Finite Group Databasebeta

← #14759895

Subgroups — #14759895

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×#10622741C211yesmaximal, characteristic, complemented
2C2×#10622319C211yesmaximal, characteristic, complemented
3C2×#10622740C211yesmaximal, characteristic, complemented
4C2×#10622302C211yesmaximal, characteristic, complemented
5#13071860C211yesmaximal, characteristic
6#13069412C211yesmaximal, characteristic, complemented
7#13069338C211yesmaximal, characteristic, complemented
8#13069231C211yesmaximal, characteristic, complemented
9#13069227C211yesmaximal, characteristic, complemented
10#13068912C211yesmaximal, characteristic, complemented
11#13068910C211yesmaximal, characteristic, complemented
12#13068599C211yesmaximal, characteristic, complemented
13#13068484C211yesmaximal, characteristic, complemented
14#13068399C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622741—24no—
31#10622740—24no—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622573C411yescharacteristic
44#10622572C411yescharacteristic
45#10622572C411yescharacteristic
46#10622561C411yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622319—24no—
52#10622302—24no—
53#10622289C411yescharacteristic
54#10622288C411yescharacteristic
55#10622285C411yescharacteristic
56#10622270C411yescharacteristic
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2311yescharacteristic
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
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11C2×C411yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C4×C22⋊D11—22no—
83C4×C22⋊D11—22no—
84C4×C22⋊D11—22no—
85C4×C22⋊D11—22no—
86C2×(C2×D11)⋊C4C2×C411yescharacteristic
87C2×(C2×D11)⋊C4C2×C411yescharacteristic
88C2×(C2×D11)⋊C4C2×C411yescharacteristic
89C2×(C2×D11)⋊C4C2×C411yescharacteristic
90C2×(C2×D11)⋊C4C2×C411yescharacteristic
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×C4⋊Dic11C2×C411yescharacteristic
95C2×Dic11⋊C4C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×#4313—22no—
108C2×#4313—22no—
109C2×#4313—22no—
110C2×#4313—22no—
111C2×#4313—22no—
112C2×#4313—22no—
113C2×C8×D11—22no—
114C2×C8×D11—22no—
115C2×C8×D11D414yescomplemented
116C4×D44—22no—
117C4×D44—22no—
118#66925—22no—
119#66925—22no—
120C11×C22⋊C8—22no—
121C11×#97—22no—
122C4×C8×C11—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(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136#66879—22no—
137#66879—22no—
138Dic11⋊C8—22no—
139Dic11⋊C8—22no—
140Dic11⋊C8—22no—
141C8×Dic11D414yescomplemented
142C4⋊(C11⋊C8)—22no—
143#66867—22no—
144#21493—111nomaximal, Sylow
145C24×C11C22×C411yescharacteristic
146C23×D11C22×C411yescharacteristic
147C23×D11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—22no—
161C2×C22⋊D11—22no—
162C2×C22⋊D11—41no—
163C2×C22⋊D11—41no—
164C2×C22⋊D11—41no—
165C2×C22⋊D11—41no—
166C22×Dic11C22×C411yescharacteristic
167C22×Dic11C22×C411yescharacteristic
168C22×Dic11C22×C411yescharacteristic
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C411yescharacteristic
172C2×D44—22no—
173C2×D44—41no—
174C2×D44—41no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—21no—
183C2×C4×D11—21no—
184C2×C4×D11—21no—
185C2×C4×D11C2×D412yes—
186C2×C4×D11#4112yes—
187C11×M16—44no—
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×C11C2×D412yes—
197C2×C8×C11C2×D412yes—
198C2×C8×C11#4112yes—
199C2×C8×C11#4112yes—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208(C2×D11)⋊C4—22no—
209(C2×D11)⋊C4—22no—
210(C2×D11)⋊C4—22no—
211(C2×D11)⋊C4—22no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—22no—
214(C2×D11)⋊C4—41no—
215(C2×D11)⋊C4—41no—
216C4⋊Dic11—22no—
217Dic11⋊C4—22no—
218Dic11⋊C4—22no—
219Dic11⋊C4—22no—
220Dic11⋊C4—22no—
221Dic11⋊C4—41no—
222Dic11⋊C4—41no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11C2×D412yes—
226C4×Dic11#4112yes—
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⋊C8C2×D412yes—
238C2×C11⋊C8C2×D412yes—
239#4313—28no—
240#4313—44no—
241C8×D11—28no—
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#1870—111no—
253#1798—111no—
254#1770—111no—
255#1753—111no—
256#1753D1111yescharacteristic, complemented
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11C23×C411yescharacteristic
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11C4×D412yes—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
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—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C22⋊D11—44no—
305C22⋊D11—44no—
306C2×Dic11—21no—
307C2×Dic11—21no—
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×Dic11C4×D412yes—
322C2×Dic11C4×D412yes—
323C2×Dic11C4×D412yes—
324D44—44no—
325C4×D11—22no—
326C4×D11—22no—
327C4×D11—22no—
328C4×D11—22no—
329C4×D11—41no—
330C4×D11—41no—
331C4×D11—41no—
332C4×D11—41no—
333C8×C11—22no—
334C8×C11—41no—
335C8×C11—41no—
336C8×C11#12114yes—
337C11⋊C8—22no—
338C11⋊C8—22no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C22×M16—111no—
342C22×M16—111no—
343C22×M16C2×D1111yescharacteristic
344C23×C8—111no—
345C2×C4×D4—111no—
346C2×C4×D4—111no—
347C2×C4×D4—111no—
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⋊C8—111no—
362C2×C22⋊C8—111no—
363C2×C22⋊C8C2×D1111yescharacteristic
364#405—224no—
365C2×#97—111no—
366C2×#97—111no—
367C2×#97—111no—
368C2×#97C2×D1111yescharacteristic
369C2×C4×C8—111no—
370C2×C4×C8C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
382#336—111no—
383#336—111no—
384#336—111no—
385#336—111no—
386#336C2×D1111yescharacteristic
387#336C2×D1111yescharacteristic
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11C2×C4×D411yescharacteristic
396C22×C11C2×C4×D411yescharacteristic
397C22×C11C4×#4111yescharacteristic
398C22×C11#56811yescharacteristic
399C22×C11#56811yescharacteristic
400C22×C11#56811yescharacteristic
401C22×C11#56811yescharacteristic
402C2×D11—22no—
403C2×D11—22no—
404C2×D11—22no—
405C2×D11—41no—
406C2×D11—41no—
407C2×D11—41no—
408C2×D11—41no—
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—41no—
412C2×D11—41no—
413C2×D11—41no—
414C2×D11—41no—
415C2×D11—41no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11C2×#12111yescharacteristic
422C4×C11#52511yescharacteristic
423C4×C11#52911yescharacteristic
424C4×C11#53211yescharacteristic
425Dic11—22no—
426Dic11—22no—
427Dic11—22no—
428Dic11—41no—
429Dic11—41no—
430Dic11—41no—
431C22×D4—111no—
432C22×D4—111no—
433C22×D4—111no—
434C23×C4—111no—
435C23×C4—111no—
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—111no—
448C22×C8—114no—
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—222no—
458C4×D4—222no—
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⋊C4—111no—
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×C42C22×D1111yescharacteristic
487C2×C42C22×D1111yescharacteristic
488C4⋊C8—222no—
489C4⋊C8—222no—
490C4⋊C8—222no—
491C4⋊C8—222no—
492C22⋊C8—22no—
493C22⋊C8—222no—
494C22⋊C8—222no—
495C22⋊C8—222no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500#97—22no—
501#97—222no—
502#97—222no—
503#97—222no—
504C4×C8—22no—
505C4×C8—114no—
506#95—111no—
507#95—111no—
508#95—111no—
509#95—111no—
510#95C4×D1111yescharacteristic
511#95C4×D1111yescharacteristic
512C2×C11—81no—
513C2×C11C4×#12111yescharacteristic
514C2×C11#293011yescharacteristic
515C2×C11#293011yescharacteristic
516C2×C11#293011yescharacteristic
517C2×C11#293211yescharacteristic
518C2×C11#296711yescharacteristic
519C2×C11#296711yescharacteristic
520D11—42no—
521D11—81no—
522C24—111no—
523C24—111no—
524C24C2×C4×D1111yescharacteristic
525C2×D4—222no—
526C2×D4—222no—
527C2×D4—222no—
528C2×D4—441no—
529C2×D4—441no—
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—111no—
541C22×C4—111no—
542C22×C4—111no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—111no—
546C22×C4—111no—
547C22×C4—111no—
548C22×C4—221no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4C2×C4×D1111yescharacteristic
559C22×C4C2×C4×D1111yescharacteristic
560C22×C4C2×C4×D1111yescharacteristic
561C22×C4C2×C4×D1111yescharacteristic
562C22×C4C2×C4×D1111yescharacteristic
563C22×C4C23×D1111yescharacteristic
564M16—44no—
565M16—228no—
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—112no—
576C2×C8—112no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—228no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8#433912yes—
589C2×C8#433912yes—
590C2×C8D4×D1112yes—
591C2×C8D4×D1112yes—
592C4⋊C4—222no—
593C4⋊C4—222no—
594C4⋊C4—222no—
595C4⋊C4—222no—
596C4⋊C4—222no—
597C4⋊C4—441no—
598C4⋊C4—441no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—222no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—222no—
606C22⋊C4—222no—
607C22⋊C4—222no—
608C22⋊C4—222no—
609C22⋊C4—441no—
610C22⋊C4—441no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—112no—
616C42—112no—
617C42—221no—
618C42—221no—
619C11#2149311yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—112no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23C22×C4×D1111yescharacteristic
642D4—444no—
643D4—444no—
644D4—444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
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—112no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
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—221no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4C2×#433911yescharacteristic
691C2×C4C2×#433911yescharacteristic
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4C2×D4×D1111yescharacteristic
694C2×C4#41×D1111yescharacteristic
695C2×C4#41×D1111yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—222no—
700C8—222no—
701C8—441no—
702C8—441no—
703C8#6693714yes—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—222no—
712C22—222no—
713C22—222no—
714C22—441no—
715C22—441no—
716C22—441no—
717C22—441no—
718C22—441no—
719C22—441no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—441no—
724C22—441no—
725C22C4×#433911yescharacteristic
726C22C4×D4×D1111yescharacteristic
727C22C4×D4×D1111yescharacteristic
728C22#1062327611yescharacteristic
729C22#1062327611yescharacteristic
730C22#1062328111yescharacteristic
731C22#1062328111yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—222no—
738C4—222no—
739C4—222no—
740C4—441no—
741C4—441no—
742C4—441no—
743C4C2×#6693711yescharacteristic
744C4#1062305911yescharacteristic
745C4#1062307811yescharacteristic
746C4#1062307911yescharacteristic
747C2—81no—
748C2—442no—
749C2—881no—
750C2C4×#6693711yescharacteristic
751C2#1307731411yescharacteristic
752C2#1307731611yescharacteristic
753C2#1307731611yescharacteristic
754C2#1307733011yescharacteristic
755C2#1307759711yescharacteristic
756C2#1307760111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1753C2
prime radical#10622573C4
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#21493
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#10622741C2semidirect
2. C2×#10622319C2semidirect
3. C2×#10622740C2semidirect
4. C2×#10622302C2semidirect
6. #13069412C2semidirect
7. #13069338C2semidirect
8. #13069231C2semidirect
9. #13069227C2semidirect
10. #13068912C2semidirect
11. #13068910C2semidirect
12. #13068599C2semidirect
13. #13068484C2semidirect
14. #13068399C2semidirect
15. C11×#1753C2semidirect
115. C2×C8×D11D4semidirect
141. C8×Dic11D4semidirect
256. #1753D11semidirect
619. C11#21493semidirect

Maximal subgroups

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

subgroupindex
C2×#106227412
C2×#106223192
C2×#106227402
C2×#106223022
#130718602
#130694122
#130693382
#130692312
#130692272
#130689122
#130689102
#130685992
#130684842
#130683992
C11×#17532
#2149311