Finite Group Databasebeta

← #15617226

Subgroups — #15617226

Order 2816.

4874 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623453C211yesmaximal, characteristic
2C2×#10623281C211yesmaximal, characteristic, complemented
3C2×D11×#131C211yesmaximal, characteristic, complemented
4#13077066C213yesmaximal, complemented
5#13077065C211yesmaximal, characteristic, complemented
6#13077064C213yesmaximal, complemented
7#13077064C213yesmaximal, complemented
8#13077063C211yesmaximal, characteristic, complemented
9#13077063C211yesmaximal, characteristic, complemented
10#13077062C213yesmaximal, complemented
11#13077059C213yesmaximal, complemented
12#13077058C213yesmaximal, complemented
13C2×#10622340C213yesmaximal, complemented
14D11×#408C213yesmaximal, complemented
15C11×#2880C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17#10623453—28no—
18#10623453—28no—
19C2×#67043C411yescharacteristic
20C2×#67043C413yes—
21C2×#67042C411yescharacteristic
22C2×#67042C413yes—
23C2×#41×D11C2213yes—
24C2×#41×D11C2211yescharacteristic
25C2×#41×D11C2213yes—
26C2×#41×D11C2211yescharacteristic
27C2×#67040C411yescharacteristic
28C2×#67040C411yescharacteristic
29C2×#67037C413yes—
30C2×#67037C413yes—
31C22×#4339C2213yes—
32C22×#4339C2213yes—
33C2×C11×#131C2211yescharacteristic, complemented
34C2×C11×#131C2211yescharacteristic, complemented
35C2×#67001C2211yescharacteristic, complemented
36C2×#67001C2211yescharacteristic, complemented
37#10623281—28no—
38D11×#131—28no—
39C2×#66960C2213yescomplemented
40C2×#66960C2213yescomplemented
41C2×M16×D11C2213yescomplemented
42C2×M16×D11C2213yescomplemented
43C2×#66954C2213yescomplemented
44C2×#66954C2213yescomplemented
45C22×#4313C2213yescomplemented
46C22×C8×D11C2213yescomplemented
47C11×#408C2213yescomplemented
48C11×#408C2213yescomplemented
49C11×#407C2213yescomplemented
50C2×C11×C22⋊C8C2213yescomplemented
51#10622847C2213yescomplemented
52#10622847C2213yescomplemented
53#10622820C2213yescomplemented
54C2×C22⋊(C11⋊C8)C2213yescomplemented
55#10622742C2213yescomplemented
56#10622742C2213yescomplemented
57#10622739C2213yescomplemented
58#10622739C2213yescomplemented
59#10622723C2213yescomplemented
60#10622723C2213yescomplemented
61C2×(C2×D11)⋊C8C2213yescomplemented
62C2×(C2×D11)⋊C8C2213yescomplemented
63#10622340C2213yescomplemented
64#10622340C2216yescomplemented
65#10622340C2211yescharacteristic, complemented
66#10622340C2213yescomplemented
67#10622340C2213yescomplemented
68#10622340C2213yescomplemented
69#10622340C2213yescomplemented
70#10622340C2213yescomplemented
71#10622340C2213yescomplemented
72#10622340C2216yescomplemented
73#10622340C2216yescomplemented
74#10622339C2216yescomplemented
75#10622339C2216yescomplemented
76D11×C22⋊C8C2216yescomplemented
77D11×C22⋊C8C2216yescomplemented
78C2×C11×#41—24no—
79C2×C11×#41—24no—
80C2×C11×#41C2×C411yescharacteristic
81C2×C11×#41C2×C413yes—
82C2×C11×#41C2313yes—
83C2×C11×#41C2311yescharacteristic
84C22×Q8×C11C2×C411yescharacteristic
85C22×D4×C11C2×C413yes—
86C23×C4×C11C2313yes—
87C22×C22⋊D11C2×C416yes—
88C22×C22⋊D11C2×C413yes—
89C22×C22⋊D11C2×C413yes—
90#67043—28no—
91#67043—224no—
92#67042—28no—
93#67042—224no—
94#41×D11—24no—
95#41×D11—24no—
96#41×D11—212no—
97#41×D11—212no—
98#41×D11—212no—
99#41×D11—212no—
100#41×D11D418yes—
101#41×D11D418yes—
102#67040—28no—
103#67040—28no—
104C2×#4343C2×C411yescharacteristic
105C2×#4343C2×C413yes—
106C2×#4343C2×C413yes—
107C2×#4343C2×C411yescharacteristic
108C2×Q8×D11C2×C411yescharacteristic
109C2×Q8×D11C2×C413yes—
110C2×Q8×D11C2×C413yes—
111C2×Q8×D11C2×C411yescharacteristic
112#67037—224no—
113#67037—224no—
114C2×#4341C2×C416yes—
115C2×#4341C2×C416yes—
116C2×#4341C2×C413yes—
117C2×#4341C2×C413yes—
118C2×#4341C2×C413yes—
119C2×#4341C2×C413yes—
120C2×D4×D11C2×C416yes—
121C2×D4×D11C2×C416yes—
122C2×D4×D11C2×C413yes—
123C2×D4×D11C2×C413yes—
124C2×D4×D11C2×C413yes—
125C2×D4×D11C2×C413yes—
126C2×#4339—212no—
127C2×#4339—212no—
128C2×#4339—212no—
129C2×#4339—212no—
130C2×#4339C2×C413yes—
131C2×#4339C2×C413yes—
132C2×#4339C2×C413yes—
133C2×#4339C2×C413yes—
134C2×#4339C2×C416yes—
135C2×#4339C2×C413yes—
136C2×#4339C2×C413yes—
137C2×#4339C2313yes—
138C2×#4339C2311yescharacteristic
139C2×#4339C2313yes—
140C2×#4339C2313yes—
141C2×#4339C2313yes—
142C2×#4339C2313yes—
143C22×D44C2×C413yes—
144C22×D44C2×C413yes—
145C22×C4×D11C2313yes—
146C22×C4×D11C2316yes—
147C22×C4×D11C2313yes—
148C22×Dic22C2×C413yes—
149C22×Dic22C2×C413yes—
150C11×#131—24no—
151C11×#131—24no—
152C2×C11×M16C2313yes—
153C2×C11×M16C2313yes—
154C22×C8×C11C2313yes—
155C22×C8×C11C2313yes—
156#67001—24no—
157#67001—24no—
158C2×#4318C2313yes—
159C2×#4318C2313yes—
160C22×C11⋊C8C2313yes—
161C22×C11⋊C8C2313yes—
162#66960—212no—
163#66960—212no—
164M16×D11—212no—
165M16×D11—212no—
166#66954—212no—
167#66954—212no—
168C2×#4313—212no—
169C2×#4313C2311yescharacteristic
170C2×#4313C2313yes—
171C2×#4313C2313yes—
172C2×#4313C2313yes—
173C2×#4313C2316yes—
174C2×C8×D11—212no—
175C2×C8×D11C2311yescharacteristic
176C2×C8×D11C2313yes—
177C2×C8×D11C2313yes—
178C2×C8×D11C2313yes—
179C2×C8×D11C2316yes—
180C11×C22⋊C8C2313yes—
181C11×C22⋊C8C2316yes—
182C11×C22⋊C8C2313yes—
183C11×C22⋊C8C2311yescharacteristic
184C11×C22⋊C8C2313yes—
185C22⋊(C11⋊C8)C2311yescharacteristic
186C22⋊(C11⋊C8)C2313yes—
187C22⋊(C11⋊C8)C2313yes—
188C22⋊(C11⋊C8)C2313yes—
189C22⋊(C11⋊C8)C2316yes—
190(C2×D11)⋊C8C2311yescharacteristic
191(C2×D11)⋊C8C2311yescharacteristic
192(C2×D11)⋊C8C2313yes—
193(C2×D11)⋊C8C2313yes—
194(C2×D11)⋊C8C2313yes—
195(C2×D11)⋊C8C2313yes—
196(C2×D11)⋊C8C2313yes—
197(C2×D11)⋊C8C2313yes—
198(C2×D11)⋊C8C2316yes—
199(C2×D11)⋊C8C2316yes—
200#60065—111nomaximal, Sylow
201C24×C11C22×C413yes—
202C23×D11C22×C413yes—
203C23×D11C22×C416yes—
204C23×D11C22×C413yes—
205C11×#41—24no—
206C11×#41—212no—
207C11×#41—26no—
208C11×#41—26no—
209C11×#41C2×D414yes—
210C11×#41C2×D414yes—
211C2×Q8×C11—24no—
212C2×Q8×C11C22×C413yes—
213C2×Q8×C11C22×C411yescharacteristic
214C2×D4×C11—212no—
215C2×D4×C11C22×C416yes—
216C2×D4×C11C22×C413yes—
217C2×D4×C11C22×C413yes—
218C22×C4×C11—26no—
219C22×C4×C11—26no—
220C22×C4×C11C22×C413yes—
221C22×C4×C11C22×C413yes—
222C22×C4×C11C22×C413yes—
223C22×C4×C11C2413yes—
224C22×C4×C11C2411yescharacteristic
225C22×C4×C11C2413yes—
226C2×C22⋊D11—224no—
227C2×C22⋊D11—212no—
228C2×C22⋊D11—212no—
229C2×C22⋊D11C22×C411yescharacteristic
230C2×C22⋊D11C22×C413yes—
231C2×C22⋊D11C22×C413yes—
232C2×C22⋊D11C22×C411yescharacteristic
233C2×C22⋊D11C22×C413yes—
234C2×C22⋊D11C22×C413yes—
235C2×C22⋊D11C22×C416yes—
236C2×C22⋊D11C22×C413yes—
237C2×C22⋊D11C22×C413yes—
238C2×C22⋊D11C22×C416yes—
239C22×Dic11C22×C416yes—
240C22×Dic11C22×C413yes—
241C22×Dic11C22×C413yes—
242#4343—212no—
243#4343—212no—
244#4343—24no—
245#4343C22⋊C418yes—
246Q8×D11—212no—
247Q8×D11—212no—
248Q8×D11—24no—
249Q8×D11C22⋊C418yes—
250#4341—224no—
251#4341—224no—
252#4341—212no—
253#4341—212no—
254#4341—212no—
255#4341C22⋊C4124yes—
256D4×D11—224no—
257D4×D11—212no—
258D4×D11—212no—
259D4×D11—224no—
260D4×D11—212no—
261D4×D11C22⋊C4124yes—
262#4339—224no—
263#4339—212no—
264#4339—212no—
265#4339—212no—
266#4339—212no—
267#4339—212no—
268#4339—22no—
269#4339—26no—
270#4339—26no—
271#4339—22no—
272#4339—26no—
273#4339—26no—
274#4339—26no—
275#4339—26no—
276#4339—212no—
277#4339—26no—
278#4339—26no—
279#4339C2×D4112yes—
280#4339C2×D4112yes—
281C2×D44—212no—
282C2×D44—212no—
283C2×D44C22×C413yes—
284C2×D44C22×C411yescharacteristic
285C2×D44C22×C413yes—
286C2×D44C22×C413yes—
287C2×D44C22×C413yes—
288C2×D44C22×C413yes—
289C2×C4×D11—212no—
290C2×C4×D11—212no—
291C2×C4×D11—26no—
292C2×C4×D11—26no—
293C2×C4×D11C22×C416yes—
294C2×C4×D11C22×C416yes—
295C2×C4×D11C22×C413yes—
296C2×C4×D11C22×C413yes—
297C2×C4×D11C22×C413yes—
298C2×C4×D11C22×C413yes—
299C2×C4×D11C2×D4112yes—
300C2×C4×D11C2×D4112yes—
301C2×C4×D11C2411yescharacteristic
302C2×C4×D11C2413yes—
303C2×C4×D11C2411yescharacteristic
304C2×C4×D11C2413yes—
305C2×Dic22—212no—
306C2×Dic22—212no—
307C2×Dic22C22×C411yescharacteristic
308C2×Dic22C22×C413yes—
309C2×Dic22C22×C413yes—
310C2×Dic22C22×C413yes—
311C2×Dic22C22×C413yes—
312C2×Dic22C22×C413yes—
313C11×M16—26no—
314C11×M16—26no—
315C2×C8×C11—26no—
316C2×C8×C11—26no—
317C2×C8×C11C2411yescharacteristic
318C2×C8×C11C2413yes—
319C2×C8×C11C2413yes—
320C2×C8×C11C2411yescharacteristic
321#4318—26no—
322#4318—26no—
323C2×C11⋊C8—26no—
324C2×C11⋊C8—26no—
325C2×C11⋊C8C2411yescharacteristic
326C2×C11⋊C8C2413yes—
327C2×C11⋊C8C2413yes—
328C2×C11⋊C8C2411yescharacteristic
329#4313—22no—
330#4313—26no—
331#4313—26no—
332#4313—26no—
333#4313—212no—
334C8×D11—22no—
335C8×D11—26no—
336C8×D11—26no—
337C8×D11—26no—
338C8×D11—212no—
339C2×#585—111no—
340C2×#568—111no—
341C22×#131—111no—
342#2880—113no—
343#2880—113no—
344#2880—113no—
345#2880—113no—
346#2880—111no—
347#2880—111no—
348#2880—111no—
349#2880D1111yescharacteristic, complemented
350#2879—113no—
351#2879—113no—
352C2×#408—113no—
353C2×#408—113no—
354C23×C11—26no—
355C23×C11—43no—
356C23×C11—43no—
357C23×C11C23×C413yes—
358C23×C11C23×C411yescharacteristic
359C23×C11C23×C413yes—
360C22×D11—26no—
361C22×D11—212no—
362C22×D11—43no—
363C22×D11—43no—
364C22×D11—46no—
365C22×D11—46no—
366C22×D11—43no—
367C22×D11—43no—
368C22×D11C2×C22⋊C4112yes—
369C22×D11C23×C411yescharacteristic
370C22×D11C23×C413yes—
371C22×D11C23×C413yes—
372C22×D11C23×C411yescharacteristic
373Q8×C11—26no—
374Q8×C11C2×C22⋊C414yes—
375D4×C11—212no—
376D4×C11—26no—
377D4×C11C2×C22⋊C4112yes—
378C2×C4×C11—26no—
379C2×C4×C11—26no—
380C2×C4×C11—26no—
381C2×C4×C11—23no—
382C2×C4×C11—23no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11C23×C411yescharacteristic
386C2×C4×C11C23×C413yes—
387C2×C4×C11C23×C413yes—
388C2×C4×C11C22×D416yes—
389C2×C4×C11C22×D416yes—
390C2×C4×C11C2511yescharacteristic
391C22⋊D11—212no—
392C22⋊D11—26no—
393C22⋊D11—22no—
394C22⋊D11—26no—
395C22⋊D11—26no—
396C22⋊D11—22no—
397C22⋊D11—26no—
398C22⋊D11—26no—
399C22⋊D11—26no—
400C22⋊D11C2×C22⋊C4124yes—
401C2×Dic11—26no—
402C2×Dic11—212no—
403C2×Dic11C2×C22⋊C4112yes—
404C2×Dic11C23×C413yes—
405C2×Dic11C23×C411yescharacteristic
406C2×Dic11C23×C411yescharacteristic
407C2×Dic11C23×C413yes—
408D44—26no—
409D44—22no—
410D44—26no—
411D44—26no—
412D44—26no—
413D44C2×C22⋊C4112yes—
414C4×D11—212no—
415C4×D11—26no—
416C4×D11—26no—
417C4×D11—23no—
418C4×D11—23no—
419C4×D11—21no—
420C4×D11—21no—
421C4×D11—212no—
422C4×D11C2×C22⋊C4112yes—
423C4×D11C2×C22⋊C4112yes—
424C4×D11C22×D412yes—
425C4×D11C22×D416yes—
426C4×D11C22×D416yes—
427C4×D11C22×D412yes—
428Dic22—26no—
429Dic22—22no—
430Dic22—26no—
431Dic22—26no—
432Dic22—26no—
433Dic22C2×C22⋊C4112yes—
434C8×C11—21no—
435C8×C11—23no—
436C8×C11—23no—
437C8×C11—21no—
438C11⋊C8—21no—
439C11⋊C8—23no—
440C11⋊C8—23no—
441C11⋊C8—21no—
442#585—228no—
443#585—228no—
444C2×2−1+4—111no—
445C2×2−1+4—113no—
446C2×2−1+4—111no—
447C2×2−1+4—111no—
448C2×H(5,𝔽2)—113no—
449C2×H(5,𝔽2)—111no—
450C2×H(5,𝔽2)—113no—
451C2×H(5,𝔽2)—113no—
452C22×#41—111no—
453C22×#41—113no—
454C22×#41—113no—
455C22×#41—111no—
456C22×#41—113no—
457C22×#41—113no—
458C22×#41C2×D1111yescharacteristic
459#568—228no—
460C2×#131—111no—
461C2×#131—111no—
462C2×#131—113no—
463C2×#131—113no—
464C2×#131—113no—
465C2×#131—113no—
466C2×#131—228no—
467C2×#131C2×D1111yescharacteristic, complemented
468C2×#131C2×D1111yescharacteristic, complemented
469C22×M16—113no—
470C22×M16—113no—
471C22×M16—113no—
472C23×C8—113no—
473#408—113no—
474#408—113no—
475#408—113no—
476#408—113no—
477#408—113no—
478#408—113no—
479#408—113no—
480#408—111no—
481#408—116no—
482#408—113no—
483#408—113no—
484#408—113no—
485#408—113no—
486#408—113no—
487#408—113no—
488#408—116no—
489#408—116no—
490#408C2×D1113yescomplemented
491#408C2×D1113yescomplemented
492#407—113no—
493#407—113no—
494#407—113no—
495#407—116no—
496#407—116no—
497#407C2×D1113yescomplemented
498C2×C22⋊C8—113no—
499C2×C22⋊C8—113no—
500C2×C22⋊C8—113no—
501C2×C22⋊C8—116no—
502C2×C22⋊C8—116no—
503C2×C22⋊C8C2×D1113yescomplemented
504C22×C11—23no—
505C22×C11—23no—
506C22×C11—21no—
507C22×C11—23no—
508C22×C11—23no—
509C22×C11—23no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—86no—
513C22×C11C22×C22⋊C416yes—
514C22×C11C24×C411yescharacteristic
515C2×D11—21no—
516C2×D11—23no—
517C2×D11—21no—
518C2×D11—23no—
519C2×D11—21no—
520C2×D11—23no—
521C2×D11—23no—
522C2×D11—21no—
523C2×D11—23no—
524C2×D11—21no—
525C2×D11—412no—
526C2×D11—812no—
527C2×D11—86no—
528C2×D11C22×C22⋊C416yes—
529C2×D11C22×C22⋊C412yes—
530C4×C11—21no—
531C4×C11—23no—
532C4×C11C22×C22⋊C416yes—
533C4×C11C23×D411yescharacteristic
534C4×C11C23×D411yescharacteristic
535Dic11—23no—
536Dic11—21no—
537Dic11C22×C22⋊C412yes—
538Dic11C22×C22⋊C416yes—
5392−1+4—228no—
5402−1+4—228no—
5412−1+4—228no—
5422−1+4—2224no—
543H(5,𝔽2)—2224no—
544H(5,𝔽2)—2224no—
545H(5,𝔽2)—2224no—
546H(5,𝔽2)—228no—
547C2×#41—24no—
548C2×#41—24no—
549C2×#41—118no—
550C2×#41—118no—
551C2×#41—111no—
552C2×#41—113no—
553C2×#41—113no—
554C2×#41—111no—
555C2×#41—113no—
556C2×#41—116no—
557C2×#41—113no—
558C2×#41—116no—
559C2×#41—113no—
560C2×#41—113no—
561C2×#41—113no—
562C2×#41—113no—
563C2×#41—113no—
564C2×#41—113no—
565C2×#41—116no—
566C2×#41—113no—
567C2×#41—113no—
568C2×#41—113no—
569C2×#41—113no—
570C2×#41—113no—
571C2×#41—111no—
572C2×#41—113no—
573C2×#41—113no—
574C2×#41—2212no—
575C2×#41—2212no—
576C2×#41—2212no—
577C2×#41—2212no—
578C2×#41—2212no—
579C2×#41—2212no—
580C2×#41—2212no—
581C2×#41—2212no—
582C2×#41—224no—
583C2×#41—224no—
584C2×#41C4×D1111yescharacteristic
585C2×#41C4×D1113yes—
586C2×#41C22×D1113yes—
587C2×#41C22×D1111yescharacteristic
588C22×Q8—111no—
589C22×Q8—113no—
590C22×Q8—113no—
591C22×Q8—111no—
592C22×Q8—113no—
593C22×Q8—113no—
594C22×Q8C4×D1111yescharacteristic
595C22×D4—113no—
596C22×D4—113no—
597C22×D4—116no—
598C22×D4—113no—
599C22×D4—113no—
600C22×D4—116no—
601C22×D4—113no—
602C22×D4—116no—
603C22×D4—113no—
604C22×D4—113no—
605C22×D4—113no—
606C22×D4C4×D1113yes—
607C23×C4—113no—
608C23×C4—116no—
609C23×C4—113no—
610C23×C4C22×D1113yes—
611#131—24no—
612#131—24no—
613#131—2212no—
614#131—2212no—
615#131—2212no—
616#131—2212no—
617#131—224no—
618#131—224no—
619C2×M16—113no—
620C2×M16—113no—
621C2×M16—113no—
622C2×M16—111no—
623C2×M16—116no—
624C2×M16—113no—
625C2×M16—113no—
626C2×M16—2212no—
627C2×M16—2212no—
628C2×M16—2212no—
629C2×M16C22×D1113yes—
630C2×M16C22×D1113yes—
631C22×C8—113no—
632C22×C8—113no—
633C22×C8—111no—
634C22×C8—113no—
635C22×C8—113no—
636C22×C8—113no—
637C22×C8—116no—
638C22×C8—2212no—
639C22×C8C22×D1113yes—
640C22×C8C22×D1113yes—
641C22⋊C8—113no—
642C22⋊C8—111no—
643C22⋊C8—113no—
644C22⋊C8—116no—
645C22⋊C8—113no—
646C22⋊C8—113no—
647C22⋊C8—111no—
648C22⋊C8—111no—
649C22⋊C8—113no—
650C22⋊C8—113no—
651C22⋊C8—113no—
652C22⋊C8—113no—
653C22⋊C8—116no—
654C22⋊C8—116no—
655C22⋊C8—113no—
656C22⋊C8C22×D1113yes—
657C22⋊C8C22×D1116yes—
658C22⋊C8C22×D1111yescharacteristic
659C22⋊C8C22×D1113yes—
660C22⋊C8C22×D1113yes—
661C2×C11—26no—
662C2×C11—43no—
663C2×C11—41no—
664C2×C11C23×C22⋊C411yescharacteristic
665C2×C11#357311yescharacteristic
666C2×C11#357311yescharacteristic
667D11—22no—
668D11—26no—
669D11—43no—
670D11—41no—
671C24—113no—
672C24—116no—
673C24—113no—
674C24C2×C4×D1113yes—
675#41—24no—
676#41—212no—
677#41—26no—
678#41—26no—
679#41—118no—
680#41—1124no—
681#41—1112no—
682#41—1112no—
683#41—222no—
684#41—226no—
685#41—226no—
686#41—222no—
687#41—226no—
688#41—226no—
689#41—226no—
690#41—226no—
691#41—2212no—
692#41—2212no—
693#41—2212no—
694#41—2212no—
695#41—2224no—
696#41—2212no—
697#41—2212no—
698#41—2224no—
699#41—2212no—
700#41—2212no—
701#41—2224no—
702#41—2212no—
703#41—2212no—
704#41—224no—
705#41—2212no—
706#41—226no—
707#41—226no—
708#41D4×D1114yes—
709#41D4×D1114yes—
710C2×Q8—24no—
711C2×Q8—118no—
712C2×Q8—113no—
713C2×Q8—113no—
714C2×Q8—113no—
715C2×Q8—111no—
716C2×Q8—113no—
717C2×Q8—113no—
718C2×Q8—2212no—
719C2×Q8—2212no—
720C2×Q8—2212no—
721C2×Q8—2212no—
722C2×Q8—224no—
723C2×Q8C2×C4×D1113yes—
724C2×Q8C2×C4×D1111yescharacteristic
725C2×D4—212no—
726C2×D4—116no—
727C2×D4—1124no—
728C2×D4—113no—
729C2×D4—113no—
730C2×D4—111no—
731C2×D4—113no—
732C2×D4—113no—
733C2×D4—113no—
734C2×D4—111no—
735C2×D4—113no—
736C2×D4—116no—
737C2×D4—113no—
738C2×D4—113no—
739C2×D4—113no—
740C2×D4—111no—
741C2×D4—113no—
742C2×D4—113no—
743C2×D4—2212no—
744C2×D4—2212no—
745C2×D4—2212no—
746C2×D4—2212no—
747C2×D4—2224no—
748C2×D4—2212no—
749C2×D4—2224no—
750C2×D4—2224no—
751C2×D4—2212no—
752C2×D4—2212no—
753C2×D4C2×C4×D1116yes—
754C2×D4C2×C4×D1113yes—
755C2×D4C2×C4×D1113yes—
756C22×C4—26no—
757C22×C4—26no—
758C22×C4—113no—
759C22×C4—113no—
760C22×C4—113no—
761C22×C4—1112no—
762C22×C4—1112no—
763C22×C4—111no—
764C22×C4—113no—
765C22×C4—116no—
766C22×C4—113no—
767C22×C4—116no—
768C22×C4—116no—
769C22×C4—113no—
770C22×C4—113no—
771C22×C4—113no—
772C22×C4—111no—
773C22×C4—2212no—
774C22×C4—2212no—
775C22×C4—226no—
776C22×C4—226no—
777C22×C4C2×C4×D1113yes—
778C22×C4C2×C4×D1113yes—
779C22×C4C2×C4×D1113yes—
780C22×C4C23×D1113yes—
781C22×C4C23×D1111yescharacteristic
782C22×C4C23×D1113yes—
783M16—26no—
784M16—26no—
785M16—222no—
786M16—226no—
787M16—226no—
788M16—226no—
789M16—2212no—
790M16—226no—
791M16—226no—
792C2×C8—26no—
793C2×C8—26no—
794C2×C8—111no—
795C2×C8—111no—
796C2×C8—113no—
797C2×C8—113no—
798C2×C8—222no—
799C2×C8—226no—
800C2×C8—226no—
801C2×C8—226no—
802C2×C8—2212no—
803C2×C8—226no—
804C2×C8—226no—
805C2×C8C23×D1111yescharacteristic
806C2×C8C23×D1113yes—
807C2×C8C23×D1113yes—
808C2×C8C23×D1111yescharacteristic
809C11#6006511yescharacteristic, complemented, Sylow
810C23—26no—
811C23—43no—
812C23—43no—
813C23—111no—
814C23—113no—
815C23—1112no—
816C23—113no—
817C23—111no—
818C23—2212no—
819C23—226no—
820C23—443no—
821C23—443no—
822C23—443no—
823C23—443no—
824C23—446no—
825C23—446no—
826C23C22×C4×D1113yes—
827C23C22×C4×D1111yescharacteristic
828C23C22×C4×D1113yes—
829Q8—26no—
830Q8—1112no—
831Q8—222no—
832Q8—226no—
833Q8—226no—
834Q8—226no—
835Q8—226no—
836Q8C22⋊C4×D1114yes—
837D4—212no—
838D4—26no—
839D4—1124no—
840D4—1112no—
841D4—222no—
842D4—226no—
843D4—226no—
844D4—226no—
845D4—222no—
846D4—226no—
847D4—226no—
848D4—226no—
849D4—222no—
850D4—226no—
851D4—226no—
852D4—226no—
853D4—2212no—
854D4—226no—
855D4C22⋊C4×D11112yes—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—26no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—23no—
862C2×C4—23no—
863C2×C4—1112no—
864C2×C4—111no—
865C2×C4—113no—
866C2×C4—1112no—
867C2×C4—1112no—
868C2×C4—112no—
869C2×C4—116no—
870C2×C4—116no—
871C2×C4—112no—
872C2×C4—113no—
873C2×C4—111no—
874C2×C4—2212no—
875C2×C4—2212no—
876C2×C4—2212no—
877C2×C4—226no—
878C2×C4—226no—
879C2×C4—226no—
880C2×C4—223no—
881C2×C4—223no—
882C2×C4—221no—
883C2×C4—221no—
884C2×C4C22×C4×D1113yes—
885C2×C4C22×C4×D1111yescharacteristic
886C2×C4C22×C4×D1113yes—
887C2×C4C2×D4×D1116yes—
888C2×C4C2×D4×D1116yes—
889C2×C4C24×D1111yescharacteristic
890C8—21no—
891C8—21no—
892C8—23no—
893C8—23no—
894C8—221no—
895C8—223no—
896C8—223no—
897C8—221no—
898C22—23no—
899C22—23no—
900C22—21no—
901C22—23no—
902C22—21no—
903C22—23no—
904C22—21no—
905C22—23no—
906C22—86no—
907C22—112no—
908C22—116no—
909C22—221no—
910C22—223no—
911C22—221no—
912C22—223no—
913C22—223no—
914C22—221no—
915C22—221no—
916C22—223no—
917C22—221no—
918C22—223no—
919C22—4412no—
920C22—886no—
921C22—8812no—
922C22C2×C22⋊C4×D1116yes—
923C22C23×C4×D1111yescharacteristic
924C4—21no—
925C4—23no—
926C4—112no—
927C4—116no—
928C4—223no—
929C4—221no—
930C4C2×C22⋊C4×D1116yes—
931C4C22×D4×D1111yescharacteristic
932C4C22×D4×D1111yescharacteristic
933C2—26no—
934C2—41no—
935C2—43no—
936C2—222no—
937C2—226no—
938C2—441no—
939C2—443no—
940C2C22×C22⋊C4×D1111yescharacteristic
941C2#1308332711yescharacteristic
942C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2880C2
prime radicalC2×#10623453C2
cosocleC2×C4×C11C25
hypercenter#2880D11
hypocenterC11#60065
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#10623281C2semidirect
3. C2×D11×#131C2semidirect
4. #13077066C2semidirect
5. #13077065C2semidirect
6. #13077064C2semidirect
7. #13077064C2semidirect
8. #13077063C2semidirect
9. #13077063C2semidirect
10. #13077062C2semidirect
11. #13077059C2semidirect
12. #13077058C2semidirect
13. C2×#10622340C2semidirect
14. D11×#408C2semidirect
15. C11×#2880C2semidirect
33. C2×C11×#131C22semidirect
34. C2×C11×#131C22semidirect
35. C2×#67001C22semidirect
36. C2×#67001C22semidirect
39. C2×#66960C22semidirect
40. C2×#66960C22semidirect
41. C2×M16×D11C22semidirect
42. C2×M16×D11C22semidirect
43. C2×#66954C22semidirect
44. C2×#66954C22semidirect
45. C22×#4313C22semidirect
46. C22×C8×D11C22semidirect
47. C11×#408C22semidirect
48. C11×#408C22semidirect
49. C11×#407C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. #10622847C22semidirect
52. #10622847C22semidirect
53. #10622820C22semidirect
54. C2×C22⋊(C11⋊C8)C22semidirect
55. #10622742C22semidirect
56. #10622742C22semidirect
57. #10622739C22semidirect
58. #10622739C22semidirect
59. #10622723C22semidirect
60. #10622723C22semidirect
61. C2×(C2×D11)⋊C8C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. #10622340C22semidirect
64. #10622340C22semidirect
65. #10622340C22semidirect
66. #10622340C22semidirect
67. #10622340C22semidirect
68. #10622340C22semidirect
69. #10622340C22semidirect
70. #10622340C22semidirect
71. #10622340C22semidirect
72. #10622340C22semidirect
73. #10622340C22semidirect
74. #10622339C22semidirect
75. #10622339C22semidirect
76. D11×C22⋊C8C22semidirect
77. D11×C22⋊C8C22semidirect
349. #2880D11semidirect
467. C2×#131C2×D11semidirect
468. C2×#131C2×D11semidirect
490. #408C2×D11semidirect
491. #408C2×D11semidirect
497. #407C2×D11semidirect
503. C2×C22⋊C8C2×D11semidirect
809. C11#60065semidirect

Maximal subgroups

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

subgroupindex
C2×#106234532
C2×#106232812
C2×D11×#1312
#130770662
#130770652
#130770642
#130770632
#130770622
#130770592
#130770582
C2×#106223402
D11×#4082
C11×#28802
#6006511