Finite Group Databasebeta

← #14769873

Subgroups — #14769873

Order 2816.

1412 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622342C211yesmaximal, characteristic, complemented
4#13069550C211yesmaximal, characteristic, complemented
5#13069550C211yesmaximal, characteristic, complemented
6#13068914C211yesmaximal, characteristic, complemented
7#13068910C211yesmaximal, characteristic, complemented
8#13068910C211yesmaximal, characteristic, complemented
9#13068683C211yesmaximal, characteristic, complemented
10#13068682C211yesmaximal, characteristic, complemented
11#13068594C211yesmaximal, characteristic, complemented
12C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
13#13068309C211yesmaximal, characteristic, complemented
14#13068308C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×#4341C411yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×D4×Dic11C411yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26C22×#4313C2211yescharacteristic
27C4×#4341—24no—
28C4×#4341—24no—
29C2×#66945C411yescharacteristic
30C2×#66940C411yescharacteristic
31C2×(C22⋊D11)⋊C4C411yescharacteristic
32C2×(C22⋊D11)⋊C4C411yescharacteristic
33C2×#66930C411yescharacteristic
34C2×#66930C411yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622741—24no—
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×Dic11⋊C8C2211yescharacteristic
47C2×Dic11⋊C8C2211yescharacteristic
48C2×C8×Dic11C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50#10622342—24no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C23×Dic11C2×C411yescharacteristic
71C23×Dic11C2×C411yescharacteristic
72C2×#4341—24no—
73C2×#4341—24no—
74C2×#4341—24no—
75C22×C4×D11C2×C411yescharacteristic
76C22×C4×D11C2×C411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×Dic22C2×C411yescharacteristic
79C2×C11×M16—22no—
80C2×C11×M16—22no—
81C2×C11×M16—41no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C22×C8×C11C2311yescharacteristic
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C2×C11×C4⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11C2×C411yescharacteristic
93C2×C22⋊Dic11C2×C411yescharacteristic
94D4×Dic11—24no—
95C4×C22⋊D11—22no—
96C4×C22⋊D11—22no—
97C4×C22⋊D11D414yes—
98C4×C22⋊D11D414yes—
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11C2×C411yescharacteristic
111C2×C4×Dic11C2×C411yescharacteristic
112C2×C4×Dic11C2×C411yescharacteristic
113C2×C4×Dic11C2×C411yescharacteristic
114C2×C4×Dic11C2×C411yescharacteristic
115C2×C4×Dic11C2×C411yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C2×#4318—22no—
120C2×#4318—22no—
121C2×#4318—41no—
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C2×#4313—22no—
127C2×#4313—22no—
128C2×#4313—22no—
129C2×#4313—22no—
130C2×#4313—41no—
131C2×#4313—41no—
132#66945—24no—
133#66940—24no—
134(C22⋊D11)⋊C4—24no—
135(C22⋊D11)⋊C4—24no—
136#66930—24no—
137#66930—24no—
138C42×D11—22no—
139C42×D11—22no—
140C4×Dic22—22no—
141C4×Dic22—22no—
142C11×C22⋊C8—22no—
143C11×C22⋊C8—22no—
144C11×C22⋊C8—41no—
145C22⋊(C11⋊C8)—22no—
146C22⋊(C11⋊C8)—22no—
147C22⋊(C11⋊C8)—41no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150Dic11⋊C8—22no—
151Dic11⋊C8—22no—
152C8×Dic11—22no—
153C8×Dic11—22no—
154#22473—111nomaximal, Sylow
155C24×C11C22×C411yescharacteristic
156C24×C11C22×C411yescharacteristic
157C23×D11C22×C411yescharacteristic
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
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—21no—
170C22×C4×C11—21no—
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C22×C411yescharacteristic
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—22no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—22no—
181C2×C22⋊D11—22no—
182C2×C22⋊D11—22no—
183C2×C22⋊D11C22⋊C414yes—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—41no—
194C22×Dic11—41no—
195C22×Dic11M1614yescomplemented
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C411yescharacteristic
198C22×Dic11C22×C411yescharacteristic
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203#4341—232no—
204C2×C4×D11—22no—
205C2×C4×D11—22no—
206C2×C4×D11—22no—
207C2×C4×D11—22no—
208C2×C4×D11—22no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—21no—
213C2×C4×D11—41no—
214C2×C4×D11C2×D412yes—
215C2×C4×D11C2×D412yes—
216C2×Dic22—22no—
217C2×Dic22—22no—
218C2×Dic22M1614yescomplemented
219C11×M16—44no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11#4112yescomplemented
232C11×C4⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—22no—
235C42×C11—21no—
236C42×C11—21no—
237C22⋊Dic11—22no—
238C22⋊Dic11C22⋊C414yes—
239(C2×D11)⋊C4—22no—
240(C2×D11)⋊C4C22⋊C414yes—
241C4⋊Dic11—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245Dic11⋊C4C22⋊C414yes—
246C4×Dic11—22no—
247C4×Dic11—22no—
248C4×Dic11—22no—
249C4×Dic11—22no—
250C4×Dic11—22no—
251C4×Dic11—22no—
252C4×Dic11—21no—
253C4×Dic11—21no—
254C4×Dic11—21no—
255C4×Dic11—21no—
256C4×Dic11C2×D412yes—
257C4×Dic11C2×D412yes—
258#4318—44no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8#4112yescomplemented
271#4313—44no—
272#4313—44no—
273C2×C4×#41—111no—
274C2×#436—111no—
275C2×#436—111no—
276#1984—111no—
277#1984—111no—
278#1870—111no—
279#1870—111no—
280#1870—111no—
281#1870D1111yescharacteristic, complemented
282#1817—111no—
283#1817—111no—
284#1797—111no—
285C4×C22⋊C8—111no—
286#1728—111no—
287#1728—111no—
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×C11C2×C22⋊C412yes—
301C23×C11C2×M1612yes—
302C23×C11C23×C411yescharacteristic
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11C2×C22⋊C412yes—
310D4×C11—28no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
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—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11C2×C22⋊C412yes—
330C2×C4×C11C2×M1612yes—
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C112−1+411yescharacteristic
337C22⋊D11—28no—
338C22⋊D11—28no—
339C2×Dic11—28no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—28no—
351C2×Dic11—21no—
352C2×Dic11—21no—
353C2×Dic11—21no—
354C2×Dic11—44no—
355C2×Dic11—44no—
356C2×Dic11C2×C22⋊C412yes—
357C2×Dic11C2×C22⋊C412yes—
358C2×Dic11C2×C22⋊C412yes—
359C2×Dic11C2×M1612yes—
360C2×Dic11C2×M1612yes—
361C2×Dic11C2×M1612yes—
362C2×Dic11C2×M1612yes—
363C2×Dic11#13112yes—
364C4×D11—28no—
365C4×D11—22no—
366C4×D11—22no—
367C4×D11—22no—
368C4×D11—22no—
369C4×D11—44no—
370Dic22—28no—
371C8×C11—22no—
372C8×C11—41no—
373C8×C11—41no—
374C8×C11—41no—
375C11⋊C8—22no—
376C11⋊C8—41no—
377C11⋊C8—41no—
378C11⋊C8—41no—
379C22×#41—111no—
380C22×M16—111no—
381C22×M16—111no—
382C22×M16—111no—
383C22×M16C2×D1111yescharacteristic
384C4×#41—224no—
385C4×#41—224no—
386C2×C4×Q8—111no—
387C2×C4×Q8—111no—
388C2×C4×D4—111no—
389C2×C4×D4—111no—
390C2×C4×D4—111no—
391C2×C4×D4—111no—
392C2×C4×D4—111no—
393C2×C4×D4C2×D1111yescharacteristic
394C2×#117—111no—
395C2×#117—111no—
396C2×#117—111no—
397C22×C42—111no—
398C22×C42—111no—
399C22×C42—111no—
400#436—224no—
401#436—224no—
402C2×C4⋊C8—111no—
403C2×C4⋊C8—111no—
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×C22⋊C8—111no—
407C2×C22⋊C8—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8C2×D1111yescharacteristic
410C2×C22⋊C8C2×D1111yescharacteristic
411C2×C22⋊C8C2×D1111yescharacteristic
412C2×C4×C8—111no—
413C2×C4×C8—111no—
414#336—111no—
415#336—111no—
416#336—111no—
417#336—111no—
418#336—111no—
419#336—111no—
420#336—111no—
421#336—111no—
422#336—111no—
423#336—111no—
424#336C2×D1111yescharacteristic
425#336C2×D1111yescharacteristic
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11C22×C22⋊C411yescharacteristic
441C22×C11C4×#4111yescharacteristic
442C22×C11#52011yescharacteristic
443C22×C11C22×M1611yescharacteristic
444C22×C11C22×M1611yescharacteristic
445C22×C11C2×#13111yescharacteristic
446C22×C11#56811yescharacteristic
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—41no—
451C2×D11—41no—
452C2×D11—41no—
453C2×D11—41no—
454C4×C11—22no—
455C4×C11—22no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11#54611yescharacteristic
459C4×C11#54611yescharacteristic
460C4×C11#54711yescharacteristic
461C4×C11#54711yescharacteristic
462Dic11—22no—
463Dic11—22no—
464Dic11—22no—
465Dic11—22no—
466Dic11—22no—
467Dic11—41no—
468Dic11#40714yes—
469C2×#41—224no—
470C2×#41—224no—
471C2×#41—224no—
472C22×Q8—111no—
473C22×D4—111no—
474C22×D4—111no—
475C22×D4C4×D1111yescharacteristic
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—111no—
482C23×C4—111no—
483C23×C4C22×D1111yescharacteristic
484C23×C4C22×D1111yescharacteristic
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C2×M16—222no—
489C2×M16—222no—
490C2×M16—222no—
491C2×M16—222no—
492C2×M16—222no—
493C2×M16—222no—
494C2×M16—441no—
495C2×M16—441no—
496C2×M16—441no—
497C22×C8—111no—
498C22×C8—111no—
499C22×C8—111no—
500C22×C8—111no—
501C22×C8C22×D1111yescharacteristic
502C22×C8C22×D1111yescharacteristic
503C22×C8C22×D1111yescharacteristic
504C22×C8C22×D1111yescharacteristic
505C4×Q8—222no—
506C4×Q8—222no—
507C4×Q8—224no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—114no—
511C4×D4—114no—
512C4×D4—224no—
513C4×D4—224no—
514C4×D4—224no—
515C4×D4—222no—
516C4×D4—222no—
517#117—224no—
518#117—224no—
519#117—224no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4C4×D1111yescharacteristic
526C2×C22⋊C4—111no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4C4×D1111yescharacteristic
531C2×C22⋊C4C4×D1111yescharacteristic
532C2×C42—111no—
533C2×C42—111no—
534C2×C42—111no—
535C2×C42—111no—
536C2×C42—111no—
537C2×C42—111no—
538C2×C42—111no—
539C2×C42—111no—
540C2×C42—111no—
541C2×C42—222no—
542C2×C42—222no—
543C2×C42—222no—
544C2×C42—222no—
545C2×C42—222no—
546C2×C42—222no—
547C2×C42C22×D1111yescharacteristic
548C4⋊C8—222no—
549C4⋊C8—222no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—41no—
553C22⋊C8—222no—
554C22⋊C8—222no—
555C22⋊C8—222no—
556C22⋊C8—222no—
557C22⋊C8—441no—
558C4×C8—222no—
559C4×C8—222no—
560C2×C11—42no—
561C2×C11—42no—
562C2×C11#233911yescharacteristic
563C2×C11C2×#40711yescharacteristic
564C2×C11#288011yescharacteristic
565C2×C11#296511yescharacteristic
566C2×C11#297111yescharacteristic
567C2×C11#298911yescharacteristic
568C2×C11#299111yescharacteristic
569D11—42no—
570C24—111no—
571C24C2×C4×D1111yescharacteristic
572C24C2×C4×D1111yescharacteristic
573#41—2232no—
574C2×Q8—114no—
575C2×Q8—222no—
576C2×Q8—222no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—114no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—111no—
597C22×C4—114no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—111no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—222no—
624C22×C4—441no—
625C22×C4—441no—
626C22×C4—441no—
627C22×C4C2×C4×D1111yescharacteristic
628C22×C4C2×C4×D1111yescharacteristic
629C22×C4C2×C4×D1111yescharacteristic
630C22×C4C2×C4×D1111yescharacteristic
631C22×C4D4×D1112yes—
632C22×C4D4×D1112yes—
633C22×C4C23×D1111yescharacteristic
634M16—44no—
635M16—444no—
636M16—444no—
637M16—444no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—112no—
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#434112yescomplemented
662C4⋊C4—22no—
663C4⋊C4—114no—
664C4⋊C4—222no—
665C4⋊C4—222no—
666C4⋊C4—222no—
667C4⋊C4—222no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—114no—
671C22⋊C4—114no—
672C22⋊C4—222no—
673C22⋊C4—222no—
674C42—21no—
675C42—21no—
676C42—112no—
677C42—112no—
678C42—222no—
679C42—222no—
680C42—222no—
681C42—222no—
682C42—222no—
683C42—222no—
684C42—221no—
685C42—221no—
686C42—221no—
687C42—221no—
688C11#2247311yescharacteristic, complemented, Sylow
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—112no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23—221no—
707C23—221no—
708C23C22⋊C4×D1112yes—
709C23M16×D1112yes—
710C23C22×C4×D1111yescharacteristic
711Q8—228no—
712D4—28no—
713D4—228no—
714D4—228no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—112no—
737C2×C4—112no—
738C2×C4—112no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—228no—
742C2×C4—228no—
743C2×C4—228no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—221no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—221no—
759C2×C4—221no—
760C2×C4—221no—
761C2×C4—444no—
762C2×C4—444no—
763C2×C4—444no—
764C2×C4C22⋊C4×D1112yes—
765C2×C4M16×D1112yes—
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4C2×D4×D1111yescharacteristic
768C2×C4C2×#434111yescharacteristic
769C2×C4#6703711yescharacteristic
770C2×C4#41×D1111yescharacteristic
771C2×C4#6704311yescharacteristic
772C8—22no—
773C8—41no—
774C8—41no—
775C8—41no—
776C8—222no—
777C8—441no—
778C8—441no—
779C8—441no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—222no—
795C22—222no—
796C22—222no—
797C22—441no—
798C22—441no—
799C22—441no—
800C22—441no—
801C22C2×C22⋊C4×D1111yescharacteristic
802C22C4×#434111yescharacteristic
803C22#1062307711yescharacteristic
804C22C2×M16×D1111yescharacteristic
805C22C2×M16×D1111yescharacteristic
806C22D11×#13111yescharacteristic
807C22#1062328111yescharacteristic
808C4—22no—
809C4—22no—
810C4—41no—
811C4—41no—
812C4—114no—
813C4—222no—
814C4—222no—
815C4—222no—
816C4—222no—
817C4—222no—
818C4—441no—
819C4#1062312211yescharacteristic
820C4#1062314111yescharacteristic
821C4#1062314211yescharacteristic
822C4#1062318611yescharacteristic
823C2—42no—
824C2—42no—
825C2—442no—
826C2#1307144211yescharacteristic
827C2D11×#40711yescharacteristic
828C2#1307706411yescharacteristic
829C2#1307757611yescharacteristic
830C2#1307763211yescharacteristic
831C2#1307772811yescharacteristic
832C2#1307774411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#22473
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×#10622342C2semidirect
4. #13069550C2semidirect
5. #13069550C2semidirect
6. #13068914C2semidirect
7. #13068910C2semidirect
8. #13068910C2semidirect
9. #13068683C2semidirect
10. #13068682C2semidirect
11. #13068594C2semidirect
12. C22⋊C8×Dic11C2semidirect
13. #13068309C2semidirect
14. #13068308C2semidirect
15. C11×#1870C2semidirect
195. C22×Dic11M16semidirect
218. C2×Dic22M16semidirect
231. C2×C8×C11#41semidirect
270. C2×C11⋊C8#41semidirect
281. #1870D11semidirect
661. C2×C8#4341semidirect
688. C11#22473semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C2×#106227412
C2×#106223422
#130695502
#130689142
#130689102
#130686832
#130686822
#130685942
C22⋊C8×Dic112
#130683092
#130683082
C11×#18702
#2247311