Finite Group Databasebeta

← #14764880

Subgroups — #14764880

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622820C211yesmaximal, characteristic, complemented
3#13069415C211yesmaximal, characteristic, complemented
4#13069411C211yesmaximal, characteristic, complemented
5#13069231C211yesmaximal, characteristic, complemented
6#13069224C211yesmaximal, characteristic, complemented
7#13069224C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13068914C211yesmaximal, characteristic, complemented
10#13068914C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic, complemented
12#13068801C211yesmaximal, characteristic, complemented
13#13068526C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C4×C11×#120C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C2×C11×#120C411yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic, complemented
24C11×#386C411yescharacteristic
25C11×#386C411yescharacteristic
26C11×#386C411yescharacteristic
27C11×#385C411yescharacteristic
28C11×#385C411yescharacteristic
29C11×#385C411yescharacteristic
30C11×#379C411yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4C2211yescharacteristic
34#10622820—24no—
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
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
46C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
47C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
48#10622625—24no—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
50C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
52C2×#66867C2211yescharacteristic, complemented
53C2×C4×C11⋊C8C2211yescharacteristic, complemented
54C2×C4×C11⋊C8C2211yescharacteristic, complemented
55#10622162C2211yescharacteristic, complemented
56#10622162C2211yescharacteristic, complemented
57#10622162C2211yescharacteristic, complemented
58#10622162C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C25×C11C2×C411yescharacteristic
62C22×D4×C11C2×C411yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C22×D4×C11C2×C411yescharacteristic
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11—41no—
70C23×C4×C11—41no—
71C23×C4×C11C2×C411yescharacteristic
72C23×C4×C11C2×C411yescharacteristic
73C23×C4×C11C2×C411yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C11×#120—24no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—41no—
82C4×D4×C11—41no—
83C4×D4×C11—41no—
84C4×D4×C11—41no—
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C4⋊C4C2×C411yescharacteristic
87C2×C11×C4⋊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×C11×C22⋊C4C2×C411yescharacteristic
94C2×C11×C22⋊C4C2×C411yescharacteristic
95C2×C11×C22⋊C4C2×C411yescharacteristic
96C2×C11×C22⋊C4C2×C411yescharacteristic
97C2×C11×C22⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4C2×C411yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318—41no—
106C2×#4318—41no—
107C2×#4318—41no—
108C2×#4318—41no—
109C2×#4318—41no—
110C2×#4318—41no—
111C2×#4318D414yescomplemented
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C11×#95C2×C411yescharacteristic
121C11×#95C2×C411yescharacteristic
122C11×#95C2×C411yescharacteristic
123C11×#95C2×C411yescharacteristic
124C11×#95C2×C411yescharacteristic
125C11×#95C2×C411yescharacteristic
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133C22⋊(C11⋊C8)—41no—
134C22⋊(C11⋊C8)—41no—
135C22⋊(C11⋊C8)—41no—
136C22⋊(C11⋊C8)—41no—
137C22⋊(C11⋊C8)—41no—
138C22⋊(C11⋊C8)—41no—
139C4⋊(C11⋊C8)—22no—
140C4⋊(C11⋊C8)—41no—
141C4⋊(C11⋊C8)—41no—
142#66867—41no—
143C4×C11⋊C8—22no—
144C4×C11⋊C8—41no—
145#22038—111nomaximal, Sylow
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—41no—
150C24×C11—41no—
151C24×C11—41no—
152C24×C11—41no—
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C24×C11C22×C411yescharacteristic
156C24×C11C22×C411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
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—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—41no—
192C22×C4×C11—41no—
193C22×C4×C11—41no—
194C22×C4×C11—41no—
195C22×C4×C11—41no—
196C22×C4×C11—41no—
197C22×C4×C11—44no—
198C22×C4×C11—44no—
199C22×C4×C11—44no—
200C22×C4×C11—44no—
201C22×C4×C11C22×C411yescharacteristic
202C22×C4×C11C22×C411yescharacteristic
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C22×C411yescharacteristic
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C22×C411yescharacteristic
208C22×C4×C11C22×C411yescharacteristic
209C22×C4×C11C22×C411yescharacteristic
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C2×D412yes—
212C22×C4×C11#4112yes—
213C22×C4×C11C2411yescharacteristic
214C11×C4⋊C4—22no—
215C11×C4⋊C4—41no—
216C11×C4⋊C4—41no—
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—
228C11×C22⋊C4M1614yescomplemented
229C42×C11—21no—
230C42×C11—21no—
231C42×C11—21no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—21no—
235#4318—44no—
236#4318—44no—
237#4318—44no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8C2×D412yes—
261C2×C11⋊C8C2×D412yes—
262C2×#436—111no—
263C2×#407—111no—
264C4×#120D1111yescharacteristic
265#1955—111no—
266#1954—111no—
267#1924—111no—
268#1923—111no—
269#1923—111no—
270#1923—111no—
271#1870—111no—
272#1870—111no—
273#1870—111no—
274#1851—111no—
275#1779—111no—
276#1753—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11C4×D412yes—
310C23×C11C2×M1612yes—
311C23×C11#13112yes—
312C23×C11C23×C411yescharacteristic
313D4×C11—44no—
314D4×C11—44no—
315D4×C11—44no—
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—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—44no—
348C2×C4×C11—44no—
349C2×C4×C11—44no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11C4×D412yes—
363C2×C4×C11C2×M1612yes—
364C2×C4×C11C2×M1612yes—
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C2×#4111yescharacteristic
367C2×C4×C11H(5,𝔽2)11yescharacteristic
368C2×C4×C11H(5,𝔽2)11yescharacteristic
369C2×C4×C11H(5,𝔽2)11yescharacteristic
370C2×C4×C11H(5,𝔽2)11yescharacteristic
371C11⋊C8—22no—
372C11⋊C8—22no—
373C11⋊C8—41no—
374C11⋊C8—41no—
375C11⋊C8—41no—
376C11⋊C8—41no—
377C11⋊C8—41no—
378C11⋊C8—41no—
379C24×C4C2×D1111yescharacteristic
380C22×M16—111no—
381C22×M16—111no—
382C22×M16—111no—
383C2×#120Dic1111yescharacteristic
384C2×C4×D4C2×D1111yescharacteristic
385C2×C4×D4C2×D1111yescharacteristic
386C2×C4×D4C2×D1111yescharacteristic
387#436—224no—
388C2×C4⋊C8—111no—
389C2×C4⋊C8—111no—
390C2×C4⋊C8—111no—
391#407—224no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×C22⋊C8—111no—
398C2×C22⋊C8—111no—
399C2×C22⋊C8—111no—
400C2×C22⋊C8—111no—
401C2×C22⋊C8—111no—
402C2×C22⋊C8—111no—
403C2×C22⋊C8—111no—
404C2×C22⋊C8—111no—
405C2×#97—111no—
406C2×C4×C8—111no—
407C2×C4×C8—111no—
408#386Dic1111yescharacteristic
409#386Dic1111yescharacteristic
410#386Dic1111yescharacteristic
411#385Dic1111yescharacteristic
412#385Dic1111yescharacteristic
413#385Dic1111yescharacteristic
414#379Dic1111yescharacteristic
415C4×C22⋊C4C2×D1111yescharacteristic
416C4×C22⋊C4C2×D1111yescharacteristic
417C4×C22⋊C4C2×D1111yescharacteristic
418#336—111no—
419#336—111no—
420#336—111no—
421#336—111no—
422#336—111no—
423#336—111no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—416no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11C2×C4×D411yescharacteristic
454C22×C11#51811yescharacteristic
455C22×C11#51811yescharacteristic
456C22×C11C22×M1611yescharacteristic
457C22×C11C2×#13111yescharacteristic
458C22×C11#56811yescharacteristic
459C22×C11#56811yescharacteristic
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—41no—
464C4×C11—41no—
465C4×C11—41no—
466C4×C11—41no—
467C4×C11—41no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11#53411yescharacteristic
471C4×C11#53511yescharacteristic
472C4×C11#53811yescharacteristic
473C4×C11#53811yescharacteristic
474C25C2×Dic1111yescharacteristic
475C22×D4C2×Dic1111yescharacteristic
476C22×D4C2×Dic1111yescharacteristic
477C22×D4C2×Dic1111yescharacteristic
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—41no—
481C23×C4—41no—
482C23×C4—41no—
483C23×C4—41no—
484C23×C4C2×Dic1111yescharacteristic
485C23×C4C2×Dic1111yescharacteristic
486C23×C4C2×Dic1111yescharacteristic
487C23×C4C22×D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C2×M16—114no—
492C2×M16—222no—
493C2×M16—222no—
494C2×M16—441no—
495C2×M16—441no—
496C2×M16—441no—
497C2×M16—441no—
498C2×M16—441no—
499C2×M16—441no—
500C22×C8—111no—
501C22×C8—111no—
502C22×C8—111no—
503C22×C8—111no—
504C22×C8—111no—
505C22×C8—111no—
506C22×C8—111no—
507C22×C8—111no—
508#120—24no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—41no—
512C4×D4—41no—
513C4×D4—41no—
514C4×D4—41no—
515C2×C4⋊C4C2×Dic1111yescharacteristic
516C2×C4⋊C4C2×Dic1111yescharacteristic
517C2×C4⋊C4C2×Dic1111yescharacteristic
518C2×C22⋊C4C2×Dic1111yescharacteristic
519C2×C22⋊C4C2×Dic1111yescharacteristic
520C2×C22⋊C4C2×Dic1111yescharacteristic
521C2×C22⋊C4C2×Dic1111yescharacteristic
522C2×C22⋊C4C2×Dic1111yescharacteristic
523C2×C22⋊C4C2×Dic1111yescharacteristic
524C2×C22⋊C4C2×Dic1111yescharacteristic
525C2×C22⋊C4C2×Dic1111yescharacteristic
526C2×C22⋊C4C2×Dic1111yescharacteristic
527C2×C22⋊C4C2×Dic1111yescharacteristic
528C2×C22⋊C4C2×Dic1111yescharacteristic
529C2×C22⋊C4C2×Dic1111yescharacteristic
530C2×C42C22×D1111yescharacteristic
531C2×C42C22×D1111yescharacteristic
532C2×C42C22×D1111yescharacteristic
533C4⋊C8—222no—
534C4⋊C8—441no—
535C4⋊C8—441no—
536C22⋊C8—222no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C22⋊C8—222no—
540C22⋊C8—222no—
541C22⋊C8—222no—
542C22⋊C8—222no—
543C22⋊C8—441no—
544C22⋊C8—441no—
545C22⋊C8—441no—
546C22⋊C8—441no—
547C22⋊C8—441no—
548C22⋊C8—441no—
549#97—441no—
550C4×C8—222no—
551C4×C8—441no—
552#95C2×Dic1111yescharacteristic
553#95C2×Dic1111yescharacteristic
554#95C2×Dic1111yescharacteristic
555#95C2×Dic1111yescharacteristic
556#95C2×Dic1111yescharacteristic
557#95C2×Dic1111yescharacteristic
558C2×C11—42no—
559C2×C11—42no—
560C2×C11—42no—
561C2×C11—81no—
562C2×C11#232111yescharacteristic
563C2×C11#293311yescharacteristic
564C2×C11D4×M1611yescharacteristic
565C2×C11#297411yescharacteristic
566C2×C11#297511yescharacteristic
567C2×C11#297611yescharacteristic
568C2×C11#297811yescharacteristic
569C24—22no—
570C24—22no—
571C24—22no—
572C24—41no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24C22×Dic1111yescharacteristic
577C24C22×Dic1111yescharacteristic
578C24C22×Dic1111yescharacteristic
579C24C22×Dic1111yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4D4×D1112yes—
625C22×C4#434112yes—
626C22×C4C22×Dic1111yescharacteristic
627C22×C4C22×Dic1111yescharacteristic
628C22×C4C22×Dic1111yescharacteristic
629C22×C4C22×Dic1111yescharacteristic
630C22×C4C22×Dic1111yescharacteristic
631C22×C4C22×Dic1111yescharacteristic
632C22×C4C22×Dic1111yescharacteristic
633C22×C4C22×Dic1111yescharacteristic
634C22×C4C22×Dic1111yescharacteristic
635C22×C4C22×Dic1111yescharacteristic
636C22×C4C23×D1111yescharacteristic
637M16—444no—
638M16—444no—
639M16—444no—
640C2×C8—112no—
641C2×C8—112no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—221no—
648C2×C8—221no—
649C2×C8—221no—
650C2×C8—221no—
651C2×C8—221no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C4⋊C4—22no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4#431814yescomplemented
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C11#2203811yescharacteristic, complemented, Sylow
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23C2×#431812yes—
719C23D4×Dic1112yes—
720C23#6700112yes—
721C23C23×Dic1111yescharacteristic
722D4—44no—
723D4—44no—
724D4—44no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4C2×#431812yes—
772C2×C4C2×#431812yes—
773C2×C4D4×Dic1112yes—
774C2×C4C2×D4×D1111yescharacteristic
775C2×C4C2×#434111yescharacteristic
776C2×C4#6703711yescharacteristic
777C2×C4#6703711yescharacteristic
778C2×C4#6703711yescharacteristic
779C2×C4#6703711yescharacteristic
780C8—222no—
781C8—222no—
782C8—441no—
783C8—441no—
784C8—441no—
785C8—441no—
786C8—441no—
787C8—441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22C22×#431811yescharacteristic
818C22C2×D4×Dic1111yescharacteristic
819C22#1062332911yescharacteristic
820C22#1062332911yescharacteristic
821C22C2×#6700111yescharacteristic
822C22#1062335011yescharacteristic
823C22#1062335011yescharacteristic
824C4—22no—
825C4—22no—
826C4—22no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4#1062312011yescharacteristic
835C4#1062312311yescharacteristic
836C4#1062312411yescharacteristic
837C4#1062312411yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—81no—
842C2#1307127711yescharacteristic
843C2#1307734311yescharacteristic
844C2D4×#431811yescharacteristic
845C2#1307765111yescharacteristic
846C2#1307765711yescharacteristic
847C2#1307766411yescharacteristic
848C2#1307767811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#120C2
prime radicalC2×C11×#120C4
cosocleC22×C4×C11C24
hypercenterC4×#120D11
hypocenterC11#22038
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. C2×#10622820C2semidirect
3. #13069415C2semidirect
4. #13069411C2semidirect
5. #13069231C2semidirect
6. #13069224C2semidirect
7. #13069224C2semidirect
8. #13069224C2semidirect
9. #13068914C2semidirect
10. #13068914C2semidirect
11. #13068914C2semidirect
12. #13068801C2semidirect
13. #13068526C2semidirect
14. #13068400C2semidirect
23. C22×#4318C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
46. C2×C22⋊(C11⋊C8)C22semidirect
47. C2×C22⋊(C11⋊C8)C22semidirect
49. C2×C4⋊(C11⋊C8)C22semidirect
50. C2×C4⋊(C11⋊C8)C22semidirect
51. C2×C4⋊(C11⋊C8)C22semidirect
52. C2×#66867C22semidirect
53. C2×C4×C11⋊C8C22semidirect
54. C2×C4×C11⋊C8C22semidirect
55. #10622162C22semidirect
56. #10622162C22semidirect
57. #10622162C22semidirect
58. #10622162C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
111. C2×#4318D4semidirect
228. C11×C22⋊C4M16semidirect
678. C22⋊C4#4318semidirect
685. C11#22038semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106228202
#130694152
#130694112
#130692312
#130692242
#130689142
#130688012
#130685262
#130684002
C4×C11×#1202
#2203811