Finite Group Databasebeta

← C2×#13080276 #15628935

Subgroups — C2×#13080276 #15628935

Order 2816.

2794 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C211yesmaximal, characteristic, complemented
2C2×#10623365C211yesmaximal, characteristic
3C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
4#13080276C2116yesmaximal, direct product factor
5C2×#10622788C211yesmaximal, characteristic, complemented
6C2×#10622747C211yesmaximal, characteristic, complemented
7C2×#10622787C211yesmaximal, characteristic, complemented
8C2×#10622795C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622800C211yesmaximal, characteristic, complemented
12C2×#10622840C211yesmaximal, characteristic, complemented
13C2×#10622783C211yesmaximal, characteristic, complemented
14C2×Q16×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622741C211yesmaximal, characteristic, complemented
16C22×C11×#137C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C22×#4343C2211yescharacteristic
20C22×Q8×D11C2211yescharacteristic
21C2×C11×#137—28no—
22C2×C11×#137C2218yescomplemented
23C22×C11×Q16C2211yescharacteristic
24C22×C11×Q16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic
26C22×C11×SD16C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28#10623365—24no—
29#10623365C2218yes—
30Q8×C22⋊D11—24no—
31Q8×C22⋊D11C2218yescomplemented
32C2×#66999—21no—
33C2×#66999C2211yescharacteristic
34C2×Q8×Dic11C2211yescharacteristic
35C2×Q8×Dic11C2211yescharacteristic
36C2×#66997—21no—
37C2×#66997C2211yescharacteristic
38C22×#4326C2211yescharacteristic
39C22×#4325C2211yescharacteristic
40C22×#4325C2211yescharacteristic
41C2×#66993—21no—
42C2×#66993C2211yescharacteristic
43C2×#66991—21no—
44C2×#66991C2211yescharacteristic
45C22×#4324C2211yescharacteristic
46C2×#66983—21no—
47C2×#66983C2211yescharacteristic
48C2×C4×C22⋊D11—21no—
49C2×C4×C22⋊D11—21no—
50C2×C4×C22⋊D11C2211yescharacteristic
51C2×#66977—21no—
52C2×#66977C2211yescharacteristic
53C2×#66971—28no—
54C2×#66971C2218yescomplemented
55C22×#4314C2211yescharacteristic
56C22×#4313C2211yescharacteristic
57#10622852C2218yescomplemented
58#10622840C2218yescomplemented
59C2×#66899C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66899C2211yescharacteristic
62C2×#66896C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622800C2218yescomplemented
65Q16×Dic11C2218yescomplemented
66#10622795C2218yescomplemented
67#10622788C2218yescomplemented
68#10622787C2218yescomplemented
69#10622783C2218yescomplemented
70#10622776C2218yescomplemented
71#10622747C2218yescomplemented
72#10622741C2218yescomplemented
73C2×#66885C2211yescharacteristic
74C2×(C2×D11)⋊C8C2211yescharacteristic
75C2×#66882C2211yescharacteristic
76C2×#66880C2211yescharacteristic
77C2×Dic11⋊C8C2211yescharacteristic
78C2×C8×Dic11C2211yescharacteristic
79C2×C11×#41—22no—
80C2×C11×#41—24no—
81C2×C11×#41—42no—
82C2×C11×#41C2314yes—
83C22×Q8×C11—21no—
84C22×Q8×C11—22no—
85C22×Q8×C11—24no—
86C22×Q8×C11—42no—
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2314yes—
89C22×Q8×C11C2311yescharacteristic
90C22×Q8×C11C2311yescharacteristic
91C22×D4×C11—21no—
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11—21no—
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11D411yescharacteristic
101C2×#4343—22no—
102C2×#4343—24no—
103C2×#4343—42no—
104C2×#4343C2314yes—
105C2×Q8×D11—22no—
106C2×Q8×D11—24no—
107C2×Q8×D11—42no—
108C2×Q8×D11C2314yes—
109C22×D44—21no—
110C22×D44C2311yescharacteristic
111C22×C4×D11—21no—
112C22×C4×D11—21no—
113C22×C4×D11C2311yescharacteristic
114C22×Dic22—21no—
115C22×Dic22C2311yescharacteristic
116C11×#137—232no—
117C2×C11×Q16—24no—
118C2×C11×Q16D418yescomplemented
119C2×C11×Q16C2314yes—
120C2×C11×Q16C2314yes—
121C2×C11×SD16—24no—
122C2×C11×SD16—24no—
123C2×C11×SD16C2314yes—
124C2×C11×SD16C2314yes—
125C2×C11×M16—24no—
126C2×C11×M16C2314yes—
127C22×C8×C11C2311yescharacteristic
128C22×C8×C11C2311yescharacteristic
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11D411yescharacteristic
132#66999—22no—
133#66999—28no—
134#66999C2314yes—
135Q8×Dic11—22no—
136Q8×Dic11—22no—
137Q8×Dic11C2314yes—
138Q8×Dic11C2314yes—
139#66997—28no—
140#66997—22no—
141#66997C2314yes—
142C2×#4326—24no—
143C2×#4326C2314yes—
144C2×#4325—24no—
145C2×#4325—42no—
146C2×#4325C2314yes—
147C2×#4325C2314yes—
148#66993—28no—
149#66993—22no—
150#66993C2314yes—
151#66991—22no—
152#66991—28no—
153#66991C2314yes—
154C2×#4324—42no—
155C2×#4324C2314yes—
156#66983—22no—
157#66983—28no—
158#66983C2314yes—
159C4×C22⋊D11—28no—
160C4×C22⋊D11—28no—
161C4×C22⋊D11D414yes—
162C4×C22⋊D11C2314yes—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4D411yescharacteristic
166C2×C4⋊Dic11—21no—
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170#66977—22no—
171#66977—28no—
172#66977C2314yes—
173C2×Dic11⋊C4—21no—
174C2×Dic11⋊C4—21no—
175C2×Dic11⋊C4—21no—
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4D411yescharacteristic
178C2×C4×Dic11—21no—
179C2×C4×Dic11—21no—
180C2×C4×Dic11C2311yescharacteristic
181C22×C11⋊C8C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183#66971—232no—
184C2×#4314—24no—
185C2×#4314C2314yes—
186C2×#4313—24no—
187C2×#4313C2314yes—
188#66899C2314yes—
189#66899C2314yes—
190#66899C2314yes—
191#66896C2314yes—
192C22⋊(C11⋊C8)C2314yes—
193#66885C2314yes—
194(C2×D11)⋊C8C2314yes—
195#66882C2314yes—
196#66880C2314yes—
197Dic11⋊C8C2314yes—
198C8×Dic11C2314yes—
199C2×#3278—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11C2×D411yescharacteristic
204C11×#41—28no—
205C11×#41—44no—
206C11×#41—48no—
207C2×Q8×C11—21no—
208C2×Q8×C11—21no—
209C2×Q8×C11—24no—
210C2×Q8×C11—21no—
211C2×Q8×C11—22no—
212C2×Q8×C11—22no—
213C2×Q8×C11—28no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11—44no—
217C2×Q8×C11—44no—
218C2×Q8×C11—48no—
219C2×Q8×C11C2×D414yes—
220C2×Q8×C11C2×D414yes—
221C2×Q8×C11C2412yes—
222C2×Q8×C11C2412yes—
223C2×Q8×C11C2412yes—
224C2×D4×C11—24no—
225C2×D4×C11—22no—
226C2×D4×C11—21no—
227C2×D4×C11—22no—
228C2×D4×C11—44no—
229C2×D4×C11C2412yes—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—21no—
235C22×C4×C11—24no—
236C22×C4×C11—24no—
237C22×C4×C11—44no—
238C22×C4×C11—44no—
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2411yescharacteristic
243C2×C22⋊D11—24no—
244C2×C22⋊D11—24no—
245C2×C22⋊D11—24no—
246C2×C22⋊D11—24no—
247C2×C22⋊D11—24no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—82no—
250C2×C22⋊D11—82no—
251C2×C22⋊D11—82no—
252C2×C22⋊D11C2×D414yes—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11C2×D411yescharacteristic
257C22×Dic11C2×D411yescharacteristic
258C22×Dic11C2×D411yescharacteristic
259#4343—28no—
260#4343—44no—
261#4343—48no—
262Q8×D11—28no—
263Q8×D11—44no—
264Q8×D11—48no—
265C2×D44—24no—
266C2×D44—21no—
267C2×D44—22no—
268C2×D44—22no—
269C2×D44—44no—
270C2×D44C2412yes—
271C2×C4×D11—24no—
272C2×C4×D11—24no—
273C2×C4×D11—22no—
274C2×C4×D11—22no—
275C2×C4×D11—44no—
276C2×C4×D11—44no—
277C2×C4×D11C2×D412yes—
278C2×C4×D11C2412yes—
279C2×Dic22—24no—
280C2×Dic22—22no—
281C2×Dic22—21no—
282C2×Dic22—22no—
283C2×Dic22—44no—
284C2×Dic22C2412yes—
285C11×Q16—28no—
286C11×Q16C2×D4116yescomplemented
287C11×SD16—28no—
288C11×SD16—28no—
289C11×M16—28no—
290C2×C8×C11—22no—
291C2×C8×C11C2×D414yes—
292C2×C8×C11C2412yes—
293C2×C8×C11C2412yes—
294C22⋊Dic11—24no—
295C22⋊Dic11—24no—
296C22⋊Dic11C2×D414yes—
297#4326—28no—
298#4325—28no—
299#4325—44no—
300#4324—44no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4C2×D414yes—
304C4⋊Dic11—24no—
305C4⋊Dic11—24no—
306C4⋊Dic11—21no—
307C4⋊Dic11—21no—
308C4⋊Dic11C2412yes—
309C4⋊Dic11C2412yes—
310Dic11⋊C4—24no—
311Dic11⋊C4—24no—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314Dic11⋊C4C2×D414yes—
315C4×Dic11—24no—
316C4×Dic11—24no—
317C4×Dic11C2×D412yes—
318C4×Dic11C2412yes—
319C2×C11⋊C8—22no—
320C2×C11⋊C8—22no—
321C2×C11⋊C8C2412yes—
322C2×C11⋊C8C2412yes—
323#4314—28no—
324#4313—28no—
325C22×#137—111no—
326C22×#137D1111yescharacteristic, complemented
327C2×#550—111no—
328C2×D4×Q8—111no—
329#3278—1116no—
330C2×#492—111no—
331C2×#468—111no—
332C2×#468—111no—
333C2×#462—111no—
334C2×#460—111no—
335C2×#452—111no—
336C2×#452—111no—
337C2×#448—111no—
338C2×#448—111no—
339C2×C4×Q16—111no—
340C2×#436—111no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—42no—
346C23×C11—42no—
347C23×C11—42no—
348C23×C11C22×D412yes—
349C23×C11C22×D411yescharacteristic
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11C22×D412yes—
358Q8×C11—24no—
359Q8×C11—24no—
360Q8×C11—22no—
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—22no—
364Q8×C11—48no—
365Q8×C11—42no—
366Q8×C11C22×D414yes—
367Q8×C11C22×D414yes—
368D4×C11—22no—
369D4×C11—22no—
370D4×C11—48no—
371D4×C11—42no—
372C2×C4×C11—24no—
373C2×C4×C11—24no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—24no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—48no—
382C2×C4×C11—48no—
383C2×C4×C11—42no—
384C2×C4×C11C22×D412yes—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D412yes—
387C2×C4×C11H(5,𝔽2)12yes—
388C2×C4×C11C2511yescharacteristic
389C22⋊D11—28no—
390C22⋊D11—48no—
391C22⋊D11—84no—
392C22⋊D11—84no—
393C22⋊D11—84no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—42no—
400C2×Dic11—42no—
401C2×Dic11—42no—
402C2×Dic11#13714yescomplemented
403C2×Dic11C22×D412yes—
404C2×Dic11C22×D412yes—
405C2×Dic11C22×D412yes—
406D44—22no—
407D44—22no—
408D44—48no—
409D44—42no—
410C4×D11—24no—
411C4×D11—22no—
412C4×D11—22no—
413C4×D11—48no—
414C4×D11—48no—
415Dic22—22no—
416Dic22—22no—
417Dic22—48no—
418Dic22—42no—
419C8×C11—22no—
420C8×C11C22×D414yes—
421C11⋊C8—22no—
422C11⋊C8—22no—
423C22×#41—111no—
424C22×#41C2×D1111yescharacteristic
425C23×Q8—111no—
426C23×Q8C2×D1111yescharacteristic
427C2×#137—28no—
428C2×#137—118no—
429C2×#137—228no—
430C2×#137C2×D1118yescomplemented
431C22×Q16—111no—
432C22×Q16C2×D1111yescharacteristic
433C22×Q16C2×D1111yescharacteristic
434C22×SD16—111no—
435C22×SD16—111no—
436C22×SD16—111no—
437C22×SD16—111no—
438C22×SD16C2×D1111yescharacteristic
439C22×SD16C2×D1111yescharacteristic
440C22×M16—111no—
441C22×M16C2×D1111yescharacteristic
442#550—118no—
443#550—224no—
444D4×Q8—118no—
445D4×Q8—224no—
446C2×C4⋊Q8—111no—
447C2×C4⋊Q8—221no—
448C2×#127—111no—
449C2×#127—221no—
450C2×C22⋊Q8—111no—
451C2×C22⋊Q8—111no—
452C2×C22⋊Q8—221no—
453C2×C22⋊Q8—221no—
454C2×#121—111no—
455C2×#121—111no—
456C2×#121—221no—
457C2×#121—221no—
458C2×C4×Q8—111no—
459C2×C4×Q8—111no—
460C2×C4×D4—111no—
461C2×C4×D4—221no—
462C2×C4×D4—221no—
463#492—118no—
464#468—118no—
465#468—118no—
466#462—118no—
467#460—118no—
468#452—118no—
469#452—118no—
470#448—118no—
471#448—118no—
472C4×Q16—118no—
473#436—118no—
474C2×#107—111no—
475C2×C4⋊C8—111no—
476C2×#103—111no—
477C2×#103—111no—
478C2×#103—111no—
479C2×#103—111no—
480C2×#102—111no—
481C2×#102—111no—
482C2×C22⋊C8—111no—
483C2×C22⋊C8—111no—
484C2×C4×C8—111no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—22no—
488C22×C11—44no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—84no—
493C22×C11D4212yes—
494C22×C11C2×#13712yes—
495C22×C11#57712yes—
496C22×C11C23×D411yescharacteristic
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—22no—
500C2×D11—44no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—84no—
505C4×C11—22no—
506C4×C11—24no—
507C4×C11—24no—
508C4×C11—42no—
509C4×C11D4212yes—
510C4×C11C23×D411yescharacteristic
511C4×C11C2×H(5,𝔽2)11yescharacteristic
512Dic11—22no—
513Dic11—22no—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517Dic11C2×#13714yescomplemented
518C2×#41—22no—
519C2×#41—24no—
520C2×#41—42no—
521C2×#41—114no—
522C2×#41—222no—
523C2×#41—224no—
524C2×#41—442no—
525C2×#41C22×D1114yes—
526C22×Q8—21no—
527C22×Q8—22no—
528C22×Q8—24no—
529C22×Q8—42no—
530C22×Q8—114no—
531C22×Q8—111no—
532C22×Q8—221no—
533C22×Q8—222no—
534C22×Q8—224no—
535C22×Q8—442no—
536C22×Q8C22×D1111yescharacteristic
537C22×Q8C22×D1114yes—
538C22×Q8C22×D1111yescharacteristic
539C22×Q8C22×D1111yescharacteristic
540C22×D4—21no—
541C22×D4—111no—
542C22×D4—111no—
543C22×D4—221no—
544C22×D4—221no—
545C22×D4—221no—
546C22×D4—221no—
547C22×D4—221no—
548C22×D4C22×D1111yescharacteristic
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—111no—
552C23×C4—221no—
553C23×C4—221no—
554C23×C4C22×D1111yescharacteristic
555#137—232no—
556#137—2232no—
557C2×Q16—24no—
558C2×Q16—114no—
559C2×Q16—224no—
560C2×Q16C22⋊D1118yescomplemented
561C2×Q16C22×D1114yes—
562C2×Q16C22×D1114yes—
563C2×SD16—24no—
564C2×SD16—24no—
565C2×SD16—114no—
566C2×SD16—114no—
567C2×SD16—114no—
568C2×SD16—114no—
569C2×SD16—224no—
570C2×SD16—224no—
571C2×SD16—442no—
572C2×SD16—442no—
573C2×SD16C22×D1114yes—
574C2×SD16C22×D1114yes—
575C2×M16—24no—
576C2×M16—114no—
577C2×M16—224no—
578C2×M16C22×D1114yes—
579C22×C8—111no—
580C22×C8—111no—
581C22×C8C22×D1111yescharacteristic
582C22×C8C22×D1111yescharacteristic
583C4⋊Q8—114no—
584C4⋊Q8—222no—
585C4⋊Q8—228no—
586#127—114no—
587#127—222no—
588#127—228no—
589C22⋊Q8—114no—
590C22⋊Q8—114no—
591C22⋊Q8—228no—
592C22⋊Q8—228no—
593C22⋊Q8—222no—
594C22⋊Q8—222no—
595#121—114no—
596#121—114no—
597#121—228no—
598#121—228no—
599#121—222no—
600#121—222no—
601C4×Q8—114no—
602C4×Q8—114no—
603C4×Q8—222no—
604C4×Q8—222no—
605C4×D4—114no—
606C4×D4—114no—
607C4×D4—228no—
608C4×D4—228no—
609C2×C4⋊C4—111no—
610C2×C4⋊C4—111no—
611C2×C4⋊C4—111no—
612C2×C4⋊C4—221no—
613C2×C4⋊C4—221no—
614C2×C4⋊C4—221no—
615C2×C4⋊C4—221no—
616C2×C4⋊C4—221no—
617C2×C4⋊C4—221no—
618C2×C22⋊C4—111no—
619C2×C22⋊C4—111no—
620C2×C22⋊C4—221no—
621C2×C22⋊C4—221no—
622C2×C22⋊C4—221no—
623C2×C22⋊C4—221no—
624C2×C42—111no—
625C2×C42—221no—
626C2×C42—221no—
627#107—114no—
628C4⋊C8—114no—
629#103—114no—
630#103—114no—
631#103—114no—
632#103—114no—
633#102—114no—
634#102—114no—
635C22⋊C8—114no—
636C22⋊C8—114no—
637C4×C8—114no—
638C2×C11—42no—
639C2×C11—82no—
640C2×C11#327814yescomplemented
641C2×C11C2×D4211yescharacteristic
642C2×C11C22×#13711yescharacteristic
643C2×C11C2×#57711yescharacteristic
644D11—42no—
645D11—82no—
646C24—21no—
647C24—111no—
648C24—221no—
649C24D4×D1111yescharacteristic
650#41—28no—
651#41—44no—
652#41—48no—
653#41—228no—
654#41—444no—
655#41—448no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—24no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8—28no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—48no—
668C2×Q8—112no—
669C2×Q8—224no—
670C2×Q8—221no—
671C2×Q8—228no—
672C2×Q8—222no—
673C2×Q8—222no—
674C2×Q8—444no—
675C2×Q8—444no—
676C2×Q8—448no—
677C2×Q8C2×C22⋊D1114yes—
678C2×Q8C2×C22⋊D1114yes—
679C2×Q8C23×D1112yes—
680C2×Q8C23×D1112yes—
681C2×Q8C23×D1112yes—
682C2×D4—24no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—44no—
687C2×D4—114no—
688C2×D4—112no—
689C2×D4—224no—
690C2×D4—224no—
691C2×D4—224no—
692C2×D4—224no—
693C2×D4—224no—
694C2×D4—224no—
695C2×D4—221no—
696C2×D4—222no—
697C2×D4—222no—
698C2×D4—444no—
699C2×D4—444no—
700C2×D4—882no—
701C2×D4—882no—
702C2×D4—882no—
703C2×D4C23×D1112yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—24no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—111no—
714C22×C4—111no—
715C22×C4—111no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—224no—
719C22×C4—224no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—444no—
726C22×C4—444no—
727C22×C4D4×D1112yes—
728C22×C4D4×D1111yescharacteristic
729C22×C4C23×D1112yes—
730C22×C4C23×D1111yescharacteristic
731Q16—28no—
732Q16—228no—
733Q16C2×C22⋊D11116yescomplemented
734SD16—28no—
735SD16—28no—
736SD16—228no—
737SD16—228no—
738SD16—444no—
739SD16—444no—
740M16—28no—
741M16—228no—
742C2×C8—22no—
743C2×C8—112no—
744C2×C8—112no—
745C2×C8—222no—
746C2×C8—222no—
747C2×C8C2×C22⋊D1114yes—
748C2×C8C23×D1112yes—
749C2×C8C23×D1112yes—
750C4⋊C4—114no—
751C4⋊C4—112no—
752C4⋊C4—112no—
753C4⋊C4—224no—
754C4⋊C4—224no—
755C4⋊C4—224no—
756C4⋊C4—224no—
757C4⋊C4—224no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4—224no—
761C22⋊C4—114no—
762C22⋊C4—114no—
763C22⋊C4—224no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C42—112no—
768C42—112no—
769C42—224no—
770C42—224no—
771C11C2×#327811yescharacteristic, complemented, Sylow
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—112no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—442no—
785C23—442no—
786C23—442no—
787C23C2×D4×D1112yes—
788C23C2×D4×D1111yescharacteristic
789Q8—24no—
790Q8—24no—
791Q8—22no—
792Q8—22no—
793Q8—22no—
794Q8—22no—
795Q8—48no—
796Q8—42no—
797Q8—222no—
798Q8—222no—
799Q8—448no—
800Q8—442no—
801Q8C22×C22⋊D1114yes—
802Q8C22×C22⋊D1114yes—
803D4—22no—
804D4—22no—
805D4—48no—
806D4—42no—
807D4—228no—
808D4—222no—
809D4—222no—
810D4—448no—
811D4—448no—
812D4—442no—
813D4—884no—
814D4—884no—
815D4—884no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—48no—
826C2×C4—48no—
827C2×C4—42no—
828C2×C4—114no—
829C2×C4—112no—
830C2×C4—112no—
831C2×C4—112no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—224no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—448no—
841C2×C4—448no—
842C2×C4—442no—
843C2×C4—442no—
844C2×C4—442no—
845C2×C4C2×D4×D1112yes—
846C2×C4C2×D4×D1111yescharacteristic
847C2×C4#6703712yes—
848C2×C4C22×C22⋊D1112yes—
849C2×C4C24×D1111yescharacteristic
850C8—22no—
851C8—222no—
852C8—222no—
853C8C22×C22⋊D1114yes—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—44no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—84no—
862C22—222no—
863C22—222no—
864C22—222no—
865C22—444no—
866C22—442no—
867C22—442no—
868C22—442no—
869C22—884no—
870C22D11×#13712yes—
871C22#1062330912yes—
872C22D4×C22⋊D1112yes—
873C22C22×D4×D1111yescharacteristic
874C4—22no—
875C4—24no—
876C4—24no—
877C4—42no—
878C4—114no—
879C4—222no—
880C4—222no—
881C4—442no—
882C4—442no—
883C4—442no—
884C4D4×C22⋊D1112yes—
885C4C2×#6703711yescharacteristic
886C4C23×C22⋊D1111yescharacteristic
887C2—42no—
888C2—82no—
889C2—442no—
890C2—882no—
891C2#1308027614yesdirect product factor
892C2C2×D4×C22⋊D1111yescharacteristic
893C2C2×D11×#13711yescharacteristic
894C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC2×#10623365C2
hypercenterC22×#137D11
hypocenterC11C2×#3278
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
3. C2×Q8×C22⋊D11C2semidirect
4. #13080276C2direct (N × H)
5. C2×#10622788C2semidirect
6. C2×#10622747C2semidirect
7. C2×#10622787C2semidirect
8. C2×#10622795C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622800C2semidirect
12. C2×#10622840C2semidirect
13. C2×#10622783C2semidirect
14. C2×Q16×Dic11C2semidirect
15. C2×#10622741C2semidirect
16. C22×C11×#137C2semidirect
22. C2×C11×#137C22semidirect
31. Q8×C22⋊D11C22semidirect
54. C2×#66971C22semidirect
57. #10622852C22semidirect
58. #10622840C22semidirect
64. #10622800C22semidirect
65. Q16×Dic11C22semidirect
66. #10622795C22semidirect
67. #10622788C22semidirect
68. #10622787C22semidirect
69. #10622783C22semidirect
70. #10622776C22semidirect
71. #10622747C22semidirect
72. #10622741C22semidirect
118. C2×C11×Q16D4semidirect
286. C11×Q16C2×D4semidirect
326. C22×#137D11semidirect
402. C2×Dic11#137semidirect
430. C2×#137C2×D11semidirect
517. Dic11C2×#137semidirect
560. C2×Q16C22⋊D11semidirect
640. C2×C11#3278semidirect
733. Q16C2×C22⋊D11semidirect
771. C11C2×#3278semidirect
891. C2#13080276direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C2×#106233652
C2×Q8×C22⋊D112
#130802762
C2×#106227882
C2×#106227472
C2×#106227872
C2×#106227952
C2×#106227762
C2×#106228522
C2×#106228002
C2×#106228402
C2×#106227832
C2×Q16×Dic112
C2×#106227412
C22×C11×#1372
C2×#327811