Finite Group Databasebeta

← C11×#22558 #14599751

Subgroups — C11×#22558 #14599751

Order 2816.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#433C211yesmaximal, characteristic, complemented
2C22×C11×C22⋊C8C211yesmaximal, characteristic
3C11×#2280C211yesmaximal, characteristic
4C11×#1924C211yesmaximal, characteristic, complemented
5C11×#1924C211yesmaximal, characteristic, complemented
6C11×#1923C211yesmaximal, characteristic, complemented
7C11×#1923C211yesmaximal, characteristic, complemented
8C11×#1850C211yesmaximal, characteristic, complemented
9C11×#1850C211yesmaximal, characteristic, complemented
10C11×#1818C211yesmaximal, characteristic, complemented
11C11×#1798C211yesmaximal, characteristic, complemented
12C11×#1779C211yesmaximal, characteristic
13C11×#1752C211yesmaximal, characteristic, complemented
14C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C11×#433—24no—
22C2×C11×C4⋊C8C2211yescharacteristic, complemented
23C2×C11×C4⋊C8C2211yescharacteristic, complemented
24C2×C11×C4⋊C8C2211yescharacteristic, complemented
25C2×C11×C4⋊C8C2211yescharacteristic, complemented
26C2×C11×C22⋊C8—24no—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C11×C22⋊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×#97C2211yescharacteristic, complemented
38C2×C11×#97C2211yescharacteristic, complemented
39C2×C4×C8×C11C2211yescharacteristic, complemented
40C2×C4×C8×C11C2211yescharacteristic, complemented
41C11×#381C411yescharacteristic
42C11×#381C411yescharacteristic
43C11×#380C411yescharacteristic
44C11×#380C411yescharacteristic
45C11×#380C411yescharacteristic
46C11×#380C411yescharacteristic
47C11×#379C411yescharacteristic
48C11×#379C411yescharacteristic
49C4×C11×C22⋊C4C2211yescharacteristic
50C4×C11×C22⋊C4C2211yescharacteristic
51C4×C11×C22⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#336C2211yescharacteristic, complemented
54C11×#336C2211yescharacteristic, complemented
55C11×#336C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57C11×#336C2211yescharacteristic, complemented
58C11×#336C2211yescharacteristic, complemented
59C11×#336C2211yescharacteristic, complemented
60C11×#336C2211yescharacteristic, complemented
61C25×C11C2×C411yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11C2×C411yescharacteristic
69C23×C4×C11C2×C411yescharacteristic
70C23×C4×C11C2×C411yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—22no—
78C22×C8×C11—41no—
79C22×C8×C11—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C11×#117—22no—
89C11×#117—22no—
90C11×#117—41no—
91C11×#117—41no—
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—41no—
115C11×C4⋊C8—41no—
116C11×C22⋊C8—22no—
117C11×C22⋊C8—22no—
118C11×C22⋊C8—22no—
119C11×C22⋊C8—22no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×C22⋊C8—41no—
124C11×C22⋊C8—41no—
125C11×C22⋊C8D414yes—
126C11×#97—22no—
127C11×#97—41no—
128C4×C8×C11—22no—
129C4×C8×C11—41no—
130C11×#95C2×C411yescharacteristic
131C11×#95C2×C411yescharacteristic
132C11×#95C2×C411yescharacteristic
133C11×#95C2×C411yescharacteristic
134C11×#95C2×C411yescharacteristic
135C11×#95C2×C411yescharacteristic
136C11×#95C2×C411yescharacteristic
137C11×#95C2×C411yescharacteristic
138#22558C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—22no—
143C24×C11—22no—
144C24×C11—41no—
145C24×C11—41no—
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C24×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
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—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
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—41no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C22×C4×C11—44no—
173C22×C4×C11—44no—
174C22×C4×C11—44no—
175C22×C4×C11—44no—
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×C11C22×C411yescharacteristic
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11#4112yes—
189C22×C4×C11#4112yes—
190C22×C4×C11#4112yes—
191C22×C4×C11C2411yescharacteristic
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—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—44no—
215C2×C8×C11—44no—
216C2×C8×C11C2×D412yes—
217C2×C8×C11C2×D412yes—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C4⋊C4—41no—
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—41no—
231C11×C22⋊C4—41no—
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×C11—21no—
241C42×C11—21no—
242C2×#433C2×C1111yescharacteristic, complemented
243C22×C22⋊C8C2×C1111yescharacteristic
244#2280C2×C1111yescharacteristic
245#1924C2×C1111yescharacteristic, complemented
246#1924C2×C1111yescharacteristic, complemented
247#1923C2×C1111yescharacteristic, complemented
248#1923C2×C1111yescharacteristic, complemented
249#1850C2×C1111yescharacteristic, complemented
250#1850C2×C1111yescharacteristic, complemented
251#1818C2×C1111yescharacteristic, complemented
252#1798C2×C1111yescharacteristic, complemented
253#1779C2×C1111yescharacteristic
254#1752C2×C1111yescharacteristic, complemented
255C8×C22⋊C4C2×C1111yescharacteristic, complemented
256#1750C2×C1111yescharacteristic, complemented
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—28no—
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—44no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11#11712yes—
281C23×C11C4×D412yes—
282C23×C11#13112yes—
283C23×C11#13112yes—
284C23×C11#13112yes—
285C23×C11C23×C411yescharacteristic
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—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
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—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11—44no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11#11712yes—
333C2×C4×C11C4×D412yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—41no—
343C8×C11—41no—
344C8×C11—41no—
345C8×C11—41no—
346C8×C11—41no—
347C8×C11—41no—
348C24×C4C22×C1111yescharacteristic
349C23×C8C22×C1111yescharacteristic
350C23×C8C22×C1111yescharacteristic
351C2×#117C22×C1111yescharacteristic
352C2×#117C22×C1111yescharacteristic
353#433—24no—
354C2×C4⋊C8C22×C1111yescharacteristic, complemented
355C2×C4⋊C8C22×C1111yescharacteristic, complemented
356C2×C4⋊C8C22×C1111yescharacteristic, complemented
357C2×C4⋊C8C22×C1111yescharacteristic, complemented
358C2×C22⋊C8—24no—
359C2×C22⋊C8C22×C1111yescharacteristic
360C2×C22⋊C8C22×C1111yescharacteristic
361C2×C22⋊C8C22×C1111yescharacteristic
362C2×C22⋊C8C22×C1111yescharacteristic
363C2×C22⋊C8C22×C1111yescharacteristic
364C2×C22⋊C8C22×C1111yescharacteristic
365C2×C22⋊C8C22×C1111yescharacteristic
366C2×C22⋊C8C22×C1111yescharacteristic
367C2×C22⋊C8C22×C1111yescharacteristic
368C2×C22⋊C8C22×C1111yescharacteristic
369C2×#97C22×C1111yescharacteristic, complemented
370C2×#97C22×C1111yescharacteristic, complemented
371C2×C4×C8C22×C1111yescharacteristic, complemented
372C2×C4×C8C22×C1111yescharacteristic, complemented
373#381C4×C1111yescharacteristic
374#381C4×C1111yescharacteristic
375#380C4×C1111yescharacteristic
376#380C4×C1111yescharacteristic
377#380C4×C1111yescharacteristic
378#380C4×C1111yescharacteristic
379#379C4×C1111yescharacteristic
380#379C4×C1111yescharacteristic
381C4×C22⋊C4C22×C1111yescharacteristic
382C4×C22⋊C4C22×C1111yescharacteristic
383C4×C22⋊C4C22×C1111yescharacteristic
384C4×C22⋊C4C22×C1111yescharacteristic
385#336C22×C1111yescharacteristic, complemented
386#336C22×C1111yescharacteristic, complemented
387#336C22×C1111yescharacteristic, complemented
388#336C22×C1111yescharacteristic, complemented
389#336C22×C1111yescharacteristic, complemented
390#336C22×C1111yescharacteristic, complemented
391#336C22×C1111yescharacteristic, complemented
392#336C22×C1111yescharacteristic, complemented
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—416no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11#43314yescomplemented
415C22×C11C2×#11711yescharacteristic
416C22×C11C2×C4×D411yescharacteristic
417C22×C11#51811yescharacteristic
418C22×C11C2×#13111yescharacteristic
419C22×C11C2×#13111yescharacteristic
420C22×C11C2×#13111yescharacteristic
421C22×C11#56811yescharacteristic
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11#54611yescharacteristic
434C4×C11#54611yescharacteristic
435C4×C11#55111yescharacteristic
436C4×C11#55111yescharacteristic
437C25C2×C4×C1111yescharacteristic
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—41no—
443C23×C4—41no—
444C23×C4C2×C4×C1111yescharacteristic
445C23×C4C2×C4×C1111yescharacteristic
446C23×C4C2×C4×C1111yescharacteristic
447C23×C4C23×C1111yescharacteristic
448C23×C4C23×C1111yescharacteristic
449C23×C4C23×C1111yescharacteristic
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—41no—
455C22×C8—41no—
456C22×C8C23×C1111yescharacteristic
457C22×C8C23×C1111yescharacteristic
458C22×C8C23×C1111yescharacteristic
459C22×C8C23×C1111yescharacteristic
460C22×C8C23×C1111yescharacteristic
461C22×C8C23×C1111yescharacteristic
462C22×C8C23×C1111yescharacteristic
463C22×C8C23×C1111yescharacteristic
464#117—22no—
465#117—22no—
466#117—41no—
467#117—41no—
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—41no—
491C4⋊C8—41no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—41no—
500C22⋊C8—41no—
501C22⋊C8D4×C1114yes—
502#97—22no—
503#97—41no—
504C4×C8—22no—
505C4×C8—41no—
506#95C2×C4×C1111yescharacteristic
507#95C2×C4×C1111yescharacteristic
508#95C2×C4×C1111yescharacteristic
509#95C2×C4×C1111yescharacteristic
510#95C2×C4×C1111yescharacteristic
511#95C2×C4×C1111yescharacteristic
512#95C2×C4×C1111yescharacteristic
513#95C2×C4×C1111yescharacteristic
514C2×C11—24no—
515C2×C11—42no—
516C2×C11—42no—
517C2×C11#234211yescharacteristic
518C2×C11C2×#43311yescharacteristic
519C2×C11#292411yescharacteristic
520C2×C11#292911yescharacteristic
521C2×C11#293311yescharacteristic
522C2×C11#297611yescharacteristic
523C2×C11#297711yescharacteristic
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—41no—
530C24—41no—
531C24C22×C4×C1111yescharacteristic
532C24C22×C4×C1111yescharacteristic
533C24C22×C4×C1111yescharacteristic
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—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4C22×C4×C1111yescharacteristic
562C22×C4C22×C4×C1111yescharacteristic
563C22×C4C22×C4×C1111yescharacteristic
564C22×C4C22×C4×C1111yescharacteristic
565C22×C4C22×C4×C1111yescharacteristic
566C22×C4C22×C4×C1111yescharacteristic
567C22×C4C22×C4×C1111yescharacteristic
568C22×C4C22×C4×C1111yescharacteristic
569C22×C4C22×C4×C1111yescharacteristic
570C22×C4C22×C4×C1111yescharacteristic
571C22×C4C22×C4×C1111yescharacteristic
572C22×C4C2×D4×C1112yes—
573C22×C4C11×#4112yes—
574C22×C4C11×#4112yes—
575C22×C4C11×#4112yes—
576C22×C4C24×C1111yescharacteristic
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—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—44no—
600C2×C8—44no—
601C2×C8C2×D4×C1112yes—
602C2×C8C2×D4×C1112yes—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C11#2255811yescharacteristic, direct product factor, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—28no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23C11×#11712yes—
652C23C4×D4×C1112yes—
653C23C11×#13112yes—
654C23C11×#13112yes—
655C23C11×#13112yes—
656C23C23×C4×C1111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
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—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4C11×#11712yes—
704C2×C4C4×D4×C1112yes—
705C2×C4C22×D4×C1111yescharacteristic
706C2×C4C2×C11×#4111yescharacteristic
707C2×C4C2×C11×#4111yescharacteristic
708C2×C4C2×C11×#4111yescharacteristic
709C2×C4C11×H(5,𝔽2)11yescharacteristic
710C2×C4C11×H(5,𝔽2)11yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—41no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—416no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22C11×#43314yescomplemented
741C22C2×C11×#11711yescharacteristic
742C22C2×C4×D4×C1111yescharacteristic
743C22C11×#51811yescharacteristic
744C22C2×C11×#13111yescharacteristic
745C22C2×C11×#13111yescharacteristic
746C22C2×C11×#13111yescharacteristic
747C22C11×#56811yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4C11×#54611yescharacteristic
760C4C11×#54611yescharacteristic
761C4C11×#55111yescharacteristic
762C4C11×#55111yescharacteristic
763C2—24no—
764C2—42no—
765C2—42no—
766C2C11×#234211yescharacteristic
767C2C2×C11×#43311yescharacteristic
768C2C11×#292411yescharacteristic
769C2C11×#292911yescharacteristic
770C2C11×#293311yescharacteristic
771C2C11×#297611yescharacteristic
772C2C11×#297711yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC23×C11C23×C4
prime radicalC25×C11C2×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×#433C2semidirect
4. C11×#1924C2semidirect
5. C11×#1924C2semidirect
6. C11×#1923C2semidirect
7. C11×#1923C2semidirect
8. C11×#1850C2semidirect
9. C11×#1850C2semidirect
10. C11×#1818C2semidirect
11. C11×#1798C2semidirect
13. C11×#1752C2semidirect
14. C8×C11×C22⋊C4C2semidirect
15. C11×#1750C2semidirect
22. C2×C11×C4⋊C8C22semidirect
23. C2×C11×C4⋊C8C22semidirect
24. C2×C11×C4⋊C8C22semidirect
25. C2×C11×C4⋊C8C22semidirect
37. C2×C11×#97C22semidirect
38. C2×C11×#97C22semidirect
39. C2×C4×C8×C11C22semidirect
40. C2×C4×C8×C11C22semidirect
53. C11×#336C22semidirect
54. C11×#336C22semidirect
55. C11×#336C22semidirect
56. C11×#336C22semidirect
57. C11×#336C22semidirect
58. C11×#336C22semidirect
59. C11×#336C22semidirect
60. C11×#336C22semidirect
138. #22558C11direct (N × H)
242. C2×#433C2×C11semidirect
245. #1924C2×C11semidirect
246. #1924C2×C11semidirect
247. #1923C2×C11semidirect
248. #1923C2×C11semidirect
249. #1850C2×C11semidirect
250. #1850C2×C11semidirect
251. #1818C2×C11semidirect
252. #1798C2×C11semidirect
254. #1752C2×C11semidirect
255. C8×C22⋊C4C2×C11semidirect
256. #1750C2×C11semidirect
354. C2×C4⋊C8C22×C11semidirect
355. C2×C4⋊C8C22×C11semidirect
356. C2×C4⋊C8C22×C11semidirect
357. C2×C4⋊C8C22×C11semidirect
369. C2×#97C22×C11semidirect
370. C2×#97C22×C11semidirect
371. C2×C4×C8C22×C11semidirect
372. C2×C4×C8C22×C11semidirect
385. #336C22×C11semidirect
386. #336C22×C11semidirect
387. #336C22×C11semidirect
388. #336C22×C11semidirect
389. #336C22×C11semidirect
390. #336C22×C11semidirect
391. #336C22×C11semidirect
392. #336C22×C11semidirect
414. C22×C11#433semidirect
627. C11#22558direct (N × H)
740. C22C11×#433semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4332
C22×C11×C22⋊C82
C11×#22802
C11×#19242
C11×#19232
C11×#18502
C11×#18182
C11×#17982
C11×#17792
C11×#17522
C8×C11×C22⋊C42
C11×#17502
#2255811