Finite Group Databasebeta

← C2×#13077162 #15617371

Subgroups — C2×#13077162 #15617371

Order 2816.

4946 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623453C211yesmaximal, characteristic
2C2×#10623276C211yesmaximal, characteristic, complemented
3C2×#10623053C211yesmaximal, characteristic, complemented
4#13077162C2116yesmaximal, direct product factor
5C2×#10622618C211yesmaximal, characteristic, complemented
6C2×#10622434C214yesmaximal, complemented
7C22×#66901C211yesmaximal, characteristic, complemented
8C22×#66889C211yesmaximal, characteristic, complemented
9C2×D11×#104C214yesmaximal, complemented
10C2×C11×#421C211yesmaximal, characteristic, complemented
11C22×C11×#41C2211yescharacteristic
12#10623453—24no—
13#10623453—24no—
14#10623453C418yescomplemented
15#10623453C2218yes—
16C2×#67043—21no—
17C2×#67043C412yescomplemented
18C2×#67042—21no—
19C2×#67042C412yescomplemented
20C2×#41×D11—22no—
21C2×#41×D11C2214yes—
22C2×#67040C412yescomplemented
23C2×#67037—22no—
24C2×#67037C412yescomplemented
25C22×#4339—22no—
26C22×#4339C2211yescharacteristic
27C22×#4339C2211yescharacteristic
28C22×C11×M16C2211yescharacteristic, complemented
29C2×C11×#117C2211yescharacteristic, complemented
30C22×C4×Dic11C2211yescharacteristic, complemented
31C22×#4318C2211yescharacteristic, complemented
32#10623276—24no—
33#10623276C2218yescomplemented
34C2×#66960—22no—
35C2×M16×D11C2214yescomplemented
36C2×#66954—22no—
37#10623053—24no—
38#10623053C2218yescomplemented
39C2×#66946—21no—
40C2×#66940—21no—
41C2×(C22⋊D11)⋊C4—22no—
42C2×#66925C2212yescomplemented
43C2×C42×D11C2212yescomplemented
44C11×#421C2218yescomplemented
45C2×C11×#104C2214yescomplemented
46C2×#66901C2212yescomplemented
47C2×#66901C2212yescomplemented
48C2×#66901C2218yescomplemented
49C2×#66889C2212yescomplemented
50C2×#66889C2212yescomplemented
51C2×#66889C2218yescomplemented
52#10622618C2218yescomplemented
53C2×#66869C2214yescomplemented
54#10622434C22132yescomplemented
55D11×#104C22132yescomplemented
56C2×C11×#41—21no—
57C2×C11×#41—21no—
58C2×C11×#41—22no—
59C2×C11×#41—22no—
60C2×C11×#41C2×C412yescomplemented
61C2×C11×#41C2×C414yescomplemented
62C2×C11×#41C2312yes—
63C2×C11×#41C2314yes—
64C22×Q8×C11C2×C411yescharacteristic, complemented
65C22×D4×C11—21no—
66C22×D4×C11C2×C411yescharacteristic, complemented
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—24no—
71C22×C22⋊D11D412yes—
72C23×Dic11—21no—
73#67043—28no—
74#67043—28no—
75#67043—28no—
76#67043C2×C4116yescomplemented
77#67042—28no—
78#67042—28no—
79#67042—28no—
80#67042C2×C4116yescomplemented
81#41×D11—216no—
82#41×D11—216no—
83#41×D11—28no—
84#41×D11—28no—
85#41×D11C2×C4116yescomplemented
86#41×D11C23116yes—
87#67040—28no—
88#67040C2×C4116yescomplemented
89C2×#4343—22no—
90C2×#4343C2×C414yescomplemented
91C2×Q8×D11—22no—
92C2×Q8×D11C2×C414yescomplemented
93#67037—216no—
94#67037—216no—
95#67037—28no—
96#67037C2×C4116yescomplemented
97C2×#4341—24no—
98C2×#4341—24no—
99C2×#4341—22no—
100C2×#4341C2×C414yescomplemented
101C2×D4×D11—24no—
102C2×D4×D11—24no—
103C2×D4×D11—22no—
104C2×D4×D11C2×C414yescomplemented
105C2×#4339—21no—
106C2×#4339—21no—
107C2×#4339—22no—
108C2×#4339—22no—
109C2×#4339—24no—
110C2×#4339—216no—
111C2×#4339—216no—
112C2×#4339—22no—
113C2×#4339—24no—
114C2×#4339—22no—
115C2×#4339C2×C412yes—
116C2×#4339C2×C412yes—
117C2×#4339C2×C414yes—
118C2×#4339C2×C412yescomplemented
119C2×#4339C2×C414yescomplemented
120C2×#4339D412yes—
121C2×#4339D412yes—
122C2×#4339D414yes—
123C2×#4339D414yes—
124C2×#4339C2312yes—
125C2×#4339C2314yes—
126C2×#4339C2314yes—
127C22×D44—22no—
128C22×D44C2×C411yescharacteristic, complemented
129C22×D44D411yescharacteristic
130C22×C4×D11—21no—
131C22×C4×D11—24no—
132C22×C4×D11—22no—
133C22×C4×D11C2312yes—
134C22×Dic22—22no—
135C22×Dic22C2×C411yescharacteristic, complemented
136C22×Dic22D411yescharacteristic
137C2×C11×M16—21no—
138C2×C11×M16—22no—
139C2×C11×M16C2312yes—
140C2×C11×M16C2314yescomplemented
141C22×C8×C11—21no—
142C11×#117—22no—
143C11×#117C2314yescomplemented
144C2×C11×C4⋊C4—21no—
145C2×C11×C22⋊C4—21no—
146C2×C42×C11C2312yes—
147C2×(C2×D11)⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×C4×Dic11—21no—
150C2×C4×Dic11—22no—
151C2×C4×Dic11—22no—
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154C2×C4×Dic11C2314yescomplemented
155C2×#4318—21no—
156C2×#4318—22no—
157C2×#4318C2312yes—
158C2×#4318C2314yescomplemented
159C22×C11⋊C8—21no—
160#66960—216no—
161M16×D11—28no—
162M16×D11C23116yescomplemented
163#66954—216no—
164C2×#4313—24no—
165C2×C8×D11—24no—
166#66946—28no—
167#66940—28no—
168(C22⋊D11)⋊C4—216no—
169#66925—24no—
170#66925C2318yescomplemented
171C42×D11—24no—
172C42×D11C2318yescomplemented
173C11×#104C23116yescomplemented
174#66901C2318yescomplemented
175#66901C2318yescomplemented
176#66889C2318yescomplemented
177#66889C2318yescomplemented
178#66869C23116yescomplemented
179C2×#2901—111nomaximal, Sylow
180C24×C11—21no—
181C24×C11C2×D411yescharacteristic
182C23×D11—21no—
183C23×D11—24no—
184C23×D11C2×D412yes—
185C11×#41—24no—
186C11×#41—24no—
187C11×#41—24no—
188C11×#41—22no—
189C11×#41—24no—
190C11×#41—22no—
191C11×#41—24no—
192C11×#41C22×C414yes—
193C11×#41C22×C418yescomplemented
194C11×#41C2414yes—
195C2×Q8×C11—21no—
196C2×Q8×C11—22no—
197C2×Q8×C11C22×C412yes—
198C2×Q8×C11C22×C414yescomplemented
199C2×D4×C11—22no—
200C2×D4×C11—24no—
201C2×D4×C11—22no—
202C2×D4×C11—24no—
203C2×D4×C11—21no—
204C2×D4×C11—22no—
205C2×D4×C11C22×C412yes—
206C2×D4×C11C22×C414yescomplemented
207C22×C4×C11—21no—
208C22×C4×C11—22no—
209C22×C4×C11—24no—
210C22×C4×C11—22no—
211C22×C4×C11—24no—
212C22×C4×C11—22no—
213C22×C4×C11C22×C411yescharacteristic
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C22×C412yes—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D412yes—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2411yescharacteristic
222C22×C4×C11C2412yes—
223C2×C22⋊D11—232no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—22no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—22no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11C22⋊C414yes—
231C2×C22⋊D11C22⋊C414yes—
232C2×C22⋊D11C22⋊C418yes—
233C2×C22⋊D11C2×D418yes—
234C22×Dic11—24no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—24no—
238C22×Dic11—21no—
239C22×Dic11—44no—
240C22×Dic11C2×D412yes—
241#4343—216no—
242#4343—28no—
243#4343C22×C4116yescomplemented
244Q8×D11—28no—
245Q8×D11—216no—
246Q8×D11C22×C4116yescomplemented
247#4341—232no—
248#4341—216no—
249#4341—216no—
250#4341—28no—
251#4341—216no—
252#4341C22×C4116yescomplemented
253D4×D11—232no—
254D4×D11—216no—
255D4×D11—28no—
256D4×D11—216no—
257D4×D11—216no—
258D4×D11C22×C4116yescomplemented
259#4339—232no—
260#4339—216no—
261#4339—216no—
262#4339—216no—
263#4339—216no—
264#4339—24no—
265#4339—24no—
266#4339—24no—
267#4339—24no—
268#4339—22no—
269#4339—22no—
270#4339—24no—
271#4339C22⋊C418yes—
272#4339C22⋊C418yes—
273#4339C22⋊C418yes—
274#4339C22⋊C418yes—
275#4339C22×C418yes—
276#4339C22×C418yes—
277#4339C22×C414yes—
278#4339C22×C418yescomplemented
279#4339C2×D418yes—
280#4339C2×D418yes—
281#4339C2414yes—
282C2×D44—216no—
283C2×D44—24no—
284C2×D44—21no—
285C2×D44—22no—
286C2×D44C22⋊C412yes—
287C2×D44C22⋊C412yes—
288C2×D44C22⋊C414yes—
289C2×D44C22×C412yes—
290C2×D44C22×C414yescomplemented
291C2×D44C2×D414yes—
292C2×C4×D11—24no—
293C2×C4×D11—216no—
294C2×C4×D11—216no—
295C2×C4×D11—24no—
296C2×C4×D11—28no—
297C2×C4×D11—22no—
298C2×C4×D11—24no—
299C2×C4×D11—22no—
300C2×C4×D11—24no—
301C2×C4×D11—48no—
302C2×C4×D11C22×C414yes—
303C2×C4×D11C22×C414yes—
304C2×C4×D11C2×D414yes—
305C2×C4×D11C2×D414yes—
306C2×C4×D11C2×D414yes—
307C2×C4×D11C2414yes—
308C2×Dic22—24no—
309C2×Dic22—216no—
310C2×Dic22—21no—
311C2×Dic22—22no—
312C2×Dic22C22⋊C412yes—
313C2×Dic22C22⋊C412yes—
314C2×Dic22C22⋊C414yes—
315C2×Dic22C22×C412yes—
316C2×Dic22C22×C414yescomplemented
317C2×Dic22C2×D414yes—
318C11×M16—22no—
319C11×M16—24no—
320C11×M16C2414yes—
321C2×C8×C11—22no—
322C2×C8×C11—24no—
323C11×C4⋊C4—24no—
324C11×C22⋊C4—24no—
325C42×C11—22no—
326C42×C11C2414yes—
327(C2×D11)⋊C4—28no—
328Dic11⋊C4—28no—
329C4×Dic11—28no—
330C4×Dic11—21no—
331C4×Dic11—21no—
332C4×Dic11—24no—
333C4×Dic11C2412yes—
334C4×Dic11C2412yes—
335#4318—24no—
336#4318—22no—
337#4318C2414yes—
338C2×C11⋊C8—22no—
339C2×C11⋊C8—24no—
340#4313—216no—
341C8×D11—216no—
342C2×#585—111no—
343C2×#568—111no—
344C2×C4×#41—111no—
345#2901—1116no—
346C2×#421—114no—
347C2×#421—111no—
348C2×#421D1111yescharacteristic, complemented
349C22×#104—114no—
350C22×#104—111no—
351C22×#104—111no—
352C23×C11—22no—
353C23×C11—24no—
354C23×C11—42no—
355C23×C11—82no—
356C23×C11C2×C22⋊C411yescharacteristic
357C23×C11C2×C22⋊C411yescharacteristic
358C23×C11C2×C22⋊C412yes—
359C23×C11C22×D411yescharacteristic
360C23×C11C22×D412yes—
361C22×D11—22no—
362C22×D11—24no—
363C22×D11—216no—
364C22×D11—44no—
365C22×D11—88no—
366C22×D11—82no—
367C22×D11C2×C22⋊C414yes—
368C22×D11C2×C22⋊C414yes—
369C22×D11C22×D414yes—
370Q8×C11—22no—
371Q8×C11—24no—
372Q8×C11C23×C414yes—
373D4×C11—24no—
374D4×C11—28no—
375D4×C11—24no—
376D4×C11—22no—
377D4×C11—24no—
378D4×C11C23×C414yes—
379C2×C4×C11—22no—
380C2×C4×C11—24no—
381C2×C4×C11—28no—
382C2×C4×C11—24no—
383C2×C4×C11—24no—
384C2×C4×C11—24no—
385C2×C4×C11—44no—
386C2×C4×C11C2×C22⋊C411yescharacteristic
387C2×C4×C11C2×C22⋊C412yes—
388C2×C4×C11C2×C22⋊C411yescharacteristic
389C2×C4×C11C2×C22⋊C412yes—
390C2×C4×C11C2×C22⋊C412yes—
391C2×C4×C11C2×C22⋊C412yes—
392C2×C4×C11C2×C22⋊C412yes—
393C2×C4×C11C23×C411yescharacteristic
394C2×C4×C11C23×C412yes—
395C2×C4×C11C23×C411yescharacteristic
396C2×C4×C11C23×C412yes—
397C2×C4×C11C22×D411yescharacteristic
398C2×C4×C11C22×D412yes—
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D411yescharacteristic
402C2×C4×C11C22×D411yescharacteristic
403C2×C4×C11C2511yescharacteristic
404C22⋊D11—28no—
405C22⋊D11—24no—
406C22⋊D11—24no—
407C22⋊D11—216no—
408C22⋊D11—216no—
409C22⋊D11C2×C22⋊C4116yes—
410C22⋊D11C2×C22⋊C4116yes—
411C2×Dic11—24no—
412C2×Dic11—22no—
413C2×Dic11—24no—
414C2×Dic11—22no—
415C2×Dic11—216no—
416C2×Dic11—22no—
417C2×Dic11—48no—
418C2×Dic11—42no—
419C2×Dic11C2×C22⋊C414yes—
420C2×Dic11C2×C22⋊C414yes—
421C2×Dic11C22×D414yes—
422D44—216no—
423D44—24no—
424D44—22no—
425D44C2×C22⋊C418yes—
426D44C2×C22⋊C418yes—
427D44C23×C414yes—
428C4×D11—216no—
429C4×D11—24no—
430C4×D11—28no—
431C4×D11—24no—
432C4×D11—216no—
433C4×D11—416no—
434C4×D11C2×C22⋊C418yes—
435C4×D11C2×C22⋊C418yes—
436C4×D11C23×C418yes—
437C4×D11C22×D418yes—
438Dic22—24no—
439Dic22—22no—
440Dic22—216no—
441Dic22C2×C22⋊C418yes—
442Dic22C2×C22⋊C418yes—
443Dic22C23×C414yes—
444C8×C11—24no—
445C11⋊C8—24no—
446#585—118no—
447#585—118no—
448#585—224no—
449#585—224no—
450C2×2−1+4—112no—
451C2×2−1+4—112no—
452C2×2−1+4—221no—
453C2×H(5,𝔽2)—112no—
454C2×H(5,𝔽2)—112no—
455C2×H(5,𝔽2)—222no—
456C2×H(5,𝔽2)—221no—
457C22×#41—111no—
458C22×#41—114no—
459C22×#41—111no—
460C22×#41—222no—
461C22×#41—222no—
462C22×#41C2×D1111yescharacteristic
463#568—118no—
464#568—224no—
465C2×#131—222no—
466C2×#131—222no—
467C22×M16—111no—
468C22×M16—114no—
469C22×M16C2×D1111yescharacteristic, complemented
470C4×#41—118no—
471C4×#41—224no—
472C2×C4×Q8—221no—
473C2×C4×D4—222no—
474C2×C4×D4—221no—
475C2×#117—112no—
476C2×#117C2×D1111yescharacteristic, complemented
477C22×C42—111no—
478C22×C42—112no—
479#421—118no—
480#421—1132no—
481#421C2×D1118yescomplemented
482C2×#104—112no—
483C2×#104—112no—
484C2×#104—118no—
485C2×#104—112no—
486C2×#104—112no—
487C2×#104—118no—
488C2×#104—114no—
489C2×#104—1132no—
490C2×#104C2×D1114yescomplemented
491C22×C11—22no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—24no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—44no—
498C22×C11—84no—
499C22×C11C22×C22⋊C412yes—
500C22×C11C22×C22⋊C412yes—
501C22×C11C22×C22⋊C411yescharacteristic
502C22×C11C22×C22⋊C411yescharacteristic
503C22×C11C23×D411yescharacteristic
504C2×D11—28no—
505C2×D11—24no—
506C2×D11—44no—
507C2×D11—44no—
508C2×D11—44no—
509C2×D11—816no—
510C2×D11—84no—
511C2×D11C22×C22⋊C418yes—
512C4×C11—24no—
513C4×C11—44no—
514C4×C11C22×C22⋊C412yes—
515C4×C11C22×C22⋊C411yescharacteristic
516C4×C11C22×C22⋊C411yescharacteristic
517C4×C11C22×C22⋊C412yes—
518C4×C11C24×C411yescharacteristic
519C4×C11C23×D411yescharacteristic
520Dic11—24no—
521Dic11—24no—
522Dic11—42no—
523Dic11C22×C22⋊C418yes—
5242−1+4—1116no—
5252−1+4—1116no—
5262−1+4—228no—
5272−1+4—228no—
5282−1+4—228no—
5292−1+4—228no—
530H(5,𝔽2)—1116no—
531H(5,𝔽2)—1116no—
532H(5,𝔽2)—2216no—
533H(5,𝔽2)—2216no—
534H(5,𝔽2)—228no—
535H(5,𝔽2)—228no—
536H(5,𝔽2)—228no—
537H(5,𝔽2)—228no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—112no—
543C2×#41—112no—
544C2×#41—114no—
545C2×#41—114no—
546C2×#41—112no—
547C2×#41—112no—
548C2×#41—114no—
549C2×#41—114no—
550C2×#41—1116no—
551C2×#41—1116no—
552C2×#41—114no—
553C2×#41—114no—
554C2×#41—112no—
555C2×#41—114no—
556C2×#41—112no—
557C2×#41—114no—
558C2×#41—224no—
559C2×#41—224no—
560C2×#41—222no—
561C2×#41—222no—
562C2×#41—2216no—
563C2×#41—2216no—
564C2×#41—224no—
565C2×#41—228no—
566C2×#41—228no—
567C2×#41—224no—
568C2×#41—222no—
569C2×#41—222no—
570C2×#41—2216no—
571C2×#41—2216no—
572C2×#41—221no—
573C2×#41—221no—
574C2×#41—222no—
575C2×#41—222no—
576C2×#41C4×D1112yescomplemented
577C2×#41C4×D1114yescomplemented
578C2×#41C22×D1112yes—
579C2×#41C22×D1114yes—
580C22×Q8—111no—
581C22×Q8—114no—
582C22×Q8—111no—
583C22×Q8—222no—
584C22×Q8—222no—
585C22×Q8C4×D1111yescharacteristic, complemented
586C22×D4—21no—
587C22×D4—112no—
588C22×D4—114no—
589C22×D4—111no—
590C22×D4—111no—
591C22×D4—222no—
592C22×D4—224no—
593C22×D4—222no—
594C22×D4—224no—
595C22×D4—224no—
596C22×D4—221no—
597C22×D4C4×D1111yescharacteristic, complemented
598C23×C4—21no—
599C23×C4—112no—
600C23×C4—224no—
601C23×C4—222no—
602C23×C4—221no—
603C23×C4—221no—
604C23×C4C22×D1111yescharacteristic
605#131—2216no—
606#131—2216no—
607C2×M16—21no—
608C2×M16—22no—
609C2×M16—112no—
610C2×M16—114no—
611C2×M16—1116no—
612C2×M16—224no—
613C2×M16—228no—
614C2×M16—221no—
615C2×M16—222no—
616C2×M16C22×D1112yes—
617C2×M16C22×D1114yescomplemented
618C22×C8—21no—
619C22×C8—224no—
620C22×C8—221no—
621C4×Q8—228no—
622C4×D4—2216no—
623C4×D4—228no—
624#117—22no—
625#117—118no—
626#117—224no—
627#117C22×D1114yescomplemented
628C2×C4⋊C4—21no—
629C2×C4⋊C4—222no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—222no—
632C2×C42—111no—
633C2×C42—114no—
634C2×C42—111no—
635C2×C42—118no—
636C2×C42—224no—
637C2×C42—222no—
638C2×C42—221no—
639C2×C42—222no—
640C2×C42C22×D1112yes—
641#104—118no—
642#104—118no—
643#104—118no—
644#104—118no—
645#104—1116no—
646#104C22×D11116yescomplemented
647C2×C11—21no—
648C2×C11—21no—
649C2×C11—22no—
650C2×C11—22no—
651C2×C11—44no—
652C2×C11#290112yescomplemented
653C2×C11C23×C22⋊C411yescharacteristic
654D11—28no—
655D11—44no—
656C24—21no—
657C24—112no—
658C24—224no—
659C24—221no—
660C24D4×D1111yescharacteristic
661#41—24no—
662#41—24no—
663#41—24no—
664#41—22no—
665#41—24no—
666#41—22no—
667#41—24no—
668#41—118no—
669#41—118no—
670#41—118no—
671#41—118no—
672#41—118no—
673#41—118no—
674#41—118no—
675#41—118no—
676#41—1116no—
677#41—1116no—
678#41—114no—
679#41—118no—
680#41—114no—
681#41—2216no—
682#41—2216no—
683#41—2232no—
684#41—2216no—
685#41—2216no—
686#41—2216no—
687#41—2216no—
688#41—228no—
689#41—228no—
690#41—2232no—
691#41—2216no—
692#41—2216no—
693#41—224no—
694#41—224no—
695#41—224no—
696#41—222no—
697#41—224no—
698#41—222no—
699#41—224no—
700#41C2×C4×D1114yes—
701#41C2×C4×D1118yescomplemented
702#41C23×D1114yes—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—112no—
706C2×Q8—112no—
707C2×Q8—114no—
708C2×Q8—114no—
709C2×Q8—1116no—
710C2×Q8—112no—
711C2×Q8—114no—
712C2×Q8—224no—
713C2×Q8—2216no—
714C2×Q8—228no—
715C2×Q8—2216no—
716C2×Q8—221no—
717C2×Q8—222no—
718C2×Q8C2×C4×D1112yes—
719C2×Q8C2×C4×D1114yescomplemented
720C2×D4—22no—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—21no—
725C2×D4—22no—
726C2×D4—114no—
727C2×D4—114no—
728C2×D4—118no—
729C2×D4—118no—
730C2×D4—1116no—
731C2×D4—112no—
732C2×D4—112no—
733C2×D4—114no—
734C2×D4—112no—
735C2×D4—114no—
736C2×D4—114no—
737C2×D4—2216no—
738C2×D4—224no—
739C2×D4—228no—
740C2×D4—224no—
741C2×D4—2232no—
742C2×D4—2216no—
743C2×D4—2216no—
744C2×D4—2216no—
745C2×D4—2232no—
746C2×D4—224no—
747C2×D4—222no—
748C2×D4—224no—
749C2×D4—222no—
750C2×D4—224no—
751C2×D4—221no—
752C2×D4—222no—
753C2×D4C2×C4×D1112yes—
754C2×D4C2×C4×D1114yescomplemented
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—112no—
762C22×C4—114no—
763C22×C4—114no—
764C22×C4—114no—
765C22×C4—114no—
766C22×C4—114no—
767C22×C4—114no—
768C22×C4—224no—
769C22×C4—2216no—
770C22×C4—2216no—
771C22×C4—224no—
772C22×C4—228no—
773C22×C4—224no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—222no—
777C22×C4—224no—
778C22×C4—224no—
779C22×C4—222no—
780C22×C4—221no—
781C22×C4—224no—
782C22×C4—448no—
783C22×C4—444no—
784C22×C4C2×C4×D1111yescharacteristic
785C22×C4C2×C4×D1111yescharacteristic
786C22×C4C2×C4×D1112yes—
787C22×C4D4×D1111yescharacteristic
788C22×C4D4×D1112yes—
789C22×C4D4×D1112yes—
790C22×C4D4×D1111yescharacteristic
791C22×C4D4×D1111yescharacteristic
792C22×C4C23×D1112yes—
793C22×C4C23×D1111yescharacteristic
794M16—22no—
795M16—24no—
796M16—114no—
797M16—2216no—
798M16—222no—
799M16—224no—
800M16C23×D1114yes—
801C2×C8—24no—
802C2×C8—22no—
803C2×C8—2216no—
804C2×C8—224no—
805C2×C8—222no—
806C4⋊C4—24no—
807C4⋊C4—228no—
808C22⋊C4—24no—
809C22⋊C4—228no—
810C42—22no—
811C42—112no—
812C42—112no—
813C42—228no—
814C42—221no—
815C42—221no—
816C42—224no—
817C42C23×D1114yes—
818C11C2×#290111yescharacteristic, complemented, Sylow
819C23—22no—
820C23—24no—
821C23—42no—
822C23—82no—
823C23—114no—
824C23—114no—
825C23—114no—
826C23—2216no—
827C23—222no—
828C23—224no—
829C23—444no—
830C23—882no—
831C23—888no—
832C23C22⋊C4×D1111yescharacteristic
833C23C22⋊C4×D1111yescharacteristic
834C23C22⋊C4×D1112yes—
835C23C2×D4×D1111yescharacteristic
836C23C2×D4×D1112yes—
837Q8—22no—
838Q8—24no—
839Q8—118no—
840Q8—118no—
841Q8—114no—
842Q8—2216no—
843Q8—224no—
844Q8—222no—
845Q8C22×C4×D1114yes—
846D4—24no—
847D4—28no—
848D4—24no—
849D4—22no—
850D4—24no—
851D4—1116no—
852D4—1116no—
853D4—118no—
854D4—118no—
855D4—114no—
856D4—2216no—
857D4—2216no—
858D4—2216no—
859D4—228no—
860D4—224no—
861D4—224no—
862D4—224no—
863D4—222no—
864D4C22×C4×D1114yes—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—44no—
872C2×C4—114no—
873C2×C4—114no—
874C2×C4—114no—
875C2×C4—118no—
876C2×C4—118no—
877C2×C4—118no—
878C2×C4—118no—
879C2×C4—2216no—
880C2×C4—2216no—
881C2×C4—2216no—
882C2×C4—224no—
883C2×C4—222no—
884C2×C4—224no—
885C2×C4—222no—
886C2×C4—224no—
887C2×C4—228no—
888C2×C4—224no—
889C2×C4—222no—
890C2×C4—4416no—
891C2×C4—448no—
892C2×C4—442no—
893C2×C4C22⋊C4×D1111yescharacteristic
894C2×C4C22⋊C4×D1112yes—
895C2×C4C22⋊C4×D1111yescharacteristic
896C2×C4C22⋊C4×D1112yes—
897C2×C4C22⋊C4×D1112yes—
898C2×C4C22⋊C4×D1112yes—
899C2×C4C22⋊C4×D1112yes—
900C2×C4C22×C4×D1111yescharacteristic
901C2×C4C22×C4×D1111yescharacteristic
902C2×C4C22×C4×D1112yes—
903C2×C4C22×C4×D1112yes—
904C2×C4C2×D4×D1111yescharacteristic
905C2×C4C2×D4×D1112yes—
906C2×C4C2×D4×D1112yes—
907C2×C4C2×D4×D1112yes—
908C2×C4C2×D4×D1111yescharacteristic
909C2×C4C2×D4×D1111yescharacteristic
910C2×C4C24×D1111yescharacteristic
911C8—24no—
912C8—224no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—44no—
920C22—84no—
921C22—118no—
922C22—228no—
923C22—224no—
924C22—444no—
925C22—444no—
926C22—444no—
927C22—884no—
928C22—8816no—
929C22C2×C22⋊C4×D1112yes—
930C22C2×C22⋊C4×D1111yescharacteristic
931C22C2×C22⋊C4×D1112yes—
932C22C2×C22⋊C4×D1111yescharacteristic
933C22C22×D4×D1111yescharacteristic
934C4—24no—
935C4—44no—
936C4—118no—
937C4—224no—
938C4—224no—
939C4—442no—
940C4C2×C22⋊C4×D1111yescharacteristic
941C4C2×C22⋊C4×D1112yes—
942C4C2×C22⋊C4×D1111yescharacteristic
943C4C2×C22⋊C4×D1112yes—
944C4C23×C4×D1111yescharacteristic
945C4C22×D4×D1111yescharacteristic
946C2—21no—
947C2—22no—
948C2—21no—
949C2—22no—
950C2—44no—
951C2—228no—
952C2—444no—
953C2#1307716212yesdirect product factor
954C2C22×C22⋊C4×D1111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#421C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623453C2
cosocleC2×C4×C11C25
hypercenterC2×#421D11
hypocenterC11C2×#2901
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#10623276C2semidirect
3. C2×#10623053C2semidirect
4. #13077162C2direct (N × H)
5. C2×#10622618C2semidirect
6. C2×#10622434C2semidirect
7. C22×#66901C2semidirect
8. C22×#66889C2semidirect
9. C2×D11×#104C2semidirect
10. C2×C11×#421C2semidirect
14. #10623453C4semidirect
17. C2×#67043C4semidirect
19. C2×#67042C4semidirect
22. C2×#67040C4semidirect
24. C2×#67037C4semidirect
28. C22×C11×M16C22semidirect
29. C2×C11×#117C22semidirect
30. C22×C4×Dic11C22semidirect
31. C22×#4318C22semidirect
33. #10623276C22semidirect
35. C2×M16×D11C22semidirect
38. #10623053C22semidirect
42. C2×#66925C22semidirect
43. C2×C42×D11C22semidirect
44. C11×#421C22semidirect
45. C2×C11×#104C22semidirect
46. C2×#66901C22semidirect
47. C2×#66901C22semidirect
48. C2×#66901C22semidirect
49. C2×#66889C22semidirect
50. C2×#66889C22semidirect
51. C2×#66889C22semidirect
52. #10622618C22semidirect
53. C2×#66869C22semidirect
54. #10622434C22semidirect
55. D11×#104C22semidirect
60. C2×C11×#41C2×C4semidirect
61. C2×C11×#41C2×C4semidirect
64. C22×Q8×C11C2×C4semidirect
66. C22×D4×C11C2×C4semidirect
76. #67043C2×C4semidirect
80. #67042C2×C4semidirect
85. #41×D11C2×C4semidirect
88. #67040C2×C4semidirect
90. C2×#4343C2×C4semidirect
92. C2×Q8×D11C2×C4semidirect
96. #67037C2×C4semidirect
100. C2×#4341C2×C4semidirect
104. C2×D4×D11C2×C4semidirect
118. C2×#4339C2×C4semidirect
119. C2×#4339C2×C4semidirect
128. C22×D44C2×C4semidirect
135. C22×Dic22C2×C4semidirect
140. C2×C11×M16C23semidirect
143. C11×#117C23semidirect
154. C2×C4×Dic11C23semidirect
158. C2×#4318C23semidirect
162. M16×D11C23semidirect
170. #66925C23semidirect
172. C42×D11C23semidirect
173. C11×#104C23semidirect
174. #66901C23semidirect
175. #66901C23semidirect
176. #66889C23semidirect
177. #66889C23semidirect
178. #66869C23semidirect
193. C11×#41C22×C4semidirect
198. C2×Q8×C11C22×C4semidirect
206. C2×D4×C11C22×C4semidirect
243. #4343C22×C4semidirect
246. Q8×D11C22×C4semidirect
252. #4341C22×C4semidirect
258. D4×D11C22×C4semidirect
278. #4339C22×C4semidirect
290. C2×D44C22×C4semidirect
316. C2×Dic22C22×C4semidirect
348. C2×#421D11semidirect
469. C22×M16C2×D11semidirect
476. C2×#117C2×D11semidirect
481. #421C2×D11semidirect
490. C2×#104C2×D11semidirect
576. C2×#41C4×D11semidirect
577. C2×#41C4×D11semidirect
585. C22×Q8C4×D11semidirect
597. C22×D4C4×D11semidirect
617. C2×M16C22×D11semidirect
627. #117C22×D11semidirect
646. #104C22×D11semidirect
652. C2×C11#2901semidirect
701. #41C2×C4×D11semidirect
719. C2×Q8C2×C4×D11semidirect
754. C2×D4C2×C4×D11semidirect
818. C11C2×#2901semidirect
953. C2#13077162direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106234532
C2×#106232762
C2×#106230532
#130771622
C2×#106226182
C2×#106224342
C22×#669012
C22×#668892
C2×D11×#1042
C2×C11×#4212
C2×#290111