Finite Group Databasebeta

← #14775920

Subgroups — #14775920

Order 2816.

1050 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×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C2×#10622537C211yesmaximal, characteristic, complemented
5#13069415C211yesmaximal, characteristic, complemented
6#13069340C211yesmaximal, characteristic, complemented
7#13069231C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13068914C211yesmaximal, characteristic, complemented
10#13068914C211yesmaximal, 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
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
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#10622625—24no—
44#10622624—24no—
45#10622624—24no—
46#10622537—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—22no—
104C2×#4318—22no—
105C2×#4318—22no—
106C2×#4318—22no—
107C2×#4318—41no—
108C2×#4318—41no—
109C2×#4318—41no—
110C22×C11⋊C8—22no—
111C22×C11⋊C8—22no—
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#22988—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—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
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—41no—
178C22×C4×C11—41no—
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—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4M1614yescomplemented
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—
220#4318—44no—
221#4318—44no—
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—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—44no—
243C2×C11⋊C8C2×D412yes—
244C2×C11⋊C8C2×D412yes—
245C2×C11⋊C8C2×D412yes—
246C2×C11⋊C8C2×D412yes—
247C2×#436—111no—
248C2×#435—111no—
249C2×#435—111no—
250C2×#423—111no—
251C4×#121D1111yescharacteristic
252#1955—111no—
253#1940—111no—
254#1924—111no—
255#1923—111no—
256#1870—111no—
257#1870—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×C11—21no—
280C23×C11—21no—
281C23×C11C4×D412yes—
282C23×C11C2×M1612yes—
283C23×C11C23×C411yescharacteristic
284D4×C11—44no—
285D4×C11—44no—
286D4×C11—44no—
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—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
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—44no—
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×C11C2×M1612yes—
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—
349C22×M16—111no—
350C22×M16—111no—
351C23×C8—111no—
352C2×#121Dic1111yescharacteristic
353C2×C4×D4C2×D1111yescharacteristic
354C2×C4×D4C2×D1111yescharacteristic
355C2×C4×D4C2×D1111yescharacteristic
356C22×C42C2×D1111yescharacteristic
357#436—224no—
358#435—224no—
359#435—224no—
360#423—224no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×C4⋊C8—111no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×C4⋊C8—111no—
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—41no—
402C22×C11—41no—
403C22×C11—41no—
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—41no—
416C22×C11C2×C4×D411yescharacteristic
417C22×C11C2×C4×D411yescharacteristic
418C22×C11#52011yescharacteristic
419C22×C11C22×M1611yescharacteristic
420C22×C11#56811yescharacteristic
421C22×C11#56811yescharacteristic
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—222no—
449C2×M16—222no—
450C2×M16—222no—
451C2×M16—222no—
452C2×M16—441no—
453C2×M16—441no—
454C2×M16—441no—
455C22×C8—111no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8—222no—
464C22×C8—222no—
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—42no—
521C2×C11—42no—
522C2×C11—81no—
523C2×C11#236111yescharacteristic
524C2×C11#293011yescharacteristic
525C2×C11#293211yescharacteristic
526C2×C11D4×M1611yescharacteristic
527C2×C11D4×M1611yescharacteristic
528C2×C11#298911yescharacteristic
529C2×C11#299511yescharacteristic
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—41no—
540C2×D4—41no—
541C2×D4—41no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
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—41no—
562C22×C4—41no—
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—
579M16—444no—
580M16—444no—
581C2×C8—112no—
582C2×C8—112no—
583C2×C8—112no—
584C2×C8—112no—
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—221no—
604C2×C8—221no—
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—41no—
619C22⋊C4—41no—
620C22⋊C4#431814yescomplemented
621C42—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42D4×D1112yes—
630C42#434112yes—
631C11#2298811yescharacteristic, 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—
649C23—21no—
650C23—21no—
651C23C2×#431812yes—
652C23D4×Dic1112yes—
653C23C23×Dic1111yescharacteristic
654D4—44no—
655D4—44no—
656D4—44no—
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—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
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—44no—
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×C4C2×#431812yes—
701C2×C4D4×Dic1112yes—
702C2×C4D4×Dic1112yes—
703C2×C4D4×Dic1112yes—
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—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22C22×#431811yescharacteristic
740C22C2×D4×Dic1111yescharacteristic
741C22C2×D4×Dic1111yescharacteristic
742C22#1062335011yescharacteristic
743C22#1062335011yescharacteristic
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—42no—
762C2—42no—
763C2—81no—
764C2#1307163611yescharacteristic
765C2#1307732011yescharacteristic
766C2#1307733411yescharacteristic
767C2D4×#431811yescharacteristic
768C2D4×#431811yescharacteristic
769C2#1307773311yescharacteristic
770C2#1307778611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#121C2
prime radicalC2×C11×#121C4
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#22988
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×#10622625C2semidirect
2. C2×#10622624C2semidirect
3. C2×#10622624C2semidirect
4. C2×#10622537C2semidirect
5. #13069415C2semidirect
6. #13069340C2semidirect
7. #13069231C2semidirect
8. #13069224C2semidirect
9. #13068914C2semidirect
10. #13068914C2semidirect
11. #13068801C2semidirect
12. #13068796C2semidirect
13. #13068491C2semidirect
14. #13068378C2semidirect
134. C22⋊(C11⋊C8)D4semidirect
140. C4⋊(C11⋊C8)D4semidirect
208. C11×C22⋊C4M16semidirect
620. C22⋊C4#4318semidirect
631. C11#22988semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106226242
C2×#106225372
#130694152
#130693402
#130692312
#130692242
#130689142
#130688012
#130687962
#130684912
#130683782
C4×C11×#1212
#2298811