Finite Group Databasebeta

← C2×#13080182 #15628814

Subgroups — C2×#13080182 #15628814

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C23×#4326C211yesmaximal, characteristic, complemented
3C2×D4×Dic22C211yesmaximal, characteristic, complemented
4#13080182C2116yesmaximal, direct product factor
5C2×#10622673C211yesmaximal, characteristic, complemented
6C2×#10622665C211yesmaximal, characteristic, complemented
7C2×#10622654C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622644C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622841C211yesmaximal, characteristic, complemented
12C2×#10622663C211yesmaximal, characteristic, complemented
13C2×#10622653C211yesmaximal, characteristic, complemented
14C2×#10622643C211yesmaximal, characteristic, complemented
15C2×#10622624C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C11×#548—24no—
22C11×#548C2218yes—
23C2×C11×#124—21no—
24C2×C11×#124C2211yescharacteristic
25C2×C11×C22⋊Q8—21no—
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121—21no—
28C2×C11×#121C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×#67004—28no—
33C2×#67004C2218yescomplemented
34C22×#4326—28no—
35C22×#4326C2211yescharacteristic
36C22×#4326C2211yescharacteristic
37C22×#4326C2211yescharacteristic
38C22×#4326C2211yescharacteristic
39C22×#4326C2211yescharacteristic
40C22×#4326C2211yescharacteristic
41C22×#4326C2218yescomplemented
42C2×D4×Dic11—21no—
43C22×#4324C2211yescharacteristic
44C22×#4324C2211yescharacteristic
45C22×#4324C2211yescharacteristic
46C2×#66977C2211yescharacteristic
47C2×#66977C2211yescharacteristic
48C22×#4318C2211yescharacteristic
49C23×C11⋊C8C2211yescharacteristic
50D4×Dic22—24no—
51D4×Dic22C2218yescomplemented
52C2×#66941—21no—
53C2×#66931—21no—
54C2×#66931—21no—
55C2×#66922C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic
57#10622852C2218yescomplemented
58#10622841C2218yescomplemented
59C2×#66899C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622673C2218yescomplemented
65#10622667C2218yescomplemented
66#10622665C2218yescomplemented
67#10622663C2218yescomplemented
68#10622654C2218yescomplemented
69#10622653C2218yescomplemented
70#10622644C2218yescomplemented
71#10622643C2218yescomplemented
72#10622624C2218yescomplemented
73C2×#66874C2211yescharacteristic
74C2×#66874C2211yescharacteristic
75C2×#66874C2211yescharacteristic
76C2×#66872C2211yescharacteristic
77C2×C4⋊(C11⋊C8)C2211yescharacteristic
78C2×#66867C2211yescharacteristic
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×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11D411yescharacteristic
93C22×D4×C11C2311yescharacteristic
94C23×C4×C11—21no—
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×Dic11—21no—
99C23×Dic11—21no—
100C22×Dic22—24no—
101C22×Dic22—24no—
102C22×Dic22—21no—
103C22×Dic22—21no—
104C22×Dic22—22no—
105C22×Dic22—22no—
106C22×Dic22—42no—
107C22×Dic22—42no—
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C22×Dic22C2314yes—
111C22×Dic22C2314yes—
112C22×Dic22C2311yescharacteristic
113C11×#124—28no—
114C11×#124—22no—
115C11×#124C2314yes—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—28no—
118C11×C22⋊Q8C2314yes—
119C11×#121—28no—
120C11×#121—22no—
121C11×#121C2314yes—
122C4×Q8×C11—22no—
123C4×Q8×C11C2314yes—
124C4×D4×C11—28no—
125C4×D4×C11D414yes—
126C4×D4×C11C2314yes—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4D411yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4—21no—
134C2×C11×C22⋊C4—21no—
135C2×C11×C22⋊C4D411yescharacteristic
136C2×C11×C22⋊C4D411yescharacteristic
137C2×C42×C11—21no—
138C2×C42×C11C2311yescharacteristic
139C2×C22⋊Dic11—21no—
140C2×C22⋊Dic11—21no—
141#67004—232no—
142C2×#4326—24no—
143C2×#4326—24no—
144C2×#4326—24no—
145C2×#4326—232no—
146C2×#4326—24no—
147C2×#4326—42no—
148C2×#4326D418yescomplemented
149C2×#4326C2314yes—
150C2×#4326C2314yes—
151C2×#4326C2314yes—
152C2×#4326C2314yes—
153C2×#4326C2314yes—
154C2×#4326C2314yes—
155D4×Dic11—28no—
156C2×#4324—24no—
157C2×#4324—24no—
158C2×#4324—42no—
159C2×#4324C2314yes—
160C2×#4324C2314yes—
161C2×#4324C2314yes—
162C2×C4⋊Dic11—21no—
163C2×C4⋊Dic11—21no—
164C2×C4⋊Dic11C2311yescharacteristic
165#66977—22no—
166#66977—22no—
167#66977C2314yes—
168#66977C2314yes—
169C2×Dic11⋊C4—21no—
170C2×Dic11⋊C4—21no—
171C2×Dic11⋊C4—21no—
172C2×C4×Dic11—21no—
173C2×#4318—24no—
174C2×#4318C2314yes—
175C22×C11⋊C8—24no—
176C22×C11⋊C8C2311yescharacteristic
177C22×C11⋊C8C2311yescharacteristic
178C22×C11⋊C8C2311yescharacteristic
179C22×C11⋊C8C2314yes—
180C22×C11⋊C8C2311yescharacteristic
181#66941—28no—
182#66931—28no—
183#66931—28no—
184#66922—22no—
185#66922C2314yes—
186C4×Dic22—22no—
187C4×Dic22C2314yes—
188#66899C2314yes—
189#66899C2314yes—
190#66896C2314yes—
191C22⋊(C11⋊C8)C2314yes—
192C22⋊(C11⋊C8)C2314yes—
193#66874C2314yes—
194#66874C2314yes—
195#66874C2314yes—
196#66872C2314yes—
197C4⋊(C11⋊C8)C2314yes—
198#66867C2314yes—
199C2×#3270—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C24×C11C2×D411yescharacteristic
203C11×#41—28no—
204C11×#41—44no—
205C11×#41—48no—
206C2×Q8×C11—21no—
207C2×Q8×C11—24no—
208C2×Q8×C11—21no—
209C2×Q8×C11—22no—
210C2×Q8×C11—28no—
211C2×Q8×C11—22no—
212C2×Q8×C11—22no—
213C2×Q8×C11—44no—
214C2×Q8×C11—44no—
215C2×Q8×C11—48no—
216C2×Q8×C11C2×D414yes—
217C2×Q8×C11C2412yes—
218C2×Q8×C11C2412yes—
219C2×D4×C11—24no—
220C2×D4×C11—24no—
221C2×D4×C11—24no—
222C2×D4×C11—22no—
223C2×D4×C11—21no—
224C2×D4×C11—22no—
225C2×D4×C11—44no—
226C2×D4×C11—44no—
227C2×D4×C11C2×D414yes—
228C2×D4×C11C2412yes—
229C22×C4×C11—21no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—24no—
237C22×C4×C11—24no—
238C22×C4×C11—44no—
239C22×C4×C11—44no—
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2411yescharacteristic
249C22×Dic11—21no—
250C22×Dic11—24no—
251C22×Dic11—24no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—44no—
256C22×Dic11—44no—
257C2×Dic22—28no—
258C2×Dic22—28no—
259C2×Dic22—21no—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22—21no—
263C2×Dic22—21no—
264C2×Dic22—24no—
265C2×Dic22—24no—
266C2×Dic22—22no—
267C2×Dic22—22no—
268C2×Dic22—22no—
269C2×Dic22—44no—
270C2×Dic22—44no—
271C2×Dic22—48no—
272C2×Dic22—48no—
273C2×Dic22—44no—
274C2×Dic22—44no—
275C2×Dic22C2×D414yes—
276C2×Dic22C2412yes—
277C2×Dic22C2412yes—
278C2×Dic22C2412yes—
279C11×C4⋊C4—24no—
280C11×C4⋊C4—24no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4C2×D414yes—
283C11×C4⋊C4C2412yes—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4C2×D414yes—
289C11×C22⋊C4C2×D414yes—
290C42×C11—24no—
291C42×C11C2×D412yes—
292C42×C11C2412yes—
293C22⋊Dic11—24no—
294C22⋊Dic11—24no—
295#4326—28no—
296#4326—28no—
297#4326—28no—
298#4326—28no—
299#4326—44no—
300#4326C2×D4116yescomplemented
301#4324—28no—
302#4324—28no—
303#4324—44no—
304C4⋊Dic11—21no—
305C4⋊Dic11—24no—
306C4⋊Dic11—24no—
307C4⋊Dic11C2412yes—
308Dic11⋊C4—24no—
309Dic11⋊C4—24no—
310Dic11⋊C4—24no—
311C4×Dic11—24no—
312#4318—28no—
313C2×C11⋊C8—28no—
314C2×C11⋊C8—22no—
315C2×C11⋊C8—22no—
316C2×C11⋊C8—22no—
317C2×C11⋊C8C2×D414yes—
318C2×C11⋊C8C2412yes—
319C2×C11⋊C8C2412yes—
320C2×C11⋊C8C2412yes—
321C2×C11⋊C8C2412yes—
322C22×#137—111no—
323C23×Q16—111no—
324C2×D4×Q8—111no—
325C2×#548D1111yescharacteristic
326#3270—1116no—
327C2×#497—111no—
328C2×#470—111no—
329C2×#465—111no—
330C2×#464—111no—
331C2×#462—111no—
332C2×#452—111no—
333C2×#451—111no—
334C2×#451—111no—
335C2×#448—111no—
336C2×#441—111no—
337C2×#435—111no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—42no—
345C23×C11—42no—
346C23×C11—42no—
347C23×C11#13714yescomplemented
348C23×C11C22×D412yes—
349C23×C11C22×D412yes—
350C23×C11C22×D411yescharacteristic
351Q8×C11—24no—
352Q8×C11—22no—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—48no—
356Q8×C11—42no—
357Q8×C11C22×D414yes—
358D4×C11—28no—
359D4×C11—22no—
360D4×C11—22no—
361D4×C11—48no—
362D4×C11—48no—
363D4×C11—42no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—24no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—24no—
371C2×C4×C11—24no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—48no—
379C2×C4×C11—48no—
380C2×C4×C11—42no—
381C2×C4×C11—42no—
382C2×C4×C11C22×D412yes—
383C2×C4×C11C22×D412yes—
384C2×C4×C11C22×D412yes—
385C2×C4×C11C22×D412yes—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11H(5,𝔽2)12yes—
389C2×C4×C11C2511yescharacteristic
390C2×Dic11—24no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—48no—
396C2×Dic11—48no—
397C2×Dic11—42no—
398C2×Dic11—42no—
399C2×Dic11—42no—
400Dic22—24no—
401Dic22—22no—
402Dic22—22no—
403Dic22—22no—
404Dic22—22no—
405Dic22—22no—
406Dic22—48no—
407Dic22—48no—
408Dic22—42no—
409Dic22—42no—
410Dic22C22×D414yes—
411C11⋊C8—22no—
412C11⋊C8—22no—
413C11⋊C8—22no—
414C11⋊C8C22×D414yes—
415C22×#41C2×D1111yescharacteristic
416C23×Q8—111no—
417C23×Q8—111no—
418C23×Q8C2×D1111yescharacteristic
419C2×#137—118no—
420C2×#137—228no—
421C22×Q16—111no—
422C22×Q16—111no—
423C22×Q16—111no—
424C22×Q16—111no—
425C22×Q16—111no—
426C22×Q16—118no—
427C22×Q16—111no—
428C22×Q16—228no—
429C22×SD16—111no—
430C22×SD16—111no—
431C22×SD16—111no—
432C22×M16—111no—
433C23×C8—111no—
434D4×Q8—118no—
435D4×Q8—224no—
436#548—24no—
437#548C2×D1118yes—
438C2×C4⋊Q8—111no—
439C2×C4⋊Q8—221no—
440C2×#124—21no—
441C2×#124C2×D1111yescharacteristic
442C2×C22⋊Q8—21no—
443C2×C22⋊Q8—111no—
444C2×C22⋊Q8—111no—
445C2×C22⋊Q8—221no—
446C2×C22⋊Q8—221no—
447C2×C22⋊Q8C2×D1111yescharacteristic
448C2×#121—21no—
449C2×#121C2×D1111yescharacteristic
450C2×C4×Q8—111no—
451C2×C4×Q8C2×D1111yescharacteristic
452C2×C4×D4—21no—
453C2×C4×D4—221no—
454C2×C4×D4C2×D1111yescharacteristic
455#497—118no—
456#470—118no—
457#465—118no—
458#464—118no—
459#462—118no—
460#452—118no—
461#451—118no—
462#451—118no—
463#448—118no—
464#441—118no—
465#435—118no—
466C2×#106—111no—
467C2×C4⋊C8—111no—
468C2×#103—111no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103—111no—
472C2×#103—111no—
473C2×#102—111no—
474C2×C22⋊C8—111no—
475C2×C22⋊C8—111no—
476C2×#97—111no—
477C22×C11—22no—
478C22×C11—28no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—44no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—84no—
488C22×C11D4212yes—
489C22×C11C2×#13712yes—
490C22×C11C2×#13714yescomplemented
491C22×C11#57812yes—
492C22×C11C23×D411yescharacteristic
493C4×C11—22no—
494C4×C11—22no—
495C4×C11—24no—
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—42no—
499C4×C11—42no—
500C4×C11D4212yes—
501C4×C11C23×D411yescharacteristic
502C4×C11C2×H(5,𝔽2)11yescharacteristic
503Dic11—24no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507C2×#41—22no—
508C2×#41—24no—
509C2×#41—42no—
510C2×#41C22×D1114yes—
511C22×Q8—21no—
512C22×Q8—22no—
513C22×Q8—24no—
514C22×Q8—42no—
515C22×Q8—111no—
516C22×Q8—111no—
517C22×Q8—111no—
518C22×Q8—114no—
519C22×Q8—114no—
520C22×Q8—224no—
521C22×Q8—224no—
522C22×Q8—221no—
523C22×Q8—221no—
524C22×Q8—222no—
525C22×Q8—222no—
526C22×Q8—442no—
527C22×Q8—442no—
528C22×Q8C22×D1111yescharacteristic
529C22×Q8C22×D1114yes—
530C22×Q8C22×D1111yescharacteristic
531C22×D4—21no—
532C22×D4—21no—
533C22×D4C22⋊D1111yescharacteristic
534C22×D4C22×D1111yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—221no—
538C23×C4—221no—
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541#137—2232no—
542C2×Q16—118no—
543C2×Q16—114no—
544C2×Q16—114no—
545C2×Q16—114no—
546C2×Q16—114no—
547C2×Q16—114no—
548C2×Q16—114no—
549C2×Q16—224no—
550C2×Q16—2232no—
551C2×Q16—224no—
552C2×Q16—224no—
553C2×Q16—224no—
554C2×Q16—442no—
555C2×SD16—114no—
556C2×SD16—114no—
557C2×SD16—114no—
558C2×SD16—224no—
559C2×SD16—224no—
560C2×SD16—442no—
561C2×M16—114no—
562C2×M16—224no—
563C22×C8—111no—
564C22×C8—111no—
565C22×C8—114no—
566C22×C8—111no—
567C22×C8—111no—
568C22×C8—224no—
569C4⋊Q8—114no—
570C4⋊Q8—228no—
571C4⋊Q8—222no—
572#124—28no—
573#124—22no—
574#124C22×D1114yes—
575C22⋊Q8—22no—
576C22⋊Q8—28no—
577C22⋊Q8—114no—
578C22⋊Q8—114no—
579C22⋊Q8—222no—
580C22⋊Q8—222no—
581C22⋊Q8—228no—
582C22⋊Q8—228no—
583C22⋊Q8C22×D1114yes—
584#121—28no—
585#121—22no—
586#121C22×D1114yes—
587C4×Q8—22no—
588C4×Q8—114no—
589C4×Q8—222no—
590C4×Q8C22×D1114yes—
591C4×D4—28no—
592C4×D4—228no—
593C4×D4C22⋊D1114yes—
594C4×D4C22×D1114yes—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4C22⋊D1111yescharacteristic
604C2×C4⋊C4C22×D1111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4C22⋊D1111yescharacteristic
612C2×C22⋊C4C22⋊D1111yescharacteristic
613C2×C42—21no—
614C2×C42—221no—
615C2×C42C22×D1111yescharacteristic
616#106—114no—
617C4⋊C8—114no—
618#103—114no—
619#103—114no—
620#103—114no—
621#103—114no—
622#103—114no—
623#102—114no—
624C22⋊C8—114no—
625C22⋊C8—114no—
626#97—114no—
627C2×C11—24no—
628C2×C11—42no—
629C2×C11—82no—
630C2×C11#327014yescomplemented
631C2×C11C2×D4211yescharacteristic
632C2×C11C22×#13711yescharacteristic
633C2×C11C2×#57811yescharacteristic
634C24—21no—
635C24C2×C22⋊D1111yescharacteristic
636C24C2×C22⋊D1111yescharacteristic
637#41—28no—
638#41—44no—
639#41—48no—
640C2×Q8—22no—
641C2×Q8—21no—
642C2×Q8—24no—
643C2×Q8—21no—
644C2×Q8—28no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—48no—
650C2×Q8—114no—
651C2×Q8—112no—
652C2×Q8—112no—
653C2×Q8—112no—
654C2×Q8—228no—
655C2×Q8—228no—
656C2×Q8—222no—
657C2×Q8—221no—
658C2×Q8—224no—
659C2×Q8—224no—
660C2×Q8—221no—
661C2×Q8—221no—
662C2×Q8—222no—
663C2×Q8—222no—
664C2×Q8—222no—
665C2×Q8—222no—
666C2×Q8—444no—
667C2×Q8—444no—
668C2×Q8—444no—
669C2×Q8—444no—
670C2×Q8—448no—
671C2×Q8—448no—
672C2×Q8D4×D1114yes—
673C2×Q8C23×D1112yes—
674C2×Q8C23×D1112yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4C2×C22⋊D1114yes—
684C2×D4C23×D1112yes—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—24no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—221no—
697C22×C4—224no—
698C22×C4—224no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—444no—
703C22×C4—444no—
704C22×C4C2×C22⋊D1112yes—
705C22×C4C2×C22⋊D1112yes—
706C22×C4C2×C22⋊D1111yescharacteristic
707C22×C4C2×C22⋊D1111yescharacteristic
708C22×C4C2×C22⋊D1111yescharacteristic
709C22×C4C2×C22⋊D1111yescharacteristic
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1111yescharacteristic
713Q16—1116no—
714Q16—228no—
715Q16—228no—
716Q16—228no—
717Q16—228no—
718Q16—444no—
719SD16—228no—
720SD16—228no—
721SD16—444no—
722M16—228no—
723C2×C8—114no—
724C2×C8—112no—
725C2×C8—112no—
726C2×C8—112no—
727C2×C8—112no—
728C2×C8—228no—
729C2×C8—222no—
730C2×C8—222no—
731C2×C8—222no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—21no—
735C4⋊C4—112no—
736C4⋊C4—221no—
737C4⋊C4—224no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4—224no—
741C4⋊C4—224no—
742C4⋊C4C2×C22⋊D1114yes—
743C4⋊C4C23×D1112yes—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4C2×C22⋊D1114yes—
751C22⋊C4C2×C22⋊D1114yes—
752C42—24no—
753C42—224no—
754C42C2×C22⋊D1112yes—
755C42C23×D1112yes—
756C11C2×#327011yescharacteristic, complemented, Sylow
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23#6700414yescomplemented
767C23C22×C22⋊D1112yes—
768C23C22×C22⋊D1112yes—
769C23C22×C22⋊D1111yescharacteristic
770Q8—24no—
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—48no—
775Q8—42no—
776Q8—114no—
777Q8—224no—
778Q8—222no—
779Q8—222no—
780Q8—222no—
781Q8—222no—
782Q8—222no—
783Q8—448no—
784Q8—448no—
785Q8—442no—
786Q8—442no—
787Q8C2×D4×D1114yes—
788D4—28no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—42no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—48no—
809C2×C4—48no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—224no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—448no—
818C2×C4—448no—
819C2×C4—442no—
820C2×C4—442no—
821C2×C4—442no—
822C2×C4C2×D4×D1112yes—
823C2×C4#6703712yes—
824C2×C4C22×C22⋊D1112yes—
825C2×C4C22×C22⋊D1112yes—
826C2×C4C22×C22⋊D1112yes—
827C2×C4C22×C22⋊D1112yes—
828C2×C4C22×C22⋊D1111yescharacteristic
829C2×C4C24×D1111yescharacteristic
830C8—114no—
831C8—222no—
832C8—222no—
833C8—222no—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—44no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—84no—
845C22D4×C22⋊D1112yes—
846C22C2×#6700412yes—
847C22C2×#6700414yescomplemented
848C22#1062336912yes—
849C22C23×C22⋊D1111yescharacteristic
850C4—22no—
851C4—22no—
852C4—24no—
853C4—22no—
854C4—22no—
855C4—42no—
856C4—42no—
857C4—224no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4D4×C22⋊D1112yes—
862C4C22×D4×D1111yescharacteristic
863C4C2×#6703711yescharacteristic
864C2—24no—
865C2—42no—
866C2—82no—
867C2#1308018214yesdirect product factor
868C2C2×D4×C22⋊D1111yescharacteristic
869C2C22×#6700411yescharacteristic
870C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#548C2
socleC23×C11C22×D4
hypercenterC2×#548D11
hypocenterC11C2×#3270
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C23×#4326C2semidirect
3. C2×D4×Dic22C2semidirect
4. #13080182C2direct (N × H)
5. C2×#10622673C2semidirect
6. C2×#10622665C2semidirect
7. C2×#10622654C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622644C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622841C2semidirect
12. C2×#10622663C2semidirect
13. C2×#10622653C2semidirect
14. C2×#10622643C2semidirect
15. C2×#10622624C2semidirect
33. C2×#67004C22semidirect
41. C22×#4326C22semidirect
51. D4×Dic22C22semidirect
57. #10622852C22semidirect
58. #10622841C22semidirect
64. #10622673C22semidirect
65. #10622667C22semidirect
66. #10622665C22semidirect
67. #10622663C22semidirect
68. #10622654C22semidirect
69. #10622653C22semidirect
70. #10622644C22semidirect
71. #10622643C22semidirect
72. #10622624C22semidirect
148. C2×#4326D4semidirect
300. #4326C2×D4semidirect
347. C23×C11#137semidirect
490. C22×C11C2×#137semidirect
630. C2×C11#3270semidirect
756. C11C2×#3270semidirect
766. C23#67004semidirect
847. C22C2×#67004semidirect
867. C2#13080182direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C23×#43262
C2×D4×Dic222
#130801822
C2×#106226732
C2×#106226652
C2×#106226542
C2×#106226672
C2×#106226442
C2×#106228522
C2×#106228412
C2×#106226632
C2×#106226532
C2×#106226432
C2×#106226242
C2×C11×#5482
C2×#327011