Finite Group Databasebeta

← C2×#13080260 #15628917

Subgroups — C2×#13080260 #15628917

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic, complemented
2C22×#66968C211yesmaximal, characteristic, complemented
3C2×#10623163C211yesmaximal, characteristic, complemented
4C2×#10623355C211yesmaximal, characteristic
5#13080260C2116yesmaximal, direct product factor
6C2×#10622794C211yesmaximal, characteristic, complemented
7C2×#10622429C211yesmaximal, characteristic, complemented
8C2×#10622665C211yesmaximal, characteristic, complemented
9C2×#10622406C211yesmaximal, characteristic, complemented
10C2×#10622775C211yesmaximal, characteristic, complemented
11C2×#10622396C211yesmaximal, characteristic, complemented
12C2×#10622352C211yesmaximal, characteristic, complemented
13C2×#10622799C211yesmaximal, characteristic, complemented
14C2×#10622371C211yesmaximal, characteristic, complemented
15C2×#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×#4341C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×Q16C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24#10623355—24no—
25#10623355C2218yes—
26C2×#67004—28no—
27C2×#67004C2218yescomplemented
28C2×#66999C2211yescharacteristic
29C2×#66997C2211yescharacteristic
30C2×#66997C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C22×#4326C2211yescharacteristic
34C2×#66992—21no—
35C2×#66988—21no—
36C2×D4×Dic11C2211yescharacteristic
37C22×#4324C2211yescharacteristic
38C22×#4324C2211yescharacteristic
39C2×#66982—21no—
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×#66977C2211yescharacteristic
42C22×Dic11⋊C4—21no—
43C22×#4318C2211yescharacteristic
44C2×#66968—28no—
45C2×#66968C2218yescomplemented
46C22×Dic44C2211yescharacteristic
47C22×Dic44C2211yescharacteristic
48C22×#4313C2211yescharacteristic
49#10623163—24no—
50#10623163C2218yescomplemented
51C2×#66950C2211yescharacteristic
52C2×#66949—21no—
53C2×#66941—21no—
54C2×#66940C2211yescharacteristic
55C2×(C22⋊D11)⋊C4—21no—
56C2×#66931—21no—
57C11×#452C2218yescomplemented
58C2×C11×#103C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C2×#66899C2211yescharacteristic
62#10622799C2218yescomplemented
63#10622794C2218yescomplemented
64#10622775C2218yescomplemented
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×Dic11⋊C8C2211yescharacteristic
69C2×C8×Dic11C2211yescharacteristic
70#10622665C2218yescomplemented
71C2×#66874C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73#10622429C2218yescomplemented
74#10622406C2218yescomplemented
75#10622396C2218yescomplemented
76#10622371C2218yescomplemented
77#10622352C2218yescomplemented
78#10622342C2218yescomplemented
79C2×C11×#41—22no—
80C2×C11×#41—24no—
81C2×C11×#41—42no—
82C2×C11×#41C2314yes—
83C22×Q8×C11C2311yescharacteristic
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11—21no—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×C22⋊D11D411yescharacteristic
91C23×Dic11—21no—
92C23×Dic11—21no—
93C23×Dic11—21no—
94C2×Q8×D11—22no—
95C2×Q8×D11—24no—
96C2×Q8×D11—42no—
97C2×Q8×D11C2314yes—
98C2×#4341—24no—
99C2×#4341—22no—
100C2×#4341—42no—
101C2×#4341C2314yes—
102C22×C4×D11—21no—
103C22×C4×D11C2311yescharacteristic
104C22×Dic22—24no—
105C22×Dic22—21no—
106C22×Dic22—22no—
107C22×Dic22—21no—
108C22×Dic22—42no—
109C22×Dic22C2311yescharacteristic
110C22×Dic22C2311yescharacteristic
111C22×Dic22C2314yes—
112C22×Dic22C2311yescharacteristic
113C2×C11×Q16—42no—
114C2×C11×Q16C2314yes—
115C2×C11×SD16—24no—
116C2×C11×SD16C2314yes—
117C22×C8×C11C2311yescharacteristic
118C22×C8×C11C2311yescharacteristic
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2314yes—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11D411yescharacteristic
127#67004—232no—
128#66999—22no—
129#66999C2314yes—
130#66997—22no—
131#66997—22no—
132#66997C2314yes—
133#66997C2314yes—
134C2×#4326—24no—
135C2×#4326—24no—
136C2×#4326—24no—
137C2×#4326C2314yes—
138C2×#4326C2314yes—
139C2×#4326C2314yes—
140#66992—28no—
141#66988—28no—
142D4×Dic11—22no—
143D4×Dic11C2314yes—
144C2×#4324—24no—
145C2×#4324D418yescomplemented
146C2×#4324C2314yes—
147C2×#4324C2314yes—
148#66982—28no—
149C4×C22⋊D11D414yes—
150C4×C22⋊D11C2314yes—
151C2×(C2×D11)⋊C4—21no—
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4D411yescharacteristic
154C2×C4⋊Dic11—21no—
155C2×C4⋊Dic11C2311yescharacteristic
156#66977—22no—
157#66977C2314yes—
158C2×Dic11⋊C4—21no—
159C2×Dic11⋊C4—21no—
160C2×Dic11⋊C4—21no—
161C2×Dic11⋊C4—21no—
162C2×Dic11⋊C4—21no—
163C2×Dic11⋊C4—21no—
164C2×Dic11⋊C4—21no—
165C2×Dic11⋊C4—28no—
166C2×Dic11⋊C4D411yescharacteristic
167C2×C4×Dic11—21no—
168C2×C4×Dic11C2311yescharacteristic
169C2×#4318—24no—
170C2×#4318C2314yes—
171C22×C11⋊C8C2311yescharacteristic
172C22×C11⋊C8C2311yescharacteristic
173#66968—232no—
174C2×Dic44—24no—
175C2×Dic44—42no—
176C2×Dic44C2314yes—
177C2×Dic44C2314yes—
178C2×#4313—24no—
179C2×#4313C2314yes—
180#66950—22no—
181#66950C2314yes—
182#66949—28no—
183#66941—28no—
184#66940—22no—
185#66940C2314yes—
186(C22⋊D11)⋊C4—28no—
187#66931—28no—
188C11×#103C2314yes—
189C11×#102C2314yes—
190C11×C22⋊C8C2314yes—
191#66899C2314yes—
192(C2×D11)⋊C8C2314yes—
193#66880C2314yes—
194#66880C2314yes—
195Dic11⋊C8C2314yes—
196C8×Dic11C2314yes—
197#66874C2314yes—
198#66872C2314yes—
199C2×#3276—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11C2×D411yescharacteristic
203C11×#41—28no—
204C11×#41—44no—
205C11×#41—48no—
206C2×Q8×C11—21no—
207C2×Q8×C11—21no—
208C2×Q8×C11—22no—
209C2×Q8×C11—22no—
210C2×Q8×C11—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11C2412yes—
213C2×Q8×C11C2412yes—
214C2×D4×C11—24no—
215C2×D4×C11—21no—
216C2×D4×C11—22no—
217C2×D4×C11—44no—
218C2×D4×C11C2×D414yes—
219C2×D4×C11C2412yes—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—24no—
226C22×C4×C11—44no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2411yescharacteristic
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11C2×D414yes—
235C22×Dic11—24no—
236C22×Dic11—24no—
237C22×Dic11—21no—
238C22×Dic11—24no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—44no—
243C22×Dic11—44no—
244C22×Dic11—44no—
245C22×Dic11C2×D411yescharacteristic
246C22×Dic11C2×D411yescharacteristic
247C22×Dic11C2×D411yescharacteristic
248Q8×D11—28no—
249Q8×D11—44no—
250Q8×D11—48no—
251#4341—28no—
252#4341—44no—
253#4341—48no—
254C2×C4×D11—24no—
255C2×C4×D11—22no—
256C2×C4×D11—22no—
257C2×C4×D11—44no—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2412yes—
260C2×Dic22—28no—
261C2×Dic22—24no—
262C2×Dic22—21no—
263C2×Dic22—22no—
264C2×Dic22—22no—
265C2×Dic22—24no—
266C2×Dic22—21no—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22—22no—
270C2×Dic22—22no—
271C2×Dic22—44no—
272C2×Dic22—48no—
273C2×Dic22—44no—
274C2×Dic22—44no—
275C2×Dic22C2×D414yes—
276C2×Dic22C2412yes—
277C2×Dic22C2412yes—
278C2×Dic22C2412yes—
279C11×Q16—44no—
280C11×SD16—28no—
281C2×C8×C11—22no—
282C2×C8×C11—22no—
283C2×C8×C11C2412yes—
284C2×C8×C11C2412yes—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—24no—
287C11×C4⋊C4C2412yes—
288C11×C22⋊C4—24no—
289C22⋊Dic11—24no—
290C22⋊Dic11—24no—
291C22⋊Dic11C2×D414yes—
292#4326—28no—
293#4326—28no—
294#4326—28no—
295#4324—28no—
296#4324C2×D4116yescomplemented
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4C2×D414yes—
300C4⋊Dic11—24no—
301C4⋊Dic11—21no—
302C4⋊Dic11C2412yes—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4—24no—
309Dic11⋊C4—24no—
310Dic11⋊C4C2×D414yes—
311C4×Dic11—24no—
312C4×Dic11C2×D412yes—
313C4×Dic11C2412yes—
314#4318—28no—
315C2×C11⋊C8—22no—
316C2×C11⋊C8C2×D414yes—
317C2×C11⋊C8C2412yes—
318C2×C11⋊C8C2412yes—
319Dic44—28no—
320Dic44—44no—
321#4313—28no—
322C22×#137—111no—
323C22×#137—111no—
324C2×D4×Q8—111no—
325C2×#547—111no—
326#3276—1116no—
327C2×#494—111no—
328C2×#470—111no—
329C2×#470—111no—
330C2×#462—111no—
331C2×#461—111no—
332C2×#452—111no—
333C2×#452D1111yescharacteristic, complemented
334C2×#451—111no—
335C2×#451—111no—
336C2×C4×SD16—111no—
337C2×#436—111no—
338C23×C11—22no—
339C23×C11—24no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—42no—
344C23×C11—42no—
345C23×C11C22×D412yes—
346C23×C11C22×D411yescharacteristic
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11C22×D412yes—
351Q8×C11—22no—
352Q8×C11—22no—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—42no—
356Q8×C11—42no—
357D4×C11—24no—
358D4×C11—22no—
359D4×C11—48no—
360D4×C11C22×D414yes—
361C2×C4×C11—22no—
362C2×C4×C11—24no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—48no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
371C2×C4×C11—42no—
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D412yes—
375C2×C4×C11H(5,𝔽2)12yes—
376C2×C4×C11C2511yescharacteristic
377C22⋊D11—28no—
378C22⋊D11—48no—
379C2×Dic11—24no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—48no—
387C2×Dic11—48no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11—48no—
392C2×Dic11#13714yescomplemented
393C2×Dic11C22×D412yes—
394C2×Dic11C22×D412yes—
395C2×Dic11C22×D412yes—
396C4×D11—24no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—48no—
400Dic22—24no—
401Dic22—22no—
402Dic22—22no—
403Dic22—22no—
404Dic22—22no—
405Dic22—22no—
406Dic22—48no—
407Dic22—48no—
408Dic22—42no—
409Dic22—42no—
410Dic22C22×D414yes—
411C8×C11—22no—
412C8×C11—22no—
413C11⋊C8—22no—
414C11⋊C8C22×D414yes—
415C22×#41—111no—
416C22×#41C2×D1111yescharacteristic
417C23×Q8—111no—
418C23×Q8—111no—
419C2×#137—118no—
420C2×#137—118no—
421C2×#137—228no—
422C2×#137—228no—
423C22×Q16—111no—
424C22×Q16—111no—
425C22×Q16—111no—
426C22×Q16—111no—
427C22×Q16—111no—
428C22×Q16C2×D1111yescharacteristic
429C22×SD16—111no—
430C22×SD16—111no—
431C22×SD16C2×D1111yescharacteristic
432C22×M16—111no—
433C22×M16—111no—
434D4×Q8—118no—
435D4×Q8—224no—
436#547—118no—
437#547—224no—
438C2×C4⋊Q8—111no—
439C2×C4⋊Q8—111no—
440C2×C4⋊Q8—221no—
441C2×#123—221no—
442C2×#123—221no—
443C2×C22⋊Q8—111no—
444C2×C22⋊Q8—111no—
445C2×C22⋊Q8—111no—
446C2×C22⋊Q8—221no—
447C2×C22⋊Q8—221no—
448C2×C22⋊Q8C2×D1111yescharacteristic
449C2×#121—221no—
450C2×C4×Q8—111no—
451C2×C4×D4—111no—
452C2×C4×D4—111no—
453C2×C4×D4—221no—
454C22×C4⋊C4—221no—
455#494—118no—
456#470—118no—
457#470—118no—
458#462—118no—
459#461—118no—
460#452—118no—
461#452C2×D1118yescomplemented
462#451—118no—
463#451—118no—
464C4×SD16—118no—
465#436—118no—
466C2×#106—111no—
467C2×C4⋊C8—111no—
468C2×#103—111no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103—111no—
472C2×#103C2×D1111yescharacteristic
473C2×#102C2×D1111yescharacteristic
474C2×C22⋊C8—111no—
475C2×C22⋊C8C2×D1111yescharacteristic
476C2×C4×C8—111no—
477C22×C11—22no—
478C22×C11—24no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—44no—
482C22×C11—48no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11D4212yes—
486C22×C11C2×#13712yes—
487C22×C11#57812yes—
488C22×C11C23×D411yescharacteristic
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—44no—
493C4×C11—22no—
494C4×C11—42no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11D4212yes—
498C4×C11C23×D411yescharacteristic
499C4×C11C2×H(5,𝔽2)11yescharacteristic
500Dic11—24no—
501Dic11—22no—
502Dic11—22no—
503Dic11—42no—
504Dic11—42no—
505Dic11—42no—
506Dic11C2×#13714yescomplemented
507C2×#41—22no—
508C2×#41—24no—
509C2×#41—42no—
510C2×#41—114no—
511C2×#41—222no—
512C2×#41—224no—
513C2×#41—442no—
514C2×#41C22×D1114yes—
515C22×Q8—114no—
516C22×Q8—111no—
517C22×Q8—111no—
518C22×Q8—111no—
519C22×Q8—114no—
520C22×Q8—221no—
521C22×Q8—224no—
522C22×Q8—222no—
523C22×Q8—221no—
524C22×Q8—222no—
525C22×Q8—224no—
526C22×Q8—442no—
527C22×Q8—442no—
528C22×Q8C22×D1111yescharacteristic
529C22×Q8C22×D1111yescharacteristic
530C22×D4—21no—
531C22×D4—111no—
532C22×D4—221no—
533C22×D4C22×D1111yescharacteristic
534C23×C4—21no—
535C23×C4—111no—
536C23×C4—221no—
537C23×C4—221no—
538C23×C4—221no—
539C23×C4—221no—
540C23×C4C22×D1111yescharacteristic
541#137—2232no—
542#137—2232no—
543C2×Q16—42no—
544C2×Q16—114no—
545C2×Q16—114no—
546C2×Q16—114no—
547C2×Q16—114no—
548C2×Q16—114no—
549C2×Q16—224no—
550C2×Q16—224no—
551C2×Q16—224no—
552C2×Q16—224no—
553C2×Q16—442no—
554C2×Q16C22×D1114yes—
555C2×SD16—24no—
556C2×SD16—118no—
557C2×SD16—114no—
558C2×SD16—114no—
559C2×SD16—224no—
560C2×SD16C22×D1114yes—
561C2×M16—114no—
562C2×M16—114no—
563C2×M16—224no—
564C2×M16—224no—
565C22×C8—111no—
566C22×C8—111no—
567C22×C8C22×D1111yescharacteristic
568C22×C8C22×D1111yescharacteristic
569C4⋊Q8—114no—
570C4⋊Q8—114no—
571C4⋊Q8—222no—
572C4⋊Q8—222no—
573C4⋊Q8—228no—
574#123—228no—
575#123—228no—
576C22⋊Q8—22no—
577C22⋊Q8—114no—
578C22⋊Q8—114no—
579C22⋊Q8—114no—
580C22⋊Q8—228no—
581C22⋊Q8—228no—
582C22⋊Q8—222no—
583C22⋊Q8—222no—
584C22⋊Q8—222no—
585C22⋊Q8C22×D1114yes—
586#121—228no—
587C4×Q8—114no—
588C4×Q8—222no—
589C4×D4—114no—
590C4×D4—114no—
591C4×D4—114no—
592C4×D4—222no—
593C4×D4—228no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—111no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—228no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—221no—
605C2×C4⋊C4—221no—
606C2×C4⋊C4C22×D1111yescharacteristic
607C2×C22⋊C4—21no—
608C2×C22⋊C4—111no—
609C2×C22⋊C4—111no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C42—111no—
615C2×C42—221no—
616#106—114no—
617C4⋊C8—114no—
618#103—114no—
619#103—114no—
620#103—114no—
621#103—114no—
622#103C22×D1114yes—
623#102C22×D1114yes—
624C22⋊C8—114no—
625C22⋊C8C22×D1114yes—
626C4×C8—114no—
627C2×C11—42no—
628C2×C11—44no—
629C2×C11#327614yescomplemented
630C2×C11C2×D4211yescharacteristic
631C2×C11C22×#13711yescharacteristic
632C2×C11C2×#57811yescharacteristic
633D11—42no—
634C24—21no—
635C24—111no—
636C24D4×D1111yescharacteristic
637#41—28no—
638#41—44no—
639#41—48no—
640#41—228no—
641#41—444no—
642#41—448no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—114no—
650C2×Q8—112no—
651C2×Q8—112no—
652C2×Q8—112no—
653C2×Q8—224no—
654C2×Q8—228no—
655C2×Q8—221no—
656C2×Q8—224no—
657C2×Q8—221no—
658C2×Q8—221no—
659C2×Q8—222no—
660C2×Q8—228no—
661C2×Q8—222no—
662C2×Q8—222no—
663C2×Q8—222no—
664C2×Q8—222no—
665C2×Q8—444no—
666C2×Q8—444no—
667C2×Q8—448no—
668C2×Q8—444no—
669C2×Q8—444no—
670C2×Q8—448no—
671C2×Q8C23×D1112yes—
672C2×Q8C23×D1112yes—
673C2×D4—24no—
674C2×D4—21no—
675C2×D4—22no—
676C2×D4—44no—
677C2×D4—114no—
678C2×D4—224no—
679C2×D4—224no—
680C2×D4—444no—
681C2×D4D4×D1114yes—
682C2×D4C23×D1112yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—44no—
690C22×C4—111no—
691C22×C4—111no—
692C22×C4—111no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—224no—
696C22×C4—224no—
697C22×C4—224no—
698C22×C4—221no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—224no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—444no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—444no—
709C22×C4D4×D1112yes—
710C22×C4D4×D1111yescharacteristic
711C22×C4C23×D1112yes—
712C22×C4C23×D1111yescharacteristic
713Q16—44no—
714Q16—228no—
715Q16—228no—
716Q16—228no—
717Q16—228no—
718Q16—444no—
719SD16—28no—
720SD16—1116no—
721SD16—228no—
722M16—228no—
723M16—228no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—114no—
727C2×C8—112no—
728C2×C8—112no—
729C2×C8—222no—
730C2×C8C23×D1112yes—
731C2×C8C23×D1112yes—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—114no—
735C4⋊C4—112no—
736C4⋊C4—224no—
737C4⋊C4—224no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4—224no—
741C4⋊C4—224no—
742C4⋊C4—224no—
743C4⋊C4—221no—
744C4⋊C4—224no—
745C4⋊C4C23×D1112yes—
746C22⋊C4—24no—
747C22⋊C4—114no—
748C22⋊C4—114no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C22⋊C4—224no—
752C22⋊C4—224no—
753C42—112no—
754C42—112no—
755C42—224no—
756C11C2×#327611yescharacteristic, complemented, Sylow
757C23—22no—
758C23—22no—
759C23—22no—
760C23—24no—
761C23—22no—
762C23—42no—
763C23—42no—
764C23—112no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23C2×D4×D1112yes—
769C23C2×D4×D1111yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—42no—
775Q8—42no—
776Q8—114no—
777Q8—224no—
778Q8—222no—
779Q8—222no—
780Q8—222no—
781Q8—222no—
782Q8—222no—
783Q8—448no—
784Q8—448no—
785Q8—442no—
786Q8—442no—
787D4—24no—
788D4—22no—
789D4—48no—
790D4—228no—
791D4—448no—
792D4C2×D4×D1114yes—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—48no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—114no—
805C2×C4—112no—
806C2×C4—112no—
807C2×C4—112no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—224no—
811C2×C4—222no—
812C2×C4—224no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—448no—
819C2×C4—448no—
820C2×C4—448no—
821C2×C4—448no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4—442no—
825C2×C4C2×D4×D1112yes—
826C2×C4C2×D4×D1111yescharacteristic
827C2×C4C2×D4×D1112yes—
828C2×C4#6703712yes—
829C2×C4C24×D1111yescharacteristic
830C8—22no—
831C8—22no—
832C8—114no—
833C8—222no—
834C22—22no—
835C22—24no—
836C22—22no—
837C22—22no—
838C22—44no—
839C22—48no—
840C22—42no—
841C22—42no—
842C22—222no—
843C22—222no—
844C22—222no—
845C22—444no—
846C22#1062312112yes—
847C22#1062330212yes—
848C22D11×#13712yes—
849C22C22×D4×D1111yescharacteristic
850C4—22no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—114no—
855C4—222no—
856C4—224no—
857C4—222no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4#1062312112yes—
862C4C22×D4×D1111yescharacteristic
863C4C2×#6703711yescharacteristic
864C2—42no—
865C2—44no—
866C2—442no—
867C2#1308026014yesdirect product factor
868C2C2×#1062312111yescharacteristic
869C2C2×D11×#13711yescharacteristic
870C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
prime radicalC2×#10623355C2
hypercenterC2×#452D11
hypocenterC11C2×#3276
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22×#67004C2semidirect
2. C22×#66968C2semidirect
3. C2×#10623163C2semidirect
5. #13080260C2direct (N × H)
6. C2×#10622794C2semidirect
7. C2×#10622429C2semidirect
8. C2×#10622665C2semidirect
9. C2×#10622406C2semidirect
10. C2×#10622775C2semidirect
11. C2×#10622396C2semidirect
12. C2×#10622352C2semidirect
13. C2×#10622799C2semidirect
14. C2×#10622371C2semidirect
15. C2×#10622342C2semidirect
16. C2×C11×#452C2semidirect
27. C2×#67004C22semidirect
45. C2×#66968C22semidirect
50. #10623163C22semidirect
57. C11×#452C22semidirect
62. #10622799C22semidirect
63. #10622794C22semidirect
64. #10622775C22semidirect
70. #10622665C22semidirect
73. #10622429C22semidirect
74. #10622406C22semidirect
75. #10622396C22semidirect
76. #10622371C22semidirect
77. #10622352C22semidirect
78. #10622342C22semidirect
145. C2×#4324D4semidirect
296. #4324C2×D4semidirect
333. C2×#452D11semidirect
392. C2×Dic11#137semidirect
461. #452C2×D11semidirect
506. Dic11C2×#137semidirect
629. C2×C11#3276semidirect
756. C11C2×#3276semidirect
867. C2#13080260direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#669682
C2×#106231632
C2×#106233552
#130802602
C2×#106227942
C2×#106224292
C2×#106226652
C2×#106224062
C2×#106227752
C2×#106223962
C2×#106223522
C2×#106227992
C2×#106223712
C2×#106223422
C2×C11×#4522
C2×#327611