Finite Group Databasebeta

← C2×#13079502 #15624463

Subgroups — C2×#13079502 #15624463

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623160C211yesmaximal, characteristic
2C2×#10623347C211yesmaximal, characteristic, complemented
3#13079502C2116yesmaximal, direct product factor
4C2×#10622422C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622418C211yesmaximal, characteristic, complemented
8C2×#10622802C211yesmaximal, characteristic, complemented
9C2×#10622425C211yesmaximal, characteristic, complemented
10C2×#10622801C211yesmaximal, characteristic, complemented
11C2×#10622420C211yesmaximal, characteristic, complemented
12C2×#10622800C211yesmaximal, characteristic, complemented
13C2×#10622800C211yesmaximal, characteristic, complemented
14C2×#10622840C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#451C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic
21C22×C11×Q16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23#10623347—24no—
24#10623347C2218yescomplemented
25C2×#67000—21no—
26C2×#66999C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C2×#66999C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C2×#66999C2211yescharacteristic
31C2×#66997—21no—
32C22×#4325C2211yescharacteristic
33C22×#4325C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66982—21no—
36C2×#66982—21no—
37C2×#66979C2211yescharacteristic
38C22×#4313C2211yescharacteristic
39C22×C8×D11C2211yescharacteristic
40#10623160—24no—
41#10623160C2218yes—
42C2×#66949—21no—
43C2×#66948—21no—
44C2×#66948C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66937—21no—
47C2×#66937—21no—
48C11×#451C2218yescomplemented
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52#10622840C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66899C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622802C2218yescomplemented
59#10622801C2218yescomplemented
60#10622800C2218yescomplemented
61#10622800C2218yescomplemented
62C2×#66885C2211yescharacteristic
63C2×#66885C2211yescharacteristic
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66882C2211yescharacteristic
67C2×#66881C2211yescharacteristic
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622425C2218yescomplemented
72#10622422C2218yescomplemented
73#10622420C2218yescomplemented
74#10622418C2218yescomplemented
75#10622350C2218yescomplemented
76#10622340C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11—22no—
79C22×Q8×C11—42no—
80C22×Q8×C11—42no—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2311yescharacteristic
84C22×Q8×C11C2314yes—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11D411yescharacteristic
89C22×C22⋊D11D411yescharacteristic
90C2×#4343—22no—
91C2×#4343—42no—
92C2×#4343—42no—
93C2×#4343C2314yes—
94C2×#4339—42no—
95C2×#4339—42no—
96C2×#4339D414yes—
97C2×#4339C2314yes—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44D411yescharacteristic
101C22×D44C2311yescharacteristic
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×Dic22D411yescharacteristic
107C2×C11×Q16—42no—
108C2×C11×Q16—42no—
109C2×C11×Q16C2314yes—
110C2×C11×Q16C2314yes—
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8C2314yes—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C22⋊Dic11—21no—
119#67000—28no—
120#66999—22no—
121#66999—22no—
122#66999—22no—
123#66999—22no—
124#66999—22no—
125#66999C2314yes—
126#66999C2314yes—
127#66999C2314yes—
128#66999C2314yes—
129#66999C2314yes—
130#66997—28no—
131C2×#4325—42no—
132C2×#4325—42no—
133C2×#4325C2314yes—
134C2×#4325C2314yes—
135#66983—22no—
136#66983C2314yes—
137#66982—28no—
138#66982—28no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146#66979—22no—
147#66979C2314yes—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×C4×Dic11—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×#4313—42no—
161C2×#4313C2314yes—
162C2×C8×D11—42no—
163C2×C8×D11C2314yes—
164#66949—28no—
165#66948—28no—
166#66948—22no—
167#66948C2314yes—
168C4⋊C4×D11—22no—
169C4⋊C4×D11C2314yes—
170#66937—28no—
171#66937—28no—
172C11×#103C2314yes—
173C11×#103C2314yes—
174C11×C22⋊C8C2314yes—
175#66899C2314yes—
176#66899C2314yes—
177#66899C2314yes—
178#66899C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66885C2314yes—
181#66885C2314yes—
182(C2×D11)⋊C8C2314yes—
183(C2×D11)⋊C8C2314yes—
184#66882C2314yes—
185#66881C2314yes—
186#66872C2314yes—
187#66871C2314yes—
188C2×#3201—111nomaximal, Sylow
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C23×D11C2×D411yescharacteristic
192C23×D11C2×D411yescharacteristic
193C2×Q8×C11—24no—
194C2×Q8×C11—21no—
195C2×Q8×C11—21no—
196C2×Q8×C11—21no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11—44no—
204C2×Q8×C11—44no—
205C2×Q8×C11—44no—
206C2×Q8×C11—48no—
207C2×Q8×C11C2412yes—
208C2×Q8×C11C2412yes—
209C2×Q8×C11C2412yes—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—24no—
217C22×C4×C11—44no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C2×C22⋊D11—24no—
223C2×C22⋊D11—42no—
224C2×C22⋊D11—42no—
225C2×C22⋊D11—82no—
226C2×C22⋊D11C2×D414yes—
227C2×C22⋊D11C2×D414yes—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233#4343—44no—
234#4343—44no—
235#4343—48no—
236#4339—48no—
237#4339—44no—
238#4339—44no—
239C2×D44—24no—
240C2×D44—24no—
241C2×D44—21no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—42no—
245C2×D44—44no—
246C2×D44—82no—
247C2×D44C2×D414yes—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—24no—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—22no—
254C2×C4×D11—22no—
255C2×C4×D11—44no—
256C2×C4×D11—82no—
257C2×C4×D11C2×D412yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2412yes—
260C2×C4×D11C2412yes—
261C2×Dic22—42no—
262C2×Dic22C2×D414yes—
263C11×Q16—44no—
264C11×Q16—44no—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—24no—
271C11×C4⋊C4C2412yes—
272C11×C22⋊C4—24no—
273C22⋊Dic11—24no—
274#4325—44no—
275#4325—44no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285C4⋊Dic11—21no—
286C4⋊Dic11C2412yes—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2412yes—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295C4×Dic11—24no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300#4313—44no—
301C8×D11—44no—
302C2×#537—111no—
303C2×#536—111no—
304#3201—1116no—
305C2×#484—111no—
306C2×#485—111no—
307C2×#482—111no—
308C2×#483—111no—
309C2×#470—111no—
310C2×#468—111no—
311C2×#467—111no—
312C2×#465—111no—
313C2×#452—111no—
314C2×#452—111no—
315C2×#451D1111yescharacteristic, complemented
316C2×#448—111no—
317C2×#408—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11C22×D412yes—
322C23×C11C22×D411yescharacteristic
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11C22×D412yes—
334C22×D11C22×D412yes—
335Q8×C11—22no—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—48no—
342Q8×C11—42no—
343Q8×C11—42no—
344Q8×C11—42no—
345C2×C4×C11—22no—
346C2×C4×C11—24no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—48no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11C22×D412yes—
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11H(5,𝔽2)12yes—
361C2×C4×C11H(5,𝔽2)12yes—
362C2×C4×C11C2511yescharacteristic
363C22⋊D11—44no—
364C22⋊D11—44no—
365C22⋊D11—84no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11C22×D412yes—
375C2×Dic11C22×D412yes—
376D44—22no—
377D44—22no—
378D44—44no—
379D44—48no—
380D44—42no—
381D44—84no—
382C4×D11—24no—
383C4×D11—24no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—48no—
389C4×D11—84no—
390Dic22—44no—
391C8×C11—22no—
392C8×C11—22no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C22×#41—111no—
396C22×#41—111no—
397C23×Q8C2×D1111yescharacteristic
398C22×Q16C2×D1111yescharacteristic
399C22×Q16C2×D1111yescharacteristic
400C22×SD16—111no—
401C22×SD16—111no—
402C22×M16—111no—
403C23×C8—111no—
404#537—118no—
405#537—224no—
406#536—118no—
407#536—224no—
408C2×C4⋊Q8—221no—
409C2×#124—221no—
410C2×#123—221no—
411C2×#123—221no—
412C2×C22⋊Q8—111no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—111no—
415C2×C22⋊Q8—111no—
416C2×C22⋊Q8—111no—
417C2×C22⋊Q8—221no—
418C2×C22⋊Q8C2×D1111yescharacteristic
419C2×#121—111no—
420C2×#121—111no—
421C2×#121—221no—
422C2×#121—221no—
423C2×#121—221no—
424C2×#117—111no—
425C22×C4⋊C4—111no—
426#485—118no—
427#484—118no—
428#483—118no—
429#482—118no—
430#470—118no—
431#468—118no—
432#467—118no—
433#465—118no—
434#452—118no—
435#452—118no—
436#451C2×D1118yescomplemented
437#448—118no—
438C2×#107—111no—
439C2×#107—111no—
440C2×#106—111no—
441C2×#106—111no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#103—111no—
446C2×#103C2×D1111yescharacteristic
447C2×#103C2×D1111yescharacteristic
448C2×#102—111no—
449C2×#102—111no—
450#408—118no—
451C2×C22⋊C8—111no—
452C2×C22⋊C8—111no—
453C2×C22⋊C8—111no—
454C2×C22⋊C8C2×D1111yescharacteristic
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—44no—
459C22×C11#53412yes—
460C22×C11#57712yes—
461C22×C11#57812yes—
462C22×C11C23×D411yescharacteristic
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—44no—
470C2×D11—44no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11—42no—
480C4×C11#53412yes—
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482C4×C11C2×H(5,𝔽2)11yescharacteristic
483Dic11—22no—
484Dic11—22no—
485Dic11—42no—
486Dic11—42no—
487Dic11—42no—
488C2×#41—114no—
489C2×#41—114no—
490C2×#41—114no—
491C2×#41—222no—
492C2×#41—442no—
493C2×#41—442no—
494C2×#41—442no—
495C2×#41—442no—
496C22×Q8—21no—
497C22×Q8—22no—
498C22×Q8—42no—
499C22×Q8—42no—
500C22×Q8—111no—
501C22×Q8C22×D1111yescharacteristic
502C22×Q8C22×D1111yescharacteristic
503C22×Q8C22×D1111yescharacteristic
504C22×Q8C22×D1114yes—
505C22×D4—111no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—221no—
512C23×C4—21no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—221no—
516C23×C4—221no—
517C23×C4C22×D1111yescharacteristic
518C2×Q16—42no—
519C2×Q16—42no—
520C2×Q16C22×D1114yes—
521C2×Q16C22×D1114yes—
522C2×SD16—114no—
523C2×SD16—114no—
524C2×SD16—442no—
525C2×SD16—442no—
526C2×M16—114no—
527C2×M16—442no—
528C22×C8—111no—
529C22×C8—111no—
530C22×C8—114no—
531C22×C8—442no—
532C22×C8C22×D1111yescharacteristic
533C22×C8C22×D1111yescharacteristic
534C4⋊Q8—228no—
535#124—228no—
536#123—228no—
537#123—228no—
538C22⋊Q8—22no—
539C22⋊Q8—114no—
540C22⋊Q8—114no—
541C22⋊Q8—114no—
542C22⋊Q8—114no—
543C22⋊Q8—114no—
544C22⋊Q8—228no—
545C22⋊Q8—222no—
546C22⋊Q8—222no—
547C22⋊Q8—222no—
548C22⋊Q8—222no—
549C22⋊Q8—222no—
550C22⋊Q8C22×D1114yes—
551#121—114no—
552#121—114no—
553#121—228no—
554#121—228no—
555#121—222no—
556#121—228no—
557#121—222no—
558#117—114no—
559#117—222no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—221no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C42—221no—
583#107—114no—
584#107—114no—
585#106—114no—
586#106—114no—
587#103—114no—
588#103—114no—
589#103—114no—
590#103—114no—
591#103C22×D1114yes—
592#103C22×D1114yes—
593#102—114no—
594#102—114no—
595C22⋊C8—114no—
596C22⋊C8—114no—
597C22⋊C8—114no—
598C22⋊C8C22×D1114yes—
599C2×C11—42no—
600C2×C11#320114yescomplemented
601C2×C11C2×#53411yescharacteristic
602C2×C11C2×#57711yescharacteristic
603C2×C11C2×#57811yescharacteristic
604D11—42no—
605D11—42no—
606D11—82no—
607C24—111no—
608C24—111no—
609C24—221no—
610C24D4×D1111yescharacteristic
611#41—448no—
612#41—444no—
613#41—444no—
614#41—444no—
615#41—444no—
616#41—448no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—24no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—44no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—48no—
631C2×Q8—114no—
632C2×Q8—442no—
633C2×Q8C23×D1112yes—
634C2×Q8C23×D1112yes—
635C2×Q8C23×D1112yes—
636C2×D4—114no—
637C2×D4—114no—
638C2×D4—114no—
639C2×D4—112no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—221no—
644C2×D4—222no—
645C2×D4—222no—
646C2×D4—442no—
647C2×D4—444no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—882no—
651C2×D4—882no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—44no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—224no—
667C22×C4—224no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—444no—
676C22×C4—882no—
677C22×C4D4×D1112yes—
678C22×C4D4×D1111yescharacteristic
679C22×C4C23×D1112yes—
680C22×C4C23×D1111yescharacteristic
681Q16—44no—
682Q16—44no—
683SD16—444no—
684SD16—444no—
685M16—444no—
686C2×C8—22no—
687C2×C8—22no—
688C2×C8—112no—
689C2×C8—112no—
690C2×C8—222no—
691C2×C8—222no—
692C2×C8—444no—
693C2×C8C23×D1112yes—
694C2×C8C23×D1112yes—
695C4⋊C4—24no—
696C4⋊C4—21no—
697C4⋊C4—112no—
698C4⋊C4—112no—
699C4⋊C4—112no—
700C4⋊C4—224no—
701C4⋊C4—224no—
702C4⋊C4—224no—
703C4⋊C4—224no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4C23×D1112yes—
710C22⋊C4—24no—
711C22⋊C4—224no—
712C22⋊C4—224no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C42—224no—
720C11C2×#320111yescharacteristic, complemented, Sylow
721C23—22no—
722C23—22no—
723C23—22no—
724C23—112no—
725C23—112no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—442no—
734C23—442no—
735C23—442no—
736C23C2×D4×D1112yes—
737C23C2×D4×D1111yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—22no—
743Q8—22no—
744Q8—48no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—444no—
749D4—222no—
750D4—222no—
751D4—444no—
752D4—448no—
753D4—444no—
754D4—444no—
755D4—442no—
756D4—884no—
757D4—884no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—48no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—112no—
772C2×C4—112no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—448no—
785C2×C4—442no—
786C2×C4—442no—
787C2×C4—442no—
788C2×C4—884no—
789C2×C4C2×D4×D1112yes—
790C2×C4C2×D4×D1111yescharacteristic
791C2×C4#6703712yes—
792C2×C4#6703712yes—
793C2×C4C24×D1111yescharacteristic
794C8—22no—
795C8—22no—
796C8—222no—
797C8—222no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—222no—
803C22—222no—
804C22—222no—
805C22—222no—
806C22—222no—
807C22—222no—
808C22—444no—
809C22—444no—
810C22—442no—
811C22—442no—
812C22—442no—
813C22—884no—
814C22#1062312012yes—
815C22#1062329712yes—
816C22#1062330912yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—222no—
824C4—222no—
825C4—442no—
826C4—442no—
827C4—442no—
828C4#1062312012yes—
829C4C2×#6703711yescharacteristic
830C4C2×#6703711yescharacteristic
831C2—42no—
832C2—442no—
833C2—442no—
834C2—882no—
835C2#1307950214yesdirect product factor
836C2C2×#1062312011yescharacteristic
837C2C2×#1062330911yescharacteristic
838C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC2×#10623160C2
hypercenterC2×#451D11
hypocenterC11C2×#3201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#10623347C2semidirect
3. #13079502C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622418C2semidirect
8. C2×#10622802C2semidirect
9. C2×#10622425C2semidirect
10. C2×#10622801C2semidirect
11. C2×#10622420C2semidirect
12. C2×#10622800C2semidirect
13. C2×#10622800C2semidirect
14. C2×#10622840C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#451C2semidirect
24. #10623347C22semidirect
48. C11×#451C22semidirect
52. #10622840C22semidirect
58. #10622802C22semidirect
59. #10622801C22semidirect
60. #10622800C22semidirect
61. #10622800C22semidirect
68. #10622658C22semidirect
71. #10622425C22semidirect
72. #10622422C22semidirect
73. #10622420C22semidirect
74. #10622418C22semidirect
75. #10622350C22semidirect
76. #10622340C22semidirect
315. C2×#451D11semidirect
436. #451C2×D11semidirect
600. C2×C11#3201semidirect
720. C11C2×#3201semidirect
835. C2#13079502direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231602
C2×#106233472
#130795022
C2×#106224222
C2×#106226582
C2×#106223502
C2×#106224182
C2×#106228022
C2×#106224252
C2×#106228012
C2×#106224202
C2×#106228002
C2×#106228402
C2×#106223402
C2×C11×#4512
C2×#320111