Finite Group Databasebeta

← C11×#21495 #14598688

Subgroups — C11×#21495 #14598688

Order 2816.

1052 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic, complemented
2C2×C11×#435C211yesmaximal, characteristic, complemented
3C2×C8×D4×C11C211yesmaximal, characteristic, complemented
4C2×C11×#405C211yesmaximal, characteristic, complemented
5C11×#2392C211yesmaximal, characteristic
6C11×#1954C211yesmaximal, characteristic, complemented
7C11×#1939C211yesmaximal, characteristic, complemented
8C11×#1923C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1870C211yesmaximal, characteristic, complemented
12C11×#1798C211yesmaximal, characteristic, complemented
13C11×#1771C211yesmaximal, characteristic, complemented
14C11×#1753C211yesmaximal, characteristic, complemented
15C11×#1752C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C11×#435—24no—
25C11×#435—24no—
26C8×D4×C11—24no—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C11×#405—24no—
40C2×C11×#97C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C2×C11×#97C2211yescharacteristic
43C2×C4×C8×C11C2211yescharacteristic
44C2×C4×C8×C11C2211yescharacteristic
45C2×C4×C8×C11C2211yescharacteristic
46C11×#398C411yescharacteristic
47C11×#397C411yescharacteristic
48C11×#396C411yescharacteristic
49C11×#396C411yescharacteristic
50C11×#394C411yescharacteristic
51C11×#394C411yescharacteristic
52C11×#394C411yescharacteristic
53C11×#392C411yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C11×#336C2211yescharacteristic
62C11×#336C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11—22no—
80C22×C8×C11D414yescomplemented
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C11×#117—22no—
96C11×#117—22no—
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C4⋊C4C2×C411yescharacteristic
99C2×C11×C4⋊C4C2×C411yescharacteristic
100C2×C11×C4⋊C4C2×C411yescharacteristic
101C2×C11×C4⋊C4C2×C411yescharacteristic
102C2×C11×C4⋊C4C2×C411yescharacteristic
103C2×C11×C4⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C11×C22⋊C4C2×C411yescharacteristic
109C2×C11×C22⋊C4C2×C411yescharacteristic
110C2×C11×C22⋊C4C2×C411yescharacteristic
111C2×C11×C22⋊C4C2×C411yescharacteristic
112C2×C11×C22⋊C4C2×C411yescharacteristic
113C2×C11×C22⋊C4C2×C411yescharacteristic
114C2×C11×C22⋊C4C2×C411yescharacteristic
115C2×C11×C22⋊C4C2×C411yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C11×C4⋊C8—22no—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—22no—
132C11×#97—22no—
133C11×#97—22no—
134C11×#97D414yescomplemented
135C4×C8×C11—22no—
136C4×C8×C11—22no—
137C4×C8×C11—22no—
138C11×#95C2×C411yescharacteristic
139C11×#95C2×C411yescharacteristic
140C11×#95C2×C411yescharacteristic
141C11×#95C2×C411yescharacteristic
142C11×#95C2×C411yescharacteristic
143C11×#95C2×C411yescharacteristic
144#21495C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C22×C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11#4112yes—
186C22×C4×C11C2411yescharacteristic
187C11×M16—28no—
188C11×M16—44no—
189C2×C8×C11—28no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—44no—
209C2×C8×C11C2×D412yes—
210C2×C8×C11C2×D412yes—
211C2×C8×C11C2×D412yes—
212C2×C8×C11C2×D412yes—
213C2×C8×C11#4112yes—
214C2×C8×C11#4112yes—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—41no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—41no—
233C11×C22⋊C4—41no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—21no—
239C42×C11—21no—
240C42×C11C2×D412yes—
241C42×C11#4112yes—
242C2×#435C2×C1111yescharacteristic, complemented
243C2×#435C2×C1111yescharacteristic, complemented
244C2×C8×D4C2×C1111yescharacteristic, complemented
245C2×#405C2×C1111yescharacteristic, complemented
246#2392C2×C1111yescharacteristic
247#1954C2×C1111yescharacteristic, complemented
248#1939C2×C1111yescharacteristic, complemented
249#1923C2×C1111yescharacteristic, complemented
250#1923C2×C1111yescharacteristic, complemented
251#1870C2×C1111yescharacteristic, complemented
252#1870C2×C1111yescharacteristic, complemented
253#1798C2×C1111yescharacteristic, complemented
254#1771C2×C1111yescharacteristic, complemented
255#1753C2×C1111yescharacteristic, complemented
256#1752C2×C1111yescharacteristic, complemented
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11C4×D412yes—
277C23×C11#13112yes—
278C23×C11C23×C411yescharacteristic
279D4×C11—28no—
280D4×C11—44no—
281D4×C11—44no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11C4×D412yes—
324C2×C4×C11C4×D412yes—
325C2×C4×C11C4×D412yes—
326C2×C4×C11#13112yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C8×C11—22no—
334C8×C11—22no—
335C8×C11—22no—
336C8×C11—41no—
337C8×C11—41no—
338C8×C11—41no—
339C8×C11—41no—
340C8×C11#12114yes—
341C22×M16C22×C1111yescharacteristic
342C22×M16C22×C1111yescharacteristic
343C23×C8C22×C1111yescharacteristic
344C23×C8C22×C1111yescharacteristic
345C2×C4×D4C22×C1111yescharacteristic
346C2×C4×D4C22×C1111yescharacteristic
347C2×C4×D4C22×C1111yescharacteristic
348C2×#117C22×C1111yescharacteristic
349#435—24no—
350#435—24no—
351C8×D4—24no—
352C2×C4⋊C8C22×C1111yescharacteristic
353C2×C4⋊C8C22×C1111yescharacteristic
354C2×C4⋊C8C22×C1111yescharacteristic
355C2×C4⋊C8C22×C1111yescharacteristic
356C2×C22⋊C8C22×C1111yescharacteristic
357C2×C22⋊C8C22×C1111yescharacteristic
358C2×C22⋊C8C22×C1111yescharacteristic
359C2×C22⋊C8C22×C1111yescharacteristic
360C2×C22⋊C8C22×C1111yescharacteristic
361C2×C22⋊C8C22×C1111yescharacteristic
362C2×C22⋊C8C22×C1111yescharacteristic
363C2×C22⋊C8C22×C1111yescharacteristic
364#405—24no—
365C2×#97C22×C1111yescharacteristic
366C2×#97C22×C1111yescharacteristic
367C2×#97C22×C1111yescharacteristic
368C2×C4×C8C22×C1111yescharacteristic
369C2×C4×C8C22×C1111yescharacteristic
370C2×C4×C8C22×C1111yescharacteristic
371#398C4×C1111yescharacteristic
372#397C4×C1111yescharacteristic
373#396C4×C1111yescharacteristic
374#396C4×C1111yescharacteristic
375#394C4×C1111yescharacteristic
376#394C4×C1111yescharacteristic
377#394C4×C1111yescharacteristic
378#392C4×C1111yescharacteristic
379C4×C4⋊C4C22×C1111yescharacteristic
380C4×C22⋊C4C22×C1111yescharacteristic
381C4×C22⋊C4C22×C1111yescharacteristic
382#336C22×C1111yescharacteristic
383#336C22×C1111yescharacteristic
384#336C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic
386#336C22×C1111yescharacteristic
387#336C22×C1111yescharacteristic
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11C2×C4×D411yescharacteristic
410C22×C11C2×C4×D411yescharacteristic
411C22×C11C4×#4111yescharacteristic
412C22×C11C2×#13111yescharacteristic
413C22×C11C2×#13111yescharacteristic
414C22×C11#56811yescharacteristic
415C22×C11#56811yescharacteristic
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11C2×#12111yescharacteristic
428C4×C11#52511yescharacteristic
429C4×C11#52911yescharacteristic
430C4×C11#53211yescharacteristic
431C22×D4C2×C4×C1111yescharacteristic
432C22×D4C2×C4×C1111yescharacteristic
433C22×D4C2×C4×C1111yescharacteristic
434C23×C4C23×C1111yescharacteristic
435C23×C4C23×C1111yescharacteristic
436C23×C4C23×C1111yescharacteristic
437C2×M16—22no—
438C2×M16—22no—
439C2×M16—22no—
440C2×M16—22no—
441C2×M16—22no—
442C2×M16—22no—
443C22×C8—22no—
444C22×C8—22no—
445C22×C8—22no—
446C22×C8—22no—
447C22×C8—22no—
448C22×C8D4×C1114yescomplemented
449C22×C8C23×C1111yescharacteristic
450C22×C8C23×C1111yescharacteristic
451C22×C8C23×C1111yescharacteristic
452C22×C8C23×C1111yescharacteristic
453C22×C8C23×C1111yescharacteristic
454C22×C8C23×C1111yescharacteristic
455C22×C8C23×C1111yescharacteristic
456C22×C8C23×C1111yescharacteristic
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463#117—22no—
464#117—22no—
465C2×C4⋊C4C2×C4×C1111yescharacteristic
466C2×C4⋊C4C2×C4×C1111yescharacteristic
467C2×C4⋊C4C2×C4×C1111yescharacteristic
468C2×C4⋊C4C2×C4×C1111yescharacteristic
469C2×C4⋊C4C2×C4×C1111yescharacteristic
470C2×C4⋊C4C2×C4×C1111yescharacteristic
471C2×C4⋊C4C2×C4×C1111yescharacteristic
472C2×C22⋊C4C2×C4×C1111yescharacteristic
473C2×C22⋊C4C2×C4×C1111yescharacteristic
474C2×C22⋊C4C2×C4×C1111yescharacteristic
475C2×C22⋊C4C2×C4×C1111yescharacteristic
476C2×C22⋊C4C2×C4×C1111yescharacteristic
477C2×C22⋊C4C2×C4×C1111yescharacteristic
478C2×C22⋊C4C2×C4×C1111yescharacteristic
479C2×C22⋊C4C2×C4×C1111yescharacteristic
480C2×C22⋊C4C2×C4×C1111yescharacteristic
481C2×C22⋊C4C2×C4×C1111yescharacteristic
482C2×C22⋊C4C2×C4×C1111yescharacteristic
483C2×C22⋊C4C2×C4×C1111yescharacteristic
484C2×C42C23×C1111yescharacteristic
485C2×C42C23×C1111yescharacteristic
486C2×C42C23×C1111yescharacteristic
487C2×C42C23×C1111yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—22no—
490C4⋊C8—22no—
491C4⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500#97—22no—
501#97—22no—
502#97D4×C1114yescomplemented
503C4×C8—22no—
504C4×C8—22no—
505C4×C8—22no—
506#95C2×C4×C1111yescharacteristic
507#95C2×C4×C1111yescharacteristic
508#95C2×C4×C1111yescharacteristic
509#95C2×C4×C1111yescharacteristic
510#95C2×C4×C1111yescharacteristic
511#95C2×C4×C1111yescharacteristic
512C2×C11—42no—
513C2×C11—42no—
514C2×C11—81no—
515C2×C11C4×#12111yescharacteristic
516C2×C11#292911yescharacteristic
517C2×C11#293011yescharacteristic
518C2×C11#293311yescharacteristic
519C2×C11#293511yescharacteristic
520C2×C11#296811yescharacteristic
521C2×C11#296911yescharacteristic
522C24C22×C4×C1111yescharacteristic
523C24C22×C4×C1111yescharacteristic
524C24C22×C4×C1111yescharacteristic
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4C22×C4×C1111yescharacteristic
551C22×C4C22×C4×C1111yescharacteristic
552C22×C4C22×C4×C1111yescharacteristic
553C22×C4C22×C4×C1111yescharacteristic
554C22×C4C22×C4×C1111yescharacteristic
555C22×C4C22×C4×C1111yescharacteristic
556C22×C4C22×C4×C1111yescharacteristic
557C22×C4C22×C4×C1111yescharacteristic
558C22×C4C22×C4×C1111yescharacteristic
559C22×C4C22×C4×C1111yescharacteristic
560C22×C4C22×C4×C1111yescharacteristic
561C22×C4C2×D4×C1112yes—
562C22×C4C11×#4112yes—
563C22×C4C24×C1111yescharacteristic
564M16—28no—
565M16—44no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—28no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—44no—
586C2×C8C2×D4×C1112yes—
587C2×C8C2×D4×C1112yes—
588C2×C8C2×D4×C1112yes—
589C2×C8C2×D4×C1112yes—
590C2×C8C11×#4112yes—
591C2×C8C11×#4112yes—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—41no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42C2×D4×C1112yes—
618C42C11×#4112yes—
619C11#2149511yescharacteristic, direct product factor, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C4×D4×C1112yes—
640C23C11×#13112yes—
641C23C23×C4×C1111yescharacteristic
642D4—28no—
643D4—44no—
644D4—44no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4C4×D4×C1112yes—
687C2×C4C4×D4×C1112yes—
688C2×C4C4×D4×C1112yes—
689C2×C4C11×#13112yes—
690C2×C4C22×D4×C1111yescharacteristic
691C2×C4C22×D4×C1111yescharacteristic
692C2×C4C2×C11×#4111yescharacteristic
693C2×C4C2×C11×#4111yescharacteristic
694C2×C4C2×C11×#4111yescharacteristic
695C2×C4C2×C11×#4111yescharacteristic
696C8—22no—
697C8—22no—
698C8—22no—
699C8—41no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8C11×#12114yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22C2×C4×D4×C1111yescharacteristic
726C22C2×C4×D4×C1111yescharacteristic
727C22C4×C11×#4111yescharacteristic
728C22C2×C11×#13111yescharacteristic
729C22C2×C11×#13111yescharacteristic
730C22C11×#56811yescharacteristic
731C22C11×#56811yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4C2×C11×#12111yescharacteristic
744C4C11×#52511yescharacteristic
745C4C11×#52911yescharacteristic
746C4C11×#53211yescharacteristic
747C2—42no—
748C2—42no—
749C2—81no—
750C2C4×C11×#12111yescharacteristic
751C2C11×#292911yescharacteristic
752C2C11×#293011yescharacteristic
753C2C11×#293311yescharacteristic
754C2C11×#293511yescharacteristic
755C2C11×#296811yescharacteristic
756C2C11×#296911yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC11×#392C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#435C2semidirect
2. C2×C11×#435C2semidirect
3. C2×C8×D4×C11C2semidirect
4. C2×C11×#405C2semidirect
6. C11×#1954C2semidirect
7. C11×#1939C2semidirect
8. C11×#1923C2semidirect
9. C11×#1923C2semidirect
10. C11×#1870C2semidirect
11. C11×#1870C2semidirect
12. C11×#1798C2semidirect
13. C11×#1771C2semidirect
14. C11×#1753C2semidirect
15. C11×#1752C2semidirect
80. C22×C8×C11D4semidirect
134. C11×#97D4semidirect
144. #21495C11direct (N × H)
242. C2×#435C2×C11semidirect
243. C2×#435C2×C11semidirect
244. C2×C8×D4C2×C11semidirect
245. C2×#405C2×C11semidirect
247. #1954C2×C11semidirect
248. #1939C2×C11semidirect
249. #1923C2×C11semidirect
250. #1923C2×C11semidirect
251. #1870C2×C11semidirect
252. #1870C2×C11semidirect
253. #1798C2×C11semidirect
254. #1771C2×C11semidirect
255. #1753C2×C11semidirect
256. #1752C2×C11semidirect
448. C22×C8D4×C11semidirect
502. #97D4×C11semidirect
619. C11#21495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4352
C2×C8×D4×C112
C2×C11×#4052
C11×#23922
C11×#19542
C11×#19392
C11×#19232
C11×#18702
C11×#17982
C11×#17712
C11×#17532
C11×#17522
#2149511