Finite Group Databasebeta

← #15620443

Subgroups — #15620443

Order 2816.

4764 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623453C211yesmaximal, characteristic, complemented
2C2×#10623353C212yesmaximal, complemented
3#13077994C214yesmaximal, complemented
4#13077987C214yesmaximal, complemented
5#13077979C214yesmaximal, complemented
6#13077972C214yesmaximal, complemented
7#13077964C218yesmaximal, complemented
8C2×#10622618C212yesmaximal, complemented
9C2×#10622850C211yesmaximal, characteristic, complemented
10C11×#3449C211yesmaximal, characteristic, complemented
11C22×C11×#41C2211yescharacteristic
12C22×C11×#41C2211yescharacteristic, complemented
13#10623453—22no—
14#10623453—22no—
15#10623453—24no—
16#10623453—24no—
17#10623453C2214yes—
18#10623453C2214yescomplemented
19C2×#67043—22no—
20C2×#67042—22no—
21C2×#41×D11—24no—
22C2×#67040C2212yescomplemented
23C2×#67037—22no—
24C2×#67037C2212yescomplemented
25C22×#4339—22no—
26C22×#4339C2212yes—
27C11×#537—22no—
28C11×#536C2212yescomplemented
29C11×#536C2212yescomplemented
30C11×#535C2212yescomplemented
31C11×#535C2212yescomplemented
32C11×#534—22no—
33C11×#532C2214yescomplemented
34C11×#525—22no—
35C11×#525—22no—
36C2×C11×#117C2211yescharacteristic, complemented
37C2×#67004—22no—
38#10623353—24no—
39#10623353—24no—
40#10623353C2218yescomplemented
41#10623353C2218yescomplemented
42C2×#67003—24no—
43C2×#67002—22no—
44C2×#66995C2214yescomplemented
45C2×#66985C2214yescomplemented
46C22×#4318C2212yescomplemented
47#10622850C2214yescomplemented
48#10622850C2214yescomplemented
49C2×#66900C2212yescomplemented
50C2×#66897C2212yescomplemented
51#10622708C22116yescomplemented
52#10622690C22116yescomplemented
53#10622675C22116yescomplemented
54#10622674C22116yescomplemented
55#10622618C2218yescomplemented
56#10622618C2218yescomplemented
57C2×#66869C2218yescomplemented
58C2×C11×#41—22no—
59C2×C11×#41—22no—
60C2×C11×#41—22no—
61C2×C11×#41—22no—
62C2×C11×#41—21no—
63C2×C11×#41—21no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41D412yes—
69C2×C11×#41D412yes—
70C2×C11×#41C2312yes—
71C2×C11×#41C2312yes—
72C2×C11×#41C2312yes—
73C2×C11×#41C2312yescomplemented
74C22×Q8×C11C2311yescharacteristic
75C22×Q8×C11C2311yescharacteristic, complemented
76C22×D4×C11—21no—
77C22×D4×C11D412yes—
78C22×D4×C11C2311yescharacteristic
79C22×D4×C11C2311yescharacteristic, complemented
80C23×C4×C11—21no—
81C23×C4×C11D412yes—
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—24no—
84C22×C22⋊D11—22no—
85#67043—28no—
86#67043—28no—
87#67043—28no—
88#67043—28no—
89#67042—28no—
90#67042—28no—
91#67042—28no—
92#67042—28no—
93#41×D11—216no—
94#41×D11—216no—
95#41×D11—216no—
96#41×D11—216no—
97#67040—24no—
98#67040—28no—
99#67040C2318yes—
100C2×#4343—24no—
101C2×Q8×D11—24no—
102#67037—216no—
103#67037—28no—
104#67037—28no—
105#67037—24no—
106#67037—28no—
107#67037C2318yes—
108C2×#4341—28no—
109C2×#4341—24no—
110C2×D4×D11—28no—
111C2×D4×D11—24no—
112C2×#4339—24no—
113C2×#4339—24no—
114C2×#4339—28no—
115C2×#4339—28no—
116C2×#4339—22no—
117C2×#4339—24no—
118C2×#4339—28no—
119C2×#4339—28no—
120C2×#4339—22no—
121C2×#4339—22no—
122C2×#4339—22no—
123C2×#4339—22no—
124C2×#4339—22no—
125C2×#4339D414yescomplemented
126C2×#4339D414yescomplemented
127C2×#4339D414yescomplemented
128C2×#4339C2314yes—
129C2×#4339C2314yes—
130C2×#4339C2314yes—
131C22×D44—22no—
132C22×D44D412yescomplemented
133C22×C4×D11—24no—
134C22×C4×D11—22no—
135C22×Dic22—22no—
136C22×Dic22D412yescomplemented
137C11×C4⋊Q8C2314yescomplemented
138C11×#127C2314yescomplemented
139C11×#124C2314yescomplemented
140C11×#124C2314yescomplemented
141C11×#123—24no—
142C11×#123—24no—
143C11×C22⋊Q8—24no—
144C11×C22⋊Q8—24no—
145C11×#121—24no—
146C11×#121—28no—
147C11×#121—24no—
148C11×#120—24no—
149C11×#120—24no—
150C4×D4×C11—28no—
151C11×#117—21no—
152C11×#117—21no—
153C11×#117C2312yes—
154C11×#117C2312yescomplemented
155C2×C11×C4⋊C4—21no—
156C2×C11×C22⋊C4—21no—
157C2×C42×C11C2312yescomplemented
158#67004—28no—
159#67004—28no—
160#67003—216no—
161#67003—216no—
162#67002—28no—
163#67002—28no—
164C2×#4326—24no—
165#66995—28no—
166#66995C23116yescomplemented
167C2×#4325—24no—
168C2×#4324—24no—
169#66985—28no—
170#66985C23116yescomplemented
171C2×#4323—24no—
172C2×#4318—22no—
173C2×#4318—22no—
174C2×#4318—22no—
175C2×#4318C2314yes—
176C2×#4318C2314yescomplemented
177C2×#4318C2314yescomplemented
178C22×C11⋊C8—22no—
179#66900C2318yescomplemented
180#66897C2318yescomplemented
181#66869C23132yescomplemented
182#60387—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D412yes—
185C24×C11C2×D411yescharacteristic
186C23×D11—24no—
187C23×D11—22no—
188C11×#41—24no—
189C11×#41—24no—
190C11×#41—24no—
191C11×#41—24no—
192C11×#41—24no—
193C11×#41—24no—
194C11×#41—24no—
195C11×#41—24no—
196C11×#41—24no—
197C11×#41—24no—
198C11×#41—24no—
199C11×#41—24no—
200C11×#41—41no—
201C11×#41—42no—
202C11×#41—41no—
203C11×#41—42no—
204C11×#41—41no—
205C11×#41—41no—
206C2×Q8×C11—22no—
207C2×Q8×C11—22no—
208C2×Q8×C11—21no—
209C2×Q8×C11—22no—
210C2×Q8×C11—22no—
211C2×Q8×C11C2×D412yes—
212C2×Q8×C11C2412yes—
213C2×Q8×C11C2412yes—
214C2×D4×C11—24no—
215C2×D4×C11—24no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—28no—
219C2×D4×C11—22no—
220C2×D4×C11—22no—
221C2×D4×C11—22no—
222C2×D4×C11—22no—
223C2×D4×C11—21no—
224C2×D4×C11—42no—
225C2×D4×C11—42no—
226C2×D4×C11C2×D414yes—
227C2×D4×C11C2×D414yes—
228C2×D4×C11C2×D412yes—
229C2×D4×C11C2412yes—
230C2×D4×C11C2412yes—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—21no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—42no—
240C22×C4×C11—42no—
241C22×C4×C11C2×D414yes—
242C22×C4×C11C2×D414yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2×D412yes—
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2411yescharacteristic
254C2×C22⋊D11—28no—
255C2×C22⋊D11—216no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—24no—
259C2×C22⋊D11—24no—
260C2×C22⋊D11—216no—
261C2×C22⋊D11—24no—
262C2×C22⋊D11—24no—
263C22×Dic11—24no—
264C22×Dic11—22no—
265#4343—216no—
266#4343—216no—
267Q8×D11—216no—
268Q8×D11—216no—
269#4341—232no—
270#4341—232no—
271#4341—216no—
272#4341—216no—
273D4×D11—232no—
274D4×D11—232no—
275D4×D11—216no—
276D4×D11—216no—
277#4339—216no—
278#4339—216no—
279#4339—216no—
280#4339—216no—
281#4339—216no—
282#4339—24no—
283#4339—24no—
284#4339—24no—
285#4339—24no—
286#4339—24no—
287#4339—24no—
288#4339—24no—
289#4339—24no—
290#4339—216no—
291#4339—24no—
292#4339—24no—
293#4339—24no—
294#4339—24no—
295#4339C2×D418yes—
296#4339C2×D418yes—
297#4339C2×D418yes—
298#4339C2418yes—
299C2×D44—24no—
300C2×D44—28no—
301C2×D44—28no—
302C2×D44—22no—
303C2×D44—22no—
304C2×D44—22no—
305C2×D44C2×D414yes—
306C2×D44C2×D414yes—
307C2×D44C2×D414yes—
308C2×C4×D11—28no—
309C2×C4×D11—216no—
310C2×C4×D11—216no—
311C2×C4×D11—24no—
312C2×C4×D11—24no—
313C2×C4×D11—24no—
314C2×C4×D11—24no—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×Dic22—24no—
318C2×Dic22—28no—
319C2×Dic22—28no—
320C2×Dic22—22no—
321C2×Dic22—22no—
322C2×Dic22—22no—
323C2×Dic22C2×D414yes—
324C2×Dic22C2×D414yes—
325C2×Dic22C2×D414yes—
326C11×C4⋊C4—22no—
327C11×C4⋊C4—22no—
328C11×C4⋊C4—28no—
329C11×C22⋊C4—22no—
330C11×C22⋊C4—22no—
331C11×C22⋊C4—28no—
332C11×C22⋊C4—28no—
333C42×C11—22no—
334C42×C11C2414yes—
335#4326—216no—
336#4325—216no—
337#4324—216no—
338#4323—216no—
339#4318—24no—
340#4318—24no—
341#4318—24no—
342#4318C2418yes—
343C2×C11⋊C8—24no—
344C2×C11⋊C8—24no—
345C2×C11⋊C8—24no—
346C2×#585—111no—
347C2×#575—112no—
348#3449D1111yescharacteristic, complemented
349#3022—114no—
350#3021—114no—
351#3020—114no—
352#3019—114no—
353#3018—118no—
354C2×#421—112no—
355C2×#413—111no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—42no—
360C23×C11—81no—
361C23×C11—82no—
362C23×C11—82no—
363C23×C11#12012yes—
364C23×C11#12012yes—
365C23×C11C22×D414yes—
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C22×D411yescharacteristic
369C22×D11—24no—
370C22×D11—216no—
371C22×D11—24no—
372C22×D11—24no—
373C22×D11—84no—
374C22×D11—88no—
375Q8×C11—24no—
376Q8×C11—24no—
377Q8×C11—24no—
378Q8×C11—41no—
379Q8×C11—41no—
380D4×C11—28no—
381D4×C11—28no—
382D4×C11—24no—
383D4×C11—24no—
384D4×C11—24no—
385D4×C11—42no—
386D4×C11—42no—
387D4×C11—44no—
388D4×C11—41no—
389D4×C11—41no—
390D4×C11—88no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—24no—
394C2×C4×C11—24no—
395C2×C4×C11—24no—
396C2×C4×C11—24no—
397C2×C4×C11—24no—
398C2×C4×C11—22no—
399C2×C4×C11—42no—
400C2×C4×C11—42no—
401C2×C4×C11—44no—
402C2×C4×C11—42no—
403C2×C4×C11—82no—
404C2×C4×C11#12011yescharacteristic
405C2×C4×C11#12012yes—
406C2×C4×C11#12012yes—
407C2×C4×C11#12011yescharacteristic
408C2×C4×C11#12012yes—
409C2×C4×C11#12012yes—
410C2×C4×C11#12011yescharacteristic
411C2×C4×C11#12011yescharacteristic
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D412yes—
414C2×C4×C11C22×D412yes—
415C2×C4×C11C22×D412yes—
416C2×C4×C11C22×D412yes—
417C2×C4×C11C22×D412yes—
418C2×C4×C11C22×D414yes—
419C2×C4×C11C22×D411yescharacteristic
420C2×C4×C11C22×D411yescharacteristic
421C2×C4×C11C22×D411yescharacteristic
422C2×C4×C11C2511yescharacteristic
423C22⋊D11—232no—
424C22⋊D11—28no—
425C22⋊D11—28no—
426C22⋊D11—28no—
427C22⋊D11—28no—
428C2×Dic11—216no—
429C2×Dic11—24no—
430C2×Dic11—24no—
431C2×Dic11—24no—
432D44—216no—
433D44—24no—
434D44—24no—
435D44—24no—
436D44C22×D418yes—
437C4×D11—232no—
438C4×D11—28no—
439C4×D11—28no—
440C4×D11—28no—
441C4×D11—28no—
442Dic22—216no—
443Dic22—24no—
444Dic22—24no—
445Dic22—24no—
446Dic22C22×D418yes—
447C11⋊C8—28no—
448#585—114no—
449#585—114no—
450#585—224no—
451#585—224no—
452#585—222no—
453#585—222no—
454C2×2−1+4—112no—
455C2×2−1+4—222no—
456C2×H(5,𝔽2)—112no—
457C2×H(5,𝔽2)—222no—
458C2×H(5,𝔽2)—222no—
459C22×#41—112no—
460C22×#41—224no—
461C22×#41—222no—
462C22×#41C2×D1111yescharacteristic
463C22×#41C2×D1111yescharacteristic, complemented
464#575—118no—
465#575—118no—
466#575—224no—
467#575—224no—
468C2×#137—114no—
469C2×#137—222no—
470C2×AGL(1,ℤ/8)—114no—
471C2×AGL(1,ℤ/8)—222no—
472C2×#135—224no—
473C22×M16—112no—
474#537—22no—
475#536C2×D1112yescomplemented
476#536C2×D1112yescomplemented
477#535C2×D1112yescomplemented
478#535C2×D1112yescomplemented
479#534—22no—
480#532C2×D1114yescomplemented
481#525—22no—
482#525—22no—
483C2×#117C2×D1111yescharacteristic, complemented
484#456—1116no—
485#455—1116no—
486#454—1116no—
487#453—1116no—
488#421—118no—
489#421—118no—
490C2×#104—118no—
491#413—114no—
492#413—114no—
493C2×#101—112no—
494C2×#100—112no—
495C22×C11—24no—
496C22×C11—41no—
497C22×C11—42no—
498C22×C11—41no—
499C22×C11—41no—
500C22×C11—42no—
501C22×C11—44no—
502C22×C11—44no—
503C22×C11—44no—
504C22×C11—42no—
505C22×C11—82no—
506C22×C11—84no—
507C22×C11C2×#12011yescharacteristic
508C22×C11C2×#12011yescharacteristic
509C22×C11C2×#12012yes—
510C22×C11C2×#12012yes—
511C22×C11C23×D411yescharacteristic
512C2×D11—28no—
513C2×D11—48no—
514C2×D11—84no—
515C2×D11—84no—
516C2×D11—816no—
517C4×C11—24no—
518C4×C11—44no—
519C4×C11—42no—
520C4×C11C2×#12011yescharacteristic
521C4×C11C2×#12011yescharacteristic
522C4×C11C2×#12011yescharacteristic
523C4×C11C2×#12012yes—
524C4×C11C2×#12011yescharacteristic
525C4×C11C23×D412yes—
526Dic11—28no—
5272−1+4—118no—
5282−1+4—228no—
5292−1+4—228no—
5302−1+4—228no—
5312−1+4—228no—
5322−1+4—228no—
5332−1+4—224no—
534H(5,𝔽2)—118no—
535H(5,𝔽2)—228no—
536H(5,𝔽2)—2216no—
537H(5,𝔽2)—228no—
538H(5,𝔽2)—228no—
539H(5,𝔽2)—228no—
540H(5,𝔽2)—228no—
541H(5,𝔽2)—224no—
542H(5,𝔽2)—228no—
543H(5,𝔽2)—228no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—114no—
555C2×#41—114no—
556C2×#41—114no—
557C2×#41—114no—
558C2×#41—114no—
559C2×#41—114no—
560C2×#41—224no—
561C2×#41—224no—
562C2×#41—228no—
563C2×#41—228no—
564C2×#41—224no—
565C2×#41—228no—
566C2×#41—224no—
567C2×#41—2216no—
568C2×#41—2216no—
569C2×#41—2216no—
570C2×#41—2216no—
571C2×#41—222no—
572C2×#41—222no—
573C2×#41—222no—
574C2×#41—222no—
575C2×#41—222no—
576C2×#41—222no—
577C2×#41—224no—
578C2×#41—228no—
579C2×#41—228no—
580C2×#41C22⋊D1112yes—
581C2×#41C22⋊D1112yes—
582C2×#41C22×D1112yes—
583C2×#41C22×D1112yes—
584C2×#41C22×D1112yes—
585C2×#41C22×D1112yescomplemented
586C22×Q8—112no—
587C22×Q8—222no—
588C22×Q8—224no—
589C22×Q8C22×D1111yescharacteristic
590C22×Q8C22×D1111yescharacteristic, complemented
591C22×D4—21no—
592C22×D4—112no—
593C22×D4—222no—
594C22×D4—224no—
595C22×D4—228no—
596C22×D4—222no—
597C22×D4—224no—
598C22×D4C22⋊D1112yes—
599C22×D4C22×D1111yescharacteristic
600C22×D4C22×D1111yescharacteristic, complemented
601C23×C4—21no—
602C23×C4—224no—
603C23×C4—222no—
604C23×C4C22⋊D1112yes—
605C23×C4C22×D1111yescharacteristic
606#137—1116no—
607#137—228no—
608#137—228no—
609#137—228no—
610AGL(1,ℤ/8)—1116no—
611AGL(1,ℤ/8)—228no—
612AGL(1,ℤ/8)—228no—
613AGL(1,ℤ/8)—228no—
614#135—2216no—
615#135—2216no—
616C2×Q16—224no—
617C2×SD16—224no—
618C2×SD16—224no—
619C2×D8—224no—
620C2×M16—114no—
621C2×M16—114no—
622C2×M16—114no—
623C2×M16—222no—
624C2×M16—222no—
625C2×M16—222no—
626C22×C8—222no—
627C4⋊Q8C22×D1114yescomplemented
628#127C22×D1114yescomplemented
629#124C22×D1114yescomplemented
630#124C22×D1114yescomplemented
631#123—24no—
632#123—24no—
633C22⋊Q8—24no—
634C22⋊Q8—24no—
635#121—24no—
636#121—28no—
637#121—24no—
638#120—24no—
639#120—24no—
640C4×D4—28no—
641#117—21no—
642#117—21no—
643#117C22×D1112yes—
644#117C22×D1112yescomplemented
645C2×C4⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C42C22×D1112yescomplemented
648#104—1132no—
649#101—118no—
650#100—118no—
651C2×C11—21no—
652C2×C11—21no—
653C2×C11—22no—
654C2×C11—22no—
655C2×C11—21no—
656C2×C11—44no—
657C2×C11—82no—
658C2×C11C22×#12011yescharacteristic
659D11—48no—
660C24—21no—
661C24—224no—
662C24—222no—
663C24C2×C22⋊D1112yes—
664C24C2×C22⋊D1111yescharacteristic
665#41—24no—
666#41—24no—
667#41—24no—
668#41—24no—
669#41—24no—
670#41—24no—
671#41—24no—
672#41—24no—
673#41—24no—
674#41—24no—
675#41—24no—
676#41—24no—
677#41—41no—
678#41—41no—
679#41—42no—
680#41—42no—
681#41—41no—
682#41—41no—
683#41—118no—
684#41—118no—
685#41—118no—
686#41—118no—
687#41—2216no—
688#41—2216no—
689#41—2216no—
690#41—2216no—
691#41—2216no—
692#41—2216no—
693#41—2232no—
694#41—2232no—
695#41—2216no—
696#41—2216no—
697#41—2216no—
698#41—224no—
699#41—224no—
700#41—224no—
701#41—224no—
702#41—224no—
703#41—224no—
704#41—224no—
705#41—224no—
706#41—224no—
707#41—224no—
708#41—224no—
709#41—224no—
710#41—2216no—
711C2×Q8—22no—
712C2×Q8—22no—
713C2×Q8—21no—
714C2×Q8—22no—
715C2×Q8—22no—
716C2×Q8—114no—
717C2×Q8—114no—
718C2×Q8—114no—
719C2×Q8—224no—
720C2×Q8—228no—
721C2×Q8—228no—
722C2×Q8—2216no—
723C2×Q8—2216no—
724C2×Q8—222no—
725C2×Q8—222no—
726C2×Q8—222no—
727C2×Q8C2×C22⋊D1112yes—
728C2×Q8C23×D1112yes—
729C2×Q8C23×D1112yes—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—28no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—22no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—114no—
743C2×D4—114no—
744C2×D4—114no—
745C2×D4—224no—
746C2×D4—228no—
747C2×D4—228no—
748C2×D4—2216no—
749C2×D4—2232no—
750C2×D4—2232no—
751C2×D4—2216no—
752C2×D4—228no—
753C2×D4—2216no—
754C2×D4—224no—
755C2×D4—224no—
756C2×D4—224no—
757C2×D4—224no—
758C2×D4—224no—
759C2×D4—224no—
760C2×D4—2216no—
761C2×D4—222no—
762C2×D4—222no—
763C2×D4—222no—
764C2×D4C2×C22⋊D1114yes—
765C2×D4C2×C22⋊D1112yes—
766C2×D4C2×C22⋊D1114yes—
767C2×D4C23×D1112yes—
768C2×D4C23×D1112yes—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—228no—
780C22×C4—2216no—
781C22×C4—2216no—
782C22×C4—224no—
783C22×C4—222no—
784C22×C4—224no—
785C22×C4—224no—
786C22×C4—224no—
787C22×C4—224no—
788C22×C4—224no—
789C22×C4—224no—
790C22×C4D4×D1112yes—
791C22×C4D4×D1112yes—
792C22×C4D4×D1112yes—
793C22×C4D4×D1112yes—
794C22×C4C2×C22⋊D1114yes—
795C22×C4C2×C22⋊D1114yes—
796C22×C4C2×C22⋊D1112yes—
797C22×C4C2×C22⋊D1111yescharacteristic
798C22×C4C2×C22⋊D1111yescharacteristic
799C22×C4C2×C22⋊D1111yescharacteristic
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803Q16—2216no—
804SD16—2216no—
805SD16—2216no—
806D8—2216no—
807M16—118no—
808M16—224no—
809M16—224no—
810M16—224no—
811C2×C8—224no—
812C2×C8—224no—
813C2×C8—224no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—28no—
817C22⋊C4—22no—
818C22⋊C4—22no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C42—22no—
822C42C23×D1114yes—
823C11#6038711yescharacteristic, complemented, Sylow
824C23—22no—
825C23—22no—
826C23—22no—
827C23—42no—
828C23—81no—
829C23—82no—
830C23—82no—
831C23—2216no—
832C23—224no—
833C23—224no—
834C23—224no—
835C23—884no—
836C23—888no—
837C23#6699012yes—
838C23#6699012yes—
839C23C22×C22⋊D1114yes—
840C23C22×C22⋊D1111yescharacteristic
841C23C22×C22⋊D1111yescharacteristic
842C23C22×C22⋊D1111yescharacteristic
843Q8—24no—
844Q8—24no—
845Q8—24no—
846Q8—41no—
847Q8—41no—
848Q8—118no—
849Q8—2216no—
850Q8—224no—
851Q8—224no—
852Q8—224no—
853D4—28no—
854D4—28no—
855D4—24no—
856D4—24no—
857D4—24no—
858D4—42no—
859D4—42no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—88no—
864D4—118no—
865D4—2216no—
866D4—2232no—
867D4—228no—
868D4—228no—
869D4—228no—
870D4—228no—
871D4—224no—
872D4—224no—
873D4—224no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—22no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—42no—
886C2×C4—82no—
887C2×C4—2232no—
888C2×C4—2216no—
889C2×C4—224no—
890C2×C4—224no—
891C2×C4—224no—
892C2×C4—228no—
893C2×C4—228no—
894C2×C4—228no—
895C2×C4—228no—
896C2×C4#6699011yescharacteristic
897C2×C4#6699011yescharacteristic
898C2×C4#6699012yes—
899C2×C4#6699012yes—
900C2×C4#6699012yes—
901C2×C4#6699011yescharacteristic
902C2×C4#6699011yescharacteristic
903C2×C4#6699012yes—
904C2×C4C2×D4×D1112yes—
905C2×C4C2×D4×D1112yes—
906C2×C4C2×D4×D1112yes—
907C2×C4C2×D4×D1112yes—
908C2×C4C2×D4×D1112yes—
909C2×C4C2×D4×D1112yes—
910C2×C4C22×C22⋊D1114yes—
911C2×C4C22×C22⋊D1111yescharacteristic
912C2×C4C22×C22⋊D1111yescharacteristic
913C2×C4C22×C22⋊D1111yescharacteristic
914C2×C4C24×D1111yescharacteristic
915C8—228no—
916C22—24no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—42no—
926C22—82no—
927C22—84no—
928C22—228no—
929C22—448no—
930C22—884no—
931C22—884no—
932C22—8816no—
933C22C2×#6699011yescharacteristic
934C22C2×#6699011yescharacteristic
935C22C2×#6699012yes—
936C22C2×#6699012yes—
937C22C23×C22⋊D1111yescharacteristic
938C4—24no—
939C4—44no—
940C4—42no—
941C4—228no—
942C4C2×#6699011yescharacteristic
943C4C2×#6699011yescharacteristic
944C4C2×#6699011yescharacteristic
945C4C2×#6699012yes—
946C4C2×#6699011yescharacteristic
947C4C22×D4×D1112yes—
948C2—21no—
949C2—21no—
950C2—22no—
951C2—21no—
952C2—22no—
953C2—44no—
954C2—82no—
955C2—448no—
956C2C22×#6699011yescharacteristic
subgroupG/H
centerC4C2×#66990
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3449C2
socleC2×C11C22×#120
hypercenter#3449D11
hypocenterC11#60387
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#10623453C2semidirect
2. C2×#10623353C2semidirect
3. #13077994C2semidirect
4. #13077987C2semidirect
5. #13077979C2semidirect
6. #13077972C2semidirect
7. #13077964C2semidirect
8. C2×#10622618C2semidirect
9. C2×#10622850C2semidirect
10. C11×#3449C2semidirect
12. C22×C11×#41C22semidirect
18. #10623453C22semidirect
22. C2×#67040C22semidirect
24. C2×#67037C22semidirect
28. C11×#536C22semidirect
29. C11×#536C22semidirect
30. C11×#535C22semidirect
31. C11×#535C22semidirect
33. C11×#532C22semidirect
36. C2×C11×#117C22semidirect
40. #10623353C22semidirect
41. #10623353C22semidirect
44. C2×#66995C22semidirect
45. C2×#66985C22semidirect
46. C22×#4318C22semidirect
47. #10622850C22semidirect
48. #10622850C22semidirect
49. C2×#66900C22semidirect
50. C2×#66897C22semidirect
51. #10622708C22semidirect
52. #10622690C22semidirect
53. #10622675C22semidirect
54. #10622674C22semidirect
55. #10622618C22semidirect
56. #10622618C22semidirect
57. C2×#66869C22semidirect
73. C2×C11×#41C23semidirect
75. C22×Q8×C11C23semidirect
79. C22×D4×C11C23semidirect
125. C2×#4339D4semidirect
126. C2×#4339D4semidirect
127. C2×#4339D4semidirect
132. C22×D44D4semidirect
136. C22×Dic22D4semidirect
137. C11×C4⋊Q8C23semidirect
138. C11×#127C23semidirect
139. C11×#124C23semidirect
140. C11×#124C23semidirect
154. C11×#117C23semidirect
157. C2×C42×C11C23semidirect
166. #66995C23semidirect
170. #66985C23semidirect
176. C2×#4318C23semidirect
177. C2×#4318C23semidirect
179. #66900C23semidirect
180. #66897C23semidirect
181. #66869C23semidirect
348. #3449D11semidirect
463. C22×#41C2×D11semidirect
475. #536C2×D11semidirect
476. #536C2×D11semidirect
477. #535C2×D11semidirect
478. #535C2×D11semidirect
480. #532C2×D11semidirect
483. C2×#117C2×D11semidirect
585. C2×#41C22×D11semidirect
590. C22×Q8C22×D11semidirect
600. C22×D4C22×D11semidirect
627. C4⋊Q8C22×D11semidirect
628. #127C22×D11semidirect
629. #124C22×D11semidirect
630. #124C22×D11semidirect
644. #117C22×D11semidirect
647. C2×C42C22×D11semidirect
823. C11#60387semidirect

Maximal subgroups

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

subgroupindex
C2×#106234532
C2×#106233532
#130779942
#130779872
#130779792
#130779722
#130779642
C2×#106226182
C2×#106228502
C11×#34492
#6038711