Finite Group Databasebeta

← #11806088

Subgroups — #11806088

Order 1152.

2784 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×#64146C211yesmaximal, characteristic
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C22×#3752C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
6#10592919C211yesmaximal, characteristic, complemented
7#10592912C211yesmaximal, characteristic, complemented
8#10592909C211yesmaximal, characteristic, complemented
9#10592689C211yesmaximal, characteristic, complemented
10#10592688C211yesmaximal, characteristic, complemented
11#10592656C211yesmaximal, characteristic, complemented
12#10592655C211yesmaximal, characteristic, complemented
13C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
14#10592639C211yesmaximal, characteristic, complemented
15C4×#3752C211yesmaximal, characteristic, complemented
16#82398—34nomaximal
17C24×C3⋊D3C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic, complemented
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C23×C3⋊Dic3C2211yescharacteristic
24C22×C4×C3⋊D3C2211yescharacteristic
25C22×C4×C3⋊D3C2211yescharacteristic
26C32×C4×D4—24no—
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic, complemented
30C2×C32×C42C2211yescharacteristic, complemented
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic, complemented
34C2×#3757C2211yescharacteristic, complemented
35#64146C418yescomplemented
36C4×#638—24no—
37C2×#3752—24no—
38C2×#3752C2211yescharacteristic
39C2×#3752C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3752C2211yescharacteristic
46C2×#3750C2211yescharacteristic, complemented
47C2×#3750C2211yescharacteristic, complemented
48C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
49C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
50C22⋊C4×C3⋊D3—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56#63658C2211yescharacteristic, complemented
57C2×C3×C4×D4D314yescomplemented
58C2×#937—34no—
59C2×C4×#67—34no—
60C22×(C2×D3)⋊C4—34no—
61C2×D3×C22⋊C4—34no—
62#5220—34no—
63#5213—34no—
64#5210—34no—
65#4990—34no—
66#4989—34no—
67#4957—34no—
68#4956—34no—
69Dic3×C22⋊C4—34no—
70#4940—34no—
71C4×(C2×D3)⋊C4—34no—
72C24×C32C2311yescharacteristic
73C24×C32C2311yescharacteristic
74C23×C3⋊D3—22no—
75C23×C3⋊D3—22no—
76C23×C3⋊D3—22no—
77C23×C3⋊D3—22no—
78C23×C3⋊D3—41no—
79C23×C3⋊D3—41no—
80C23×C3⋊D3C2×C414yescomplemented
81C23×C3⋊D3C2311yescharacteristic
82C23×C3⋊D3C2311yescharacteristic
83C2×C32×D4—22no—
84C2×C32×D4—22no—
85C2×C32×D4C2×C414yescomplemented
86C22×C32×C4—22no—
87C22×C32×C4—22no—
88C22×C32×C4—22no—
89C22×C32×C4—22no—
90C22×C32×C4—41no—
91C22×C32×C4—41no—
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—22no—
98C2×#638—22no—
99C2×#638—41no—
100C2×#638—41no—
101C2×#638C2×C414yescomplemented
102C2×#638C2×C414yescomplemented
103C22×C3⋊Dic3—22no—
104C22×C3⋊Dic3—22no—
105C22×C3⋊Dic3—41no—
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×C4×C3⋊D3—22no—
113C2×C4×C3⋊D3—22no—
114C2×C4×C3⋊D3—22no—
115C2×C4×C3⋊D3—22no—
116C2×C4×C3⋊D3—41no—
117C2×C4×C3⋊D3—41no—
118C32×C4⋊C4—22no—
119C32×C22⋊C4—22no—
120C32×C22⋊C4D414yescomplemented
121C32×C42—22no—
122#3757—22no—
123#3757—22no—
124#3757—41no—
125#3757C2×C414yescomplemented
126#3752—22no—
127#3752—22no—
128#3752—22no—
129#3752—22no—
130#3752—22no—
131#3752C2×C414yescomplemented
132#3752C2×C414yescomplemented
133#3752D414yescomplemented
134#3750—22no—
135#3750—41no—
136C4×C3⋊Dic3—22no—
137C4×C3⋊Dic3—41no—
138#2358—91noSylow
139C24×D3—34no—
140C22×C3×D4C2×D314yes—
141C23×C3×C4C2×D314yes—
142C23×C3×C4C2×D314yescomplemented
143C22×#67—34no—
144C22×#67—34no—
145C23×Dic3—34no—
146C22×C4×D3—34no—
147C22×C4×D3—34no—
148C3×C4×D4—216no—
149C2×C3×C4⋊C4C2×D314yescomplemented
150C2×C3×C22⋊C4C2×D314yes—
151C2×C3×C22⋊C4C2×D314yescomplemented
152C2×C3×C42C2×D314yescomplemented
153C2×#217—34no—
154C2×#217—34no—
155C2×#217—34no—
156C2×#217—34no—
157#937—332no—
158C4×#67—616no—
159C2×(C2×D3)⋊C4—34no—
160C2×(C2×D3)⋊C4—34no—
161C2×(C2×D3)⋊C4—34no—
162C2×(C2×D3)⋊C4—34no—
163C2×(C2×D3)⋊C4—34no—
164C2×(C2×D3)⋊C4—34no—
165C2×(C2×D3)⋊C4—34no—
166C2×(C2×D3)⋊C4—34no—
167C2×(C2×D3)⋊C4—616no—
168C2×Dic3⋊C4—34no—
169C2×Dic3⋊C4—34no—
170C2×C4×Dic3—34no—
171C2×C4×Dic3—34no—
172D3×C22⋊C4—616no—
173C3⋊#95—34no—
174C3⋊#95—34no—
175C3⋊#95—34no—
176C3⋊#95—34no—
177C3⋊#95—34no—
178C3⋊#95—34no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—21no—
189C23×C32C22×C412yes—
190C23×C32C22×C412yes—
191C23×C32C2×D412yes—
192C23×C32#4112yes—
193C23×C32C2411yescharacteristic
194C22×C3⋊D3—21no—
195C22×C3⋊D3—21no—
196C22×C3⋊D3—21no—
197C22×C3⋊D3—21no—
198C22×C3⋊D3—28no—
199C22×C3⋊D3—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3—28no—
206C22×C3⋊D3—44no—
207C22×C3⋊D3—44no—
208C22×C3⋊D3—44no—
209C22×C3⋊D3—44no—
210C22×C3⋊D3—44no—
211C22×C3⋊D3C22×C412yes—
212C22×C3⋊D3C22×C412yes—
213C22×C3⋊D3C2×D412yes—
214C22×C3⋊D3#4112yes—
215C32×D4—28no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—44no—
228C2×C32×C4—44no—
229C2×C32×C4C22×C412yes—
230C2×C32×C4C2×D412yes—
231C2×C32×C4C2×D412yes—
232C2×C32×C4C2×D412yes—
233#638—28no—
234#638—44no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—44no—
251C2×C3⋊Dic3C22×C412yes—
252C2×C3⋊Dic3C22×C412yes—
253C2×C3⋊Dic3C2×D412yes—
254C4×C3⋊D3—44no—
255C4×C3⋊D3—44no—
256C2×#120—91no—
257C2×C4×D4—91no—
258C2×C4×D4C3⋊D311yescharacteristic, complemented
259C22×C22⋊C4—91no—
260C22×C22⋊C4—91no—
261#390—91no—
262#388—91no—
263#388—91no—
264#386—91no—
265#386—91no—
266#386—91no—
267#385—91no—
268#385—91no—
269C4×C22⋊C4—91no—
270C4×C22⋊C4—91no—
271C24×C3C22×D314yes—
272C24×C3C22×D314yes—
273C23×D3—34no—
274C23×D3—34no—
275C23×D3—316no—
276C23×D3—68no—
277C23×D3—68no—
278C23×D3—68no—
279C23×D3—68no—
280C23×D3—124no—
281C23×D3—124no—
282C2×C3×D4—28no—
283C2×C3×D4—28no—
284C2×C3×D4C4×D3116yescomplemented
285C22×C3×C4—28no—
286C22×C3×C4—28no—
287C22×C3×C4—28no—
288C22×C3×C4—28no—
289C22×C3×C4—44no—
290C22×C3×C4—44no—
291C22×C3×C4C22×D314yes—
292C22×C3×C4C22×D314yes—
293C22×C3×C4C22×D314yes—
294C22×C3×C4C22×D314yes—
295C22×C3×C4C22×D314yes—
296C2×#67—316no—
297C2×#67—316no—
298C2×#67—68no—
299C2×#67—68no—
300C2×#67—124no—
301C2×#67—124no—
302C22×Dic3—34no—
303C22×Dic3—34no—
304C22×Dic3—34no—
305C22×Dic3—34no—
306C22×Dic3—34no—
307C22×Dic3—34no—
308C22×Dic3—68no—
309C22×Dic3—68no—
310C22×Dic3—124no—
311C2×C4×D3—68no—
312C2×C4×D3—68no—
313C2×C4×D3—68no—
314C2×C4×D3—68no—
315C2×C4×D3—124no—
316C2×C4×D3—124no—
317C3×C4⋊C4—28no—
318C3×C22⋊C4—28no—
319C3×C22⋊C4#67116yescomplemented
320C3×C42—28no—
321#217—316no—
322#217—68no—
323#217—68no—
324#217—124no—
325(C2×D3)⋊C4—316no—
326(C2×D3)⋊C4—316no—
327(C2×D3)⋊C4—316no—
328(C2×D3)⋊C4—68no—
329(C2×D3)⋊C4—68no—
330(C2×D3)⋊C4—68no—
331(C2×D3)⋊C4—68no—
332(C2×D3)⋊C4—68no—
333Dic3⋊C4—68no—
334Dic3⋊C4—124no—
335C4×Dic3—68no—
336C4×Dic3—124no—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32C4×D414yescomplemented
351C22×C32C23×C411yescharacteristic
352C22×C32C22×D411yescharacteristic
353C22×C32C22×D411yescharacteristic
354C22×C32C2×#4111yescharacteristic
355C22×C32C2×#4111yescharacteristic
356C22×C32H(5,𝔽2)11yescharacteristic
357C22×C32H(5,𝔽2)11yescharacteristic
358C2×C3⋊D3—22no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—22no—
363C2×C3⋊D3—22no—
364C2×C3⋊D3—22no—
365C2×C3⋊D3—22no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—416no—
368C2×C3⋊D3—41no—
369C2×C3⋊D3—41no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3—41no—
372C2×C3⋊D3C4×D414yescomplemented
373C32×C4—22no—
374C32×C4—22no—
375C32×C4—22no—
376C32×C4—22no—
377C32×C4—41no—
378C3⋊Dic3—22no—
379C3⋊Dic3—22no—
380C3⋊Dic3—22no—
381C3⋊Dic3—41no—
382C3⋊Dic3—41no—
383C3⋊Dic3—41no—
384C25—91no—
385C22×D4—91no—
386C22×D4—91no—
387C22×D4C2×C3⋊D311yescharacteristic
388C23×C4—91no—
389C23×C4—91no—
390C23×C4—91no—
391C23×C4C2×C3⋊D311yescharacteristic
392C23×C4C2×C3⋊D311yescharacteristic, complemented
393#120—98no—
394C4×D4—24no—
395C4×D4—184no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
399C2×C22⋊C4—91no—
400C2×C22⋊C4—91no—
401C2×C22⋊C4—91no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4—91no—
404C2×C22⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C22⋊C4—91no—
410C2×C22⋊C4—91no—
411C2×C22⋊C4—184no—
412C2×C22⋊C4—184no—
413C2×C22⋊C4C2×C3⋊D311yescharacteristic
414C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
415C2×C42—91no—
416C2×C42—91no—
417C2×C42C2×C3⋊D311yescharacteristic, complemented
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3—24no—
433C23×C3—24no—
434C23×C3C2×C4×D318yes—
435C23×C3C2×C4×D318yes—
436C23×C3#23518yes—
437C23×C3C2×#6718yes—
438C23×C3C23×D314yes—
439C22×D3—38no—
440C22×D3—38no—
441C22×D3—38no—
442C22×D3—38no—
443C22×D3—632no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C22×D3—64no—
448C22×D3—632no—
449C22×D3—64no—
450C22×D3—64no—
451C22×D3—64no—
452C22×D3—64no—
453C22×D3—64no—
454C22×D3—64no—
455C22×D3—1216no—
456C22×D3—1216no—
457C22×D3—1216no—
458C22×D3—1216no—
459C22×D3—1216no—
460C3×D4—232no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—24no—
472C2×C3×C4—416no—
473C2×C3×C4—416no—
474C2×C3×C4C2×C4×D318yes—
475C2×C3×C4D3×D418yes—
476C2×C3×C4C2×#6718yes—
477C2×C3×C4C2×#6718yes—
478#67—632no—
479#67—1216no—
480C2×Dic3—38no—
481C2×Dic3—38no—
482C2×Dic3—38no—
483C2×Dic3—64no—
484C2×Dic3—64no—
485C2×Dic3—64no—
486C2×Dic3—64no—
487C2×Dic3—64no—
488C2×Dic3—64no—
489C2×Dic3—64no—
490C2×Dic3—64no—
491C2×Dic3—64no—
492C2×Dic3—64no—
493C2×Dic3—64no—
494C2×Dic3—64no—
495C2×Dic3—64no—
496C2×Dic3—64no—
497C2×Dic3—64no—
498C2×Dic3—1216no—
499C4×D3—1216no—
500C4×D3—1216no—
501C2×C32—24no—
502C2×C32—42no—
503C2×C32C2×C4×D411yescharacteristic
504C2×C32C2×C4×D411yescharacteristic
505C2×C32#51811yescharacteristic
506C2×C32D4211yescharacteristic
507C2×C32#54611yescharacteristic
508C2×C32#54611yescharacteristic
509C2×C32#55111yescharacteristic
510C3⋊D3—24no—
511C3⋊D3—42no—
512C24—91no—
513C24—91no—
514C24—94no—
515C24—182no—
516C24—182no—
517C24—182no—
518C24—182no—
519C24—361no—
520C24—361no—
521C24C22×C3⋊D311yescharacteristic
522C24C22×C3⋊D311yescharacteristic
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—94no—
526C2×D4—94no—
527C2×D4—182no—
528C2×D4—182no—
529C2×D4—361no—
530C2×D4—361no—
531C2×D4C4×C3⋊D314yescomplemented
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—91no—
539C22×C4—91no—
540C22×C4—91no—
541C22×C4—91no—
542C22×C4—91no—
543C22×C4—91no—
544C22×C4—182no—
545C22×C4—182no—
546C22×C4—182no—
547C22×C4—182no—
548C22×C4—182no—
549C22×C4—182no—
550C22×C4—361no—
551C22×C4—361no—
552C22×C4—361no—
553C22×C4C22×C3⋊D311yescharacteristic
554C22×C4C22×C3⋊D311yescharacteristic
555C22×C4C22×C3⋊D311yescharacteristic
556C22×C4C22×C3⋊D311yescharacteristic
557C22×C4C22×C3⋊D311yescharacteristic
558C4⋊C4—22no—
559C4⋊C4—182no—
560C4⋊C4—361no—
561C22⋊C4—22no—
562C22⋊C4—94no—
563C22⋊C4—94no—
564C22⋊C4—94no—
565C22⋊C4—94no—
566C22⋊C4—182no—
567C22⋊C4—182no—
568C22⋊C4—182no—
569C22⋊C4—182no—
570C22⋊C4—182no—
571C22⋊C4—182no—
572C22⋊C4—182no—
573C22⋊C4—361no—
574C22⋊C4#63814yescomplemented
575C42—22no—
576C42—182no—
577C42—361no—
578C22×C3—28no—
579C22×C3—28no—
580C22×C3—28no—
581C22×C3—28no—
582C22×C3—28no—
583C22×C3—28no—
584C22×C3—28no—
585C22×C3—28no—
586C22×C3—28no—
587C22×C3—44no—
588C22×C3—44no—
589C22×C3—44no—
590C22×C3—44no—
591C22×C3C4×#67116yescomplemented
592C22×C3C22×C4×D314yes—
593C22×C3C2×#23514yes—
594C22×C3C2×D3×D414yes—
595C22×C3#100414yes—
596C22×C3D3×#4114yes—
597C22×C3#100914yes—
598C22×C3C22×#6714yes—
599C2×D3—316no—
600C2×D3—68no—
601C2×D3—68no—
602C2×D3—68no—
603C2×D3—68no—
604C2×D3—68no—
605C2×D3—68no—
606C2×D3—68no—
607C2×D3—68no—
608C2×D3—68no—
609C2×D3—1264no—
610C2×D3—124no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—124no—
614C3×C4—28no—
615C3×C4—28no—
616C3×C4—28no—
617C3×C4—28no—
618C3×C4—44no—
619Dic3—68no—
620Dic3—68no—
621Dic3—68no—
622Dic3—124no—
623Dic3—124no—
624Dic3—124no—
625C32#235811yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—92no—
637C23—92no—
638C23—92no—
639C23—92no—
640C23—188no—
641C23—181no—
642C23—181no—
643C23—181no—
644C23—181no—
645C23—181no—
646C23—181no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—188no—
652C23—364no—
653C23—364no—
654C23—364no—
655C23—364no—
656C23—364no—
657C23C2×C4×C3⋊D312yes—
658C23C2×C4×C3⋊D312yes—
659C23#382812yes—
660C23C2×#63812yes—
661C23C23×C3⋊D311yescharacteristic
662D4—28no—
663D4—188no—
664D4—364no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—92no—
679C2×C4—92no—
680C2×C4—92no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4—181no—
686C2×C4—181no—
687C2×C4—181no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—364no—
697C2×C4—364no—
698C2×C4—364no—
699C2×C4C2×C4×C3⋊D312yes—
700C2×C4D4×C3⋊D312yes—
701C2×C4C2×#63812yes—
702C2×C4C2×#63812yes—
703C2×C3—216no—
704C2×C3—48no—
705C2×C3C4×D3×D414yes—
706C2×C3#554514yes—
707C2×C3#555014yes—
708C2×C3#555614yes—
709C2×C3C2×C4×#6714yes—
710C2×C3D4×#6714yes—
711C2×C3#582914yes—
712D3—616no—
713D3—128no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—94no—
728C22—182no—
729C22—182no—
730C22—182no—
731C22—182no—
732C22—182no—
733C22—182no—
734C22—182no—
735C22—182no—
736C22—182no—
737C22—3616no—
738C22—361no—
739C22—361no—
740C22—361no—
741C22—361no—
742C22C4×#63814yescomplemented
743C22C22×C4×C3⋊D311yescharacteristic
744C22C2×#382811yescharacteristic
745C22C2×D4×C3⋊D311yescharacteristic
746C22#6436111yescharacteristic
747C22#41×C3⋊D311yescharacteristic
748C22#6436611yescharacteristic
749C22C22×#63811yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—41no—
755C4—182no—
756C4—182no—
757C4—182no—
758C4—361no—
759C4—361no—
760C4—361no—
761C3#8239814yescomplemented
762C2—24no—
763C2—42no—
764C2—184no—
765C2—362no—
766C2C4×D4×C3⋊D311yescharacteristic
767C2#1059601611yescharacteristic
768C2#1059602111yescharacteristic
769C2#1059602711yescharacteristic
770C2C2×C4×#63811yescharacteristic
771C2D4×#63811yescharacteristic
772C2#1059630011yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC2×C32×C4×D4C2
socle, cosocleC23×C32C24
prime radicalC2×#64146C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#2358
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C4×#638C2semidirect
4. C22×#3752C2semidirect
5. C2×C22⋊C4×C3⋊D3C2semidirect
6. #10592919C2semidirect
7. #10592912C2semidirect
8. #10592909C2semidirect
9. #10592689C2semidirect
10. #10592688C2semidirect
11. #10592656C2semidirect
12. #10592655C2semidirect
13. C22⋊C4×C3⋊Dic3C2semidirect
14. #10592639C2semidirect
15. C4×#3752C2semidirect
20. C23×C32×C4C22semidirect
27. C2×C32×C4⋊C4C22semidirect
29. C2×C32×C22⋊C4C22semidirect
30. C2×C32×C42C22semidirect
33. C2×#3757C22semidirect
34. C2×#3757C22semidirect
35. #64146C4semidirect
46. C2×#3750C22semidirect
47. C2×#3750C22semidirect
48. C2×C4×C3⋊Dic3C22semidirect
49. C2×C4×C3⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. #63658C22semidirect
57. C2×C3×C4×D4D3semidirect
80. C23×C3⋊D3C2×C4semidirect
85. C2×C32×D4C2×C4semidirect
101. C2×#638C2×C4semidirect
102. C2×#638C2×C4semidirect
120. C32×C22⋊C4D4semidirect
125. #3757C2×C4semidirect
131. #3752C2×C4semidirect
132. #3752C2×C4semidirect
133. #3752D4semidirect
142. C23×C3×C4C2×D3semidirect
149. C2×C3×C4⋊C4C2×D3semidirect
151. C2×C3×C22⋊C4C2×D3semidirect
152. C2×C3×C42C2×D3semidirect
258. C2×C4×D4C3⋊D3semidirect
284. C2×C3×D4C4×D3semidirect
319. C3×C22⋊C4#67semidirect
350. C22×C32C4×D4semidirect
372. C2×C3⋊D3C4×D4semidirect
392. C23×C4C2×C3⋊D3semidirect
398. C2×C4⋊C4C2×C3⋊D3semidirect
414. C2×C22⋊C4C2×C3⋊D3semidirect
417. C2×C42C2×C3⋊D3semidirect
531. C2×D4C4×C3⋊D3semidirect
574. C22⋊C4#638semidirect
591. C22×C3C4×#67semidirect
625. C32#2358semidirect
742. C22C4×#638semidirect
761. C3#82398semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×#641462
C2×C4×#6382
C22×#37522
C2×C22⋊C4×C3⋊D32
#105929192
#105929122
#105929092
#105926892
#105926882
#105926562
#105926552
C22⋊C4×C3⋊Dic32
#105926392
C4×#37522
#823983