Finite Group Databasebeta

← C2×#13080124 #15628752

Subgroups — C2×#13080124 #15628752

Order 2816.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C22×SD16×D11C211yesmaximal, characteristic, complemented
3C2×#10623163C211yesmaximal, characteristic, complemented
4C2×#10623360C211yesmaximal, characteristic
5#13080124C2116yesmaximal, direct product factor
6C2×#10622803C211yesmaximal, characteristic, complemented
7C2×#10622662C211yesmaximal, characteristic, complemented
8C2×#10622426C211yesmaximal, characteristic, complemented
9C2×#10622411C211yesmaximal, characteristic, complemented
10C2×#10622775C211yesmaximal, characteristic, complemented
11C2×#10622799C211yesmaximal, characteristic, complemented
12C2×#10622351C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic, complemented
14C2×#10622370C211yesmaximal, characteristic, complemented
15C2×#10622341C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic, complemented
21C22×C11×Q16C2211yescharacteristic, complemented
22C22×C11×SD16C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic, complemented
24#10623360—24no—
25#10623360C2218yes—
26C2×#67004—28no—
27C2×#67004C2218yescomplemented
28C2×#67000C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×#66997C2211yescharacteristic, complemented
31C22×#4326C2211yescharacteristic, complemented
32C22×#4326C2211yescharacteristic, complemented
33C22×#4325C2211yescharacteristic
34C2×#66992—21no—
35C2×#66990—21no—
36C2×D4×Dic11C2211yescharacteristic
37C22×#4324C2211yescharacteristic
38C22×#4324C2211yescharacteristic
39C2×#66983C2211yescharacteristic
40C2×#66982—21no—
41C2×C4×C22⋊D11C2211yescharacteristic
42C22×(C2×D11)⋊C4—21no—
43C22×#4318C2211yescharacteristic, complemented
44C2×SD16×D11—28no—
45C2×SD16×D11C2218yescomplemented
46C22×#4314C2211yescharacteristic
47C22×#4314C2211yescharacteristic
48C22×C8×D11C2211yescharacteristic
49#10623163—24no—
50#10623163C2218yescomplemented
51C2×#66950C2211yescharacteristic
52C2×#66949—21no—
53C2×#66941—21no—
54C2×#66940C2211yescharacteristic, complemented
55C2×(C22⋊D11)⋊C4—21no—
56C2×#66931—21no—
57C11×#452C2218yescomplemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic, complemented
61C2×#66899C2211yescharacteristic, complemented
62#10622803C2218yescomplemented
63#10622799C2218yescomplemented
64#10622775C2218yescomplemented
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66880C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68C2×#66879C2211yescharacteristic, complemented
69C2×Dic11⋊C8C2211yescharacteristic, complemented
70#10622662C2218yescomplemented
71C2×#66873C2211yescharacteristic
72C2×#66871C2211yescharacteristic, complemented
73#10622426C2218yescomplemented
74#10622411C2218yescomplemented
75#10622389C2218yescomplemented
76#10622370C2218yescomplemented
77#10622351C2218yescomplemented
78#10622341C2218yescomplemented
79C24×D11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C22×Q8×C11C2311yescharacteristic
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11—21no—
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11—21no—
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11D411yescharacteristic
93C23×Dic11—21no—
94C23×Dic11—21no—
95C2×Q8×D11—22no—
96C2×Q8×D11—24no—
97C2×Q8×D11—42no—
98C2×Q8×D11C2314yes—
99C2×D4×D11—24no—
100C2×D4×D11—22no—
101C2×D4×D11—42no—
102C2×D4×D11C2314yes—
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—24no—
107C22×Dic22—21no—
108C22×Dic22—22no—
109C22×Dic22—21no—
110C22×Dic22—42no—
111C22×Dic22C2311yescharacteristic
112C22×Dic22C2311yescharacteristic
113C22×Dic22C2314yescomplemented
114C2×C11×Q16—42no—
115C2×C11×Q16C2314yescomplemented
116C2×C11×SD16—24no—
117C2×C11×SD16C2314yes—
118C22×C8×C11C2311yescharacteristic
119C22×C8×C11C2311yescharacteristic
120C11×C22⋊Q8—22no—
121C11×C22⋊Q8C2314yescomplemented
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11D411yescharacteristic
127#67004—232no—
128#67000—22no—
129#67000C2314yes—
130#66999—22no—
131#66999C2314yes—
132#66997—22no—
133#66997C2314yescomplemented
134C2×#4326—24no—
135C2×#4326—24no—
136C2×#4326C2314yescomplemented
137C2×#4326C2314yescomplemented
138C2×#4325—24no—
139C2×#4325C2314yes—
140#66992—28no—
141#66990—28no—
142D4×Dic11—22no—
143D4×Dic11C2314yes—
144C2×#4324—24no—
145C2×#4324D418yescomplemented
146C2×#4324C2314yes—
147C2×#4324C2314yes—
148#66983—22no—
149#66983C2314yes—
150#66982—28no—
151C4×C22⋊D11D414yes—
152C4×C22⋊D11C2314yes—
153C2×(C2×D11)⋊C4—21no—
154C2×(C2×D11)⋊C4—21no—
155C2×(C2×D11)⋊C4—21no—
156C2×(C2×D11)⋊C4—21no—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4—28no—
159C2×(C2×D11)⋊C4D411yescharacteristic
160C2×C4⋊Dic11—21no—
161C2×C4⋊Dic11C2311yescharacteristic
162C2×Dic11⋊C4—21no—
163C2×Dic11⋊C4—21no—
164C2×Dic11⋊C4—21no—
165C2×Dic11⋊C4—21no—
166C2×Dic11⋊C4D411yescharacteristic
167C2×C4×Dic11—21no—
168C2×C4×Dic11C2311yescharacteristic
169C2×#4318—24no—
170C2×#4318C2314yescomplemented
171C22×C11⋊C8C2311yescharacteristic
172C22×C11⋊C8C2311yescharacteristic
173SD16×D11—232no—
174C2×#4314—24no—
175C2×#4314—42no—
176C2×#4314C2314yes—
177C2×#4314C2314yes—
178C2×C8×D11—24no—
179C2×C8×D11C2314yes—
180#66950—22no—
181#66950C2314yes—
182#66949—28no—
183#66941—28no—
184#66940—22no—
185#66940C2314yescomplemented
186(C22⋊D11)⋊C4—28no—
187#66931—28no—
188C11×#103C2314yescomplemented
189C11×#102C2314yes—
190C11×C22⋊C8C2314yescomplemented
191#66899C2314yescomplemented
192(C2×D11)⋊C8C2314yes—
193#66880C2314yescomplemented
194#66880C2314yescomplemented
195#66879C2314yescomplemented
196Dic11⋊C8C2314yescomplemented
197#66873C2314yes—
198#66871C2314yescomplemented
199C2×#3266—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—24no—
204C23×D11—44no—
205C23×D11—44no—
206C23×D11—82no—
207C23×D11C2×D411yescharacteristic
208C11×#41—28no—
209C11×#41—44no—
210C11×#41—48no—
211C2×Q8×C11—21no—
212C2×Q8×C11—21no—
213C2×Q8×C11—22no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11—22no—
217C2×Q8×C11C2412yes—
218C2×Q8×C11C2412yes—
219C2×D4×C11—24no—
220C2×D4×C11—21no—
221C2×D4×C11—22no—
222C2×D4×C11—44no—
223C2×D4×C11C2×D414yes—
224C2×D4×C11C2412yes—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—24no—
231C22×C4×C11—44no—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2411yescharacteristic
236C2×C22⋊D11—24no—
237C2×C22⋊D11—24no—
238C2×C22⋊D11—24no—
239C2×C22⋊D11—44no—
240C2×C22⋊D11—82no—
241C2×C22⋊D11C2×D414yes—
242C22×Dic11—24no—
243C22×Dic11—21no—
244C22×Dic11—24no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—44no—
248C22×Dic11—82no—
249C22×Dic11C2×D411yescharacteristic
250C22×Dic11C2×D411yescharacteristic
251C22×Dic11C2×D411yescharacteristic
252Q8×D11—28no—
253Q8×D11—44no—
254Q8×D11—48no—
255D4×D11—28no—
256D4×D11—44no—
257D4×D11—48no—
258C2×D44—21no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44C2412yes—
262C2×C4×D11—24no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—44no—
266C2×C4×D11C2×D412yes—
267C2×C4×D11C2412yes—
268C2×Dic22—28no—
269C2×Dic22—24no—
270C2×Dic22—21no—
271C2×Dic22—22no—
272C2×Dic22—24no—
273C2×Dic22—21no—
274C2×Dic22—22no—
275C2×Dic22—22no—
276C2×Dic22—44no—
277C2×Dic22—48no—
278C2×Dic22—44no—
279C2×Dic22—44no—
280C2×Dic22C2×D414yes—
281C2×Dic22C2412yes—
282C2×Dic22C2412yes—
283C11×Q16—44no—
284C11×SD16—28no—
285C2×C8×C11—22no—
286C2×C8×C11—22no—
287C2×C8×C11C2412yes—
288C2×C8×C11C2412yes—
289C11×C4⋊C4—21no—
290C11×C4⋊C4—24no—
291C11×C4⋊C4C2412yes—
292C11×C22⋊C4—24no—
293C22⋊Dic11—24no—
294C22⋊Dic11C2×D414yes—
295#4326—28no—
296#4326—28no—
297#4325—28no—
298#4324—28no—
299#4324C2×D4116yescomplemented
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4C2×D414yes—
306C4⋊Dic11—24no—
307C4⋊Dic11—21no—
308C4⋊Dic11C2412yes—
309Dic11⋊C4—24no—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4—24no—
313Dic11⋊C4C2×D414yes—
314C4×Dic11—24no—
315C4×Dic11C2×D412yes—
316C4×Dic11C2412yes—
317#4318—28no—
318C2×C11⋊C8—22no—
319C2×C11⋊C8C2×D414yes—
320C2×C11⋊C8C2412yes—
321C2×C11⋊C8C2412yes—
322#4314—28no—
323#4314—44no—
324C8×D11—28no—
325C22×#137—111no—
326C23×SD16—111no—
327C2×D4×Q8—111no—
328C2×#546—111no—
329#3266—1116no—
330C2×#497—111no—
331C2×#468—111no—
332C2×#467—111no—
333C2×#464—111no—
334C2×#461—111no—
335C2×#452D1111yescharacteristic, complemented
336C2×#451—111no—
337C2×#448—111no—
338C2×#450—111no—
339C2×#440—111no—
340C2×#435—111no—
341C23×C11—22no—
342C23×C11—24no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11C22×D412yes—
349C23×C11C22×D411yescharacteristic
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—48no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—48no—
358C22×D11—84no—
359C22×D11—816no—
360C22×D11#13714yescomplemented
361C22×D11C22×D412yes—
362Q8×C11—22no—
363Q8×C11—22no—
364Q8×C11—22no—
365Q8×C11—22no—
366Q8×C11—42no—
367Q8×C11—42no—
368D4×C11—24no—
369D4×C11—22no—
370D4×C11—48no—
371D4×C11C22×D414yes—
372C2×C4×C11—22no—
373C2×C4×C11—24no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—48no—
380C2×C4×C11—42no—
381C2×C4×C11—42no—
382C2×C4×C11—42no—
383C2×C4×C11C22×D412yes—
384C2×C4×C11C22×D411yescharacteristic
385C2×C4×C11C22×D412yes—
386C2×C4×C11H(5,𝔽2)12yes—
387C2×C4×C11C2511yescharacteristic
388C22⋊D11—28no—
389C22⋊D11—48no—
390C22⋊D11—84no—
391C2×Dic11—24no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—48no—
399C2×Dic11—42no—
400C2×Dic11—42no—
401C2×Dic11—84no—
402C2×Dic11C22×D412yes—
403C2×Dic11C22×D412yes—
404C2×Dic11C22×D412yes—
405D44—22no—
406D44—22no—
407D44—42no—
408C4×D11—24no—
409C4×D11—22no—
410C4×D11—22no—
411C4×D11—48no—
412Dic22—24no—
413Dic22—22no—
414Dic22—22no—
415Dic22—22no—
416Dic22—48no—
417Dic22—48no—
418Dic22—42no—
419Dic22C22×D414yes—
420C8×C11—22no—
421C8×C11—22no—
422C11⋊C8—22no—
423C11⋊C8C22×D414yes—
424C22×#41C2×D1111yescharacteristic
425C23×Q8—111no—
426C23×Q8—111no—
427C23×D4—111no—
428C2×#137—118no—
429C2×#137—228no—
430C22×Q16—111no—
431C22×Q16—111no—
432C22×Q16C2×D1111yescharacteristic, complemented
433C22×SD16—111no—
434C22×SD16—111no—
435C22×SD16—111no—
436C22×SD16—118no—
437C22×SD16—111no—
438C22×SD16—111no—
439C22×SD16—228no—
440C22×SD16C2×D1111yescharacteristic
441C22×M16—111no—
442C23×C8—111no—
443D4×Q8—118no—
444D4×Q8—224no—
445#546—118no—
446#546—224no—
447C2×C4⋊Q8—111no—
448C2×C4⋊Q8—221no—
449C2×#124—111no—
450C2×#123—221no—
451C2×C22⋊Q8—111no—
452C2×C22⋊Q8—111no—
453C2×C22⋊Q8—221no—
454C2×C22⋊Q8—221no—
455C2×C22⋊Q8C2×D1111yescharacteristic, complemented
456C2×#121—111no—
457C2×#121—221no—
458C2×#120—221no—
459C2×C4×Q8—111no—
460C2×C4×D4—111no—
461C2×C4×D4—111no—
462C2×C4×D4—221no—
463C22×C22⋊C4—221no—
464#497—118no—
465#468—118no—
466#467—118no—
467#464—118no—
468#461—118no—
469#452C2×D1118yescomplemented
470#451—118no—
471#450—118no—
472#448—118no—
473#440—118no—
474#435—118no—
475C2×#107—111no—
476C2×C4⋊C8—111no—
477C2×#103—111no—
478C2×#103—111no—
479C2×#103—111no—
480C2×#103C2×D1111yescharacteristic, complemented
481C2×#102—111no—
482C2×#102C2×D1111yescharacteristic
483C2×C22⋊C8—111no—
484C2×C22⋊C8C2×D1111yescharacteristic, complemented
485C2×#97—111no—
486C22×C11—22no—
487C22×C11—24no—
488C22×C11—22no—
489C22×C11—22no—
490C22×C11—48no—
491C22×C11—44no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11D4212yes—
495C22×C11C2×#13712yes—
496C22×C11#57712yes—
497C22×C11C23×D411yescharacteristic
498C2×D11—22no—
499C2×D11—28no—
500C2×D11—22no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—816no—
505C2×D11—84no—
506C2×D11C2×#13714yescomplemented
507C4×C11—22no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11D4212yes—
512C4×C11C23×D411yescharacteristic
513C4×C11C2×H(5,𝔽2)11yescharacteristic
514Dic11—24no—
515Dic11—22no—
516Dic11—22no—
517Dic11—22no—
518Dic11—42no—
519Dic11—42no—
520C25—221no—
521C2×#41—22no—
522C2×#41—24no—
523C2×#41—42no—
524C2×#41C22×D1114yes—
525C22×Q8—114no—
526C22×Q8—111no—
527C22×Q8—111no—
528C22×Q8—114no—
529C22×Q8—221no—
530C22×Q8—224no—
531C22×Q8—222no—
532C22×Q8—221no—
533C22×Q8—222no—
534C22×Q8—224no—
535C22×Q8—442no—
536C22×Q8—442no—
537C22×Q8C22×D1111yescharacteristic
538C22×Q8C22×D1111yescharacteristic
539C22×D4—21no—
540C22×D4—111no—
541C22×D4—114no—
542C22×D4—111no—
543C22×D4—222no—
544C22×D4—221no—
545C22×D4—224no—
546C22×D4—221no—
547C22×D4—442no—
548C22×D4C22×D1111yescharacteristic
549C23×C4—21no—
550C23×C4—111no—
551C23×C4—221no—
552C23×C4—221no—
553C23×C4—221no—
554C23×C4C22×D1111yescharacteristic
555#137—2232no—
556C2×Q16—42no—
557C2×Q16—114no—
558C2×Q16—114no—
559C2×Q16—224no—
560C2×Q16—224no—
561C2×Q16C22×D1114yescomplemented
562C2×SD16—24no—
563C2×SD16—118no—
564C2×SD16—114no—
565C2×SD16—114no—
566C2×SD16—114no—
567C2×SD16—114no—
568C2×SD16—114no—
569C2×SD16—224no—
570C2×SD16—224no—
571C2×SD16—2232no—
572C2×SD16—224no—
573C2×SD16—442no—
574C2×SD16C22×D1114yes—
575C2×M16—114no—
576C2×M16—224no—
577C22×C8—111no—
578C22×C8—111no—
579C22×C8—114no—
580C22×C8—224no—
581C22×C8C22×D1111yescharacteristic
582C22×C8C22×D1111yescharacteristic
583C4⋊Q8—114no—
584C4⋊Q8—222no—
585C4⋊Q8—228no—
586#124—114no—
587#124—222no—
588#123—228no—
589C22⋊Q8—22no—
590C22⋊Q8—114no—
591C22⋊Q8—114no—
592C22⋊Q8—228no—
593C22⋊Q8—228no—
594C22⋊Q8—222no—
595C22⋊Q8—222no—
596C22⋊Q8C22×D1114yescomplemented
597#121—114no—
598#121—228no—
599#121—222no—
600#120—228no—
601C4×Q8—114no—
602C4×Q8—222no—
603C4×D4—114no—
604C4×D4—114no—
605C4×D4—114no—
606C4×D4—222no—
607C4×D4—228no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—221no—
612C2×C4⋊C4—221no—
613C2×C4⋊C4—221no—
614C2×C4⋊C4—221no—
615C2×C4⋊C4—221no—
616C2×C4⋊C4C22×D1111yescharacteristic
617C2×C22⋊C4—21no—
618C2×C22⋊C4—111no—
619C2×C22⋊C4—111no—
620C2×C22⋊C4—228no—
621C2×C22⋊C4—221no—
622C2×C22⋊C4—221no—
623C2×C22⋊C4—221no—
624C2×C22⋊C4—221no—
625C2×C22⋊C4—221no—
626C2×C22⋊C4—221no—
627C2×C42—111no—
628C2×C42—221no—
629#107—114no—
630C4⋊C8—114no—
631#103—114no—
632#103—114no—
633#103—114no—
634#103C22×D1114yescomplemented
635#102—114no—
636#102C22×D1114yes—
637C22⋊C8—114no—
638C22⋊C8C22×D1114yescomplemented
639#97—114no—
640C2×C11—44no—
641C2×C11—42no—
642C2×C11#326614yescomplemented
643C2×C11C2×D4211yescharacteristic
644C2×C11C22×#13711yescharacteristic
645C2×C11C2×#57711yescharacteristic
646D11—24no—
647D11—82no—
648C24—21no—
649C24—111no—
650C24—224no—
651C24—221no—
652C24—444no—
653C24—444no—
654C24—882no—
655C24D4×D1111yescharacteristic
656#41—28no—
657#41—44no—
658#41—48no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—114no—
666C2×Q8—112no—
667C2×Q8—112no—
668C2×Q8—224no—
669C2×Q8—228no—
670C2×Q8—221no—
671C2×Q8—224no—
672C2×Q8—221no—
673C2×Q8—222no—
674C2×Q8—228no—
675C2×Q8—222no—
676C2×Q8—222no—
677C2×Q8—444no—
678C2×Q8—444no—
679C2×Q8—448no—
680C2×Q8—444no—
681C2×Q8—444no—
682C2×Q8—448no—
683C2×Q8C23×D1112yes—
684C2×Q8C23×D1112yes—
685C2×D4—24no—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—44no—
689C2×D4—114no—
690C2×D4—112no—
691C2×D4—224no—
692C2×D4—224no—
693C2×D4—228no—
694C2×D4—224no—
695C2×D4—222no—
696C2×D4—221no—
697C2×D4—222no—
698C2×D4—444no—
699C2×D4—448no—
700C2×D4—444no—
701C2×D4—882no—
702C2×D4D4×D1114yes—
703C2×D4C23×D1112yes—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—24no—
710C22×C4—44no—
711C22×C4—111no—
712C22×C4—111no—
713C22×C4—111no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—224no—
717C22×C4—224no—
718C22×C4—221no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—224no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—444no—
725C22×C4—444no—
726C22×C4—882no—
727C22×C4D4×D1112yes—
728C22×C4D4×D1111yescharacteristic
729C22×C4C23×D1112yes—
730C22×C4C23×D1111yescharacteristic
731Q16—44no—
732Q16—228no—
733Q16—228no—
734SD16—28no—
735SD16—1116no—
736SD16—228no—
737SD16—228no—
738SD16—228no—
739SD16—444no—
740M16—228no—
741C2×C8—22no—
742C2×C8—22no—
743C2×C8—114no—
744C2×C8—112no—
745C2×C8—112no—
746C2×C8—228no—
747C2×C8—222no—
748C2×C8C23×D1112yes—
749C2×C8C23×D1112yes—
750C4⋊C4—24no—
751C4⋊C4—21no—
752C4⋊C4—114no—
753C4⋊C4—112no—
754C4⋊C4—224no—
755C4⋊C4—224no—
756C4⋊C4—224no—
757C4⋊C4—224no—
758C4⋊C4—224no—
759C4⋊C4—221no—
760C4⋊C4C23×D1112yes—
761C22⋊C4—24no—
762C22⋊C4—114no—
763C22⋊C4—114no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C22⋊C4—224no—
768C22⋊C4—224no—
769C22⋊C4—224no—
770C42—112no—
771C42—112no—
772C42—224no—
773C11C2×#326611yescharacteristic, complemented, Sylow
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—22no—
779C23—42no—
780C23—42no—
781C23—114no—
782C23—112no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—448no—
787C23—448no—
788C23—442no—
789C23—442no—
790C23—442no—
791C23—884no—
792C23—8816no—
793C23C2×D4×D1112yes—
794C23C2×D4×D1111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—22no—
798Q8—22no—
799Q8—42no—
800Q8—42no—
801Q8—114no—
802Q8—224no—
803Q8—222no—
804Q8—222no—
805Q8—222no—
806Q8—448no—
807Q8—448no—
808Q8—442no—
809D4—24no—
810D4—22no—
811D4—48no—
812D4—228no—
813D4—222no—
814D4—222no—
815D4—448no—
816D4—442no—
817D4—884no—
818D4C2×D4×D1114yes—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—48no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—112no—
831C2×C4—112no—
832C2×C4—112no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—224no—
837C2×C4—222no—
838C2×C4—224no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—448no—
844C2×C4—448no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4—884no—
848C2×C4C2×D4×D1112yes—
849C2×C4C2×D4×D1111yescharacteristic
850C2×C4C2×D4×D1112yes—
851C2×C4#6703712yes—
852C2×C4C24×D1111yescharacteristic
853C8—22no—
854C8—22no—
855C8—114no—
856C8—222no—
857C22—22no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—44no—
862C22—48no—
863C22—42no—
864C22—42no—
865C22—114no—
866C22—228no—
867C22—222no—
868C22—222no—
869C22—442no—
870C22—442no—
871C22—442no—
872C22—8816no—
873C22—884no—
874C22#1062312112yes—
875C22#1062330112yes—
876C22D11×#13712yes—
877C22C22×D4×D1111yescharacteristic
878C4—22no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—222no—
883C4—224no—
884C4—222no—
885C4—222no—
886C4—442no—
887C4—442no—
888C4#1062312112yes—
889C4C22×D4×D1111yescharacteristic
890C4C2×#6703711yescharacteristic
891C2—42no—
892C2—44no—
893C2—224no—
894C2—882no—
895C2#1308012414yesdirect product factor
896C2C2×#1062312111yescharacteristic
897C2C2×D11×#13711yescharacteristic
898C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
prime radicalC2×#10623360C2
hypercenterC2×#452D11
hypocenterC11C2×#3266
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C22×SD16×D11C2semidirect
3. C2×#10623163C2semidirect
5. #13080124C2direct (N × H)
6. C2×#10622803C2semidirect
7. C2×#10622662C2semidirect
8. C2×#10622426C2semidirect
9. C2×#10622411C2semidirect
10. C2×#10622775C2semidirect
11. C2×#10622799C2semidirect
12. C2×#10622351C2semidirect
13. C2×#10622389C2semidirect
14. C2×#10622370C2semidirect
15. C2×#10622341C2semidirect
16. C2×C11×#452C2semidirect
20. C23×Dic22C22semidirect
21. C22×C11×Q16C22semidirect
23. C2×C11×C22⋊Q8C22semidirect
27. C2×#67004C22semidirect
30. C2×#66997C22semidirect
31. C22×#4326C22semidirect
32. C22×#4326C22semidirect
43. C22×#4318C22semidirect
45. C2×SD16×D11C22semidirect
50. #10623163C22semidirect
54. C2×#66940C22semidirect
57. C11×#452C22semidirect
58. C2×C11×#103C22semidirect
60. C2×C11×C22⋊C8C22semidirect
61. C2×#66899C22semidirect
62. #10622803C22semidirect
63. #10622799C22semidirect
64. #10622775C22semidirect
66. C2×#66880C22semidirect
67. C2×#66880C22semidirect
68. C2×#66879C22semidirect
69. C2×Dic11⋊C8C22semidirect
70. #10622662C22semidirect
72. C2×#66871C22semidirect
73. #10622426C22semidirect
74. #10622411C22semidirect
75. #10622389C22semidirect
76. #10622370C22semidirect
77. #10622351C22semidirect
78. #10622341C22semidirect
113. C22×Dic22C23semidirect
115. C2×C11×Q16C23semidirect
121. C11×C22⋊Q8C23semidirect
133. #66997C23semidirect
136. C2×#4326C23semidirect
137. C2×#4326C23semidirect
145. C2×#4324D4semidirect
170. C2×#4318C23semidirect
185. #66940C23semidirect
188. C11×#103C23semidirect
190. C11×C22⋊C8C23semidirect
191. #66899C23semidirect
193. #66880C23semidirect
194. #66880C23semidirect
195. #66879C23semidirect
196. Dic11⋊C8C23semidirect
198. #66871C23semidirect
299. #4324C2×D4semidirect
335. C2×#452D11semidirect
360. C22×D11#137semidirect
432. C22×Q16C2×D11semidirect
455. C2×C22⋊Q8C2×D11semidirect
469. #452C2×D11semidirect
480. C2×#103C2×D11semidirect
484. C2×C22⋊C8C2×D11semidirect
506. C2×D11C2×#137semidirect
561. C2×Q16C22×D11semidirect
596. C22⋊Q8C22×D11semidirect
634. #103C22×D11semidirect
638. C22⋊C8C22×D11semidirect
642. C2×C11#3266semidirect
773. C11C2×#3266semidirect
895. C2#13080124direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C22×SD16×D112
C2×#106231632
C2×#106233602
#130801242
C2×#106228032
C2×#106226622
C2×#106224262
C2×#106224112
C2×#106227752
C2×#106227992
C2×#106223512
C2×#106223892
C2×#106223702
C2×#106223412
C2×C11×#4522
C2×#326611