Finite Group Databasebeta

← C2×#13072201 #14921654

Subgroups — C2×#13072201 #14921654

Order 2816.

5062 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4C22×#66992C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
6#13072201C2116yesmaximal, direct product factor
7C2×#10622604C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622570C211yesmaximal, characteristic, complemented
12C2×#10622585C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×C22⋊D11C2211yescharacteristic
27C24×Dic11C2211yescharacteristic
28C23×D44C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C2×C11×#121—28no—
31C2×C11×#121C2218yescomplemented
32C22×C11×C4⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic
40C2×#66993—28no—
41C2×#66993C2218yescomplemented
42C2×#66992—28no—
43C2×#66992—28no—
44C2×#66992C2218yescomplemented
45C2×#66992C2218yescomplemented
46C2×C4×C22⋊D11—28no—
47C2×C4×C22⋊D11C2218yescomplemented
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C2211yescharacteristic
51C22×(C2×D11)⋊C4C2211yescharacteristic
52C22×(C2×D11)⋊C4C2211yescharacteristic
53C22×Dic11⋊C4C2211yescharacteristic
54C22×Dic11⋊C4C2211yescharacteristic
55C22×Dic11⋊C4C2211yescharacteristic
56C22×C4×Dic11C2211yescharacteristic
57C22×C4×Dic11C2211yescharacteristic
58C2×#66937—28no—
59C2×#66937C2218yescomplemented
60#10622836C2218yescomplemented
61#10622836C2218yescomplemented
62#10622835C2218yescomplemented
63#10622826C2218yescomplemented
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66C2×C11⋊#95C2211yescharacteristic
67C2×C11⋊#95C2211yescharacteristic
68#10622604C2218yescomplemented
69#10622585C2218yescomplemented
70#10622570C2218yescomplemented
71#10622569C2218yescomplemented
72C22⋊C4×Dic11C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C25×C11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C24×D11C2311yescharacteristic
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—24no—
84C22×D4×C11—42no—
85C22×D4×C11—42no—
86C22×D4×C11—42no—
87C22×D4×C11C2314yes—
88C22×D4×C11C2314yes—
89C22×D4×C11C2314yes—
90C23×C4×C11—24no—
91C23×C4×C11—24no—
92C23×C4×C11—42no—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2314yes—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—24no—
105C22×C22⋊D11—24no—
106C22×C22⋊D11—24no—
107C22×C22⋊D11—24no—
108C22×C22⋊D11—24no—
109C22×C22⋊D11—24no—
110C22×C22⋊D11—24no—
111C22×C22⋊D11—42no—
112C22×C22⋊D11—42no—
113C22×C22⋊D11—42no—
114C22×C22⋊D11—42no—
115C22×C22⋊D11D418yescomplemented
116C22×C22⋊D11C2314yes—
117C22×C22⋊D11C2314yes—
118C22×C22⋊D11C2314yes—
119C22×C22⋊D11C2314yes—
120C22×C22⋊D11C2314yes—
121C22×C22⋊D11C2314yes—
122C23×Dic11—24no—
123C23×Dic11—24no—
124C23×Dic11—24no—
125C23×Dic11C2311yescharacteristic
126C23×Dic11C2311yescharacteristic
127C23×Dic11C2311yescharacteristic
128C23×Dic11C2314yes—
129C23×Dic11C2311yescharacteristic
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C22×D44—24no—
133C22×D44—24no—
134C22×D44—42no—
135C22×D44C2314yes—
136C22×C4×D11—24no—
137C22×C4×D11—24no—
138C22×C4×D11—42no—
139C22×C4×D11C2314yes—
140C11×#121—232no—
141C2×C11×C4⋊C4—24no—
142C2×C11×C4⋊C4C2314yes—
143C2×C11×C22⋊C4—24no—
144C2×C11×C22⋊C4D418yescomplemented
145C2×C11×C22⋊C4C2314yes—
146C2×C11×C22⋊C4C2314yes—
147C2×C22⋊Dic11—24no—
148C2×C22⋊Dic11—24no—
149C2×C22⋊Dic11—24no—
150C2×C22⋊Dic11—24no—
151C2×C22⋊Dic11—42no—
152C2×C22⋊Dic11C2314yes—
153C2×C22⋊Dic11C2314yes—
154C2×C22⋊Dic11C2314yes—
155C2×C22⋊Dic11C2314yes—
156C2×C22⋊Dic11C2314yes—
157#66993—232no—
158#66992—232no—
159#66992—232no—
160C4×C22⋊D11—232no—
161C2×(C2×D11)⋊C4—24no—
162C2×(C2×D11)⋊C4—24no—
163C2×(C2×D11)⋊C4—24no—
164C2×(C2×D11)⋊C4—24no—
165C2×(C2×D11)⋊C4—42no—
166C2×(C2×D11)⋊C4C2314yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×Dic11⋊C4—24no—
172C2×Dic11⋊C4—24no—
173C2×Dic11⋊C4D418yescomplemented
174C2×Dic11⋊C4C2314yes—
175C2×Dic11⋊C4C2314yes—
176C2×Dic11⋊C4C2314yes—
177C2×C4×Dic11—24no—
178C2×C4×Dic11—24no—
179C2×C4×Dic11C2314yes—
180C2×C4×Dic11C2314yes—
181#66937—232no—
182C11⋊#95C2314yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2314yes—
186C2×#2428—111nomaximal, Sylow
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—22no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—22no—
199C24×C11—22no—
200C24×C11—22no—
201C24×C11—22no—
202C24×C11—22no—
203C24×C11—22no—
204C24×C11—22no—
205C24×C11—22no—
206C24×C11C2×D414yes—
207C24×C11C2×D414yes—
208C24×C11C2412yes—
209C24×C11C2412yes—
210C24×C11C2412yes—
211C24×C11C2411yescharacteristic
212C23×D11—22no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—22no—
217C23×D11—22no—
218C23×D11—22no—
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11C2×D414yes—
226C23×D11C2412yes—
227C23×D11C2412yes—
228C2×D4×C11—28no—
229C2×D4×C11—28no—
230C2×D4×C11—28no—
231C2×D4×C11—28no—
232C2×D4×C11—28no—
233C2×D4×C11—28no—
234C2×D4×C11—44no—
235C2×D4×C11—44no—
236C2×D4×C11—44no—
237C2×D4×C11—416no—
238C2×D4×C11—416no—
239C2×D4×C11—416no—
240C22×C4×C11—22no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—28no—
250C22×C4×C11—28no—
251C22×C4×C11—44no—
252C22×C4×C11—416no—
253C22×C4×C11C2×D414yes—
254C22×C4×C11C2×D414yes—
255C22×C4×C11C2×D414yes—
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2412yes—
259C22×C4×C11C2412yes—
260C2×C22⋊D11—232no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—28no—
264C2×C22⋊D11—28no—
265C2×C22⋊D11—28no—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—28no—
271C2×C22⋊D11—28no—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—28no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—44no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—416no—
279C2×C22⋊D11—416no—
280C2×C22⋊D11—416no—
281C2×C22⋊D11—416no—
282C2×C22⋊D11—416no—
283C2×C22⋊D11C2×D4116yescomplemented
284C22×Dic11—28no—
285C22×Dic11—28no—
286C22×Dic11—28no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—22no—
291C22×Dic11—22no—
292C22×Dic11—22no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11—416no—
301C22×Dic11C2×D414yes—
302C22×Dic11C2×D414yes—
303C22×Dic11C2×D414yes—
304C22×Dic11#4114yes—
305C22×Dic11#4114yes—
306C22×Dic11C2412yes—
307C22×Dic11C2412yes—
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C2×D44—28no—
313C2×D44—28no—
314C2×D44—44no—
315C2×D44—416no—
316C2×C4×D11—28no—
317C2×C4×D11—28no—
318C2×C4×D11—44no—
319C2×C4×D11—416no—
320C11×C4⋊C4—28no—
321C11×C22⋊C4—28no—
322C11×C22⋊C4C2×D4116yescomplemented
323C22⋊Dic11—28no—
324C22⋊Dic11—28no—
325C22⋊Dic11—28no—
326C22⋊Dic11—28no—
327C22⋊Dic11—44no—
328(C2×D11)⋊C4—28no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—28no—
332(C2×D11)⋊C4—44no—
333Dic11⋊C4—28no—
334Dic11⋊C4—28no—
335Dic11⋊C4C2×D4116yescomplemented
336C4×Dic11—28no—
337C4×Dic11—28no—
338C22×#127—111no—
339C22×#121—111no—
340C22×#121—111no—
341C22×#121—111no—
342C22×#121D1111yescharacteristic, complemented
343C22×C4×D4—111no—
344#2428—1116no—
345C2×#394—111no—
346C2×#394—111no—
347C2×#392—111no—
348C2×#392—111no—
349C2×#390—111no—
350C2×#389—111no—
351C2×#386—111no—
352C2×#386—111no—
353C2×C4×C22⋊C4—111no—
354C23×C11—28no—
355C23×C11—28no—
356C23×C11—28no—
357C23×C11—28no—
358C23×C11—28no—
359C23×C11—28no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11—44no—
383C23×C11—44no—
384C23×C11—44no—
385C23×C11—44no—
386C23×C11—44no—
387C23×C11—44no—
388C23×C11—44no—
389C23×C11—44no—
390C23×C11—44no—
391C23×C11—44no—
392C23×C11—44no—
393C23×C11—44no—
394C23×C11C22×D414yes—
395C23×C11C22×D412yes—
396C23×C11C22×D412yes—
397C23×C11C22×D414yes—
398C23×C11C22×D412yes—
399C23×C11C2×#4112yes—
400C23×C11C2×#4112yes—
401C23×C11H(5,𝔽2)12yes—
402C23×C11H(5,𝔽2)12yes—
403C23×C11C2511yescharacteristic
404C22×D11—28no—
405C22×D11—28no—
406C22×D11—28no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—44no—
421C22×D11—44no—
422C22×D11—44no—
423C22×D11—44no—
424C22×D11—44no—
425C22×D11—44no—
426C22×D11—44no—
427C22×D11—44no—
428C22×D11—44no—
429C22×D11—44no—
430C22×D11—44no—
431C22×D11C22×D414yes—
432D4×C11—416no—
433D4×C11—416no—
434D4×C11—416no—
435C2×C4×C11—28no—
436C2×C4×C11—28no—
437C2×C4×C11—28no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—416no—
448C2×C4×C11—44no—
449C2×C4×C11C22×D414yes—
450C2×C4×C11C22×D414yes—
451C2×C4×C11C22×D414yes—
452C22⋊D11—232no—
453C22⋊D11—416no—
454C22⋊D11—416no—
455C22⋊D11—416no—
456C22⋊D11—416no—
457C22⋊D11—416no—
458C2×Dic11—28no—
459C2×Dic11—28no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—44no—
474C2×Dic11—44no—
475C2×Dic11—44no—
476C2×Dic11—416no—
477C2×Dic11#121116yescomplemented
478C2×Dic11C22×D414yes—
479C2×Dic11C22×D414yes—
480C2×Dic11C22×D414yes—
481C2×Dic11C2×#4114yes—
482C2×Dic11C2×#4114yes—
483D44—416no—
484C4×D11—416no—
485C23×D4—111no—
486C23×D4—111no—
487C23×D4—111no—
488C23×D4—111no—
489C23×D4—111no—
490C23×D4—111no—
491C23×D4—111no—
492C23×D4C2×D1111yescharacteristic
493C23×D4C2×D1111yescharacteristic
494C23×D4C2×D1111yescharacteristic
495C24×C4—111no—
496C24×C4—111no—
497C24×C4C2×D1111yescharacteristic
498C2×#127—118no—
499C2×#127—228no—
500C2×#121—28no—
501C2×#121—118no—
502C2×#121—118no—
503C2×#121—118no—
504C2×#121—228no—
505C2×#121—228no—
506C2×#121—228no—
507C2×#121C2×D1118yescomplemented
508C2×C4×D4—118no—
509C2×C4×D4—228no—
510C22×C4⋊C4—111no—
511C22×C4⋊C4—111no—
512C22×C4⋊C4—111no—
513C22×C4⋊C4C2×D1111yescharacteristic
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4C2×D1111yescharacteristic
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C42—111no—
527C22×C42—111no—
528#394—118no—
529#394—118no—
530#392—118no—
531#392—118no—
532#390—118no—
533#389—118no—
534#386—118no—
535#386—118no—
536C4×C22⋊C4—118no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C22×C11—24no—
542C22×C11—24no—
543C22×C11—24no—
544C22×C11—24no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—416no—
550C22×C11—416no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—88no—
565C22×C11C2×#12114yes—
566C22×C11#53214yes—
567C22×C11#54014yes—
568C22×C11D4214yes—
569C22×C11D4214yes—
570C22×C11#54614yes—
571C22×C11#55014yes—
572C22×C11C23×D411yescharacteristic
573C22×C11C23×D411yescharacteristic
574C22×C11C23×D411yescharacteristic
575C22×C11C22×#4111yescharacteristic
576C22×C11C22×#4111yescharacteristic
577C22×C11C2×H(5,𝔽2)11yescharacteristic
578C22×C11C2×H(5,𝔽2)11yescharacteristic
579C2×D11—24no—
580C2×D11—24no—
581C2×D11—24no—
582C2×D11—42no—
583C2×D11—416no—
584C2×D11—42no—
585C2×D11—42no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—88no—
595C4×C11—24no—
596C4×C11—24no—
597C4×C11—24no—
598C4×C11—42no—
599Dic11—24no—
600Dic11—24no—
601Dic11—42no—
602Dic11—42no—
603Dic11—42no—
604Dic11C2×#12118yescomplemented
605C25—111no—
606C25—111no—
607C25C22×D1111yescharacteristic
608C25C22×D1111yescharacteristic
609C25C22×D1111yescharacteristic
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—24no—
613C22×D4—24no—
614C22×D4—24no—
615C22×D4—24no—
616C22×D4—42no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4—118no—
620C22×D4—114no—
621C22×D4—114no—
622C22×D4—114no—
623C22×D4—114no—
624C22×D4—114no—
625C22×D4—114no—
626C22×D4—114no—
627C22×D4—224no—
628C22×D4—224no—
629C22×D4—224no—
630C22×D4—224no—
631C22×D4—224no—
632C22×D4—224no—
633C22×D4—224no—
634C22×D4—224no—
635C22×D4—224no—
636C22×D4—224no—
637C22×D4—224no—
638C22×D4—224no—
639C22×D4—224no—
640C22×D4—224no—
641C22×D4—224no—
642C22×D4—442no—
643C22×D4—442no—
644C22×D4—442no—
645C22×D4—442no—
646C22×D4—442no—
647C22×D4C22×D1114yes—
648C22×D4C22×D1114yes—
649C22×D4C22×D1114yes—
650C23×C4—24no—
651C23×C4—24no—
652C23×C4—42no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—114no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—114no—
661C23×C4—224no—
662C23×C4—224no—
663C23×C4—224no—
664C23×C4—224no—
665C23×C4—224no—
666C23×C4—442no—
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1114yes—
669C23×C4C22×D1111yescharacteristic
670C23×C4C22×D1111yescharacteristic
671C23×C4C22×D1111yescharacteristic
672#127—2232no—
673#121—232no—
674#121—2232no—
675#121—2232no—
676#121—2232no—
677C4×D4—2232no—
678C2×C4⋊C4—24no—
679C2×C4⋊C4—118no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—114no—
682C2×C4⋊C4—114no—
683C2×C4⋊C4—224no—
684C2×C4⋊C4—224no—
685C2×C4⋊C4C22×D1114yes—
686C2×C22⋊C4—24no—
687C2×C22⋊C4—114no—
688C2×C22⋊C4—114no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—114no—
691C2×C22⋊C4—114no—
692C2×C22⋊C4—114no—
693C2×C22⋊C4—114no—
694C2×C22⋊C4—114no—
695C2×C22⋊C4—114no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—224no—
698C2×C22⋊C4—224no—
699C2×C22⋊C4—224no—
700C2×C22⋊C4—224no—
701C2×C22⋊C4—224no—
702C2×C22⋊C4—224no—
703C2×C22⋊C4—224no—
704C2×C22⋊C4—224no—
705C2×C22⋊C4—442no—
706C2×C22⋊C4—442no—
707C2×C22⋊C4C22⋊D1118yescomplemented
708C2×C22⋊C4C22×D1114yes—
709C2×C22⋊C4C22×D1114yes—
710C2×C42—114no—
711C2×C42—114no—
712C2×C42—224no—
713C2×C42—224no—
714#95—114no—
715#95—114no—
716#95—114no—
717#95—114no—
718C2×C11—44no—
719C2×C11—44no—
720C2×C11—82no—
721C2×C11#242818yescomplemented
722C2×C11C22×#12111yescharacteristic
723C2×C11C2×#53211yescharacteristic
724C2×C11C2×#54011yescharacteristic
725C2×C11C2×D4211yescharacteristic
726C2×C11C2×D4211yescharacteristic
727C2×C11C2×#54611yescharacteristic
728C2×C11C2×#55011yescharacteristic
729D11—44no—
730D11—82no—
731C24—22no—
732C24—22no—
733C24—22no—
734C24—22no—
735C24—22no—
736C24—22no—
737C24—22no—
738C24—22no—
739C24—22no—
740C24—22no—
741C24—22no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—114no—
751C24—112no—
752C24—112no—
753C24—222no—
754C24—222no—
755C24—222no—
756C24—222no—
757C24—222no—
758C24—222no—
759C24—222no—
760C24—222no—
761C24—222no—
762C24—222no—
763C24—222no—
764C24—222no—
765C24—222no—
766C24D4×D1114yes—
767C24C2×C22⋊D1114yes—
768C24C23×D1112yes—
769C24C23×D1112yes—
770C24C23×D1112yes—
771C24C23×D1111yescharacteristic
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—28no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—416no—
782C2×D4—416no—
783C2×D4—416no—
784C2×D4—1116no—
785C2×D4—228no—
786C2×D4—228no—
787C2×D4—2232no—
788C2×D4—228no—
789C2×D4—228no—
790C2×D4—228no—
791C2×D4—228no—
792C2×D4—228no—
793C2×D4—228no—
794C2×D4—228no—
795C2×D4—228no—
796C2×D4—228no—
797C2×D4—228no—
798C2×D4—228no—
799C2×D4—228no—
800C2×D4—228no—
801C2×D4—444no—
802C2×D4—4416no—
803C2×D4—4416no—
804C2×D4—444no—
805C2×D4—444no—
806C2×D4—444no—
807C2×D4—444no—
808C2×D4—4416no—
809C2×D4—4416no—
810C2×D4—4416no—
811C2×D4—4416no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—44no—
824C22×C4—416no—
825C22×C4—114no—
826C22×C4—114no—
827C22×C4—114no—
828C22×C4—112no—
829C22×C4—114no—
830C22×C4—114no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—228no—
837C22×C4—228no—
838C22×C4—228no—
839C22×C4—228no—
840C22×C4—222no—
841C22×C4—222no—
842C22×C4—222no—
843C22×C4—222no—
844C22×C4—222no—
845C22×C4—222no—
846C22×C4—222no—
847C22×C4—222no—
848C22×C4—222no—
849C22×C4—222no—
850C22×C4—222no—
851C22×C4—222no—
852C22×C4—222no—
853C22×C4—228no—
854C22×C4—444no—
855C22×C4—4416no—
856C22×C4—4416no—
857C22×C4D4×D1114yes—
858C22×C4C2×C22⋊D1114yes—
859C22×C4C2×C22⋊D1114yes—
860C22×C4C23×D1112yes—
861C22×C4C23×D1112yes—
862C22×C4C23×D1112yes—
863C22×C4C23×D1112yes—
864C4⋊C4—28no—
865C4⋊C4—1116no—
866C4⋊C4—228no—
867C4⋊C4—228no—
868C22⋊C4—28no—
869C22⋊C4—228no—
870C22⋊C4—228no—
871C22⋊C4—228no—
872C22⋊C4—228no—
873C22⋊C4—228no—
874C22⋊C4—228no—
875C22⋊C4—228no—
876C22⋊C4—228no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C22⋊C4C2×C22⋊D11116yescomplemented
880C42—228no—
881C42—228no—
882C11C2×#242811yescharacteristic, complemented, Sylow
883C23—28no—
884C23—28no—
885C23—28no—
886C23—28no—
887C23—28no—
888C23—28no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—44no—
921C23—44no—
922C23—44no—
923C23—114no—
924C23—228no—
925C23—228no—
926C23—228no—
927C23—222no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—444no—
941C23—444no—
942C23—444no—
943C23—444no—
944C23—444no—
945C23—444no—
946C23—444no—
947C23—444no—
948C23—444no—
949C23—444no—
950C23—444no—
951C23C2×D4×D1114yes—
952C23C2×D4×D1112yes—
953C23C2×D4×D1112yes—
954C23#6703712yes—
955C23#6703712yes—
956C23#41×D1112yes—
957C23#41×D1112yes—
958C23C22×C22⋊D1114yes—
959C23C22×C22⋊D1112yes—
960C23C24×D1111yescharacteristic
961D4—416no—
962D4—416no—
963D4—416no—
964D4—2232no—
965D4—4416no—
966D4—4416no—
967D4—4416no—
968D4—4416no—
969D4—4416no—
970D4—4416no—
971C2×C4—28no—
972C2×C4—28no—
973C2×C4—28no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—416no—
984C2×C4—44no—
985C2×C4—1116no—
986C2×C4—114no—
987C2×C4—114no—
988C2×C4—114no—
989C2×C4—114no—
990C2×C4—114no—
991C2×C4—228no—
992C2×C4—228no—
993C2×C4—222no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—222no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—4416no—
1007C2×C4—4416no—
1008C2×C4—444no—
1009C2×C4—444no—
1010C2×C4—444no—
1011C2×C4C2×D4×D1114yes—
1012C2×C4C22×C22⋊D1114yes—
1013C2×C4C22×C22⋊D1114yes—
1014C22—24no—
1015C22—24no—
1016C22—24no—
1017C22—24no—
1018C22—24no—
1019C22—24no—
1020C22—42no—
1021C22—416no—
1022C22—416no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—88no—
1038C22—224no—
1039C22—224no—
1040C22—224no—
1041C22—442no—
1042C22—4416no—
1043C22—442no—
1044C22—442no—
1045C22—442no—
1046C22—442no—
1047C22—442no—
1048C22—442no—
1049C22—442no—
1050C22—442no—
1051C22—442no—
1052C22—442no—
1053C22—888no—
1054C22#1062313014yes—
1055C22D11×#12114yes—
1056C22#1062314114yes—
1057C22#1062314614yes—
1058C22D4×C22⋊D1114yes—
1059C22D4×C22⋊D1114yes—
1060C22#1062336314yes—
1061C22C22×D4×D1111yescharacteristic
1062C22C22×D4×D1111yescharacteristic
1063C22C2×#6703711yescharacteristic
1064C22C2×#6703711yescharacteristic
1065C22C2×#41×D1111yescharacteristic
1066C22C2×#41×D1111yescharacteristic
1067C22C23×C22⋊D1111yescharacteristic
1068C4—24no—
1069C4—24no—
1070C4—24no—
1071C4—42no—
1072C4—118no—
1073C4—224no—
1074C4—224no—
1075C4—442no—
1076C4—442no—
1077C4—442no—
1078C2—44no—
1079C2—44no—
1080C2—82no—
1081C2—444no—
1082C2—882no—
1083C2#1307220118yesdirect product factor
1084C2C2×D11×#12111yescharacteristic
1085C2C2×#1062336311yescharacteristic
1086C2C2×#1062314611yescharacteristic
1087C2C2×D4×C22⋊D1111yescharacteristic
1088C2C2×D4×C22⋊D1111yescharacteristic
1089C2C2×#1062314111yescharacteristic
1090C2C2×#1062313011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66993C2semidirect
2. C22×#66937C2semidirect
3. C22×#66992C2semidirect
4. C22×#66992C2semidirect
5. C22×C4×C22⋊D11C2semidirect
6. #13072201C2direct (N × H)
7. C2×#10622604C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622570C2semidirect
12. C2×#10622585C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622569C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C22×C11×#121C2semidirect
31. C2×C11×#121C22semidirect
41. C2×#66993C22semidirect
44. C2×#66992C22semidirect
45. C2×#66992C22semidirect
47. C2×C4×C22⋊D11C22semidirect
59. C2×#66937C22semidirect
60. #10622836C22semidirect
61. #10622836C22semidirect
62. #10622835C22semidirect
63. #10622826C22semidirect
68. #10622604C22semidirect
69. #10622585C22semidirect
70. #10622570C22semidirect
71. #10622569C22semidirect
72. C22⋊C4×Dic11C22semidirect
115. C22×C22⋊D11D4semidirect
144. C2×C11×C22⋊C4D4semidirect
173. C2×Dic11⋊C4D4semidirect
283. C2×C22⋊D11C2×D4semidirect
322. C11×C22⋊C4C2×D4semidirect
335. Dic11⋊C4C2×D4semidirect
342. C22×#121D11semidirect
477. C2×Dic11#121semidirect
507. C2×#121C2×D11semidirect
604. Dic11C2×#121semidirect
707. C2×C22⋊C4C22⋊D11semidirect
721. C2×C11#2428semidirect
879. C22⋊C4C2×C22⋊D11semidirect
882. C11C2×#2428semidirect
1083. C2#13072201direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×#669372
C22×#669922
C22×C4×C22⋊D112
#130722012
C2×#106226042
C2×#106228352
C2×#106228362
C2×#106225702
C2×#106225852
C2×#106228262
C2×#106225692
C2×C22⋊C4×Dic112
C22×C11×#1212
C2×#242811