Finite Group Databasebeta

← #15626789

Subgroups — #15626789

Order 2816.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2#13080012C214yesmaximal, complemented
3#13079989C212yesmaximal, complemented
4#13079978C212yesmaximal, complemented
5#13079963C214yesmaximal, complemented
6#13079953C212yesmaximal, complemented
7#13079942C212yesmaximal, complemented
8#13078434C212yesmaximal, complemented
9#13078421C211yesmaximal, characteristic, complemented
10#13078413C211yesmaximal, characteristic, complemented
11#13078242C212yesmaximal, complemented
12#13078231C212yesmaximal, complemented
13#13078106C212yesmaximal, complemented
14#13078088C211yesmaximal, characteristic, complemented
15#13078080C211yesmaximal, characteristic, complemented
16C2×#10622537C211yesmaximal, characteristic, complemented
17C2×C11×#529C211yesmaximal, characteristic, complemented
18C11×#529—21no—
19C11×#529—21no—
20C11×#529—21no—
21C11×#529—21no—
22C11×#529C2212yes—
23C11×#529C2212yes—
24C11×#529C2212yes—
25C11×#529C2212yes—
26C2×C11×#126—21no—
27C2×C11×#125C2211yescharacteristic
28C2×C11×#124C2211yescharacteristic
29C2×C11×#123—21no—
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×#121C2211yescharacteristic
32C2×C4×Q8×C11C2211yescharacteristic
33C2×C4×D4×C11—21no—
34C2×C4×D4×C11C2211yescharacteristic
35C2×C11×#117—21no—
36C22×C42×C11C2211yescharacteristic
37C2×#66995C2212yes—
38C2×#66985C2212yes—
39#10623322—21no—
40#10623322—21no—
41#10623322C2212yes—
42C22×#4318C2212yes—
43#10623010—21no—
44#10623010—21no—
45#10623010—21no—
46#10623010—21no—
47#10623010C2212yescomplemented
48#10623010C2212yescomplemented
49#10623008C2211yescharacteristic
50#10623008C2211yescharacteristic, complemented
51#10623008C2211yescharacteristic, complemented
52C4×#4339—21no—
53C4×#4339—21no—
54C4×#4339C2212yes—
55#10623001C2211yescharacteristic
56#10623001C2211yescharacteristic, complemented
57#10623001C2211yescharacteristic, complemented
58#10622838C2212yes—
59#10622828C2212yes—
60#10622679C2214yescomplemented
61#10622679C2214yescomplemented
62#10622676C2214yescomplemented
63#10622676C2214yescomplemented
64#10622670C2214yescomplemented
65#10622670C2214yescomplemented
66#10622667C2214yescomplemented
67#10622667C2214yescomplemented
68#10622665C2214yescomplemented
69#10622664C2214yescomplemented
70#10622662C2214yescomplemented
71#10622661C2214yescomplemented
72#10622655C2214yes—
73#10622654C2214yes—
74#10622652C2214yes—
75#10622651C2214yes—
76#10622644C2212yescomplemented
77#10622641C2214yescomplemented
78#10622640C2212yescomplemented
79#10622635C2214yescomplemented
80#10622634C2212yescomplemented
81#10622633C2212yescomplemented
82#10622632C2212yescomplemented
83#10622629C2214yescomplemented
84#10622628C2212yescomplemented
85#10622622C2214yescomplemented
86#10622621C2212yescomplemented
87#10622620C2212yescomplemented
88#10622579C2212yes—
89#10622579C2212yes—
90#10622577C2212yes—
91#10622577C2212yes—
92#10622537C2211yescharacteristic
93#10622537C2211yescharacteristic
94#10622537C2212yes—
95#10622537C2212yescomplemented
96#10622537C2212yescomplemented
97C2×C4⋊(C11⋊C8)C2212yescomplemented
98C2×C4⋊(C11⋊C8)C2212yescomplemented
99C22×Q8×C11C2311yescharacteristic
100C22×D4×C11—21no—
101C22×D4×C11C2311yescharacteristic
102C23×C4×C11—21no—
103C23×C4×C11D411yescharacteristic
104C23×C4×C11D411yescharacteristic
105C23×C4×C11C2311yescharacteristic
106C2×#4339—21no—
107C2×#4339—21no—
108C2×#4339C2312yes—
109C11×#126—22no—
110C11×#126—22no—
111C11×#126—22no—
112C11×#126—22no—
113C11×#125—21no—
114C11×#125—21no—
115C11×#125C2312yes—
116C11×#125C2312yes—
117C11×#124—21no—
118C11×#124—21no—
119C11×#124C2312yes—
120C11×#124C2312yes—
121C11×#123—22no—
122C11×#123—22no—
123C11×#123—22no—
124C11×#123—22no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8C2312yes—
128C11×C22⋊Q8C2312yes—
129C11×#121—21no—
130C11×#121—21no—
131C11×#121C2312yes—
132C11×#121C2312yes—
133C4×Q8×C11—21no—
134C4×Q8×C11—21no—
135C4×Q8×C11C2312yes—
136C4×Q8×C11C2312yes—
137C4×D4×C11—22no—
138C4×D4×C11—22no—
139C4×D4×C11—22no—
140C4×D4×C11—22no—
141C4×D4×C11—21no—
142C4×D4×C11—21no—
143C4×D4×C11C2312yes—
144C4×D4×C11C2312yes—
145C11×#117—22no—
146C11×#117—22no—
147C11×#117—22no—
148C11×#117—22no—
149C2×C11×C4⋊C4—21no—
150C2×C11×C4⋊C4—21no—
151C2×C11×C4⋊C4—21no—
152C2×C11×C4⋊C4—21no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C22⋊C4—21no—
156C2×C11×C22⋊C4—21no—
157C2×C11×C22⋊C4—21no—
158C2×C11×C22⋊C4—21no—
159C2×C11×C22⋊C4—21no—
160C2×C42×C11—21no—
161C2×C42×C11D411yescharacteristic
162C2×C42×C11D411yescharacteristic
163C2×C42×C11D411yescharacteristic
164C2×C42×C11D411yescharacteristic
165C2×C42×C11D411yescharacteristic
166C2×C42×C11D411yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173#67006—22no—
174C2×#4326C2314yes—
175#66995—44no—
176C2×#4325C2314yes—
177C2×#4324C2314yes—
178#66985—44no—
179C2×#4323C2314yes—
180#66983—21no—
181#66983—21no—
182#66983—21no—
183#66983—21no—
184#66983C2312yes—
185#66983C2312yes—
186#66982—22no—
187#66982—22no—
188#66982—22no—
189C4×C22⋊D11—22no—
190C4×C22⋊D11—22no—
191C4×C22⋊D11—22no—
192C4×C22⋊D11—22no—
193C4×C22⋊D11—22no—
194C4×C22⋊D11—22no—
195#66979—21no—
196#66979—21no—
197#66979C2312yes—
198#66977—21no—
199#66977—21no—
200#66977—21no—
201#66977—21no—
202#66977C2312yes—
203#66977C2312yes—
204C2×#4318—44no—
205C2×#4318C2312yes—
206C2×#4318C2312yes—
207C2×#4318C2314yes—
208C22×C11⋊C8C2314yes—
209#66929—22no—
210#66929—22no—
211#66928—21no—
212#66928—21no—
213#66928C2312yes—
214#66927C2311yescharacteristic
215C4×D44—21no—
216C4×D44—21no—
217C4×D44—21no—
218C4×D44—21no—
219C4×D44C2312yes—
220C4×D44C2312yes—
221#66925—22no—
222#66925—22no—
223#66925—22no—
224C42×D11—22no—
225#66923—21no—
226#66923—21no—
227#66923C2312yes—
228#66922C2311yescharacteristic
229#66922C2311yescharacteristic
230#66922C2311yescharacteristic
231C4×Dic22—21no—
232C4×Dic22—21no—
233C4×Dic22—21no—
234C4×Dic22—21no—
235C4×Dic22C2312yes—
236C4×Dic22C2312yes—
237#66899C2314yes—
238#66899C2314yes—
239#66896C2314yes—
240#66896C2314yes—
241#66874C2314yes—
242#66874C2314yes—
243#66873C2314yes—
244#66873C2314yes—
245#66872C2314yes—
246#66872C2314yes—
247#66871C2314yes—
248#66871C2314yes—
249C4⋊(C11⋊C8)C2312yes—
250C4⋊(C11⋊C8)C2312yes—
251C4⋊(C11⋊C8)C2312yes—
252C4⋊(C11⋊C8)C2312yes—
253C4⋊(C11⋊C8)C2314yes—
254C4⋊(C11⋊C8)C2314yes—
255#60917—111nomaximal, Sylow
256C24×C11—21no—
257C24×C11C2×D411yescharacteristic
258C2×Q8×C11—21no—
259C2×Q8×C11—22no—
260C2×Q8×C11—22no—
261C2×Q8×C11C2412yes—
262C2×D4×C11—22no—
263C2×D4×C11—22no—
264C2×D4×C11—21no—
265C2×D4×C11—22no—
266C2×D4×C11—22no—
267C2×D4×C11—44no—
268C2×D4×C11C2412yes—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—21no—
274C22×C4×C11—22no—
275C22×C4×C11—22no—
276C22×C4×C11—42no—
277C22×C4×C11—42no—
278C22×C4×C11—44no—
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2×D411yescharacteristic
285C22×C4×C11C2×D411yescharacteristic
286C22×C4×C11C2×D411yescharacteristic
287C22×C4×C11C2×D411yescharacteristic
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2×D411yescharacteristic
292C22×C4×C11C2×D411yescharacteristic
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300#4339—24no—
301#4339—24no—
302#4339—44no—
303#4339—44no—
304C2×D44—21no—
305C2×D44—21no—
306C2×D44C2412yes—
307C2×C4×D11—22no—
308C2×C4×D11—22no—
309C2×C4×D11—22no—
310C2×Dic22—21no—
311C2×Dic22—21no—
312C2×Dic22C2412yes—
313C11×C4⋊C4—22no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—22no—
317C11×C4⋊C4—22no—
318C11×C4⋊C4—22no—
319C11×C4⋊C4—22no—
320C11×C4⋊C4—22no—
321C11×C4⋊C4—21no—
322C11×C4⋊C4—21no—
323C11×C4⋊C4C2412yes—
324C11×C4⋊C4C2412yes—
325C11×C22⋊C4—22no—
326C11×C22⋊C4—22no—
327C11×C22⋊C4—22no—
328C11×C22⋊C4—22no—
329C11×C22⋊C4—22no—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—22no—
332C11×C22⋊C4—22no—
333C11×C22⋊C4—22no—
334C11×C22⋊C4—22no—
335C42×C11—22no—
336C42×C11—22no—
337C42×C11C2×D411yescharacteristic
338C42×C11C2×D411yescharacteristic
339C42×C11C2×D411yescharacteristic
340C42×C11C2×D411yescharacteristic
341C42×C11C2×D411yescharacteristic
342C42×C11C2×D411yescharacteristic
343C42×C11C2×D411yescharacteristic
344C42×C11C2×D411yescharacteristic
345C42×C11C2×D411yescharacteristic
346C42×C11C2×D411yescharacteristic
347C42×C11C2×D411yescharacteristic
348C42×C11C2×D411yescharacteristic
349C42×C11C2411yescharacteristic
350C42×C11C2411yescharacteristic
351C42×C11C2411yescharacteristic
352C42×C11C2411yescharacteristic
353C22⋊Dic11—22no—
354C22⋊Dic11—22no—
355C22⋊Dic11—22no—
356#4326—44no—
357#4325—44no—
358#4324—44no—
359#4323—44no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—22no—
363(C2×D11)⋊C4—22no—
364(C2×D11)⋊C4—22no—
365(C2×D11)⋊C4—22no—
366C4⋊Dic11—21no—
367C4⋊Dic11—21no—
368C4⋊Dic11—21no—
369C4⋊Dic11—21no—
370C4⋊Dic11C2412yes—
371C4⋊Dic11C2412yes—
372Dic11⋊C4—22no—
373Dic11⋊C4—22no—
374Dic11⋊C4—22no—
375Dic11⋊C4—22no—
376Dic11⋊C4—22no—
377Dic11⋊C4—22no—
378C4×Dic11—22no—
379C4×Dic11—22no—
380C4×Dic11—22no—
381#4318—24no—
382#4318—24no—
383#4318—44no—
384C2×C11⋊C8—44no—
385C2×C11⋊C8C2414yes—
386C2×C11⋊C8C2414yes—
387#3444—111no—
388C2×#529D1111yescharacteristic, complemented
389#3256—114no—
390#3252—112no—
391#3251—112no—
392#3250—114no—
393#3248—112no—
394#3247—112no—
395#3080—112no—
396#3078—111no—
397#3077—111no—
398#3056—112no—
399#3055—112no—
400#3040—112no—
401#3037—111no—
402#3036—111no—
403C2×#423—111no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—41no—
408C23×C11—42no—
409C23×C11—42no—
410C23×C11—42no—
411C23×C11C22×D411yescharacteristic
412C23×C11C22×D411yescharacteristic
413C23×C11C22×D411yescharacteristic
414C22×D11—22no—
415Q8×C11—22no—
416Q8×C11—22no—
417Q8×C11—42no—
418D4×C11—22no—
419D4×C11—22no—
420D4×C11—44no—
421D4×C11—44no—
422D4×C11—42no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—21no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—44no—
446C2×C4×C11—42no—
447C2×C4×C11—42no—
448C2×C4×C11—42no—
449C2×C4×C11—44no—
450C2×C4×C11C22×D411yescharacteristic
451C2×C4×C11C22×D411yescharacteristic
452C2×C4×C11C22×D411yescharacteristic
453C2×C4×C11C22×D411yescharacteristic
454C2×C4×C11C22×D411yescharacteristic
455C2×C4×C11C22×D411yescharacteristic
456C2×C4×C11C22×D411yescharacteristic
457C2×C4×C11C22×D411yescharacteristic
458C2×C4×C11C22×D411yescharacteristic
459C2×C4×C11C22×D411yescharacteristic
460C2×C4×C11C22×D411yescharacteristic
461C2×C4×C11H(5,𝔽2)12yes—
462C2×C4×C112−1+412yes—
463C2×C4×C11C2511yescharacteristic
464C22⋊D11—44no—
465C22⋊D11—44no—
466C22⋊D11—44no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470D44—22no—
471D44—22no—
472D44—42no—
473D44—42no—
474C4×D11—44no—
475C4×D11—44no—
476C4×D11—44no—
477Dic22—22no—
478Dic22—22no—
479Dic22—42no—
480Dic22—42no—
481C11⋊C8—24no—
482C11⋊C8—24no—
483C2×#137—112no—
484C2×AGL(1,ℤ/8)—112no—
485C22×M16—112no—
486#533—111no—
487#533—111no—
488#533—111no—
489#532—111no—
490#532—111no—
491#532—111no—
492#529—21no—
493#529—21no—
494#529—21no—
495#529—21no—
496#529—112no—
497#529—112no—
498#529—221no—
499#529—221no—
500#529—221no—
501#529—221no—
502#529C2×D1112yes—
503#529C2×D1112yes—
504#529C2×D1112yes—
505#529C2×D1112yes—
506C2×#126—21no—
507C2×#125C2×D1111yescharacteristic
508C2×#124C2×D1111yescharacteristic
509#525—112no—
510#525—221no—
511#525—221no—
512C2×#123—21no—
513C2×C22⋊Q8C2×D1111yescharacteristic
514C2×#121C2×D1111yescharacteristic
515C4×#41—112no—
516C4×#41—221no—
517C4×#41—221no—
518C2×C4×Q8C2×D1111yescharacteristic
519C2×C4×D4—21no—
520C2×C4×D4C2×D1111yescharacteristic
521C2×#117—21no—
522C22×C42C2×D1111yescharacteristic
523#479—114no—
524#479—114no—
525#479—114no—
526#478—114no—
527#478—114no—
528#478—114no—
529#477—112no—
530#476—112no—
531#475—112no—
532#474—112no—
533#470—114no—
534#469—114no—
535#468—114no—
536#468—114no—
537#467—114no—
538#466—114no—
539#465—114no—
540#465—114no—
541#464—114no—
542#464—114no—
543#464—114no—
544#463—114no—
545#463—114no—
546#463—114no—
547#462—112no—
548#461—112no—
549#460—112no—
550#459—112no—
551#428—112no—
552#428—112no—
553#423—111no—
554#423—111no—
555#423—112no—
556#423—112no—
557#423—112no—
558C2×C4⋊C8—112no—
559C2×C4⋊C8—112no—
560#419—112no—
561#418—112no—
562#417—112no—
563#417—112no—
564C22×C11—21no—
565C22×C11—21no—
566C22×C11—21no—
567C22×C11—21no—
568C22×C11—21no—
569C22×C11—21no—
570C22×C11—21no—
571C22×C11—44no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—84no—
576C22×C11#53712yes—
577C22×C11#57512yes—
578C22×C11C23×D411yescharacteristic
579C2×D11—42no—
580C2×D11—42no—
581C2×D11—42no—
582C4×C11—21no—
583C4×C11—21no—
584C4×C11—21no—
585C4×C11—21no—
586C4×C11—21no—
587C4×C11—21no—
588C4×C11—21no—
589C4×C11—21no—
590C4×C11—21no—
591C4×C11—42no—
592C4×C11—42no—
593C4×C11—42no—
594C4×C11#53712yes—
595C4×C11#57512yes—
596C4×C11C2×H(5,𝔽2)11yescharacteristic
597C4×C11C2×2−1+411yescharacteristic
598Dic11—42no—
599Dic11—42no—
600Dic11—42no—
601C2×#41—112no—
602C2×#41—221no—
603C2×#41—221no—
604C22×Q8C22×D1111yescharacteristic
605C22×D4—21no—
606C22×D4C22×D1111yescharacteristic
607C23×C4—21no—
608C23×C4C22⋊D1111yescharacteristic
609C23×C4C22⋊D1111yescharacteristic
610C23×C4C22×D1111yescharacteristic
611#137—444no—
612AGL(1,ℤ/8)—444no—
613C2×Q16—114no—
614C2×SD16—114no—
615C2×SD16—114no—
616C2×D8—114no—
617C2×M16—112no—
618C2×M16—112no—
619C2×M16—114no—
620C2×M16—444no—
621C22×C8—114no—
622C4⋊Q8—111no—
623C4⋊Q8—111no—
624C4⋊Q8—111no—
625#127—111no—
626#126—22no—
627#126—22no—
628#126—22no—
629#126—22no—
630#126—222no—
631#126—222no—
632#125—21no—
633#125—21no—
634#125—112no—
635#125—221no—
636#125—221no—
637#125C22×D1112yes—
638#125C22×D1112yes—
639#124—21no—
640#124—21no—
641#124—112no—
642#124—221no—
643#124—221no—
644#124C22×D1112yes—
645#124C22×D1112yes—
646#123—22no—
647#123—22no—
648#123—22no—
649#123—22no—
650#123—222no—
651#123—222no—
652#123—222no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—112no—
656C22⋊Q8—112no—
657C22⋊Q8—221no—
658C22⋊Q8—221no—
659C22⋊Q8—221no—
660C22⋊Q8—221no—
661C22⋊Q8C22×D1112yes—
662C22⋊Q8C22×D1112yes—
663#121—21no—
664#121—21no—
665#121—112no—
666#121—112no—
667#121—221no—
668#121—221no—
669#121—221no—
670#121—221no—
671#121C22×D1112yes—
672#121C22×D1112yes—
673#120—222no—
674C4×Q8—21no—
675C4×Q8—21no—
676C4×Q8—112no—
677C4×Q8—112no—
678C4×Q8—221no—
679C4×Q8—221no—
680C4×Q8—221no—
681C4×Q8—221no—
682C4×Q8C22×D1112yes—
683C4×Q8C22×D1112yes—
684C4×D4—22no—
685C4×D4—22no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—21no—
690C4×D4—112no—
691C4×D4—112no—
692C4×D4—222no—
693C4×D4—222no—
694C4×D4—222no—
695C4×D4—222no—
696C4×D4—222no—
697C4×D4—222no—
698C4×D4—221no—
699C4×D4—221no—
700C4×D4—221no—
701C4×D4—221no—
702C4×D4C22×D1112yes—
703C4×D4C22×D1112yes—
704#117—22no—
705#117—22no—
706#117—22no—
707#117—22no—
708#117—112no—
709#117—221no—
710#117—221no—
711#117—222no—
712#117—222no—
713#117—222no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4C22×D1111yescharacteristic
719C2×C4⋊C4C22×D1111yescharacteristic
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C42—21no—
726C2×C42—222no—
727C2×C42C22⋊D1111yescharacteristic
728C2×C42C22⋊D1111yescharacteristic
729C2×C42C22⋊D1111yescharacteristic
730C2×C42C22⋊D1111yescharacteristic
731C2×C42C22⋊D1111yescharacteristic
732C2×C42C22⋊D1111yescharacteristic
733C2×C42C22×D1111yescharacteristic
734C2×C42C22×D1111yescharacteristic
735C2×C42C22×D1111yescharacteristic
736C2×C42C22×D1111yescharacteristic
737C2×C42C22×D1111yescharacteristic
738C2×C42C22×D1111yescharacteristic
739#107—114no—
740#107—114no—
741#106—114no—
742#106—114no—
743C4⋊C8—112no—
744C4⋊C8—112no—
745C4⋊C8—112no—
746C4⋊C8—114no—
747C4⋊C8—114no—
748C4⋊C8—112no—
749#103—114no—
750#103—114no—
751#103—114no—
752#103—114no—
753#102—114no—
754#102—114no—
755#102—114no—
756#102—114no—
757C2×C11—22no—
758C2×C11—22no—
759C2×C11—41no—
760C2×C11—82no—
761C2×C11C2×#53711yescharacteristic
762C2×C11C2×#57511yescharacteristic
763C2×C11C2×#57511yescharacteristic
764D11—82no—
765C24—21no—
766C24C2×C22⋊D1111yescharacteristic
767#41—224no—
768#41—224no—
769#41—444no—
770#41—444no—
771C2×Q8—21no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—112no—
775C2×Q8—221no—
776C2×Q8—221no—
777C2×Q8C23×D1112yes—
778C2×D4—22no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—112no—
785C2×D4—222no—
786C2×D4—222no—
787C2×D4—222no—
788C2×D4—221no—
789C2×D4—221no—
790C2×D4C23×D1112yes—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—44no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4C2×C22⋊D1111yescharacteristic
805C22×C4C2×C22⋊D1111yescharacteristic
806C22×C4C2×C22⋊D1111yescharacteristic
807C22×C4C2×C22⋊D1111yescharacteristic
808C22×C4C2×C22⋊D1111yescharacteristic
809C22×C4C2×C22⋊D1111yescharacteristic
810C22×C4C2×C22⋊D1111yescharacteristic
811C22×C4C2×C22⋊D1111yescharacteristic
812C22×C4C2×C22⋊D1111yescharacteristic
813C22×C4C2×C22⋊D1111yescharacteristic
814C22×C4C2×C22⋊D1111yescharacteristic
815C22×C4C2×C22⋊D1111yescharacteristic
816C22×C4C2×C22⋊D1111yescharacteristic
817C22×C4C2×C22⋊D1111yescharacteristic
818C22×C4C2×C22⋊D1111yescharacteristic
819C22×C4C23×D1111yescharacteristic
820C22×C4C23×D1111yescharacteristic
821C22×C4C23×D1111yescharacteristic
822Q16—444no—
823SD16—444no—
824SD16—444no—
825D8—444no—
826M16—224no—
827M16—224no—
828M16—444no—
829C2×C8—114no—
830C2×C8—114no—
831C2×C8—444no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—112no—
843C4⋊C4—112no—
844C4⋊C4—222no—
845C4⋊C4—222no—
846C4⋊C4—221no—
847C4⋊C4—221no—
848C4⋊C4—221no—
849C4⋊C4—221no—
850C4⋊C4—222no—
851C4⋊C4—222no—
852C4⋊C4—222no—
853C4⋊C4—222no—
854C4⋊C4C23×D1112yes—
855C4⋊C4C23×D1112yes—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—22no—
866C22⋊C4—222no—
867C22⋊C4—222no—
868C22⋊C4—222no—
869C22⋊C4—222no—
870C22⋊C4—222no—
871C22⋊C4—222no—
872C22⋊C4—222no—
873C22⋊C4—222no—
874C22⋊C4—222no—
875C42—22no—
876C42—22no—
877C42—222no—
878C42—222no—
879C42—222no—
880C42C2×C22⋊D1111yescharacteristic
881C42C2×C22⋊D1111yescharacteristic
882C42C2×C22⋊D1111yescharacteristic
883C42C2×C22⋊D1111yescharacteristic
884C42C2×C22⋊D1111yescharacteristic
885C42C2×C22⋊D1111yescharacteristic
886C42C2×C22⋊D1111yescharacteristic
887C42C2×C22⋊D1111yescharacteristic
888C42C2×C22⋊D1111yescharacteristic
889C42C2×C22⋊D1111yescharacteristic
890C42C2×C22⋊D1111yescharacteristic
891C42C2×C22⋊D1111yescharacteristic
892C42C23×D1111yescharacteristic
893C42C23×D1111yescharacteristic
894C42C23×D1111yescharacteristic
895C42C23×D1111yescharacteristic
896C11#6091711yescharacteristic, complemented, Sylow
897C23—22no—
898C23—22no—
899C23—22no—
900C23—41no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—222no—
905C23C22×C22⋊D1111yescharacteristic
906C23C22×C22⋊D1111yescharacteristic
907C23C22×C22⋊D1111yescharacteristic
908Q8—22no—
909Q8—22no—
910Q8—42no—
911Q8—222no—
912Q8—222no—
913Q8—442no—
914Q8—442no—
915D4—22no—
916D4—22no—
917D4—44no—
918D4—44no—
919D4—42no—
920D4—222no—
921D4—222no—
922D4—442no—
923D4—444no—
924D4—444no—
925D4—444no—
926D4—442no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—44no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—44no—
954C2×C4—222no—
955C2×C4—222no—
956C2×C4—222no—
957C2×C4—444no—
958C2×C4—444no—
959C2×C4—444no—
960C2×C4#6704212yes—
961C2×C4#6704312yes—
962C2×C4C22×C22⋊D1111yescharacteristic
963C2×C4C22×C22⋊D1111yescharacteristic
964C2×C4C22×C22⋊D1111yescharacteristic
965C2×C4C22×C22⋊D1111yescharacteristic
966C2×C4C22×C22⋊D1111yescharacteristic
967C2×C4C22×C22⋊D1111yescharacteristic
968C2×C4C22×C22⋊D1111yescharacteristic
969C2×C4C22×C22⋊D1111yescharacteristic
970C2×C4C22×C22⋊D1111yescharacteristic
971C2×C4C22×C22⋊D1111yescharacteristic
972C2×C4C22×C22⋊D1111yescharacteristic
973C2×C4C24×D1111yescharacteristic
974C8—224no—
975C8—224no—
976C22—21no—
977C22—21no—
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—84no—
988C22—442no—
989C22—442no—
990C22—442no—
991C22#1062335312yes—
992C22#1062336412yes—
993C22C23×C22⋊D1111yescharacteristic
994C4—21no—
995C4—21no—
996C4—21no—
997C4—21no—
998C4—21no—
999C4—21no—
1000C4—21no—
1001C4—21no—
1002C4—21no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—442no—
1007C4—442no—
1008C4—442no—
1009C4#1062335312yes—
1010C4#1062336412yes—
1011C4C2×#6704211yescharacteristic
1012C4C2×#6704311yescharacteristic
1013C2—22no—
1014C2—22no—
1015C2—41no—
1016C2—82no—
1017C2—882no—
1018C2C2×#1062336411yescharacteristic
1019C2C2×#1062335311yescharacteristic
1020C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC22×C11C23×D4
hypercenterC2×#529D11
hypocenterC11#60917
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. #13080012C2semidirect
3. #13079989C2semidirect
4. #13079978C2semidirect
5. #13079963C2semidirect
6. #13079953C2semidirect
7. #13079942C2semidirect
8. #13078434C2semidirect
9. #13078421C2semidirect
10. #13078413C2semidirect
11. #13078242C2semidirect
12. #13078231C2semidirect
13. #13078106C2semidirect
14. #13078088C2semidirect
15. #13078080C2semidirect
16. C2×#10622537C2semidirect
17. C2×C11×#529C2semidirect
47. #10623010C22semidirect
48. #10623010C22semidirect
50. #10623008C22semidirect
51. #10623008C22semidirect
56. #10623001C22semidirect
57. #10623001C22semidirect
60. #10622679C22semidirect
61. #10622679C22semidirect
62. #10622676C22semidirect
63. #10622676C22semidirect
64. #10622670C22semidirect
65. #10622670C22semidirect
66. #10622667C22semidirect
67. #10622667C22semidirect
68. #10622665C22semidirect
69. #10622664C22semidirect
70. #10622662C22semidirect
71. #10622661C22semidirect
76. #10622644C22semidirect
77. #10622641C22semidirect
78. #10622640C22semidirect
79. #10622635C22semidirect
80. #10622634C22semidirect
81. #10622633C22semidirect
82. #10622632C22semidirect
83. #10622629C22semidirect
84. #10622628C22semidirect
85. #10622622C22semidirect
86. #10622621C22semidirect
87. #10622620C22semidirect
95. #10622537C22semidirect
96. #10622537C22semidirect
97. C2×C4⋊(C11⋊C8)C22semidirect
98. C2×C4⋊(C11⋊C8)C22semidirect
388. C2×#529D11semidirect
896. C11#60917semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130800122
#130799892
#130799782
#130799632
#130799532
#130799422
#130784342
#130784212
#130784132
#130782422
#130782312
#130781062
#130780882
#130780802
C2×#106225372
C2×C11×#5292
#6091711