Finite Group Databasebeta

← #11633120

Subgroups — #11633120

Order 768.

4080 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#120C211yesmaximal, characteristic
2C2×#5587C211yesmaximal, characteristic, complemented
3C3×#2358C211yesmaximal, characteristic, complemented
4#82414C212yesmaximal, complemented
5D4×(C2×D3)⋊C4C212yesmaximal, complemented
6C2×#4955C212yesmaximal, complemented
7#82108C212yesmaximal, complemented
8#76469C211yesmaximal, characteristic, complemented
9#76315C211yesmaximal, characteristic, complemented
10#75918C212yesmaximal, complemented
11#75540C212yesmaximal, complemented
12#74918C211yesmaximal, characteristic, complemented
13#74891C212yesmaximal, complemented
14#74686C211yesmaximal, characteristic, complemented
15#74686C212yesmaximal, complemented
16#74602C212yesmaximal, complemented
17#74413C212yesmaximal, complemented
18#73594C212yesmaximal, complemented
19#73575C212yesmaximal, complemented
20#59006—31nomaximal, Sylow
21C25×D3C2211yescharacteristic
22C22×D3×D4C2212yes—
23C22×D3×D4C2211yescharacteristic
24C2×C3×#120C2211yescharacteristic
25C2×C3×C4×D4C2212yescomplemented
26C22×C3×C22⋊C4C2212yescomplemented
27C2×#953C2211yescharacteristic
28C22×#217C2212yescomplemented
29C2×#937C2212yes—
30C2×#937C2211yescharacteristic
31C2×#936C2211yescharacteristic, complemented
32C2×#935C2211yescharacteristic, complemented
33C2×#935C2212yescomplemented
34C2×D4×Dic3C2212yescomplemented
35C22×(C2×D3)⋊C4C2212yes—
36C22×(C2×D3)⋊C4C2212yes—
37C22×(C2×D3)⋊C4C2212yescomplemented
38C22×(C2×D3)⋊C4C2212yescomplemented
39C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
40D3×#120—28no—
41#5587—28no—
42C2×#897C2211yescharacteristic, complemented
43C2×#886C2211yescharacteristic, complemented
44C2×#886C2212yescomplemented
45C2×#882C2212yes—
46C2×#882C2211yescharacteristic
47C2×D3×C22⋊C4C2211yescharacteristic
48C2×D3×C22⋊C4C2212yes—
49C2×#879C2212yescomplemented
50C2×#878C2212yescomplemented
51C2×#877C2212yescomplemented
52C2×#875C2211yescharacteristic, complemented
53C3×#390C2211yescharacteristic, complemented
54C3×#388C2212yescomplemented
55C3×#386C2211yescharacteristic, complemented
56C3×#386C2212yescomplemented
57C3×#385C2212yescomplemented
58C3×C4×C22⋊C4C2212yescomplemented
59#5213C2212yescomplemented
60#5213C2211yescharacteristic, complemented
61#5213C2212yescomplemented
62#5213C2212yescomplemented
63#5212C2212yescomplemented
64#5212C2212yescomplemented
65#4994C2212yescomplemented
66#4994C2212yescomplemented
67#4994C2212yescomplemented
68#4988C2211yescharacteristic, complemented
69#4988C2212yescomplemented
70#4987C2212yescomplemented
71#4961C2212yescomplemented
72#4961C2212yescomplemented
73#4961C2212yescomplemented
74#4961C2212yescomplemented
75#4961C2212yescomplemented
76#4958C2212yescomplemented
77#4958C2212yescomplemented
78#4955C2212yes—
79#4955C2212yes—
80#4955C2212yes—
81#4955C2212yes—
82#4955C2212yescomplemented
83#4955C2212yescomplemented
84#4955C2212yescomplemented
85#4955C2212yescomplemented
86#4955C2212yescomplemented
87#4955C2211yescharacteristic, complemented
88#4953C2212yescomplemented
89#4953C2212yescomplemented
90#4950C2212yescomplemented
91#4943C2212yescomplemented
92#4940C2212yescomplemented
93#4940C2212yescomplemented
94#4940C2212yescomplemented
95#4939C2212yescomplemented
96C4×(C2×D3)⋊C4C2212yescomplemented
97C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
98#4677C2212yescomplemented
99#4674C2212yescomplemented
100#4673C2212yescomplemented
101#4672C2212yescomplemented
102#4672C2212yescomplemented
103#4672C2212yescomplemented
104#4670C2212yescomplemented
105#4670C2212yescomplemented
106#4670C2212yescomplemented
107#4668C2212yescomplemented
108#4668C2212yescomplemented
109#4668C2212yescomplemented
110C2×#551—31no—
111C22×#120—31no—
112#2697—31no—
113#2685—32no—
114#2684—31no—
115#2534—32no—
116#2480—32no—
117#2472—32no—
118#2437—32no—
119#2435—31no—
120#2418—32no—
121#2412—32no—
122#2411—32no—
123#2405—32no—
124#2405—31no—
125#2358D311yescharacteristic, complemented
126#2342—32no—
127D4×C22⋊C4—32no—
128C2×#379—32no—
129C25×C3C2311yescharacteristic
130C24×D3—24no—
131C24×D3—28no—
132C24×D3—42no—
133C24×D3—42no—
134C24×D3—44no—
135C24×D3C2311yescharacteristic
136C24×D3C2312yes—
137C24×D3C2311yescharacteristic
138C24×D3C2312yes—
139C24×D3C2311yescharacteristic
140C22×C3×D4C2312yes—
141C22×C3×D4C2311yescharacteristic
142C23×C3×C4C2312yes—
143C23×C3×C4C2312yes—
144C23×C3×C4C2311yescharacteristic, complemented
145C22×#67C2312yes—
146C22×#67C2312yes—
147C22×#67C2311yescharacteristic
148C22×#67C2311yescharacteristic
149C23×Dic3C2312yes—
150C23×Dic3C2312yes—
151C23×Dic3C2311yescharacteristic, complemented
152C2×D3×D4—28no—
153C2×D3×D4—28no—
154C2×D3×D4—24no—
155C2×D3×D4—42no—
156C2×D3×D4—42no—
157C2×D3×D4—44no—
158C22×D12C2312yes—
159C22×D12C2311yescharacteristic
160C22×C4×D3C2312yes—
161C22×C4×D3C2311yescharacteristic
162C22×Dic6C2311yescharacteristic, complemented
163C3×#120D418yes—
164C3×C4×D4—44no—
165C2×C3×C4⋊C4C2312yescomplemented
166C2×C3×C4⋊C4C2311yescharacteristic, complemented
167C2×C3×C22⋊C4—44no—
168C2×C3×C22⋊C4C2312yes—
169C2×C3×C22⋊C4C2312yes—
170C2×C3×C22⋊C4C2312yes—
171C2×C3×C22⋊C4C2312yes—
172C2×C3×C22⋊C4C2312yes—
173C2×C3×C22⋊C4C2311yescharacteristic
174C2×C3×C22⋊C4C2312yescomplemented
175C2×C3×C22⋊C4C2311yescharacteristic, complemented
176C2×C3×C42C2312yescomplemented
177C2×C3×C42C2311yescharacteristic, complemented
178#953—24no—
179C2×#217—28no—
180C2×#217C2312yes—
181C2×#217C2311yescharacteristic
182C2×#217C2312yes—
183C2×#217C2312yes—
184C2×#217C2312yes—
185C2×#217C2312yes—
186C2×#217C2312yescomplemented
187C2×#217C2311yescharacteristic, complemented
188#937—28no—
189#937—24no—
190#936—24no—
191#935—24no—
192#935—28no—
193D4×Dic3—28no—
194C2×(C2×D3)⋊C4—28no—
195C2×(C2×D3)⋊C4—44no—
196C2×(C2×D3)⋊C4—44no—
197C2×(C2×D3)⋊C4—42no—
198C2×(C2×D3)⋊C4—44no—
199C2×(C2×D3)⋊C4C2312yes—
200C2×(C2×D3)⋊C4C2312yes—
201C2×(C2×D3)⋊C4C2312yes—
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×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2312yescomplemented
219C2×(C2×D3)⋊C4C2312yescomplemented
220C2×(C2×D3)⋊C4C2312yescomplemented
221C2×(C2×D3)⋊C4C2312yescomplemented
222C2×C4⋊Dic3C2312yescomplemented
223C2×C4⋊Dic3C2312yescomplemented
224C2×C4⋊Dic3C2312yescomplemented
225C2×C4⋊Dic3C2312yescomplemented
226C2×C4⋊Dic3C2312yescomplemented
227C2×Dic3⋊C4C2312yescomplemented
228C2×Dic3⋊C4C2312yescomplemented
229C2×Dic3⋊C4C2312yescomplemented
230C2×C4×Dic3C2311yescharacteristic, complemented
231C2×C4×Dic3C2312yescomplemented
232#897—42no—
233#886—42no—
234#886—44no—
235#882—28no—
236#882—24no—
237D3×C22⋊C4—28no—
238D3×C22⋊C4—24no—
239#879—28no—
240#878—28no—
241#877—28no—
242#875—42no—
243C3×#95C2312yescomplemented
244C3×#95C2312yescomplemented
245C3×#95C2312yescomplemented
246C3⋊#95C2312yescomplemented
247C3⋊#95C2312yescomplemented
248C3⋊#95C2312yescomplemented
249C3⋊#95C2312yescomplemented
250C3⋊#95C2312yescomplemented
251C3⋊#95C2312yescomplemented
252C3⋊#95C2312yescomplemented
253C3⋊#95C2312yescomplemented
254C26—31no—
255C23×D4—32no—
256C23×D4—31no—
257#551—68no—
258C2×#126—32no—
259C2×#124—31no—
260C2×#124—31no—
261C2×#123—31no—
262C2×#123—32no—
263C2×#123—32no—
264C2×#123—31no—
265C2×C22⋊Q8—31no—
266C2×C22⋊Q8—32no—
267C2×#120—31no—
268C2×#120—32no—
269C2×#120—31no—
270C2×#120—32no—
271C2×#120—31no—
272C2×#120—68no—
273C2×#120C2×D311yescharacteristic
274C2×C4×D4—32no—
275C2×C4×D4C2×D312yescomplemented
276C2×#117—32no—
277C22×C22⋊C4—32no—
278C22×C22⋊C4—32no—
279C22×C22⋊C4—32no—
280C22×C22⋊C4—32no—
281C22×C22⋊C4—32no—
282C22×C22⋊C4—31no—
283C22×C22⋊C4—32no—
284C22×C22⋊C4—31no—
285C22×C22⋊C4C2×D312yescomplemented
286#399—32no—
287#397—32no—
288#397—32no—
289#397—32no—
290#396—32no—
291#396—32no—
292#396—32no—
293#394—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#390—32no—
303#390—31no—
304#390—32no—
305#390C2×D311yescharacteristic, complemented
306#388—32no—
307#388—32no—
308#388—32no—
309#388—32no—
310#388—32no—
311#388—32no—
312#388C2×D312yescomplemented
313#386—32no—
314#386—32no—
315#386—32no—
316#386—31no—
317#386—32no—
318#386—32no—
319#386C2×D311yescharacteristic, complemented
320#386C2×D312yescomplemented
321#385—32no—
322#385—32no—
323#385—32no—
324#385—32no—
325#385C2×D312yescomplemented
326#381—32no—
327#380—32no—
328#380—32no—
329#380—32no—
330#379—32no—
331#379—32no—
332#379—32no—
333#379—32no—
334#379—32no—
335#379—32no—
336#379—32no—
337#379—32no—
338#379—32no—
339#379—31no—
340C4×C22⋊C4—32no—
341C4×C22⋊C4—31no—
342C4×C22⋊C4C2×D312yescomplemented
343C24×C3—24no—
344C24×C3—24no—
345C24×C3—41no—
346C24×C3—41no—
347C24×C3C2×D414yes—
348C24×C3C2411yescharacteristic
349C24×C3C2411yescharacteristic
350C24×C3C2412yes—
351C23×D3—22no—
352C23×D3—24no—
353C23×D3—24no—
354C23×D3—24no—
355C23×D3—24no—
356C23×D3—24no—
357C23×D3—24no—
358C23×D3—24no—
359C23×D3—22no—
360C23×D3—22no—
361C23×D3—22no—
362C23×D3—24no—
363C23×D3—22no—
364C23×D3—24no—
365C23×D3—24no—
366C23×D3—24no—
367C23×D3—24no—
368C23×D3—22no—
369C23×D3—42no—
370C23×D3—42no—
371C23×D3—42no—
372C23×D3—41no—
373C23×D3—41no—
374C23×D3—42no—
375C23×D3—42no—
376C23×D3—42no—
377C23×D3—416no—
378C23×D3—41no—
379C23×D3—42no—
380C23×D3—432no—
381C23×D3—416no—
382C23×D3—432no—
383C23×D3—416no—
384C23×D3#4118yes—
385C23×D3C2411yescharacteristic
386C23×D3C2412yes—
387C23×D3C2411yescharacteristic
388C23×D3C2411yescharacteristic
389C2×C3×D4—24no—
390C2×C3×D4—24no—
391C2×C3×D4—41no—
392C2×C3×D4—41no—
393C2×C3×D4C2×D418yes—
394C2×C3×D4C2×D414yes—
395C22×C3×C4—24no—
396C22×C3×C4—24no—
397C22×C3×C4—42no—
398C22×C3×C4—42no—
399C22×C3×C4—41no—
400C22×C3×C4—42no—
401C22×C3×C4—42no—
402C22×C3×C4—42no—
403C22×C3×C4C2412yes—
404C22×C3×C4C2412yes—
405C22×C3×C4C2412yes—
406C22×C3×C4C2412yes—
407C22×C3×C4C2412yes—
408C22×C3×C4C2411yescharacteristic
409C2×#67—22no—
410C2×#67—24no—
411C2×#67—24no—
412C2×#67—22no—
413C2×#67—24no—
414C2×#67—24no—
415C2×#67—24no—
416C2×#67—22no—
417C2×#67—41no—
418C2×#67—41no—
419C2×#67—42no—
420C2×#67—41no—
421C22×Dic3—24no—
422C22×Dic3—24no—
423C22×Dic3—24no—
424C22×Dic3—24no—
425C22×Dic3—22no—
426C22×Dic3—41no—
427C22×Dic3—42no—
428C22×Dic3—42no—
429C22×Dic3—41no—
430C22×Dic3C2412yes—
431C22×Dic3C2411yescharacteristic
432C22×Dic3C2412yes—
433C22×Dic3C2412yes—
434C22×Dic3C2412yes—
435C22×Dic3C2412yes—
436D3×D4—432no—
437D3×D4—416no—
438C2×D12—24no—
439C2×D12—22no—
440C2×D12—24no—
441C2×D12—22no—
442C2×D12—42no—
443C2×D12—41no—
444C2×C4×D3—24no—
445C2×C4×D3—22no—
446C2×C4×D3—24no—
447C2×C4×D3—22no—
448C2×C4×D3—42no—
449C2×C4×D3—41no—
450C2×Dic6—22no—
451C2×Dic6—41no—
452C2×Dic6—41no—
453C3×C4⋊C4—41no—
454C3×C4⋊C4—42no—
455C3×C22⋊C4—24no—
456C3×C22⋊C4—24no—
457C3×C22⋊C4—41no—
458C3×C22⋊C4—42no—
459C3×C22⋊C4—42no—
460C3×C22⋊C4—42no—
461C3×C22⋊C4C2×D418yes—
462C3×C22⋊C4C2×D414yes—
463C3×C42—41no—
464C3×C42—42no—
465#217—24no—
466#217—24no—
467#217—24no—
468#217—24no—
469#217—22no—
470#217—24no—
471#217—24no—
472#217—22no—
473(C2×D3)⋊C4—24no—
474(C2×D3)⋊C4—24no—
475(C2×D3)⋊C4—24no—
476(C2×D3)⋊C4—24no—
477(C2×D3)⋊C4—24no—
478(C2×D3)⋊C4—24no—
479(C2×D3)⋊C4—24no—
480(C2×D3)⋊C4—24no—
481(C2×D3)⋊C4—24no—
482(C2×D3)⋊C4—24no—
483(C2×D3)⋊C4—24no—
484(C2×D3)⋊C4—42no—
485(C2×D3)⋊C4—42no—
486(C2×D3)⋊C4—42no—
487(C2×D3)⋊C4—42no—
488(C2×D3)⋊C4—42no—
489(C2×D3)⋊C4—42no—
490(C2×D3)⋊C4—42no—
491(C2×D3)⋊C4—42no—
492(C2×D3)⋊C4—42no—
493(C2×D3)⋊C4—42no—
494(C2×D3)⋊C4—42no—
495(C2×D3)⋊C4—42no—
496C4⋊Dic3—24no—
497C4⋊Dic3—42no—
498C4⋊Dic3—42no—
499C4⋊Dic3—42no—
500C4⋊Dic3—42no—
501Dic3⋊C4—24no—
502Dic3⋊C4—24no—
503Dic3⋊C4—24no—
504C4×Dic3—22no—
505C4×Dic3—24no—
506C25—32no—
507C25—32no—
508C25—31no—
509C25—31no—
510C25—31no—
511C25—68no—
512C25—64no—
513C25—124no—
514C25—122no—
515C25—122no—
516C25C22×D311yescharacteristic
517C22×Q8—31no—
518C22×D4—32no—
519C22×D4—31no—
520C22×D4—32no—
521C22×D4—31no—
522C22×D4—31no—
523C22×D4—32no—
524C22×D4—68no—
525C22×D4—68no—
526C22×D4—64no—
527C22×D4—122no—
528C22×D4—124no—
529C22×D4—122no—
530C22×D4C22×D312yes—
531C22×D4C22×D311yescharacteristic
532C23×C4—32no—
533C23×C4—32no—
534C23×C4—31no—
535C23×C4—31no—
536C23×C4—32no—
537C23×C4C22×D312yes—
538C23×C4C22×D312yes—
539C23×C4C22×D311yescharacteristic, complemented
540#126—68no—
541#124—64no—
542#124—122no—
543#123—68no—
544#123—64no—
545#123—124no—
546#123—122no—
547C22⋊Q8—68no—
548C22⋊Q8—122no—
549#120—64no—
550#120—68no—
551#120—64no—
552#120—68no—
553#120—64no—
554#120D1218yes—
555C4×D4—44no—
556C4×D4—68no—
557#117—68no—
558C2×C4⋊C4—32no—
559C2×C4⋊C4—32no—
560C2×C4⋊C4—32no—
561C2×C4⋊C4—32no—
562C2×C4⋊C4—32no—
563C2×C4⋊C4—32no—
564C2×C4⋊C4—32no—
565C2×C4⋊C4—32no—
566C2×C4⋊C4C22×D312yescomplemented
567C2×C4⋊C4C22×D311yescharacteristic, complemented
568C2×C22⋊C4—32no—
569C2×C22⋊C4—32no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—32no—
572C2×C22⋊C4—32no—
573C2×C22⋊C4—32no—
574C2×C22⋊C4—32no—
575C2×C22⋊C4—31no—
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⋊C4—32no—
584C2×C22⋊C4—32no—
585C2×C22⋊C4—32no—
586C2×C22⋊C4—32no—
587C2×C22⋊C4—32no—
588C2×C22⋊C4—32no—
589C2×C22⋊C4—32no—
590C2×C22⋊C4—32no—
591C2×C22⋊C4—32no—
592C2×C22⋊C4—32no—
593C2×C22⋊C4—32no—
594C2×C22⋊C4—32no—
595C2×C22⋊C4—32no—
596C2×C22⋊C4—32no—
597C2×C22⋊C4—32no—
598C2×C22⋊C4—32no—
599C2×C22⋊C4—44no—
600C2×C22⋊C4—68no—
601C2×C22⋊C4—68no—
602C2×C22⋊C4—68no—
603C2×C22⋊C4—64no—
604C2×C22⋊C4—122no—
605C2×C22⋊C4—124no—
606C2×C22⋊C4—124no—
607C2×C22⋊C4—124no—
608C2×C22⋊C4C22×D312yes—
609C2×C22⋊C4C22×D312yes—
610C2×C22⋊C4C22×D312yes—
611C2×C22⋊C4C22×D312yes—
612C2×C22⋊C4C22×D312yes—
613C2×C22⋊C4C22×D311yescharacteristic
614C2×C22⋊C4C22×D312yescomplemented
615C2×C22⋊C4C22×D311yescharacteristic, complemented
616C2×C42—31no—
617C2×C42—32no—
618C2×C42C22×D312yescomplemented
619C2×C42C22×D311yescharacteristic, complemented
620#95—32no—
621#95—32no—
622#95—32no—
623#95—32no—
624#95—32no—
625#95—32no—
626#95—32no—
627#95—32no—
628#95C22×D312yescomplemented
629#95C22×D312yescomplemented
630#95C22×D312yescomplemented
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—216no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—21no—
640C23×C3—22no—
641C23×C3—21no—
642C23×C3—21no—
643C23×C3—21no—
644C23×C3—44no—
645C23×C3—44no—
646C23×C3—48no—
647C23×C3—44no—
648C23×C3C22×D412yes—
649C23×C3C22×D412yes—
650C23×C3C22×D414yes—
651C23×C3C2×#4114yes—
652C23×C3H(5,𝔽2)14yes—
653C23×C3C2511yescharacteristic
654C22×D3—21no—
655C22×D3—22no—
656C22×D3—21no—
657C22×D3—28no—
658C22×D3—216no—
659C22×D3—216no—
660C22×D3—22no—
661C22×D3—21no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—21no—
670C22×D3—216no—
671C22×D3—21no—
672C22×D3—22no—
673C22×D3—21no—
674C22×D3—22no—
675C22×D3—21no—
676C22×D3—48no—
677C22×D3—48no—
678C22×D3—44no—
679C22×D3—48no—
680C22×D3—48no—
681C22×D3—48no—
682C22×D3—48no—
683C22×D3—48no—
684C22×D3—48no—
685C22×D3—48no—
686C22×D3—48no—
687C22×D3—48no—
688C22×D3—48no—
689C22×D3—44no—
690C22×D3—48no—
691C22×D3—48no—
692C22×D3—44no—
693C22×D3—48no—
694C22×D3—44no—
695C22×D3—4128no—
696C22×D3—44no—
697C22×D3—48no—
698C22×D3—44no—
699C22×D3—44no—
700C22×D3—84no—
701C22×D3—82no—
702C22×D3C2×#4114yes—
703C22×D3C2×#4114yes—
704C22×D3H(5,𝔽2)12yes—
705C22×D3H(5,𝔽2)12yes—
706C3×D4—216no—
707C3×D4—44no—
708C2×C3×C4—22no—
709C2×C3×C4—22no—
710C2×C3×C4—21no—
711C2×C3×C4—21no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—84no—
725C2×C3×C4—84no—
726C2×C3×C4—82no—
727C2×C3×C4C22×D414yes—
728C2×C3×C4C22×D412yes—
729#67—48no—
730#67—44no—
731#67—44no—
732#67—48no—
733C2×Dic3—22no—
734C2×Dic3—22no—
735C2×Dic3—22no—
736C2×Dic3—22no—
737C2×Dic3—22no—
738C2×Dic3—21no—
739C2×Dic3—22no—
740C2×Dic3—22no—
741C2×Dic3—22no—
742C2×Dic3—21no—
743C2×Dic3—22no—
744C2×Dic3—21no—
745C2×Dic3—22no—
746C2×Dic3—22no—
747C2×Dic3—22no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—22no—
751C2×Dic3—48no—
752C2×Dic3—84no—
753C2×Dic3—82no—
754D12—48no—
755D12—44no—
756C4×D3—48no—
757C4×D3—44no—
758Dic6—82no—
759C24—24no—
760C24—24no—
761C24—31no—
762C24—32no—
763C24—31no—
764C24—38no—
765C24—31no—
766C24—41no—
767C24—41no—
768C24—64no—
769C24—64no—
770C24—62no—
771C24—62no—
772C24—64no—
773C24—64no—
774C24—64no—
775C24—64no—
776C24—62no—
777C24—64no—
778C24—62no—
779C24—64no—
780C24—64no—
781C24—64no—
782C24—62no—
783C24—64no—
784C24—62no—
785C24—64no—
786C24—122no—
787C24—122no—
788C24—122no—
789C24—122no—
790C24—122no—
791C24—122no—
792C24—121no—
793C24—121no—
794C24—122no—
795C24—121no—
796C24—1232no—
797C24—1216no—
798C24—1216no—
799C24—1232no—
800C24—1216no—
801C24C2×D1214yes—
802C24C23×D311yescharacteristic
803C24C23×D311yescharacteristic
804C24C23×D312yes—
805C2×Q8—62no—
806C2×Q8—121no—
807C2×Q8—121no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—41no—
811C2×D4—41no—
812C2×D4—62no—
813C2×D4—64no—
814C2×D4—62no—
815C2×D4—64no—
816C2×D4—62no—
817C2×D4—64no—
818C2×D4—62no—
819C2×D4—64no—
820C2×D4—64no—
821C2×D4—64no—
822C2×D4—64no—
823C2×D4—62no—
824C2×D4—122no—
825C2×D4—121no—
826C2×D4—122no—
827C2×D4—121no—
828C2×D4—121no—
829C2×D4—121no—
830C2×D4—1232no—
831C2×D4—1216no—
832C2×D4C2×D1218yes—
833C2×D4C2×D1214yes—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—32no—
837C22×C4—31no—
838C22×C4—32no—
839C22×C4—32no—
840C22×C4—32no—
841C22×C4—32no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—41no—
847C22×C4—42no—
848C22×C4—62no—
849C22×C4—64no—
850C22×C4—64no—
851C22×C4—64no—
852C22×C4—64no—
853C22×C4—64no—
854C22×C4—62no—
855C22×C4—64no—
856C22×C4—62no—
857C22×C4—122no—
858C22×C4—121no—
859C22×C4—121no—
860C22×C4—122no—
861C22×C4—122no—
862C22×C4—121no—
863C22×C4C23×D312yes—
864C22×C4C23×D312yes—
865C22×C4C23×D312yes—
866C22×C4C23×D312yes—
867C22×C4C23×D312yes—
868C22×C4C23×D311yescharacteristic
869C4⋊C4—42no—
870C4⋊C4—41no—
871C4⋊C4—64no—
872C4⋊C4—64no—
873C4⋊C4—64no—
874C4⋊C4—64no—
875C4⋊C4—122no—
876C4⋊C4—122no—
877C4⋊C4—122no—
878C4⋊C4—122no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—42no—
882C22⋊C4—42no—
883C22⋊C4—42no—
884C22⋊C4—41no—
885C22⋊C4—64no—
886C22⋊C4—64no—
887C22⋊C4—64no—
888C22⋊C4—64no—
889C22⋊C4—64no—
890C22⋊C4—64no—
891C22⋊C4—64no—
892C22⋊C4—64no—
893C22⋊C4—64no—
894C22⋊C4—62no—
895C22⋊C4—64no—
896C22⋊C4—64no—
897C22⋊C4—64no—
898C22⋊C4—64no—
899C22⋊C4—64no—
900C22⋊C4—62no—
901C22⋊C4—64no—
902C22⋊C4—64no—
903C22⋊C4—64no—
904C22⋊C4—122no—
905C22⋊C4—122no—
906C22⋊C4—122no—
907C22⋊C4—122no—
908C22⋊C4—122no—
909C22⋊C4—122no—
910C22⋊C4—122no—
911C22⋊C4—122no—
912C22⋊C4—122no—
913C22⋊C4—122no—
914C22⋊C4—122no—
915C22⋊C4—122no—
916C22⋊C4C2×D1218yes—
917C22⋊C4C2×D1214yes—
918C42—42no—
919C42—41no—
920C42—62no—
921C42—64no—
922C22×C3—24no—
923C22×C3—24no—
924C22×C3—24no—
925C22×C3—24no—
926C22×C3—24no—
927C22×C3—24no—
928C22×C3—24no—
929C22×C3—24no—
930C22×C3—22no—
931C22×C3—22no—
932C22×C3—416no—
933C22×C3—41no—
934C22×C3—41no—
935C22×C3—42no—
936C22×C3—42no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3#54618yes—
940C22×C3C23×D411yescharacteristic
941C22×C3C22×#4112yes—
942C22×C3C2×H(5,𝔽2)12yes—
943C22×C3C2×H(5,𝔽2)11yescharacteristic
944C22×C3C2×H(5,𝔽2)11yescharacteristic
945C2×D3—24no—
946C2×D3—22no—
947C2×D3—24no—
948C2×D3—22no—
949C2×D3—24no—
950C2×D3—24no—
951C2×D3—22no—
952C2×D3—24no—
953C2×D3—24no—
954C2×D3—432no—
955C2×D3—416no—
956C2×D3—432no—
957C2×D3—416no—
958C2×D3—42no—
959C2×D3—42no—
960C2×D3—41no—
961C2×D3—42no—
962C2×D3—42no—
963C2×D3—42no—
964C2×D3—41no—
965C2×D3—42no—
966C2×D3—41no—
967C2×D3—41no—
968C2×D3—42no—
969C2×D3—41no—
970C2×D3—88no—
971C2×D3#55114yescomplemented
972C3×C4—24no—
973C3×C4—22no—
974C3×C4—42no—
975C3×C4—42no—
976C3×C4—42no—
977C3×C4—42no—
978Dic3—42no—
979Dic3—42no—
980Dic3—42no—
981Dic3—42no—
982Dic3—41no—
983Dic3—42no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—216no—
997C23—34no—
998C23—32no—
999C23—34no—
1000C23—32no—
1001C23—44no—
1002C23—44no—
1003C23—44no—
1004C23—48no—
1005C23—616no—
1006C23—68no—
1007C23—616no—
1008C23—61no—
1009C23—62no—
1010C23—61no—
1011C23—62no—
1012C23—61no—
1013C23—62no—
1014C23—62no—
1015C23—62no—
1016C23—62no—
1017C23—62no—
1018C23—62no—
1019C23—62no—
1020C23—61no—
1021C23—616no—
1022C23—61no—
1023C23—62no—
1024C23—62no—
1025C23—61no—
1026C23—61no—
1027C23—128no—
1028C23—128no—
1029C23—128no—
1030C23—128no—
1031C23—128no—
1032C23—128no—
1033C23—128no—
1034C23—128no—
1035C23—128no—
1036C23—128no—
1037C23—128no—
1038C23—128no—
1039C23—124no—
1040C23—128no—
1041C23—124no—
1042C23—124no—
1043C23—124no—
1044C23—124no—
1045C23—128no—
1046C23—124no—
1047C23—128no—
1048C23—12128no—
1049C23—124no—
1050C23—128no—
1051C23—242no—
1052C23—244no—
1053C23C22×D1212yes—
1054C23C22×D1212yes—
1055C23C22×D1214yes—
1056C23#100414yes—
1057C23D3×#4114yes—
1058C23C24×D311yescharacteristic
1059Q8—242no—
1060D4—216no—
1061D4—44no—
1062D4—128no—
1063D4—124no—
1064D4—128no—
1065D4—124no—
1066D4—124no—
1067D4—128no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—62no—
1085C2×C4—62no—
1086C2×C4—62no—
1087C2×C4—61no—
1088C2×C4—62no—
1089C2×C4—62no—
1090C2×C4—62no—
1091C2×C4—62no—
1092C2×C4—62no—
1093C2×C4—62no—
1094C2×C4—62no—
1095C2×C4—62no—
1096C2×C4—62no—
1097C2×C4—62no—
1098C2×C4—62no—
1099C2×C4—62no—
1100C2×C4—61no—
1101C2×C4—61no—
1102C2×C4—84no—
1103C2×C4—84no—
1104C2×C4—82no—
1105C2×C4—128no—
1106C2×C4—124no—
1107C2×C4—128no—
1108C2×C4—242no—
1109C2×C4—244no—
1110C2×C4C22×D1214yes—
1111C2×C4C22×D1212yes—
1112C2×C3—28no—
1113C2×C3—42no—
1114C2×C3—42no—
1115C2×C3C2×#54612yes—
1116C2×C3C2×#55111yescharacteristic
1117C2×C3#348411yescharacteristic
1118C2×C3#349012yes—
1119C2×C3#353211yescharacteristic
1120D3—24no—
1121D3—44no—
1122D3—42no—
1123D3—81no—
1124C22—24no—
1125C22—24no—
1126C22—24no—
1127C22—24no—
1128C22—24no—
1129C22—24no—
1130C22—24no—
1131C22—24no—
1132C22—22no—
1133C22—22no—
1134C22—34no—
1135C22—416no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—42no—
1141C22—42no—
1142C22—64no—
1143C22—62no—
1144C22—62no—
1145C22—64no—
1146C22—64no—
1147C22—64no—
1148C22—62no—
1149C22—64no—
1150C22—64no—
1151C22—1232no—
1152C22—1232no—
1153C22—1216no—
1154C22—1216no—
1155C22—122no—
1156C22—122no—
1157C22—121no—
1158C22—121no—
1159C22—122no—
1160C22—122no—
1161C22—122no—
1162C22—122no—
1163C22—121no—
1164C22—121no—
1165C22—121no—
1166C22—122no—
1167C22—248no—
1168C22#555418yes—
1169C22C23×D1211yescharacteristic
1170C22C2×#100412yes—
1171C22C2×D3×#4112yes—
1172C22D3×H(5,𝔽2)11yescharacteristic
1173C22D3×H(5,𝔽2)11yescharacteristic
1174C4—24no—
1175C4—22no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—42no—
1180C4—122no—
1181C4—122no—
1182C4—122no—
1183C4—121no—
1184C4—122no—
1185C4—122no—
1186C3#5900611yescharacteristic, complemented, Sylow
1187C2—28no—
1188C2—42no—
1189C2—42no—
1190C2—64no—
1191C2—124no—
1192C2—122no—
1193C2—241no—
1194C2C2×#555412yes—
1195C2#8586711yescharacteristic
1196C2#8662211yescharacteristic
1197C2#8666412yes—
1198C2D3×#55111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2358C2
prime radicalC2×D3×#120C2
hypercenter#2358D3
hypocenterC3#59006
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2358

Complements

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

NH ≅ G/Ntype
2. C2×#5587C2semidirect
3. C3×#2358C2semidirect
4. #82414C2semidirect
5. D4×(C2×D3)⋊C4C2semidirect
6. C2×#4955C2semidirect
7. #82108C2semidirect
8. #76469C2semidirect
9. #76315C2semidirect
10. #75918C2semidirect
11. #75540C2semidirect
12. #74918C2semidirect
13. #74891C2semidirect
14. #74686C2semidirect
15. #74686C2semidirect
16. #74602C2semidirect
17. #74413C2semidirect
18. #73594C2semidirect
19. #73575C2semidirect
25. C2×C3×C4×D4C22semidirect
26. C22×C3×C22⋊C4C22semidirect
28. C22×#217C22semidirect
31. C2×#936C22semidirect
32. C2×#935C22semidirect
33. C2×#935C22semidirect
34. C2×D4×Dic3C22semidirect
37. C22×(C2×D3)⋊C4C22semidirect
38. C22×(C2×D3)⋊C4C22semidirect
39. C22×(C2×D3)⋊C4C22semidirect
42. C2×#897C22semidirect
43. C2×#886C22semidirect
44. C2×#886C22semidirect
49. C2×#879C22semidirect
50. C2×#878C22semidirect
51. C2×#877C22semidirect
52. C2×#875C22semidirect
53. C3×#390C22semidirect
54. C3×#388C22semidirect
55. C3×#386C22semidirect
56. C3×#386C22semidirect
57. C3×#385C22semidirect
58. C3×C4×C22⋊C4C22semidirect
59. #5213C22semidirect
60. #5213C22semidirect
61. #5213C22semidirect
62. #5213C22semidirect
63. #5212C22semidirect
64. #5212C22semidirect
65. #4994C22semidirect
66. #4994C22semidirect
67. #4994C22semidirect
68. #4988C22semidirect
69. #4988C22semidirect
70. #4987C22semidirect
71. #4961C22semidirect
72. #4961C22semidirect
73. #4961C22semidirect
74. #4961C22semidirect
75. #4961C22semidirect
76. #4958C22semidirect
77. #4958C22semidirect
82. #4955C22semidirect
83. #4955C22semidirect
84. #4955C22semidirect
85. #4955C22semidirect
86. #4955C22semidirect
87. #4955C22semidirect
88. #4953C22semidirect
89. #4953C22semidirect
90. #4950C22semidirect
91. #4943C22semidirect
92. #4940C22semidirect
93. #4940C22semidirect
94. #4940C22semidirect
95. #4939C22semidirect
96. C4×(C2×D3)⋊C4C22semidirect
97. C4×(C2×D3)⋊C4C22semidirect
98. #4677C22semidirect
99. #4674C22semidirect
100. #4673C22semidirect
101. #4672C22semidirect
102. #4672C22semidirect
103. #4672C22semidirect
104. #4670C22semidirect
105. #4670C22semidirect
106. #4670C22semidirect
107. #4668C22semidirect
108. #4668C22semidirect
109. #4668C22semidirect
125. #2358D3semidirect
144. C23×C3×C4C23semidirect
151. C23×Dic3C23semidirect
162. C22×Dic6C23semidirect
165. C2×C3×C4⋊C4C23semidirect
166. C2×C3×C4⋊C4C23semidirect
174. C2×C3×C22⋊C4C23semidirect
175. C2×C3×C22⋊C4C23semidirect
176. C2×C3×C42C23semidirect
177. C2×C3×C42C23semidirect
186. C2×#217C23semidirect
187. C2×#217C23semidirect
218. C2×(C2×D3)⋊C4C23semidirect
219. C2×(C2×D3)⋊C4C23semidirect
220. C2×(C2×D3)⋊C4C23semidirect
221. C2×(C2×D3)⋊C4C23semidirect
222. C2×C4⋊Dic3C23semidirect
223. C2×C4⋊Dic3C23semidirect
224. C2×C4⋊Dic3C23semidirect
225. C2×C4⋊Dic3C23semidirect
226. C2×C4⋊Dic3C23semidirect
227. C2×Dic3⋊C4C23semidirect
228. C2×Dic3⋊C4C23semidirect
229. C2×Dic3⋊C4C23semidirect
230. C2×C4×Dic3C23semidirect
231. C2×C4×Dic3C23semidirect
243. C3×#95C23semidirect
244. C3×#95C23semidirect
245. C3×#95C23semidirect
246. C3⋊#95C23semidirect
247. C3⋊#95C23semidirect
248. C3⋊#95C23semidirect
249. C3⋊#95C23semidirect
250. C3⋊#95C23semidirect
251. C3⋊#95C23semidirect
252. C3⋊#95C23semidirect
253. C3⋊#95C23semidirect
275. C2×C4×D4C2×D3semidirect
285. C22×C22⋊C4C2×D3semidirect
305. #390C2×D3semidirect
312. #388C2×D3semidirect
319. #386C2×D3semidirect
320. #386C2×D3semidirect
325. #385C2×D3semidirect
342. C4×C22⋊C4C2×D3semidirect
539. C23×C4C22×D3semidirect
566. C2×C4⋊C4C22×D3semidirect
567. C2×C4⋊C4C22×D3semidirect
614. C2×C22⋊C4C22×D3semidirect
615. C2×C22⋊C4C22×D3semidirect
618. C2×C42C22×D3semidirect
619. C2×C42C22×D3semidirect
628. #95C22×D3semidirect
629. #95C22×D3semidirect
630. #95C22×D3semidirect
971. C2×D3#551semidirect
1186. C3#59006semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#1202
C2×#55872
C3×#23582
#824142
D4×(C2×D3)⋊C42
C2×#49552
#821082
#764692
#763152
#759182
#755402
#749182
#748912
#746862
#746022
#744132
#735942
#735752
#590063