Finite Group Databasebeta

← #14770781

Subgroups — #14770781

Order 2816.

1060 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×#10622613C211yesmaximal, characteristic, complemented
2C2×#10622820C211yesmaximal, characteristic
3#13069231C211yesmaximal, characteristic, complemented
4#13069231C211yesmaximal, characteristic, complemented
5#13069224C211yesmaximal, characteristic, complemented
6#13069224C211yesmaximal, characteristic, complemented
7#13068801C211yesmaximal, characteristic, complemented
8#13068801C211yesmaximal, characteristic, complemented
9#13068687C211yesmaximal, characteristic, complemented
10#13068600C211yesmaximal, characteristic, complemented
11#13068526C211yesmaximal, characteristic
12#13068400C211yesmaximal, characteristic, complemented
13#13068400C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C11×#2280C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C11×#381C411yescharacteristic
22C11×#381C411yescharacteristic
23C11×#380C411yescharacteristic
24C11×#380C411yescharacteristic
25C11×#380C411yescharacteristic
26C11×#380C411yescharacteristic
27C11×#379C411yescharacteristic
28C11×#379C411yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33#10622820—24no—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
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
44#10622613—24no—
45C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
46C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
47C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
48C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
49C2×#66867C2211yescharacteristic, complemented
50C2×#66867C2211yescharacteristic, complemented
51C2×C4×C11⋊C8C2211yescharacteristic, complemented
52C2×C4×C11⋊C8C2211yescharacteristic, complemented
53#10622162C2211yescharacteristic, complemented
54#10622162C2211yescharacteristic, complemented
55#10622162C2211yescharacteristic, complemented
56#10622162C2211yescharacteristic, complemented
57#10622162C2211yescharacteristic, complemented
58#10622162C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, 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
74C11×#117—22no—
75C11×#117—22no—
76C11×#117—41no—
77C11×#117—41no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C11×C4⋊C4C2×C411yescharacteristic
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊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×C11×C22⋊C4C2×C411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×#4318—22no—
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318—41no—
103C2×#4318—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×#95C2×C411yescharacteristic
113C11×#95C2×C411yescharacteristic
114C11×#95C2×C411yescharacteristic
115C11×#95C2×C411yescharacteristic
116C11×#95C2×C411yescharacteristic
117C11×#95C2×C411yescharacteristic
118C11×#95C2×C411yescharacteristic
119C11×#95C2×C411yescharacteristic
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—22no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—41no—
128C22⋊(C11⋊C8)—41no—
129C22⋊(C11⋊C8)D414yes—
130C4⋊(C11⋊C8)—22no—
131C4⋊(C11⋊C8)—22no—
132C4⋊(C11⋊C8)—41no—
133C4⋊(C11⋊C8)—41no—
134#66867—22no—
135#66867—41no—
136C4×C11⋊C8—22no—
137C4×C11⋊C8—41no—
138#22559—111nomaximal, Sylow
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—41no—
143C24×C11—41no—
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
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216#4318—44no—
217#4318—44no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
241C2×C11⋊C8C2×D412yes—
242C2×#433—111no—
243C2×#407—111no—
244#2280D1111yescharacteristic
245#1924—111no—
246#1924—111no—
247#1923—111no—
248#1923—111no—
249#1851—111no—
250#1851—111no—
251#1818—111no—
252#1798—111no—
253#1779—111no—
254#1753—111no—
255#1753—111no—
256#1750—111no—
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×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11#11712yes—
283C23×C11C4×D412yes—
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
340C11⋊C8—22no—
341C11⋊C8—22no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C11⋊C8—41no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C24×C4C2×D1111yescharacteristic
349C22×M16—111no—
350C22×M16—111no—
351C2×#117C2×D1111yescharacteristic
352C2×#117C2×D1111yescharacteristic
353#433—224no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8—111no—
356C2×C4⋊C8—111no—
357C2×C4⋊C8—111no—
358#407—224no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8—111no—
366C2×C22⋊C8—111no—
367C2×C22⋊C8—111no—
368C2×C22⋊C8—111no—
369C2×#97—111no—
370C2×#97—111no—
371C2×C4×C8—111no—
372C2×C4×C8—111no—
373#381Dic1111yescharacteristic
374#381Dic1111yescharacteristic
375#380Dic1111yescharacteristic
376#380Dic1111yescharacteristic
377#380Dic1111yescharacteristic
378#380Dic1111yescharacteristic
379#379Dic1111yescharacteristic
380#379Dic1111yescharacteristic
381C4×C22⋊C4C2×D1111yescharacteristic
382C4×C22⋊C4C2×D1111yescharacteristic
383C4×C22⋊C4C2×D1111yescharacteristic
384C4×C22⋊C4C2×D1111yescharacteristic
385#336—111no—
386#336—111no—
387#336—111no—
388#336—111no—
389#336—111no—
390#336—111no—
391#336—111no—
392#336—111no—
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—416no—
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×C11C2×#11711yescharacteristic
416C22×C11C2×C4×D411yescharacteristic
417C22×C11#51811yescharacteristic
418C22×C11C2×#13111yescharacteristic
419C22×C11#56811yescharacteristic
420C22×C11#56811yescharacteristic
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×Dic1111yescharacteristic
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—41no—
443C23×C4—41no—
444C23×C4C2×Dic1111yescharacteristic
445C23×C4C2×Dic1111yescharacteristic
446C23×C4C2×Dic1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C2×M16—222no—
451C2×M16—222no—
452C2×M16—222no—
453C2×M16—222no—
454C2×M16—441no—
455C2×M16—441no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8—111no—
464#117—22no—
465#117—22no—
466#117—41no—
467#117—41no—
468C2×C4⋊C4C2×Dic1111yescharacteristic
469C2×C4⋊C4C2×Dic1111yescharacteristic
470C2×C4⋊C4C2×Dic1111yescharacteristic
471C2×C4⋊C4C2×Dic1111yescharacteristic
472C2×C22⋊C4C2×Dic1111yescharacteristic
473C2×C22⋊C4C2×Dic1111yescharacteristic
474C2×C22⋊C4C2×Dic1111yescharacteristic
475C2×C22⋊C4C2×Dic1111yescharacteristic
476C2×C22⋊C4C2×Dic1111yescharacteristic
477C2×C22⋊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×C42C22×D1111yescharacteristic
485C2×C42C22×D1111yescharacteristic
486C2×C42C22×D1111yescharacteristic
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—222no—
489C4⋊C8—222no—
490C4⋊C8—441no—
491C4⋊C8—441no—
492C22⋊C8—114no—
493C22⋊C8—222no—
494C22⋊C8—222no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500C22⋊C8—441no—
501C22⋊C8—441no—
502#97—222no—
503#97—441no—
504C4×C8—222no—
505C4×C8—441no—
506#95C2×Dic1111yescharacteristic
507#95C2×Dic1111yescharacteristic
508#95C2×Dic1111yescharacteristic
509#95C2×Dic1111yescharacteristic
510#95C2×Dic1111yescharacteristic
511#95C2×Dic1111yescharacteristic
512#95C2×Dic1111yescharacteristic
513#95C2×Dic1111yescharacteristic
514C2×C11—42no—
515C2×C11—42no—
516C2×C11—42no—
517C2×C11#234211yescharacteristic
518C2×C11#292111yescharacteristic
519C2×C11#292411yescharacteristic
520C2×C11#293011yescharacteristic
521C2×C11#293311yescharacteristic
522C2×C11#297611yescharacteristic
523C2×C11#297811yescharacteristic
524C24—22no—
525C24—22no—
526C24—22no—
527C24—41no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24C22×Dic1111yescharacteristic
532C24C22×Dic1111yescharacteristic
533C24C22×Dic1111yescharacteristic
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×C4#433912yes—
562C22×C4#433912yes—
563C22×C4D4×D1112yes—
564C22×C4#434112yes—
565C22×C4C22×Dic1111yescharacteristic
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×C4C23×D1111yescharacteristic
577M16—444no—
578M16—444no—
579C2×C8—112no—
580C2×C8—112no—
581C2×C8—221no—
582C2×C8—221no—
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—
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—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
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#2255911yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
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—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#6697912yes—
654C23D4×Dic1112yes—
655C23#6700112yes—
656C23C23×Dic1111yescharacteristic
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×C4#6697912yes—
704C2×C4D4×Dic1112yes—
705C2×C4C2×#433911yescharacteristic
706C2×C4C2×#433911yescharacteristic
707C2×C4C2×D4×D1111yescharacteristic
708C2×C4C2×#434111yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4#6703711yescharacteristic
711C8—222no—
712C8—222no—
713C8—441no—
714C8—441no—
715C8—441no—
716C8—441no—
717C8—441no—
718C8—441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—416no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×#6697911yescharacteristic
742C22C2×D4×Dic1111yescharacteristic
743C22#1062332911yescharacteristic
744C22C2×#6700111yescharacteristic
745C22#1062335011yescharacteristic
746C22#1062335011yescharacteristic
747C22#1062335011yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4#1062302111yescharacteristic
760C4#1062302111yescharacteristic
761C4#1062302611yescharacteristic
762C4#1062302611yescharacteristic
763C2—42no—
764C2—42no—
765C2—42no—
766C2#1307146511yescharacteristic
767C2#1307725411yescharacteristic
768C2#1307727411yescharacteristic
769C2#1307732011yescharacteristic
770C2#1307734311yescharacteristic
771C2#1307766411yescharacteristic
772C2#1307767811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2280C2
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#2280D11
hypocenterC11#22559
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. C2×#10622613C2semidirect
3. #13069231C2semidirect
4. #13069231C2semidirect
5. #13069224C2semidirect
6. #13069224C2semidirect
7. #13068801C2semidirect
8. #13068801C2semidirect
9. #13068687C2semidirect
10. #13068600C2semidirect
12. #13068400C2semidirect
13. #13068400C2semidirect
14. #13068382C2semidirect
45. C2×C4⋊(C11⋊C8)C22semidirect
46. C2×C4⋊(C11⋊C8)C22semidirect
47. C2×C4⋊(C11⋊C8)C22semidirect
48. C2×C4⋊(C11⋊C8)C22semidirect
49. C2×#66867C22semidirect
50. C2×#66867C22semidirect
51. C2×C4×C11⋊C8C22semidirect
52. C2×C4×C11⋊C8C22semidirect
53. #10622162C22semidirect
54. #10622162C22semidirect
55. #10622162C22semidirect
56. #10622162C22semidirect
57. #10622162C22semidirect
58. #10622162C22semidirect
59. #10622162C22semidirect
60. #10622162C22semidirect
627. C11#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
C2×#106228202
#130692312
#130692242
#130688012
#130686872
#130686002
#130685262
#130684002
#130683822
C11×#22802
#2255911