Finite Group Databasebeta

← C11×#22107 #14599300

Subgroups — C11×#22107 #14599300

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#446C211yesmaximal, characteristic, complemented
2C2×C11×#433C211yesmaximal, characteristic
3C11×#2396C211yesmaximal, characteristic
4C11×#1984C211yesmaximal, characteristic, complemented
5C11×#1940C211yesmaximal, characteristic, complemented
6C11×#1939C211yesmaximal, characteristic, complemented
7C11×#1939C211yesmaximal, characteristic, complemented
8C11×#1924C211yesmaximal, characteristic
9C11×#1924C211yesmaximal, characteristic
10C11×#1923C211yesmaximal, characteristic
11C11×#1923C211yesmaximal, characteristic
12C11×#1917C211yesmaximal, characteristic, complemented
13C11×#1916C211yesmaximal, characteristic, complemented
14C11×#1798C211yesmaximal, characteristic
15C11×#1771C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C11×#446—24no—
19C11×#433—24no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×#97C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C2×C4×C8×C11C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic
38C11×#400C411yescharacteristic
39C11×#399C411yescharacteristic
40C11×#398C411yescharacteristic
41C11×#398C411yescharacteristic
42C11×#396C411yescharacteristic
43C11×#396C411yescharacteristic
44C11×#395C411yescharacteristic
45C11×#393C411yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×Q8×C11C2×C411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C11×#117—22no—
74C11×#117—22no—
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C4⋊C4C2×C411yescharacteristic
83C2×C11×C4⋊C4C2×C411yescharacteristic
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C11×C22⋊C4C2×C411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C11×C4⋊C8—22no—
99C11×C4⋊C8—22no—
100C11×C4⋊C8—22no—
101C11×C4⋊C8—22no—
102C11×C4⋊C8—22no—
103C11×C4⋊C8—22no—
104C11×C4⋊C8—41no—
105C11×C4⋊C8—41no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—41no—
109C11×C22⋊C8—41no—
110C11×#97—22no—
111C11×#97—41no—
112C11×#97D414yes—
113C4×C8×C11—22no—
114C4×C8×C11—22no—
115C4×C8×C11—41no—
116C11×#95C2×C411yescharacteristic
117C11×#95C2×C411yescharacteristic
118C11×#95C2×C411yescharacteristic
119C11×#95C2×C411yescharacteristic
120C11×#95C2×C411yescharacteristic
121C11×#95C2×C411yescharacteristic
122C11×#95C2×C411yescharacteristic
123C11×#95C2×C411yescharacteristic
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126#22107C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11C22×C411yescharacteristic
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—41no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D412yes—
174C2×C8×C11C2×D412yes—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—41no—
191C11×C22⋊C4—41no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11C2×D412yes—
203C42×C11#4112yes—
204C2×#446C2×C1111yescharacteristic, complemented
205C2×#433C2×C1111yescharacteristic
206#2396C2×C1111yescharacteristic
207#1984C2×C1111yescharacteristic, complemented
208#1940C2×C1111yescharacteristic, complemented
209#1939C2×C1111yescharacteristic, complemented
210#1939C2×C1111yescharacteristic, complemented
211#1924C2×C1111yescharacteristic
212#1924C2×C1111yescharacteristic
213#1923C2×C1111yescharacteristic
214#1923C2×C1111yescharacteristic
215#1917C2×C1111yescharacteristic, complemented
216#1916C2×C1111yescharacteristic, complemented
217#1798C2×C1111yescharacteristic
218#1771C2×C1111yescharacteristic, complemented
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11C23×C411yescharacteristic
227Q8×C11—44no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C4×D412yes—
268C2×C4×C11C4×D412yes—
269C2×C4×C11#13112yes—
270C2×C4×C11#13112yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C8×C11—22no—
278C8×C11—22no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—41no—
285C2×C4×Q8C22×C1111yescharacteristic
286C2×#117C22×C1111yescharacteristic
287#446—24no—
288#433—24no—
289C2×C4⋊C8C22×C1111yescharacteristic
290C2×C4⋊C8C22×C1111yescharacteristic
291C2×C4⋊C8C22×C1111yescharacteristic
292C2×C4⋊C8C22×C1111yescharacteristic
293C2×C4⋊C8C22×C1111yescharacteristic
294C2×C4⋊C8C22×C1111yescharacteristic
295C2×C4⋊C8C22×C1111yescharacteristic
296C2×C4⋊C8C22×C1111yescharacteristic
297C2×C22⋊C8C22×C1111yescharacteristic
298C2×C22⋊C8C22×C1111yescharacteristic
299C2×C22⋊C8C22×C1111yescharacteristic
300C2×C22⋊C8C22×C1111yescharacteristic
301C2×#97C22×C1111yescharacteristic
302C2×#97C22×C1111yescharacteristic
303C2×#97C22×C1111yescharacteristic
304C2×C4×C8C22×C1111yescharacteristic
305C2×C4×C8C22×C1111yescharacteristic
306C2×C4×C8C22×C1111yescharacteristic
307#400C4×C1111yescharacteristic
308#399C4×C1111yescharacteristic
309#398C4×C1111yescharacteristic
310#398C4×C1111yescharacteristic
311#396C4×C1111yescharacteristic
312#396C4×C1111yescharacteristic
313#395C4×C1111yescharacteristic
314#393C4×C1111yescharacteristic
315C4×C4⋊C4C22×C1111yescharacteristic
316C4×C4⋊C4C22×C1111yescharacteristic
317C4×C4⋊C4C22×C1111yescharacteristic
318C4×C22⋊C4C22×C1111yescharacteristic
319C4×C22⋊C4C22×C1111yescharacteristic
320#336C22×C1111yescharacteristic
321#336C22×C1111yescharacteristic
322#336C22×C1111yescharacteristic
323#336C22×C1111yescharacteristic
324#336C22×C1111yescharacteristic
325#336C22×C1111yescharacteristic
326#336C22×C1111yescharacteristic
327#336C22×C1111yescharacteristic
328#336C22×C1111yescharacteristic
329#336C22×C1111yescharacteristic
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×C4×D411yescharacteristic
338C22×C11#51911yescharacteristic
339C22×C11#52011yescharacteristic
340C22×C11C2×#13111yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11#56811yescharacteristic
343C22×C11#56811yescharacteristic
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11#53611yescharacteristic
358C4×C11#53711yescharacteristic
359C4×C11#54111yescharacteristic
360C4×C11#54211yescharacteristic
361C22×Q8C2×C4×C1111yescharacteristic
362C23×C4C23×C1111yescharacteristic
363C22×C8C23×C1111yescharacteristic
364C22×C8C23×C1111yescharacteristic
365C22×C8C23×C1111yescharacteristic
366C22×C8C23×C1111yescharacteristic
367C22×C8C23×C1111yescharacteristic
368C22×C8C23×C1111yescharacteristic
369C22×C8C23×C1111yescharacteristic
370C22×C8C23×C1111yescharacteristic
371C4×Q8—22no—
372C4×Q8—22no—
373#117—22no—
374#117—22no—
375C2×C4⋊C4C2×C4×C1111yescharacteristic
376C2×C4⋊C4C2×C4×C1111yescharacteristic
377C2×C4⋊C4C2×C4×C1111yescharacteristic
378C2×C4⋊C4C2×C4×C1111yescharacteristic
379C2×C4⋊C4C2×C4×C1111yescharacteristic
380C2×C4⋊C4C2×C4×C1111yescharacteristic
381C2×C4⋊C4C2×C4×C1111yescharacteristic
382C2×C4⋊C4C2×C4×C1111yescharacteristic
383C2×C4⋊C4C2×C4×C1111yescharacteristic
384C2×C4⋊C4C2×C4×C1111yescharacteristic
385C2×C4⋊C4C2×C4×C1111yescharacteristic
386C2×C22⋊C4C2×C4×C1111yescharacteristic
387C2×C22⋊C4C2×C4×C1111yescharacteristic
388C2×C22⋊C4C2×C4×C1111yescharacteristic
389C2×C22⋊C4C2×C4×C1111yescharacteristic
390C2×C22⋊C4C2×C4×C1111yescharacteristic
391C2×C22⋊C4C2×C4×C1111yescharacteristic
392C2×C42C23×C1111yescharacteristic
393C2×C42C23×C1111yescharacteristic
394C2×C42C23×C1111yescharacteristic
395C2×C42C23×C1111yescharacteristic
396C2×C42C23×C1111yescharacteristic
397C2×C42C23×C1111yescharacteristic
398C4⋊C8—22no—
399C4⋊C8—22no—
400C4⋊C8—22no—
401C4⋊C8—22no—
402C4⋊C8—22no—
403C4⋊C8—22no—
404C4⋊C8—41no—
405C4⋊C8—41no—
406C22⋊C8—22no—
407C22⋊C8—22no—
408C22⋊C8—41no—
409C22⋊C8—41no—
410#97—22no—
411#97—41no—
412#97D4×C1114yes—
413C4×C8—22no—
414C4×C8—22no—
415C4×C8—41no—
416#95C2×C4×C1111yescharacteristic
417#95C2×C4×C1111yescharacteristic
418#95C2×C4×C1111yescharacteristic
419#95C2×C4×C1111yescharacteristic
420#95C2×C4×C1111yescharacteristic
421#95C2×C4×C1111yescharacteristic
422#95C2×C4×C1111yescharacteristic
423#95C2×C4×C1111yescharacteristic
424#95C2×C4×C1111yescharacteristic
425#95C2×C4×C1111yescharacteristic
426C2×C11—81no—
427C2×C11#232311yescharacteristic
428C2×C11#293311yescharacteristic
429C2×C11#293511yescharacteristic
430C2×C11#298511yescharacteristic
431C2×C11#298511yescharacteristic
432C2×C11#299411yescharacteristic
433C2×C11#299511yescharacteristic
434C24C22×C4×C1111yescharacteristic
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—41no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C22×C4×C1111yescharacteristic
445C22×C4C22×C4×C1111yescharacteristic
446C22×C4C22×C4×C1111yescharacteristic
447C22×C4C22×C4×C1111yescharacteristic
448C22×C4C22×C4×C1111yescharacteristic
449C22×C4C22×C4×C1111yescharacteristic
450C22×C4C22×C4×C1111yescharacteristic
451C22×C4C22×C4×C1111yescharacteristic
452C22×C4C22×C4×C1111yescharacteristic
453C22×C4C22×C4×C1111yescharacteristic
454C22×C4C22×C4×C1111yescharacteristic
455C22×C4C22×C4×C1111yescharacteristic
456C22×C4C22×C4×C1111yescharacteristic
457C22×C4C24×C1111yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8C2×D4×C1112yes—
481C2×C8C2×D4×C1112yes—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42C2×D4×C1112yes—
510C42C11×#4112yes—
511C11#2210711yescharacteristic, direct product factor, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23C23×C4×C1111yescharacteristic
520Q8—44no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4C4×D4×C1112yes—
561C2×C4C4×D4×C1112yes—
562C2×C4C11×#13112yes—
563C2×C4C11×#13112yes—
564C2×C4C22×D4×C1111yescharacteristic
565C2×C4C2×C11×#4111yescharacteristic
566C2×C4C11×H(5,𝔽2)11yescharacteristic
567C2×C4C11×2−1+411yescharacteristic
568C2×C4C11×2−1+411yescharacteristic
569C2×C4C11×2−1+411yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×D4×C1111yescharacteristic
586C22C11×#51911yescharacteristic
587C22C11×#52011yescharacteristic
588C22C2×C11×#13111yescharacteristic
589C22C2×C11×#13111yescharacteristic
590C22C11×#56811yescharacteristic
591C22C11×#56811yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4C11×#53611yescharacteristic
606C4C11×#53711yescharacteristic
607C4C11×#54111yescharacteristic
608C4C11×#54211yescharacteristic
609C2—81no—
610C2C11×#232311yescharacteristic
611C2C11×#293311yescharacteristic
612C2C11×#293511yescharacteristic
613C2C11×#298511yescharacteristic
614C2C11×#298511yescharacteristic
615C2C11×#299411yescharacteristic
616C2C11×#299511yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
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×#446C2semidirect
4. C11×#1984C2semidirect
5. C11×#1940C2semidirect
6. C11×#1939C2semidirect
7. C11×#1939C2semidirect
12. C11×#1917C2semidirect
13. C11×#1916C2semidirect
15. C11×#1771C2semidirect
126. #22107C11direct (N × H)
204. C2×#446C2×C11semidirect
207. #1984C2×C11semidirect
208. #1940C2×C11semidirect
209. #1939C2×C11semidirect
210. #1939C2×C11semidirect
215. #1917C2×C11semidirect
216. #1916C2×C11semidirect
218. #1771C2×C11semidirect
511. C11#22107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4462
C2×C11×#4332
C11×#23962
C11×#19842
C11×#19402
C11×#19392
C11×#19242
C11×#19232
C11×#19172
C11×#19162
C11×#17982
C11×#17712
#2210711