Finite Group Databasebeta

← C2×#13079450 #15624395

Subgroups — C2×#13079450 #15624395

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
3#13079450C2116yesmaximal, direct product factor
4C2×#10622497C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622609C211yesmaximal, characteristic, complemented
7C2×#10622481C211yesmaximal, characteristic, complemented
8C2×#10622429C211yesmaximal, characteristic, complemented
9C2×#10622425C211yesmaximal, characteristic, complemented
10C2×#10622499C211yesmaximal, characteristic, complemented
11C2×#10622346C211yesmaximal, characteristic, complemented
12C2×#10622660C211yesmaximal, characteristic, complemented
13C2×#10622421C211yesmaximal, characteristic, complemented
14C2×#10622419C211yesmaximal, characteristic, complemented
15C2×#10622339C211yesmaximal, characteristic, complemented
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C22×#4326C2211yescharacteristic, complemented
24C22×#4325C2211yescharacteristic, complemented
25C2×#66977C2211yescharacteristic
26C22×Dic44C2211yescharacteristic, complemented
27C22×#4314C2211yescharacteristic, complemented
28C22×#4313C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30D11×C22⋊Q8—24no—
31D11×C22⋊Q8C2218yescomplemented
32#10623055—24no—
33#10623055C2218yes—
34C2×#66950C2211yescharacteristic
35C2×#66950C2211yescharacteristic
36C2×#66950C2211yescharacteristic
37C2×#66949—21no—
38C2×#66948C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×C4⋊C4×D11—21no—
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66939—21no—
43C2×#66935—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66931—21no—
46C2×C4×D44—21no—
47C2×C4×D44—21no—
48C11×#485C2218yescomplemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×#106C2211yescharacteristic, complemented
51C2×C11×#103C2211yescharacteristic, complemented
52C2×C11×#103C2211yescharacteristic, complemented
53C2×C11×C22⋊C8C2211yescharacteristic
54C2×C22⋊(C11⋊C8)C2211yescharacteristic
55C2×#66885C2211yescharacteristic, complemented
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66880C2211yescharacteristic, complemented
59#10622660C2218yescomplemented
60#10622609C2218yescomplemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66874C2211yescharacteristic, complemented
63C2×#66874C2211yescharacteristic, complemented
64C2×#66873C2211yescharacteristic, complemented
65C2×#66872C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622499C2218yescomplemented
68#10622497C2218yescomplemented
69#10622481C2218yescomplemented
70#10622476C2218yescomplemented
71#10622429C2218yescomplemented
72#10622425C2218yescomplemented
73#10622421C2218yescomplemented
74#10622419C2218yescomplemented
75#10622346C2218yescomplemented
76#10622339C2218yescomplemented
77C24×D11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C23×Dic11D411yescharacteristic
82C2×Q8×D11—22no—
83C2×Q8×D11—42no—
84C2×Q8×D11—42no—
85C2×Q8×D11C2314yes—
86C2×#4339—22no—
87C2×#4339—42no—
88C2×#4339—42no—
89C2×#4339C2314yes—
90C22×D44—21no—
91C22×D44—21no—
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11—21no—
96C22×C4×D11—42no—
97C22×C4×D11—42no—
98C22×C4×D11D411yescharacteristic
99C22×C4×D11D411yescharacteristic
100C22×C4×D11D414yes—
101C22×C4×D11C2311yescharacteristic
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2314yes—
104C22×Dic22—21no—
105C22×Dic22C2311yescharacteristic
106C22×Dic22C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8C2314yes—
111C11×#117—22no—
112C11×#117C2314yes—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4—21no—
119C2×C42×C11—21no—
120C2×C22⋊Dic11—21no—
121#66999—22no—
122#66999C2314yes—
123C2×#4326—42no—
124C2×#4326C2314yescomplemented
125C2×#4325—42no—
126C2×#4325C2314yescomplemented
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11C2311yescharacteristic
137#66977—22no—
138#66977C2314yes—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C2×Dic44—42no—
145C2×Dic44C2314yescomplemented
146C2×#4314—42no—
147C2×#4314C2314yescomplemented
148C2×#4313—42no—
149C2×#4313—42no—
150C2×#4313C2314yes—
151C2×#4313C2314yes—
152#66950—22no—
153#66950—22no—
154#66950—22no—
155#66950C2314yes—
156#66950C2314yes—
157#66950C2314yes—
158#66949—28no—
159#66948—22no—
160#66948—22no—
161#66948C2314yes—
162#66948C2314yes—
163C4⋊C4×D11—28no—
164C4⋊C4×D11—22no—
165C4⋊C4×D11C2314yes—
166#66939—28no—
167#66935—28no—
168C22⋊C4×D11—28no—
169#66931—28no—
170C4×D44—28no—
171C4×D44—28no—
172C11×#107C2314yescomplemented
173C11×#106C2314yescomplemented
174C11×#103C2314yescomplemented
175C11×#103C2314yescomplemented
176C11×C22⋊C8C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178#66885C2314yescomplemented
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181#66880C2314yescomplemented
182#66874C2314yescomplemented
183#66874C2314yescomplemented
184#66874C2314yescomplemented
185#66873C2314yescomplemented
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3196—111nomaximal, Sylow
189C24×C11C2×D411yescharacteristic
190C23×D11—24no—
191C23×D11—21no—
192C23×D11—42no—
193C23×D11—42no—
194C23×D11C2×D411yescharacteristic
195C23×D11C2×D411yescharacteristic
196C23×D11C2×D414yes—
197C2×Q8×C11—21no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11C2412yes—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—24no—
212C2×C22⋊D11—44no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—42no—
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D414yes—
220Q8×D11—44no—
221Q8×D11—44no—
222Q8×D11—48no—
223#4339—44no—
224#4339—44no—
225#4339—48no—
226C2×D44—24no—
227C2×D44—24no—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—44no—
232C2×D44—44no—
233C2×D44C2412yes—
234C2×C4×D11—24no—
235C2×C4×D11—24no—
236C2×C4×D11—24no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—42no—
242C2×C4×D11—42no—
243C2×C4×D11—48no—
244C2×C4×D11—44no—
245C2×C4×D11—44no—
246C2×C4×D11—44no—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11C2×D412yes—
250C2×C4×D11C2×D412yes—
251C2×C4×D11C2×D414yes—
252C2×C4×D11C2×D414yes—
253C2×C4×D11C2412yes—
254C2×C4×D11C2412yes—
255C2×Dic22—24no—
256C2×Dic22—21no—
257C2×Dic22—21no—
258C2×Dic22—22no—
259C2×Dic22—22no—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22—44no—
263C2×Dic22C2412yes—
264C2×Dic22C2412yes—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4C2412yes—
274C11×C4⋊C4C2412yes—
275C11×C4⋊C4C2412yes—
276C11×C22⋊C4—24no—
277C11×C22⋊C4—24no—
278C42×C11—24no—
279C22⋊Dic11—24no—
280#4326—44no—
281#4325—44no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288C4⋊Dic11—24no—
289C4⋊Dic11—24no—
290C4⋊Dic11—24no—
291C4⋊Dic11—21no—
292C4⋊Dic11C2412yes—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295Dic11⋊C4—24no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300Dic44—44no—
301#4314—44no—
302#4313—44no—
303#4313—44no—
304C2×#525—111no—
305C22×C22⋊Q8—111no—
306#3196—1116no—
307C2×#484—111no—
308C2×#481—111no—
309C2×#485—111no—
310C2×#485D1111yescharacteristic, complemented
311C2×#470—111no—
312C2×#470—111no—
313C2×#468—111no—
314C2×#468—111no—
315C2×#452—111no—
316C2×#452—111no—
317C2×#451—111no—
318C2×#448—111no—
319C2×#407—111no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11C22×D412yes—
324C23×C11C22×D411yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—28no—
331C22×D11—22no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—416no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11#13714yes—
339C22×D11C22×D412yes—
340C22×D11C22×D412yes—
341Q8×C11—22no—
342Q8×C11—22no—
343Q8×C11—42no—
344C2×C4×C11—22no—
345C2×C4×C11—24no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C11H(5,𝔽2)12yes—
360C2×C4×C11C2511yescharacteristic
361C22⋊D11—48no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—44no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11C22×D412yes—
372C2×Dic11C22×D412yes—
373D44—22no—
374D44—22no—
375D44—48no—
376D44—48no—
377D44—42no—
378C4×D11—24no—
379C4×D11—24no—
380C4×D11—22no—
381C4×D11—22no—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—44no—
385C4×D11—44no—
386C4×D11—48no—
387C4×D11—48no—
388C4×D11—48no—
389Dic22—22no—
390Dic22—22no—
391Dic22—22no—
392Dic22—22no—
393Dic22—48no—
394Dic22—42no—
395Dic22—42no—
396C8×C11—22no—
397C8×C11—22no—
398C11⋊C8—22no—
399C11⋊C8—22no—
400C22×#41—111no—
401C23×Q8—111no—
402C24×C4—111no—
403C22×Q16—111no—
404C22×Q16—111no—
405C22×SD16—111no—
406C22×SD16—111no—
407C22×M16—111no—
408C22×M16—111no—
409#525—118no—
410#525—224no—
411C2×#123—221no—
412C2×C22⋊Q8—111no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—118no—
415C2×C22⋊Q8—111no—
416C2×C22⋊Q8—111no—
417C2×C22⋊Q8—111no—
418C2×C22⋊Q8—221no—
419C2×C22⋊Q8—221no—
420C2×C22⋊Q8—224no—
421C2×C22⋊Q8C2×D1111yescharacteristic
422C2×#121—111no—
423C2×#121—111no—
424C2×#120—221no—
425C2×C4×D4—221no—
426C2×C4×D4—221no—
427C2×#117C2×D1111yescharacteristic
428C22×C4⋊C4—111no—
429C22×C4⋊C4—221no—
430C22×C22⋊C4—221no—
431#485—118no—
432#485C2×D1118yescomplemented
433#484—118no—
434#481—118no—
435#470—118no—
436#470—118no—
437#468—118no—
438#468—118no—
439#452—118no—
440#452—118no—
441#451—118no—
442#448—118no—
443C2×#107—111no—
444C2×#107C2×D1111yescharacteristic, complemented
445C2×#106—111no—
446C2×#106C2×D1111yescharacteristic, complemented
447C2×#103—111no—
448C2×#103—111no—
449C2×#103—111no—
450C2×#103—111no—
451C2×#103C2×D1111yescharacteristic, complemented
452C2×#103C2×D1111yescharacteristic, complemented
453C2×#102—111no—
454C2×#102—111no—
455#407—118no—
456C2×C22⋊C8—111no—
457C2×C22⋊C8—111no—
458C2×C22⋊C8—111no—
459C2×C22⋊C8C2×D1111yescharacteristic
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—44no—
464C22×C11#53412yes—
465C22×C11C2×#13712yes—
466C22×C11#57512yes—
467C22×C11C23×D411yescharacteristic
468C2×D11—22no—
469C2×D11—28no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—416no—
475C2×D11—44no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—84no—
480C2×D11C2×#13714yes—
481C4×C11—22no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11#53412yes—
487C4×C11C2×H(5,𝔽2)11yescharacteristic
488C4×C11C2×H(5,𝔽2)11yescharacteristic
489Dic11—22no—
490Dic11—22no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494C25—111no—
495C2×#41—114no—
496C2×#41—222no—
497C2×#41—442no—
498C2×#41—442no—
499C22×Q8—114no—
500C22×Q8—111no—
501C22×Q8—111no—
502C22×Q8—221no—
503C22×Q8—222no—
504C22×Q8—442no—
505C22×Q8—442no—
506C22×Q8C22×D1111yescharacteristic
507C22×D4—111no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—114no—
517C23×C4—114no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4—442no—
522C23×C4—442no—
523C23×C4C22×D1111yescharacteristic
524C2×Q16—114no—
525C2×Q16—114no—
526C2×Q16—442no—
527C2×Q16—442no—
528C2×SD16—114no—
529C2×SD16—114no—
530C2×SD16—442no—
531C2×SD16—442no—
532C2×M16—114no—
533C2×M16—114no—
534C2×M16—442no—
535C2×M16—442no—
536C22×C8—111no—
537C22×C8—111no—
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540#123—228no—
541C22⋊Q8—22no—
542C22⋊Q8—114no—
543C22⋊Q8—114no—
544C22⋊Q8—114no—
545C22⋊Q8—114no—
546C22⋊Q8—114no—
547C22⋊Q8—228no—
548C22⋊Q8—228no—
549C22⋊Q8—222no—
550C22⋊Q8—222no—
551C22⋊Q8—222no—
552C22⋊Q8—222no—
553C22⋊Q8—222no—
554C22⋊Q8C22×D1114yes—
555#121—114no—
556#121—114no—
557#121—222no—
558#121—222no—
559#120—228no—
560C4×D4—228no—
561C4×D4—228no—
562#117—22no—
563#117C22×D1114yes—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—111no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—228no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4—221no—
573C2×C4⋊C4—221no—
574C2×C4⋊C4—221no—
575C2×C4⋊C4C22×D1111yescharacteristic
576C2×C4⋊C4C22×D1111yescharacteristic
577C2×C4⋊C4C22×D1111yescharacteristic
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—228no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4—221no—
583C2×C22⋊C4—221no—
584C2×C22⋊C4—221no—
585C2×C22⋊C4—221no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C42—21no—
589#107—114no—
590#107C22×D1114yescomplemented
591#106—114no—
592#106C22×D1114yescomplemented
593#103—114no—
594#103—114no—
595#103—114no—
596#103—114no—
597#103C22×D1114yescomplemented
598#103C22×D1114yescomplemented
599#102—114no—
600#102—114no—
601C22⋊C8—114no—
602C22⋊C8—114no—
603C22⋊C8—114no—
604C22⋊C8C22×D1114yes—
605C2×C11—42no—
606C2×C11#319614yescomplemented
607C2×C11C2×#53411yescharacteristic
608C2×C11C22×#13711yescharacteristic
609C2×C11C2×#57511yescharacteristic
610D11—24no—
611D11—42no—
612D11—82no—
613C24—111no—
614C24—111no—
615C24—114no—
616C24—224no—
617C24—221no—
618C24—442no—
619C24—442no—
620C24D4×D1111yescharacteristic
621#41—444no—
622#41—444no—
623#41—448no—
624C2×Q8—21no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—112no—
628C2×Q8—112no—
629C2×Q8—224no—
630C2×Q8—221no—
631C2×Q8—221no—
632C2×Q8—222no—
633C2×Q8—222no—
634C2×Q8—222no—
635C2×Q8—222no—
636C2×Q8—444no—
637C2×Q8—444no—
638C2×Q8—444no—
639C2×Q8—448no—
640C2×Q8C23×D1112yes—
641C2×D4—112no—
642C2×D4—224no—
643C2×D4—224no—
644C2×D4—224no—
645C2×D4—221no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—444no—
649C2×D4—444no—
650C2×D4—444no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—114no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—114no—
665C22×C4—114no—
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—224no—
676C22×C4—448no—
677C22×C4—444no—
678C22×C4—444no—
679C22×C4—442no—
680C22×C4—442no—
681C22×C4—444no—
682C22×C4—444no—
683C22×C4—444no—
684C22×C4—442no—
685C22×C4D4×D1112yes—
686C22×C4D4×D1111yescharacteristic
687C22×C4C23×D1112yes—
688C22×C4C23×D1111yescharacteristic
689Q16—444no—
690Q16—444no—
691SD16—444no—
692SD16—444no—
693M16—444no—
694M16—444no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—112no—
698C2×C8—112no—
699C2×C8—222no—
700C2×C8—222no—
701C2×C8C23×D1112yes—
702C2×C8C23×D1112yes—
703C4⋊C4—24no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—112no—
708C4⋊C4—224no—
709C4⋊C4—224no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—221no—
714C4⋊C4—224no—
715C4⋊C4C23×D1112yes—
716C4⋊C4C23×D1112yes—
717C4⋊C4C23×D1112yes—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—224no—
721C22⋊C4—224no—
722C22⋊C4—224no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C42—24no—
728C11C2×#319611yescharacteristic, complemented, Sylow
729C23—22no—
730C23—22no—
731C23—22no—
732C23—114no—
733C23—112no—
734C23—112no—
735C23—228no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—444no—
743C23—444no—
744C23—4416no—
745C23—442no—
746C23—442no—
747C23—442no—
748C23C2×D4×D1112yes—
749C23C2×D4×D1111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—42no—
753Q8—222no—
754Q8—222no—
755Q8—222no—
756Q8—222no—
757Q8—448no—
758Q8—442no—
759Q8—442no—
760D4—222no—
761D4—222no—
762D4—448no—
763D4—448no—
764D4—448no—
765D4—442no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—112no—
779C2×C4—112no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—224no—
783C2×C4—224no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—444no—
792C2×C4—444no—
793C2×C4—448no—
794C2×C4—448no—
795C2×C4—448no—
796C2×C4—444no—
797C2×C4—442no—
798C2×C4—442no—
799C2×C4—442no—
800C2×C4C2×D4×D1112yes—
801C2×C4C2×D4×D1111yescharacteristic
802C2×C4#6704212yes—
803C2×C4#6704212yes—
804C2×C4C24×D1111yescharacteristic
805C8—22no—
806C8—22no—
807C8—222no—
808C8—222no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—114no—
814C22—222no—
815C22—228no—
816C22—222no—
817C22—222no—
818C22—222no—
819C22—222no—
820C22—4416no—
821C22—444no—
822C22—442no—
823C22—442no—
824C22—442no—
825C22—884no—
826C22#1062318412yes—
827C22#1062329912yes—
828C22D11×#13712yes—
829C22C22×D4×D1111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—222no—
836C4—222no—
837C4—442no—
838C4—442no—
839C4—442no—
840C4#1062318412yes—
841C4C2×#6704211yescharacteristic
842C4C2×#6704211yescharacteristic
843C2—42no—
844C2—224no—
845C2—442no—
846C2—882no—
847C2#1307945014yesdirect product factor
848C2C2×#1062318411yescharacteristic
849C2C2×D11×#13711yescharacteristic
850C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC2×#10623055C2
hypercenterC2×#485D11
hypocenterC11C2×#3196
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊Q8C2semidirect
3. #13079450C2direct (N × H)
4. C2×#10622497C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622609C2semidirect
7. C2×#10622481C2semidirect
8. C2×#10622429C2semidirect
9. C2×#10622425C2semidirect
10. C2×#10622499C2semidirect
11. C2×#10622346C2semidirect
12. C2×#10622660C2semidirect
13. C2×#10622421C2semidirect
14. C2×#10622419C2semidirect
15. C2×#10622339C2semidirect
16. C2×C11×#485C2semidirect
23. C22×#4326C22semidirect
24. C22×#4325C22semidirect
26. C22×Dic44C22semidirect
27. C22×#4314C22semidirect
31. D11×C22⋊Q8C22semidirect
48. C11×#485C22semidirect
49. C2×C11×#107C22semidirect
50. C2×C11×#106C22semidirect
51. C2×C11×#103C22semidirect
52. C2×C11×#103C22semidirect
55. C2×#66885C22semidirect
58. C2×#66880C22semidirect
59. #10622660C22semidirect
60. #10622609C22semidirect
61. C2×#66874C22semidirect
62. C2×#66874C22semidirect
63. C2×#66874C22semidirect
64. C2×#66873C22semidirect
65. C2×#66872C22semidirect
66. C2×#66871C22semidirect
67. #10622499C22semidirect
68. #10622497C22semidirect
69. #10622481C22semidirect
70. #10622476C22semidirect
71. #10622429C22semidirect
72. #10622425C22semidirect
73. #10622421C22semidirect
74. #10622419C22semidirect
75. #10622346C22semidirect
76. #10622339C22semidirect
124. C2×#4326C23semidirect
126. C2×#4325C23semidirect
145. C2×Dic44C23semidirect
147. C2×#4314C23semidirect
172. C11×#107C23semidirect
173. C11×#106C23semidirect
174. C11×#103C23semidirect
175. C11×#103C23semidirect
178. #66885C23semidirect
181. #66880C23semidirect
182. #66874C23semidirect
183. #66874C23semidirect
184. #66874C23semidirect
185. #66873C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
310. C2×#485D11semidirect
432. #485C2×D11semidirect
444. C2×#107C2×D11semidirect
446. C2×#106C2×D11semidirect
451. C2×#103C2×D11semidirect
452. C2×#103C2×D11semidirect
590. #107C22×D11semidirect
592. #106C22×D11semidirect
597. #103C22×D11semidirect
598. #103C22×D11semidirect
606. C2×C11#3196semidirect
728. C11C2×#3196semidirect
847. C2#13079450direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×D11×C22⋊Q82
#130794502
C2×#106224972
C2×#106224762
C2×#106226092
C2×#106224812
C2×#106224292
C2×#106224252
C2×#106224992
C2×#106223462
C2×#106226602
C2×#106224212
C2×#106224192
C2×#106223392
C2×C11×#4852
C2×#319611