Finite Group Databasebeta

← C11×#22398 #14599591

Subgroups — C11×#22398 #14599591

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#525C211yesmaximal, characteristic
2C2×C11×#435C211yesmaximal, characteristic, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C2×C11×#408C211yesmaximal, characteristic, complemented
5C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
6C11×#1955C211yesmaximal, characteristic, complemented
7C11×#1954C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic, complemented
9C11×#1869C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1798C211yesmaximal, characteristic, complemented
13C11×#1780C211yesmaximal, characteristic, complemented
14C11×#1779C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C23×C8×C11C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic, complemented
22C11×#525—24no—
23C11×#525—24no—
24C2×C11×#123C411yescharacteristic
25C2×C11×#123C411yescharacteristic
26C2×C11×C22⋊Q8C411yescharacteristic
27C2×C11×C22⋊Q8C411yescharacteristic
28C2×C11×#121C411yescharacteristic
29C2×C11×#121C411yescharacteristic
30C2×C11×#120C411yescharacteristic
31C2×C11×#120C411yescharacteristic
32C2×C4×D4×C11C2211yescharacteristic
33C2×C4×D4×C11C2211yescharacteristic
34C2×C4×D4×C11C2211yescharacteristic
35C2×C4×D4×C11C2211yescharacteristic
36C2×C11×#117C2211yescharacteristic
37C11×#435—24no—
38C8×D4×C11—24no—
39C2×C11×C4⋊C8C2211yescharacteristic, complemented
40C2×C11×C4⋊C8C2211yescharacteristic, complemented
41C11×#408—24no—
42C2×C11×C22⋊C8—24no—
43C2×C11×C22⋊C8C2211yescharacteristic
44C2×C11×C22⋊C8C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C2×C11×C22⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C11×C22⋊C8C2211yescharacteristic
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54C2×C11×C22⋊C8C2211yescharacteristic, complemented
55C2×C11×C22⋊C8C2211yescharacteristic, complemented
56C2×C11×C22⋊C8C2211yescharacteristic, complemented
57C2×C11×C22⋊C8C2211yescharacteristic, complemented
58C2×C11×C22⋊C8C2211yescharacteristic, complemented
59C2×C11×#97C2211yescharacteristic, complemented
60C2×C4×C8×C11C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63C11×#336C2211yescharacteristic, complemented
64C11×#336C2211yescharacteristic, complemented
65C25×C11C2×C411yescharacteristic
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—22no—
70C2×C11×#41—41no—
71C2×C11×#41—41no—
72C22×Q8×C11C2×C411yescharacteristic
73C22×D4×C11C2×C411yescharacteristic
74C22×D4×C11C2×C411yescharacteristic
75C22×D4×C11C2×C411yescharacteristic
76C22×D4×C11C2×C411yescharacteristic
77C22×D4×C11C2×C411yescharacteristic
78C22×D4×C11C2×C411yescharacteristic
79C22×D4×C11C2×C411yescharacteristic
80C23×C4×C11—22no—
81C23×C4×C11—22no—
82C23×C4×C11—22no—
83C23×C4×C11—22no—
84C23×C4×C11—41no—
85C23×C4×C11—41no—
86C23×C4×C11C2×C411yescharacteristic
87C23×C4×C11C2×C411yescharacteristic
88C23×C4×C11C2×C411yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C2×C11×M16—22no—
95C2×C11×M16—22no—
96C2×C11×M16—41no—
97C22×C8×C11—22no—
98C22×C8×C11—22no—
99C22×C8×C11—22no—
100C22×C8×C11—22no—
101C22×C8×C11—22no—
102C22×C8×C11—22no—
103C22×C8×C11—41no—
104C22×C8×C11—41no—
105C22×C8×C11—41no—
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×#123—24no—
115C11×#123—24no—
116C11×C22⋊Q8—24no—
117C11×C22⋊Q8—24no—
118C11×#121—24no—
119C11×#121—24no—
120C11×#120—24no—
121C11×#120—24no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—22no—
128C4×D4×C11D414yes—
129C4×D4×C11D414yes—
130C11×#117—22no—
131C11×#117—22no—
132C2×C11×C4⋊C4C2×C411yescharacteristic
133C2×C11×C4⋊C4C2×C411yescharacteristic
134C2×C11×C4⋊C4C2×C411yescharacteristic
135C2×C11×C4⋊C4C2×C411yescharacteristic
136C2×C11×C4⋊C4C2×C411yescharacteristic
137C2×C11×C4⋊C4C2×C411yescharacteristic
138C2×C11×C22⋊C4C2×C411yescharacteristic
139C2×C11×C22⋊C4C2×C411yescharacteristic
140C2×C11×C22⋊C4C2×C411yescharacteristic
141C2×C11×C22⋊C4C2×C411yescharacteristic
142C2×C11×C22⋊C4C2×C411yescharacteristic
143C2×C11×C22⋊C4C2×C411yescharacteristic
144C2×C11×C22⋊C4C2×C411yescharacteristic
145C2×C11×C22⋊C4C2×C411yescharacteristic
146C2×C11×C22⋊C4C2×C411yescharacteristic
147C2×C11×C22⋊C4C2×C411yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C11×C4⋊C8—22no—
151C11×C4⋊C8—22no—
152C11×C22⋊C8—22no—
153C11×C22⋊C8—22no—
154C11×C22⋊C8—22no—
155C11×C22⋊C8—22no—
156C11×C22⋊C8—22no—
157C11×C22⋊C8—22no—
158C11×C22⋊C8—22no—
159C11×C22⋊C8—22no—
160C11×C22⋊C8—22no—
161C11×C22⋊C8—22no—
162C11×C22⋊C8—22no—
163C11×C22⋊C8—41no—
164C11×C22⋊C8—41no—
165C11×C22⋊C8—41no—
166C11×C22⋊C8—41no—
167C11×C22⋊C8D414yescomplemented
168C11×#97—22no—
169C4×C8×C11—22no—
170#22398C1111yesmaximal, characteristic, direct product factor, Sylow
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—41no—
177C24×C11—41no—
178C24×C11C22×C411yescharacteristic
179C24×C11C22×C411yescharacteristic
180C24×C11C22×C411yescharacteristic
181C24×C11C22×C411yescharacteristic
182C24×C11C22×C411yescharacteristic
183C11×#41—44no—
184C11×#41—44no—
185C11×#41—44no—
186C11×#41—44no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—41no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11—22no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—22no—
198C2×D4×C11—22no—
199C2×D4×C11—22no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—41no—
206C2×D4×C11—41no—
207C2×D4×C11—41no—
208C2×D4×C11—41no—
209C2×D4×C11—41no—
210C2×D4×C11C22⋊C414yes—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—41no—
242C22×C4×C11—41no—
243C22×C4×C11—41no—
244C22×C4×C11—44no—
245C22×C4×C11—44no—
246C22×C4×C11—44no—
247C22×C4×C11—44no—
248C22×C4×C11C22×C411yescharacteristic
249C22×C4×C11C22×C411yescharacteristic
250C22×C4×C11C22×C411yescharacteristic
251C22×C4×C11C22×C411yescharacteristic
252C22×C4×C11C22×C411yescharacteristic
253C22×C4×C11C22×C411yescharacteristic
254C22×C4×C11C22×C411yescharacteristic
255C22×C4×C11C22×C411yescharacteristic
256C22×C4×C11C22×C411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2×D412yes—
262C22×C4×C11#4112yes—
263C22×C4×C11C2411yescharacteristic
264C11×M16—44no—
265C2×C8×C11—21no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C2×C8×C11—21no—
272C2×C8×C11—21no—
273C2×C8×C11—21no—
274C2×C8×C11—21no—
275C2×C8×C11—21no—
276C2×C8×C11—21no—
277C2×C8×C11—21no—
278C2×C8×C11—21no—
279C2×C8×C11—21no—
280C2×C8×C11—21no—
281C2×C8×C11—21no—
282C2×C8×C11—21no—
283C2×C8×C11—21no—
284C2×C8×C11—21no—
285C2×C8×C11—21no—
286C2×C8×C11—21no—
287C2×C8×C11—44no—
288C2×C8×C11—44no—
289C2×C8×C11—44no—
290C2×C8×C11C2×D412yes—
291C2×C8×C11C2×D412yes—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—22no—
294C11×C4⋊C4—22no—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4C22⋊C414yes—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—22no—
305C11×C22⋊C4—22no—
306C11×C22⋊C4C22⋊C414yes—
307C11×C22⋊C4C22⋊C414yes—
308C42×C11—21no—
309C42×C11—21no—
310C42×C11C2×D412yes—
311C42×C11C2×D412yes—
312C2×#525C2×C1111yescharacteristic
313C2×#435C2×C1111yescharacteristic, complemented
314C2×C8×D4C2×C1111yescharacteristic, complemented
315C2×#408C2×C1111yescharacteristic, complemented
316C22×C22⋊C8C2×C1111yescharacteristic, complemented
317#1955C2×C1111yescharacteristic, complemented
318#1954C2×C1111yescharacteristic, complemented
319#1870C2×C1111yescharacteristic, complemented
320#1869C2×C1111yescharacteristic, complemented
321#1869C2×C1111yescharacteristic, complemented
322#1869C2×C1111yescharacteristic, complemented
323#1798C2×C1111yescharacteristic, complemented
324#1780C2×C1111yescharacteristic, complemented
325#1779C2×C1111yescharacteristic, complemented
326#1750C2×C1111yescharacteristic, complemented
327C23×C11—21no—
328C23×C11—21no—
329C23×C11—21no—
330C23×C11—21no—
331C23×C11—28no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—21no—
336C23×C11—21no—
337C23×C11—21no—
338C23×C11—21no—
339C23×C11—21no—
340C23×C11—21no—
341C23×C11—21no—
342C23×C11—21no—
343C23×C11—21no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11—21no—
347C23×C11—21no—
348C23×C11—21no—
349C23×C11—21no—
350C23×C11—21no—
351C23×C11—21no—
352C23×C11—21no—
353C23×C11—21no—
354C23×C11—21no—
355C23×C11—21no—
356C23×C11—21no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11C2×C22⋊C412yes—
364C23×C11C2×C22⋊C412yes—
365C23×C11C4×D412yes—
366C23×C11#13112yes—
367C23×C11#13112yes—
368C23×C11#13112yes—
369C23×C11C23×C411yescharacteristic
370Q8×C11—44no—
371D4×C11—28no—
372D4×C11—44no—
373D4×C11—44no—
374D4×C11—44no—
375D4×C11—44no—
376D4×C11—44no—
377D4×C11—44no—
378C2×C4×C11—21no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—21no—
412C2×C4×C11—44no—
413C2×C4×C11—44no—
414C2×C4×C11—44no—
415C2×C4×C11—41no—
416C2×C4×C11—41no—
417C2×C4×C11—41no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—41no—
422C2×C4×C11—41no—
423C2×C4×C11C2×C22⋊C412yes—
424C2×C4×C11C2×C22⋊C412yes—
425C2×C4×C11C2×C22⋊C412yes—
426C2×C4×C11C2×C22⋊C412yes—
427C2×C4×C11C4×D412yes—
428C2×C4×C11C22×D411yescharacteristic
429C2×C4×C11C22×D411yescharacteristic
430C2×C4×C11C22×D411yescharacteristic
431C2×C4×C11C2×#4111yescharacteristic
432C2×C4×C11H(5,𝔽2)11yescharacteristic
433C2×C4×C11H(5,𝔽2)11yescharacteristic
434C8×C11—22no—
435C8×C11—22no—
436C8×C11—41no—
437C8×C11—41no—
438C8×C11—41no—
439C8×C11—41no—
440C8×C11—41no—
441C8×C11—41no—
442C22×#41C22×C1111yescharacteristic
443C24×C4C22×C1111yescharacteristic
444C22×M16C22×C1111yescharacteristic, complemented
445C23×C8C22×C1111yescharacteristic
446C23×C8C22×C1111yescharacteristic
447C23×C8C22×C1111yescharacteristic, complemented
448#525—24no—
449#525—24no—
450C2×#123C4×C1111yescharacteristic
451C2×#123C4×C1111yescharacteristic
452C2×C22⋊Q8C4×C1111yescharacteristic
453C2×C22⋊Q8C4×C1111yescharacteristic
454C2×#121C4×C1111yescharacteristic
455C2×#121C4×C1111yescharacteristic
456C2×#120C4×C1111yescharacteristic
457C2×#120C4×C1111yescharacteristic
458C2×C4×D4C22×C1111yescharacteristic
459C2×C4×D4C22×C1111yescharacteristic
460C2×C4×D4C22×C1111yescharacteristic
461C2×C4×D4C22×C1111yescharacteristic
462C2×#117C22×C1111yescharacteristic
463#435—24no—
464C8×D4—24no—
465C2×C4⋊C8C22×C1111yescharacteristic, complemented
466C2×C4⋊C8C22×C1111yescharacteristic, complemented
467#408—24no—
468C2×C22⋊C8—24no—
469C2×C22⋊C8C22×C1111yescharacteristic
470C2×C22⋊C8C22×C1111yescharacteristic
471C2×C22⋊C8C22×C1111yescharacteristic
472C2×C22⋊C8C22×C1111yescharacteristic
473C2×C22⋊C8C22×C1111yescharacteristic
474C2×C22⋊C8C22×C1111yescharacteristic
475C2×C22⋊C8C22×C1111yescharacteristic
476C2×C22⋊C8C22×C1111yescharacteristic
477C2×C22⋊C8C22×C1111yescharacteristic
478C2×C22⋊C8C22×C1111yescharacteristic
479C2×C22⋊C8C22×C1111yescharacteristic, complemented
480C2×C22⋊C8C22×C1111yescharacteristic, complemented
481C2×C22⋊C8C22×C1111yescharacteristic, complemented
482C2×C22⋊C8C22×C1111yescharacteristic, complemented
483C2×C22⋊C8C22×C1111yescharacteristic, complemented
484C2×C22⋊C8C22×C1111yescharacteristic, complemented
485C2×#97C22×C1111yescharacteristic, complemented
486C2×C4×C8C22×C1111yescharacteristic, complemented
487#336C22×C1111yescharacteristic, complemented
488#336C22×C1111yescharacteristic, complemented
489#336C22×C1111yescharacteristic, complemented
490#336C22×C1111yescharacteristic, complemented
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—22no—
495C22×C11—22no—
496C22×C11—22no—
497C22×C11—22no—
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—22no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—416no—
507C22×C11—41no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11—41no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11—41no—
514C22×C11—41no—
515C22×C11—41no—
516C22×C11—41no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11—41no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11—41no—
523C22×C11—41no—
524C22×C11—41no—
525C22×C11—41no—
526C22×C11#40814yescomplemented
527C22×C11C22×C22⋊C411yescharacteristic
528C22×C11C2×C4×D411yescharacteristic
529C22×C11#51811yescharacteristic
530C22×C11C2×#13111yescharacteristic
531C22×C11C2×#13111yescharacteristic
532C22×C11C2×#13111yescharacteristic
533C22×C11#56811yescharacteristic
534C4×C11—22no—
535C4×C11—22no—
536C4×C11—22no—
537C4×C11—22no—
538C4×C11—22no—
539C4×C11—41no—
540C4×C11—41no—
541C4×C11—41no—
542C4×C11—41no—
543C4×C11D4211yescharacteristic
544C4×C11D4211yescharacteristic
545C4×C11#54611yescharacteristic
546C4×C11#54611yescharacteristic
547C25C2×C4×C1111yescharacteristic
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C2×C4×C1111yescharacteristic
555C22×D4C2×C4×C1111yescharacteristic
556C22×D4C2×C4×C1111yescharacteristic
557C22×D4C2×C4×C1111yescharacteristic
558C22×D4C2×C4×C1111yescharacteristic
559C22×D4C2×C4×C1111yescharacteristic
560C22×D4C2×C4×C1111yescharacteristic
561C22×D4C2×C4×C1111yescharacteristic
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—41no—
567C23×C4—41no—
568C23×C4C2×C4×C1111yescharacteristic
569C23×C4C2×C4×C1111yescharacteristic
570C23×C4C2×C4×C1111yescharacteristic
571C23×C4C23×C1111yescharacteristic
572C23×C4C23×C1111yescharacteristic
573C23×C4C23×C1111yescharacteristic
574C23×C4C23×C1111yescharacteristic
575C23×C4C23×C1111yescharacteristic
576C2×M16—22no—
577C2×M16—22no—
578C2×M16—41no—
579C22×C8—22no—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—22no—
585C22×C8—41no—
586C22×C8—41no—
587C22×C8—41no—
588C22×C8C23×C1111yescharacteristic
589C22×C8C23×C1111yescharacteristic
590C22×C8C23×C1111yescharacteristic
591C22×C8C23×C1111yescharacteristic
592C22×C8C23×C1111yescharacteristic
593C22×C8C23×C1111yescharacteristic
594C22×C8C23×C1111yescharacteristic
595C22×C8C23×C1111yescharacteristic
596#123—24no—
597#123—24no—
598C22⋊Q8—24no—
599C22⋊Q8—24no—
600#121—24no—
601#121—24no—
602#120—24no—
603#120—24no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4D4×C1114yes—
611C4×D4D4×C1114yes—
612#117—22no—
613#117—22no—
614C2×C4⋊C4C2×C4×C1111yescharacteristic
615C2×C4⋊C4C2×C4×C1111yescharacteristic
616C2×C4⋊C4C2×C4×C1111yescharacteristic
617C2×C4⋊C4C2×C4×C1111yescharacteristic
618C2×C4⋊C4C2×C4×C1111yescharacteristic
619C2×C4⋊C4C2×C4×C1111yescharacteristic
620C2×C22⋊C4C2×C4×C1111yescharacteristic
621C2×C22⋊C4C2×C4×C1111yescharacteristic
622C2×C22⋊C4C2×C4×C1111yescharacteristic
623C2×C22⋊C4C2×C4×C1111yescharacteristic
624C2×C22⋊C4C2×C4×C1111yescharacteristic
625C2×C22⋊C4C2×C4×C1111yescharacteristic
626C2×C22⋊C4C2×C4×C1111yescharacteristic
627C2×C22⋊C4C2×C4×C1111yescharacteristic
628C2×C22⋊C4C2×C4×C1111yescharacteristic
629C2×C22⋊C4C2×C4×C1111yescharacteristic
630C2×C42C23×C1111yescharacteristic
631C2×C42C23×C1111yescharacteristic
632C4⋊C8—22no—
633C4⋊C8—22no—
634C22⋊C8—22no—
635C22⋊C8—22no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—22no—
640C22⋊C8—22no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647C22⋊C8—41no—
648C22⋊C8—41no—
649C22⋊C8D4×C1114yescomplemented
650#97—22no—
651C4×C8—22no—
652C2×C11—24no—
653C2×C11—42no—
654C2×C11—42no—
655C2×C11—42no—
656C2×C11—81no—
657C2×C11D4×C22⋊C411yescharacteristic
658C2×C11C2×#40811yescharacteristic
659C2×C11#288011yescharacteristic
660C2×C11#292911yescharacteristic
661C2×C11#293311yescharacteristic
662C2×C11#297611yescharacteristic
663C2×C11#297711yescharacteristic
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—41no—
670C24—41no—
671C24C22×C4×C1111yescharacteristic
672C24C22×C4×C1111yescharacteristic
673C24C22×C4×C1111yescharacteristic
674C24C22×C4×C1111yescharacteristic
675C24C22×C4×C1111yescharacteristic
676#41—44no—
677#41—44no—
678#41—44no—
679#41—44no—
680C2×Q8—22no—
681C2×Q8—22no—
682C2×Q8—41no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—22no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4C11×C22⋊C414yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—41no—
735C22×C4—41no—
736C22×C4—41no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4C22×C4×C1111yescharacteristic
742C22×C4C22×C4×C1111yescharacteristic
743C22×C4C22×C4×C1111yescharacteristic
744C22×C4C22×C4×C1111yescharacteristic
745C22×C4C22×C4×C1111yescharacteristic
746C22×C4C22×C4×C1111yescharacteristic
747C22×C4C22×C4×C1111yescharacteristic
748C22×C4C22×C4×C1111yescharacteristic
749C22×C4C22×C4×C1111yescharacteristic
750C22×C4C2×D4×C1112yes—
751C22×C4C2×D4×C1112yes—
752C22×C4C2×D4×C1112yes—
753C22×C4C2×D4×C1112yes—
754C22×C4C2×D4×C1112yes—
755C22×C4C11×#4112yes—
756C22×C4C24×C1111yescharacteristic
757M16—44no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—44no—
781C2×C8—44no—
782C2×C8—44no—
783C2×C8C2×D4×C1112yes—
784C2×C8C2×D4×C1112yes—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4C11×C22⋊C414yes—
791C22⋊C4—22no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4C11×C22⋊C414yes—
800C22⋊C4C11×C22⋊C414yes—
801C42—21no—
802C42—21no—
803C42C2×D4×C1112yes—
804C42C2×D4×C1112yes—
805C11#2239811yescharacteristic, direct product factor, Sylow
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—28no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23—44no—
840C23—44no—
841C23—44no—
842C23C2×C11×C22⋊C412yes—
843C23C2×C11×C22⋊C412yes—
844C23C4×D4×C1112yes—
845C23C11×#13112yes—
846C23C11×#13112yes—
847C23C11×#13112yes—
848C23C23×C4×C1111yescharacteristic
849Q8—44no—
850D4—28no—
851D4—44no—
852D4—44no—
853D4—44no—
854D4—44no—
855D4—44no—
856D4—44no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4C2×C11×C22⋊C412yes—
903C2×C4C2×C11×C22⋊C412yes—
904C2×C4C2×C11×C22⋊C412yes—
905C2×C4C2×C11×C22⋊C412yes—
906C2×C4C4×D4×C1112yes—
907C2×C4C22×D4×C1111yescharacteristic
908C2×C4C22×D4×C1111yescharacteristic
909C2×C4C22×D4×C1111yescharacteristic
910C2×C4C2×C11×#4111yescharacteristic
911C2×C4C11×H(5,𝔽2)11yescharacteristic
912C2×C4C11×H(5,𝔽2)11yescharacteristic
913C8—22no—
914C8—22no—
915C8—41no—
916C8—41no—
917C8—41no—
918C8—41no—
919C8—41no—
920C8—41no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—416no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22C11×#40814yescomplemented
957C22C22×C11×C22⋊C411yescharacteristic
958C22C2×C4×D4×C1111yescharacteristic
959C22C11×#51811yescharacteristic
960C22C2×C11×#13111yescharacteristic
961C22C2×C11×#13111yescharacteristic
962C22C2×C11×#13111yescharacteristic
963C22C11×#56811yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—22no—
968C4—22no—
969C4—41no—
970C4—41no—
971C4—41no—
972C4—41no—
973C4D42×C1111yescharacteristic
974C4D42×C1111yescharacteristic
975C4C11×#54611yescharacteristic
976C4C11×#54611yescharacteristic
977C2—24no—
978C2—42no—
979C2—42no—
980C2—42no—
981C2—81no—
982C2D4×C11×C22⋊C411yescharacteristic
983C2C2×C11×#40811yescharacteristic
984C2C11×#288011yescharacteristic
985C2C11×#292911yescharacteristic
986C2C11×#293311yescharacteristic
987C2C11×#297611yescharacteristic
988C2C11×#297711yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC2×C11×#525C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#435C2semidirect
3. C2×C8×D4×C11C2semidirect
4. C2×C11×#408C2semidirect
5. C22×C11×C22⋊C8C2semidirect
6. C11×#1955C2semidirect
7. C11×#1954C2semidirect
8. C11×#1870C2semidirect
9. C11×#1869C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1798C2semidirect
13. C11×#1780C2semidirect
14. C11×#1779C2semidirect
15. C11×#1750C2semidirect
18. C22×C11×M16C22semidirect
21. C23×C8×C11C22semidirect
39. C2×C11×C4⋊C8C22semidirect
40. C2×C11×C4⋊C8C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. C2×C11×C22⋊C8C22semidirect
55. C2×C11×C22⋊C8C22semidirect
56. C2×C11×C22⋊C8C22semidirect
57. C2×C11×C22⋊C8C22semidirect
58. C2×C11×C22⋊C8C22semidirect
59. C2×C11×#97C22semidirect
60. C2×C4×C8×C11C22semidirect
61. C11×#336C22semidirect
62. C11×#336C22semidirect
63. C11×#336C22semidirect
64. C11×#336C22semidirect
167. C11×C22⋊C8D4semidirect
170. #22398C11direct (N × H)
313. C2×#435C2×C11semidirect
314. C2×C8×D4C2×C11semidirect
315. C2×#408C2×C11semidirect
316. C22×C22⋊C8C2×C11semidirect
317. #1955C2×C11semidirect
318. #1954C2×C11semidirect
319. #1870C2×C11semidirect
320. #1869C2×C11semidirect
321. #1869C2×C11semidirect
322. #1869C2×C11semidirect
323. #1798C2×C11semidirect
324. #1780C2×C11semidirect
325. #1779C2×C11semidirect
326. #1750C2×C11semidirect
444. C22×M16C22×C11semidirect
447. C23×C8C22×C11semidirect
465. C2×C4⋊C8C22×C11semidirect
466. C2×C4⋊C8C22×C11semidirect
479. C2×C22⋊C8C22×C11semidirect
480. C2×C22⋊C8C22×C11semidirect
481. C2×C22⋊C8C22×C11semidirect
482. C2×C22⋊C8C22×C11semidirect
483. C2×C22⋊C8C22×C11semidirect
484. C2×C22⋊C8C22×C11semidirect
485. C2×#97C22×C11semidirect
486. C2×C4×C8C22×C11semidirect
487. #336C22×C11semidirect
488. #336C22×C11semidirect
489. #336C22×C11semidirect
490. #336C22×C11semidirect
526. C22×C11#408semidirect
649. C22⋊C8D4×C11semidirect
805. C11#22398direct (N × H)
956. C22C11×#408semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5252
C2×C11×#4352
C2×C8×D4×C112
C2×C11×#4082
C22×C11×C22⋊C82
C11×#19552
C11×#19542
C11×#18702
C11×#18692
C11×#17982
C11×#17802
C11×#17792
C11×#17502
#2239811