Finite Group Databasebeta

← C2×#13080340 #15629020

Subgroups — C2×#13080340 #15629020

Order 2816.

2858 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66969C211yesmaximal, characteristic, complemented
2C2×#10623365C211yesmaximal, characteristic, complemented
3C2×#10623355C211yesmaximal, characteristic, complemented
4#13080340C2116yesmaximal, direct product factor
5C2×#10622788C211yesmaximal, characteristic, complemented
6C2×#10622727C211yesmaximal, characteristic, complemented
7C2×#10622784C211yesmaximal, characteristic, complemented
8C2×#10622795C211yesmaximal, characteristic, complemented
9C2×#10622763C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622800C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic, complemented
13C2×#10622771C211yesmaximal, characteristic, complemented
14C2×SD16×Dic11C211yesmaximal, characteristic, complemented
15C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
16C22×C11×#135C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic
19C22×#4343C2211yescharacteristic
20C22×#4341C2211yescharacteristic
21C2×C11×#135—28no—
22C2×C11×#135C2218yescomplemented
23C22×C11×Q16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C23×C8×C11C2211yescharacteristic
28#10623365—24no—
29#10623365C2218yescomplemented
30#10623355—24no—
31#10623355C2218yescomplemented
32C2×#66999C2211yescharacteristic
33C2×Q8×Dic11C2211yescharacteristic
34C2×#66997C2211yescharacteristic
35C22×#4326C2211yescharacteristic
36C22×#4325C2211yescharacteristic
37C2×#66993—21no—
38C2×#66993C2211yescharacteristic
39C2×#66992—21no—
40C2×#66991—21no—
41C2×#66991C2211yescharacteristic
42C2×#66988—21no—
43C2×D4×Dic11C2211yescharacteristic
44C22×#4324C2211yescharacteristic
45C22×#4323C2211yescharacteristic
46C2×#66983—21no—
47C2×#66983C2211yescharacteristic
48C2×#66982—21no—
49C2×C4×C22⋊D11—21no—
50C2×C4×C22⋊D11C2211yescharacteristic
51C2×#66977C2211yescharacteristic
52C22×Dic11⋊C4—21no—
53C2×#66969—28no—
54C2×#66969C2218yescomplemented
55C22×#4314C2211yescharacteristic
56C22×C8×D11C2211yescharacteristic
57#10622852C2218yescomplemented
58#10622851C2218yescomplemented
59C2×#66899C2211yescharacteristic
60C2×#66899C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62C2×#66896C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622800C2218yescomplemented
65#10622795C2218yescomplemented
66#10622788C2218yescomplemented
67#10622784C2218yescomplemented
68SD16×Dic11C2218yescomplemented
69#10622771C2218yescomplemented
70#10622763C2218yescomplemented
71#10622727C2218yescomplemented
72C2×#66885C2211yescharacteristic
73C8×C22⋊D11C2218yescomplemented
74C2×(C2×D11)⋊C8C2211yescharacteristic
75C2×#66881C2211yescharacteristic
76C2×#66880C2211yescharacteristic
77C2×Dic11⋊C8C2211yescharacteristic
78C2×C8×Dic11C2211yescharacteristic
79C2×C11×#41—22no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—24no—
83C2×C11×#41—42no—
84C2×C11×#41—42no—
85C2×C11×#41C2314yes—
86C2×C11×#41C2314yes—
87C22×Q8×C11C2311yescharacteristic
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11C2311yescharacteristic
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⋊D11—21no—
101C22×C22⋊D11D411yescharacteristic
102C23×Dic11—21no—
103C23×Dic11—21no—
104C2×#4343—22no—
105C2×#4343—24no—
106C2×#4343—42no—
107C2×#4343C2314yes—
108C2×#4341—24no—
109C2×#4341—22no—
110C2×#4341—42no—
111C2×#4341C2314yes—
112C22×D44—21no—
113C22×D44C2311yescharacteristic
114C22×C4×D11—21no—
115C22×C4×D11C2311yescharacteristic
116C22×Dic22C2311yescharacteristic
117C11×#135—232no—
118C2×C11×Q16—24no—
119C2×C11×Q16C2314yes—
120C2×C11×SD16—24no—
121C2×C11×SD16D418yescomplemented
122C2×C11×SD16C2314yes—
123C2×C11×SD16C2314yes—
124C2×C11×D8—24no—
125C2×C11×D8C2314yes—
126C22×C8×C11—24no—
127C22×C8×C11C2311yescharacteristic
128C22×C8×C11C2314yes—
129C22×C8×C11C2311yescharacteristic
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11—21no—
133C2×C22⋊Dic11D411yescharacteristic
134#66999—22no—
135#66999C2314yes—
136Q8×Dic11—22no—
137Q8×Dic11C2314yes—
138#66997—22no—
139#66997C2314yes—
140C2×#4326—24no—
141C2×#4326C2314yes—
142C2×#4325—42no—
143C2×#4325C2314yes—
144#66993—28no—
145#66993—22no—
146#66993C2314yes—
147#66992—28no—
148#66991—22no—
149#66991—28no—
150#66991C2314yes—
151#66988—28no—
152D4×Dic11—22no—
153D4×Dic11C2314yes—
154C2×#4324—42no—
155C2×#4324C2314yes—
156C2×#4323—24no—
157C2×#4323C2314yes—
158#66983—22no—
159#66983—28no—
160#66983C2314yes—
161#66982—28no—
162C4×C22⋊D11—28no—
163C4×C22⋊D11D414yes—
164C4×C22⋊D11C2314yes—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×(C2×D11)⋊C4D411yescharacteristic
168C2×C4⋊Dic11—21no—
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2311yescharacteristic
171#66977—22no—
172#66977C2314yes—
173C2×Dic11⋊C4—21no—
174C2×Dic11⋊C4—21no—
175C2×Dic11⋊C4—21no—
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4—28no—
178C2×Dic11⋊C4D411yescharacteristic
179C2×C4×Dic11—21no—
180C2×C4×Dic11C2311yescharacteristic
181C22×C11⋊C8C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183#66969—232no—
184C2×#4314—24no—
185C2×#4314C2314yes—
186C2×C8×D11—24no—
187C2×C8×D11C2314yes—
188#66899C2314yes—
189#66899C2314yes—
190#66896C2314yes—
191#66896C2314yes—
192C22⋊(C11⋊C8)C2314yes—
193#66885C2314yes—
194(C2×D11)⋊C8C2314yes—
195#66881C2314yes—
196#66880C2314yes—
197Dic11⋊C8C2314yes—
198C8×Dic11C2314yes—
199C2×#3284—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11—21no—
202C24×C11C2×D411yescharacteristic
203C23×D11—21no—
204C23×D11C2×D411yescharacteristic
205C11×#41—28no—
206C11×#41—28no—
207C11×#41—44no—
208C11×#41—44no—
209C11×#41—48no—
210C11×#41—48no—
211C2×Q8×C11—21no—
212C2×Q8×C11—21no—
213C2×Q8×C11—22no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11C2×D414yes—
217C2×Q8×C11C2412yes—
218C2×Q8×C11C2412yes—
219C2×D4×C11—24no—
220C2×D4×C11—24no—
221C2×D4×C11—21no—
222C2×D4×C11—22no—
223C2×D4×C11—21no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—44no—
227C2×D4×C11—44no—
228C2×D4×C11C2×D414yes—
229C2×D4×C11C2412yes—
230C2×D4×C11C2412yes—
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—24no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—82no—
252C2×C22⋊D11—82no—
253C2×C22⋊D11—82no—
254C2×C22⋊D11C2×D414yes—
255C22×Dic11—24no—
256C22×Dic11—24no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—44no—
261C22×Dic11—44no—
262C22×Dic11C2×D411yescharacteristic
263C22×Dic11C2×D411yescharacteristic
264C22×Dic11C2×D411yescharacteristic
265#4343—28no—
266#4343—44no—
267#4343—48no—
268#4341—28no—
269#4341—44no—
270#4341—48no—
271C2×D44—24no—
272C2×D44—21no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—44no—
276C2×D44C2412yes—
277C2×C4×D11—24no—
278C2×C4×D11—22no—
279C2×C4×D11—22no—
280C2×C4×D11—44no—
281C2×C4×D11C2×D412yes—
282C2×C4×D11C2412yes—
283C2×Dic22—22no—
284C2×Dic22—21no—
285C2×Dic22—22no—
286C2×Dic22C2412yes—
287C11×Q16—28no—
288C11×SD16—28no—
289C11×SD16C2×D4116yescomplemented
290C11×D8—28no—
291C2×C8×C11—28no—
292C2×C8×C11—22no—
293C2×C8×C11C2×D414yes—
294C2×C8×C11C2412yes—
295C2×C8×C11C2412yes—
296C22⋊Dic11—24no—
297C22⋊Dic11—24no—
298C22⋊Dic11—24no—
299C22⋊Dic11C2×D414yes—
300#4326—28no—
301#4325—44no—
302#4324—44no—
303#4323—28no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4C2×D414yes—
307C4⋊Dic11—24no—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11C2412yes—
311C4⋊Dic11C2412yes—
312Dic11⋊C4—24no—
313Dic11⋊C4—24no—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316Dic11⋊C4C2×D414yes—
317C4×Dic11—24no—
318C4×Dic11C2×D412yes—
319C4×Dic11C2412yes—
320C2×C11⋊C8—22no—
321C2×C11⋊C8—22no—
322C2×C11⋊C8C2412yes—
323C2×C11⋊C8C2412yes—
324#4314—28no—
325C8×D11—28no—
326C22×#135—111no—
327C22×#135D1111yescharacteristic, complemented
328C2×#550—111no—
329C2×#547—111no—
330#3284—1116no—
331C2×#492—111no—
332C2×#465—111no—
333C2×#465—111no—
334C2×#462—111no—
335C2×#459—111no—
336C2×#452—111no—
337C2×#452—111no—
338C2×#449—111no—
339C2×#449—111no—
340C2×C4×SD16—111no—
341C2×C8×D4—111no—
342C23×C11—24no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—42no—
349C23×C11—42no—
350C23×C11—42no—
351C23×C11—42no—
352C23×C11—42no—
353C23×C11C22×D412yes—
354C23×C11C22×D411yescharacteristic
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—42no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11C22×D412yes—
363Q8×C11—24no—
364Q8×C11—22no—
365Q8×C11—22no—
366Q8×C11—22no—
367Q8×C11—42no—
368Q8×C11C22×D414yes—
369D4×C11—24no—
370D4×C11—22no—
371D4×C11—22no—
372D4×C11—22no—
373D4×C11—48no—
374D4×C11—48no—
375D4×C11—42no—
376D4×C11C22×D414yes—
377C2×C4×C11—24no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—24no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—48no—
385C2×C4×C11—48no—
386C2×C4×C11—42no—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C22×D412yes—
390C2×C4×C11H(5,𝔽2)12yes—
391C2×C4×C11C2511yescharacteristic
392C22⋊D11—28no—
393C22⋊D11—48no—
394C22⋊D11—48no—
395C22⋊D11—84no—
396C22⋊D11—84no—
397C22⋊D11—84no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—48no—
404C2×Dic11—42no—
405C2×Dic11—42no—
406C2×Dic11—42no—
407C2×Dic11—48no—
408C2×Dic11#13514yescomplemented
409C2×Dic11C22×D412yes—
410C2×Dic11C22×D412yes—
411C2×Dic11C22×D412yes—
412D44—22no—
413D44—22no—
414D44—48no—
415D44—42no—
416C4×D11—24no—
417C4×D11—22no—
418C4×D11—22no—
419C4×D11—48no—
420Dic22—22no—
421Dic22—22no—
422Dic22—42no—
423C8×C11—22no—
424C8×C11C22×D414yes—
425C11⋊C8—22no—
426C11⋊C8—22no—
427C22×#41—111no—
428C22×#41—111no—
429C22×#41C2×D1111yescharacteristic
430C22×#41C2×D1111yescharacteristic
431C2×#135—28no—
432C2×#135—118no—
433C2×#135—228no—
434C2×#135C2×D1118yescomplemented
435C22×Q16—111no—
436C22×Q16C2×D1111yescharacteristic
437C22×SD16—111no—
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16C2×D1111yescharacteristic
441C22×SD16C2×D1111yescharacteristic
442C22×D8—111no—
443C22×D8C2×D1111yescharacteristic
444C23×C8—111no—
445C23×C8C2×D1111yescharacteristic
446#550—118no—
447#550—224no—
448#547—118no—
449#547—224no—
450C2×C4⋊Q8—111no—
451C2×#127—111no—
452C2×#127—221no—
453C2×#123—221no—
454C2×#123—221no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—111no—
457C2×#121—111no—
458C2×#121—111no—
459C2×#121—221no—
460C2×#121—221no—
461C2×#121—221no—
462C2×C4×Q8—111no—
463C2×C4×D4—111no—
464C2×C4×D4—111no—
465C2×C4×D4—221no—
466C22×C4⋊C4—221no—
467#492—118no—
468#465—118no—
469#465—118no—
470#462—118no—
471#459—118no—
472#452—118no—
473#452—118no—
474#449—118no—
475#449—118no—
476C4×SD16—118no—
477C8×D4—118no—
478C2×#106—111no—
479C2×C4⋊C8—111no—
480C2×#103—111no—
481C2×#103—111no—
482C2×#103—111no—
483C2×#102—111no—
484C2×#102—111no—
485C2×#102—111no—
486C2×C22⋊C8—111no—
487C2×C22⋊C8—111no—
488C2×C4×C8—111no—
489C22×C11—22no—
490C22×C11—24no—
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—44no—
494C22×C11—48no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—84no—
501C22×C11D4212yes—
502C22×C11C2×#13512yes—
503C22×C11#57712yes—
504C22×C11C23×D411yescharacteristic
505C2×D11—22no—
506C2×D11—22no—
507C2×D11—22no—
508C2×D11—44no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—84no—
513C4×C11—22no—
514C4×C11—24no—
515C4×C11—42no—
516C4×C11D4212yes—
517C4×C11C23×D411yescharacteristic
518C4×C11C2×H(5,𝔽2)11yescharacteristic
519Dic11—22no—
520Dic11—22no—
521Dic11—42no—
522Dic11—42no—
523Dic11—42no—
524Dic11C2×#13514yescomplemented
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41—42no—
530C2×#41—42no—
531C2×#41—114no—
532C2×#41—114no—
533C2×#41—222no—
534C2×#41—222no—
535C2×#41—224no—
536C2×#41—224no—
537C2×#41—442no—
538C2×#41—442no—
539C2×#41C22×D1114yes—
540C2×#41C22×D1114yes—
541C22×Q8—111no—
542C22×Q8C22×D1111yescharacteristic
543C22×Q8C22×D1111yescharacteristic
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—111no—
547C22×D4—111no—
548C22×D4—221no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—221no—
553C22×D4—221no—
554C22×D4C22×D1111yescharacteristic
555C22×D4C22×D1111yescharacteristic
556C23×C4—21no—
557C23×C4—21no—
558C23×C4—111no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563#135—232no—
564#135—2232no—
565C2×Q16—24no—
566C2×Q16—114no—
567C2×Q16—224no—
568C2×Q16C22×D1114yes—
569C2×SD16—24no—
570C2×SD16—114no—
571C2×SD16—114no—
572C2×SD16—114no—
573C2×SD16—224no—
574C2×SD16—442no—
575C2×SD16—442no—
576C2×SD16C22⋊D1118yescomplemented
577C2×SD16C22×D1114yes—
578C2×SD16C22×D1114yes—
579C2×D8—24no—
580C2×D8—114no—
581C2×D8—224no—
582C2×D8C22×D1114yes—
583C22×C8—24no—
584C22×C8—111no—
585C22×C8—111no—
586C22×C8—114no—
587C22×C8—224no—
588C22×C8C22×D1111yescharacteristic
589C22×C8C22×D1114yes—
590C22×C8C22×D1111yescharacteristic
591C4⋊Q8—114no—
592C4⋊Q8—222no—
593#127—114no—
594#127—222no—
595#127—228no—
596#123—228no—
597#123—228no—
598C22⋊Q8—114no—
599C22⋊Q8—114no—
600C22⋊Q8—222no—
601C22⋊Q8—222no—
602#121—114no—
603#121—114no—
604#121—228no—
605#121—228no—
606#121—222no—
607#121—228no—
608#121—222no—
609C4×Q8—114no—
610C4×Q8—222no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—114no—
614C4×D4—222no—
615C4×D4—228no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—228no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C4⋊C4—221no—
623C2×C4⋊C4—221no—
624C2×C4⋊C4—221no—
625C2×C22⋊C4—111no—
626C2×C22⋊C4—111no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C42—111no—
633C2×C42—221no—
634#106—114no—
635C4⋊C8—114no—
636#103—114no—
637#103—114no—
638#103—114no—
639#102—114no—
640#102—114no—
641#102—114no—
642C22⋊C8—114no—
643C22⋊C8—114no—
644C4×C8—114no—
645C2×C11—42no—
646C2×C11—44no—
647C2×C11—82no—
648C2×C11#328414yescomplemented
649C2×C11C2×D4211yescharacteristic
650C2×C11C22×#13511yescharacteristic
651C2×C11C2×#57711yescharacteristic
652D11—42no—
653D11—82no—
654C24—21no—
655C24—21no—
656C24—111no—
657C24—221no—
658C24D4×D1111yescharacteristic
659#41—28no—
660#41—28no—
661#41—44no—
662#41—44no—
663#41—48no—
664#41—48no—
665#41—228no—
666#41—228no—
667#41—444no—
668#41—448no—
669#41—444no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—22no—
676C2×Q8—112no—
677C2×Q8—221no—
678C2×Q8—222no—
679C2×Q8—222no—
680C2×Q8C2×C22⋊D1114yes—
681C2×Q8C23×D1112yes—
682C2×Q8C23×D1112yes—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—114no—
693C2×D4—112no—
694C2×D4—224no—
695C2×D4—224no—
696C2×D4—224no—
697C2×D4—224no—
698C2×D4—224no—
699C2×D4—224no—
700C2×D4—224no—
701C2×D4—221no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—444no—
705C2×D4—444no—
706C2×D4—444no—
707C2×D4—882no—
708C2×D4—882no—
709C2×D4—882no—
710C2×D4C2×C22⋊D1114yes—
711C2×D4C23×D1112yes—
712C2×D4C23×D1112yes—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—111no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—224no—
727C22×C4—224no—
728C22×C4—224no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—444no—
735C22×C4—444no—
736C22×C4—444no—
737C22×C4D4×D1112yes—
738C22×C4D4×D1111yescharacteristic
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—28no—
742Q16—228no—
743SD16—28no—
744SD16—228no—
745SD16—444no—
746SD16—444no—
747SD16C2×C22⋊D11116yescomplemented
748D8—28no—
749D8—228no—
750C2×C8—22no—
751C2×C8—28no—
752C2×C8—112no—
753C2×C8—112no—
754C2×C8—222no—
755C2×C8—222no—
756C2×C8—228no—
757C2×C8C2×C22⋊D1114yes—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—114no—
761C4⋊C4—112no—
762C4⋊C4—112no—
763C4⋊C4—224no—
764C4⋊C4—224no—
765C4⋊C4—224no—
766C4⋊C4—224no—
767C4⋊C4—221no—
768C4⋊C4—221no—
769C4⋊C4—224no—
770C22⋊C4—114no—
771C22⋊C4—114no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C42—112no—
778C42—112no—
779C42—224no—
780C11C2×#328411yescharacteristic, complemented, Sylow
781C23—22no—
782C23—22no—
783C23—22no—
784C23—24no—
785C23—22no—
786C23—22no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—112no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—442no—
798C23—442no—
799C23—442no—
800C23C2×D4×D1112yes—
801C23C2×D4×D1111yescharacteristic
802Q8—24no—
803Q8—22no—
804Q8—22no—
805Q8—22no—
806Q8—42no—
807Q8—222no—
808Q8—222no—
809Q8—442no—
810Q8C22×C22⋊D1114yes—
811D4—24no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—42no—
818D4—228no—
819D4—222no—
820D4—222no—
821D4—448no—
822D4—448no—
823D4—448no—
824D4—442no—
825D4—884no—
826D4—884no—
827D4—884no—
828D4C22×C22⋊D1114yes—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—42no—
839C2×C4—114no—
840C2×C4—112no—
841C2×C4—112no—
842C2×C4—112no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—224no—
846C2×C4—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—448no—
852C2×C4—448no—
853C2×C4—448no—
854C2×C4—442no—
855C2×C4—442no—
856C2×C4—442no—
857C2×C4C2×D4×D1112yes—
858C2×C4C2×D4×D1111yescharacteristic
859C2×C4#6703712yes—
860C2×C4C22×C22⋊D1112yes—
861C2×C4C24×D1111yescharacteristic
862C8—22no—
863C8—222no—
864C8—222no—
865C8C22×C22⋊D1114yes—
866C22—22no—
867C22—24no—
868C22—22no—
869C22—22no—
870C22—44no—
871C22—48no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—84no—
878C22—222no—
879C22—222no—
880C22—222no—
881C22—444no—
882C22—442no—
883C22—442no—
884C22—442no—
885C22—884no—
886C22D11×#13512yes—
887C22#1062330112yes—
888C22D4×C22⋊D1112yes—
889C22C22×D4×D1111yescharacteristic
890C4—22no—
891C4—24no—
892C4—42no—
893C4—114no—
894C4—222no—
895C4—222no—
896C4—442no—
897C4—442no—
898C4—442no—
899C4D4×C22⋊D1112yes—
900C4C2×#6703711yescharacteristic
901C4C23×C22⋊D1111yescharacteristic
902C2—42no—
903C2—44no—
904C2—82no—
905C2—442no—
906C2—882no—
907C2#1308034014yesdirect product factor
908C2C2×D4×C22⋊D1111yescharacteristic
909C2C2×D11×#13511yescharacteristic
910C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#135C2
socleC23×C11C22×D4
hypercenterC22×#135D11
hypocenterC11C2×#3284
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×#66969C2semidirect
2. C2×#10623365C2semidirect
3. C2×#10623355C2semidirect
4. #13080340C2direct (N × H)
5. C2×#10622788C2semidirect
6. C2×#10622727C2semidirect
7. C2×#10622784C2semidirect
8. C2×#10622795C2semidirect
9. C2×#10622763C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622800C2semidirect
12. C2×#10622851C2semidirect
13. C2×#10622771C2semidirect
14. C2×SD16×Dic11C2semidirect
15. C2×C8×C22⋊D11C2semidirect
16. C22×C11×#135C2semidirect
22. C2×C11×#135C22semidirect
29. #10623365C22semidirect
31. #10623355C22semidirect
54. C2×#66969C22semidirect
57. #10622852C22semidirect
58. #10622851C22semidirect
64. #10622800C22semidirect
65. #10622795C22semidirect
66. #10622788C22semidirect
67. #10622784C22semidirect
68. SD16×Dic11C22semidirect
69. #10622771C22semidirect
70. #10622763C22semidirect
71. #10622727C22semidirect
73. C8×C22⋊D11C22semidirect
121. C2×C11×SD16D4semidirect
289. C11×SD16C2×D4semidirect
327. C22×#135D11semidirect
408. C2×Dic11#135semidirect
434. C2×#135C2×D11semidirect
524. Dic11C2×#135semidirect
576. C2×SD16C22⋊D11semidirect
648. C2×C11#3284semidirect
747. SD16C2×C22⋊D11semidirect
780. C11C2×#3284semidirect
907. C2#13080340direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669692
C2×#106233652
C2×#106233552
#130803402
C2×#106227882
C2×#106227272
C2×#106227842
C2×#106227952
C2×#106227632
C2×#106228522
C2×#106228002
C2×#106228512
C2×#106227712
C2×SD16×Dic112
C2×C8×C22⋊D112
C22×C11×#1352
C2×#328411