Finite Group Databasebeta

← C11×#22144 #14599337

Subgroups — C11×#22144 #14599337

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#435C211yesmaximal, characteristic, complemented
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2392C211yesmaximal, characteristic
4C11×#1955C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic, complemented
6C11×#1954C211yesmaximal, characteristic, complemented
7C11×#1939C211yesmaximal, characteristic, complemented
8C11×#1924C211yesmaximal, characteristic, complemented
9C11×#1923C211yesmaximal, characteristic, complemented
10C11×#1870C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1798C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C11×#435—24no—
23C11×#433—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×C22⋊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
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C11×#97C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C2×C4×C8×C11C2211yescharacteristic
43C2×C4×C8×C11C2211yescharacteristic
44C11×#398C411yescharacteristic
45C11×#397C411yescharacteristic
46C11×#396C411yescharacteristic
47C11×#396C411yescharacteristic
48C11×#394C411yescharacteristic
49C11×#394C411yescharacteristic
50C11×#394C411yescharacteristic
51C11×#392C411yescharacteristic
52C4×C11×C4⋊C4C2211yescharacteristic
53C4×C11×C22⋊C4C2211yescharacteristic
54C4×C11×C22⋊C4C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59C11×#336C2211yescharacteristic
60C11×#336C2211yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C22×D4×C11C2×C411yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—41no—
69C2×C11×M16—41no—
70C22×C8×C11—22no—
71C22×C8×C11—41no—
72C22×C8×C11—41no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C4×D4×C11—41no—
86C4×D4×C11—41no—
87C11×#117—22no—
88C11×#117—22no—
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C11×C4⋊C4C2×C411yescharacteristic
91C2×C11×C4⋊C4C2×C411yescharacteristic
92C2×C11×C4⋊C4C2×C411yescharacteristic
93C2×C11×C4⋊C4C2×C411yescharacteristic
94C2×C11×C4⋊C4C2×C411yescharacteristic
95C2×C11×C4⋊C4C2×C411yescharacteristic
96C2×C11×C22⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4C2×C411yescharacteristic
100C2×C11×C22⋊C4C2×C411yescharacteristic
101C2×C11×C22⋊C4C2×C411yescharacteristic
102C2×C11×C22⋊C4C2×C411yescharacteristic
103C2×C11×C22⋊C4C2×C411yescharacteristic
104C2×C11×C22⋊C4C2×C411yescharacteristic
105C2×C11×C22⋊C4C2×C411yescharacteristic
106C2×C11×C22⋊C4C2×C411yescharacteristic
107C2×C11×C22⋊C4C2×C411yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112C11×C4⋊C8—22no—
113C11×C4⋊C8—22no—
114C11×C4⋊C8—22no—
115C11×C4⋊C8—22no—
116C11×C4⋊C8—41no—
117C11×C4⋊C8—41no—
118C11×C22⋊C8—22no—
119C11×C22⋊C8—22no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—41no—
123C11×C22⋊C8—41no—
124C11×C22⋊C8—41no—
125C11×C22⋊C8—41no—
126C11×C22⋊C8—41no—
127C11×C22⋊C8—41no—
128C11×#97—41no—
129C11×#97D414yescomplemented
130C4×C8×C11—22no—
131C4×C8×C11—41no—
132C11×#95C2×C411yescharacteristic
133C11×#95C2×C411yescharacteristic
134C11×#95C2×C411yescharacteristic
135C11×#95C2×C411yescharacteristic
136C11×#95C2×C411yescharacteristic
137C11×#95C2×C411yescharacteristic
138#22144C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—41no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
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×C11C22×C411yescharacteristic
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
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×C11C2411yescharacteristic
181C11×M16—44no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
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—44no—
205C2×C8×C11C2×D412yes—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—41no—
212C11×C4⋊C4—41no—
213C11×C4⋊C4—41no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—41no—
221C11×C22⋊C4—41no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—41no—
224C11×C22⋊C4—41no—
225C11×C22⋊C4—41no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11C2×D412yes—
233C42×C11#4112yes—
234C2×#435C2×C1111yescharacteristic, complemented
235C2×#433C2×C1111yescharacteristic, complemented
236#2392C2×C1111yescharacteristic
237#1955C2×C1111yescharacteristic, complemented
238#1954C2×C1111yescharacteristic, complemented
239#1954C2×C1111yescharacteristic, complemented
240#1939C2×C1111yescharacteristic, complemented
241#1924C2×C1111yescharacteristic, complemented
242#1923C2×C1111yescharacteristic, complemented
243#1870C2×C1111yescharacteristic, complemented
244#1869C2×C1111yescharacteristic, complemented
245#1851C2×C1111yescharacteristic, complemented
246#1850C2×C1111yescharacteristic, complemented
247#1798C2×C1111yescharacteristic, complemented
248#1771C2×C1111yescharacteristic, complemented
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
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#13112yes—
270C23×C11C23×C411yescharacteristic
271D4×C11—44no—
272D4×C11—44no—
273D4×C11—44no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
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—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
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—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11C4×D412yes—
317C2×C4×C11C4×D412yes—
318C2×C4×C11#13112yes—
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C112−1+411yescharacteristic
325C8×C11—22no—
326C8×C11—22no—
327C8×C11—41no—
328C8×C11—41no—
329C8×C11—41no—
330C8×C11—41no—
331C8×C11—41no—
332C8×C11—41no—
333C22×M16C22×C1111yescharacteristic
334C23×C8C22×C1111yescharacteristic
335C2×C4×D4C22×C1111yescharacteristic
336C2×C4×D4C22×C1111yescharacteristic
337C2×C4×D4C22×C1111yescharacteristic
338C2×#117C22×C1111yescharacteristic
339#435—24no—
340#433—24no—
341C2×C4⋊C8C22×C1111yescharacteristic
342C2×C4⋊C8C22×C1111yescharacteristic
343C2×C4⋊C8C22×C1111yescharacteristic
344C2×C4⋊C8C22×C1111yescharacteristic
345C2×C4⋊C8C22×C1111yescharacteristic
346C2×C4⋊C8C22×C1111yescharacteristic
347C2×C22⋊C8C22×C1111yescharacteristic
348C2×C22⋊C8C22×C1111yescharacteristic
349C2×C22⋊C8C22×C1111yescharacteristic
350C2×C22⋊C8C22×C1111yescharacteristic
351C2×C22⋊C8C22×C1111yescharacteristic
352C2×C22⋊C8C22×C1111yescharacteristic
353C2×C22⋊C8C22×C1111yescharacteristic
354C2×C22⋊C8C22×C1111yescharacteristic
355C2×C22⋊C8C22×C1111yescharacteristic
356C2×C22⋊C8C22×C1111yescharacteristic
357C2×#97C22×C1111yescharacteristic
358C2×#97C22×C1111yescharacteristic
359C2×C4×C8C22×C1111yescharacteristic
360C2×C4×C8C22×C1111yescharacteristic
361#398C4×C1111yescharacteristic
362#397C4×C1111yescharacteristic
363#396C4×C1111yescharacteristic
364#396C4×C1111yescharacteristic
365#394C4×C1111yescharacteristic
366#394C4×C1111yescharacteristic
367#394C4×C1111yescharacteristic
368#392C4×C1111yescharacteristic
369C4×C4⋊C4C22×C1111yescharacteristic
370C4×C22⋊C4C22×C1111yescharacteristic
371C4×C22⋊C4C22×C1111yescharacteristic
372#336C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376#336C22×C1111yescharacteristic
377#336C22×C1111yescharacteristic
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11C2×C4×D411yescharacteristic
400C22×C11#51811yescharacteristic
401C22×C11#52011yescharacteristic
402C22×C11C2×#13111yescharacteristic
403C22×C11C2×#13111yescharacteristic
404C22×C11#56811yescharacteristic
405C22×C11#56811yescharacteristic
406C4×C11—22no—
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—41no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11#53511yescharacteristic
418C4×C11#53711yescharacteristic
419C4×C11#54011yescharacteristic
420C4×C11#54211yescharacteristic
421C22×D4C2×C4×C1111yescharacteristic
422C22×D4C2×C4×C1111yescharacteristic
423C22×D4C2×C4×C1111yescharacteristic
424C23×C4C23×C1111yescharacteristic
425C23×C4C23×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C2×M16—22no—
428C2×M16—41no—
429C2×M16—41no—
430C22×C8—22no—
431C22×C8—41no—
432C22×C8—41no—
433C22×C8C23×C1111yescharacteristic
434C22×C8C23×C1111yescharacteristic
435C22×C8C23×C1111yescharacteristic
436C22×C8C23×C1111yescharacteristic
437C22×C8C23×C1111yescharacteristic
438C22×C8C23×C1111yescharacteristic
439C22×C8C23×C1111yescharacteristic
440C22×C8C23×C1111yescharacteristic
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—41no—
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447#117—22no—
448#117—22no—
449C2×C4⋊C4C2×C4×C1111yescharacteristic
450C2×C4⋊C4C2×C4×C1111yescharacteristic
451C2×C4⋊C4C2×C4×C1111yescharacteristic
452C2×C4⋊C4C2×C4×C1111yescharacteristic
453C2×C4⋊C4C2×C4×C1111yescharacteristic
454C2×C4⋊C4C2×C4×C1111yescharacteristic
455C2×C4⋊C4C2×C4×C1111yescharacteristic
456C2×C22⋊C4C2×C4×C1111yescharacteristic
457C2×C22⋊C4C2×C4×C1111yescharacteristic
458C2×C22⋊C4C2×C4×C1111yescharacteristic
459C2×C22⋊C4C2×C4×C1111yescharacteristic
460C2×C22⋊C4C2×C4×C1111yescharacteristic
461C2×C22⋊C4C2×C4×C1111yescharacteristic
462C2×C22⋊C4C2×C4×C1111yescharacteristic
463C2×C22⋊C4C2×C4×C1111yescharacteristic
464C2×C22⋊C4C2×C4×C1111yescharacteristic
465C2×C22⋊C4C2×C4×C1111yescharacteristic
466C2×C22⋊C4C2×C4×C1111yescharacteristic
467C2×C22⋊C4C2×C4×C1111yescharacteristic
468C2×C42C23×C1111yescharacteristic
469C2×C42C23×C1111yescharacteristic
470C2×C42C23×C1111yescharacteristic
471C2×C42C23×C1111yescharacteristic
472C4⋊C8—22no—
473C4⋊C8—22no—
474C4⋊C8—22no—
475C4⋊C8—22no—
476C4⋊C8—41no—
477C4⋊C8—41no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481C22⋊C8—22no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487C22⋊C8—41no—
488#97—41no—
489#97D4×C1114yescomplemented
490C4×C8—22no—
491C4×C8—41no—
492#95C2×C4×C1111yescharacteristic
493#95C2×C4×C1111yescharacteristic
494#95C2×C4×C1111yescharacteristic
495#95C2×C4×C1111yescharacteristic
496#95C2×C4×C1111yescharacteristic
497#95C2×C4×C1111yescharacteristic
498C2×C11—42no—
499C2×C11—81no—
500C2×C11—81no—
501C2×C11#232411yescharacteristic
502C2×C11#293311yescharacteristic
503C2×C11#293511yescharacteristic
504C2×C11#297711yescharacteristic
505C2×C11#297811yescharacteristic
506C2×C11#299211yescharacteristic
507C2×C11#299311yescharacteristic
508C24C22×C4×C1111yescharacteristic
509C24C22×C4×C1111yescharacteristic
510C24C22×C4×C1111yescharacteristic
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4C22×C4×C1111yescharacteristic
539C22×C4C22×C4×C1111yescharacteristic
540C22×C4C22×C4×C1111yescharacteristic
541C22×C4C22×C4×C1111yescharacteristic
542C22×C4C22×C4×C1111yescharacteristic
543C22×C4C22×C4×C1111yescharacteristic
544C22×C4C22×C4×C1111yescharacteristic
545C22×C4C22×C4×C1111yescharacteristic
546C22×C4C22×C4×C1111yescharacteristic
547C22×C4C22×C4×C1111yescharacteristic
548C22×C4C22×C4×C1111yescharacteristic
549C22×C4C24×C1111yescharacteristic
550M16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—44no—
574C2×C8C2×D4×C1112yes—
575C2×C8C2×D4×C1112yes—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42C2×D4×C1112yes—
602C42C11×#4112yes—
603C11#2214411yescharacteristic, direct product factor, Sylow
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23C11×#13112yes—
625C23C23×C4×C1111yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
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—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4C4×D4×C1112yes—
672C2×C4C4×D4×C1112yes—
673C2×C4C11×#13112yes—
674C2×C4C22×D4×C1111yescharacteristic
675C2×C4C2×C11×#4111yescharacteristic
676C2×C4C11×H(5,𝔽2)11yescharacteristic
677C2×C4C11×H(5,𝔽2)11yescharacteristic
678C2×C4C11×H(5,𝔽2)11yescharacteristic
679C2×C4C11×2−1+411yescharacteristic
680C8—22no—
681C8—22no—
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C2×C4×D4×C1111yescharacteristic
710C22C11×#51811yescharacteristic
711C22C11×#52011yescharacteristic
712C22C2×C11×#13111yescharacteristic
713C22C2×C11×#13111yescharacteristic
714C22C11×#56811yescharacteristic
715C22C11×#56811yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4C11×#53511yescharacteristic
728C4C11×#53711yescharacteristic
729C4C11×#54011yescharacteristic
730C4C11×#54211yescharacteristic
731C2—42no—
732C2—81no—
733C2—81no—
734C2C11×#232411yescharacteristic
735C2C11×#293311yescharacteristic
736C2C11×#293511yescharacteristic
737C2C11×#297711yescharacteristic
738C2C11×#297811yescharacteristic
739C2C11×#299211yescharacteristic
740C2C11×#299311yescharacteristic
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×#433C2semidirect
4. C11×#1955C2semidirect
5. C11×#1954C2semidirect
6. C11×#1954C2semidirect
7. C11×#1939C2semidirect
8. C11×#1924C2semidirect
9. C11×#1923C2semidirect
10. C11×#1870C2semidirect
11. C11×#1869C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1798C2semidirect
15. C11×#1771C2semidirect
129. C11×#97D4semidirect
138. #22144C11direct (N × H)
234. C2×#435C2×C11semidirect
235. C2×#433C2×C11semidirect
237. #1955C2×C11semidirect
238. #1954C2×C11semidirect
239. #1954C2×C11semidirect
240. #1939C2×C11semidirect
241. #1924C2×C11semidirect
242. #1923C2×C11semidirect
243. #1870C2×C11semidirect
244. #1869C2×C11semidirect
245. #1851C2×C11semidirect
246. #1850C2×C11semidirect
247. #1798C2×C11semidirect
248. #1771C2×C11semidirect
489. #97D4×C11semidirect
603. C11#22144direct (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×C11×#4332
C11×#23922
C11×#19552
C11×#19542
C11×#19392
C11×#19242
C11×#19232
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#17982
C11×#17712
#2214411