Finite Group Databasebeta

← C2×#13080818 #15630571

Subgroups — C2×#13080818 #15630571

Order 2816.

2318 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×#10623045C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic, complemented
3#13080818C2116yesmaximal, direct product factor
4C2×#10622413C211yesmaximal, characteristic, complemented
5C2×#10622428C211yesmaximal, characteristic, complemented
6C2×#10622580C211yesmaximal, characteristic, complemented
7C2×#10622376C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622425C211yesmaximal, characteristic, complemented
10C2×#10622432C211yesmaximal, characteristic, complemented
11C2×#10622851C211yesmaximal, characteristic, complemented
12C2×#10622386C211yesmaximal, characteristic, complemented
13C2×#10622369C211yesmaximal, characteristic, complemented
14C2×#10622741C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#417C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic, complemented
20C22×C11×C4⋊C4C2211yescharacteristic, complemented
21#10623360—24no—
22#10623360C2218yescomplemented
23C2×#67000C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C22×#4325C2211yescharacteristic, complemented
26C2×#66992—21no—
27C2×#66990—21no—
28C2×D4×Dic11C2211yescharacteristic
29C22×#4323C2211yescharacteristic
30C2×#66983—21no—
31C2×#66983C2211yescharacteristic
32C2×#66983C2211yescharacteristic, complemented
33C2×#66982—21no—
34C2×C4×C22⋊D11—21no—
35C2×C4×C22⋊D11C2211yescharacteristic
36C22×(C2×D11)⋊C4—21no—
37C22×D88C2211yescharacteristic
38C22×#4313C2211yescharacteristic
39#10623045—24no—
40#10623045C2218yescomplemented
41C2×#66951—21no—
42C2×#66948C2211yescharacteristic
43C2×#66947—21no—
44C2×#66946C2211yescharacteristic, complemented
45C2×#66945C2211yescharacteristic
46C2×#66943C2211yescharacteristic, complemented
47C11×#417C2218yescomplemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622748C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic, complemented
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66881C2211yescharacteristic, complemented
62C2×Dic11⋊C8C2211yescharacteristic, complemented
63C2×C8×Dic11C2211yescharacteristic, complemented
64#10622580C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66871C2211yescharacteristic, complemented
68C2×#66871C2211yescharacteristic, complemented
69#10622432C2218yescomplemented
70#10622428C2218yescomplemented
71#10622425C2218yescomplemented
72#10622413C2218yescomplemented
73#10622386C2218yescomplemented
74#10622383C2218yescomplemented
75#10622376C2218yescomplemented
76#10622369C2218yescomplemented
77C24×D11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11D411yescharacteristic
92C23×Dic11—21no—
93C2×D4×D11—24no—
94C2×D4×D11—22no—
95C2×D4×D11—42no—
96C2×D4×D11C2314yes—
97C22×D44—21no—
98C22×D44C2311yescharacteristic
99C22×D44C2311yescharacteristic
100C22×C4×D11—21no—
101C22×C4×D11C2311yescharacteristic
102C2×C11×M16—42no—
103C2×C11×M16C2314yescomplemented
104C22×C8×C11C2311yescharacteristic
105C22×C8×C11C2311yescharacteristic
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2314yescomplemented
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11D411yescharacteristic
113#67000—22no—
114#67000C2314yes—
115#66999—22no—
116#66999C2314yes—
117C2×#4325—42no—
118C2×#4325C2314yescomplemented
119#66992—28no—
120#66990—28no—
121D4×Dic11—22no—
122D4×Dic11C2314yes—
123C2×#4323—24no—
124C2×#4323C2314yes—
125#66983—22no—
126#66983—22no—
127#66983—28no—
128#66983C2314yes—
129#66983C2314yescomplemented
130#66982—28no—
131C4×C22⋊D11—28no—
132C4×C22⋊D11D414yes—
133C4×C22⋊D11C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—28no—
143C2×(C2×D11)⋊C4D411yescharacteristic
144C2×C4⋊Dic11—21no—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4D411yescharacteristic
150C2×C4×Dic11—21no—
151C2×C4×Dic11C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C2×D88—42no—
155C2×D88C2314yes—
156C2×#4313—42no—
157C2×#4313C2314yes—
158#66951—28no—
159#66948—22no—
160#66948C2314yes—
161#66947—28no—
162#66946—22no—
163#66946C2314yescomplemented
164#66945—22no—
165#66945C2314yes—
166#66943—22no—
167#66943C2314yescomplemented
168C11×#103C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66899C2314yescomplemented
173#66896C2314yes—
174C22⋊(C11⋊C8)C2314yescomplemented
175#66885C2314yes—
176#66885C2314yescomplemented
177(C2×D11)⋊C8C2314yes—
178#66881C2314yescomplemented
179Dic11⋊C8C2314yescomplemented
180C8×Dic11C2314yescomplemented
181#66873C2314yes—
182#66873C2314yes—
183#66871C2314yescomplemented
184#66871C2314yescomplemented
185C2×#3322—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—24no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—82no—
194C23×D11C2×D411yescharacteristic
195C11×#41—28no—
196C11×#41—44no—
197C11×#41—48no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C2×D4×C11—24no—
203C2×D4×C11—21no—
204C2×D4×C11—22no—
205C2×D4×C11—44no—
206C2×D4×C11#4114yes—
207C2×D4×C11C2412yes—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—24no—
214C22×C4×C11—24no—
215C22×C4×C11—44no—
216C22×C4×C11—82no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—42no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11C2×D414yes—
229C22×Dic11—24no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—82no—
233C22×Dic11C2×D411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236D4×D11—28no—
237D4×D11—44no—
238D4×D11—48no—
239C2×D44—24no—
240C2×D44—21no—
241C2×D44—21no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—82no—
247C2×D44C2412yes—
248C2×D44C2412yes—
249C2×C4×D11—24no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—82no—
253C2×C4×D11C2×D412yes—
254C2×C4×D11C2412yes—
255C11×M16—44no—
256C2×C8×C11—22no—
257C2×C8×C11—22no—
258C2×C8×C11C2412yes—
259C2×C8×C11C2412yes—
260C11×C4⋊C4—21no—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—24no—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C22⋊Dic11—24no—
266C22⋊Dic11C2×D414yes—
267#4325—44no—
268#4323—28no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4C2×D414yes—
278C4⋊Dic11—24no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11C2412yes—
282C4⋊Dic11C2412yes—
283Dic11⋊C4—24no—
284Dic11⋊C4—24no—
285Dic11⋊C4C2×D414yes—
286C4×Dic11—24no—
287C4×Dic11C2×D412yes—
288C4×Dic11C2412yes—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8C2412yes—
292C2×C11⋊C8C2412yes—
293D88—44no—
294#4313—44no—
295C2×#553—111no—
296C2×#546—111no—
297#3322—1116no—
298C2×#488—111no—
299C2×#485—111no—
300C2×#480—111no—
301C2×#478—111no—
302C2×#469—111no—
303C2×#468—111no—
304C2×#463—111no—
305C2×#449—111no—
306C2×#447—111no—
307C2×C4×D8—111no—
308C2×#436—111no—
309C2×#417D1111yescharacteristic, complemented
310C2×#418—111no—
311C23×C11—24no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11C22×D412yes—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—48no—
326C22×D11—48no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—84no—
334C22×D11—816no—
335C22×D11C22×D412yes—
336Q8×C11—22no—
337Q8×C11—22no—
338Q8×C11—42no—
339D4×C11—24no—
340D4×C11—22no—
341D4×C11—48no—
342D4×C11C2×#4114yes—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—48no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—84no—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4112yes—
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C11C2511yescharacteristic
360C22⋊D11—44no—
361C22⋊D11—48no—
362C22⋊D11—48no—
363C22⋊D11—84no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—84no—
372C2×Dic11C22×D412yes—
373C2×Dic11C22×D412yes—
374C2×Dic11C22×D412yes—
375D44—22no—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—42no—
380D44—42no—
381D44—84no—
382C4×D11—24no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—84no—
386C8×C11—22no—
387C8×C11—22no—
388C11⋊C8—22no—
389C11⋊C8—22no—
390C22×#41C2×D1111yescharacteristic
391C23×D4—111no—
392C22×SD16—111no—
393C22×D8—111no—
394C22×D8—111no—
395C22×M16—111no—
396C22×M16C2×D1111yescharacteristic, complemented
397#553—118no—
398#553—224no—
399#546—118no—
400#546—224no—
401C2×#126—221no—
402C2×#125—111no—
403C2×#124—111no—
404C2×#123—221no—
405C2×#123—221no—
406C2×C22⋊Q8—111no—
407C2×#121—111no—
408C2×#121—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#121—221no—
412C2×#120—221no—
413C2×C4×D4—111no—
414C2×C4×D4—111no—
415C2×C4×D4—111no—
416C2×C4×D4—221no—
417C2×#117—111no—
418C22×C4⋊C4C2×D1111yescharacteristic, complemented
419C22×C22⋊C4—221no—
420#488—118no—
421#485—118no—
422#480—118no—
423#478—118no—
424#469—118no—
425#468—118no—
426#463—118no—
427#449—118no—
428#447—118no—
429C4×D8—118no—
430#436—118no—
431C2×#107—111no—
432C2×#107—111no—
433C2×#106—111no—
434C2×C4⋊C8—111no—
435#418—118no—
436#417C2×D1118yescomplemented
437C2×#103—111no—
438C2×#103C2×D1111yescharacteristic, complemented
439C2×#103C2×D1111yescharacteristic, complemented
440C2×#102—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×#102C2×D1111yescharacteristic
446C2×#102C2×D1111yescharacteristic
447C2×C22⋊C8—111no—
448C2×C22⋊C8—111no—
449C2×C4×C8—111no—
450C22×C11—22no—
451C22×C11—24no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—48no—
455C22×C11—44no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11#54612yes—
459C22×C11#57512yes—
460C22×C11#57612yes—
461C22×C11C23×D411yescharacteristic
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—44no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—816no—
473C2×D11—84no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—42no—
479C4×C11#54612yes—
480C4×C11C22×#4111yescharacteristic
481C4×C11C2×H(5,𝔽2)11yescharacteristic
482Dic11—22no—
483Dic11—22no—
484Dic11—22no—
485Dic11—42no—
486Dic11—42no—
487C25—221no—
488C2×#41—22no—
489C2×#41—24no—
490C2×#41—42no—
491C2×#41C22×D1114yes—
492C22×Q8C22×D1111yescharacteristic
493C22×D4—21no—
494C22×D4—111no—
495C22×D4—114no—
496C22×D4—111no—
497C22×D4—111no—
498C22×D4—221no—
499C22×D4—222no—
500C22×D4—221no—
501C22×D4—224no—
502C22×D4—221no—
503C22×D4—221no—
504C22×D4—442no—
505C22×D4C22×D1111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—111no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4C22×D1111yescharacteristic
512C2×SD16—114no—
513C2×SD16—442no—
514C2×D8—114no—
515C2×D8—114no—
516C2×D8—224no—
517C2×D8—442no—
518C2×M16—42no—
519C2×M16—114no—
520C2×M16—442no—
521C2×M16C22×D1114yescomplemented
522C22×C8—111no—
523C22×C8—111no—
524C22×C8C22×D1111yescharacteristic
525C22×C8C22×D1111yescharacteristic
526#126—228no—
527#125—114no—
528#125—222no—
529#124—114no—
530#124—222no—
531#123—228no—
532#123—228no—
533C22⋊Q8—114no—
534C22⋊Q8—222no—
535#121—114no—
536#121—114no—
537#121—114no—
538#121—228no—
539#121—222no—
540#121—228no—
541#121—222no—
542#121—222no—
543#120—228no—
544C4×D4—114no—
545C4×D4—114no—
546C4×D4—114no—
547C4×D4—114no—
548C4×D4—222no—
549C4×D4—222no—
550C4×D4—228no—
551#117—114no—
552#117—222no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—111no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4C22×D1111yescharacteristic
562C2×C4⋊C4C22×D1111yescharacteristic
563C2×C4⋊C4C22×D1114yescomplemented
564C2×C22⋊C4—111no—
565C2×C22⋊C4—111no—
566C2×C22⋊C4—228no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4—221no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C42—111no—
577C2×C42—221no—
578#107—114no—
579#107—114no—
580#106—114no—
581C4⋊C8—114no—
582#103—114no—
583#103C22×D1114yescomplemented
584#103C22×D1114yescomplemented
585#102—114no—
586#102—114no—
587#102—114no—
588#102—114no—
589#102—114no—
590#102C22×D1114yes—
591#102C22×D1114yes—
592C22⋊C8—114no—
593C22⋊C8—114no—
594C4×C8—114no—
595C2×C11—44no—
596C2×C11—42no—
597C2×C11#332214yescomplemented
598C2×C11C2×#54611yescharacteristic
599C2×C11C2×#57511yescharacteristic
600C2×C11C2×#57611yescharacteristic
601D11—42no—
602D11—82no—
603D11—82no—
604C24—21no—
605C24—111no—
606C24—224no—
607C24—221no—
608C24—221no—
609C24—444no—
610C24—444no—
611C24—882no—
612C24D4×D1111yescharacteristic
613#41—28no—
614#41—44no—
615#41—48no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8C23×D1112yes—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—44no—
624C2×D4—114no—
625C2×D4—112no—
626C2×D4—112no—
627C2×D4—224no—
628C2×D4—224no—
629C2×D4—228no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—222no—
633C2×D4—222no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—222no—
637C2×D4—222no—
638C2×D4—444no—
639C2×D4—448no—
640C2×D4—442no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—882no—
644C2×D4—882no—
645C2×D4#433914yes—
646C2×D4C23×D1112yes—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—82no—
656C22×C4—111no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—224no—
662C22×C4—224no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—882no—
668C22×C4—882no—
669C22×C4D4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4C23×D1112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—444no—
674D8—228no—
675D8—444no—
676M16—44no—
677M16—444no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—222no—
683C2×C8—222no—
684C2×C8C23×D1112yes—
685C2×C8C23×D1112yes—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—24no—
689C4⋊C4—114no—
690C4⋊C4—112no—
691C4⋊C4—112no—
692C4⋊C4—224no—
693C4⋊C4—224no—
694C4⋊C4—224no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4C23×D1112yes—
698C4⋊C4C23×D1112yes—
699C22⋊C4—114no—
700C22⋊C4—114no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—224no—
710C42—112no—
711C42—112no—
712C42—224no—
713C11C2×#332211yescharacteristic, complemented, Sylow
714C23—22no—
715C23—24no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—112no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—448no—
728C23—448no—
729C23—442no—
730C23—442no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23—442no—
735C23—884no—
736C23—8816no—
737C23C2×D4×D1112yes—
738C23C2×D4×D1111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—24no—
743D4—22no—
744D4—48no—
745D4—222no—
746D4—222no—
747D4—222no—
748D4—222no—
749D4—444no—
750D4—448no—
751D4—448no—
752D4—442no—
753D4—442no—
754D4—884no—
755D4—884no—
756D4C2×#433914yes—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—48no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—84no—
769C2×C4—112no—
770C2×C4—112no—
771C2×C4—112no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—224no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—442no—
781C2×C4—442no—
782C2×C4—884no—
783C2×C4—884no—
784C2×C4C2×#433912yes—
785C2×C4C2×D4×D1112yes—
786C2×C4C2×D4×D1111yescharacteristic
787C2×C4#6703712yes—
788C2×C4C24×D1111yescharacteristic
789C8—22no—
790C8—22no—
791C8—222no—
792C8—222no—
793C22—22no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—48no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—444no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—8816no—
812C22—884no—
813C22—884no—
814C22#1062302112yes—
815C22#1062330512yes—
816C22#1062330812yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—222no—
823C4—222no—
824C4—222no—
825C4—442no—
826C4—442no—
827C4#1062302112yes—
828C4C22×#433911yescharacteristic
829C4C2×#6703711yescharacteristic
830C2—42no—
831C2—44no—
832C2—442no—
833C2—882no—
834C2—882no—
835C2#1308081814yesdirect product factor
836C2C2×#1062302111yescharacteristic
837C2C2×#1062330811yescharacteristic
838C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
hypercenterC2×#417D11
hypocenterC11C2×#3322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10623045C2semidirect
2. C2×#10623360C2semidirect
3. #13080818C2direct (N × H)
4. C2×#10622413C2semidirect
5. C2×#10622428C2semidirect
6. C2×#10622580C2semidirect
7. C2×#10622376C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622425C2semidirect
10. C2×#10622432C2semidirect
11. C2×#10622851C2semidirect
12. C2×#10622386C2semidirect
13. C2×#10622369C2semidirect
14. C2×#10622741C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#417C2semidirect
19. C22×C11×M16C22semidirect
20. C22×C11×C4⋊C4C22semidirect
22. #10623360C22semidirect
25. C22×#4325C22semidirect
32. C2×#66983C22semidirect
40. #10623045C22semidirect
44. C2×#66946C22semidirect
46. C2×#66943C22semidirect
47. C11×#417C22semidirect
48. C2×C11×#103C22semidirect
49. C2×C11×#103C22semidirect
52. #10622851C22semidirect
53. C2×#66899C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622748C22semidirect
57. #10622741C22semidirect
59. C2×#66885C22semidirect
61. C2×#66881C22semidirect
62. C2×Dic11⋊C8C22semidirect
63. C2×C8×Dic11C22semidirect
64. #10622580C22semidirect
67. C2×#66871C22semidirect
68. C2×#66871C22semidirect
69. #10622432C22semidirect
70. #10622428C22semidirect
71. #10622425C22semidirect
72. #10622413C22semidirect
73. #10622386C22semidirect
74. #10622383C22semidirect
75. #10622376C22semidirect
76. #10622369C22semidirect
103. C2×C11×M16C23semidirect
110. C2×C11×C4⋊C4C23semidirect
118. C2×#4325C23semidirect
129. #66983C23semidirect
163. #66946C23semidirect
167. #66943C23semidirect
168. C11×#103C23semidirect
169. C11×#103C23semidirect
172. #66899C23semidirect
174. C22⋊(C11⋊C8)C23semidirect
176. #66885C23semidirect
178. #66881C23semidirect
179. Dic11⋊C8C23semidirect
180. C8×Dic11C23semidirect
183. #66871C23semidirect
184. #66871C23semidirect
309. C2×#417D11semidirect
396. C22×M16C2×D11semidirect
418. C22×C4⋊C4C2×D11semidirect
436. #417C2×D11semidirect
438. C2×#103C2×D11semidirect
439. C2×#103C2×D11semidirect
521. C2×M16C22×D11semidirect
563. C2×C4⋊C4C22×D11semidirect
583. #103C22×D11semidirect
584. #103C22×D11semidirect
597. C2×C11#3322semidirect
713. C11C2×#3322semidirect
835. C2#13080818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230452
C2×#106233602
#130808182
C2×#106224132
C2×#106224282
C2×#106225802
C2×#106223762
C2×#106227482
C2×#106224252
C2×#106224322
C2×#106228512
C2×#106223862
C2×#106223692
C2×#106227412
C2×#106223832
C2×C11×#4172
C2×#332211