Finite Group Databasebeta

← #11809003

Subgroups — #11809003

Order 1152.

3809 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C23×#626C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×#63981C212yesmaximal, complemented
5C2×#63977C211yesmaximal, characteristic, complemented
6C3×#5220C211yesmaximal, characteristic, complemented
7#10591724C212yesmaximal, complemented
8#10591714C211yesmaximal, characteristic, complemented
9#10591711C211yesmaximal, characteristic, complemented
10#10591395C212yesmaximal, complemented
11#10591387C212yesmaximal, complemented
12#82604—31nomaximal
13#74884—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C24×C3⋊D3C2211yescharacteristic, complemented
16C24×C3×D3C2211yescharacteristic, complemented
17C22×C32×D4C2211yescharacteristic
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic, complemented
20C2×D4×C3⋊D3—24no—
21C2×D4×C3⋊D3—24no—
22C2×D4×C3⋊D3—24no—
23C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C3×#67C2212yescomplemented
26C23×C3×Dic3C2211yescharacteristic, complemented
27C22×#626—28no—
28C22×#626—24no—
29C22×#626C2212yes—
30C22×#626C2212yescomplemented
31C22×#626C2212yescomplemented
32C2×C3×#217C2211yescharacteristic, complemented
33C2×C3×#217C2211yescharacteristic, complemented
34C2×C3×#217C2212yescomplemented
35C3×#937—24no—
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37#63981—28no—
38#63977—24no—
39C2×#3722C2212yescomplemented
40C2×#3722C2212yescomplemented
41C2×#3722C2212yescomplemented
42C2×(C2×D3)⋊Dic3C2212yescomplemented
43C3×C3⋊#95C2212yescomplemented
44#63579C2212yescomplemented
45C23×#67—31no—
46C22×D3×D4—31no—
47C22×D3×D4—31no—
48C22×D3×D4—61no—
49C23×D12—31no—
50C2×C3×#120—31no—
51C2×#953—31no—
52C2×#937—32no—
53C2×#937D311yescharacteristic, complemented
54C2×#882—31no—
55C2×#882—32no—
56C3×#386—31no—
57#5223—32no—
58#5220D311yescharacteristic, complemented
59#5213—31no—
60#4960—32no—
61#4960—32no—
62#4958—31no—
63#4956—32no—
64#4955—31no—
65#4955—31no—
66#4671—32no—
67#4665—32no—
68C24×C32C2311yescharacteristic
69C24×C32C2311yescharacteristic
70C23×C3⋊D3—22no—
71C23×C3⋊D3—22no—
72C23×C3⋊D3—22no—
73C23×C3⋊D3—22no—
74C23×C3⋊D3—24no—
75C23×C3⋊D3—22no—
76C23×C3⋊D3—24no—
77C23×C3⋊D3—42no—
78C23×C3⋊D3—42no—
79C23×C3⋊D3D414yescomplemented
80C23×C3⋊D3C2311yescharacteristic
81C23×C3⋊D3C2311yescharacteristic
82C23×C3⋊D3C2311yescharacteristic
83C23×C3×D3—22no—
84C23×C3×D3—24no—
85C23×C3×D3—22no—
86C23×C3×D3—22no—
87C23×C3×D3—42no—
88C23×C3×D3C2312yes—
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4D414yescomplemented
92C22×C32×C4C2311yescharacteristic
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—22no—
96C2×#638—22no—
97C2×#638—22no—
98C2×#638D414yescomplemented
99C22×C3⋊Dic3C2311yescharacteristic
100D4×C3⋊D3—232no—
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—22no—
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—22no—
107C2×C3×#67—24no—
108C2×C3×#67—24no—
109C2×C3×#67—42no—
110C22×C3×Dic3—22no—
111C22×C3×Dic3—24no—
112C22×C3×Dic3C2312yes—
113C22×C3×Dic3C2312yes—
114C22×C3×Dic3C2312yes—
115C2×#626—232no—
116C2×#626—24no—
117C2×#626—24no—
118C2×#626—24no—
119C2×#626—24no—
120C2×#626—24no—
121C2×#626—24no—
122C2×#626—24no—
123C2×#626—42no—
124C2×#626D418yescomplemented
125C3×#217—22no—
126C3×#217—22no—
127C3×#217—24no—
128C3×(C2×D3)⋊C4—24no—
129#3722—24no—
130#3722—24no—
131#3722—42no—
132(C2×D3)⋊Dic3—24no—
133#2403—91noSylow
134C25×C3—31no—
135C24×D3—31no—
136C24×D3—31no—
137C24×D3—31no—
138C24×D3—31no—
139C24×D3—61no—
140C24×D3—61no—
141C24×D3C2×D311yescharacteristic, complemented
142C22×C3×D4—21no—
143C22×C3×D4—32no—
144C22×C3×D4C2×D311yescharacteristic
145C22×C3×D4C2×D311yescharacteristic
146C23×C3×C4—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—32no—
152C22×#67—32no—
153C22×#67—32no—
154C22×#67—61no—
155C22×#67—61no—
156C22×#67—68no—
157C22×#67—64no—
158C22×#67C2×D312yescomplemented
159C23×Dic3C2×D311yescharacteristic, complemented
160C2×D3×D4—64no—
161C2×D3×D4—64no—
162C2×D3×D4—64no—
163C2×D3×D4—64no—
164C2×D3×D4—68no—
165C2×D3×D4—68no—
166C2×D3×D4—68no—
167C2×D3×D4—64no—
168C2×D3×D4—64no—
169C22×D12—32no—
170C22×D12—32no—
171C22×D12—31no—
172C22×D12—31no—
173C22×D12—32no—
174C22×D12—61no—
175C22×D12—68no—
176C22×D12—64no—
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×C4×D3—61no—
180C3×#120—64no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—32no—
184C2×C3×C22⋊C4—32no—
185#953—64no—
186C2×#217—32no—
187C2×#217C2×D311yescharacteristic, complemented
188C2×#217C2×D311yescharacteristic, complemented
189C2×#217C2×D312yescomplemented
190#937—24no—
191#937—68no—
192C2×(C2×D3)⋊C4—32no—
193C2×(C2×D3)⋊C4—32no—
194C2×(C2×D3)⋊C4—32no—
195C2×(C2×D3)⋊C4—32no—
196C2×(C2×D3)⋊C4—32no—
197C2×(C2×D3)⋊C4—32no—
198C2×(C2×D3)⋊C4—32no—
199C2×(C2×D3)⋊C4C2×D312yescomplemented
200#882—68no—
201#882—64no—
202C3×#95—32no—
203C3⋊#95—32no—
204C3⋊#95—32no—
205C3⋊#95C2×D312yescomplemented
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32—22no—
211C23×C32—22no—
212C23×C32C2×D412yes—
213C23×C32C2×D412yes—
214C23×C32C2×D412yes—
215C23×C32C2×D412yescomplemented
216C23×C32C2411yescharacteristic
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—22no—
220C22×C3⋊D3—28no—
221C22×C3⋊D3—28no—
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—22no—
227C22×C3⋊D3—22no—
228C22×C3⋊D3—22no—
229C22×C3⋊D3—22no—
230C22×C3⋊D3—28no—
231C22×C3⋊D3—44no—
232C22×C3⋊D3—48no—
233C22×C3⋊D3—48no—
234C22×C3⋊D3—48no—
235C22×C3⋊D3—48no—
236C22×C3⋊D3—44no—
237C22×C3⋊D3—44no—
238C22×C3⋊D3C2×D412yes—
239C22×C3⋊D3C2×D414yes—
240C22×C3⋊D3C2×D412yes—
241C22×C3⋊D3C2×D412yescomplemented
242C22×C3×D3—28no—
243C22×C3×D3—22no—
244C22×C3×D3—22no—
245C22×C3×D3—22no—
246C22×C3×D3—22no—
247C22×C3×D3—22no—
248C22×C3×D3—22no—
249C22×C3×D3—48no—
250C22×C3×D3—48no—
251C22×C3×D3—44no—
252C22×C3×D3—44no—
253C22×C3×D3C2×D414yescomplemented
254C32×D4—28no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D412yescomplemented
258#638—28no—
259#638—28no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3C2×D412yescomplemented
263C4⋊(C3⋊D3)—28no—
264C4×C3⋊D3—28no—
265C3×#67—48no—
266C2×C3×Dic3—28no—
267C2×C3×Dic3—22no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—22no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3C2×D414yescomplemented
276#626—216no—
277#626—216no—
278#626—48no—
279C23×D4—91no—
280C23×D4—91no—
281C2×#120—31no—
282C2×#120—92no—
283C2×#120—91no—
284#392—92no—
285#392—92no—
286#386—31no—
287#386—92no—
288#386—91no—
289#379—91no—
290C24×C3—21no—
291C24×C3—21no—
292C24×C3—32no—
293C24×C3—64no—
294C24×C3—62no—
295C24×C3—62no—
296C24×C3—62no—
297C24×C3—122no—
298C24×C3C22×D311yescharacteristic
299C24×C3C22×D311yescharacteristic
300C24×C3C22×D311yescharacteristic
301C24×C3C22×D311yescharacteristic
302C23×D3—22no—
303C23×D3—24no—
304C23×D3—22no—
305C23×D3—22no—
306C23×D3—31no—
307C23×D3—31no—
308C23×D3—31no—
309C23×D3—31no—
310C23×D3—31no—
311C23×D3—31no—
312C23×D3—34no—
313C23×D3—34no—
314C23×D3—42no—
315C23×D3—61no—
316C23×D3—64no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—64no—
320C23×D3—62no—
321C23×D3—62no—
322C23×D3—62no—
323C23×D3—62no—
324C23×D3—64no—
325C23×D3—64no—
326C23×D3—64no—
327C23×D3—64no—
328C23×D3—64no—
329C23×D3—64no—
330C23×D3—64no—
331C23×D3—64no—
332C23×D3—62no—
333C23×D3—62no—
334C23×D3—62no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—62no—
338C23×D3—124no—
339C23×D3—124no—
340C23×D3—122no—
341C23×D3—122no—
342C23×D3—122no—
343C23×D3—122no—
344C23×D3—124no—
345C23×D3—124no—
346C23×D3C22×D312yes—
347C2×C3×D4—24no—
348C2×C3×D4—24no—
349C2×C3×D4—22no—
350C2×C3×D4—22no—
351C2×C3×D4—22no—
352C2×C3×D4—22no—
353C2×C3×D4—24no—
354C2×C3×D4—64no—
355C2×C3×D4—64no—
356C2×C3×D4—122no—
357C2×C3×D4D1214yescomplemented
358C2×C3×D4#6714yescomplemented
359C22×C3×C4—21no—
360C22×C3×C4—32no—
361C22×C3×C4—32no—
362C22×C3×C4—32no—
363C22×C3×C4—64no—
364C22×C3×C4—62no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C2×#67—24no—
368C2×#67—24no—
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—38no—
372C2×#67—42no—
373C2×#67—64no—
374C2×#67—64no—
375C2×#67—64no—
376C2×#67—64no—
377C2×#67—64no—
378C2×#67—632no—
379C2×#67—64no—
380C2×#67—64no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67—62no—
384C2×#67—62no—
385C2×#67—64no—
386C2×#67—64no—
387C2×#67—64no—
388C2×#67—64no—
389C2×#67—64no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—62no—
395C2×#67—62no—
396C2×#67—64no—
397C2×#67—122no—
398C22×Dic3—22no—
399C22×Dic3—24no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—61no—
403C22×Dic3C22×D312yes—
404C22×Dic3C22×D312yes—
405C22×Dic3C22×D312yes—
406D3×D4—664no—
407D3×D4—632no—
408D3×D4—632no—
409C2×D12—38no—
410C2×D12—62no—
411C2×D12—62no—
412C2×D12—62no—
413C2×D12—62no—
414C2×D12—64no—
415C2×D12—64no—
416C2×D12—64no—
417C2×D12—64no—
418C2×D12—64no—
419C2×D12—64no—
420C2×D12—64no—
421C2×D12—632no—
422C2×D12—64no—
423C2×D12—62no—
424C2×D12—62no—
425C2×D12—64no—
426C2×D12—64no—
427C2×D12—122no—
428C2×C4×D3—62no—
429C2×C4×D3—62no—
430C2×C4×D3—62no—
431C2×C4×D3—62no—
432C2×C4×D3—64no—
433C2×C4×D3—64no—
434C2×C4×D3—64no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C3×C22⋊C4—64no—
438C3×C22⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—64no—
441#217—22no—
442#217—22no—
443#217—24no—
444#217—64no—
445(C2×D3)⋊C4—24no—
446(C2×D3)⋊C4—64no—
447(C2×D3)⋊C4—64no—
448(C2×D3)⋊C4—64no—
449(C2×D3)⋊C4—64no—
450(C2×D3)⋊C4—64no—
451(C2×D3)⋊C4—122no—
452(C2×D3)⋊C4—122no—
453C22×C32—22no—
454C22×C32—22no—
455C22×C32—22no—
456C22×C32—24no—
457C22×C32—24no—
458C22×C32—24no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—42no—
462C22×C32#12014yescomplemented
463C22×C32C22×D411yescharacteristic
464C22×C32C22×D411yescharacteristic
465C22×C32C22×D412yes—
466C22×C32C22×D411yescharacteristic
467C22×C32H(5,𝔽2)12yes—
468C2×C3⋊D3—22no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—24no—
471C2×C3⋊D3—24no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—24no—
477C2×C3⋊D3—416no—
478C2×C3⋊D3—416no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—42no—
482C2×C3⋊D3—42no—
483C2×C3⋊D3—42no—
484C2×C3⋊D3#12014yescomplemented
485C2×C3×D3—24no—
486C2×C3×D3—24no—
487C2×C3×D3—24no—
488C2×C3×D3—416no—
489C2×C3×D3—42no—
490C2×C3×D3—42no—
491C2×C3×D3—42no—
492C2×C3×D3—42no—
493C32×C4—22no—
494C3⋊Dic3—22no—
495C3×Dic3—24no—
496C3×Dic3—42no—
497C3×Dic3—42no—
498C25—31no—
499C25—91no—
500C25—91no—
501C22×D4—32no—
502C22×D4—92no—
503C22×D4—92no—
504C22×D4—92no—
505C22×D4—91no—
506C22×D4—91no—
507C22×D4—91no—
508C22×D4—188no—
509C22×D4—184no—
510C22×D4—184no—
511C22×D4—184no—
512C22×D4—184no—
513C22×D4D3211yescharacteristic
514C23×C4—31no—
515C23×C4—91no—
516#120—64no—
517#120—188no—
518#120—184no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—32no—
522C2×C22⋊C4—32no—
523C2×C22⋊C4—92no—
524C2×C22⋊C4—92no—
525C2×C22⋊C4—92no—
526C2×C22⋊C4—92no—
527#95—32no—
528#95—92no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—21no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—34no—
549C23×C3—42no—
550C23×C3—42no—
551C23×C3—42no—
552C23×C3—42no—
553C23×C3—68no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—128no—
561C23×C3—128no—
562C23×C3—124no—
563C23×C3—124no—
564C23×C3C2×D1212yes—
565C23×C3C2×D1212yescomplemented
566C23×C3D3×D412yes—
567C23×C3D3×D412yes—
568C23×C3D3×D412yes—
569C23×C3D3×D412yes—
570C23×C3C2×#6712yes—
571C23×C3C2×#6712yescomplemented
572C23×C3C23×D311yescharacteristic
573C23×C3C23×D311yescharacteristic
574C22×D3—28no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—34no—
582C22×D3—34no—
583C22×D3—32no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—32no—
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—48no—
590C22×D3—48no—
591C22×D3—44no—
592C22×D3—44no—
593C22×D3—62no—
594C22×D3—64no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—68no—
598C22×D3—68no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—64no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—61no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—616no—
613C22×D3—68no—
614C22×D3—68no—
615C22×D3—616no—
616C22×D3—68no—
617C22×D3—68no—
618C22×D3—61no—
619C22×D3—61no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—61no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—61no—
633C22×D3—61no—
634C22×D3—128no—
635C22×D3—122no—
636C22×D3—122no—
637C22×D3—122no—
638C22×D3—122no—
639C22×D3—124no—
640C22×D3—124no—
641C22×D3—124no—
642C22×D3—124no—
643C22×D3—128no—
644C22×D3—128no—
645C22×D3—128no—
646C22×D3—128no—
647C22×D3—128no—
648C22×D3—128no—
649C22×D3—128no—
650C22×D3—128no—
651C22×D3—128no—
652C22×D3—1216no—
653C22×D3—1216no—
654C22×D3—1216no—
655C22×D3—128no—
656C22×D3—1216no—
657C22×D3—128no—
658C22×D3—124no—
659C22×D3—124no—
660C22×D3D3×D414yescomplemented
661C3×D4—216no—
662C3×D4—28no—
663C3×D4—28no—
664C3×D4—128no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—22no—
672C2×C3×C4—34no—
673C2×C3×C4—68no—
674C2×C3×C4—62no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—62no—
679C2×C3×C4—62no—
680C2×C3×C4—62no—
681C2×C3×C4—62no—
682C2×C3×C4C2×D1212yescomplemented
683C2×C3×C4C2×#6712yescomplemented
684#67—48no—
685#67—616no—
686#67—616no—
687#67—616no—
688#67—68no—
689#67—68no—
690#67—616no—
691#67—68no—
692#67—68no—
693#67—128no—
694C2×Dic3—28no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—32no—
704C2×Dic3—32no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—62no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3D3×D414yescomplemented
713D12—616no—
714D12—68no—
715D12—68no—
716D12—616no—
717D12—616no—
718D12—128no—
719C4×D3—616no—
720C4×D3—68no—
721C4×D3—68no—
722C2×C32—24no—
723C2×C32—42no—
724C2×C32C2×#12011yescharacteristic
725C2×C32C2×#12011yescharacteristic
726C2×C32#53411yescharacteristic
727C2×C32D4212yes—
728C2×C32D4212yes—
729C3⋊D3—24no—
730C3⋊D3—42no—
731C3⋊D3—42no—
732C3×D3—44no—
733C24—32no—
734C24—64no—
735C24—62no—
736C24—62no—
737C24—62no—
738C24—91no—
739C24—91no—
740C24—91no—
741C24—94no—
742C24—122no—
743C24—182no—
744C24—182no—
745C24—184no—
746C24—184no—
747C24—182no—
748C24—182no—
749C24—182no—
750C24—362no—
751C24—362no—
752C24C2×D3211yescharacteristic
753C24C2×D3211yescharacteristic
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—64no—
757C2×D4—64no—
758C2×D4—98no—
759C2×D4—94no—
760C2×D4—122no—
761C2×D4—182no—
762C2×D4—182no—
763C2×D4—184no—
764C2×D4—184no—
765C2×D4—184no—
766C2×D4—184no—
767C2×D4—184no—
768C2×D4—1832no—
769C2×D4—184no—
770C2×D4—184no—
771C2×D4—182no—
772C2×D4—1832no—
773C2×D4—182no—
774C2×D4—182no—
775C2×D4—182no—
776C2×D4—182no—
777C2×D4—182no—
778C2×D4—362no—
779C2×D4#62614yescomplemented
780C22×C4—32no—
781C22×C4—32no—
782C22×C4—32no—
783C22×C4—64no—
784C22×C4—62no—
785C22×C4—91no—
786C22×C4—182no—
787C22×C4—182no—
788C22×C4—182no—
789C22×C4C2×D3211yescharacteristic
790C22⋊C4—64no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—64no—
794C22⋊C4—184no—
795C22⋊C4—184no—
796C22⋊C4—184no—
797C22⋊C4—362no—
798C22×C3—22no—
799C22×C3—24no—
800C22×C3—24no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—24no—
805C22×C3—24no—
806C22×C3—24no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—24no—
810C22×C3—24no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—24no—
817C22×C3—44no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—44no—
821C22×C3—44no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—44no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—42no—
830C22×C3—42no—
831C22×C3—64no—
832C22×C3—64no—
833C22×C3—64no—
834C22×C3—1216no—
835C22×C3—122no—
836C22×C3—122no—
837C22×C3—122no—
838C22×C3—122no—
839C22×C3#88214yescomplemented
840C22×C3#93714yescomplemented
841C22×C3C22×D1211yescharacteristic
842C22×C3C2×D3×D412yes—
843C22×C3C2×D3×D412yes—
844C22×C3C2×D3×D411yescharacteristic
845C22×C3C2×D3×D411yescharacteristic
846C22×C3C2×D3×D411yescharacteristic
847C22×C3C2×D3×D411yescharacteristic
848C22×C3#100412yes—
849C22×C3#100912yes—
850C22×C3C22×#6711yescharacteristic
851C2×D3—24no—
852C2×D3—24no—
853C2×D3—24no—
854C2×D3—34no—
855C2×D3—34no—
856C2×D3—416no—
857C2×D3—42no—
858C2×D3—42no—
859C2×D3—42no—
860C2×D3—42no—
861C2×D3—64no—
862C2×D3—64no—
863C2×D3—68no—
864C2×D3—64no—
865C2×D3—68no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—64no—
870C2×D3—64no—
871C2×D3—62no—
872C2×D3—64no—
873C2×D3—64no—
874C2×D3—64no—
875C2×D3—64no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—64no—
885C2×D3—64no—
886C2×D3—122no—
887C2×D3—122no—
888C2×D3—124no—
889C2×D3—1216no—
890C2×D3—1216no—
891C2×D3—1232no—
892C2×D3—1232no—
893C2×D3—1216no—
894C2×D3—1216no—
895C2×D3—124no—
896C2×D3—124no—
897C2×D3—122no—
898C2×D3—122no—
899C2×D3—124no—
900C2×D3—121no—
901C2×D3—122no—
902C2×D3—122no—
903C2×D3—122no—
904C2×D3—122no—
905C2×D3—121no—
906C2×D3—121no—
907C2×D3—121no—
908C2×D3—122no—
909C2×D3—122no—
910C3×C4—24no—
911C3×C4—22no—
912C3×C4—22no—
913C3×C4—64no—
914C3×C4—122no—
915C3×C4—122no—
916Dic3—24no—
917Dic3—42no—
918Dic3—42no—
919Dic3—64no—
920Dic3—62no—
921Dic3—62no—
922C32#240311yescharacteristic, complemented, Sylow
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—21no—
928C23—21no—
929C23—34no—
930C23—68no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—94no—
938C23—92no—
939C23—92no—
940C23—92no—
941C23—128no—
942C23—128no—
943C23—124no—
944C23—124no—
945C23—188no—
946C23—188no—
947C23—182no—
948C23—181no—
949C23—181no—
950C23—182no—
951C23—182no—
952C23—182no—
953C23—182no—
954C23—181no—
955C23—181no—
956C23—181no—
957C23—181no—
958C23—188no—
959C23—364no—
960C23—368no—
961C23—368no—
962C23—368no—
963C23—364no—
964C23—368no—
965C23—364no—
966C23C2×#62612yes—
967C23C2×#62612yescomplemented
968C23#381112yes—
969C23#381112yes—
970C23C22×D3211yescharacteristic
971D4—28no—
972D4—128no—
973D4—188no—
974D4—1816no—
975D4—1816no—
976D4—188no—
977D4—188no—
978D4—368no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—34no—
982C2×C4—68no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—62no—
990C2×C4—62no—
991C2×C4—92no—
992C2×C4—188no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4C2×#62612yescomplemented
996C2×C3—24no—
997C2×C3—24no—
998C2×C3—22no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—22no—
1003C2×C3—44no—
1004C2×C3—44no—
1005C2×C3—42no—
1006C2×C3—42no—
1007C2×C3—124no—
1008C2×C3C2×#88211yescharacteristic
1009C2×C3D4×D1212yes—
1010C2×C3D3×#12011yescharacteristic
1011C2×C3D3×#12011yescharacteristic
1012C2×C3#558911yescharacteristic
1013C2×C3#559012yes—
1014C2×C3#560912yes—
1015C2×C3#565311yescharacteristic
1016C2×C3C2×#93711yescharacteristic
1017C2×C3D4×#6712yes—
1018D3—44no—
1019D3—68no—
1020D3—64no—
1021D3—64no—
1022D3—124no—
1023D3—124no—
1024D3—122no—
1025D3—122no—
1026D3—122no—
1027D3—122no—
1028C22—24no—
1029C22—22no—
1030C22—22no—
1031C22—24no—
1032C22—24no—
1033C22—22no—
1034C22—41no—
1035C22—41no—
1036C22—42no—
1037C22—64no—
1038C22—64no—
1039C22—64no—
1040C22—94no—
1041C22—1216no—
1042C22—122no—
1043C22—122no—
1044C22—122no—
1045C22—122no—
1046C22—184no—
1047C22—182no—
1048C22—182no—
1049C22—184no—
1050C22—182no—
1051C22—182no—
1052C22—182no—
1053C22—182no—
1054C22—184no—
1055C22—3616no—
1056C22—3616no—
1057C22—362no—
1058C22—362no—
1059C22—361no—
1060C22—361no—
1061C22—362no—
1062C22#6398114yescomplemented
1063C22D32×D412yes—
1064C22#6431412yes—
1065C22C22×#62611yescharacteristic
1066C22C2×#381111yescharacteristic
1067C22C2×#381111yescharacteristic
1068C4—22no—
1069C4—64no—
1070C4—122no—
1071C4—122no—
1072C4—182no—
1073C3—21no—
1074C3#7488411yescharacteristic, complemented
1075C3#8260411yescharacteristic, complemented
1076C2—24no—
1077C2—42no—
1078C2—124no—
1079C2—184no—
1080C2—362no—
1081C2—362no—
1082C2D4×#62612yes—
1083C2#1059524211yescharacteristic
1084C2#1059527811yescharacteristic
1085C2#1059529212yes—
1086C2C2×#6398111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2403
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C3⋊D3C2semidirect
2. C23×#626C2semidirect
3. C2×C3×#937C2semidirect
4. C2×#63981C2semidirect
5. C2×#63977C2semidirect
6. C3×#5220C2semidirect
7. #10591724C2semidirect
8. #10591714C2semidirect
9. #10591711C2semidirect
10. #10591395C2semidirect
11. #10591387C2semidirect
15. C24×C3⋊D3C22semidirect
16. C24×C3×D3C22semidirect
19. C22×#638C22semidirect
23. C22×C4⋊(C3⋊D3)C22semidirect
24. C22×C4×C3⋊D3C22semidirect
25. C22×C3×#67C22semidirect
26. C23×C3×Dic3C22semidirect
30. C22×#626C22semidirect
31. C22×#626C22semidirect
32. C2×C3×#217C22semidirect
33. C2×C3×#217C22semidirect
34. C2×C3×#217C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×#3722C22semidirect
40. C2×#3722C22semidirect
41. C2×#3722C22semidirect
42. C2×(C2×D3)⋊Dic3C22semidirect
43. C3×C3⋊#95C22semidirect
44. #63579C22semidirect
53. C2×#937D3semidirect
58. #5220D3semidirect
79. C23×C3⋊D3D4semidirect
91. C2×C32×D4D4semidirect
98. C2×#638D4semidirect
124. C2×#626D4semidirect
141. C24×D3C2×D3semidirect
158. C22×#67C2×D3semidirect
159. C23×Dic3C2×D3semidirect
187. C2×#217C2×D3semidirect
188. C2×#217C2×D3semidirect
189. C2×#217C2×D3semidirect
199. C2×(C2×D3)⋊C4C2×D3semidirect
205. C3⋊#95C2×D3semidirect
215. C23×C32C2×D4semidirect
241. C22×C3⋊D3C2×D4semidirect
253. C22×C3×D3C2×D4semidirect
257. C2×C32×C4C2×D4semidirect
262. C2×C3⋊Dic3C2×D4semidirect
275. C2×C3×Dic3C2×D4semidirect
357. C2×C3×D4D12semidirect
358. C2×C3×D4#67semidirect
462. C22×C32#120semidirect
484. C2×C3⋊D3#120semidirect
565. C23×C3C2×D12semidirect
571. C23×C3C2×#67semidirect
660. C22×D3D3×D4semidirect
682. C2×C3×C4C2×D12semidirect
683. C2×C3×C4C2×#67semidirect
712. C2×Dic3D3×D4semidirect
779. C2×D4#626semidirect
839. C22×C3#882semidirect
840. C22×C3#937semidirect
922. C32#2403semidirect
967. C23C2×#626semidirect
995. C2×C4C2×#626semidirect
1062. C22#63981semidirect
1074. C3#74884semidirect
1075. C3#82604semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C23×#6262
C2×C3×#9372
C2×#639812
C2×#639772
C3×#52202
#105917242
#105917142
#105917112
#105913952
#105913872
#826043
#748843