Finite Group Databasebeta

← C2×#13080343 #15629023

Subgroups — C2×#13080343 #15629023

Order 2816.

2858 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66957C211yesmaximal, characteristic, complemented
2C22×#66969C211yesmaximal, characteristic, complemented
3C2×#10623130C211yesmaximal, characteristic, complemented
4C2×#10623162C211yesmaximal, characteristic, complemented
5#13080343C2116yesmaximal, direct product factor
6C2×#10622788C211yesmaximal, characteristic, complemented
7C2×#10622477C211yesmaximal, characteristic, complemented
8C2×#10622406C211yesmaximal, characteristic, complemented
9C2×#10622399C211yesmaximal, characteristic, complemented
10C2×#10622396C211yesmaximal, characteristic, complemented
11C2×#10622660C211yesmaximal, characteristic, complemented
12C2×#10622424C211yesmaximal, characteristic, complemented
13C2×#10622650C211yesmaximal, characteristic, complemented
14C2×#10622465C211yesmaximal, characteristic, complemented
15C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4325C2211yescharacteristic
28C2×#66993—21no—
29C2×#66993C2211yescharacteristic
30C2×#66992—21no—
31C22×#4324C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×#66969—28no—
35C2×#66969C2218yescomplemented
36C22×Dic44C2211yescharacteristic
37C2×#66957—28no—
38C2×#66957C2218yescomplemented
39C22×D88C2211yescharacteristic
40C22×#4314C2211yescharacteristic
41C22×#4314C2211yescharacteristic
42C22×C8×D11C2211yescharacteristic
43#10623162—24no—
44#10623162C2218yescomplemented
45#10623130—24no—
46#10623130C2218yescomplemented
47C2×#66950C2211yescharacteristic
48C2×#66948C2211yescharacteristic
49C2×#66947—21no—
50C2×#66946C2211yescharacteristic
51C2×C4⋊C4×D11—21no—
52C2×#66940C2211yescharacteristic
53C2×#66937—21no—
54C2×#66937—21no—
55C2×#66936—21no—
56C2×(C22⋊D11)⋊C4—21no—
57C11×#465C2218yescomplemented
58C2×C11×#106C2211yescharacteristic
59C2×C11×#103C2211yescharacteristic
60C2×C11×#102C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic
62#10622788C2218yescomplemented
63C8×C22⋊D11C2218yescomplemented
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66C2×C8×Dic11C2211yescharacteristic
67#10622660C2218yescomplemented
68#10622650C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66874C2211yescharacteristic
71C2×#66873C2211yescharacteristic
72C2×#66873C2211yescharacteristic
73#10622477C2218yescomplemented
74#10622465C2218yescomplemented
75#10622424C2218yescomplemented
76#10622406C2218yescomplemented
77#10622399C2218yescomplemented
78#10622396C2218yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11D411yescharacteristic
89C23×Dic11—21no—
90C2×#4343—22no—
91C2×#4343—24no—
92C2×#4343—42no—
93C2×#4343C2314yes—
94C2×#4341—22no—
95C2×#4341—24no—
96C2×#4341—42no—
97C2×#4341C2314yes—
98C2×#4339—22no—
99C2×#4339—22no—
100C2×#4339—24no—
101C2×#4339—24no—
102C2×#4339—42no—
103C2×#4339—42no—
104C2×#4339C2314yes—
105C2×#4339C2314yes—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44C2311yescharacteristic
109C22×D44C2311yescharacteristic
110C22×C4×D11—21no—
111C22×C4×D11—21no—
112C22×C4×D11—21no—
113C22×C4×D11—21no—
114C22×C4×D11C2311yescharacteristic
115C22×Dic22C2311yescharacteristic
116C22×Dic22C2311yescharacteristic
117C2×C11×SD16—24no—
118C2×C11×SD16C2314yes—
119C22×C8×C11—24no—
120C22×C8×C11C2311yescharacteristic
121C22×C8×C11C2314yes—
122C22×C8×C11C2311yescharacteristic
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8C2314yes—
125C11×#121—22no—
126C11×#121C2314yes—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C22⋊Dic11D411yescharacteristic
133#66997—22no—
134#66997C2314yes—
135C2×#4326—24no—
136C2×#4326C2314yes—
137C2×#4325—42no—
138C2×#4325C2314yes—
139#66993—28no—
140#66993—22no—
141#66993C2314yes—
142#66992—28no—
143C2×#4324—42no—
144C2×#4324C2314yes—
145C2×#4323—24no—
146C2×#4323C2314yes—
147C4×C22⋊D11D414yes—
148C4×C22⋊D11C2314yes—
149C2×(C2×D11)⋊C4—21no—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4D411yescharacteristic
153C2×C4⋊Dic11—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×Dic11⋊C4D411yescharacteristic
158C2×C4×Dic11—21no—
159C2×C4×Dic11C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162#66969—232no—
163C2×Dic44—24no—
164C2×Dic44C2314yes—
165#66957—232no—
166C2×D88—24no—
167C2×D88C2314yes—
168C2×#4314—24no—
169C2×#4314D418yescomplemented
170C2×#4314C2314yes—
171C2×#4314C2314yes—
172C2×C8×D11—24no—
173C2×C8×D11C2314yes—
174#66950—22no—
175#66950C2314yes—
176#66948—22no—
177#66948C2314yes—
178#66947—28no—
179#66946—22no—
180#66946C2314yes—
181C4⋊C4×D11—28no—
182#66940—22no—
183#66940C2314yes—
184#66937—28no—
185#66937—28no—
186#66936—28no—
187(C22⋊D11)⋊C4—28no—
188C11×#106C2314yes—
189C11×#103C2314yes—
190C11×#102C2314yes—
191C22⋊(C11⋊C8)C2314yes—
192(C2×D11)⋊C8C2314yes—
193Dic11⋊C8C2314yes—
194C8×Dic11C2314yes—
195#66874C2314yes—
196#66874C2314yes—
197#66873C2314yes—
198#66873C2314yes—
199C2×#3284—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11C2×D411yescharacteristic
205C2×Q8×C11—21no—
206C2×Q8×C11—22no—
207C2×Q8×C11—22no—
208C2×Q8×C11C2412yes—
209C2×D4×C11—24no—
210C2×D4×C11—22no—
211C2×D4×C11—21no—
212C2×D4×C11—22no—
213C2×D4×C11—82no—
214C2×D4×C11C2412yes—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2411yescharacteristic
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—82no—
235C2×C22⋊D11C2×D414yes—
236C22×Dic11—24no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—44no—
240C22×Dic11C2×D411yescharacteristic
241C22×Dic11C2×D411yescharacteristic
242C22×Dic11C2×D411yescharacteristic
243#4343—28no—
244#4343—44no—
245#4343—48no—
246#4341—28no—
247#4341—44no—
248#4341—48no—
249#4339—28no—
250#4339—28no—
251#4339—44no—
252#4339—44no—
253#4339—48no—
254#4339—48no—
255C2×D44—24no—
256C2×D44—24no—
257C2×D44—21no—
258C2×D44—21no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—44no—
263C2×D44—82no—
264C2×D44C2×D414yes—
265C2×D44C2412yes—
266C2×D44C2412yes—
267C2×C4×D11—24no—
268C2×C4×D11—24no—
269C2×C4×D11—22no—
270C2×C4×D11—24no—
271C2×C4×D11—24no—
272C2×C4×D11—22no—
273C2×C4×D11—44no—
274C2×C4×D11—44no—
275C2×C4×D11—44no—
276C2×C4×D11—44no—
277C2×C4×D11C2×D412yes—
278C2×C4×D11C2412yes—
279C2×Dic22—21no—
280C2×Dic22—22no—
281C2×Dic22—21no—
282C2×Dic22—22no—
283C2×Dic22—22no—
284C2×Dic22C2×D414yes—
285C2×Dic22C2412yes—
286C2×Dic22C2412yes—
287C11×SD16—28no—
288C2×C8×C11—28no—
289C2×C8×C11—22no—
290C2×C8×C11C2×D414yes—
291C2×C8×C11C2412yes—
292C2×C8×C11C2412yes—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—24no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4C2412yes—
297C11×C4⋊C4C2412yes—
298C11×C22⋊C4—24no—
299C11×C22⋊C4—24no—
300C22⋊Dic11C2×D414yes—
301#4326—28no—
302#4325—44no—
303#4324—44no—
304#4323—28no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4C2×D414yes—
309C4⋊Dic11—24no—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4—24no—
313Dic11⋊C4C2×D414yes—
314C4×Dic11—24no—
315C4×Dic11C2×D412yes—
316C4×Dic11C2412yes—
317C2×C11⋊C8—22no—
318C2×C11⋊C8—22no—
319C2×C11⋊C8C2412yes—
320C2×C11⋊C8C2412yes—
321Dic44—28no—
322D88—28no—
323#4314—28no—
324#4314C2×D4116yescomplemented
325C8×D11—28no—
326C22×#135—111no—
327C22×#135—111no—
328C2×#550—111no—
329C2×#547—111no—
330#3284—1116no—
331C2×#492—111no—
332C2×#465—111no—
333C2×#465D1111yescharacteristic, complemented
334C2×#462—111no—
335C2×#459—111no—
336C2×#452—111no—
337C2×#452—111no—
338C2×#449—111no—
339C2×#449—111no—
340C2×C4×SD16—111no—
341C2×C8×D4—111no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11—42no—
349C23×C11C22×D412yes—
350C23×C11C22×D411yescharacteristic
351C22×D11—22no—
352C22×D11—24no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—42no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11C22×D412yes—
363Q8×C11—22no—
364Q8×C11—22no—
365Q8×C11—42no—
366D4×C11—22no—
367D4×C11—22no—
368D4×C11—42no—
369D4×C11—84no—
370C2×C4×C11—22no—
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—42no—
378C2×C4×C11—42no—
379C2×C4×C11—42no—
380C2×C4×C11C22×D412yes—
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D412yes—
383C2×C4×C11H(5,𝔽2)12yes—
384C2×C4×C11C2511yescharacteristic
385C22⋊D11—28no—
386C22⋊D11—48no—
387C22⋊D11—48no—
388C22⋊D11—48no—
389C22⋊D11—48no—
390C22⋊D11—84no—
391C2×Dic11—24no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—48no—
397C2×Dic11—42no—
398C2×Dic11#13514yescomplemented
399C2×Dic11C22×D412yes—
400C2×Dic11C22×D412yes—
401C2×Dic11C22×D412yes—
402D44—24no—
403D44—22no—
404D44—22no—
405D44—22no—
406D44—48no—
407D44—42no—
408D44—84no—
409D44C22×D414yes—
410C4×D11—24no—
411C4×D11—22no—
412C4×D11—22no—
413C4×D11—48no—
414C4×D11—48no—
415C4×D11—48no—
416C4×D11—48no—
417Dic22—24no—
418Dic22—22no—
419Dic22—22no—
420Dic22—22no—
421Dic22—42no—
422Dic22C22×D414yes—
423C8×C11—22no—
424C8×C11C22×D414yes—
425C11⋊C8—22no—
426C11⋊C8—22no—
427C22×#41—111no—
428C22×#41—111no—
429C22×#41—111no—
430C22×#41—111no—
431C2×#135—118no—
432C2×#135—118no—
433C2×#135—228no—
434C2×#135—228no—
435C22×Q16—111no—
436C22×Q16—111no—
437C22×SD16—111no—
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16—111no—
441C22×SD16C2×D1111yescharacteristic
442C22×D8—111no—
443C22×D8—111no—
444C23×C8—111no—
445C23×C8C2×D1111yescharacteristic
446#550—118no—
447#550—224no—
448#547—118no—
449#547—224no—
450C2×C4⋊Q8—111no—
451C2×#127—111no—
452C2×#127—221no—
453C2×#123—221no—
454C2×#123—221no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8C2×D1111yescharacteristic
457C2×#121—111no—
458C2×#121—221no—
459C2×#121—221no—
460C2×#121—221no—
461C2×#121C2×D1111yescharacteristic
462C2×C4×Q8—111no—
463C2×C4×D4—111no—
464C2×C4×D4—111no—
465C2×C4×D4—221no—
466C22×C4⋊C4—221no—
467#492—118no—
468#465—118no—
469#465C2×D1118yescomplemented
470#462—118no—
471#459—118no—
472#452—118no—
473#452—118no—
474#449—118no—
475#449—118no—
476C4×SD16—118no—
477C8×D4—118no—
478C2×#106C2×D1111yescharacteristic
479C2×C4⋊C8—111no—
480C2×#103—111no—
481C2×#103—111no—
482C2×#103C2×D1111yescharacteristic
483C2×#102—111no—
484C2×#102—111no—
485C2×#102C2×D1111yescharacteristic
486C2×C22⋊C8—111no—
487C2×C22⋊C8—111no—
488C2×C4×C8—111no—
489C22×C11—22no—
490C22×C11—22no—
491C22×C11—22no—
492C22×C11—44no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—84no—
497C22×C11D4212yes—
498C22×C11C2×#13512yes—
499C22×C11#57712yes—
500C22×C11C23×D411yescharacteristic
501C2×D11—24no—
502C2×D11—22no—
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—44no—
506C2×D11—48no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—84no—
513C4×C11—22no—
514C4×C11—42no—
515C4×C11—42no—
516C4×C11—42no—
517C4×C11D4212yes—
518C4×C11C23×D411yescharacteristic
519C4×C11C2×H(5,𝔽2)11yescharacteristic
520Dic11—24no—
521Dic11—22no—
522Dic11—22no—
523Dic11—42no—
524Dic11C2×#13514yescomplemented
525C2×#41—114no—
526C2×#41—114no—
527C2×#41—114no—
528C2×#41—114no—
529C2×#41—224no—
530C2×#41—224no—
531C2×#41—222no—
532C2×#41—222no—
533C2×#41—222no—
534C2×#41—222no—
535C2×#41—224no—
536C2×#41—224no—
537C2×#41—442no—
538C2×#41—442no—
539C2×#41—442no—
540C2×#41—442no—
541C22×Q8—111no—
542C22×Q8—111no—
543C22×Q8C22×D1111yescharacteristic
544C22×D4—21no—
545C22×D4—111no—
546C22×D4—111no—
547C22×D4—111no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4—221no—
554C22×D4—221no—
555C22×D4C22×D1111yescharacteristic
556C23×C4—111no—
557C23×C4—221no—
558C23×C4—221no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563#135—2232no—
564#135—2232no—
565C2×Q16—114no—
566C2×Q16—114no—
567C2×Q16—224no—
568C2×Q16—224no—
569C2×SD16—24no—
570C2×SD16—114no—
571C2×SD16—114no—
572C2×SD16—118no—
573C2×SD16—114no—
574C2×SD16—114no—
575C2×SD16—224no—
576C2×SD16—442no—
577C2×SD16—442no—
578C2×SD16C22×D1114yes—
579C2×D8—114no—
580C2×D8—114no—
581C2×D8—224no—
582C2×D8—224no—
583C22×C8—24no—
584C22×C8—111no—
585C22×C8—111no—
586C22×C8—114no—
587C22×C8—224no—
588C22×C8C22×D1111yescharacteristic
589C22×C8C22×D1114yes—
590C22×C8C22×D1111yescharacteristic
591C4⋊Q8—114no—
592C4⋊Q8—222no—
593#127—114no—
594#127—222no—
595#127—228no—
596#123—228no—
597#123—228no—
598C22⋊Q8—22no—
599C22⋊Q8—114no—
600C22⋊Q8—222no—
601C22⋊Q8C22×D1114yes—
602#121—22no—
603#121—114no—
604#121—228no—
605#121—228no—
606#121—228no—
607#121—222no—
608#121C22×D1114yes—
609C4×Q8—114no—
610C4×Q8—222no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—114no—
614C4×D4—222no—
615C4×D4—228no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—228no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C4⋊C4—221no—
623C2×C4⋊C4C22×D1111yescharacteristic
624C2×C4⋊C4C22×D1111yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—111no—
628C2×C22⋊C4—111no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C42—111no—
633C2×C42—221no—
634#106C22×D1114yes—
635C4⋊C8—114no—
636#103—114no—
637#103—114no—
638#103C22×D1114yes—
639#102—114no—
640#102—114no—
641#102C22×D1114yes—
642C22⋊C8—114no—
643C22⋊C8—114no—
644C4×C8—114no—
645C2×C11—42no—
646C2×C11—82no—
647C2×C11#328414yescomplemented
648C2×C11C2×D4211yescharacteristic
649C2×C11C22×#13511yescharacteristic
650C2×C11C2×#57711yescharacteristic
651D11—42no—
652D11—44no—
653D11—82no—
654C24—21no—
655C24—111no—
656C24—221no—
657C24—221no—
658C24D4×D1111yescharacteristic
659#41—228no—
660#41—228no—
661#41—228no—
662#41—228no—
663#41—444no—
664#41—444no—
665#41—448no—
666#41—448no—
667#41—444no—
668#41—448no—
669#41—444no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—22no—
674C2×Q8—114no—
675C2×Q8—112no—
676C2×Q8—112no—
677C2×Q8—221no—
678C2×Q8—221no—
679C2×Q8—222no—
680C2×Q8—222no—
681C2×Q8—222no—
682C2×Q8C23×D1112yes—
683C2×D4—24no—
684C2×D4—22no—
685C2×D4—21no—
686C2×D4—22no—
687C2×D4—82no—
688C2×D4—114no—
689C2×D4—114no—
690C2×D4—112no—
691C2×D4—112no—
692C2×D4—224no—
693C2×D4—224no—
694C2×D4—224no—
695C2×D4—224no—
696C2×D4—224no—
697C2×D4—224no—
698C2×D4—224no—
699C2×D4—224no—
700C2×D4—221no—
701C2×D4—222no—
702C2×D4—221no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—444no—
706C2×D4—444no—
707C2×D4—444no—
708C2×D4—444no—
709C2×D4—444no—
710C2×D4—882no—
711C2×D4—882no—
712C2×D4C23×D1112yes—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—111no—
719C22×C4—111no—
720C22×C4—111no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—224no—
724C22×C4—224no—
725C22×C4—224no—
726C22×C4—221no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—221no—
730C22×C4—224no—
731C22×C4—224no—
732C22×C4—444no—
733C22×C4—444no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—444no—
737C22×C4D4×D1112yes—
738C22×C4D4×D1111yescharacteristic
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—228no—
742Q16—228no—
743SD16—28no—
744SD16—1116no—
745SD16—228no—
746SD16—444no—
747SD16—444no—
748D8—228no—
749D8—228no—
750C2×C8—22no—
751C2×C8—28no—
752C2×C8—112no—
753C2×C8—112no—
754C2×C8—222no—
755C2×C8—222no—
756C2×C8—228no—
757C2×C8D4×D1114yes—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—24no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—114no—
764C4⋊C4—224no—
765C4⋊C4—224no—
766C4⋊C4—224no—
767C4⋊C4—224no—
768C4⋊C4C23×D1112yes—
769C4⋊C4C23×D1112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—114no—
773C22⋊C4—114no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C42—112no—
778C42—112no—
779C42—224no—
780C11C2×#328411yescharacteristic, complemented, Sylow
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—112no—
789C23—222no—
790C23—222no—
791C23—222no—
792C23—224no—
793C23—222no—
794C23—222no—
795C23—442no—
796C23—442no—
797C23—442no—
798C23—442no—
799C23—442no—
800C23C2×D4×D1112yes—
801C23C2×D4×D1111yescharacteristic
802Q8—22no—
803Q8—22no—
804Q8—42no—
805Q8—114no—
806Q8—224no—
807Q8—222no—
808Q8—222no—
809Q8—222no—
810Q8—442no—
811D4—22no—
812D4—22no—
813D4—42no—
814D4—84no—
815D4—114no—
816D4—228no—
817D4—224no—
818D4—222no—
819D4—222no—
820D4—222no—
821D4—448no—
822D4—448no—
823D4—448no—
824D4—448no—
825D4—448no—
826D4—442no—
827D4—884no—
828D4—884no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—114no—
840C2×C4—112no—
841C2×C4—112no—
842C2×C4—112no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—224no—
846C2×C4—222no—
847C2×C4—224no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—448no—
852C2×C4—448no—
853C2×C4—448no—
854C2×C4—448no—
855C2×C4—448no—
856C2×C4—442no—
857C2×C4C2×D4×D1112yes—
858C2×C4C2×D4×D1111yescharacteristic
859C2×C4C2×D4×D1112yes—
860C2×C4#6704212yes—
861C2×C4C24×D1111yescharacteristic
862C8—22no—
863C8—222no—
864C8—222no—
865C8C2×D4×D1114yes—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—44no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—84no—
874C22—222no—
875C22—224no—
876C22—222no—
877C22—222no—
878C22—444no—
879C22—448no—
880C22—442no—
881C22—442no—
882C22—442no—
883C22—442no—
884C22—442no—
885C22—884no—
886C22#1062314012yes—
887C22#1062329312yes—
888C22D11×#13512yes—
889C22C22×D4×D1111yescharacteristic
890C4—22no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—114no—
895C4—222no—
896C4—224no—
897C4—222no—
898C4—442no—
899C4#1062314012yes—
900C4C22×D4×D1111yescharacteristic
901C4C2×#6704211yescharacteristic
902C2—42no—
903C2—82no—
904C2—442no—
905C2—444no—
906C2—882no—
907C2#1308034314yesdirect product factor
908C2C2×#1062314011yescharacteristic
909C2C2×D11×#13511yescharacteristic
910C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
hypercenterC2×#465D11
hypocenterC11C2×#3284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#66957C2semidirect
2. C22×#66969C2semidirect
3. C2×#10623130C2semidirect
4. C2×#10623162C2semidirect
5. #13080343C2direct (N × H)
6. C2×#10622788C2semidirect
7. C2×#10622477C2semidirect
8. C2×#10622406C2semidirect
9. C2×#10622399C2semidirect
10. C2×#10622396C2semidirect
11. C2×#10622660C2semidirect
12. C2×#10622424C2semidirect
13. C2×#10622650C2semidirect
14. C2×#10622465C2semidirect
15. C2×C8×C22⋊D11C2semidirect
16. C2×C11×#465C2semidirect
35. C2×#66969C22semidirect
38. C2×#66957C22semidirect
44. #10623162C22semidirect
46. #10623130C22semidirect
57. C11×#465C22semidirect
62. #10622788C22semidirect
63. C8×C22⋊D11C22semidirect
67. #10622660C22semidirect
68. #10622650C22semidirect
73. #10622477C22semidirect
74. #10622465C22semidirect
75. #10622424C22semidirect
76. #10622406C22semidirect
77. #10622399C22semidirect
78. #10622396C22semidirect
169. C2×#4314D4semidirect
324. #4314C2×D4semidirect
333. C2×#465D11semidirect
398. C2×Dic11#135semidirect
469. #465C2×D11semidirect
524. Dic11C2×#135semidirect
647. C2×C11#3284semidirect
780. C11C2×#3284semidirect
907. C2#13080343direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669572
C22×#669692
C2×#106231302
C2×#106231622
#130803432
C2×#106227882
C2×#106224772
C2×#106224062
C2×#106223992
C2×#106223962
C2×#106226602
C2×#106224242
C2×#106226502
C2×#106224652
C2×C8×C22⋊D112
C2×C11×#4652
C2×#328411