Finite Group Databasebeta

← C2×#13077336 #15617657

Subgroups — C2×#13077336 #15617657

Order 2816.

2926 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66954C211yesmaximal, characteristic, complemented
2C23×#4313C211yesmaximal, characteristic, complemented
3C2×#10623078C211yesmaximal, characteristic
4#13077336C2116yesmaximal, direct product factor
5C2×#10622301C211yesmaximal, characteristic, complemented
6C2×#10622342C211yesmaximal, characteristic, complemented
7C2×#10622624C211yesmaximal, characteristic, complemented
8C2×#10622724C211yesmaximal, characteristic, complemented
9C2×#10622724C211yesmaximal, characteristic, complemented
10C2×#10622449C211yesmaximal, characteristic, complemented
11C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
12C2×#10622452C211yesmaximal, characteristic, complemented
13C2×#10622340C211yesmaximal, characteristic, complemented
14C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
15C2×#10622302C211yesmaximal, characteristic, complemented
16C2×C8×D4×C11C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66992C411yescharacteristic
23C2×#66990C411yescharacteristic
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×C4×C22⋊D11C2211yescharacteristic
26C22×#4318C2211yescharacteristic, complemented
27C23×C11⋊C8C2211yescharacteristic
28C2×#66954—28no—
29C2×#66954C2218yescomplemented
30C22×#4313—28no—
31C22×#4313C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33C22×#4313C2211yescharacteristic
34C22×#4313C2211yescharacteristic
35C22×#4313C2218yescomplemented
36C22×#4313C2211yescharacteristic, complemented
37C22×C8×D11C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39C22×C8×D11C2211yescharacteristic, complemented
40#10623078C418yes—
41#10623078C2218yes—
42C2×#66949C411yescharacteristic
43C2×#66947C411yescharacteristic
44C2×#66937C411yescharacteristic
45C2×#66936C411yescharacteristic
46C2×#66935C411yescharacteristic
47C2×#66931C411yescharacteristic
48C2×C4×D44C2211yescharacteristic
49C2×#66925C2211yescharacteristic
50C8×D4×C11C2218yescomplemented
51C2×C11×C4⋊C8C2211yescharacteristic, complemented
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C2×C4×C8×C11C2211yescharacteristic, complemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622724C2218yescomplemented
58#10622724C2218yescomplemented
59C2×(C2×D11)⋊C8C2211yescharacteristic
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×#66879C2211yescharacteristic, complemented
64C2×Dic11⋊C8C2211yescharacteristic, complemented
65C2×Dic11⋊C8C2211yescharacteristic, complemented
66C2×C8×Dic11C2211yescharacteristic, complemented
67#10622624C2218yescomplemented
68C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
69C2×#66867C2211yescharacteristic, complemented
70#10622452C2218yescomplemented
71#10622449C2218yescomplemented
72#10622342C2218yescomplemented
73#10622340C2218yescomplemented
74(C22⋊D11)⋊C8C2218yescomplemented
75D11×C22⋊C8C2218yescomplemented
76#10622302C2218yescomplemented
77#10622301C2218yescomplemented
78C24×D11C2×C411yescharacteristic
79C22×D4×C11C2×C411yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11C2×C411yescharacteristic
83C22×C22⋊D11C2×C411yescharacteristic
84C22×C22⋊D11C2×C411yescharacteristic
85C22×C22⋊D11C2×C411yescharacteristic
86C23×Dic11C2×C411yescharacteristic
87C2×#4339—24no—
88C2×#4339—24no—
89C2×#4339C2×C414yes—
90C2×#4339C2314yes—
91C22×D44C2×C411yescharacteristic
92C22×D44C2×C411yescharacteristic
93C22×C4×D11—24no—
94C22×C4×D11—24no—
95C22×C4×D11C2×C411yescharacteristic
96C22×C4×D11C2×C411yescharacteristic
97C22×C4×D11C2×C414yes—
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2314yes—
101C22×C4×D11C2311yescharacteristic
102C22×Dic22C2×C411yescharacteristic
103C22×C8×C11—24no—
104C22×C8×C11—24no—
105C22×C8×C11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2314yes—
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2314yescomplemented
111C4×D4×C11C2×C414yes—
112C4×D4×C11C2314yes—
113C2×C11×C4⋊C4C2×C411yescharacteristic
114C2×C11×C22⋊C4C2×C411yescharacteristic
115C2×C11×C22⋊C4C2×C411yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C22⋊Dic11C2×C411yescharacteristic
118C2×C22⋊Dic11C2×C411yescharacteristic
119#66992C2×C418yes—
120#66990C2×C418yes—
121C4×C22⋊D11C2×C414yes—
122C4×C22⋊D11C2×C414yes—
123C4×C22⋊D11C2314yes—
124C4×C22⋊D11C2314yes—
125C2×(C2×D11)⋊C4C2×C411yescharacteristic
126C2×(C2×D11)⋊C4C2×C411yescharacteristic
127C2×(C2×D11)⋊C4C2×C411yescharacteristic
128C2×(C2×D11)⋊C4C2×C411yescharacteristic
129C2×(C2×D11)⋊C4C2×C411yescharacteristic
130C2×(C2×D11)⋊C4C2×C411yescharacteristic
131C2×C4⋊Dic11C2×C411yescharacteristic
132C2×Dic11⋊C4C2×C411yescharacteristic
133C2×Dic11⋊C4C2×C411yescharacteristic
134C2×Dic11⋊C4C2×C411yescharacteristic
135C2×Dic11⋊C4C2×C411yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C2×#4318—24no—
138C2×#4318C2314yescomplemented
139C22×C11⋊C8—24no—
140C22×C11⋊C8C2311yescharacteristic
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2314yes—
144C22×C11⋊C8C2311yescharacteristic
145#66954—232no—
146C2×#4313—24no—
147C2×#4313—24no—
148C2×#4313—24no—
149C2×#4313—24no—
150C2×#4313—232no—
151C2×#4313D418yescomplemented
152C2×#4313C2314yes—
153C2×#4313C2314yes—
154C2×#4313C2314yes—
155C2×#4313C2314yes—
156C2×#4313C2314yescomplemented
157C2×C8×D11—24no—
158C2×C8×D11—24no—
159C2×C8×D11—24no—
160C2×C8×D11C2314yes—
161C2×C8×D11C2314yes—
162C2×C8×D11C2314yescomplemented
163#66949C2×C418yes—
164#66947C2×C418yes—
165#66937C2×C418yes—
166#66936C2×C418yes—
167#66935C2×C418yes—
168#66931C2×C418yes—
169C4×D44C2×C414yes—
170C4×D44C2314yes—
171#66925C2×C414yes—
172#66925C2314yes—
173C11×C4⋊C8C2314yescomplemented
174C11×C22⋊C8C2314yes—
175C11×C22⋊C8C2314yescomplemented
176C4×C8×C11C2314yescomplemented
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yescomplemented
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yescomplemented
182(C2×D11)⋊C8C2314yescomplemented
183#66879C2314yescomplemented
184Dic11⋊C8C2314yescomplemented
185Dic11⋊C8C2314yescomplemented
186C8×Dic11C2314yescomplemented
187C4⋊(C11⋊C8)C2314yescomplemented
188#66867C2314yescomplemented
189C2×#2933—111nomaximal, Sylow
190C24×C11C22×C411yescharacteristic
191C24×C11C22×C411yescharacteristic
192C23×D11—24no—
193C23×D11—24no—
194C23×D11—42no—
195C23×D11C22×C411yescharacteristic
196C23×D11C22×C411yescharacteristic
197C23×D11C22×C414yes—
198C23×D11C22×C411yescharacteristic
199C2×D4×C11—24no—
200C2×D4×C11C22×C414yes—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C412yes—
210C22×C4×C11C22×C412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—24no—
217C2×C22⋊D11—42no—
218C2×C22⋊D11C22×C414yes—
219C2×C22⋊D11C22×C414yes—
220C2×C22⋊D11C22×C414yes—
221C2×C22⋊D11C22×C414yes—
222C22×Dic11—24no—
223C22×Dic11C22×C414yes—
224C22×Dic11C22×C411yescharacteristic
225C22×Dic11C22×C411yescharacteristic
226C22×Dic11C22×C411yescharacteristic
227C22×Dic11C22×C411yescharacteristic
228C22×Dic11C22×C411yescharacteristic
229#4339—216no—
230#4339—28no—
231#4339—28no—
232C2×D44—24no—
233C2×D44—42no—
234C2×D44C22×C414yes—
235C2×D44C22×C414yes—
236C2×C4×D11—24no—
237C2×C4×D11—216no—
238C2×C4×D11—28no—
239C2×C4×D11—28no—
240C2×C4×D11—24no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11C22×C412yes—
246C2×C4×D11C22×C412yes—
247C2×C4×D11C22×C414yes—
248C2×C4×D11C22×C414yes—
249C2×C4×D11C22×C412yes—
250C2×C4×D11C2×D414yes—
251C2×C4×D11#4114yes—
252C2×C4×D11C2412yes—
253C2×C4×D11C2412yes—
254C2×C4×D11C2412yes—
255C2×Dic22—24no—
256C2×Dic22C22×C414yes—
257C2×C8×C11—28no—
258C2×C8×C11—28no—
259C2×C8×C11—22no—
260C2×C8×C11—22no—
261C2×C8×C11—22no—
262C2×C8×C11C2×D414yes—
263C2×C8×C11C2412yes—
264C2×C8×C11C2412yes—
265C2×C8×C11C2412yes—
266C2×C8×C11C2412yes—
267C11×C4⋊C4C22×C414yes—
268C11×C22⋊C4C22×C414yes—
269C11×C22⋊C4C22×C414yes—
270C42×C11C22×C412yes—
271C42×C11C2412yes—
272C22⋊Dic11C22×C414yes—
273C22⋊Dic11C22×C414yes—
274(C2×D11)⋊C4C22×C414yes—
275(C2×D11)⋊C4C22×C414yes—
276(C2×D11)⋊C4C22×C414yes—
277(C2×D11)⋊C4C22×C414yes—
278(C2×D11)⋊C4C22×C414yes—
279(C2×D11)⋊C4C22×C414yes—
280C4⋊Dic11C22×C414yes—
281Dic11⋊C4C22×C414yes—
282Dic11⋊C4C22×C414yes—
283Dic11⋊C4C22×C414yes—
284Dic11⋊C4C22×C414yes—
285C4×Dic11C22×C412yes—
286C4×Dic11C2412yes—
287#4318—28no—
288C2×C11⋊C8—28no—
289C2×C11⋊C8—22no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8C2×D414yes—
293C2×C11⋊C8C2412yes—
294C2×C11⋊C8C2412yes—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297#4313—28no—
298#4313—28no—
299#4313—28no—
300#4313—28no—
301#4313C2×D4116yescomplemented
302C8×D11—28no—
303C8×D11—28no—
304C8×D11—28no—
305C22×#131—111no—
306C23×M16—111no—
307C2×#525—111no—
308#2933—1116no—
309C2×#436—111no—
310C2×#436—111no—
311C2×#435—111no—
312C2×#435—111no—
313C2×#435—111no—
314C2×#435—111no—
315C2×C8×D4—111no—
316C2×C8×D4D1111yescharacteristic, complemented
317C2×#424—111no—
318C2×#408—111no—
319C22×C22⋊C8—111no—
320C2×#405—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11#13114yescomplemented
327C23×C11C23×C412yes—
328C23×C11C23×C412yes—
329C23×C11C23×C411yescharacteristic
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—28no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—28no—
340C22×D11—44no—
341C22×D11—416no—
342C22×D11C4×D414yes—
343C22×D11C23×C412yes—
344C22×D11C23×C412yes—
345C22×D11C23×C412yes—
346D4×C11—28no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—24no—
352C2×C4×C11—24no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11C23×C412yes—
358C2×C4×C11C23×C412yes—
359C2×C4×C11C23×C412yes—
360C2×C4×C11C23×C412yes—
361C2×C4×C11C23×C411yescharacteristic
362C2×C4×C11C22×D412yes—
363C2×C4×C11C2×#4112yes—
364C2×C4×C11C2511yescharacteristic
365C22⋊D11—28no—
366C22⋊D11—28no—
367C22⋊D11—28no—
368C22⋊D11—44no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—28no—
374C2×Dic11C4×D414yes—
375C2×Dic11C23×C412yes—
376C2×Dic11C23×C412yes—
377C2×Dic11C23×C412yes—
378C2×Dic11C23×C412yes—
379C2×Dic11C23×C412yes—
380D44—28no—
381D44—44no—
382C4×D11—28no—
383C4×D11—24no—
384C4×D11—24no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—28no—
390C4×D11C4×D418yes—
391C4×D11C22×D414yes—
392C4×D11C2×#4114yes—
393Dic22—28no—
394C8×C11—22no—
395C8×C11—22no—
396C8×C11—22no—
397C8×C11C22×D414yes—
398C11⋊C8—22no—
399C11⋊C8—22no—
400C11⋊C8—22no—
401C11⋊C8C22×D414yes—
402C22×#41—111no—
403C24×C4—111no—
404C2×#131—118no—
405C2×#131—228no—
406C22×M16—111no—
407C22×M16—111no—
408C22×M16—111no—
409C22×M16—111no—
410C22×M16—111no—
411C22×M16—111no—
412C22×M16—118no—
413C22×M16—228no—
414C23×C8—111no—
415C23×C8—111no—
416C23×C8—111no—
417C23×C8—111no—
418C23×C8C2×D1111yescharacteristic
419C23×C8C2×D1111yescharacteristic, complemented
420#525—118no—
421#525—118no—
422C2×#123—111no—
423C2×#123—111no—
424C2×C22⋊Q8—111no—
425C2×C22⋊Q8—111no—
426C2×#121—111no—
427C2×#121—111no—
428C2×#120—111no—
429C2×#120—111no—
430C2×C4×D4—111no—
431C2×C4×D4—111no—
432C2×C4×D4—111no—
433C2×C4×D4C2×D1111yescharacteristic
434C2×#117—111no—
435#436—118no—
436#436—118no—
437#435—118no—
438#435—118no—
439#435—118no—
440#435—118no—
441C8×D4—118no—
442C8×D4C2×D1118yescomplemented
443#424—118no—
444C2×C4⋊C8—111no—
445C2×C4⋊C8—111no—
446C2×C4⋊C8—111no—
447C2×C4⋊C8C2×D1111yescharacteristic, complemented
448#408—118no—
449C2×C22⋊C8—111no—
450C2×C22⋊C8—111no—
451C2×C22⋊C8—111no—
452C2×C22⋊C8—111no—
453C2×C22⋊C8—111no—
454C2×C22⋊C8—111no—
455C2×C22⋊C8—118no—
456C2×C22⋊C8C2×D1111yescharacteristic
457C2×C22⋊C8C2×D1111yescharacteristic, complemented
458#405—118no—
459C2×#97—111no—
460C2×#97—111no—
461C2×C4×C8—111no—
462C2×C4×C8C2×D1111yescharacteristic, complemented
463C22×C11—22no—
464C22×C11—28no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—44no—
470C22×C11C2×C4×D412yes—
471C22×C11C2×#13112yes—
472C22×C11C2×#13114yescomplemented
473C22×C11#56812yes—
474C22×C11C24×C411yescharacteristic
475C2×D11—28no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—22no—
482C2×D11—22no—
483C2×D11—22no—
484C2×D11—416no—
485C2×D11—44no—
486C2×D11—44no—
487C2×D11C2×C4×D414yes—
488C4×C11—22no—
489C4×C11—22no—
490C4×C11—22no—
491C4×C11—22no—
492C4×C11C2×C4×D412yes—
493C4×C11C23×D411yescharacteristic
494C4×C11C22×#4111yescharacteristic
495Dic11—22no—
496Dic11—22no—
497Dic11—22no—
498Dic11—22no—
499Dic11C2×C4×D414yes—
500C25—111no—
501C2×#41—114no—
502C2×#41—114no—
503C2×#41—224no—
504C2×#41—224no—
505C22×Q8—111no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—111no—
510C22×D4—111no—
511C22×D4—111no—
512C22×D4C4×D1111yescharacteristic
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—114no—
518C23×C4—114no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—224no—
522C23×C4—224no—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525#131—2232no—
526C2×M16—114no—
527C2×M16—118no—
528C2×M16—114no—
529C2×M16—114no—
530C2×M16—114no—
531C2×M16—114no—
532C2×M16—114no—
533C2×M16—224no—
534C2×M16—2232no—
535C2×M16—224no—
536C2×M16—224no—
537C2×M16—224no—
538C2×M16—224no—
539C22×C8—24no—
540C22×C8—24no—
541C22×C8—111no—
542C22×C8—114no—
543C22×C8—111no—
544C22×C8—111no—
545C22×C8—111no—
546C22×C8—114no—
547C22×C8—114no—
548C22×C8—114no—
549C22×C8—224no—
550C22×C8—224no—
551C22×C8—224no—
552C22×C8—224no—
553C22×C8C22×D1114yes—
554C22×C8C22×D1111yescharacteristic
555C22×C8C22×D1111yescharacteristic
556C22×C8C22×D1111yescharacteristic
557C22×C8C22×D1111yescharacteristic
558C22×C8C22×D1114yescomplemented
559#123—118no—
560#123—118no—
561C22⋊Q8—118no—
562C22⋊Q8—118no—
563#121—118no—
564#121—118no—
565#120—118no—
566#120—118no—
567C4×D4—114no—
568C4×D4—114no—
569C4×D4—114no—
570C4×D4—114no—
571C4×D4—114no—
572C4×D4—114no—
573C4×D4C4×D1114yes—
574C4×D4C22×D1114yes—
575#117—114no—
576#117—114no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—111no—
581C2×C4⋊C4—111no—
582C2×C4⋊C4C4×D1111yescharacteristic
583C2×C22⋊C4—111no—
584C2×C22⋊C4—111no—
585C2×C22⋊C4—111no—
586C2×C22⋊C4—111no—
587C2×C22⋊C4—111no—
588C2×C22⋊C4—111no—
589C2×C22⋊C4—111no—
590C2×C22⋊C4—111no—
591C2×C22⋊C4C4×D1111yescharacteristic
592C2×C22⋊C4C4×D1111yescharacteristic
593C2×C42—111no—
594C2×C42C22×D1111yescharacteristic
595C4⋊C8—114no—
596C4⋊C8—114no—
597C4⋊C8—114no—
598C4⋊C8C22×D1114yescomplemented
599C22⋊C8—114no—
600C22⋊C8—114no—
601C22⋊C8—114no—
602C22⋊C8—114no—
603C22⋊C8—114no—
604C22⋊C8—114no—
605C22⋊C8C22×D1114yes—
606C22⋊C8C22×D1114yescomplemented
607#97—114no—
608#97—114no—
609C4×C8—114no—
610C4×C8C22×D1114yescomplemented
611C2×C11—24no—
612C2×C11—42no—
613C2×C11#293314yescomplemented
614C2×C11C22×C4×D411yescharacteristic
615C2×C11C22×#13111yescharacteristic
616C2×C11C2×#56811yescharacteristic
617D11—24no—
618D11—42no—
619D11—42no—
620C24—111no—
621C24—111no—
622C24—111no—
623C24—114no—
624C24—224no—
625C24—224no—
626C24—442no—
627C24C2×C4×D1111yescharacteristic
628C24C2×C4×D1111yescharacteristic
629#41—228no—
630#41—2216no—
631#41—228no—
632C2×Q8—114no—
633C2×Q8—224no—
634C2×D4—24no—
635C2×D4—114no—
636C2×D4—114no—
637C2×D4—114no—
638C2×D4—114no—
639C2×D4—114no—
640C2×D4—114no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—224no—
644C2×D4—224no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4C2×C4×D1114yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—111no—
653C22×C4—112no—
654C22×C4—114no—
655C22×C4—114no—
656C22×C4—112no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—114no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—114no—
665C22×C4—114no—
666C22×C4—112no—
667C22×C4—112no—
668C22×C4—228no—
669C22×C4—224no—
670C22×C4—2216no—
671C22×C4—228no—
672C22×C4—224no—
673C22×C4—224no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4C2×C4×D1111yescharacteristic
679C22×C4C2×C4×D1111yescharacteristic
680C22×C4C2×C4×D1111yescharacteristic
681C22×C4C2×C4×D1111yescharacteristic
682C22×C4C2×C4×D1112yes—
683C22×C4C2×C4×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1111yescharacteristic
687M16—1116no—
688M16—228no—
689M16—228no—
690M16—228no—
691M16—228no—
692M16—228no—
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—28no—
697C2×C8—28no—
698C2×C8—114no—
699C2×C8—112no—
700C2×C8—112no—
701C2×C8—112no—
702C2×C8—112no—
703C2×C8—228no—
704C2×C8—228no—
705C2×C8—228no—
706C2×C8—228no—
707C2×C8—222no—
708C2×C8—222no—
709C2×C8—222no—
710C2×C8D4×D1114yes—
711C2×C8C23×D1112yes—
712C2×C8C23×D1112yes—
713C2×C8C23×D1112yes—
714C2×C8C23×D1112yes—
715C4⋊C4—114no—
716C4⋊C4—114no—
717C4⋊C4—114no—
718C4⋊C4—114no—
719C4⋊C4—114no—
720C4⋊C4C2×C4×D1114yes—
721C22⋊C4—114no—
722C22⋊C4—114no—
723C22⋊C4—114no—
724C22⋊C4—114no—
725C22⋊C4—114no—
726C22⋊C4—114no—
727C22⋊C4—114no—
728C22⋊C4—114no—
729C22⋊C4C2×C4×D1114yes—
730C22⋊C4C2×C4×D1114yes—
731C42—112no—
732C42—112no—
733C42C2×C4×D1112yes—
734C42C23×D1112yes—
735C11C2×#293311yescharacteristic, complemented, Sylow
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—114no—
742C23—112no—
743C23—112no—
744C23—112no—
745C23—228no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—228no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—444no—
756C23—4416no—
757C23#6695414yescomplemented
758C23C22×C4×D1112yes—
759C23C22×C4×D1112yes—
760C23C22×C4×D1111yescharacteristic
761Q8—228no—
762D4—28no—
763D4—228no—
764D4—228no—
765D4—228no—
766D4—228no—
767D4—444no—
768D4—444no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—114no—
780C2×C4—112no—
781C2×C4—118no—
782C2×C4—114no—
783C2×C4—114no—
784C2×C4—112no—
785C2×C4—112no—
786C2×C4—112no—
787C2×C4—112no—
788C2×C4—228no—
789C2×C4—228no—
790C2×C4—228no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—224no—
796C2×C4—224no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4C22×C4×D1112yes—
802C2×C4C22×C4×D1112yes—
803C2×C4C22×C4×D1112yes—
804C2×C4C22×C4×D1112yes—
805C2×C4C22×C4×D1111yescharacteristic
806C2×C4C2×D4×D1112yes—
807C2×C4#41×D1112yes—
808C2×C4C24×D1111yescharacteristic
809C8—22no—
810C8—22no—
811C8—22no—
812C8—114no—
813C8—222no—
814C8—222no—
815C8—222no—
816C8C2×D4×D1114yes—
817C22—28no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—44no—
824C22—114no—
825C22—228no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—222no—
833C22—222no—
834C22—4416no—
835C22—444no—
836C22—444no—
837C22C4×D4×D1112yes—
838C22C2×#6695412yes—
839C22C2×#6695414yescomplemented
840C22#1062328112yes—
841C22C23×C4×D1111yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—114no—
847C4—222no—
848C4—222no—
849C4—222no—
850C4—222no—
851C4C4×D4×D1112yes—
852C4C22×D4×D1111yescharacteristic
853C4C2×#41×D1111yescharacteristic
854C2—24no—
855C2—42no—
856C2—224no—
857C2—442no—
858C2—442no—
859C2#1307733614yesdirect product factor
860C2C2×C4×D4×D1111yescharacteristic
861C2C22×#6695411yescharacteristic
862C2C2×#1062328111yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C8×D4×C11C2
socleC23×C11C23×C4
prime radicalC2×#10623078C2
cosocleC2×C4×C11C25
hypercenterC2×C8×D4D11
hypocenterC11C2×#2933
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66954C2semidirect
2. C23×#4313C2semidirect
4. #13077336C2direct (N × H)
5. C2×#10622301C2semidirect
6. C2×#10622342C2semidirect
7. C2×#10622624C2semidirect
8. C2×#10622724C2semidirect
9. C2×#10622724C2semidirect
10. C2×#10622449C2semidirect
11. C2×(C22⋊D11)⋊C8C2semidirect
12. C2×#10622452C2semidirect
13. C2×#10622340C2semidirect
14. C2×D11×C22⋊C8C2semidirect
15. C2×#10622302C2semidirect
16. C2×C8×D4×C11C2semidirect
20. C23×C8×C11C22semidirect
26. C22×#4318C22semidirect
29. C2×#66954C22semidirect
35. C22×#4313C22semidirect
36. C22×#4313C22semidirect
39. C22×C8×D11C22semidirect
50. C8×D4×C11C22semidirect
51. C2×C11×C4⋊C8C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. C2×C4×C8×C11C22semidirect
56. C2×C22⋊(C11⋊C8)C22semidirect
57. #10622724C22semidirect
58. #10622724C22semidirect
61. C2×(C2×D11)⋊C8C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×#66879C22semidirect
64. C2×Dic11⋊C8C22semidirect
65. C2×Dic11⋊C8C22semidirect
66. C2×C8×Dic11C22semidirect
67. #10622624C22semidirect
68. C2×C4⋊(C11⋊C8)C22semidirect
69. C2×#66867C22semidirect
70. #10622452C22semidirect
71. #10622449C22semidirect
72. #10622342C22semidirect
73. #10622340C22semidirect
74. (C22⋊D11)⋊C8C22semidirect
75. D11×C22⋊C8C22semidirect
76. #10622302C22semidirect
77. #10622301C22semidirect
110. C22×C8×C11C23semidirect
138. C2×#4318C23semidirect
151. C2×#4313D4semidirect
156. C2×#4313C23semidirect
162. C2×C8×D11C23semidirect
173. C11×C4⋊C8C23semidirect
175. C11×C22⋊C8C23semidirect
176. C4×C8×C11C23semidirect
178. C22⋊(C11⋊C8)C23semidirect
181. (C2×D11)⋊C8C23semidirect
182. (C2×D11)⋊C8C23semidirect
183. #66879C23semidirect
184. Dic11⋊C8C23semidirect
185. Dic11⋊C8C23semidirect
186. C8×Dic11C23semidirect
187. C4⋊(C11⋊C8)C23semidirect
188. #66867C23semidirect
301. #4313C2×D4semidirect
316. C2×C8×D4D11semidirect
326. C23×C11#131semidirect
419. C23×C8C2×D11semidirect
442. C8×D4C2×D11semidirect
447. C2×C4⋊C8C2×D11semidirect
457. C2×C22⋊C8C2×D11semidirect
462. C2×C4×C8C2×D11semidirect
472. C22×C11C2×#131semidirect
558. C22×C8C22×D11semidirect
598. C4⋊C8C22×D11semidirect
606. C22⋊C8C22×D11semidirect
610. C4×C8C22×D11semidirect
613. C2×C11#2933semidirect
735. C11C2×#2933semidirect
757. C23#66954semidirect
839. C22C2×#66954semidirect
859. C2#13077336direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669542
C23×#43132
C2×#106230782
#130773362
C2×#106223012
C2×#106223422
C2×#106226242
C2×#106227242
C2×#106224492
C2×(C22⋊D11)⋊C82
C2×#106224522
C2×#106223402
C2×D11×C22⋊C82
C2×#106223022
C2×C8×D4×C112
C2×#293311