Finite Group Databasebeta

← #11258768

Subgroups — #11258768

Order 768.

2616 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#543C211yesmaximal, characteristic, complemented
2C2×#5629C211yesmaximal, characteristic, complemented
3#82833C211yesmaximal, characteristic, complemented
4#82830C212yesmaximal, complemented
5#82827C212yesmaximal, complemented
6#82827C212yesmaximal, complemented
7#82826C212yesmaximal, complemented
8#82817C212yesmaximal, complemented
9#82812C212yesmaximal, complemented
10#82807C212yesmaximal, complemented
11#82792C212yesmaximal, complemented
12#82779C212yesmaximal, complemented
13#82766C212yesmaximal, complemented
14#82759C211yesmaximal, characteristic, complemented
15#82746C211yesmaximal, characteristic, complemented
16#82125C211yesmaximal, characteristic, complemented
17#82115C211yesmaximal, characteristic, complemented
18#82109C212yesmaximal, complemented
19#82109C212yesmaximal, complemented
20#46356—31nomaximal, Sylow
21C22×#239C2211yescharacteristic, complemented
22C22×#235C2211yescharacteristic
23C3×#543—28no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2212yes—
26C2×C3×C22⋊Q8C2212yes—
27C2×C3×C22⋊Q8C2212yes—
28C2×C3×C22⋊Q8C2212yes—
29C2×C3×C22⋊Q8C2212yes—
30C2×C3×C22⋊Q8C2211yescharacteristic
31C22×C3×C22⋊C4C2212yes—
32C22×C3×C22⋊C4C2211yescharacteristic
33C2×#953C2212yes—
34C2×#953C2211yescharacteristic
35C2×#953C2211yescharacteristic
36C2×#947C2211yescharacteristic, complemented
37C2×#947C2212yescomplemented
38C2×#946C2211yescharacteristic, complemented
39C2×#946C2212yescomplemented
40C2×#944C2211yescharacteristic, complemented
41C2×#930C2211yescharacteristic
42C2×#930C2212yes—
43C2×#930C2212yes—
44C2×#929C2212yes—
45C2×C4×#67C2212yes—
46C2×C4×#67C2212yes—
47#5629—28no—
48C2×#896C2212yescomplemented
49C2×#895C2212yescomplemented
50C2×#895C2211yescharacteristic, complemented
51C2×D3×C4⋊C4C2211yescharacteristic, complemented
52C2×#884C2212yes—
53C2×#884C2212yes—
54#5231C2212yescomplemented
55#5231C2212yescomplemented
56#5230C2212yescomplemented
57#5229C2212yescomplemented
58#5213C2211yescharacteristic
59#5213C2212yes—
60#5213C2211yescharacteristic
61#5213C2212yes—
62#5211C2211yescharacteristic
63#5210C2212yes—
64#5210C2212yes—
65C4×#217C2211yescharacteristic
66#4994C2212yescomplemented
67#4994C2212yescomplemented
68#4993C2212yescomplemented
69#4993C2212yescomplemented
70#4991C2212yescomplemented
71#4991C2212yescomplemented
72#4991C2212yescomplemented
73#4989C2212yescomplemented
74#4989C2212yescomplemented
75#4989C2212yescomplemented
76#4989C2212yescomplemented
77#4988C2211yescharacteristic, complemented
78#4988C2212yescomplemented
79#4987C2212yescomplemented
80#4983C2212yescomplemented
81#4981C2212yescomplemented
82#4980C2212yescomplemented
83#4980C2212yescomplemented
84#4976C2212yescomplemented
85#4976C2212yescomplemented
86Dic3×C4⋊C4C2212yescomplemented
87#4973C2211yescharacteristic, complemented
88#4960C2212yes—
89#4960C2212yes—
90#4960C2212yes—
91#4960C2212yes—
92#4959C2212yes—
93#4959C2212yes—
94#4959C2212yes—
95#4959C2212yes—
96#4957C2212yes—
97#4957C2212yes—
98#4957C2212yes—
99#4957C2212yes—
100#4956C2212yes—
101#4956C2212yes—
102#4956C2212yes—
103#4956C2212yes—
104#4951C2212yes—
105#4951C2212yes—
106#4949C2212yes—
107#4948C2212yes—
108#4948C2212yes—
109#4947C2212yes—
110C2×#543D311yescharacteristic, complemented
111C2×#537—31no—
112#2816—31no—
113#2732—32no—
114#2692—32no—
115#2681—32no—
116#2676—32no—
117#2676—32no—
118#2672—32no—
119#2540—32no—
120#2539—31no—
121#2452—32no—
122#2449—32no—
123#2432—31no—
124#2424—32no—
125#2424—32no—
126#2407—32no—
127#2404—31no—
128#2332—31no—
129C25×C3C2311yescharacteristic
130C22×C3×Q8C2312yes—
131C22×C3×Q8C2311yescharacteristic
132C22×C3×Q8C2311yescharacteristic
133C23×C3×C4C2312yes—
134C23×C3×C4C2312yes—
135C23×C3×C4C2311yescharacteristic
136C23×C3×C4C2311yescharacteristic
137C22×#67C2311yescharacteristic
138C22×#67C2311yescharacteristic
139C22×#67C2312yes—
140C22×#67C2312yes—
141C22×#67C2312yes—
142C22×#67C2312yes—
143C22×#67C2312yes—
144C2×#239—24no—
145C2×#239—42no—
146C2×#239—42no—
147C2×#235—24no—
148C2×#235—42no—
149C2×#235—42no—
150C22×D12C2311yescharacteristic
151C22×D12C2312yes—
152C22×D12C2311yescharacteristic
153C22×D12C2312yes—
154C22×C4×D3C2311yescharacteristic
155C22×C4×D3C2312yes—
156C22×C4×D3C2311yescharacteristic
157C22×C4×D3C2312yes—
158C22×Dic6C2311yescharacteristic
159C3×C22⋊Q8—28no—
160C3×C22⋊Q8—24no—
161C3×C22⋊Q8—28no—
162C3×C22⋊Q8—28no—
163C3×C22⋊Q8—28no—
164C3×C22⋊Q8—28no—
165C3×C22⋊Q8D418yescomplemented
166C2×C3×C4⋊C4C2311yescharacteristic
167C2×C3×C4⋊C4C2312yes—
168C2×C3×C4⋊C4C2312yes—
169C2×C3×C4⋊C4C2312yes—
170C2×C3×C4⋊C4C2312yes—
171C2×C3×C4⋊C4C2312yes—
172C2×C3×C4⋊C4C2311yescharacteristic
173C2×C3×C22⋊C4—24no—
174C2×C3×C22⋊C4—28no—
175C2×C3×C22⋊C4C2312yes—
176C2×C3×C22⋊C4C2312yes—
177C2×C3×C22⋊C4C2312yes—
178C2×C3×C22⋊C4C2312yes—
179C2×C3×C22⋊C4C2312yes—
180C2×C3×C22⋊C4C2312yes—
181#953—42no—
182#953—44no—
183#953—42no—
184C2×#217C2312yes—
185C2×#217C2312yes—
186C2×#217C2312yes—
187C2×#217C2312yes—
188C2×#217C2312yes—
189C2×#217C2311yescharacteristic
190C2×#217C2311yescharacteristic
191#947—44no—
192#947—42no—
193#946—24no—
194#946—44no—
195#944—42no—
196#930—24no—
197#930—44no—
198#930—44no—
199#929—44no—
200C4×#67—44no—
201C4×#67—44no—
202C2×(C2×D3)⋊C4C2312yes—
203C2×(C2×D3)⋊C4C2312yes—
204C2×(C2×D3)⋊C4C2312yes—
205C2×(C2×D3)⋊C4C2312yes—
206C2×(C2×D3)⋊C4C2312yes—
207C2×(C2×D3)⋊C4C2312yes—
208C2×(C2×D3)⋊C4C2312yes—
209C2×(C2×D3)⋊C4C2312yes—
210C2×(C2×D3)⋊C4C2312yes—
211C2×(C2×D3)⋊C4C2312yes—
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2312yes—
214C2×(C2×D3)⋊C4C2312yes—
215C2×(C2×D3)⋊C4C2312yes—
216C2×(C2×D3)⋊C4C2312yes—
217C2×C4⋊Dic3C2312yes—
218C2×C4⋊Dic3C2311yescharacteristic
219C2×C4⋊Dic3C2312yes—
220C2×Dic3⋊C4C2312yes—
221C2×Dic3⋊C4C2312yes—
222C2×Dic3⋊C4C2312yes—
223C2×Dic3⋊C4C2312yes—
224C2×Dic3⋊C4C2312yes—
225C2×Dic3⋊C4C2312yes—
226C2×Dic3⋊C4C2312yes—
227C2×Dic3⋊C4C2312yes—
228C2×C4×Dic3C2312yes—
229C2×C4×Dic3C2312yes—
230C2×C4×Dic3C2311yescharacteristic
231C2×C4×Dic3C2311yescharacteristic
232#896—28no—
233#895—24no—
234#895—28no—
235D3×C4⋊C4—24no—
236#884—28no—
237#884—28no—
238C3⋊#95C2312yes—
239C3⋊#95C2312yes—
240C3⋊#95C2312yes—
241C3⋊#95C2312yes—
242C3⋊#95C2312yes—
243C3⋊#95C2312yes—
244C3⋊#95C2312yes—
245C3⋊#95C2312yes—
246C3⋊#95C2312yes—
247C3⋊#95C2312yes—
248C3⋊#95C2312yes—
249C3⋊#95C2312yes—
250C3⋊#95C2312yes—
251C22×#41—31no—
252C22×#41—31no—
253#543—28no—
254#537—68no—
255C2×C4⋊Q8—31no—
256C2×#124—32no—
257C2×#124—31no—
258C2×#123—32no—
259C2×C22⋊Q8—31no—
260C2×C22⋊Q8—32no—
261C2×C22⋊Q8—32no—
262C2×C22⋊Q8C2×D311yescharacteristic
263C2×C22⋊Q8C2×D312yes—
264C2×C22⋊Q8C2×D312yes—
265C2×C22⋊Q8C2×D312yes—
266C2×C22⋊Q8C2×D312yes—
267C2×C22⋊Q8C2×D312yes—
268C2×C22⋊Q8C2×D311yescharacteristic
269C2×#121—31no—
270C2×#121—32no—
271C2×#121—32no—
272C2×#121—31no—
273C2×#121—32no—
274C2×#121—32no—
275C2×#121—32no—
276C2×#120—31no—
277C2×#120—31no—
278C2×#120—32no—
279C2×C4×D4—32no—
280C2×C4×D4—32no—
281C22×C4⋊C4—31no—
282C22×C22⋊C4C2×D311yescharacteristic
283C22×C22⋊C4C2×D312yes—
284#399—32no—
285#399—32no—
286#399—32no—
287#398—32no—
288#398—32no—
289#396—32no—
290#396—32no—
291#396—32no—
292#396—32no—
293#395—32no—
294#394—32no—
295#394—32no—
296#394—32no—
297#394—32no—
298#394—32no—
299#394—32no—
300#394—32no—
301#393—32no—
302#393—32no—
303#393—32no—
304#392—32no—
305#392—32no—
306#392—32no—
307#392—32no—
308#391—32no—
309#391—31no—
310#390—32no—
311#390—31no—
312#390—32no—
313#390—32no—
314#390—32no—
315#390—32no—
316#389—32no—
317#389—32no—
318#388—32no—
319#388—32no—
320#387—32no—
321#387—32no—
322#386—31no—
323#386—31no—
324#386—32no—
325#386—32no—
326#386—32no—
327#386—32no—
328#386—32no—
329#386—32no—
330#385—32no—
331#385—32no—
332#385—32no—
333#385—32no—
334#385—32no—
335#385—32no—
336#381—31no—
337#380—32no—
338C4×C4⋊C4—32no—
339C4×C22⋊C4—31no—
340C24×C3—22no—
341C24×C3—24no—
342C24×C3—42no—
343C24×C3—41no—
344C24×C3—41no—
345C24×C3C2411yescharacteristic
346C24×C3C2412yes—
347C23×D3C2412yes—
348C23×D3C2411yescharacteristic
349C23×D3C2411yescharacteristic
350C2×C3×Q8—24no—
351C2×C3×Q8—22no—
352C2×C3×Q8—41no—
353C2×C3×Q8—41no—
354C2×C3×Q8—41no—
355C2×C3×Q8—42no—
356C2×C3×Q8—42no—
357C2×C3×Q8—41no—
358C2×C3×Q8C2×D414yes—
359C22×C3×C4—22no—
360C22×C3×C4—24no—
361C22×C3×C4—24no—
362C22×C3×C4—41no—
363C22×C3×C4—41no—
364C22×C3×C4—42no—
365C22×C3×C4—42no—
366C22×C3×C4—42no—
367C22×C3×C4—42no—
368C22×C3×C4—42no—
369C22×C3×C4C2×D414yes—
370C22×C3×C4C2412yes—
371C22×C3×C4C2412yes—
372C22×C3×C4C2412yes—
373C22×C3×C4C2411yescharacteristic
374C22×C3×C4C2411yescharacteristic
375C22×C3×C4C2412yes—
376C22×C3×C4C2412yes—
377C2×#67—22no—
378C2×#67—22no—
379C2×#67—24no—
380C2×#67—24no—
381C2×#67—24no—
382C2×#67—22no—
383C2×#67—24no—
384C2×#67—24no—
385C2×#67—24no—
386C2×#67—24no—
387C2×#67—22no—
388C2×#67—42no—
389C2×#67—42no—
390C2×#67—41no—
391C2×#67—41no—
392C2×#67—42no—
393C2×#67—42no—
394C2×#67—42no—
395C2×#67—42no—
396C2×#67—42no—
397C2×#67—42no—
398C22×Dic3C2412yes—
399C22×Dic3C2412yes—
400C22×Dic3C2412yes—
401C22×Dic3C2411yescharacteristic
402C22×Dic3C2412yes—
403C22×Dic3C2411yescharacteristic
404C22×Dic3C2412yes—
405#239—416no—
406#235—416no—
407C2×D12—24no—
408C2×D12—22no—
409C2×D12—24no—
410C2×D12—22no—
411C2×D12—22no—
412C2×D12—24no—
413C2×D12—41no—
414C2×D12—42no—
415C2×D12—41no—
416C2×D12—41no—
417C2×D12—42no—
418C2×D12—42no—
419C2×C4×D3—22no—
420C2×C4×D3—22no—
421C2×C4×D3—22no—
422C2×C4×D3—24no—
423C2×C4×D3—22no—
424C2×C4×D3—24no—
425C2×C4×D3—24no—
426C2×C4×D3—41no—
427C2×C4×D3—41no—
428C2×C4×D3—42no—
429C2×C4×D3—42no—
430C2×C4×D3—42no—
431C2×Dic6—22no—
432C2×Dic6—22no—
433C2×Dic6—41no—
434C3×C4⋊C4—24no—
435C3×C4⋊C4—24no—
436C3×C4⋊C4—24no—
437C3×C4⋊C4—24no—
438C3×C4⋊C4—22no—
439C3×C4⋊C4C2×D414yes—
440C3×C4⋊C4C2×D418yes—
441C3×C22⋊C4—24no—
442C3×C22⋊C4—24no—
443C3×C22⋊C4—24no—
444C3×C22⋊C4—24no—
445C3×C22⋊C4—24no—
446C3×C22⋊C4C2×D418yes—
447#217—24no—
448#217—24no—
449#217—24no—
450#217—41no—
451#217—42no—
452#217—41no—
453#217—42no—
454(C2×D3)⋊C4—24no—
455(C2×D3)⋊C4—24no—
456(C2×D3)⋊C4—24no—
457(C2×D3)⋊C4—24no—
458(C2×D3)⋊C4—24no—
459(C2×D3)⋊C4—24no—
460(C2×D3)⋊C4—24no—
461(C2×D3)⋊C4—42no—
462(C2×D3)⋊C4—42no—
463(C2×D3)⋊C4—42no—
464(C2×D3)⋊C4—42no—
465(C2×D3)⋊C4—42no—
466(C2×D3)⋊C4—42no—
467(C2×D3)⋊C4—42no—
468(C2×D3)⋊C4—42no—
469C4⋊Dic3—22no—
470C4⋊Dic3—24no—
471C4⋊Dic3—42no—
472Dic3⋊C4—24no—
473Dic3⋊C4—24no—
474Dic3⋊C4—24no—
475Dic3⋊C4—24no—
476Dic3⋊C4—42no—
477Dic3⋊C4—42no—
478Dic3⋊C4—42no—
479Dic3⋊C4—42no—
480C4×Dic3—24no—
481C4×Dic3—42no—
482C4×Dic3—41no—
483C4×Dic3—41no—
484C25C22×D311yescharacteristic
485C2×#41—64no—
486C2×#41—64no—
487C2×#41—122no—
488C2×#41—122no—
489C2×#41—122no—
490C2×#41—122no—
491C22×Q8—31no—
492C22×Q8C22×D312yes—
493C22×Q8C22×D311yescharacteristic
494C22×Q8C22×D311yescharacteristic
495C22×D4—32no—
496C22×D4—32no—
497C22×D4—31no—
498C22×D4—31no—
499C22×D4—32no—
500C22×D4—32no—
501C22×D4—32no—
502C22×D4—32no—
503C22×D4—31no—
504C22×D4—32no—
505C22×D4—31no—
506C23×C4—31no—
507C23×C4—32no—
508C23×C4—32no—
509C23×C4—31no—
510C23×C4C22×D312yes—
511C23×C4C22×D312yes—
512C23×C4C22×D311yescharacteristic
513C23×C4C22×D311yescharacteristic
514C4⋊Q8—122no—
515#124—124no—
516#124—122no—
517#123—124no—
518C22⋊Q8—28no—
519C22⋊Q8—24no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—28no—
524C22⋊Q8—64no—
525C22⋊Q8—68no—
526C22⋊Q8—124no—
527C22⋊Q8#6718yescomplemented
528#121—64no—
529#121—64no—
530#121—68no—
531#121—68no—
532#121—68no—
533#121—124no—
534#121—124no—
535#120—122no—
536#120—124no—
537#120—122no—
538C4×D4—124no—
539C4×D4—124no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—32no—
543C2×C4⋊C4—32no—
544C2×C4⋊C4—32no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—32no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—32no—
549C2×C4⋊C4—32no—
550C2×C4⋊C4—32no—
551C2×C4⋊C4—64no—
552C2×C4⋊C4C22×D312yes—
553C2×C4⋊C4C22×D312yes—
554C2×C4⋊C4C22×D312yes—
555C2×C4⋊C4C22×D312yes—
556C2×C4⋊C4C22×D311yescharacteristic
557C2×C4⋊C4C22×D311yescharacteristic
558C2×C4⋊C4C22×D312yes—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—28no—
561C2×C22⋊C4—32no—
562C2×C22⋊C4—32no—
563C2×C22⋊C4—32no—
564C2×C22⋊C4—32no—
565C2×C22⋊C4—32no—
566C2×C22⋊C4—32no—
567C2×C22⋊C4—32no—
568C2×C22⋊C4—32no—
569C2×C22⋊C4—32no—
570C2×C22⋊C4—32no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—32no—
574C2×C22⋊C4—32no—
575C2×C22⋊C4—32no—
576C2×C22⋊C4—32no—
577C2×C22⋊C4—32no—
578C2×C22⋊C4—32no—
579C2×C22⋊C4—32no—
580C2×C22⋊C4—32no—
581C2×C22⋊C4—32no—
582C2×C22⋊C4—32no—
583C2×C22⋊C4C22×D312yes—
584C2×C22⋊C4C22×D312yes—
585C2×C22⋊C4C22×D312yes—
586C2×C22⋊C4C22×D312yes—
587C2×C22⋊C4C22×D312yes—
588C2×C22⋊C4C22×D312yes—
589C2×C42—32no—
590C2×C42—32no—
591C2×C42—31no—
592C2×C42—31no—
593#95—32no—
594#95—32no—
595#95—32no—
596#95—32no—
597#95—32no—
598#95—32no—
599#95—32no—
600#95—32no—
601#95—32no—
602#95—32no—
603#95—32no—
604#95—32no—
605#95—32no—
606C23×C3—28no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—82no—
618C23×C3—82no—
619C23×C3—84no—
620C23×C3—84no—
621C23×C3C22×D412yes—
622C23×C32−1+414yes—
623C23×C3C2511yescharacteristic
624C22×D3—21no—
625C22×D3—22no—
626C22×D3—21no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—21no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—21no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—21no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3H(5,𝔽2)12yes—
641C3×Q8—44no—
642C3×Q8—82no—
643C3×Q8—84no—
644C2×C3×C4—22no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—44no—
662C2×C3×C4—84no—
663C2×C3×C4—84no—
664C2×C3×C4—82no—
665C2×C3×C4C22×D414yes—
666C2×C3×C4C22×D414yes—
667C2×C3×C4C22×D412yes—
668C2×C3×C4C22×D412yes—
669#67—44no—
670#67—48no—
671#67—44no—
672#67—48no—
673#67—84no—
674#67—84no—
675#67—84no—
676C2×Dic3—21no—
677C2×Dic3—22no—
678C2×Dic3—21no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—21no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—21no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—21no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3H(5,𝔽2)14yes—
696C2×Dic3H(5,𝔽2)12yes—
697D12—44no—
698D12—48no—
699D12—44no—
700D12—84no—
701C4×D3—28no—
702C4×D3—48no—
703C4×D3—44no—
704C4×D3—84no—
705Dic6—44no—
706C24—24no—
707C24—22no—
708C24—31no—
709C24—32no—
710C24—31no—
711C24—42no—
712C24—41no—
713C24—41no—
714C24C23×D312yes—
715C24C23×D311yescharacteristic
716#41—1216no—
717#41—1216no—
718C2×Q8—22no—
719C2×Q8—24no—
720C2×Q8—41no—
721C2×Q8—41no—
722C2×Q8—42no—
723C2×Q8—42no—
724C2×Q8—41no—
725C2×Q8—41no—
726C2×Q8—62no—
727C2×Q8—62no—
728C2×Q8—121no—
729C2×Q8C2×#6714yes—
730C2×D4—64no—
731C2×D4—62no—
732C2×D4—64no—
733C2×D4—62no—
734C2×D4—64no—
735C2×D4—62no—
736C2×D4—64no—
737C2×D4—64no—
738C2×D4—62no—
739C2×D4—62no—
740C2×D4—64no—
741C2×D4—64no—
742C2×D4—64no—
743C2×D4—62no—
744C2×D4—62no—
745C2×D4—64no—
746C2×D4—64no—
747C2×D4—122no—
748C2×D4—121no—
749C2×D4—121no—
750C2×D4—121no—
751C2×D4—122no—
752C2×D4—122no—
753C2×D4—122no—
754C2×D4—122no—
755C2×D4—121no—
756C2×D4—121no—
757C2×D4—122no—
758C2×D4—122no—
759C2×D4—122no—
760C2×D4—122no—
761C2×D4—122no—
762C2×D4—122no—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—31no—
767C22×C4—32no—
768C22×C4—32no—
769C22×C4—32no—
770C22×C4—32no—
771C22×C4—31no—
772C22×C4—32no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—62no—
781C22×C4—64no—
782C22×C4—62no—
783C22×C4—62no—
784C22×C4—64no—
785C22×C4—62no—
786C22×C4—64no—
787C22×C4—122no—
788C22×C4—121no—
789C22×C4—121no—
790C22×C4—122no—
791C22×C4—122no—
792C22×C4C2×#6714yes—
793C22×C4C23×D312yes—
794C22×C4C23×D312yes—
795C22×C4C23×D312yes—
796C22×C4C23×D311yescharacteristic
797C22×C4C23×D311yescharacteristic
798C22×C4C23×D312yes—
799C22×C4C23×D312yes—
800C4⋊C4—22no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—64no—
806C4⋊C4—64no—
807C4⋊C4—64no—
808C4⋊C4—64no—
809C4⋊C4—62no—
810C4⋊C4—64no—
811C4⋊C4—122no—
812C4⋊C4—122no—
813C4⋊C4—122no—
814C4⋊C4—122no—
815C4⋊C4—122no—
816C4⋊C4C2×#6714yes—
817C4⋊C4C2×#6718yes—
818C22⋊C4—24no—
819C22⋊C4—24no—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—64no—
824C22⋊C4—64no—
825C22⋊C4—64no—
826C22⋊C4—64no—
827C22⋊C4—64no—
828C22⋊C4—64no—
829C22⋊C4—64no—
830C22⋊C4—64no—
831C22⋊C4—64no—
832C22⋊C4—64no—
833C22⋊C4—122no—
834C22⋊C4—122no—
835C22⋊C4—122no—
836C22⋊C4—122no—
837C22⋊C4—122no—
838C22⋊C4—122no—
839C22⋊C4—122no—
840C22⋊C4—122no—
841C22⋊C4—121no—
842C22⋊C4—122no—
843C22⋊C4—121no—
844C22⋊C4—122no—
845C22⋊C4C2×#6718yes—
846C42—64no—
847C42—122no—
848C42—121no—
849C42—121no—
850C22×C3—22no—
851C22×C3—22no—
852C22×C3—24no—
853C22×C3—22no—
854C22×C3—24no—
855C22×C3—24no—
856C22×C3—42no—
857C22×C3—42no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—42no—
861C22×C3—42no—
862C22×C3—88no—
863C22×C3C23×D411yescharacteristic
864C22×C3C2×H(5,𝔽2)11yescharacteristic
865C22×C3C2×H(5,𝔽2)11yescharacteristic
866C22×C3C2×H(5,𝔽2)12yes—
867C22×C3C2×2−1+412yes—
868C2×D3—22no—
869C2×D3—24no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—41no—
875C2×D3—42no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—42no—
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—42no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—24no—
888C3×C4—24no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892Dic3—22no—
893Dic3—24no—
894Dic3—41no—
895Dic3—42no—
896Dic3—42no—
897Dic3—42no—
898Dic3—42no—
899C23—28no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—21no—
908C23—21no—
909C23—22no—
910C23—32no—
911C23—62no—
912C23—62no—
913C23—61no—
914C23—61no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—61no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—61no—
925C23—61no—
926C23—62no—
927C23—84no—
928C23—84no—
929C23—82no—
930C23—82no—
931C23#100714yes—
932C23C22×#6712yes—
933C23C24×D311yescharacteristic
934Q8—44no—
935Q8—84no—
936Q8—82no—
937Q8—124no—
938D4—124no—
939D4—128no—
940D4—124no—
941D4—124no—
942D4—128no—
943D4—124no—
944D4—128no—
945D4—244no—
946D4—244no—
947D4—244no—
948D4—244no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—34no—
967C2×C4—32no—
968C2×C4—44no—
969C2×C4—68no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—62no—
980C2×C4—62no—
981C2×C4—62no—
982C2×C4—62no—
983C2×C4—62no—
984C2×C4—61no—
985C2×C4—62no—
986C2×C4—61no—
987C2×C4—62no—
988C2×C4—61no—
989C2×C4—84no—
990C2×C4—84no—
991C2×C4—82no—
992C2×C4—128no—
993C2×C4—124no—
994C2×C4—244no—
995C2×C4C22×#6712yes—
996C2×C4C22×#6712yes—
997C2×C4C22×#6714yes—
998C2×C4C22×#6714yes—
999C2×C3—42no—
1000C2×C3—44no—
1001C2×C3#348411yescharacteristic
1002C2×C3#348611yescharacteristic
1003C2×C3#349811yescharacteristic
1004C2×C3#353612yes—
1005C2×C3#353612yes—
1006D3—42no—
1007D3—82no—
1008D3—81no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—64no—
1022C22—62no—
1023C22—88no—
1024C22—122no—
1025C22—121no—
1026C22—121no—
1027C22—122no—
1028C22—122no—
1029C22—122no—
1030C22—122no—
1031C22—122no—
1032C22—122no—
1033C22—122no—
1034C22—121no—
1035C22—121no—
1036C22—122no—
1037C22—122no—
1038C22—121no—
1039C22C2×#100712yes—
1040C22D3×H(5,𝔽2)12yes—
1041C22D3×H(5,𝔽2)11yescharacteristic
1042C22D3×H(5,𝔽2)11yescharacteristic
1043C22C23×#6711yescharacteristic
1044C4—24no—
1045C4—22no—
1046C4—22no—
1047C4—24no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—64no—
1052C4—62no—
1053C4—122no—
1054C4—122no—
1055C4—122no—
1056C4—122no—
1057C4—121no—
1058C3#4635611yescharacteristic, complemented, Sylow
1059C2—44no—
1060C2—42no—
1061C2—122no—
1062C2—242no—
1063C2—241no—
1064C2#8657512yes—
1065C2#8657512yes—
1066C2#8725111yescharacteristic
1067C2#8728211yescharacteristic
1068C2#8728411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#543C2
hypercenterC2×#543D3
hypocenterC3#46356
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. C2×C3×#543C2semidirect
2. C2×#5629C2semidirect
3. #82833C2semidirect
4. #82830C2semidirect
5. #82827C2semidirect
6. #82827C2semidirect
7. #82826C2semidirect
8. #82817C2semidirect
9. #82812C2semidirect
10. #82807C2semidirect
11. #82792C2semidirect
12. #82779C2semidirect
13. #82766C2semidirect
14. #82759C2semidirect
15. #82746C2semidirect
16. #82125C2semidirect
17. #82115C2semidirect
18. #82109C2semidirect
19. #82109C2semidirect
21. C22×#239C22semidirect
36. C2×#947C22semidirect
37. C2×#947C22semidirect
38. C2×#946C22semidirect
39. C2×#946C22semidirect
40. C2×#944C22semidirect
48. C2×#896C22semidirect
49. C2×#895C22semidirect
50. C2×#895C22semidirect
51. C2×D3×C4⋊C4C22semidirect
54. #5231C22semidirect
55. #5231C22semidirect
56. #5230C22semidirect
57. #5229C22semidirect
66. #4994C22semidirect
67. #4994C22semidirect
68. #4993C22semidirect
69. #4993C22semidirect
70. #4991C22semidirect
71. #4991C22semidirect
72. #4991C22semidirect
73. #4989C22semidirect
74. #4989C22semidirect
75. #4989C22semidirect
76. #4989C22semidirect
77. #4988C22semidirect
78. #4988C22semidirect
79. #4987C22semidirect
80. #4983C22semidirect
81. #4981C22semidirect
82. #4980C22semidirect
83. #4980C22semidirect
84. #4976C22semidirect
85. #4976C22semidirect
86. Dic3×C4⋊C4C22semidirect
87. #4973C22semidirect
110. C2×#543D3semidirect
165. C3×C22⋊Q8D4semidirect
527. C22⋊Q8#67semidirect
1058. C3#46356semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5432
C2×#56292
#828332
#828302
#828272
#828262
#828172
#828122
#828072
#827922
#827792
#827662
#827592
#827462
#821252
#821152
#821092
#463563