
765. C11C2×#3277semidirect
883. C2#13080267direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C2×#106233482
C2×#106233622
#130802672
C2×#106227812
C2×#106227472
C2×#106227872
C2×#106227982
C2×#106227792
C2×#106228512
C2×#106227852
C2×#106228412
C2×#106227992
C2×Q16×Dic112
C2×#106227412
C22×C11×#1372
C2×#327711