Finite Group Databasebeta

← #14775905

Subgroups — #14775905

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622624C211yesmaximal, characteristic, complemented
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
4C22×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5#13069415C211yesmaximal, characteristic, complemented
6#13069340C211yesmaximal, characteristic, complemented
7#13069231C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068909C211yesmaximal, characteristic, complemented
11#13068801C211yesmaximal, characteristic, complemented
12#13068796C211yesmaximal, characteristic, complemented
13#13068491C211yesmaximal, characteristic, complemented
14#13068378C211yesmaximal, characteristic, complemented
15C4×C11×#121C211yesmaximal, characteristic
16C2×C11×#121C411yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C11×#390C411yescharacteristic
26C11×#389C411yescharacteristic
27C11×#388C411yescharacteristic
28C11×#388C411yescharacteristic
29C11×#386C411yescharacteristic
30C11×#386C411yescharacteristic
31C11×#380C411yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4C2211yescharacteristic
34C4×C11×C22⋊C4C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622624—24no—
44#10622624—24no—
45D4×C11⋊C8—24no—
46C2×C4⋊(C11⋊C8)—24no—
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×#66867C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C22×D4×C11C2×C411yescharacteristic
66C23×C4×C11C2×C411yescharacteristic
67C23×C4×C11C2×C411yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C11×#121—24no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
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×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊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×C11×C22⋊C4C2×C411yescharacteristic
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C42×C11C2×C411yescharacteristic
96C2×C42×C11C2×C411yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318—41no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—22no—
108C22×C11⋊C8—22no—
109C22×C11⋊C8—22no—
110C22×C11⋊C8—41no—
111C22×C11⋊C8—41no—
112C22×C11⋊C8—41no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C11×#95C2×C411yescharacteristic
122C11×#95C2×C411yescharacteristic
123C11×#95C2×C411yescharacteristic
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126C11×#95C2×C411yescharacteristic
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—41no—
133C22⋊(C11⋊C8)—41no—
134C22⋊(C11⋊C8)D414yescomplemented
135C4⋊(C11⋊C8)—22no—
136C4⋊(C11⋊C8)—22no—
137C4⋊(C11⋊C8)—22no—
138C4⋊(C11⋊C8)—22no—
139C4⋊(C11⋊C8)—22no—
140C4⋊(C11⋊C8)D414yescomplemented
141#66867—22no—
142#66867—22no—
143#66867—22no—
144C4×C11⋊C8—22no—
145#22987—111nomaximal, Sylow
146C24×C11C22×C411yescharacteristic
147C24×C11C22×C411yescharacteristic
148C24×C11C22×C411yescharacteristic
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—41no—
157C2×D4×C11M1614yescomplemented
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
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×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—41no—
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×C11C22×C411yescharacteristic
188C22×C4×C11C22×C411yescharacteristic
189C22×C4×C11C22×C411yescharacteristic
190C22×C4×C11C22×C411yescharacteristic
191C22×C4×C11C2×D412yes—
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—41no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C42×C11—22no—
210C42×C11—22no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11C2×D412yes—
218C42×C11#4112yes—
219#4318—44no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—44no—
241C2×C11⋊C8—44no—
242C2×C11⋊C8—44no—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245C2×C11⋊C8C2×D412yes—
246C2×C11⋊C8C2×D412yes—
247C2×#435—111no—
248C2×#435—111no—
249C2×C8×D4—111no—
250C22×C4⋊C8—111no—
251C4×#121D1111yescharacteristic
252#1955—111no—
253#1940—111no—
254#1924—111no—
255#1923—111no—
256#1869—111no—
257#1869—111no—
258#1851—111no—
259#1850—111no—
260#1771—111no—
261#1749—111no—
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×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11C4×D412yes—
280C23×C11C2×M1612yes—
281C23×C11C2×M1612yes—
282C23×C11#13112yes—
283C23×C11C23×C411yescharacteristic
284D4×C11—28no—
285D4×C11—44no—
286D4×C11—44no—
287C2×C4×C11—28no—
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—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
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—44no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11C4×D412yes—
330C2×C4×C11C4×D412yes—
331C2×C4×C11C4×D412yes—
332C2×C4×C11C2×M1612yes—
333C2×C4×C11#13112yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C22×D411yescharacteristic
336C2×C4×C11C2×#4111yescharacteristic
337C2×C4×C11C2×#4111yescharacteristic
338C2×C4×C11H(5,𝔽2)11yescharacteristic
339C2×C4×C112−1+411yescharacteristic
340C11⋊C8—22no—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C11⋊C8—22no—
344C11⋊C8—41no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C22×M16—111no—
349C23×C8—111no—
350C23×C8—111no—
351C23×C8—111no—
352C2×#121Dic1111yescharacteristic
353C2×C4×D4C2×D1111yescharacteristic
354C2×C4×D4C2×D1111yescharacteristic
355C2×C4×D4C2×D1111yescharacteristic
356C22×C42C2×D1111yescharacteristic
357#435—224no—
358#435—224no—
359C8×D4—224no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×C4⋊C8—224no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373C2×C22⋊C8—111no—
374C2×C22⋊C8—111no—
375C2×#97—111no—
376C2×#97—111no—
377C2×#97—111no—
378C2×C4×C8—111no—
379#390Dic1111yescharacteristic
380#389Dic1111yescharacteristic
381#388Dic1111yescharacteristic
382#388Dic1111yescharacteristic
383#386Dic1111yescharacteristic
384#386Dic1111yescharacteristic
385#380Dic1111yescharacteristic
386C4×C4⋊C4C2×D1111yescharacteristic
387C4×C22⋊C4C2×D1111yescharacteristic
388C4×C22⋊C4C2×D1111yescharacteristic
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
393#336—111no—
394#336—111no—
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—41no—
405C22×C11—41no—
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—41no—
415C22×C11#43514yescomplemented
416C22×C11C2×C4×D411yescharacteristic
417C22×C11C2×C4×D411yescharacteristic
418C22×C11#52011yescharacteristic
419C22×C11C22×M1611yescharacteristic
420C22×C11C2×#13111yescharacteristic
421C22×C11C2×#13111yescharacteristic
422C22×C11#56811yescharacteristic
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—22no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—41no—
433C4×C11—41no—
434C4×C11D4211yescharacteristic
435C4×C11#54711yescharacteristic
436C4×C11#54811yescharacteristic
437C4×C11#55311yescharacteristic
438C22×D4C2×Dic1111yescharacteristic
439C22×D4C2×Dic1111yescharacteristic
440C22×D4C2×Dic1111yescharacteristic
441C23×C4C2×Dic1111yescharacteristic
442C23×C4C2×Dic1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C2×M16—222no—
447C2×M16—222no—
448C2×M16—441no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—111no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—222no—
458C22×C8—222no—
459C22×C8—222no—
460C22×C8—222no—
461C22×C8—222no—
462C22×C8—222no—
463C22×C8—441no—
464C22×C8—441no—
465C22×C8—441no—
466#121—24no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C2×C4⋊C4C2×Dic1111yescharacteristic
474C2×C4⋊C4C2×Dic1111yescharacteristic
475C2×C4⋊C4C2×Dic1111yescharacteristic
476C2×C4⋊C4C2×Dic1111yescharacteristic
477C2×C4⋊C4C2×Dic1111yescharacteristic
478C2×C22⋊C4C2×Dic1111yescharacteristic
479C2×C22⋊C4C2×Dic1111yescharacteristic
480C2×C22⋊C4C2×Dic1111yescharacteristic
481C2×C22⋊C4C2×Dic1111yescharacteristic
482C2×C22⋊C4C2×Dic1111yescharacteristic
483C2×C22⋊C4C2×Dic1111yescharacteristic
484C2×C22⋊C4C2×Dic1111yescharacteristic
485C2×C22⋊C4C2×Dic1111yescharacteristic
486C2×C22⋊C4C2×Dic1111yescharacteristic
487C2×C22⋊C4C2×Dic1111yescharacteristic
488C2×C42—22no—
489C2×C42—22no—
490C2×C42C2×Dic1111yescharacteristic
491C2×C42C2×Dic1111yescharacteristic
492C2×C42C22×D1111yescharacteristic
493C2×C42C22×D1111yescharacteristic
494C2×C42C22×D1111yescharacteristic
495C2×C42C22×D1111yescharacteristic
496C4⋊C8—114no—
497C4⋊C8—222no—
498C4⋊C8—222no—
499C4⋊C8—222no—
500C4⋊C8—222no—
501C4⋊C8—222no—
502C22⋊C8—114no—
503C22⋊C8—222no—
504C22⋊C8—222no—
505C22⋊C8—222no—
506C22⋊C8—222no—
507C22⋊C8—222no—
508C22⋊C8—441no—
509C22⋊C8—441no—
510#97—222no—
511#97—222no—
512#97—222no—
513C4×C8—222no—
514#95C2×Dic1111yescharacteristic
515#95C2×Dic1111yescharacteristic
516#95C2×Dic1111yescharacteristic
517#95C2×Dic1111yescharacteristic
518#95C2×Dic1111yescharacteristic
519#95C2×Dic1111yescharacteristic
520C2×C11—24no—
521C2×C11—42no—
522C2×C11—81no—
523C2×C11#236111yescharacteristic
524C2×C11C2×#43511yescharacteristic
525C2×C11#292911yescharacteristic
526C2×C11D4×M1611yescharacteristic
527C2×C11#293511yescharacteristic
528C2×C11#299011yescharacteristic
529C2×C11#299211yescharacteristic
530C24C22×Dic1111yescharacteristic
531C24C22×Dic1111yescharacteristic
532C24C22×Dic1111yescharacteristic
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4#431814yescomplemented
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—41no—
564C22×C4D4×D1112yes—
565C22×C4#434112yes—
566C22×C4C22×Dic1111yescharacteristic
567C22×C4C22×Dic1111yescharacteristic
568C22×C4C22×Dic1111yescharacteristic
569C22×C4C22×Dic1111yescharacteristic
570C22×C4C22×Dic1111yescharacteristic
571C22×C4C22×Dic1111yescharacteristic
572C22×C4C22×Dic1111yescharacteristic
573C22×C4C22×Dic1111yescharacteristic
574C22×C4C22×Dic1111yescharacteristic
575C22×C4C22×Dic1111yescharacteristic
576C22×C4C22×Dic1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578M16—444no—
579C2×C8—112no—
580C2×C8—112no—
581C2×C8—112no—
582C2×C8—112no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—444no—
604C2×C8—444no—
605C2×C8—444no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—41no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C42—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42D4×D1112yes—
630C42#434112yes—
631C11#2298711yescharacteristic, complemented, Sylow
632C23—21no—
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—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23C2×#431812yes—
650C23C2×#431812yes—
651C23D4×Dic1112yes—
652C23#6700112yes—
653C23C23×Dic1111yescharacteristic
654D4—28no—
655D4—44no—
656D4—44no—
657C2×C4—28no—
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—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
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—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4C2×#431812yes—
700C2×C4D4×Dic1112yes—
701C2×C4D4×Dic1112yes—
702C2×C4D4×Dic1112yes—
703C2×C4#6700112yes—
704C2×C4C2×D4×D1111yescharacteristic
705C2×C4C2×D4×D1111yescharacteristic
706C2×C4C2×#434111yescharacteristic
707C2×C4C2×#434111yescharacteristic
708C2×C4#6704211yescharacteristic
709C2×C4#6704311yescharacteristic
710C8—222no—
711C8—222no—
712C8—222no—
713C8—222no—
714C8—441no—
715C8—441no—
716C8—441no—
717C8—441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22#1062262414yescomplemented
739C22C22×#431811yescharacteristic
740C22C2×D4×Dic1111yescharacteristic
741C22C2×D4×Dic1111yescharacteristic
742C22C2×#6700111yescharacteristic
743C22C2×#6700111yescharacteristic
744C22#1062335011yescharacteristic
745C22#1062335811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4#1062312911yescharacteristic
758C4#1062314011yescharacteristic
759C4#1062314211yescharacteristic
760C4#1062314911yescharacteristic
761C2—24no—
762C2—42no—
763C2—81no—
764C2#1307163611yescharacteristic
765C2C2×#1062262411yescharacteristic
766C2#1307731111yescharacteristic
767C2D4×#431811yescharacteristic
768C2#1307736011yescharacteristic
769C2#1307774111yescharacteristic
770C2#1307775511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#121C2
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#22987
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622624C2semidirect
2. C2×#10622624C2semidirect
3. C2×D4×C11⋊C8C2semidirect
4. C22×C4⋊(C11⋊C8)C2semidirect
5. #13069415C2semidirect
6. #13069340C2semidirect
7. #13069231C2semidirect
8. #13069224C2semidirect
9. #13068909C2semidirect
10. #13068909C2semidirect
11. #13068801C2semidirect
12. #13068796C2semidirect
13. #13068491C2semidirect
14. #13068378C2semidirect
134. C22⋊(C11⋊C8)D4semidirect
140. C4⋊(C11⋊C8)D4semidirect
157. C2×D4×C11M16semidirect
415. C22×C11#435semidirect
541. C2×D4#4318semidirect
631. C11#22987semidirect
738. C22#10622624semidirect

Maximal subgroups

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

subgroupindex
C2×#106226242
C2×D4×C11⋊C82
C22×C4⋊(C11⋊C8)2
#130694152
#130693402
#130692312
#130692242
#130689092
#130688012
#130687962
#130684912
#130683782
C4×C11×#1212
#2298711