Finite Group Databasebeta

← #11058556

Subgroups — #11058556

Order 768.

2778 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5507C211yesmaximal, characteristic, complemented
3#84068C211yesmaximal, characteristic, complemented
4#84066C211yesmaximal, characteristic, complemented
5#84032C211yesmaximal, characteristic, complemented
6C4×#953C211yesmaximal, characteristic, complemented
7#82830C214yesmaximal, complemented
8#82798C214yesmaximal, complemented
9#82779C212yesmaximal, complemented
10#82773C212yesmaximal, complemented
11#82756C212yesmaximal, complemented
12#82752C212yesmaximal, complemented
13#82200C212yesmaximal, complemented
14#82186C212yesmaximal, complemented
15#82159C211yesmaximal, characteristic, complemented
16#82125C212yesmaximal, complemented
17#82106C212yesmaximal, complemented
18#38905—31nomaximal, Sylow
19C23×C3×Q8C2211yescharacteristic
20C24×C3×C4C2211yescharacteristic
21C22×#235C2212yes—
22C2×C3×C22⋊Q8—28no—
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×C22⋊Q8C2214yes—
26C22×C3×C4⋊C4C2212yes—
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2212yes—
29C2×#953C2211yescharacteristic
30C2×#953C2212yes—
31C2×#947C2212yescomplemented
32C2×#946C2212yescomplemented
33C2×#930C2211yescharacteristic
34C2×#930C2212yes—
35C2×#929C2212yes—
36C2×C4×#67C2211yescharacteristic
37C2×C4×#67C2212yes—
38C2×#926C2212yes—
39C2×#896C2212yescomplemented
40#5507—28no—
41C2×#895C2211yescharacteristic, complemented
42C2×#894C2212yescomplemented
43C2×#893C2211yescharacteristic, complemented
44C2×D3×C4⋊C4C2211yescharacteristic, complemented
45C2×#888C2211yescharacteristic, complemented
46#5247C2211yescharacteristic
47#5231C2214yescomplemented
48#5231C2212yescomplemented
49#5230C2212yescomplemented
50#5229C2212yescomplemented
51#5229C2212yescomplemented
52#5213C2211yescharacteristic
53#5213C2212yes—
54#5213C2212yes—
55#5213C2212yes—
56#5213C2212yes—
57#5213C2212yes—
58#5213C2214yes—
59#5212C2212yes—
60#5212C2211yescharacteristic
61#5211C2212yes—
62#5210C2211yescharacteristic
63#5210C2212yes—
64#5210C2212yes—
65C4×#217C2212yes—
66C4×#217C2211yescharacteristic
67#4993C2214yescomplemented
68#4992C2214yescomplemented
69#4988C2214yescomplemented
70#4987C2214yescomplemented
71#4987C2214yescomplemented
72#4985C2214yescomplemented
73#4984C2212yescomplemented
74#4983C2214yescomplemented
75#4980C2214yescomplemented
76Dic3×C4⋊C4C2212yescomplemented
77#4973C2214yescomplemented
78#4961C2214yes—
79#4960C2214yes—
80#4957C2214yes—
81#4956C2214yes—
82#4956C2214yes—
83#4948C2214yes—
84#4947C2214yes—
85#4945C2214yes—
86C2×#547—31no—
87C22×C22⋊Q8D311yescharacteristic, complemented
88#2847—31no—
89#2696—34no—
90#2692—34no—
91#2623—32no—
92#2540—32no—
93#2492—32no—
94#2436—31no—
95#2427—32no—
96#2417—32no—
97#2411—32no—
98#2409—31no—
99#2404—32no—
100#2344—31no—
101#2311—32no—
102C4×#120—31no—
103C25×C3C2311yescharacteristic
104C22×C3×Q8—24no—
105C22×C3×Q8—44no—
106C22×C3×Q8C2312yes—
107C22×C3×Q8C2312yes—
108C23×C3×C4—24no—
109C23×C3×C4—44no—
110C23×C3×C4C2312yes—
111C23×C3×C4C2312yes—
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2312yes—
115C23×C3×C4C2312yes—
116C22×#67C2312yes—
117C22×#67C2312yes—
118C22×#67C2311yescharacteristic
119C22×#67C2314yes—
120C2×#235—28no—
121C2×#235—28no—
122C2×#235—44no—
123C22×D12C2311yescharacteristic
124C22×D12C2312yes—
125C22×C4×D3C2311yescharacteristic
126C22×C4×D3C2312yes—
127C22×C4×D3C2312yes—
128C22×Dic6C2312yes—
129C3×C22⋊Q8—28no—
130C3×C22⋊Q8—28no—
131C3×C22⋊Q8—216no—
132C2×C3×C4⋊C4—28no—
133C2×C3×C4⋊C4D418yescomplemented
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C22⋊C4—28no—
140C2×C3×C22⋊C4C2314yes—
141C2×C3×C22⋊C4C2314yes—
142#953—24no—
143#953—44no—
144C2×#217C2312yes—
145C2×#217C2312yes—
146C2×#217C2311yescharacteristic
147C2×#217C2311yescharacteristic
148C2×#217C2311yescharacteristic
149C2×#217C2312yes—
150C2×#217C2314yes—
151C2×#217C2312yes—
152#947—44no—
153#946—44no—
154#930—24no—
155#930—44no—
156#929—28no—
157C4×#67—24no—
158C4×#67—44no—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2311yescharacteristic
161C2×(C2×D3)⋊C4C2312yes—
162C2×(C2×D3)⋊C4C2312yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2312yes—
167C2×(C2×D3)⋊C4C2314yes—
168#926—44no—
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2312yes—
171C2×C4⋊Dic3C2314yes—
172C2×Dic3⋊C4C2312yes—
173C2×Dic3⋊C4C2312yes—
174C2×Dic3⋊C4C2311yescharacteristic
175C2×Dic3⋊C4C2314yes—
176C2×Dic3⋊C4C2312yes—
177C2×C4×Dic3C2311yescharacteristic
178C2×C4×Dic3C2312yes—
179C2×C4×Dic3C2314yes—
180#896—28no—
181#895—24no—
182#894—28no—
183#893—24no—
184D3×C4⋊C4—24no—
185#888—24no—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2312yes—
193C3⋊#95C2312yes—
194C3⋊#95C2314yes—
195C3⋊#95C2314yes—
196C3⋊#95C2312yes—
197C22×#41—32no—
198C23×Q8C2×D311yescharacteristic
199C24×C4C2×D311yescharacteristic
200#547—68no—
201C2×C4⋊Q8—31no—
202C2×#124—32no—
203C2×#123—32no—
204C2×#123—32no—
205C2×C22⋊Q8—28no—
206C2×C22⋊Q8—32no—
207C2×C22⋊Q8—32no—
208C2×C22⋊Q8C2×D312yes—
209C2×C22⋊Q8C2×D314yes—
210C2×C22⋊Q8C2×D312yes—
211C2×#121—31no—
212C2×#121—32no—
213C2×#121—31no—
214C2×#120—31no—
215C2×#120—32no—
216C2×C4×D4—31no—
217C2×C4×D4—32no—
218C2×C4×D4—31no—
219C2×#117—32no—
220C22×C4⋊C4—31no—
221C22×C4⋊C4C2×D312yes—
222C22×C4⋊C4C2×D311yescharacteristic
223C22×C22⋊C4C2×D312yes—
224#400—34no—
225#399—34no—
226#398—34no—
227#397—34no—
228#396—34no—
229#395—32no—
230#394—34no—
231#393—32no—
232#393—34no—
233#393—34no—
234#392—34no—
235#391—32no—
236#391—32no—
237#391—34no—
238#390—34no—
239#390—34no—
240#389—32no—
241#388—34no—
242#387—34no—
243#386—31no—
244#386—32no—
245#386—32no—
246#386—32no—
247#386—34no—
248#386—32no—
249#386—32no—
250#386—34no—
251#386—34no—
252#385—31no—
253#385—32no—
254#385—32no—
255#381—32no—
256#380—31no—
257#380—32no—
258#380—34no—
259#380—34no—
260#379—31no—
261C4×C4⋊C4—32no—
262C4×C22⋊C4—31no—
263C4×C22⋊C4—32no—
264C24×C3—22no—
265C24×C3—24no—
266C24×C3—22no—
267C24×C3—22no—
268C24×C3—42no—
269C24×C3C2412yes—
270C24×C3C2411yescharacteristic
271C23×D3C2412yes—
272C23×D3C2411yescharacteristic
273C2×C3×Q8—24no—
274C2×C3×Q8—24no—
275C2×C3×Q8—24no—
276C2×C3×Q8—24no—
277C2×C3×Q8—44no—
278C2×C3×Q8—416no—
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4—24no—
282C22×C3×C4—24no—
283C22×C3×C4—22no—
284C22×C3×C4—24no—
285C22×C3×C4—24no—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—42no—
289C22×C3×C4—42no—
290C22×C3×C4—42no—
291C22×C3×C4—44no—
292C22×C3×C4—416no—
293C22×C3×C4C2×D414yes—
294C22×C3×C4C2×D418yes—
295C22×C3×C4C2414yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2411yescharacteristic
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2411yescharacteristic
301C2×#67—22no—
302C2×#67—22no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—24no—
306C2×#67—24no—
307C2×#67—24no—
308C2×#67—28no—
309C2×#67—42no—
310C2×#67—44no—
311C2×#67—44no—
312C2×#67#4114yes—
313C22×Dic3C2412yes—
314C22×Dic3C2411yescharacteristic
315C22×Dic3C2414yes—
316C22×Dic3C2412yes—
317C22×Dic3C2412yes—
318C22×Dic3C2411yescharacteristic
319C22×Dic3C2411yescharacteristic
320#235—432no—
321C2×D12—24no—
322C2×D12—22no—
323C2×D12—24no—
324C2×D12—24no—
325C2×D12—42no—
326C2×C4×D3—24no—
327C2×C4×D3—24no—
328C2×C4×D3—22no—
329C2×C4×D3—24no—
330C2×C4×D3—24no—
331C2×C4×D3—24no—
332C2×C4×D3—42no—
333C2×C4×D3—42no—
334C2×Dic6—24no—
335C2×Dic6—24no—
336C2×Dic6—42no—
337C3×C4⋊C4—28no—
338C3×C4⋊C4—28no—
339C3×C4⋊C4C2×D414yes—
340C3×C4⋊C4C2×D414yes—
341C3×C4⋊C4C2×D418yes—
342C3×C22⋊C4—28no—
343C3×C22⋊C4—28no—
344#217—22no—
345#217—22no—
346#217—22no—
347#217—24no—
348#217—24no—
349#217—24no—
350#217—42no—
351#217—44no—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4—22no—
354(C2×D3)⋊C4—24no—
355(C2×D3)⋊C4—24no—
356(C2×D3)⋊C4—42no—
357(C2×D3)⋊C4—44no—
358(C2×D3)⋊C4—44no—
359(C2×D3)⋊C4—44no—
360(C2×D3)⋊C4—44no—
361C4⋊Dic3—22no—
362C4⋊Dic3—24no—
363C4⋊Dic3—44no—
364Dic3⋊C4—24no—
365Dic3⋊C4—24no—
366Dic3⋊C4—22no—
367Dic3⋊C4—42no—
368Dic3⋊C4—44no—
369C4×Dic3—22no—
370C4×Dic3—24no—
371C4×Dic3—44no—
372C25C22×D311yescharacteristic
373C2×#41—68no—
374C2×#41—68no—
375C2×#41—124no—
376C22×Q8—24no—
377C22×Q8—32no—
378C22×Q8—44no—
379C22×Q8C22×D312yes—
380C22×Q8C22×D312yes—
381C22×D4—31no—
382C22×D4—32no—
383C22×D4—32no—
384C22×D4—34no—
385C22×D4—31no—
386C22×D4—32no—
387C23×C4—24no—
388C23×C4—31no—
389C23×C4—32no—
390C23×C4—32no—
391C23×C4—44no—
392C23×C4C22×D312yes—
393C23×C4C22×D312yes—
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D312yes—
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D312yes—
398C4⋊Q8—64no—
399#124—124no—
400#123—68no—
401#123—68no—
402C22⋊Q8—28no—
403C22⋊Q8—28no—
404C22⋊Q8—216no—
405C22⋊Q8—68no—
406C22⋊Q8—124no—
407#121—64no—
408#121—64no—
409#121—124no—
410#120—64no—
411#120—124no—
412C4×D4—64no—
413C4×D4—64no—
414C4×D4—124no—
415#117—124no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—32no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—32no—
422C2×C4⋊C4—34no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—34no—
425C2×C4⋊C4—64no—
426C2×C4⋊C4#6718yescomplemented
427C2×C4⋊C4C22×D314yes—
428C2×C4⋊C4C22×D314yes—
429C2×C4⋊C4C22×D311yescharacteristic
430C2×C4⋊C4C22×D311yescharacteristic
431C2×C4⋊C4C22×D312yes—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—32no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—32no—
442C2×C22⋊C4—32no—
443C2×C22⋊C4—32no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—32no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—34no—
449C2×C22⋊C4—34no—
450C2×C22⋊C4C22×D314yes—
451C2×C22⋊C4C22×D314yes—
452C2×C42—31no—
453C2×C42—32no—
454C2×C42—34no—
455#95—32no—
456#95—32no—
457#95—32no—
458#95—34no—
459#95—34no—
460#95—32no—
461#95—34no—
462#95—34no—
463#95—34no—
464#95—34no—
465#95—34no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—28no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—48no—
476C23×C3—48no—
477C23×C3—44no—
478C23×C3—44no—
479C23×C3C22×D412yes—
480C23×C3C2×#4112yes—
481C23×C3H(5,𝔽2)12yes—
482C23×C32−1+414yes—
483C23×C3C2511yescharacteristic
484C22×D3—21no—
485C22×D3—22no—
486C22×D3—21no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—24no—
491C22×D3—22no—
492C22×D3—24no—
493C22×D3C2×#4112yes—
494C3×Q8—48no—
495C3×Q8—48no—
496C2×C3×C4—216no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—28no—
503C2×C3×C4—24no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—24no—
507C2×C3×C4—22no—
508C2×C3×C4—24no—
509C2×C3×C4—48no—
510C2×C3×C4—44no—
511C2×C3×C4—48no—
512C2×C3×C4—48no—
513C2×C3×C4C22×D412yes—
514C2×C3×C4C22×D414yes—
515C2×C3×C4C22×D414yes—
516C2×C3×C4C22×D412yes—
517C2×C3×C4H(5,𝔽2)14yes—
518#67—28no—
519#67—48no—
520#67—48no—
521#67—88no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—24no—
533C2×Dic3—22no—
534C2×Dic3—24no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—24no—
540C2×Dic3C2×#4112yes—
541D12—48no—
542D12—44no—
543C4×D3—48no—
544C4×D3—48no—
545C4×D3—44no—
546Dic6—48no—
547C24—24no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—31no—
552C24—32no—
553C24—42no—
554C24C23×D312yes—
555C24C23×D311yescharacteristic
556#41—1232no—
557C2×Q8—24no—
558C2×Q8—24no—
559C2×Q8—24no—
560C2×Q8—24no—
561C2×Q8—44no—
562C2×Q8—416no—
563C2×Q8—64no—
564C2×Q8—64no—
565C2×Q8—122no—
566C2×D4—34no—
567C2×D4—64no—
568C2×D4—62no—
569C2×D4—62no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—64no—
573C2×D4—64no—
574C2×D4—64no—
575C2×D4—68no—
576C2×D4—64no—
577C2×D4—62no—
578C2×D4—64no—
579C2×D4—122no—
580C2×D4—122no—
581C2×D4—124no—
582C2×D4—124no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—31no—
593C22×C4—32no—
594C22×C4—31no—
595C22×C4—34no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—31no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—416no—
604C22×C4—64no—
605C22×C4—64no—
606C22×C4—64no—
607C22×C4—62no—
608C22×C4—64no—
609C22×C4—64no—
610C22×C4—122no—
611C22×C4—122no—
612C22×C4C2×#6718yes—
613C22×C4C2×#6714yes—
614C22×C4C23×D314yes—
615C22×C4C23×D312yes—
616C22×C4C23×D311yescharacteristic
617C22×C4C23×D312yes—
618C22×C4C23×D312yes—
619C22×C4C23×D311yescharacteristic
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—64no—
623C4⋊C4—62no—
624C4⋊C4—64no—
625C4⋊C4—62no—
626C4⋊C4—64no—
627C4⋊C4—124no—
628C4⋊C4—122no—
629C4⋊C4—124no—
630C4⋊C4C2×#6714yes—
631C4⋊C4C2×#6714yes—
632C4⋊C4C2×#6718yes—
633C22⋊C4—28no—
634C22⋊C4—28no—
635C22⋊C4—64no—
636C22⋊C4—64no—
637C22⋊C4—62no—
638C22⋊C4—62no—
639C22⋊C4—64no—
640C22⋊C4—62no—
641C22⋊C4—64no—
642C22⋊C4—62no—
643C22⋊C4—64no—
644C22⋊C4—64no—
645C22⋊C4—122no—
646C22⋊C4—124no—
647C22⋊C4—124no—
648C22⋊C4—124no—
649C22⋊C4—124no—
650C22⋊C4—122no—
651C22⋊C4—124no—
652C42—64no—
653C42—62no—
654C42—124no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—24no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—416no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3#54614yes—
668C22×C3C23×D411yescharacteristic
669C22×C3C22×#4111yescharacteristic
670C22×C3C2×H(5,𝔽2)12yes—
671C22×C3C2×H(5,𝔽2)11yescharacteristic
672C22×C3C2×2−1+412yes—
673C2×D3—22no—
674C2×D3—24no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—42no—
681C2×D3—44no—
682C2×D3—44no—
683C3×C4—22no—
684C3×C4—24no—
685C3×C4—24no—
686C3×C4—42no—
687C3×C4—44no—
688C3×C4#53514yes—
689Dic3—22no—
690Dic3—41no—
691Dic3—42no—
692Dic3—41no—
693Dic3—42no—
694Dic3—42no—
695Dic3—44no—
696C23—22no—
697C23—22no—
698C23—28no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—32no—
706C23—48no—
707C23—48no—
708C23—44no—
709C23—44no—
710C23—62no—
711C23—62no—
712C23—61no—
713C23—61no—
714C23—64no—
715C23—64no—
716C23—62no—
717C23—62no—
718C23—62no—
719C23#100714yes—
720C23D3×#4112yes—
721C23#100912yes—
722C23C22×#6712yes—
723C23C24×D311yescharacteristic
724Q8—48no—
725Q8—48no—
726Q8—128no—
727D4—68no—
728D4—128no—
729D4—128no—
730D4—128no—
731D4—124no—
732D4—248no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—216no—
739C2×C4—28no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—32no—
747C2×C4—48no—
748C2×C4—44no—
749C2×C4—48no—
750C2×C4—48no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—64no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—64no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—64no—
765C2×C4—62no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—62no—
769C2×C4—128no—
770C2×C4—128no—
771C2×C4—124no—
772C2×C4#100414yes—
773C2×C4C22×#6714yes—
774C2×C4C22×#6714yes—
775C2×C4C22×#6712yes—
776C2×C4C22×#6712yes—
777C2×C3—24no—
778C2×C3—44no—
779C2×C3C2×#53511yescharacteristic
780C2×C3C2×#54611yescharacteristic
781C2×C3#348611yescharacteristic
782C2×C3#352012yes—
783C2×C3#353612yes—
784D3—42no—
785D3—82no—
786C22—22no—
787C22—22no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—416no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—64no—
799C22—62no—
800C22—121no—
801C22—121no—
802C22—122no—
803C22—122no—
804C22—122no—
805C22—124no—
806C22—122no—
807C22—124no—
808C22#582914yes—
809C22C2×#100412yes—
810C22C2×#100712yes—
811C22C2×D3×#4111yescharacteristic
812C22C2×#100911yescharacteristic
813C22C23×#6711yescharacteristic
814C4—22no—
815C4—24no—
816C4—24no—
817C4—42no—
818C4—44no—
819C4—62no—
820C4—121no—
821C4—121no—
822C4—122no—
823C4—122no—
824C4—124no—
825C4—122no—
826C4#580514yes—
827C3#3890511yescharacteristic, complemented, Sylow
828C2—24no—
829C2—44no—
830C2—122no—
831C2—242no—
832C2#8598712yes—
833C2#8599012yes—
834C2C2×#580511yescharacteristic
835C2#8725111yescharacteristic
836C2C2×#582911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC22×C3×C22⋊Q8C2
hypercenterC22×C22⋊Q8D3
hypocenterC3#38905
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C2×#5507C2semidirect
3. #84068C2semidirect
4. #84066C2semidirect
5. #84032C2semidirect
6. C4×#953C2semidirect
7. #82830C2semidirect
8. #82798C2semidirect
9. #82779C2semidirect
10. #82773C2semidirect
11. #82756C2semidirect
12. #82752C2semidirect
13. #82200C2semidirect
14. #82186C2semidirect
15. #82159C2semidirect
16. #82125C2semidirect
17. #82106C2semidirect
31. C2×#947C22semidirect
32. C2×#946C22semidirect
39. C2×#896C22semidirect
41. C2×#895C22semidirect
42. C2×#894C22semidirect
43. C2×#893C22semidirect
44. C2×D3×C4⋊C4C22semidirect
45. C2×#888C22semidirect
47. #5231C22semidirect
48. #5231C22semidirect
49. #5230C22semidirect
50. #5229C22semidirect
51. #5229C22semidirect
67. #4993C22semidirect
68. #4992C22semidirect
69. #4988C22semidirect
70. #4987C22semidirect
71. #4987C22semidirect
72. #4985C22semidirect
73. #4984C22semidirect
74. #4983C22semidirect
75. #4980C22semidirect
76. Dic3×C4⋊C4C22semidirect
77. #4973C22semidirect
87. C22×C22⋊Q8D3semidirect
133. C2×C3×C4⋊C4D4semidirect
426. C2×C4⋊C4#67semidirect
827. C3#38905semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×#55072
#840682
#840662
#840322
C4×#9532
#828302
#827982
#827792
#827732
#827562
#827522
#822002
#821862
#821592
#821252
#821062
#389053