Finite Group Databasebeta

← C2×#13080698 #15630300

Subgroups — C2×#13080698 #15630300

Order 2816.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623042C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic
3#13080698C2116yesmaximal, direct product factor
4C2×#10622408C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622580C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622747C211yesmaximal, characteristic, complemented
9C2×#10622426C211yesmaximal, characteristic, complemented
10C2×#10622411C211yesmaximal, characteristic, complemented
11C2×#10622852C211yesmaximal, characteristic, complemented
12C2×#10622389C211yesmaximal, characteristic, complemented
13C2×#10622370C211yesmaximal, characteristic, complemented
14C2×#10622740C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, 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#10623360C2218yes—
23C2×#67000C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C22×#4326C2211yescharacteristic, complemented
26C2×#66992—21no—
27C2×#66990—21no—
28C2×D4×Dic11C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×#66982—21no—
32C2×C4×C22⋊D11—21no—
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×(C2×D11)⋊C4—21no—
35C2×#66977—21no—
36C2×#66977C2211yescharacteristic, complemented
37C22×#4314C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39#10623042—24no—
40#10623042C2218yescomplemented
41C2×#66950C2211yescharacteristic
42C2×#66949—21no—
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×#66942—21no—
45C2×#66941C2211yescharacteristic, complemented
46C2×#66940C2211yescharacteristic, complemented
47C11×#417C2218yescomplemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622852C2218yescomplemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622747C2218yescomplemented
57#10622740C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×#66882C2211yescharacteristic, complemented
61C2×#66880C2211yescharacteristic, complemented
62C2×#66879C2211yescharacteristic, complemented
63C2×Dic11⋊C8C2211yescharacteristic, complemented
64#10622580C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66871C2211yescharacteristic, complemented
68C2×#66871C2211yescharacteristic, complemented
69#10622426C2218yescomplemented
70#10622422C2218yescomplemented
71#10622411C2218yescomplemented
72#10622408C2218yescomplemented
73#10622389C2218yescomplemented
74D11×#102C2218yescomplemented
75#10622372C2218yescomplemented
76#10622370C2218yescomplemented
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⋊D11D411yescharacteristic
91C23×Dic11—21no—
92C2×D4×D11—24no—
93C2×D4×D11—22no—
94C2×D4×D11—42no—
95C2×D4×D11C2314yes—
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C22×C4×D11C2311yescharacteristic
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C2×C11×M16—42no—
102C2×C11×M16C2314yescomplemented
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2314yescomplemented
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11D411yescharacteristic
113#67000—22no—
114#67000C2314yes—
115#66999—22no—
116#66999C2314yes—
117C2×#4326—42no—
118C2×#4326C2314yescomplemented
119#66992—28no—
120#66990—28no—
121D4×Dic11—22no—
122D4×Dic11C2314yes—
123C2×#4324—24no—
124C2×#4324C2314yes—
125#66983—22no—
126#66983C2314yes—
127#66982—28no—
128C4×C22⋊D11—28no—
129C4×C22⋊D11D414yes—
130C4×C22⋊D11C2314yes—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—28no—
137C2×(C2×D11)⋊C4D411yescharacteristic
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—22no—
142#66977—28no—
143#66977C2314yescomplemented
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
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×#4314—42no—
155C2×#4314C2314yes—
156C2×C8×D11—42no—
157C2×C8×D11C2314yes—
158#66950—22no—
159#66950C2314yes—
160#66949—28no—
161C4⋊C4×D11—22no—
162C4⋊C4×D11C2314yes—
163#66942—28no—
164#66941—22no—
165#66941C2314yescomplemented
166#66940—22no—
167#66940C2314yescomplemented
168C11×#103C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#102C2314yes—
171C11×#102C2314yes—
172#66899C2314yescomplemented
173#66896C2314yes—
174C22⋊(C11⋊C8)C2314yescomplemented
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177#66882C2314yescomplemented
178#66880C2314yescomplemented
179#66879C2314yescomplemented
180Dic11⋊C8C2314yescomplemented
181#66873C2314yes—
182#66873C2314yes—
183#66871C2314yescomplemented
184#66871C2314yescomplemented
185C2×#3314—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C23×D11—21no—
189C23×D11—24no—
190C23×D11—44no—
191C23×D11—44no—
192C23×D11—82no—
193C23×D11C2×D411yescharacteristic
194C11×#41—28no—
195C11×#41—44no—
196C11×#41—48no—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11C2412yes—
201C2×D4×C11—24no—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—44no—
205C2×D4×C11#4114yes—
206C2×D4×C11C2412yes—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—24no—
213C22×C4×C11—24no—
214C22×C4×C11—44no—
215C22×C4×C11—82no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—82no—
225C2×C22⋊D11C2×D414yes—
226C22×Dic11—24no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—82no—
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234D4×D11—28no—
235D4×D11—44no—
236D4×D11—48no—
237C2×D44—21no—
238C2×D44—22no—
239C2×D44—22no—
240C2×D44C2412yes—
241C2×C4×D11—24no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—82no—
245C2×C4×D11C2×D412yes—
246C2×C4×D11C2412yes—
247C2×Dic22—24no—
248C2×Dic22—21no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22—82no—
252C2×Dic22C2412yes—
253C11×M16—44no—
254C2×C8×C11—22no—
255C2×C8×C11—22no—
256C2×C8×C11C2412yes—
257C2×C8×C11C2412yes—
258C11×C4⋊C4—21no—
259C11×C4⋊C4—21no—
260C11×C4⋊C4—24no—
261C11×C4⋊C4C2412yes—
262C11×C4⋊C4C2412yes—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11C2×D414yes—
266#4326—44no—
267#4324—28no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4C2×D414yes—
274C4⋊Dic11—24no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11C2412yes—
278C4⋊Dic11C2412yes—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—24no—
284Dic11⋊C4C2×D414yes—
285C4×Dic11—24no—
286C4×Dic11C2×D412yes—
287C4×Dic11C2412yes—
288C2×C11⋊C8—22no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8C2412yes—
291C2×C11⋊C8C2412yes—
292#4314—44no—
293C8×D11—44no—
294C2×#554—111no—
295C2×#546—111no—
296#3314—1116no—
297C2×#489—111no—
298C2×#484—111no—
299C2×#480—111no—
300C2×#474—111no—
301C2×#468—111no—
302C2×#467—111no—
303C2×#464—111no—
304C2×#452—111no—
305C2×#450—111no—
306C2×#440—111no—
307C2×#435—111no—
308C2×#417D1111yescharacteristic, complemented
309C22×#102—111no—
310C23×C11—24no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11C22×D412yes—
318C23×C11C22×D411yescharacteristic
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—48no—
323C22×D11—42no—
324C22×D11—42no—
325C22×D11—42no—
326C22×D11—48no—
327C22×D11—84no—
328C22×D11—816no—
329C22×D11#13714yes—
330C22×D11C22×D412yes—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—42no—
334D4×C11—24no—
335D4×C11—22no—
336D4×C11—48no—
337D4×C11C2×#4114yes—
338C2×C4×C11—22no—
339C2×C4×C11—24no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—48no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—84no—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C2×#4112yes—
353C2×C4×C11H(5,𝔽2)12yes—
354C2×C4×C11C2511yescharacteristic
355C22⋊D11—28no—
356C22⋊D11—48no—
357C22⋊D11—84no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—84no—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371D44—22no—
372D44—22no—
373D44—42no—
374C4×D11—24no—
375C4×D11—22no—
376C4×D11—22no—
377C4×D11—84no—
378Dic22—22no—
379Dic22—22no—
380Dic22—42no—
381Dic22—84no—
382C8×C11—22no—
383C8×C11—22no—
384C11⋊C8—22no—
385C11⋊C8—22no—
386C22×#41C2×D1111yescharacteristic
387C23×D4—111no—
388C22×Q16—111no—
389C22×SD16—111no—
390C22×SD16—111no—
391C22×M16C2×D1111yescharacteristic, complemented
392C23×C8—111no—
393#554—118no—
394#554—224no—
395#546—118no—
396#546—224no—
397C2×C4⋊Q8—111no—
398C2×#125—221no—
399C2×#124—111no—
400C2×#123—221no—
401C2×C22⋊Q8—111no—
402C2×C22⋊Q8—111no—
403C2×C22⋊Q8—111no—
404C2×C22⋊Q8—221no—
405C2×C22⋊Q8—221no—
406C2×#121—111no—
407C2×#121—221no—
408C2×#120—221no—
409C2×C4×Q8—111no—
410C2×C4×D4—111no—
411C2×C4×D4—111no—
412C2×C4×D4—221no—
413C22×C4⋊C4—111no—
414C22×C4⋊C4C2×D1111yescharacteristic, complemented
415C22×C22⋊C4—221no—
416#489—118no—
417#484—118no—
418#480—118no—
419#474—118no—
420#468—118no—
421#467—118no—
422#464—118no—
423#452—118no—
424#450—118no—
425#440—118no—
426#435—118no—
427C2×#107—111no—
428C2×#107—111no—
429C2×#107—111no—
430C2×C4⋊C8—111no—
431#417C2×D1118yescomplemented
432C2×#103—111no—
433C2×#103—111no—
434C2×#103C2×D1111yescharacteristic, complemented
435C2×#103C2×D1111yescharacteristic, complemented
436C2×#102—111no—
437C2×#102—111no—
438C2×#102—111no—
439C2×#102—111no—
440C2×#102—118no—
441C2×#102C2×D1111yescharacteristic
442C2×#102C2×D1111yescharacteristic
443C2×C22⋊C8—111no—
444C2×C22⋊C8—111no—
445C2×#97—111no—
446C22×C11—22no—
447C22×C11—24no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—48no—
451C22×C11—44no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11#54612yes—
455C22×C11C2×#13712yes—
456C22×C11#57612yes—
457C22×C11C23×D411yescharacteristic
458C2×D11—22no—
459C2×D11—28no—
460C2×D11—22no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—816no—
465C2×D11—84no—
466C2×D11C2×#13714yes—
467C4×C11—22no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11#54612yes—
472C4×C11C22×#4111yescharacteristic
473C4×C11C2×H(5,𝔽2)11yescharacteristic
474Dic11—22no—
475Dic11—22no—
476Dic11—22no—
477Dic11—42no—
478Dic11—42no—
479Dic11—42no—
480C25—221no—
481C2×#41—22no—
482C2×#41—24no—
483C2×#41—42no—
484C2×#41C22×D1114yes—
485C22×Q8—111no—
486C22×Q8—221no—
487C22×Q8C22×D1111yescharacteristic
488C22×D4—21no—
489C22×D4—111no—
490C22×D4—114no—
491C22×D4—111no—
492C22×D4—222no—
493C22×D4—221no—
494C22×D4—224no—
495C22×D4—221no—
496C22×D4—442no—
497C22×D4C22×D1111yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—111no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4C22×D1111yescharacteristic
504C2×Q16—114no—
505C2×Q16—442no—
506C2×SD16—114no—
507C2×SD16—114no—
508C2×SD16—224no—
509C2×SD16—442no—
510C2×M16—42no—
511C2×M16C22×D1114yescomplemented
512C22×C8—111no—
513C22×C8—111no—
514C22×C8—114no—
515C22×C8—442no—
516C22×C8C22×D1111yescharacteristic
517C22×C8C22×D1111yescharacteristic
518C4⋊Q8—114no—
519C4⋊Q8—222no—
520#125—228no—
521#124—114no—
522#124—222no—
523#123—228no—
524C22⋊Q8—114no—
525C22⋊Q8—114no—
526C22⋊Q8—114no—
527C22⋊Q8—228no—
528C22⋊Q8—228no—
529C22⋊Q8—222no—
530C22⋊Q8—222no—
531C22⋊Q8—222no—
532#121—114no—
533#121—228no—
534#121—222no—
535#120—228no—
536C4×Q8—114no—
537C4×Q8—222no—
538C4×D4—114no—
539C4×D4—114no—
540C4×D4—114no—
541C4×D4—222no—
542C4×D4—228no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—114no—
549C2×C4⋊C4—222no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C4⋊C4C22×D1114yescomplemented
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—228no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C42—111no—
570C2×C42—221no—
571#107—114no—
572#107—114no—
573#107—114no—
574C4⋊C8—114no—
575#103—114no—
576#103—114no—
577#103C22×D1114yescomplemented
578#103C22×D1114yescomplemented
579#102—114no—
580#102—114no—
581#102—114no—
582#102—114no—
583#102C22×D1114yes—
584#102C22×D1114yes—
585C22⋊C8—114no—
586C22⋊C8—114no—
587#97—114no—
588C2×C11—44no—
589C2×C11—42no—
590C2×C11#331414yescomplemented
591C2×C11C2×#54611yescharacteristic
592C2×C11C22×#13711yescharacteristic
593C2×C11C2×#57611yescharacteristic
594D11—24no—
595D11—82no—
596C24—21no—
597C24—111no—
598C24—224no—
599C24—221no—
600C24—444no—
601C24—444no—
602C24—882no—
603C24D4×D1111yescharacteristic
604#41—28no—
605#41—44no—
606#41—48no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—112no—
611C2×Q8—224no—
612C2×Q8—221no—
613C2×Q8—222no—
614C2×Q8—222no—
615C2×Q8—882no—
616C2×Q8C23×D1112yes—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—44no—
621C2×D4—114no—
622C2×D4—112no—
623C2×D4—224no—
624C2×D4—224no—
625C2×D4—228no—
626C2×D4—224no—
627C2×D4—222no—
628C2×D4—221no—
629C2×D4—222no—
630C2×D4—444no—
631C2×D4—448no—
632C2×D4—444no—
633C2×D4—882no—
634C2×D4#433914yes—
635C2×D4C23×D1112yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—82no—
645C22×C4—111no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—882no—
658C22×C4—882no—
659C22×C4D4×D1112yes—
660C22×C4D4×D1111yescharacteristic
661C22×C4C23×D1112yes—
662C22×C4C23×D1111yescharacteristic
663Q16—444no—
664SD16—228no—
665SD16—444no—
666M16—44no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—112no—
670C2×C8—112no—
671C2×C8—222no—
672C2×C8—222no—
673C2×C8—444no—
674C2×C8C23×D1112yes—
675C2×C8C23×D1112yes—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—24no—
679C4⋊C4—114no—
680C4⋊C4—112no—
681C4⋊C4—112no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—221no—
688C4⋊C4—221no—
689C4⋊C4—224no—
690C4⋊C4C23×D1112yes—
691C4⋊C4C23×D1112yes—
692C22⋊C4—114no—
693C22⋊C4—114no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C42—112no—
702C42—112no—
703C42—224no—
704C11C2×#331411yescharacteristic, complemented, Sylow
705C23—22no—
706C23—24no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—114no—
713C23—112no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—448no—
718C23—448no—
719C23—442no—
720C23—442no—
721C23—442no—
722C23—884no—
723C23—8816no—
724C23C2×D4×D1112yes—
725C23C2×D4×D1111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—222no—
730Q8—222no—
731Q8—442no—
732Q8—884no—
733D4—24no—
734D4—22no—
735D4—48no—
736D4—228no—
737D4—222no—
738D4—222no—
739D4—448no—
740D4—442no—
741D4—884no—
742D4C2×#433914yes—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—84no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—112no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—224no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—884no—
771C2×C4—884no—
772C2×C4C2×#433912yes—
773C2×C4C2×D4×D1112yes—
774C2×C4C2×D4×D1111yescharacteristic
775C2×C4#6703712yes—
776C2×C4C24×D1111yescharacteristic
777C8—22no—
778C8—22no—
779C8—222no—
780C8—222no—
781C22—22no—
782C22—24no—
783C22—22no—
784C22—22no—
785C22—44no—
786C22—48no—
787C22—42no—
788C22—42no—
789C22—114no—
790C22—228no—
791C22—222no—
792C22—222no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—8816no—
797C22—884no—
798C22#1062302112yes—
799C22#1062330512yes—
800C22D11×#13712yes—
801C22C22×D4×D1111yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—222no—
807C4—222no—
808C4—222no—
809C4—442no—
810C4—442no—
811C4—442no—
812C4#1062302112yes—
813C4C22×#433911yescharacteristic
814C4C2×#6703711yescharacteristic
815C2—42no—
816C2—44no—
817C2—224no—
818C2—882no—
819C2#1308069814yesdirect product factor
820C2C2×#1062302111yescharacteristic
821C2C2×D11×#13711yescharacteristic
822C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623360C2
hypercenterC2×#417D11
hypocenterC11C2×#3314
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×#10623042C2semidirect
3. #13080698C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622580C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622747C2semidirect
9. C2×#10622426C2semidirect
10. C2×#10622411C2semidirect
11. C2×#10622852C2semidirect
12. C2×#10622389C2semidirect
13. C2×#10622370C2semidirect
14. C2×#10622740C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#417C2semidirect
19. C22×C11×M16C22semidirect
20. C22×C11×C4⋊C4C22semidirect
25. C22×#4326C22semidirect
36. C2×#66977C22semidirect
40. #10623042C22semidirect
45. C2×#66941C22semidirect
46. C2×#66940C22semidirect
47. C11×#417C22semidirect
48. C2×C11×#103C22semidirect
49. C2×C11×#103C22semidirect
52. #10622852C22semidirect
53. C2×#66899C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622747C22semidirect
57. #10622740C22semidirect
60. C2×#66882C22semidirect
61. C2×#66880C22semidirect
62. C2×#66879C22semidirect
63. C2×Dic11⋊C8C22semidirect
64. #10622580C22semidirect
67. C2×#66871C22semidirect
68. C2×#66871C22semidirect
69. #10622426C22semidirect
70. #10622422C22semidirect
71. #10622411C22semidirect
72. #10622408C22semidirect
73. #10622389C22semidirect
74. D11×#102C22semidirect
75. #10622372C22semidirect
76. #10622370C22semidirect
102. C2×C11×M16C23semidirect
109. C2×C11×C4⋊C4C23semidirect
118. C2×#4326C23semidirect
143. #66977C23semidirect
165. #66941C23semidirect
167. #66940C23semidirect
168. C11×#103C23semidirect
169. C11×#103C23semidirect
172. #66899C23semidirect
174. C22⋊(C11⋊C8)C23semidirect
177. #66882C23semidirect
178. #66880C23semidirect
179. #66879C23semidirect
180. Dic11⋊C8C23semidirect
183. #66871C23semidirect
184. #66871C23semidirect
308. C2×#417D11semidirect
391. C22×M16C2×D11semidirect
414. C22×C4⋊C4C2×D11semidirect
431. #417C2×D11semidirect
434. C2×#103C2×D11semidirect
435. C2×#103C2×D11semidirect
511. C2×M16C22×D11semidirect
558. C2×C4⋊C4C22×D11semidirect
577. #103C22×D11semidirect
578. #103C22×D11semidirect
590. C2×C11#3314semidirect
704. C11C2×#3314semidirect
819. C2#13080698direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230422
C2×#106233602
#130806982
C2×#106224082
C2×#106224222
C2×#106225802
C2×#106223722
C2×#106227472
C2×#106224262
C2×#106224112
C2×#106228522
C2×#106223892
C2×#106223702
C2×#106227402
C2×D11×#1022
C2×C11×#4172
C2×#331411