Finite Group Databasebeta

← C11×#22175 #14599368

Subgroups — C11×#22175 #14599368

Order 2816.

912 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×#436C211yesmaximal, characteristic, complemented
2C2×C11×#435C211yesmaximal, characteristic, complemented
3C11×#2392C211yesmaximal, characteristic
4C11×#1924C211yesmaximal, characteristic, complemented
5C11×#1923C211yesmaximal, characteristic, complemented
6C11×#1917C211yesmaximal, characteristic, complemented
7C11×#1916C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic, complemented
9C11×#1869C211yesmaximal, characteristic, complemented
10C11×#1869C211yesmaximal, characteristic, complemented
11C11×#1869C211yesmaximal, characteristic, complemented
12C11×#1851C211yesmaximal, characteristic, complemented
13C11×#1850C211yesmaximal, characteristic, complemented
14C11×#1798C211yesmaximal, characteristic, complemented
15C11×#1729C211yesmaximal, 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×#436—24no—
25C11×#435—24no—
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×#97C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C11×#398C411yescharacteristic
41C11×#397C411yescharacteristic
42C11×#396C411yescharacteristic
43C11×#396C411yescharacteristic
44C11×#394C411yescharacteristic
45C11×#394C411yescharacteristic
46C11×#394C411yescharacteristic
47C11×#392C411yescharacteristic
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×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—
70C2×C11×M16—41no—
71C2×C11×M16—41no—
72C2×C11×M16D414yescomplemented
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11—41no—
76C22×C8×C11—41no—
77C22×C8×C11—41no—
78C22×C8×C11—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—41no—
92C4×D4×C11—41no—
93C11×#117—41no—
94C11×#117—41no—
95C2×C11×C4⋊C4C2×C411yescharacteristic
96C2×C11×C4⋊C4C2×C411yescharacteristic
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×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×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×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C11×C4⋊C8—22no—
119C11×C4⋊C8—22no—
120C11×C4⋊C8—41no—
121C11×C4⋊C8—41no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—41no—
127C11×C22⋊C8—41no—
128C11×C22⋊C8—41no—
129C11×C22⋊C8—41no—
130C11×#97—22no—
131C4×C8×C11—22no—
132C11×#95C2×C411yescharacteristic
133C11×#95C2×C411yescharacteristic
134C11×#95C2×C411yescharacteristic
135C11×#95C2×C411yescharacteristic
136C11×#95C2×C411yescharacteristic
137C11×#95C2×C411yescharacteristic
138#22175C1111yesmaximal, 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—22no—
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×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
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×C11C2×D412yes—
179C22×C4×C11#4112yes—
180C22×C4×C11C2411yescharacteristic
181C11×M16—44no—
182C11×M16—44no—
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—21no—
205C2×C8×C11—44no—
206C2×C8×C11—44no—
207C2×C8×C11C2×D412yes—
208C2×C8×C11C2×D412yes—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—41no—
213C11×C4⋊C4—41no—
214C11×C4⋊C4—41no—
215C11×C4⋊C4—41no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—41no—
223C11×C22⋊C4—41no—
224C11×C22⋊C4—41no—
225C11×C22⋊C4—41no—
226C11×C22⋊C4—41no—
227C11×C22⋊C4—41no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235C42×C11—21no—
236C2×#436C2×C1111yescharacteristic, complemented
237C2×#435C2×C1111yescharacteristic, complemented
238#2392C2×C1111yescharacteristic
239#1924C2×C1111yescharacteristic, complemented
240#1923C2×C1111yescharacteristic, complemented
241#1917C2×C1111yescharacteristic, complemented
242#1916C2×C1111yescharacteristic, complemented
243#1870C2×C1111yescharacteristic, complemented
244#1869C2×C1111yescharacteristic, complemented
245#1869C2×C1111yescharacteristic, complemented
246#1869C2×C1111yescharacteristic, complemented
247#1851C2×C1111yescharacteristic, complemented
248#1850C2×C1111yescharacteristic, complemented
249#1798C2×C1111yescharacteristic, complemented
250#1729C2×C1111yescharacteristic, complemented
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—21no—
270C23×C11C4×D412yes—
271C23×C11#13112yes—
272C23×C11C23×C411yescharacteristic
273D4×C11—44no—
274D4×C11—44no—
275D4×C11—44no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
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—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—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11C4×D412yes—
320C2×C4×C11#13112yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C112−1+411yescharacteristic
327C8×C11—22no—
328C8×C11—22no—
329C8×C11—41no—
330C8×C11—41no—
331C8×C11—41no—
332C8×C11—41no—
333C8×C11—41no—
334C8×C11—41no—
335C22×M16C22×C1111yescharacteristic
336C22×M16C22×C1111yescharacteristic
337C23×C8C22×C1111yescharacteristic
338C23×C8C22×C1111yescharacteristic
339C2×C4×D4C22×C1111yescharacteristic
340C2×C4×D4C22×C1111yescharacteristic
341C2×C4×D4C22×C1111yescharacteristic
342C2×#117C22×C1111yescharacteristic
343#436—24no—
344#435—24no—
345C2×C4⋊C8C22×C1111yescharacteristic
346C2×C4⋊C8C22×C1111yescharacteristic
347C2×C4⋊C8C22×C1111yescharacteristic
348C2×C4⋊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×C4×C8C22×C1111yescharacteristic
359#398C4×C1111yescharacteristic
360#397C4×C1111yescharacteristic
361#396C4×C1111yescharacteristic
362#396C4×C1111yescharacteristic
363#394C4×C1111yescharacteristic
364#394C4×C1111yescharacteristic
365#394C4×C1111yescharacteristic
366#392C4×C1111yescharacteristic
367C4×C4⋊C4C22×C1111yescharacteristic
368C4×C22⋊C4C22×C1111yescharacteristic
369C4×C22⋊C4C22×C1111yescharacteristic
370#336C22×C1111yescharacteristic
371#336C22×C1111yescharacteristic
372#336C22×C1111yescharacteristic
373#336C22×C1111yescharacteristic
374#336C22×C1111yescharacteristic
375#336C22×C1111yescharacteristic
376#336C22×C1111yescharacteristic
377#336C22×C1111yescharacteristic
378#336C22×C1111yescharacteristic
379#336C22×C1111yescharacteristic
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
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×C11—41no—
400C22×C11—41no—
401C22×C11C2×C4×D411yescharacteristic
402C22×C11#51811yescharacteristic
403C22×C11#52011yescharacteristic
404C22×C11C2×#13111yescharacteristic
405C22×C11C2×#13111yescharacteristic
406C22×C11#56811yescharacteristic
407C22×C11#56811yescharacteristic
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11#53411yescharacteristic
420C4×C11#53711yescharacteristic
421C4×C11#53811yescharacteristic
422C4×C11#53911yescharacteristic
423C22×D4C2×C4×C1111yescharacteristic
424C22×D4C2×C4×C1111yescharacteristic
425C22×D4C2×C4×C1111yescharacteristic
426C23×C4C23×C1111yescharacteristic
427C23×C4C23×C1111yescharacteristic
428C23×C4C23×C1111yescharacteristic
429C2×M16—22no—
430C2×M16—41no—
431C2×M16—41no—
432C2×M16—41no—
433C2×M16—41no—
434C2×M16D4×C1114yescomplemented
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8—41no—
439C22×C8—41no—
440C22×C8—41no—
441C22×C8C23×C1111yescharacteristic
442C22×C8C23×C1111yescharacteristic
443C22×C8C23×C1111yescharacteristic
444C22×C8C23×C1111yescharacteristic
445C22×C8C23×C1111yescharacteristic
446C22×C8C23×C1111yescharacteristic
447C22×C8C23×C1111yescharacteristic
448C22×C8C23×C1111yescharacteristic
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—41no—
454C4×D4—41no—
455#117—41no—
456#117—41no—
457C2×C4⋊C4C2×C4×C1111yescharacteristic
458C2×C4⋊C4C2×C4×C1111yescharacteristic
459C2×C4⋊C4C2×C4×C1111yescharacteristic
460C2×C4⋊C4C2×C4×C1111yescharacteristic
461C2×C4⋊C4C2×C4×C1111yescharacteristic
462C2×C4⋊C4C2×C4×C1111yescharacteristic
463C2×C4⋊C4C2×C4×C1111yescharacteristic
464C2×C22⋊C4C2×C4×C1111yescharacteristic
465C2×C22⋊C4C2×C4×C1111yescharacteristic
466C2×C22⋊C4C2×C4×C1111yescharacteristic
467C2×C22⋊C4C2×C4×C1111yescharacteristic
468C2×C22⋊C4C2×C4×C1111yescharacteristic
469C2×C22⋊C4C2×C4×C1111yescharacteristic
470C2×C22⋊C4C2×C4×C1111yescharacteristic
471C2×C22⋊C4C2×C4×C1111yescharacteristic
472C2×C22⋊C4C2×C4×C1111yescharacteristic
473C2×C22⋊C4C2×C4×C1111yescharacteristic
474C2×C22⋊C4C2×C4×C1111yescharacteristic
475C2×C22⋊C4C2×C4×C1111yescharacteristic
476C2×C42C23×C1111yescharacteristic
477C2×C42C23×C1111yescharacteristic
478C2×C42C23×C1111yescharacteristic
479C2×C42C23×C1111yescharacteristic
480C4⋊C8—22no—
481C4⋊C8—22no—
482C4⋊C8—41no—
483C4⋊C8—41no—
484C22⋊C8—22no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492#97—22no—
493C4×C8—22no—
494#95C2×C4×C1111yescharacteristic
495#95C2×C4×C1111yescharacteristic
496#95C2×C4×C1111yescharacteristic
497#95C2×C4×C1111yescharacteristic
498#95C2×C4×C1111yescharacteristic
499#95C2×C4×C1111yescharacteristic
500C2×C11—42no—
501C2×C11—42no—
502C2×C11—81no—
503C2×C11#232511yescharacteristic
504C2×C11#293311yescharacteristic
505C2×C11#293311yescharacteristic
506C2×C11#297611yescharacteristic
507C2×C11#298111yescharacteristic
508C2×C11#299411yescharacteristic
509C2×C11#299511yescharacteristic
510C24C22×C4×C1111yescharacteristic
511C24C22×C4×C1111yescharacteristic
512C24C22×C4×C1111yescharacteristic
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
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×C4C2×D4×C1112yes—
550C22×C4C11×#4112yes—
551C22×C4C24×C1111yescharacteristic
552M16—44no—
553M16—44no—
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—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—44no—
577C2×C8—44no—
578C2×C8C2×D4×C1112yes—
579C2×C8C2×D4×C1112yes—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C11#2217511yescharacteristic, direct product factor, Sylow
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—
624C23—21no—
625C23—21no—
626C23—21no—
627C23C4×D4×C1112yes—
628C23C11×#13112yes—
629C23C23×C4×C1111yescharacteristic
630D4—44no—
631D4—44no—
632D4—44no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
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—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—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4C4×D4×C1112yes—
677C2×C4C11×#13112yes—
678C2×C4C22×D4×C1111yescharacteristic
679C2×C4C2×C11×#4111yescharacteristic
680C2×C4C11×H(5,𝔽2)11yescharacteristic
681C2×C4C11×H(5,𝔽2)11yescharacteristic
682C2×C4C11×H(5,𝔽2)11yescharacteristic
683C2×C4C11×2−1+411yescharacteristic
684C8—22no—
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—41no—
691C8—41no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22C2×C4×D4×C1111yescharacteristic
714C22C11×#51811yescharacteristic
715C22C11×#52011yescharacteristic
716C22C2×C11×#13111yescharacteristic
717C22C2×C11×#13111yescharacteristic
718C22C11×#56811yescharacteristic
719C22C11×#56811yescharacteristic
720C4—22no—
721C4—22no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4C11×#53411yescharacteristic
732C4C11×#53711yescharacteristic
733C4C11×#53811yescharacteristic
734C4C11×#53911yescharacteristic
735C2—42no—
736C2—42no—
737C2—81no—
738C2C11×#232511yescharacteristic
739C2C11×#293311yescharacteristic
740C2C11×#293311yescharacteristic
741C2C11×#297611yescharacteristic
742C2C11×#298111yescharacteristic
743C2C11×#299411yescharacteristic
744C2C11×#299511yescharacteristic
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×#436C2semidirect
2. C2×C11×#435C2semidirect
4. C11×#1924C2semidirect
5. C11×#1923C2semidirect
6. C11×#1917C2semidirect
7. C11×#1916C2semidirect
8. C11×#1870C2semidirect
9. C11×#1869C2semidirect
10. C11×#1869C2semidirect
11. C11×#1869C2semidirect
12. C11×#1851C2semidirect
13. C11×#1850C2semidirect
14. C11×#1798C2semidirect
15. C11×#1729C2semidirect
72. C2×C11×M16D4semidirect
138. #22175C11direct (N × H)
236. C2×#436C2×C11semidirect
237. C2×#435C2×C11semidirect
239. #1924C2×C11semidirect
240. #1923C2×C11semidirect
241. #1917C2×C11semidirect
242. #1916C2×C11semidirect
243. #1870C2×C11semidirect
244. #1869C2×C11semidirect
245. #1869C2×C11semidirect
246. #1869C2×C11semidirect
247. #1851C2×C11semidirect
248. #1850C2×C11semidirect
249. #1798C2×C11semidirect
250. #1729C2×C11semidirect
434. C2×M16D4×C11semidirect
607. C11#22175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4362
C2×C11×#4352
C11×#23922
C11×#19242
C11×#19232
C11×#19172
C11×#19162
C11×#18702
C11×#18692
C11×#18512
C11×#18502
C11×#17982
C11×#17292
#2217511