Finite Group Databasebeta

← #11804763

Subgroups — #11804763

Order 1152.

2621 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#625C211yesmaximal, characteristic
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×D3×#217C211yesmaximal, characteristic, complemented
4C2×#63879C212yesmaximal, complemented
5#10592641C211yesmaximal, characteristic, complemented
6C3×#4955C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591705C211yesmaximal, characteristic, complemented
9#10591386C212yesmaximal, complemented
10#10591381C212yesmaximal, complemented
11#10591363C212yesmaximal, complemented
12C22⋊C4×#67—31nomaximal
13#73850—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C24×C3×D3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×C4×D3C2212yescomplemented
18C22×#625—28no—
19C22×#625C418yescomplemented
20C22×#625C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2212yescomplemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3750C2212yescomplemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2212yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yescomplemented
33C3×D3×C22⋊C4—24no—
34D3×#217—24no—
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36C2×(C2×D3)⋊Dic3C2212yescomplemented
37C2×(C2×D3)⋊Dic3C2212yescomplemented
38C2×Dic32C2212yescomplemented
39#63879—28no—
40#63658C2212yescomplemented
41#63579C2212yescomplemented
42C23×#67—31no—
43C23×#67—31no—
44C22×C3×C22⋊C4—31no—
45C22×#217—31no—
46C2×C4×#67—32no—
47C2×#67⋊C4—32no—
48C2×D3×C22⋊C4—31no—
49C2×D3×C22⋊C4D311yescharacteristic, complemented
50C3×#379—31no—
51#5247—31no—
52#5213—32no—
53#4958—32no—
54#4957—32no—
55#4957—32no—
56#4956—32no—
57#4956—32no—
58#4955—31no—
59#4955D311yescharacteristic, complemented
60#4942—31no—
61#4942—31no—
62#4942—61no—
63Dic3×C22⋊C4—31no—
64Dic3×C22⋊C4—31no—
65C24×C32C2311yescharacteristic
66C23×C3×D3—22no—
67C23×C3×D3—22no—
68C23×C3×D3—22no—
69C23×C3×D3—22no—
70C23×C3×D3—24no—
71C23×C3×D3—24no—
72C23×C3×D3—42no—
73C23×C3×D3—42no—
74C23×C3×D3C2×C414yescomplemented
75C23×C3×D3C2×C414yescomplemented
76C23×C3×D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C22×C32×C4C2312yes—
81C22×C3⋊Dic3—24no—
82C22×C3⋊Dic3C2×C414yescomplemented
83C22×C3⋊Dic3C2312yes—
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2312yes—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—42no—
91C2×#625—24no—
92C2×#625—24no—
93C2×#625—24no—
94C2×#625—232no—
95C2×#625C2×C414yes—
96C2×#625C2×C414yescomplemented
97C2×#625C2×C414yescomplemented
98C2×#625C2×C414yescomplemented
99C2×#625D418yes—
100C2×D3×Dic3—24no—
101C2×D3×Dic3—24no—
102C2×D3×Dic3—42no—
103C32×C22⋊C4—22no—
104#3757—22no—
105#3750—24no—
106C3×#217—22no—
107C3×#217D414yescomplemented
108C3×(C2×D3)⋊C4—24no—
109C3×(C2×D3)⋊C4—24no—
110C3×(C2×D3)⋊C4—42no—
111(C2×D3)⋊Dic3—24no—
112(C2×D3)⋊Dic3—24no—
113(C2×D3)⋊Dic3—42no—
114Dic32—24no—
115D4×C22⋊C4—91noSylow
116C25×C3—31no—
117C25×C3—31no—
118C24×D3C2×D311yescharacteristic
119C24×D3C2×D311yescharacteristic
120C23×C3×C4—32no—
121C22×#67—31no—
122C22×#67—31no—
123C22×#67—38no—
124C22×#67—38no—
125C22×#67—31no—
126C22×#67—31no—
127C22×#67—31no—
128C22×#67—31no—
129C22×#67—31no—
130C22×#67—31no—
131C22×#67—68no—
132C22×#67—68no—
133C23×Dic3—31no—
134C23×Dic3—31no—
135C23×Dic3—32no—
136C23×Dic3—61no—
137C22×C4×D3—32no—
138C22×C4×D3C2×D312yescomplemented
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—32no—
143C2×C3×C22⋊C4—32no—
144C2×C3×C22⋊C4—32no—
145C2×C3×C22⋊C4—64no—
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—32no—
151C2×#217—32no—
152C2×#217—32no—
153C2×#217—61no—
154C2×#217—64no—
155C2×#217C2×D311yescharacteristic
156C2×#217C2×D311yescharacteristic
157C4×#67—68no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—32no—
160C2×(C2×D3)⋊C4—32no—
161C2×(C2×D3)⋊C4C2×D312yescomplemented
162C2×(C2×D3)⋊C4C2×D312yescomplemented
163C2×(C2×D3)⋊C4C2×D312yescomplemented
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—62no—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169#67⋊C4—68no—
170D3×C22⋊C4—24no—
171D3×C22⋊C4—64no—
172C3⋊#95—32no—
173C3⋊#95—32no—
174C3⋊#95—32no—
175C3⋊#95—32no—
176C3⋊#95—62no—
177C23×C32—22no—
178C23×C32—22no—
179C23×C32C22×C412yes—
180C23×C32C2×D412yes—
181C23×C32#4112yes—
182C23×C32C2411yescharacteristic
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3—28no—
190C22×C3×D3—28no—
191C22×C3×D3—21no—
192C22×C3×D3—21no—
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—21no—
196C22×C3×D3—21no—
197C22×C3×D3—22no—
198C22×C3×D3—22no—
199C22×C3×D3—28no—
200C22×C3×D3—28no—
201C22×C3×D3—44no—
202C22×C3×D3—44no—
203C22×C3×D3—48no—
204C22×C3×D3—48no—
205C22×C3×D3—48no—
206C22×C3×D3—48no—
207C22×C3×D3C22×C412yes—
208C22×C3×D3C22×C412yes—
209C22×C3×D3C22×C412yes—
210C22×C3×D3C22×C412yes—
211C22×C3×D3C2×D414yes—
212C22×C3×D3C2×D414yes—
213C2×C32×C4—22no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3—28no—
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3C22×C412yes—
222C2×C3⋊Dic3C22×C412yes—
223C2×C3⋊Dic3C2×D414yes—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3C2×D414yescomplemented
230C3×C4×D3—48no—
231#625—28no—
232#625—28no—
233#625—28no—
234#625C22⋊C4116yescomplemented
235D3×Dic3—48no—
236C23×D4—91no—
237C2×C4×D4—92no—
238C22×C22⋊C4—31no—
239C22×C22⋊C4—91no—
240#390—92no—
241#386—92no—
242#386—92no—
243#380—91no—
244#379—31no—
245#379—91no—
246C4×C22⋊C4—91no—
247C24×C3—21no—
248C24×C3—31no—
249C24×C3—31no—
250C24×C3—31no—
251C24×C3—31no—
252C24×C3—34no—
253C24×C3—34no—
254C24×C3—64no—
255C24×C3—64no—
256C24×C3—62no—
257C24×C3—62no—
258C24×C3—62no—
259C24×C3—62no—
260C24×C3—122no—
261C24×C3—122no—
262C24×C3C22×D311yescharacteristic
263C24×C3C22×D311yescharacteristic
264C23×D3—22no—
265C23×D3—22no—
266C23×D3—22no—
267C23×D3—22no—
268C23×D3—24no—
269C23×D3—24no—
270C23×D3—42no—
271C23×D3—42no—
272C23×D3C4×D314yescomplemented
273C23×D3C4×D314yescomplemented
274C23×D3C22×D311yescharacteristic
275C23×D3C22×D311yescharacteristic
276C23×D3C22×D311yescharacteristic
277C23×D3C22×D311yescharacteristic
278C22×C3×C4—22no—
279C22×C3×C4—32no—
280C22×C3×C4—32no—
281C22×C3×C4—64no—
282C22×C3×C4—64no—
283C22×C3×C4—122no—
284C22×C3×C4C22×D312yes—
285C22×C3×C4C22×D312yes—
286C2×#67—34no—
287C2×#67—34no—
288C2×#67—38no—
289C2×#67—38no—
290C2×#67—34no—
291C2×#67—34no—
292C2×#67—34no—
293C2×#67—34no—
294C2×#67—34no—
295C2×#67—34no—
296C2×#67—64no—
297C2×#67—64no—
298C2×#67—632no—
299C2×#67—632no—
300C2×#67—64no—
301C2×#67—64no—
302C2×#67—64no—
303C2×#67—64no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—34no—
307C22×Dic3—34no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—32no—
311C22×Dic3—32no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—64no—
315C22×Dic3—62no—
316C22×Dic3—64no—
317C22×Dic3—64no—
318C22×Dic3—64no—
319C22×Dic3—64no—
320C22×Dic3—124no—
321C22×Dic3—122no—
322C22×Dic3C22×D312yes—
323C22×Dic3C22×D312yes—
324C2×C4×D3—24no—
325C2×C4×D3—24no—
326C2×C4×D3—42no—
327C2×C4×D3—64no—
328C2×C4×D3—64no—
329C2×C4×D3—122no—
330C3×C22⋊C4—22no—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—42no—
334C3×C22⋊C4—64no—
335C3×C22⋊C4—64no—
336C3×C22⋊C4—62no—
337C3×C22⋊C4—122no—
338#217—22no—
339#217—64no—
340#217—62no—
341#217—62no—
342#217—64no—
343#217—122no—
344#217—122no—
345#217#6714yescomplemented
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—42no—
349(C2×D3)⋊C4—64no—
350(C2×D3)⋊C4—64no—
351(C2×D3)⋊C4—122no—
352Dic3⋊C4—64no—
353Dic3⋊C4—64no—
354Dic3⋊C4—124no—
355C4×Dic3—64no—
356C4×Dic3—64no—
357C22×C32—22no—
358C22×C32—22no—
359C22×C32—24no—
360C22×C32—24no—
361C22×C32C4×D414yescomplemented
362C22×C32C23×C411yescharacteristic
363C22×C32C22×D412yes—
364C22×C32C22×D411yescharacteristic
365C22×C32C2×#4111yescharacteristic
366C22×C32H(5,𝔽2)12yes—
367C2×C3×D3—22no—
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—24no—
372C2×C3×D3—24no—
373C2×C3×D3—24no—
374C2×C3×D3—24no—
375C2×C3×D3—22no—
376C2×C3×D3—22no—
377C2×C3×D3—22no—
378C2×C3×D3—22no—
379C2×C3×D3—22no—
380C2×C3×D3—22no—
381C2×C3×D3—416no—
382C2×C3×D3—416no—
383C2×C3×D3—42no—
384C2×C3×D3—42no—
385C2×C3×D3—42no—
386C2×C3×D3—42no—
387C2×C3×D3C2×C22⋊C414yescomplemented
388C2×C3×D3C2×C22⋊C414yescomplemented
389C32×C4—42no—
390C3⋊Dic3—22no—
391C3⋊Dic3—42no—
392C3⋊Dic3C2×C22⋊C414yescomplemented
393C3×Dic3—24no—
394C3×Dic3—42no—
395C25—31no—
396C25—31no—
397C22×D4—91no—
398C22×D4—91no—
399C22×D4—91no—
400C22×D4—91no—
401C22×D4—98no—
402C22×D4—188no—
403C23×C4—32no—
404C23×C4—92no—
405C23×C4—91no—
406C4×D4—188no—
407C2×C4⋊C4—92no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4—31no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—64no—
414C2×C22⋊C4—92no—
415C2×C22⋊C4—92no—
416C2×C22⋊C4—91no—
417C2×C22⋊C4—92no—
418C2×C22⋊C4—184no—
419C2×C22⋊C4D3211yescharacteristic
420C2×C42—92no—
421#95—92no—
422#95—92no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—21no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—32no—
432C23×C3—32no—
433C23×C3—34no—
434C23×C3—34no—
435C23×C3—32no—
436C23×C3—32no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—68no—
440C23×C3—68no—
441C23×C3—61no—
442C23×C3—61no—
443C23×C3—61no—
444C23×C3—62no—
445C23×C3—62no—
446C23×C3—61no—
447C23×C3—68no—
448C23×C3—68no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3—62no—
452C23×C3—62no—
453C23×C3—61no—
454C23×C3—62no—
455C23×C3—62no—
456C23×C3—61no—
457C23×C3—124no—
458C23×C3—124no—
459C23×C3—128no—
460C23×C3—128no—
461C23×C3—128no—
462C23×C3—128no—
463C23×C3C2×C4×D312yes—
464C23×C3C2×C4×D312yes—
465C23×C3#23512yes—
466C23×C3D3×D412yes—
467C23×C3#23712yes—
468C23×C3C2×#6712yes—
469C23×C3C23×D311yescharacteristic
470C23×C3C23×D311yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—21no—
477C22×D3—28no—
478C22×D3—28no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—21no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—21no—
487C22×D3—28no—
488C22×D3—28no—
489C22×D3—44no—
490C22×D3—44no—
491C22×D3—48no—
492C22×D3—48no—
493C22×D3—48no—
494C22×D3—48no—
495C22×D3C2×C4×D312yes—
496C22×D3C2×C4×D312yes—
497C22×D3C2×C4×D312yes—
498C22×D3C2×C4×D312yes—
499C22×D3D3×D414yes—
500C22×D3D3×D414yes—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—34no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4—42no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—128no—
517#67—316no—
518#67—316no—
519#67—68no—
520#67—68no—
521#67—68no—
522#67—68no—
523#67—68no—
524#67—68no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—34no—
533C2×Dic3—34no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—62no—
537C2×Dic3—64no—
538C2×Dic3—62no—
539C2×Dic3—68no—
540C2×Dic3—68no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—62no—
548C2×Dic3—62no—
549C2×Dic3—128no—
550C2×Dic3—122no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—122no—
554C2×Dic3—128no—
555C2×Dic3C2×#6714yescomplemented
556C4×D3—48no—
557C4×D3—128no—
558C2×C32—24no—
559C2×C32C22×C22⋊C411yescharacteristic
560C2×C32C2×C4×D411yescharacteristic
561C2×C32#51811yescharacteristic
562C2×C32D4212yes—
563C2×C32#54612yes—
564C3×D3—24no—
565C3×D3—24no—
566C3×D3—42no—
567C3×D3—42no—
568C24—31no—
569C24—31no—
570C24—31no—
571C24—31no—
572C24—34no—
573C24—34no—
574C24—64no—
575C24—64no—
576C24—62no—
577C24—62no—
578C24—62no—
579C24—62no—
580C24—122no—
581C24—122no—
582C24C2×D3211yescharacteristic
583C2×D4—98no—
584C2×D4—94no—
585C2×D4—94no—
586C2×D4—94no—
587C2×D4—94no—
588C2×D4—184no—
589C2×D4—1832no—
590C2×D4—184no—
591C2×D4—184no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—64no—
595C22×C4—64no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—94no—
599C22×C4—92no—
600C22×C4—122no—
601C22×C4—184no—
602C22×C4—184no—
603C22×C4—184no—
604C22×C4—362no—
605C22×C4C2×D3212yes—
606C4⋊C4—184no—
607C22⋊C4—22no—
608C22⋊C4—34no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—62no—
612C22⋊C4—122no—
613C22⋊C4—184no—
614C22⋊C4—184no—
615C22⋊C4—182no—
616C22⋊C4—362no—
617C42—184no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—24no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—24no—
632C22×C3—34no—
633C22×C3—34no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—44no—
637C22×C3—44no—
638C22×C3—62no—
639C22×C3—62no—
640C22×C3—62no—
641C22×C3—64no—
642C22×C3—62no—
643C22×C3—64no—
644C22×C3—64no—
645C22×C3—64no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—62no—
649C22×C3—62no—
650C22×C3—62no—
651C22×C3—62no—
652C22×C3—1216no—
653C22×C3—1216no—
654C22×C3—122no—
655C22×C3—122no—
656C22×C3—122no—
657C22×C3—122no—
658C22×C3#67⋊C414yescomplemented
659C22×C3C4×#6714yescomplemented
660C22×C3C22×C4×D311yescharacteristic
661C22×C3C22×C4×D311yescharacteristic
662C22×C3C2×#23511yescharacteristic
663C22×C3C2×D3×D412yes—
664C22×C3C2×D3×D412yes—
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C2×#23711yescharacteristic
667C22×C3#100412yes—
668C22×C3#100412yes—
669C22×C3C22×#6711yescharacteristic
670C2×D3—22no—
671C2×D3—22no—
672C2×D3—22no—
673C2×D3—24no—
674C2×D3—22no—
675C2×D3—24no—
676C2×D3—24no—
677C2×D3—24no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—22no—
684C2×D3—416no—
685C2×D3—416no—
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—42no—
689C2×D3—42no—
690C2×D3D3×C22⋊C414yescomplemented
691C2×D3D3×C22⋊C414yescomplemented
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—64no—
695C3×C4—82no—
696C3×C4—122no—
697Dic3—24no—
698Dic3—34no—
699Dic3—34no—
700Dic3—42no—
701Dic3—64no—
702Dic3—62no—
703Dic3—62no—
704Dic3—122no—
705Dic3—122no—
706Dic3—122no—
707Dic3—242no—
708C32D4×C22⋊C411yescharacteristic, complemented, Sylow
709C23—22no—
710C23—22no—
711C23—32no—
712C23—32no—
713C23—34no—
714C23—34no—
715C23—32no—
716C23—32no—
717C23—68no—
718C23—68no—
719C23—61no—
720C23—61no—
721C23—62no—
722C23—62no—
723C23—61no—
724C23—61no—
725C23—61no—
726C23—61no—
727C23—62no—
728C23—62no—
729C23—62no—
730C23—62no—
731C23—61no—
732C23—61no—
733C23—68no—
734C23—68no—
735C23—124no—
736C23—124no—
737C23—128no—
738C23—128no—
739C23—128no—
740C23—128no—
741C23#379512yes—
742C23C4×D3212yes—
743C23D3×#6712yes—
744C23C22×D3211yescharacteristic
745D4—916no—
746D4—188no—
747D4—188no—
748D4—188no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—34no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—92no—
759C2×C4—94no—
760C2×C4—92no—
761C2×C4—128no—
762C2×C4—188no—
763C2×C4—182no—
764C2×C4—182no—
765C2×C4—182no—
766C2×C4—182no—
767C2×C4—368no—
768C2×C3—24no—
769C2×C3—24no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—22no—
773C2×C3—21no—
774C2×C3—22no—
775C2×C3—44no—
776C2×C3—64no—
777C2×C3—64no—
778C2×C3—122no—
779C2×C3—122no—
780C2×C3C2×D3×C22⋊C411yescharacteristic
781C2×C3C2×D3×C22⋊C411yescharacteristic
782C2×C3C2×#67⋊C411yescharacteristic
783C2×C3#548611yescharacteristic
784C2×C3#548611yescharacteristic
785C2×C3#549012yes—
786C2×C3#559012yes—
787C2×C3#559112yes—
788C2×C3C2×C4×#6711yescharacteristic
789C2×C3D4×#6712yes—
790D3—24no—
791D3—24no—
792D3—42no—
793D3—42no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—24no—
798C22—34no—
799C22—34no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—62no—
804C22—64no—
805C22—64no—
806C22—64no—
807C22—64no—
808C22—62no—
809C22—62no—
810C22—62no—
811C22—62no—
812C22—62no—
813C22—62no—
814C22—1216no—
815C22—1216no—
816C22—122no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22#6387914yescomplemented
821C22C2×#379511yescharacteristic
822C22C2×C4×D3211yescharacteristic
823C22D32×D412yes—
824C22#6431312yes—
825C22C2×D3×#6711yescharacteristic
826C4—42no—
827C4—64no—
828C4—94no—
829C4—122no—
830C4—182no—
831C4—362no—
832C3—21no—
833C3#7385011yescharacteristic, complemented
834C3C22⋊C4×#6711yescharacteristic, complemented
835C2—24no—
836C2—64no—
837C2—64no—
838C2—122no—
839C2—122no—
840C2#1059418111yescharacteristic
841C2#1059418412yes—
842C2D32×C22⋊C411yescharacteristic
843C2C2×#6387911yescharacteristic
844C2#1059528712yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×#625C2
hypercenterC2×C22⋊C4D32
hypocenterC32D4×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C22⋊C4C2semidirect
3. C2×D3×#217C2semidirect
4. C2×#63879C2semidirect
5. #10592641C2semidirect
6. C3×#4955C2semidirect
7. #10591706C2semidirect
8. #10591705C2semidirect
9. #10591386C2semidirect
10. #10591381C2semidirect
11. #10591363C2semidirect
17. C22×C3×C4×D3C22semidirect
19. C22×#625C4semidirect
24. C22×D3×Dic3C22semidirect
27. C2×#3750C22semidirect
30. C2×C3×(C2×D3)⋊C4C22semidirect
31. C2×C3×(C2×D3)⋊C4C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. C2×(C2×D3)⋊Dic3C22semidirect
37. C2×(C2×D3)⋊Dic3C22semidirect
38. C2×Dic32C22semidirect
40. #63658C22semidirect
41. #63579C22semidirect
49. C2×D3×C22⋊C4D3semidirect
59. #4955D3semidirect
74. C23×C3×D3C2×C4semidirect
75. C23×C3×D3C2×C4semidirect
82. C22×C3⋊Dic3C2×C4semidirect
96. C2×#625C2×C4semidirect
97. C2×#625C2×C4semidirect
98. C2×#625C2×C4semidirect
107. C3×#217D4semidirect
138. C22×C4×D3C2×D3semidirect
161. C2×(C2×D3)⋊C4C2×D3semidirect
162. C2×(C2×D3)⋊C4C2×D3semidirect
163. C2×(C2×D3)⋊C4C2×D3semidirect
229. C2×C3×Dic3C2×D4semidirect
234. #625C22⋊C4semidirect
272. C23×D3C4×D3semidirect
273. C23×D3C4×D3semidirect
345. #217#67semidirect
361. C22×C32C4×D4semidirect
387. C2×C3×D3C2×C22⋊C4semidirect
388. C2×C3×D3C2×C22⋊C4semidirect
392. C3⋊Dic3C2×C22⋊C4semidirect
555. C2×Dic3C2×#67semidirect
658. C22×C3#67⋊C4semidirect
659. C22×C3C4×#67semidirect
690. C2×D3D3×C22⋊C4semidirect
691. C2×D3D3×C22⋊C4semidirect
708. C32D4×C22⋊C4semidirect
820. C22#63879semidirect
833. C3#73850semidirect
834. C3C22⋊C4×#67semidirect

Maximal subgroups

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

subgroupindex
C23×#6252
C2×C3×D3×C22⋊C42
C2×D3×#2172
C2×#638792
#105926412
C3×#49552
#105917062
#105917052
#105913862
#105913812
#105913632
C22⋊C4×#673
#738503