Finite Group Databasebeta

← C11×#60146 #14637339

Subgroups — C11×#60146 #14637339

Order 2816.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#568C211yesmaximal, characteristic, complemented
2C22×C11×#131C211yesmaximal, characteristic, complemented
3D4×C11×#41C211yesmaximal, characteristic
4C11×#2935C213yesmaximal, complemented
5D4×C11×M16C213yesmaximal, complemented
6C11×#2933C213yesmaximal, complemented
7C11×#2933C213yesmaximal, complemented
8C11×#2932C213yesmaximal, complemented
9C11×#2930C213yesmaximal, complemented
10C11×#2929C213yesmaximal, complemented
11C2×C11×#435C213yesmaximal, complemented
12C11×#2906C211yesmaximal, characteristic, complemented
13C11×#2880C211yesmaximal, characteristic, complemented
14C11×#2880C211yesmaximal, characteristic, complemented
15C11×#2875C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#568—28no—
19C2×C11×#131—28no—
20C2×C11×#131C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic
22C2×C11×#131C2211yescharacteristic
23C2×C11×#131C2211yescharacteristic
24C2×C11×#131C2213yescomplemented
25C2×C11×#131C2213yescomplemented
26C2×C11×#131C2213yescomplemented
27C2×C11×#131C2213yescomplemented
28C22×C11×M16C2213yescomplemented
29C22×C11×M16C2213yescomplemented
30C22×C11×M16C2213yescomplemented
31C23×C8×C11C2213yescomplemented
32C11×#550C411yescharacteristic
33D4×Q8×C11C411yescharacteristic
34C11×#548C411yescharacteristic
35C11×#548C411yescharacteristic
36C11×#547C413yes—
37C11×#546C413yes—
38C11×#546C413yes—
39D42×C11C413yes—
40C11×#532C2213yes—
41C11×#525C2213yes—
42C11×#525C2213yes—
43C4×C11×#41C2211yescharacteristic
44C2×C4×D4×C11C2213yes—
45C11×#436C2216yescomplemented
46C11×#436C2216yescomplemented
47C11×#435C2211yescharacteristic
48C11×#435C2213yes—
49C11×#435C2213yescomplemented
50C11×#435C2213yescomplemented
51C11×#435C2213yescomplemented
52C11×#435C2213yescomplemented
53C11×#435C2213yescomplemented
54C11×#435C2213yescomplemented
55C11×#435C2216yescomplemented
56C11×#435C2216yescomplemented
57C11×#435C2216yescomplemented
58C8×D4×C11C2216yescomplemented
59C8×D4×C11C2216yescomplemented
60C11×#424C2213yescomplemented
61C11×#424C2213yescomplemented
62C11×#423C2213yescomplemented
63C2×C11×C4⋊C8C2213yescomplemented
64C11×#408C2213yescomplemented
65C11×#408C2213yescomplemented
66C11×#408C2213yescomplemented
67C11×#408C2213yescomplemented
68C11×#407C2213yescomplemented
69C11×#407C2213yescomplemented
70C2×C11×C22⋊C8C2213yescomplemented
71C2×C11×C22⋊C8C2213yescomplemented
72C11×#405C2213yescomplemented
73C11×#405C2213yescomplemented
74C4×C11×M16C2213yescomplemented
75C2×C11×#97C2213yescomplemented
76C2×C11×#41—24no—
77C2×C11×#41—24no—
78C2×C11×#41—24no—
79C2×C11×#41—24no—
80C2×C11×#41C2×C413yes—
81C2×C11×#41C2×C413yes—
82C2×C11×#41C2×C411yescharacteristic
83C2×C11×#41C2×C411yescharacteristic
84C2×C11×#41C2313yes—
85C2×C11×#41C2313yes—
86C2×C11×#41C2311yescharacteristic
87C22×Q8×C11C2×C411yescharacteristic
88C22×Q8×C11C2×C411yescharacteristic
89C22×D4×C11C2×C413yes—
90C22×D4×C11C2×C413yes—
91C22×D4×C11C2×C413yes—
92C23×C4×C11C2313yes—
93C23×C4×C11C2313yes—
94C11×#131—24no—
95C11×#131—24no—
96C11×#131—24no—
97C11×#131—212no—
98C11×#131—212no—
99C11×#131—212no—
100C11×#131—212no—
101C11×#131D418yescomplemented
102C2×C11×M16—212no—
103C2×C11×M16—212no—
104C2×C11×M16—212no—
105C2×C11×M16C2313yes—
106C2×C11×M16C2313yes—
107C2×C11×M16C2313yes—
108C2×C11×M16C2311yescharacteristic
109C2×C11×M16C2313yes—
110C2×C11×M16C2313yes—
111C2×C11×M16C2313yes—
112C2×C11×M16C2316yes—
113C2×C11×M16C2313yes—
114C22×C8×C11—212no—
115C22×C8×C11C2313yes—
116C22×C8×C11C2313yes—
117C22×C8×C11C2313yes—
118C22×C8×C11C2311yescharacteristic
119C22×C8×C11C2313yes—
120C22×C8×C11C2313yes—
121C22×C8×C11C2313yes—
122C22×C8×C11C2316yes—
123C22×C8×C11C2313yes—
124C11×C4⋊Q8C2×C413yes—
125C11×#127C2×C413yes—
126C11×#124C2×C413yes—
127C11×#124C2×C413yes—
128C11×#123C2×C416yes—
129C11×#123C2×C416yes—
130C11×C22⋊Q8C2×C413yes—
131C11×C22⋊Q8C2×C413yes—
132C11×C22⋊Q8C2×C413yes—
133C11×C22⋊Q8C2×C413yes—
134C11×#121C2×C413yes—
135C11×#121C2×C413yes—
136C11×#121C2×C413yes—
137C11×#121C2×C413yes—
138C11×#121C2×C416yes—
139C11×#121C2×C416yes—
140C11×#120C2×C416yes—
141C11×#120C2×C416yes—
142C4×Q8×C11C2×C411yescharacteristic
143C4×Q8×C11C2×C411yescharacteristic
144C4×D4×C11C2×C413yes—
145C4×D4×C11C2×C413yes—
146C4×D4×C11C2×C413yes—
147C4×D4×C11C2×C413yes—
148C4×D4×C11C2×C413yes—
149C4×D4×C11C2×C413yes—
150C4×D4×C11C2311yescharacteristic
151C4×D4×C11C2313yes—
152C4×D4×C11C2313yes—
153C4×D4×C11C2313yes—
154C4×D4×C11C2316yes—
155C11×#117C2313yes—
156C2×C11×C4⋊C4C2×C413yes—
157C2×C11×C22⋊C4C2×C413yes—
158C2×C11×C22⋊C4C2×C413yes—
159C2×C42×C11C2313yes—
160C11×C4⋊C8C2311yescharacteristic
161C11×C4⋊C8C2313yes—
162C11×C4⋊C8C2313yes—
163C11×C4⋊C8C2313yes—
164C11×C4⋊C8C2316yes—
165C11×C22⋊C8C2311yescharacteristic
166C11×C22⋊C8C2311yescharacteristic
167C11×C22⋊C8C2313yes—
168C11×C22⋊C8C2313yes—
169C11×C22⋊C8C2313yes—
170C11×C22⋊C8C2313yes—
171C11×C22⋊C8C2313yes—
172C11×C22⋊C8C2313yes—
173C11×C22⋊C8C2316yes—
174C11×C22⋊C8C2316yes—
175C11×#97C2311yescharacteristic
176C11×#97C2313yes—
177C11×#97C2313yes—
178C11×#97C2313yes—
179C4×C8×C11C2316yes—
180#60146C1111yesmaximal, characteristic, direct product factor, Sylow
181C24×C11C22×C413yes—
182C24×C11C22×C413yes—
183C11×#41—24no—
184C11×#41—24no—
185C11×#41—212no—
186C11×#41—212no—
187C11×#41—26no—
188C11×#41—26no—
189C11×#41—26no—
190C11×#41—26no—
191C11×#41C2×D414yes—
192C11×#41#4114yes—
193C2×Q8×C11—24no—
194C2×Q8×C11—24no—
195C2×Q8×C11C22×C413yes—
196C2×Q8×C11C22×C413yes—
197C2×Q8×C11C22×C411yescharacteristic
198C2×D4×C11—212no—
199C2×D4×C11—212no—
200C2×D4×C11—46no—
201C2×D4×C11C22×C411yescharacteristic
202C2×D4×C11C22×C413yes—
203C2×D4×C11C22×C416yes—
204C2×D4×C11C22×C416yes—
205C2×D4×C11C22×C413yes—
206C2×D4×C11C22×C413yes—
207C2×D4×C11C22×C413yes—
208C2×D4×C11C22×C413yes—
209C2×D4×C11C22×C416yes—
210C2×D4×C11C22×C413yes—
211C22×C4×C11—26no—
212C22×C4×C11—26no—
213C22×C4×C11—26no—
214C22×C4×C11—26no—
215C22×C4×C11C22×C413yes—
216C22×C4×C11C22×C413yes—
217C22×C4×C11C22×C413yes—
218C22×C4×C11C22×C413yes—
219C22×C4×C11C22×C413yes—
220C22×C4×C11C22×C413yes—
221C22×C4×C11C22×C413yes—
222C22×C4×C11C22×C413yes—
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2413yes—
225C22×C4×C11C2413yes—
226C22×C4×C11C2411yescharacteristic
227C22×C4×C11C2413yes—
228C11×M16—22no—
229C11×M16—26no—
230C11×M16—26no—
231C11×M16—212no—
232C11×M16—26no—
233C11×M16—26no—
234C11×M16—26no—
235C11×M16—26no—
236C11×M16C2×D4112yescomplemented
237C2×C8×C11—22no—
238C2×C8×C11—26no—
239C2×C8×C11—26no—
240C2×C8×C11—26no—
241C2×C8×C11—212no—
242C2×C8×C11—26no—
243C2×C8×C11—26no—
244C2×C8×C11—26no—
245C2×C8×C11C2×D4112yescomplemented
246C2×C8×C11C2413yes—
247C2×C8×C11C2411yescharacteristic
248C2×C8×C11C2411yescharacteristic
249C2×C8×C11C2411yescharacteristic
250C2×C8×C11C2413yes—
251C2×C8×C11C2413yes—
252C2×C8×C11C2413yes—
253C2×C8×C11C2411yescharacteristic
254C11×C4⋊C4C22×C411yescharacteristic
255C11×C4⋊C4C22×C413yes—
256C11×C4⋊C4C22×C413yes—
257C11×C4⋊C4C22×C413yes—
258C11×C4⋊C4C22×C413yes—
259C11×C4⋊C4C22×C413yes—
260C11×C4⋊C4C22×C416yes—
261C11×C22⋊C4C22×C411yescharacteristic
262C11×C22⋊C4C22×C411yescharacteristic
263C11×C22⋊C4C22×C413yes—
264C11×C22⋊C4C22×C413yes—
265C11×C22⋊C4C22×C413yes—
266C11×C22⋊C4C22×C413yes—
267C11×C22⋊C4C22×C413yes—
268C11×C22⋊C4C22×C413yes—
269C11×C22⋊C4C22×C416yes—
270C11×C22⋊C4C22×C416yes—
271C11×C22⋊C4C22×C416yes—
272C42×C11C22×C413yes—
273C42×C11C22×C413yes—
274C42×C11C2413yes—
275C42×C11C2411yescharacteristic
276C2×#568C2×C1111yescharacteristic, complemented
277C22×#131C2×C1111yescharacteristic, complemented
278D4×#41C2×C1111yescharacteristic
279#2935C2×C1113yescomplemented
280D4×M16C2×C1113yescomplemented
281#2933C2×C1113yescomplemented
282#2933C2×C1113yescomplemented
283#2932C2×C1113yescomplemented
284#2930C2×C1113yescomplemented
285#2929C2×C1113yescomplemented
286C2×#435C2×C1113yescomplemented
287#2906C2×C1111yescharacteristic, complemented
288#2880C2×C1111yescharacteristic, complemented
289#2880C2×C1111yescharacteristic, complemented
290#2875C2×C1111yescharacteristic, complemented
291C23×C11—26no—
292C23×C11—26no—
293C23×C11—26no—
294C23×C11—43no—
295C23×C11—43no—
296C23×C11—43no—
297C23×C11C23×C411yescharacteristic
298C23×C11C23×C413yes—
299C23×C11C23×C413yes—
300C23×C11C23×C413yes—
301C23×C11C23×C411yescharacteristic
302Q8×C11—26no—
303Q8×C11—26no—
304Q8×C11C4×D414yes—
305D4×C11—212no—
306D4×C11—212no—
307D4×C11—22no—
308D4×C11—26no—
309D4×C11—26no—
310D4×C11—26no—
311D4×C11—43no—
312D4×C11—43no—
313D4×C11—46no—
314D4×C11C4×D4112yes—
315C2×C4×C11—26no—
316C2×C4×C11—26no—
317C2×C4×C11—26no—
318C2×C4×C11—26no—
319C2×C4×C11—26no—
320C2×C4×C11—26no—
321C2×C4×C11—21no—
322C2×C4×C11—23no—
323C2×C4×C11—23no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—23no—
328C2×C4×C11—23no—
329C2×C4×C11—43no—
330C2×C4×C11—43no—
331C2×C4×C11C23×C411yescharacteristic
332C2×C4×C11C23×C411yescharacteristic
333C2×C4×C11C23×C413yes—
334C2×C4×C11C23×C413yes—
335C2×C4×C11C23×C411yescharacteristic
336C2×C4×C11C23×C411yescharacteristic
337C2×C4×C11C23×C413yes—
338C2×C4×C11C23×C413yes—
339C2×C4×C11C23×C413yes—
340C2×C4×C11C22×D416yes—
341C2×C4×C11C2×#4116yes—
342C2×C4×C11C2511yescharacteristic
343C8×C11—21no—
344C8×C11—23no—
345C8×C11—23no—
346C8×C11—21no—
347C8×C11—21no—
348C8×C11—23no—
349C8×C11C22×D412yes—
350C8×C11C22×D416yes—
351C22×#41C22×C1111yescharacteristic
352C22×#41C22×C1111yescharacteristic
353#568—28no—
354C2×#131—28no—
355C2×#131C22×C1111yescharacteristic
356C2×#131C22×C1111yescharacteristic
357C2×#131C22×C1111yescharacteristic
358C2×#131C22×C1111yescharacteristic
359C2×#131C22×C1113yescomplemented
360C2×#131C22×C1113yescomplemented
361C2×#131C22×C1113yescomplemented
362C2×#131C22×C1113yescomplemented
363C22×M16C22×C1113yescomplemented
364C22×M16C22×C1113yescomplemented
365C22×M16C22×C1113yescomplemented
366C23×C8C22×C1113yescomplemented
367#550C4×C1111yescharacteristic
368D4×Q8C4×C1111yescharacteristic
369#548C4×C1111yescharacteristic
370#548C4×C1111yescharacteristic
371#547C4×C1113yes—
372#546C4×C1113yes—
373#546C4×C1113yes—
374D42C4×C1113yes—
375#532C22×C1113yes—
376#525C22×C1113yes—
377#525C22×C1113yes—
378C4×#41C22×C1111yescharacteristic
379C2×C4×D4C22×C1113yes—
380#436C22×C1116yescomplemented
381#436C22×C1116yescomplemented
382#435C22×C1111yescharacteristic
383#435C22×C1113yes—
384#435C22×C1113yescomplemented
385#435C22×C1113yescomplemented
386#435C22×C1113yescomplemented
387#435C22×C1113yescomplemented
388#435C22×C1113yescomplemented
389#435C22×C1113yescomplemented
390#435C22×C1116yescomplemented
391#435C22×C1116yescomplemented
392#435C22×C1116yescomplemented
393C8×D4C22×C1116yescomplemented
394C8×D4C22×C1116yescomplemented
395#424C22×C1113yescomplemented
396#424C22×C1113yescomplemented
397#423C22×C1113yescomplemented
398C2×C4⋊C8C22×C1113yescomplemented
399#408C22×C1113yescomplemented
400#408C22×C1113yescomplemented
401#408C22×C1113yescomplemented
402#408C22×C1113yescomplemented
403#407C22×C1113yescomplemented
404#407C22×C1113yescomplemented
405C2×C22⋊C8C22×C1113yescomplemented
406C2×C22⋊C8C22×C1113yescomplemented
407#405C22×C1113yescomplemented
408#405C22×C1113yescomplemented
409C4×M16C22×C1113yescomplemented
410C2×#97C22×C1113yescomplemented
411C22×C11—21no—
412C22×C11—23no—
413C22×C11—23no—
414C22×C11—21no—
415C22×C11—21no—
416C22×C11—23no—
417C22×C11—23no—
418C22×C11—21no—
419C22×C11—23no—
420C22×C11—23no—
421C22×C11—23no—
422C22×C11—23no—
423C22×C11—21no—
424C22×C11—412no—
425C22×C11—86no—
426C22×C11C2×C4×D416yes—
427C22×C11#56812yescomplemented
428C22×C11C24×C411yescharacteristic
429C4×C11—21no—
430C4×C11—21no—
431C4×C11—23no—
432C4×C11—23no—
433C4×C11—21no—
434C4×C11—23no—
435C4×C11—21no—
436C4×C11—23no—
437C4×C11C2×C4×D416yes—
438C4×C11C23×D411yescharacteristic
439C4×C11C22×#4111yescharacteristic
440C2×#41—24no—
441C2×#41—24no—
442C2×#41—24no—
443C2×#41—24no—
444C2×#41C2×C4×C1113yes—
445C2×#41C2×C4×C1113yes—
446C2×#41C2×C4×C1111yescharacteristic
447C2×#41C2×C4×C1111yescharacteristic
448C2×#41C23×C1113yes—
449C2×#41C23×C1113yes—
450C2×#41C23×C1111yescharacteristic
451C22×Q8C2×C4×C1111yescharacteristic
452C22×Q8C2×C4×C1111yescharacteristic
453C22×D4C2×C4×C1113yes—
454C22×D4C2×C4×C1113yes—
455C22×D4C2×C4×C1113yes—
456C23×C4C23×C1113yes—
457C23×C4C23×C1113yes—
458#131—24no—
459#131—24no—
460#131—24no—
461#131—212no—
462#131—212no—
463#131—212no—
464#131—212no—
465#131D4×C1118yescomplemented
466C2×M16—212no—
467C2×M16—212no—
468C2×M16—212no—
469C2×M16C23×C1111yescharacteristic
470C2×M16C23×C1113yes—
471C2×M16C23×C1113yes—
472C2×M16C23×C1113yes—
473C2×M16C23×C1113yes—
474C2×M16C23×C1113yes—
475C2×M16C23×C1116yes—
476C2×M16C23×C1113yes—
477C2×M16C23×C1113yes—
478C22×C8—212no—
479C22×C8C23×C1111yescharacteristic
480C22×C8C23×C1113yes—
481C22×C8C23×C1113yes—
482C22×C8C23×C1113yes—
483C22×C8C23×C1113yes—
484C22×C8C23×C1113yes—
485C22×C8C23×C1116yes—
486C22×C8C23×C1113yes—
487C22×C8C23×C1113yes—
488C4⋊Q8C2×C4×C1113yes—
489#127C2×C4×C1113yes—
490#124C2×C4×C1113yes—
491#124C2×C4×C1113yes—
492#123C2×C4×C1116yes—
493#123C2×C4×C1116yes—
494C22⋊Q8C2×C4×C1113yes—
495C22⋊Q8C2×C4×C1113yes—
496C22⋊Q8C2×C4×C1113yes—
497C22⋊Q8C2×C4×C1113yes—
498#121C2×C4×C1113yes—
499#121C2×C4×C1113yes—
500#121C2×C4×C1113yes—
501#121C2×C4×C1113yes—
502#121C2×C4×C1116yes—
503#121C2×C4×C1116yes—
504#120C2×C4×C1116yes—
505#120C2×C4×C1116yes—
506C4×Q8C2×C4×C1111yescharacteristic
507C4×Q8C2×C4×C1111yescharacteristic
508C4×D4C2×C4×C1113yes—
509C4×D4C2×C4×C1113yes—
510C4×D4C2×C4×C1113yes—
511C4×D4C2×C4×C1113yes—
512C4×D4C2×C4×C1113yes—
513C4×D4C2×C4×C1113yes—
514C4×D4C23×C1111yescharacteristic
515C4×D4C23×C1113yes—
516C4×D4C23×C1113yes—
517C4×D4C23×C1113yes—
518C4×D4C23×C1116yes—
519#117C23×C1113yes—
520C2×C4⋊C4C2×C4×C1113yes—
521C2×C22⋊C4C2×C4×C1113yes—
522C2×C22⋊C4C2×C4×C1113yes—
523C2×C42C23×C1113yes—
524C4⋊C8C23×C1111yescharacteristic
525C4⋊C8C23×C1113yes—
526C4⋊C8C23×C1113yes—
527C4⋊C8C23×C1113yes—
528C4⋊C8C23×C1116yes—
529C22⋊C8C23×C1111yescharacteristic
530C22⋊C8C23×C1111yescharacteristic
531C22⋊C8C23×C1113yes—
532C22⋊C8C23×C1113yes—
533C22⋊C8C23×C1113yes—
534C22⋊C8C23×C1113yes—
535C22⋊C8C23×C1113yes—
536C22⋊C8C23×C1113yes—
537C22⋊C8C23×C1116yes—
538C22⋊C8C23×C1116yes—
539#97C23×C1111yescharacteristic
540#97C23×C1113yes—
541#97C23×C1113yes—
542#97C23×C1113yes—
543C4×C8C23×C1116yes—
544C2×C11—22no—
545C2×C11—26no—
546C2×C11—43no—
547C2×C11—43no—
548C2×C11—41no—
549C2×C11C22×C4×D411yescharacteristic
550C2×C11C2×#56811yescharacteristic
551C2×C11#357311yescharacteristic
552C24C22×C4×C1113yes—
553C24C22×C4×C1113yes—
554#41—24no—
555#41—24no—
556#41—212no—
557#41—212no—
558#41—26no—
559#41—26no—
560#41—26no—
561#41—26no—
562#41C2×D4×C1114yes—
563#41C11×#4114yes—
564C2×Q8—24no—
565C2×Q8—24no—
566C2×Q8C22×C4×C1113yes—
567C2×Q8C22×C4×C1113yes—
568C2×Q8C22×C4×C1111yescharacteristic
569C2×D4—212no—
570C2×D4—212no—
571C2×D4—46no—
572C2×D4C22×C4×C1111yescharacteristic
573C2×D4C22×C4×C1113yes—
574C2×D4C22×C4×C1116yes—
575C2×D4C22×C4×C1116yes—
576C2×D4C22×C4×C1113yes—
577C2×D4C22×C4×C1113yes—
578C2×D4C22×C4×C1113yes—
579C2×D4C22×C4×C1113yes—
580C2×D4C22×C4×C1116yes—
581C2×D4C22×C4×C1113yes—
582C22×C4—26no—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4C22×C4×C1113yes—
587C22×C4C22×C4×C1113yes—
588C22×C4C22×C4×C1113yes—
589C22×C4C22×C4×C1113yes—
590C22×C4C22×C4×C1113yes—
591C22×C4C22×C4×C1113yes—
592C22×C4C22×C4×C1113yes—
593C22×C4C22×C4×C1113yes—
594C22×C4C24×C1111yescharacteristic
595C22×C4C24×C1113yes—
596C22×C4C24×C1113yes—
597C22×C4C24×C1111yescharacteristic
598C22×C4C24×C1113yes—
599M16—26no—
600M16—26no—
601M16—26no—
602M16—22no—
603M16—26no—
604M16—26no—
605M16—212no—
606M16—26no—
607M16C2×D4×C11112yescomplemented
608C2×C8—26no—
609C2×C8—26no—
610C2×C8—26no—
611C2×C8—22no—
612C2×C8—26no—
613C2×C8—26no—
614C2×C8—26no—
615C2×C8—212no—
616C2×C8C2×D4×C11112yescomplemented
617C2×C8C24×C1113yes—
618C2×C8C24×C1111yescharacteristic
619C2×C8C24×C1111yescharacteristic
620C2×C8C24×C1111yescharacteristic
621C2×C8C24×C1113yes—
622C2×C8C24×C1113yes—
623C2×C8C24×C1113yes—
624C2×C8C24×C1111yescharacteristic
625C4⋊C4C22×C4×C1111yescharacteristic
626C4⋊C4C22×C4×C1113yes—
627C4⋊C4C22×C4×C1113yes—
628C4⋊C4C22×C4×C1113yes—
629C4⋊C4C22×C4×C1113yes—
630C4⋊C4C22×C4×C1113yes—
631C4⋊C4C22×C4×C1116yes—
632C22⋊C4C22×C4×C1111yescharacteristic
633C22⋊C4C22×C4×C1111yescharacteristic
634C22⋊C4C22×C4×C1113yes—
635C22⋊C4C22×C4×C1113yes—
636C22⋊C4C22×C4×C1113yes—
637C22⋊C4C22×C4×C1113yes—
638C22⋊C4C22×C4×C1113yes—
639C22⋊C4C22×C4×C1113yes—
640C22⋊C4C22×C4×C1116yes—
641C22⋊C4C22×C4×C1116yes—
642C22⋊C4C22×C4×C1116yes—
643C42C22×C4×C1113yes—
644C42C22×C4×C1113yes—
645C42C24×C1113yes—
646C42C24×C1111yescharacteristic
647C11#6014611yescharacteristic, direct product factor, Sylow
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×C4×C1111yescharacteristic
655C23C23×C4×C1113yes—
656C23C23×C4×C1113yes—
657C23C23×C4×C1113yes—
658C23C23×C4×C1111yescharacteristic
659Q8—26no—
660Q8—26no—
661Q8C4×D4×C1114yes—
662D4—212no—
663D4—212no—
664D4—22no—
665D4—26no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4C4×D4×C11112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—26no—
678C2×C4—21no—
679C2×C4—23no—
680C2×C4—23no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—43no—
687C2×C4—43no—
688C2×C4C23×C4×C1111yescharacteristic
689C2×C4C23×C4×C1111yescharacteristic
690C2×C4C23×C4×C1113yes—
691C2×C4C23×C4×C1113yes—
692C2×C4C23×C4×C1111yescharacteristic
693C2×C4C23×C4×C1111yescharacteristic
694C2×C4C23×C4×C1113yes—
695C2×C4C23×C4×C1113yes—
696C2×C4C23×C4×C1113yes—
697C2×C4C22×D4×C1116yes—
698C2×C4C2×C11×#4116yes—
699C2×C4C25×C1111yescharacteristic
700C8—21no—
701C8—23no—
702C8—21no—
703C8—23no—
704C8—21no—
705C8—23no—
706C8C22×D4×C1112yes—
707C8C22×D4×C1116yes—
708C22—21no—
709C22—23no—
710C22—23no—
711C22—21no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—23no—
717C22—23no—
718C22—23no—
719C22—23no—
720C22—21no—
721C22—412no—
722C22—86no—
723C22C2×C4×D4×C1116yes—
724C22C11×#56812yescomplemented
725C22C24×C4×C1111yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×C4×D4×C1116yes—
735C4C23×D4×C1111yescharacteristic
736C4C22×C11×#4111yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×C4×D4×C1111yescharacteristic
743C2C2×C11×#56811yescharacteristic
744C2C11×#357311yescharacteristic
subgroupG/H
centerC2×C4×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC2×C4C25×C11
socleC22×C11C24×C4
prime radicalD4×C11×#41C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#568C2semidirect
2. C22×C11×#131C2semidirect
4. C11×#2935C2semidirect
5. D4×C11×M16C2semidirect
6. C11×#2933C2semidirect
7. C11×#2933C2semidirect
8. C11×#2932C2semidirect
9. C11×#2930C2semidirect
10. C11×#2929C2semidirect
11. C2×C11×#435C2semidirect
12. C11×#2906C2semidirect
13. C11×#2880C2semidirect
14. C11×#2880C2semidirect
15. C11×#2875C2semidirect
24. C2×C11×#131C22semidirect
25. C2×C11×#131C22semidirect
26. C2×C11×#131C22semidirect
27. C2×C11×#131C22semidirect
28. C22×C11×M16C22semidirect
29. C22×C11×M16C22semidirect
30. C22×C11×M16C22semidirect
31. C23×C8×C11C22semidirect
45. C11×#436C22semidirect
46. C11×#436C22semidirect
49. C11×#435C22semidirect
50. C11×#435C22semidirect
51. C11×#435C22semidirect
52. C11×#435C22semidirect
53. C11×#435C22semidirect
54. C11×#435C22semidirect
55. C11×#435C22semidirect
56. C11×#435C22semidirect
57. C11×#435C22semidirect
58. C8×D4×C11C22semidirect
59. C8×D4×C11C22semidirect
60. C11×#424C22semidirect
61. C11×#424C22semidirect
62. C11×#423C22semidirect
63. C2×C11×C4⋊C8C22semidirect
64. C11×#408C22semidirect
65. C11×#408C22semidirect
66. C11×#408C22semidirect
67. C11×#408C22semidirect
68. C11×#407C22semidirect
69. C11×#407C22semidirect
70. C2×C11×C22⋊C8C22semidirect
71. C2×C11×C22⋊C8C22semidirect
72. C11×#405C22semidirect
73. C11×#405C22semidirect
74. C4×C11×M16C22semidirect
75. C2×C11×#97C22semidirect
101. C11×#131D4semidirect
180. #60146C11direct (N × H)
236. C11×M16C2×D4semidirect
245. C2×C8×C11C2×D4semidirect
276. C2×#568C2×C11semidirect
277. C22×#131C2×C11semidirect
279. #2935C2×C11semidirect
280. D4×M16C2×C11semidirect
281. #2933C2×C11semidirect
282. #2933C2×C11semidirect
283. #2932C2×C11semidirect
284. #2930C2×C11semidirect
285. #2929C2×C11semidirect
286. C2×#435C2×C11semidirect
287. #2906C2×C11semidirect
288. #2880C2×C11semidirect
289. #2880C2×C11semidirect
290. #2875C2×C11semidirect
359. C2×#131C22×C11semidirect
360. C2×#131C22×C11semidirect
361. C2×#131C22×C11semidirect
362. C2×#131C22×C11semidirect
363. C22×M16C22×C11semidirect
364. C22×M16C22×C11semidirect
365. C22×M16C22×C11semidirect
366. C23×C8C22×C11semidirect
380. #436C22×C11semidirect
381. #436C22×C11semidirect
384. #435C22×C11semidirect
385. #435C22×C11semidirect
386. #435C22×C11semidirect
387. #435C22×C11semidirect
388. #435C22×C11semidirect
389. #435C22×C11semidirect
390. #435C22×C11semidirect
391. #435C22×C11semidirect
392. #435C22×C11semidirect
393. C8×D4C22×C11semidirect
394. C8×D4C22×C11semidirect
395. #424C22×C11semidirect
396. #424C22×C11semidirect
397. #423C22×C11semidirect
398. C2×C4⋊C8C22×C11semidirect
399. #408C22×C11semidirect
400. #408C22×C11semidirect
401. #408C22×C11semidirect
402. #408C22×C11semidirect
403. #407C22×C11semidirect
404. #407C22×C11semidirect
405. C2×C22⋊C8C22×C11semidirect
406. C2×C22⋊C8C22×C11semidirect
407. #405C22×C11semidirect
408. #405C22×C11semidirect
409. C4×M16C22×C11semidirect
410. C2×#97C22×C11semidirect
427. C22×C11#568semidirect
465. #131D4×C11semidirect
607. M16C2×D4×C11semidirect
616. C2×C8C2×D4×C11semidirect
647. C11#60146direct (N × H)
724. C22C11×#568semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5682
C22×C11×#1312
D4×C11×#412
C11×#29352
D4×C11×M162
C11×#29332
C11×#29322
C11×#29302
C11×#29292
C2×C11×#4352
C11×#29062
C11×#28802
C11×#28752
#6014611