Finite Group Databasebeta

← #11806094

Subgroups — #11806094

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
1C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#64162C211yesmaximal, characteristic
3C22×#3757C211yesmaximal, characteristic, complemented
4C2×C4×#638C211yesmaximal, characteristic, complemented
5C2×#64090C211yesmaximal, characteristic, complemented
6#10592912C211yesmaximal, characteristic, complemented
7#10592909C211yesmaximal, characteristic, complemented
8C4×#3757C211yesmaximal, characteristic, complemented
9#10592657C211yesmaximal, characteristic, complemented
10#10592656C211yesmaximal, characteristic, complemented
11#10592655C211yesmaximal, characteristic, complemented
12#10592645C211yesmaximal, characteristic, complemented
13#10592644C211yesmaximal, characteristic, complemented
14#10592643C211yesmaximal, characteristic, complemented
15C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
16#82099—34nomaximal
17C25×C32C2211yescharacteristic
18C23×C32×C4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C23×C3⋊Dic3C2211yescharacteristic
24C23×C3⋊Dic3C2211yescharacteristic
25C22×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C32×C22⋊C4—24no—
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31#64162C418yescomplemented
32C2×#3757—24no—
33C2×#3757C2211yescharacteristic
34C2×#3757C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37C2×#3757C2211yescharacteristic
38C2×#3757C2211yescharacteristic
39C2×#3757C2211yescharacteristic
40C4×#638—24no—
41C2×#3752C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
48C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
49C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
50#64090—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56#63658C2211yescharacteristic, complemented
57C22×C3×C22⋊C4D314yescomplemented
58C2×#953—34no—
59C22×#217—34no—
60C2×C4×#67—34no—
61C2×#67⋊C4—34no—
62#5213—34no—
63#5210—34no—
64C4×#217—34no—
65#4958—34no—
66#4957—34no—
67#4956—34no—
68#4946—34no—
69#4945—34no—
70#4944—34no—
71Dic3×C22⋊C4—34no—
72C24×C32—22no—
73C24×C32—22no—
74C24×C32—22no—
75C24×C32—22no—
76C24×C32—41no—
77C24×C32—41no—
78C24×C32C2×C414yescomplemented
79C24×C32C2311yescharacteristic
80C24×C32C2311yescharacteristic
81C24×C32C2311yescharacteristic
82C23×C3⋊D3C2311yescharacteristic
83C22×C32×C4—22no—
84C22×C32×C4—22no—
85C22×C32×C4—22no—
86C22×C32×C4—22no—
87C22×C32×C4—41no—
88C22×C32×C4—41no—
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—41no—
98C2×#638—41no—
99C2×#638C2×C414yescomplemented
100C2×#638C2×C414yescomplemented
101C2×#638C2×C414yescomplemented
102C22×C3⋊Dic3—22no—
103C22×C3⋊Dic3—22no—
104C22×C3⋊Dic3—22no—
105C22×C3⋊Dic3—22no—
106C22×C3⋊Dic3—41no—
107C22×C3⋊Dic3—41no—
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4×C3⋊D3—22no—
116C2×C4×C3⋊D3—22no—
117C2×C4×C3⋊D3—41no—
118C32×C22⋊C4—22no—
119C32×C22⋊C4—22no—
120C32×C22⋊C4—22no—
121C32×C22⋊C4D414yescomplemented
122#3757—22no—
123#3757—22no—
124#3757—22no—
125#3757C2×C414yescomplemented
126#3757C2×C414yescomplemented
127#3757C2×C414yescomplemented
128#3757D414yescomplemented
129#3752—22no—
130#3752—22no—
131#3752—41no—
132#3750—22no—
133#3750—22no—
134#3750—41no—
135C4×C3⋊Dic3—22no—
136C4×C3⋊Dic3—22no—
137C4×C3⋊Dic3—41no—
138#2358—91noSylow
139C25×C3C2×D314yes—
140C23×C3×C4C2×D314yes—
141C23×C3×C4C2×D314yes—
142C22×#67—34no—
143C22×#67—34no—
144C22×#67—34no—
145C23×Dic3—34no—
146C23×Dic3—34no—
147C22×C4×D3—34no—
148C2×C3×C22⋊C4—216no—
149C2×C3×C22⋊C4C2×D314yes—
150C2×C3×C22⋊C4C2×D314yes—
151C2×C3×C22⋊C4C2×D314yes—
152C2×C3×C22⋊C4C2×D314yes—
153#953—332no—
154C2×#217—34no—
155C2×#217—34no—
156C2×#217—34no—
157C2×#217—34no—
158C2×#217—34no—
159C2×#217—34no—
160C2×#217—34no—
161C2×#217—616no—
162C4×#67—616no—
163C2×(C2×D3)⋊C4—34no—
164C2×(C2×D3)⋊C4—34no—
165C2×(C2×D3)⋊C4—34no—
166C2×Dic3⋊C4—34no—
167C2×Dic3⋊C4—34no—
168C2×Dic3⋊C4—34no—
169C2×C4×Dic3—34no—
170C2×C4×Dic3—34no—
171C2×C4×Dic3—34no—
172#67⋊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—28no—
188C23×C32—28no—
189C23×C32—21no—
190C23×C32—21no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—44no—
196C23×C32—44no—
197C23×C32—44no—
198C23×C32—44no—
199C23×C32—44no—
200C23×C32C22×C412yes—
201C23×C32C22×C412yes—
202C23×C32C22×C412yes—
203C23×C32C2×D412yes—
204C23×C32C2×D412yes—
205C23×C32#4112yes—
206C23×C32#4112yes—
207C23×C32C2411yescharacteristic
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3C22×C412yes—
215C2×C32×C4—21no—
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—44no—
226C2×C32×C4—44no—
227C2×C32×C4C2×D412yes—
228C2×C32×C4C2×D412yes—
229#638—28no—
230#638—28no—
231#638—44no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
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—44no—
249C2×C3⋊Dic3—44no—
250C2×C3⋊Dic3C22×C412yes—
251C2×C3⋊Dic3C22×C412yes—
252C2×C3⋊Dic3C22×C412yes—
253C2×C3⋊Dic3C2×D412yes—
254C2×C3⋊Dic3C2×D412yes—
255C4×C3⋊D3—44no—
256C2×#120—91no—
257C2×C4×D4—91no—
258C2×C4×D4—91no—
259C22×C22⋊C4—91no—
260C22×C22⋊C4C3⋊D311yescharacteristic, complemented
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×C3—28no—
272C24×C3—28no—
273C24×C3—28no—
274C24×C3—28no—
275C24×C3—44no—
276C24×C3—44no—
277C24×C3C4×D3116yescomplemented
278C24×C3C22×D314yes—
279C24×C3C22×D314yes—
280C24×C3C22×D314yes—
281C23×D3—34no—
282C22×C3×C4—28no—
283C22×C3×C4—28no—
284C22×C3×C4—28no—
285C22×C3×C4—28no—
286C22×C3×C4—44no—
287C22×C3×C4—44no—
288C22×C3×C4C22×D314yes—
289C22×C3×C4C22×D314yes—
290C22×C3×C4C22×D314yes—
291C22×C3×C4C22×D314yes—
292C2×#67—316no—
293C2×#67—316no—
294C2×#67—316no—
295C2×#67—68no—
296C2×#67—68no—
297C2×#67—68no—
298C2×#67—68no—
299C2×#67—124no—
300C2×#67—124no—
301C22×Dic3—34no—
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—68no—
311C22×Dic3—68no—
312C22×Dic3—124no—
313C22×Dic3—124no—
314C2×C4×D3—68no—
315C2×C4×D3—68no—
316C2×C4×D3—124no—
317C3×C22⋊C4—28no—
318C3×C22⋊C4—28no—
319C3×C22⋊C4—28no—
320C3×C22⋊C4#67116yescomplemented
321#217—316no—
322#217—316no—
323#217—316no—
324#217—316no—
325#217—68no—
326#217—68no—
327#217—68no—
328(C2×D3)⋊C4—68no—
329(C2×D3)⋊C4—68no—
330(C2×D3)⋊C4—124no—
331Dic3⋊C4—68no—
332Dic3⋊C4—68no—
333Dic3⋊C4—124no—
334C4×Dic3—68no—
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—22no—
347C22×C32—22no—
348C22×C32—22no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—416no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32C4×D414yescomplemented
358C22×C32C4×D414yescomplemented
359C22×C32C23×C411yescharacteristic
360C22×C32C22×D411yescharacteristic
361C22×C32C22×D411yescharacteristic
362C22×C32C2×#4111yescharacteristic
363C22×C32C2×#4111yescharacteristic
364C22×C32H(5,𝔽2)11yescharacteristic
365C22×C32H(5,𝔽2)11yescharacteristic
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—22no—
369C2×C3⋊D3—41no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3—41no—
372C2×C3⋊D3—41no—
373C32×C4—22no—
374C32×C4—22no—
375C32×C4—41no—
376C32×C4—41no—
377C3⋊Dic3—22no—
378C3⋊Dic3—22no—
379C3⋊Dic3—22no—
380C3⋊Dic3—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—41no—
383C3⋊Dic3—41no—
384C25C2×C3⋊D311yescharacteristic
385C22×D4—91no—
386C22×D4—91no—
387C22×D4—91no—
388C23×C4—91no—
389C23×C4—91no—
390C23×C4—91no—
391C23×C4C2×C3⋊D311yescharacteristic
392C23×C4C2×C3⋊D311yescharacteristic
393#120—98no—
394C4×D4—184no—
395C4×D4—184no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4—91no—
399C2×C22⋊C4—24no—
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—184no—
411C2×C22⋊C4C2×C3⋊D311yescharacteristic
412C2×C22⋊C4C2×C3⋊D311yescharacteristic
413C2×C22⋊C4C2×C3⋊D311yescharacteristic
414C2×C22⋊C4C2×C3⋊D311yescharacteristic
415C2×C42—91no—
416C2×C42—91no—
417C2×C42—91no—
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—232no—
433C23×C3—232no—
434C23×C3—24no—
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—24no—
440C23×C3—416no—
441C23×C3—416no—
442C23×C3—416no—
443C23×C3—416no—
444C23×C3—416no—
445C23×C3C2×C4×D318yes—
446C23×C3C2×C4×D318yes—
447C23×C3C2×C4×D318yes—
448C23×C3#23518yes—
449C23×C3D3×D418yes—
450C23×C3#23718yes—
451C23×C3C2×#6718yes—
452C23×C3C23×D314yes—
453C22×D3—38no—
454C22×D3—64no—
455C22×D3—64no—
456C22×D3—64no—
457C22×D3—64no—
458C22×D3—64no—
459C22×D3—64no—
460C2×C3×C4—24no—
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—416no—
471C2×C3×C4—416no—
472C2×C3×C4C2×#6718yes—
473C2×C3×C4C2×#6718yes—
474#67—632no—
475#67—632no—
476#67—1216no—
477C2×Dic3—38no—
478C2×Dic3—38no—
479C2×Dic3—38no—
480C2×Dic3—38no—
481C2×Dic3—38no—
482C2×Dic3—64no—
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—
499C2×Dic3—1216no—
500C4×D3—1216no—
501C2×C32—24no—
502C2×C32—24no—
503C2×C32—42no—
504C2×C32C2×C4×D411yescharacteristic
505C2×C32C2×C4×D411yescharacteristic
506C2×C32#51811yescharacteristic
507C2×C32D4211yescharacteristic
508C2×C32#54611yescharacteristic
509C2×C32#54611yescharacteristic
510C2×C32#55111yescharacteristic
511C3⋊D3—42no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—41no—
517C24—41no—
518C24—91no—
519C24C4×C3⋊D314yescomplemented
520C24C22×C3⋊D311yescharacteristic
521C24C22×C3⋊D311yescharacteristic
522C24C22×C3⋊D311yescharacteristic
523C2×D4—94no—
524C2×D4—94no—
525C2×D4—94no—
526C2×D4—182no—
527C2×D4—182no—
528C2×D4—182no—
529C2×D4—182no—
530C2×D4—361no—
531C2×D4—361no—
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—91no—
545C22×C4—182no—
546C22×C4—182no—
547C22×C4—182no—
548C22×C4—182no—
549C22×C4—182no—
550C22×C4—182no—
551C22×C4—361no—
552C22×C4—361no—
553C22×C4—361no—
554C22×C4C22×C3⋊D311yescharacteristic
555C22×C4C22×C3⋊D311yescharacteristic
556C22×C4C22×C3⋊D311yescharacteristic
557C22×C4C22×C3⋊D311yescharacteristic
558C4⋊C4—182no—
559C4⋊C4—182no—
560C4⋊C4—361no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—94no—
565C22⋊C4—94no—
566C22⋊C4—94no—
567C22⋊C4—94no—
568C22⋊C4—182no—
569C22⋊C4—182no—
570C22⋊C4—182no—
571C22⋊C4—182no—
572C22⋊C4—182no—
573C22⋊C4—361no—
574C22⋊C4#63814yescomplemented
575C42—182no—
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—28no—
588C22×C3—28no—
589C22×C3—28no—
590C22×C3—28no—
591C22×C3—28no—
592C22×C3—28no—
593C22×C3—464no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3#67⋊C4116yescomplemented
599C22×C3C4×#67116yescomplemented
600C22×C3C22×C4×D314yes—
601C22×C3C2×#23514yes—
602C22×C3C2×D3×D414yes—
603C22×C3C2×#23714yes—
604C22×C3#100414yes—
605C22×C3#100414yes—
606C22×C3C22×#6714yes—
607C2×D3—68no—
608C2×D3—68no—
609C2×D3—68no—
610C2×D3—124no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—124no—
614C3×C4—28no—
615C3×C4—28no—
616C3×C4—44no—
617C3×C4—44no—
618Dic3—68no—
619Dic3—68no—
620Dic3—68no—
621Dic3—68no—
622Dic3—68no—
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—28no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—28no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—92no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23—181no—
653C23—181no—
654C23C2×C4×C3⋊D312yes—
655C23C2×C4×C3⋊D312yes—
656C23C2×C4×C3⋊D312yes—
657C23#382812yes—
658C23D4×C3⋊D312yes—
659C23#383012yes—
660C23C2×#63812yes—
661C23C23×C3⋊D311yescharacteristic
662D4—188no—
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—44no—
676C2×C4—44no—
677C2×C4—92no—
678C2×C4—92no—
679C2×C4—92no—
680C2×C4—92no—
681C2×C4—92no—
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—181no—
697C2×C4—181no—
698C2×C4—364no—
699C2×C4—364no—
700C2×C4—364no—
701C2×C4C2×#63812yes—
702C2×C4C2×#63812yes—
703C2×C3—216no—
704C2×C3—216no—
705C2×C3—48no—
706C2×C3C2×#67⋊C414yes—
707C2×C3#548614yes—
708C2×C3#549014yes—
709C2×C3#549514yes—
710C2×C3C2×C4×#6714yes—
711C2×C3D4×#6714yes—
712C2×C3#580614yes—
713D3—128no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—416no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—182no—
735C22—182no—
736C22—182no—
737C22—361no—
738C22—361no—
739C22—361no—
740C22—361no—
741C22#6409014yescomplemented
742C22C4×#63814yescomplemented
743C22C22×C4×C3⋊D311yescharacteristic
744C22C2×#382811yescharacteristic
745C22C2×D4×C3⋊D311yescharacteristic
746C22C2×#383011yescharacteristic
747C22#6436111yescharacteristic
748C22#6436111yescharacteristic
749C22C22×#63811yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—182no—
755C4—182no—
756C4—182no—
757C4—182no—
758C4—182no—
759C4—361no—
760C4—361no—
761C3#8209914yescomplemented
762C2—24no—
763C2—24no—
764C2—42no—
765C2—362no—
766C2C2×#6409011yescharacteristic
767C2#1059595711yescharacteristic
768C2#1059596111yescharacteristic
769C2#1059596611yescharacteristic
770C2C2×C4×#63811yescharacteristic
771C2D4×#63811yescharacteristic
772C2#1059627711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC22×C32×C22⋊C4C2
socle, cosocleC23×C32C24
prime radicalC2×#64162C2
hypercenterC22×C22⋊C4C3⋊D3
hypocenterC32#2358
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C22⋊C4C2semidirect
3. C22×#3757C2semidirect
4. C2×C4×#638C2semidirect
5. C2×#64090C2semidirect
6. #10592912C2semidirect
7. #10592909C2semidirect
8. C4×#3757C2semidirect
9. #10592657C2semidirect
10. #10592656C2semidirect
11. #10592655C2semidirect
12. #10592645C2semidirect
13. #10592644C2semidirect
14. #10592643C2semidirect
15. C22⋊C4×C3⋊Dic3C2semidirect
25. C22×C4×C3⋊D3C22semidirect
31. #64162C4semidirect
41. C2×#3752C22semidirect
42. C2×#3752C22semidirect
43. C2×#3752C22semidirect
44. C2×#3750C22semidirect
45. C2×#3750C22semidirect
46. C2×#3750C22semidirect
47. C2×C4×C3⋊Dic3C22semidirect
48. C2×C4×C3⋊Dic3C22semidirect
49. C2×C4×C3⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. #63658C22semidirect
57. C22×C3×C22⋊C4D3semidirect
78. C24×C32C2×C4semidirect
99. C2×#638C2×C4semidirect
100. C2×#638C2×C4semidirect
101. C2×#638C2×C4semidirect
121. C32×C22⋊C4D4semidirect
125. #3757C2×C4semidirect
126. #3757C2×C4semidirect
127. #3757C2×C4semidirect
128. #3757D4semidirect
260. C22×C22⋊C4C3⋊D3semidirect
277. C24×C3C4×D3semidirect
320. C3×C22⋊C4#67semidirect
357. C22×C32C4×D4semidirect
358. C22×C32C4×D4semidirect
519. C24C4×C3⋊D3semidirect
574. C22⋊C4#638semidirect
598. C22×C3#67⋊C4semidirect
599. C22×C3C4×#67semidirect
625. C32#2358semidirect
741. C22#64090semidirect
742. C22C4×#638semidirect
761. C3#82099semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C2×#641622
C22×#37572
C2×C4×#6382
C2×#640902
#105929122
#105929092
C4×#37572
#105926572
#105926562
#105926552
#105926452
#105926442
#105926432
C22⋊C4×C3⋊Dic32
#820993