Finite Group Databasebeta

← C2×#13079500 #15624461

Subgroups — C2×#13079500 #15624461

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×#10623364C211yesmaximal, characteristic
2C2×#10623356C211yesmaximal, characteristic, complemented
3#13079500C2116yesmaximal, direct product factor
4C2×#10622335C211yesmaximal, characteristic, complemented
5C2×#10622336C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622334C211yesmaximal, characteristic, complemented
8C2×#10622750C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622729C211yesmaximal, characteristic, complemented
11C2×#10622727C211yesmaximal, characteristic, complemented
12C2×#10622346C211yesmaximal, characteristic, complemented
13C2×#10622346C211yesmaximal, characteristic, complemented
14C2×#10622352C211yesmaximal, characteristic, complemented
15C2×#10622351C211yesmaximal, characteristic, complemented
16C2×C11×#408C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic
22#10623364—24no—
23#10623364C2218yes—
24#10623356—24no—
25#10623356C2218yescomplemented
26C2×#66999—21no—
27C2×#66997—21no—
28C2×#66992—21no—
29C2×#66992—21no—
30C2×#66991—21no—
31C2×#66989—21no—
32C2×#66988—21no—
33C2×#66988—21no—
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36C2×#66979C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39C2×#66977C2211yescharacteristic
40C2×#66977C2211yescharacteristic
41C2×#66977C2211yescharacteristic
42C2×#66977C2211yescharacteristic
43C2×#66977C2211yescharacteristic
44C22×Dic44C2211yescharacteristic
45C22×Dic44C2211yescharacteristic
46C22×#4314C2211yescharacteristic
47C22×#4314C2211yescharacteristic
48C11×#408C2218yescomplemented
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53#10622750C2218yescomplemented
54#10622747C2218yescomplemented
55#10622729C2218yescomplemented
56#10622727C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66881C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65C2×#66880C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69#10622352C2218yescomplemented
70#10622351C2218yescomplemented
71#10622350C2218yescomplemented
72#10622346C2218yescomplemented
73#10622346C2218yescomplemented
74#10622336C2218yescomplemented
75#10622335C2218yescomplemented
76#10622334C2218yescomplemented
77C2×C11×#41—42no—
78C2×C11×#41—42no—
79C2×C11×#41D414yes—
80C2×C11×#41C2314yes—
81C22×Q8×C11D411yescharacteristic
82C22×D4×C11D411yescharacteristic
83C22×D4×C11D411yescharacteristic
84C22×D4×C11D411yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C23×Dic11—21no—
92C23×Dic11—21no—
93C2×#4339—22no—
94C2×#4339—42no—
95C2×#4339—42no—
96C2×#4339C2314yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C22×Dic22—21no—
100C22×Dic22—22no—
101C22×Dic22—42no—
102C22×Dic22—42no—
103C22×Dic22C2311yescharacteristic
104C22×Dic22C2311yescharacteristic
105C22×Dic22C2311yescharacteristic
106C22×Dic22C2314yes—
107C2×C11×M16—42no—
108C2×C11×M16C2314yes—
109C22×C8×C11—42no—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2314yes—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122#66999—28no—
123#66997—28no—
124#66992—28no—
125#66992—28no—
126#66991—28no—
127#66989—28no—
128#66988—28no—
129#66988—28no—
130#66983—22no—
131#66983—22no—
132#66983C2314yes—
133#66983C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136#66979—22no—
137#66979C2314yes—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11—22no—
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2314yes—
145#66977—22no—
146#66977—22no—
147#66977—22no—
148#66977—22no—
149#66977—22no—
150#66977—22no—
151#66977C2314yes—
152#66977C2314yes—
153#66977C2314yes—
154#66977C2314yes—
155#66977C2314yes—
156#66977C2314yes—
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4—21no—
159C2×Dic11⋊C4—21no—
160C2×Dic11⋊C4—21no—
161C2×Dic11⋊C4—21no—
162C2×Dic11⋊C4—21no—
163C2×C4×Dic11—21no—
164C2×Dic44—42no—
165C2×Dic44—42no—
166C2×Dic44C2314yes—
167C2×Dic44C2314yes—
168C2×#4314—42no—
169C2×#4314—42no—
170C2×#4314C2314yes—
171C2×#4314C2314yes—
172C11×C22⋊C8C2314yes—
173C11×C22⋊C8C2314yes—
174C11×C22⋊C8C2314yes—
175C11×C22⋊C8C2314yes—
176#66885C2314yes—
177#66885C2314yes—
178#66882C2314yes—
179#66882C2314yes—
180#66881C2314yes—
181#66881C2314yes—
182#66880C2314yes—
183#66880C2314yes—
184#66880C2314yes—
185#66880C2314yes—
186#66880C2314yes—
187#66880C2314yes—
188C2×#3201—111nomaximal, Sylow
189C24×C11C2×D411yescharacteristic
190C24×C11C2×D411yescharacteristic
191C24×C11C2×D411yescharacteristic
192C23×D11—21no—
193C11×#41—48no—
194C11×#41—44no—
195C11×#41—44no—
196C2×Q8×C11—42no—
197C2×Q8×C11C2×D414yes—
198C2×D4×C11—42no—
199C2×D4×C11—42no—
200C2×D4×C11—42no—
201C2×D4×C11C2×D414yes—
202C2×D4×C11C2×D414yes—
203C2×D4×C11C2×D414yes—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
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⋊D11—82no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—24no—
234C22×Dic11—24no—
235C22×Dic11—44no—
236C22×Dic11—82no—
237#4339—44no—
238#4339—44no—
239#4339—48no—
240C2×D44—21no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44C2412yes—
244C2×C4×D11—24no—
245C2×C4×D11—44no—
246C2×Dic22—21no—
247C2×Dic22—21no—
248C2×Dic22—21no—
249C2×Dic22—24no—
250C2×Dic22—22no—
251C2×Dic22—22no—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22—22no—
256C2×Dic22—44no—
257C2×Dic22—44no—
258C2×Dic22—44no—
259C2×Dic22—48no—
260C2×Dic22C2412yes—
261C2×Dic22C2412yes—
262C2×Dic22C2412yes—
263C11×M16—44no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C2×C8×C11—22no—
268C2×C8×C11—44no—
269C2×C8×C11C2412yes—
270C2×C8×C11C2412yes—
271C2×C8×C11C2412yes—
272C2×C8×C11C2412yes—
273C22⋊Dic11—24no—
274C22⋊Dic11—24no—
275C22⋊Dic11—24no—
276C22⋊Dic11—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279C22⋊Dic11—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285C4⋊Dic11—21no—
286C4⋊Dic11—24no—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2412yes—
289C4⋊Dic11C2412yes—
290C4⋊Dic11C2412yes—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295Dic11⋊C4—24no—
296Dic11⋊C4—24no—
297C4×Dic11—24no—
298Dic44—44no—
299Dic44—44no—
300#4314—44no—
301#4314—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×#451—111no—
316C2×#448—111no—
317C2×#408D1111yescharacteristic, complemented
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11C22×D412yes—
328C23×C11C22×D412yes—
329C23×C11C22×D412yes—
330C23×C11C22×D411yescharacteristic
331C22×D11—22no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335Q8×C11—44no—
336D4×C11—44no—
337D4×C11—44no—
338D4×C11—44no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—24no—
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—22no—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D412yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C11H(5,𝔽2)12yes—
357C2×C4×C11C2511yescharacteristic
358C22⋊D11—48no—
359C22⋊D11—84no—
360C22⋊D11—84no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—48no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—42no—
376C2×Dic11—84no—
377D44—22no—
378D44—22no—
379D44—42no—
380C4×D11—48no—
381Dic22—22no—
382Dic22—22no—
383Dic22—22no—
384Dic22—22no—
385Dic22—22no—
386Dic22—22no—
387Dic22—48no—
388Dic22—42no—
389Dic22—42no—
390Dic22—42no—
391C8×C11—22no—
392C8×C11—22no—
393C8×C11—22no—
394C8×C11—22no—
395C22×#41—111no—
396C22×#41C2×D1111yescharacteristic
397C23×Q8—111no—
398C22×Q16—111no—
399C22×Q16—111no—
400C22×SD16—111no—
401C22×SD16—111no—
402C22×M16C2×D1111yescharacteristic
403C23×C8C2×D1111yescharacteristic
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—111no—
418C2×C22⋊Q8—221no—
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#451—118no—
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×#103—111no—
447C2×#103—111no—
448C2×#102—111no—
449C2×#102—111no—
450#408C2×D1118yescomplemented
451C2×C22⋊C8C2×D1111yescharacteristic
452C2×C22⋊C8C2×D1111yescharacteristic
453C2×C22⋊C8C2×D1111yescharacteristic
454C2×C22⋊C8C2×D1111yescharacteristic
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—44no—
465C22×C11—44no—
466C22×C11—44no—
467C22×C11#53412yes—
468C22×C11#57712yes—
469C22×C11#57812yes—
470C22×C11C23×D411yescharacteristic
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—84no—
475C4×C11—22no—
476C4×C11—22no—
477C4×C11—22no—
478C4×C11#53412yes—
479C4×C11C2×H(5,𝔽2)11yescharacteristic
480C4×C11C2×H(5,𝔽2)11yescharacteristic
481Dic11—42no—
482Dic11—42no—
483Dic11—42no—
484Dic11—42no—
485Dic11—42no—
486Dic11—42no—
487Dic11—42no—
488C2×#41—42no—
489C2×#41—42no—
490C2×#41—114no—
491C2×#41—222no—
492C2×#41—442no—
493C2×#41—442no—
494C2×#41D4414yes—
495C2×#41C22×D1114yes—
496C22×Q8—111no—
497C22×Q8—111no—
498C22×Q8—111no—
499C22×Q8—114no—
500C22×Q8—221no—
501C22×Q8—222no—
502C22×Q8—442no—
503C22×Q8—442no—
504C22×Q8D4411yescharacteristic
505C22×D4—111no—
506C22×D4—221no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4D4411yescharacteristic
510C22×D4D4411yescharacteristic
511C22×D4D4411yescharacteristic
512C23×C4—221no—
513C23×C4—221no—
514C23×C4—221no—
515C23×C4C22×D1111yescharacteristic
516C23×C4C22×D1111yescharacteristic
517C23×C4C22×D1111yescharacteristic
518C2×Q16—114no—
519C2×Q16—114no—
520C2×Q16—442no—
521C2×Q16—442no—
522C2×SD16—114no—
523C2×SD16—114no—
524C2×SD16—442no—
525C2×SD16—442no—
526C2×M16—42no—
527C2×M16C22×D1114yes—
528C22×C8—42no—
529C22×C8C22×D1111yescharacteristic
530C22×C8C22×D1111yescharacteristic
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533C22×C8C22×D1114yes—
534C4⋊Q8—228no—
535#124—228no—
536#123—228no—
537#123—228no—
538C22⋊Q8—114no—
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⋊Q8—222no—
551#121—114no—
552#121—114no—
553#121—228no—
554#121—228no—
555#121—228no—
556#121—222no—
557#121—222no—
558#117—114no—
559#117—222no—
560C2×C4⋊C4—111no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—111no—
565C2×C4⋊C4—221no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4—221no—
573C2×C22⋊C4—221no—
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#103—114no—
592#103—114no—
593#102—114no—
594#102—114no—
595C22⋊C8C22×D1114yes—
596C22⋊C8C22×D1114yes—
597C22⋊C8C22×D1114yes—
598C22⋊C8C22×D1114yes—
599C2×C11—42no—
600C2×C11—42no—
601C2×C11—42no—
602C2×C11#320114yescomplemented
603C2×C11C2×#53411yescharacteristic
604C2×C11C2×#57711yescharacteristic
605C2×C11C2×#57811yescharacteristic
606D11—82no—
607C24—221no—
608C24C2×D4411yescharacteristic
609C24C2×D4411yescharacteristic
610C24C2×D4411yescharacteristic
611#41—44no—
612#41—44no—
613#41—48no—
614#41—444no—
615#41—444no—
616#41—448no—
617C2×Q8—42no—
618C2×Q8—112no—
619C2×Q8—112no—
620C2×Q8—112no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×Q8—224no—
625C2×Q8—222no—
626C2×Q8—222no—
627C2×Q8—222no—
628C2×Q8—222no—
629C2×Q8—222no—
630C2×Q8—222no—
631C2×Q8—444no—
632C2×Q8—444no—
633C2×Q8—444no—
634C2×Q8—448no—
635C2×Q8C2×D4414yes—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—112no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—221no—
644C2×D4—222no—
645C2×D4—222no—
646C2×D4—444no—
647C2×D4—882no—
648C2×D4—882no—
649C2×D4C2×D4414yes—
650C2×D4C2×D4414yes—
651C2×D4C2×D4414yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—224no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—224no—
667C22×C4—224no—
668C22×C4—444no—
669C22×C4—444no—
670C22×C4—882no—
671C22×C4C2×D4412yes—
672C22×C4C2×D4412yes—
673C22×C4C2×D4412yes—
674C22×C4C2×D4411yescharacteristic
675C22×C4C2×D4411yescharacteristic
676C22×C4C2×D4411yescharacteristic
677C22×C4C23×D1112yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1111yescharacteristic
681Q16—444no—
682Q16—444no—
683SD16—444no—
684SD16—444no—
685M16—44no—
686C2×C8—22no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—44no—
691C2×C8C23×D1112yes—
692C2×C8C23×D1112yes—
693C2×C8C23×D1112yes—
694C2×C8C23×D1112yes—
695C4⋊C4—112no—
696C4⋊C4—112no—
697C4⋊C4—112no—
698C4⋊C4—112no—
699C4⋊C4—224no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—224no—
707C4⋊C4—224no—
708C4⋊C4—224no—
709C4⋊C4—224no—
710C22⋊C4—224no—
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—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—222no—
731C23—442no—
732C23—442no—
733C23—442no—
734C23C22×D4412yes—
735C23C22×D4412yes—
736C23C22×D4412yes—
737C23C22×D4411yescharacteristic
738Q8—44no—
739Q8—222no—
740Q8—222no—
741Q8—222no—
742Q8—222no—
743Q8—222no—
744Q8—222no—
745Q8—448no—
746Q8—442no—
747Q8—442no—
748Q8—442no—
749D4—44no—
750D4—44no—
751D4—44no—
752D4—222no—
753D4—222no—
754D4—448no—
755D4—442no—
756D4—884no—
757D4—884no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—448no—
778C2×C4—448no—
779C2×C4—442no—
780C2×C4—442no—
781C2×C4—442no—
782C2×C4—442no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4—442no—
786C2×C4—884no—
787C2×C4C22×D4412yes—
788C2×C4C22×D4412yes—
789C2×C4C22×D4412yes—
790C2×C4C22×D4411yescharacteristic
791C2×C4#6703712yes—
792C2×C4#6703712yes—
793C2×C4C24×D1111yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—442no—
811C22—442no—
812C22—442no—
813C22—884no—
814C22#1062302412yes—
815C22#1062328212yes—
816C22#1062328412yes—
817C22C23×D4411yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—442no—
822C4—442no—
823C4—442no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4—442no—
828C4#1062302412yes—
829C4C2×#6703711yescharacteristic
830C4C2×#6703711yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—882no—
835C2#1307950014yesdirect product factor
836C2C2×#1062302411yescharacteristic
837C2C2×#1062328211yescharacteristic
838C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#408C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC2×#408D11
hypocenterC11C2×#3201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#10623356C2semidirect
3. #13079500C2direct (N × H)
4. C2×#10622335C2semidirect
5. C2×#10622336C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622334C2semidirect
8. C2×#10622750C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622729C2semidirect
11. C2×#10622727C2semidirect
12. C2×#10622346C2semidirect
13. C2×#10622346C2semidirect
14. C2×#10622352C2semidirect
15. C2×#10622351C2semidirect
16. C2×C11×#408C2semidirect
25. #10623356C22semidirect
48. C11×#408C22semidirect
53. #10622750C22semidirect
54. #10622747C22semidirect
55. #10622729C22semidirect
56. #10622727C22semidirect
69. #10622352C22semidirect
70. #10622351C22semidirect
71. #10622350C22semidirect
72. #10622346C22semidirect
73. #10622346C22semidirect
74. #10622336C22semidirect
75. #10622335C22semidirect
76. #10622334C22semidirect
317. C2×#408D11semidirect
450. #408C2×D11semidirect
602. C2×C11#3201semidirect
720. C11C2×#3201semidirect
835. C2#13079500direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106233562
#130795002
C2×#106223352
C2×#106223362
C2×#106223502
C2×#106223342
C2×#106227502
C2×#106227472
C2×#106227292
C2×#106227272
C2×#106223462
C2×#106223522
C2×#106223512
C2×C11×#4082
C2×#320111