Finite Group Databasebeta

← #14759894

Subgroups — #14759894

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622342C211yesmaximal, characteristic, complemented
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×#10622343C211yesmaximal, characteristic, complemented
4C2×#10622735C211yesmaximal, characteristic, complemented
5#13071858C211yesmaximal, characteristic
6#13069412C211yesmaximal, characteristic, complemented
7#13069338C211yesmaximal, characteristic, complemented
8#13069230C211yesmaximal, characteristic, complemented
9#13069226C211yesmaximal, characteristic, complemented
10#13068913C211yesmaximal, characteristic, complemented
11#13068598C211yesmaximal, characteristic, complemented
12#13068482C211yesmaximal, characteristic, complemented
13#13068402C211yesmaximal, characteristic, complemented
14#13068398C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622836C411yescharacteristic
28#10622835C411yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622735—24no—
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43C2×C8×Dic11C2211yescharacteristic
44#10622624—24no—
45#10622607C411yescharacteristic
46#10622597C411yescharacteristic
47#10622574C411yescharacteristic
48#10622572C411yescharacteristic
49#10622565C411yescharacteristic
50#10622561C411yescharacteristic
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C4×Dic11⋊C4C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×#66867C2211yescharacteristic
55#10622343—24no—
56#10622342—24no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622188C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84C2×C22⋊Dic11C2×C411yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C4×C22⋊D11—22no—
89C4×C22⋊D11—22no—
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96#66979—22no—
97#66979—22no—
98C2×C4⋊Dic11C2×C411yescharacteristic
99C2×C4⋊Dic11C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×Dic11⋊C4C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×#4318—22no—
108C2×#4318—22no—
109C2×#4318—22no—
110C22×C11⋊C8—22no—
111C22×C11⋊C8—22no—
112C22×C11⋊C8D414yescomplemented
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×#4313—22no—
118C2×#4313—22no—
119C2×#4313—22no—
120C11×C22⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11⋊#95C2×C411yescharacteristic
124C11⋊#95C2×C411yescharacteristic
125C11⋊#95C2×C411yescharacteristic
126C11⋊#95C2×C411yescharacteristic
127C11⋊#95C2×C411yescharacteristic
128C11⋊#95C2×C411yescharacteristic
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134#66879—22no—
135#66879—22no—
136#66879—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140C8×Dic11—22no—
141C8×Dic11D414yescomplemented
142C4⋊(C11⋊C8)—22no—
143#66867—22no—
144#21493—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C24×C11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C2×D4×C11—22no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
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—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—22no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C2×C22⋊D11—41no—
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C22×Dic11C22×C411yescharacteristic
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C11×M16—28no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
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×C11C2×D412yes—
199C2×C8×C11#4112yes—
200C11×C4⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C42×C11—21no—
204C42×C11—21no—
205C22⋊Dic11—22no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—22no—
209C22⋊Dic11—41no—
210C22⋊Dic11—41no—
211(C2×D11)⋊C4—22no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—41no—
214(C2×D11)⋊C4—41no—
215C4⋊Dic11—22no—
216C4⋊Dic11—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—41no—
220Dic11⋊C4—41no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11C2×D412yes—
226C4×Dic11#4112yes—
227#4318—44no—
228C2×C11⋊C8—28no—
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⋊C8C2×D412yes—
238C2×C11⋊C8C2×D412yes—
239C2×C11⋊C8C2×D412yes—
240C2×C11⋊C8#4112yes—
241#4313—44no—
242C2×#436—111no—
243C2×#435—111no—
244C2×#435—111no—
245C2×#405—111no—
246#2392—111no—
247#1955—111no—
248#1940—111no—
249#1924—111no—
250#1924—111no—
251#1870—111no—
252#1870D1111yescharacteristic, complemented
253#1798—111no—
254#1770—111no—
255#1753—111no—
256#1753—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×C11C4×D412yes—
271C23×C11C23×C411yescharacteristic
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279D4×C11—44no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—21no—
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—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11C4×D412yes—
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C22⋊D11—44no—
307C22⋊D11—44no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11C4×D412yes—
328C2×Dic11C4×D412yes—
329C4×D11—41no—
330C4×D11—41no—
331C4×D11—41no—
332C4×D11—41no—
333C8×C11—22no—
334C8×C11—22no—
335C8×C11—41no—
336C8×C11—41no—
337C11⋊C8—22no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C11⋊C8#12114yes—
341C22×M16—111no—
342C22×M16—111no—
343C22×M16C2×D1111yescharacteristic
344C23×C8—111no—
345C2×C4×D4—111no—
346C2×C4×D4—111no—
347C2×C4×D4C2×D1111yescharacteristic
348C2×#117—111no—
349#436—224no—
350#435—224no—
351#435—224no—
352C2×C4⋊C8—111no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×C4⋊C8—111no—
356C2×C22⋊C8—111no—
357C2×C22⋊C8—111no—
358C2×C22⋊C8—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×C22⋊C8C2×D1111yescharacteristic
362C2×C22⋊C8C2×D1111yescharacteristic
363C2×C22⋊C8C2×D1111yescharacteristic
364#405—224no—
365C2×#97—111no—
366C2×#97—111no—
367C2×#97—111no—
368C2×#97—111no—
369C2×C4×C8—111no—
370C2×C4×C8—111no—
371#398—111no—
372#397—111no—
373#396—111no—
374#396—111no—
375#394—111no—
376#394—111no—
377#394—111no—
378#392—111no—
379C4×C4⋊C4—111no—
380C4×C22⋊C4—111no—
381C4×C22⋊C4—111no—
382#336—111no—
383#336—111no—
384#336—111no—
385#336—111no—
386#336C2×D1111yescharacteristic
387#336C2×D1111yescharacteristic
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C2×C4×D411yescharacteristic
404C22×C11C4×#4111yescharacteristic
405C22×C11#56811yescharacteristic
406C22×C11#56811yescharacteristic
407C22×C11#56811yescharacteristic
408C22×C11#56811yescharacteristic
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—41no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C4×C11—22no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11C2×#12111yescharacteristic
421C4×C11#52511yescharacteristic
422C4×C11#52911yescharacteristic
423C4×C11#53211yescharacteristic
424Dic11—22no—
425Dic11—22no—
426Dic11—41no—
427Dic11—41no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431C22×D4—111no—
432C22×D4—111no—
433C22×D4C4×D1111yescharacteristic
434C23×C4—111no—
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C2×M16—22no—
438C2×M16—22no—
439C2×M16—22no—
440C2×M16—222no—
441C2×M16—222no—
442C2×M16—222no—
443C2×M16—222no—
444C2×M16—222no—
445C2×M16—222no—
446C22×C8—111no—
447C22×C8—114no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—222no—
452C22×C8—222no—
453C22×C8C22×D1111yescharacteristic
454C22×C8C22×D1111yescharacteristic
455C22×C8C22×D1111yescharacteristic
456C22×C8C22×D1111yescharacteristic
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—222no—
460C4×D4—222no—
461C4×D4—222no—
462C4×D4—222no—
463#117—222no—
464#117—222no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4C4×D1111yescharacteristic
472C2×C22⋊C4—111no—
473C2×C22⋊C4—111no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4C4×D1111yescharacteristic
483C2×C22⋊C4C4×D1111yescharacteristic
484C2×C42—111no—
485C2×C42—111no—
486C2×C42—111no—
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—222no—
489C4⋊C8—222no—
490C4⋊C8—222no—
491C4⋊C8—222no—
492C22⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500#97—222no—
501#97—222no—
502#97—222no—
503#97—222no—
504C4×C8—114no—
505C4×C8—222no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95—111no—
511#95—111no—
512C2×C11—42no—
513C2×C11—81no—
514C2×C11C4×#12111yescharacteristic
515C2×C11#293011yescharacteristic
516C2×C11#293011yescharacteristic
517C2×C11#293011yescharacteristic
518C2×C11#293211yescharacteristic
519C2×C11#296711yescharacteristic
520C2×C11#296711yescharacteristic
521D11—81no—
522C24—111no—
523C24C2×C4×D1111yescharacteristic
524C24C2×C4×D1111yescharacteristic
525C2×D4—22no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—222no—
529C2×D4—222no—
530C2×D4—441no—
531C2×D4—441no—
532C2×D4—441no—
533C2×D4—441no—
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—21no—
543C22×C4—21no—
544C22×C4—111no—
545C22×C4—111no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—111no—
549C22×C4—111no—
550C22×C4—111no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4C2×C4×D1111yescharacteristic
558C22×C4C2×C4×D1111yescharacteristic
559C22×C4C2×C4×D1111yescharacteristic
560C22×C4C2×C4×D1111yescharacteristic
561C22×C4D4×D1112yes—
562C22×C4#434112yes—
563C22×C4C23×D1111yescharacteristic
564M16—28no—
565M16—444no—
566M16—444no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—112no—
578C2×C8—112no—
579C2×C8—112no—
580C2×C8—112no—
581C2×C8—228no—
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×C8D4×D1112yes—
591C2×C8#434112yes—
592C4⋊C4—22no—
593C4⋊C4—222no—
594C4⋊C4—222no—
595C4⋊C4—222no—
596C4⋊C4—222no—
597C4⋊C4—441no—
598C4⋊C4—441no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—222no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—222no—
607C22⋊C4—441no—
608C22⋊C4—441no—
609C22⋊C4—441no—
610C22⋊C4—441no—
611C42—21no—
612C42—21no—
613C42—112no—
614C42—112no—
615C42—221no—
616C42—221no—
617C42—221no—
618C42—221no—
619C11#2149311yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23(C22⋊D11)⋊C412yes—
641C23C22×C4×D1111yescharacteristic
642D4—44no—
643D4—444no—
644D4—444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—112no—
665C2×C4—112no—
666C2×C4—221no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4(C22⋊D11)⋊C412yes—
690C2×C4C2×D4×D1111yescharacteristic
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4C2×#434111yescharacteristic
693C2×C4C2×#434111yescharacteristic
694C2×C4#41×D1111yescharacteristic
695C2×C4#41×D1111yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—114no—
701C8—222no—
702C8—441no—
703C8—441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—441no—
719C22—441no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22C2×(C22⋊D11)⋊C411yescharacteristic
726C22C4×#434111yescharacteristic
727C22C4×D4×D1111yescharacteristic
728C22#1062327611yescharacteristic
729C22#1062327611yescharacteristic
730C22#1062328111yescharacteristic
731C22#1062328111yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—222no—
737C4—222no—
738C4—441no—
739C4—441no—
740C4—441no—
741C4—441no—
742C4—441no—
743C4#1062311711yescharacteristic
744C4#1062312711yescharacteristic
745C4D11×#12111yescharacteristic
746C4#1062318011yescharacteristic
747C2—42no—
748C2—81no—
749C2—881no—
750C2#1307112611yescharacteristic
751C2#1307731511yescharacteristic
752C2#1307731611yescharacteristic
753C2#1307732211yescharacteristic
754C2#1307733011yescharacteristic
755C2#1307759811yescharacteristic
756C2#1307760211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radical#10622836C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#21493
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#10622342C2semidirect
2. C2×#10622624C2semidirect
3. C2×#10622343C2semidirect
4. C2×#10622735C2semidirect
6. #13069412C2semidirect
7. #13069338C2semidirect
8. #13069230C2semidirect
9. #13069226C2semidirect
10. #13068913C2semidirect
11. #13068598C2semidirect
12. #13068482C2semidirect
13. #13068402C2semidirect
14. #13068398C2semidirect
15. C11×#1870C2semidirect
112. C22×C11⋊C8D4semidirect
141. C8×Dic11D4semidirect
252. #1870D11semidirect
619. C11#21493semidirect

Maximal subgroups

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

subgroupindex
C2×#106223422
C2×#106226242
C2×#106223432
C2×#106227352
#130718582
#130694122
#130693382
#130692302
#130692262
#130689132
#130685982
#130684822
#130684022
#130683982
C11×#18702
#2149311