Finite Group Databasebeta

← C2×#10595234 #11900964

Subgroups — C2×#10595234 #11900964

Order 1152.

4299 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C23×#626C211yesmaximal, characteristic, complemented
3C2×#64146C211yesmaximal, characteristic, complemented
4C2×C3×#935C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6C2×#63977C212yesmaximal, complemented
7C2×#63971C212yesmaximal, complemented
8C2×D3×#217C211yesmaximal, characteristic, complemented
9C2×#63961C211yesmaximal, characteristic, complemented
10#10595234C2116yesmaximal, direct product factor
11C2×#63886C212yesmaximal, complemented
12C2×#63850C212yesmaximal, complemented
13C2×#5804—31nomaximal
14C2×#5653—31nomaximal
15C24×C3⋊D3C2211yescharacteristic, complemented
16C24×C3×D3C2211yescharacteristic
17C24×C3×D3C2211yescharacteristic, complemented
18C22×C32×D4C2211yescharacteristic
19C22×#638C2212yescomplemented
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic, complemented
22C23×C3×Dic3C2211yescharacteristic, complemented
23C2×C3×D3×D4—28no—
24C2×C3×D3×D4C2218yescomplemented
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×#626—28no—
28C22×#626C2212yes—
29C22×#626C2212yescomplemented
30C22×#626C2212yescomplemented
31C22×#626C2218yescomplemented
32C22×D3×Dic3C2212yescomplemented
33C2×#3757C2211yescharacteristic, complemented
34#64146C2218yescomplemented
35C2×#3752C2212yescomplemented
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×#217C2212yescomplemented
38C3×#935C2218yescomplemented
39C2×C3×Dic3⋊C4C2212yescomplemented
40#63981C2218yescomplemented
41#63977C22116yescomplemented
42#63971C22116yescomplemented
43D3×#217C2218yescomplemented
44C2×#3724C2212yescomplemented
45C2×#3722C2212yescomplemented
46#63961C2218yescomplemented
47C2×(C2×D3)⋊Dic3C2212yescomplemented
48C2×(C2×D3)⋊Dic3C2212yescomplemented
49#63886C22116yescomplemented
50#63850C22116yescomplemented
51C23×C3×D4—31no—
52C23×#67—31no—
53C22×D3×D4D311yescharacteristic, complemented
54C23×D12—31no—
55C2×C3×#123—31no—
56C2×#953—32no—
57C22×#217—31no—
58#5804—316no—
59C2×#939—32no—
60C2×#939—32no—
61C2×#937—31no—
62C2×#937—31no—
63C2×#937—31no—
64C2×#937—61no—
65C2×#935—31no—
66C2×#935D311yescharacteristic, complemented
67C2×#929—31no—
68C2×#929—32no—
69#5653—316no—
70C2×#895—32no—
71C2×#894—32no—
72C2×#884—32no—
73C2×#882—32no—
74C2×#882—31no—
75C2×D3×C22⋊C4—31no—
76C24×C32C2311yescharacteristic
77C24×C32C2311yescharacteristic
78C23×C3⋊D3—24no—
79C23×C3⋊D3—44no—
80C23×C3⋊D3C2312yes—
81C23×C3⋊D3C2314yescomplemented
82C23×C3×D3—24no—
83C23×C3×D3—44no—
84C23×C3×D3—44no—
85C23×C3×D3D418yescomplemented
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2314yes—
90C23×C3×D3C2314yescomplemented
91C2×C32×D4—24no—
92C2×C32×D4C2314yes—
93C22×C32×C4C2311yescharacteristic
94C2×#638—44no—
95C2×#638C2318yescomplemented
96C22×C3⋊Dic3C2312yes—
97C2×C3×#67—24no—
98C2×C3×#67—24no—
99C2×C3×#67C2314yes—
100C2×C3×#67C2314yescomplemented
101C22×C3×Dic3—24no—
102C22×C3×Dic3C2312yes—
103C22×C3×Dic3C2312yes—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2314yescomplemented
106C3×D3×D4—232no—
107C2×C3×D12—24no—
108C2×C3×D12C2314yescomplemented
109C2×C3×C4×D3—24no—
110C2×C3×C4×D3C2314yescomplemented
111C2×#626—28no—
112C2×#626—28no—
113C2×#626—232no—
114C2×#626—44no—
115C2×#626C2318yes—
116C2×#626C2318yescomplemented
117C2×#626C2318yescomplemented
118C2×D3×Dic3—44no—
119C2×D3×Dic3C2318yescomplemented
120#3757C2314yescomplemented
121#3752C2318yescomplemented
122C3×#217C2314yescomplemented
123C3×#217C2318yescomplemented
124C3×Dic3⋊C4C2318yescomplemented
125#3724C2318yescomplemented
126#3722C2318yescomplemented
127(C2×D3)⋊Dic3C2318yescomplemented
128(C2×D3)⋊Dic3C2318yescomplemented
129C2×#534—91noSylow
130C25×C3—31no—
131C25×C3—31no—
132C24×D3—31no—
133C24×D3—31no—
134C24×D3—61no—
135C24×D3C2×D311yescharacteristic
136C24×D3C2×D311yescharacteristic, complemented
137C22×C3×D4—21no—
138C22×C3×D4—31no—
139C22×C3×D4—31no—
140C22×C3×D4—38no—
141C22×C3×D4—31no—
142C22×C3×D4—68no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C2×D311yescharacteristic
145C23×C3×C4—31no—
146C23×C3×C4—31no—
147C22×#67—32no—
148C22×#67—32no—
149C22×#67—32no—
150C22×#67—32no—
151C22×#67—32no—
152C22×#67—38no—
153C22×#67—62no—
154C22×#67—68no—
155C22×#67C2×D311yescharacteristic
156C22×#67C2×D311yescharacteristic, complemented
157C23×Dic3—32no—
158C23×Dic3C2×D311yescharacteristic, complemented
159C2×D3×D4—28no—
160C2×D3×D4C2×D318yescomplemented
161C22×D12—38no—
162C22×D12—32no—
163C22×D12—32no—
164C22×D12—32no—
165C22×D12—68no—
166C22×D12C2×D311yescharacteristic, complemented
167C22×C4×D3—32no—
168C22×C4×D3C2×D311yescharacteristic, complemented
169C3×#123—38no—
170C2×C3×C4⋊C4—32no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—32no—
173#953—316no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—32no—
177C2×#217—32no—
178C2×#217—38no—
179C2×#217—61no—
180C2×#217C2×D311yescharacteristic, complemented
181C2×#217C2×D312yescomplemented
182#939—316no—
183#939—316no—
184#937—38no—
185#937—38no—
186#937—38no—
187#937—68no—
188#935—38no—
189#935C2×D318yescomplemented
190#929—38no—
191#929—316no—
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—62no—
199C2×Dic3⋊C4—32no—
200C2×Dic3⋊C4—32no—
201C2×Dic3⋊C4C2×D312yescomplemented
202#895—316no—
203#894—316no—
204#884—316no—
205#882—316no—
206#882—38no—
207D3×C22⋊C4—38no—
208C23×C32—24no—
209C23×C32—22no—
210C23×C32—24no—
211C23×C32C2×D414yes—
212C23×C32C2412yes—
213C23×C32C2412yes—
214C23×C32C2411yescharacteristic
215C22×C3⋊D3—24no—
216C22×C3⋊D3—24no—
217C22×C3⋊D3—28no—
218C22×C3⋊D3—24no—
219C22×C3⋊D3—48no—
220C22×C3⋊D3—416no—
221C22×C3⋊D3C2414yes—
222C22×C3×D3—24no—
223C22×C3×D3—24no—
224C22×C3×D3—22no—
225C22×C3×D3—24no—
226C22×C3×D3—28no—
227C22×C3×D3—416no—
228C22×C3×D3—48no—
229C22×C3×D3—48no—
230C22×C3×D3—416no—
231C22×C3×D3C2×D414yes—
232C22×C3×D3C2×D414yes—
233C22×C3×D3C2×D4116yescomplemented
234C22×C3×D3C2412yes—
235C22×C3×D3C2412yes—
236C22×C3×D3C2412yes—
237C32×D4—28no—
238C2×C32×C4—22no—
239C2×C32×C4C2412yes—
240#638—48no—
241C2×C3⋊Dic3—24no—
242C2×C3⋊Dic3C2414yes—
243C3×#67—28no—
244C3×#67—28no—
245C2×C3×Dic3—24no—
246C2×C3×Dic3—28no—
247C2×C3×Dic3—22no—
248C2×C3×Dic3—24no—
249C2×C3×Dic3C2414yes—
250C2×C3×Dic3C2414yes—
251C2×C3×Dic3C2412yes—
252C3×D12—28no—
253C3×C4×D3—28no—
254#626—216no—
255#626—216no—
256#626—48no—
257D3×Dic3—48no—
258C23×D4—31no—
259C23×D4—91no—
260#534—916no—
261C2×#123—31no—
262C2×#123—92no—
263C2×#123—91no—
264C2×#121—92no—
265C2×#121—92no—
266C2×#120—91no—
267C2×#120—92no—
268C2×#120—91no—
269C22×C22⋊C4—91no—
270C24×C3—21no—
271C24×C3—21no—
272C24×C3—31no—
273C24×C3—31no—
274C24×C3—38no—
275C24×C3—34no—
276C24×C3—31no—
277C24×C3—34no—
278C24×C3—64no—
279C24×C3—124no—
280C24×C3—124no—
281C24×C3C22×D311yescharacteristic
282C24×C3C22×D311yescharacteristic
283C24×C3C22×D311yescharacteristic
284C24×C3C22×D311yescharacteristic
285C23×D3—24no—
286C23×D3—32no—
287C23×D3—32no—
288C23×D3—34no—
289C23×D3—34no—
290C23×D3—44no—
291C23×D3—44no—
292C23×D3—62no—
293C23×D3—64no—
294C23×D3—64no—
295C23×D3—64no—
296C23×D3—124no—
297C23×D3—124no—
298C23×D3—124no—
299C23×D3—128no—
300C23×D3#6718yescomplemented
301C23×D3C22×D311yescharacteristic
302C23×D3C22×D311yescharacteristic
303C23×D3C22×D311yescharacteristic
304C23×D3C22×D314yes—
305C23×D3C22×D314yescomplemented
306C2×C3×D4—24no—
307C2×C3×D4—24no—
308C2×C3×D4—24no—
309C2×C3×D4—34no—
310C2×C3×D4—34no—
311C2×C3×D4—34no—
312C2×C3×D4—44no—
313C2×C3×D4—64no—
314C2×C3×D4—632no—
315C2×C3×D4—64no—
316C2×C3×D4—64no—
317C2×C3×D4C22×D314yes—
318C2×C3×D4C22×D314yes—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—32no—
322C22×C3×C4—32no—
323C22×C3×C4—34no—
324C22×C3×C4—34no—
325C22×C3×C4—64no—
326C22×C3×C4—64no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C2×#67—24no—
330C2×#67—24no—
331C2×#67—38no—
332C2×#67—38no—
333C2×#67—38no—
334C2×#67—38no—
335C2×#67—38no—
336C2×#67—68no—
337C2×#67—68no—
338C2×#67—68no—
339C2×#67—632no—
340C2×#67—124no—
341C2×#67—124no—
342C2×#67—124no—
343C2×#67—128no—
344C2×#67C22×D314yes—
345C2×#67C22×D314yescomplemented
346C22×Dic3—24no—
347C22×Dic3—32no—
348C22×Dic3—32no—
349C22×Dic3—38no—
350C22×Dic3—62no—
351C22×Dic3—124no—
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D312yes—
354C22×Dic3C22×D312yes—
355C22×Dic3C22×D314yescomplemented
356D3×D4—232no—
357C2×D12—24no—
358C2×D12—38no—
359C2×D12—38no—
360C2×D12—38no—
361C2×D12—68no—
362C2×D12—68no—
363C2×D12—632no—
364C2×D12—124no—
365C2×D12C22×D314yescomplemented
366C2×C4×D3—24no—
367C2×C4×D3—38no—
368C2×C4×D3—124no—
369C2×C4×D3C22×D314yescomplemented
370C3×C4⋊C4—38no—
371C3×C22⋊C4—34no—
372C3×C22⋊C4—38no—
373#217—34no—
374#217—34no—
375#217—38no—
376#217—38no—
377#217—64no—
378#217C22×D314yescomplemented
379#217C22×D318yescomplemented
380(C2×D3)⋊C4—38no—
381(C2×D3)⋊C4—38no—
382(C2×D3)⋊C4—38no—
383(C2×D3)⋊C4—38no—
384(C2×D3)⋊C4—38no—
385(C2×D3)⋊C4—38no—
386(C2×D3)⋊C4—68no—
387Dic3⋊C4—38no—
388Dic3⋊C4—38no—
389Dic3⋊C4C22×D318yescomplemented
390C22×C32—28no—
391C22×C32—24no—
392C22×C32—22no—
393C22×C32—24no—
394C22×C32—44no—
395C22×C32C22×D414yes—
396C22×C32C22×D412yes—
397C22×C32H(5,𝔽2)14yes—
398C22×C32C2511yescharacteristic
399C2×C3⋊D3—24no—
400C2×C3⋊D3—24no—
401C2×C3⋊D3—24no—
402C2×C3⋊D3—416no—
403C2×C3⋊D3—48no—
404C2×C3×D3—28no—
405C2×C3×D3—28no—
406C2×C3×D3—24no—
407C2×C3×D3—24no—
408C2×C3×D3—22no—
409C2×C3×D3—24no—
410C2×C3×D3—416no—
411C2×C3×D3—416no—
412C2×C3×D3—44no—
413C2×C3×D3C22×D414yes—
414C2×C3×D3C22×D414yes—
415C32×C4—22no—
416C3⋊Dic3—24no—
417C3×Dic3—24no—
418C3×Dic3—22no—
419C3×Dic3—24no—
420C25—31no—
421C25—31no—
422C25—91no—
423C22×D4—31no—
424C22×D4—31no—
425C22×D4—38no—
426C22×D4—31no—
427C22×D4—68no—
428C22×D4—92no—
429C22×D4—92no—
430C22×D4—98no—
431C22×D4—92no—
432C22×D4—92no—
433C22×D4—188no—
434C22×D4D3211yescharacteristic
435C23×C4—31no—
436C23×C4—31no—
437C23×C4—92no—
438#123—38no—
439#123—916no—
440#123—98no—
441#121—916no—
442#121—916no—
443#120—98no—
444#120—916no—
445#120—98no—
446C2×C4⋊C4—32no—
447C2×C4⋊C4—92no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4—32no—
450C2×C22⋊C4—98no—
451C2×C22⋊C4—92no—
452C2×C22⋊C4—92no—
453C2×C22⋊C4—92no—
454C2×C22⋊C4—91no—
455C2×C22⋊C4—92no—
456C23×C3—24no—
457C23×C3—24no—
458C23×C3—22no—
459C23×C3—24no—
460C23×C3—24no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—21no—
465C23×C3—24no—
466C23×C3—34no—
467C23×C3—34no—
468C23×C3—32no—
469C23×C3—32no—
470C23×C3—316no—
471C23×C3—32no—
472C23×C3—44no—
473C23×C3—44no—
474C23×C3—42no—
475C23×C3—68no—
476C23×C3—64no—
477C23×C3—64no—
478C23×C3—62no—
479C23×C3—64no—
480C23×C3—1216no—
481C23×C3—128no—
482C23×C3—128no—
483C23×C3—1216no—
484C23×C3D3×D414yes—
485C23×C3C2×#6714yes—
486C23×C3C23×D312yes—
487C23×C3C23×D312yes—
488C23×C3C23×D312yes—
489C23×C3C23×D312yes—
490C23×C3C23×D311yescharacteristic
491C23×C3C23×D311yescharacteristic
492C22×D3—24no—
493C22×D3—24no—
494C22×D3—24no—
495C22×D3—22no—
496C22×D3—28no—
497C22×D3—34no—
498C22×D3—34no—
499C22×D3—416no—
500C22×D3—48no—
501C22×D3—48no—
502C22×D3—416no—
503C22×D3—64no—
504C22×D3—68no—
505C22×D3—68no—
506C22×D3—64no—
507C22×D3—64no—
508C22×D3—64no—
509C22×D3—64no—
510C22×D3—64no—
511C22×D3—68no—
512C22×D3—64no—
513C22×D3—124no—
514C22×D3—124no—
515C22×D3—128no—
516C22×D3—128no—
517C22×D3—128no—
518C22×D3—1216no—
519C22×D3—1216no—
520C22×D3—1216no—
521C22×D3—1232no—
522C22×D3C2×#6714yes—
523C22×D3C2×#6714yes—
524C22×D3C2×#67116yescomplemented
525C22×D3C23×D312yes—
526C22×D3C23×D312yes—
527C22×D3C23×D312yes—
528C3×D4—28no—
529C3×D4—28no—
530C3×D4—48no—
531C3×D4—68no—
532C3×D4—68no—
533C3×D4—68no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—32no—
538C2×C3×C4—34no—
539C2×C3×C4—34no—
540C2×C3×C4—42no—
541C2×C3×C4—68no—
542C2×C3×C4—62no—
543C2×C3×C4—64no—
544C2×C3×C4—68no—
545C2×C3×C4—64no—
546C2×C3×C4C23×D312yes—
547C2×C3×C4C23×D312yes—
548#67—28no—
549#67—28no—
550#67—616no—
551#67—616no—
552#67—128no—
553#67—128no—
554#67—128no—
555#67—1216no—
556C2×Dic3—24no—
557C2×Dic3—28no—
558C2×Dic3—24no—
559C2×Dic3—22no—
560C2×Dic3—34no—
561C2×Dic3—34no—
562C2×Dic3—64no—
563C2×Dic3—64no—
564C2×Dic3—64no—
565C2×Dic3—124no—
566C2×Dic3—128no—
567C2×Dic3C23×D312yes—
568C2×Dic3C23×D314yes—
569C2×Dic3C23×D314yes—
570D12—28no—
571D12—616no—
572D12—616no—
573D12—128no—
574C4×D3—28no—
575C4×D3—128no—
576C2×C32—24no—
577C2×C32—42no—
578C2×C32#53414yescomplemented
579C2×C32C23×D411yescharacteristic
580C2×C32C2×H(5,𝔽2)12yes—
581C3⋊D3—44no—
582C3×D3—24no—
583C3×D3—24no—
584C3×D3—42no—
585C24—31no—
586C24—31no—
587C24—34no—
588C24—38no—
589C24—31no—
590C24—34no—
591C24—64no—
592C24—92no—
593C24—94no—
594C24—124no—
595C24—124no—
596C24—184no—
597C24—364no—
598C24C2×D3211yescharacteristic
599C24C2×D3211yescharacteristic
600C2×D4—24no—
601C2×D4—34no—
602C2×D4—34no—
603C2×D4—34no—
604C2×D4—64no—
605C2×D4—632no—
606C2×D4—64no—
607C2×D4—64no—
608C2×D4—98no—
609C2×D4—98no—
610C2×D4—98no—
611C2×D4—98no—
612C2×D4—188no—
613C2×D4—188no—
614C2×D4—1832no—
615C2×D4—364no—
616C2×D4—364no—
617C2×D4C2×D3214yes—
618C22×C4—34no—
619C22×C4—32no—
620C22×C4—32no—
621C22×C4—31no—
622C22×C4—34no—
623C22×C4—64no—
624C22×C4—64no—
625C22×C4—98no—
626C22×C4—92no—
627C22×C4—364no—
628C22×C4C2×D3211yescharacteristic
629C4⋊C4—38no—
630C4⋊C4—98no—
631C22⋊C4—34no—
632C22⋊C4—38no—
633C22⋊C4—98no—
634C22⋊C4—98no—
635C22⋊C4—98no—
636C22⋊C4—94no—
637C22⋊C4—98no—
638C22×C3—28no—
639C22×C3—24no—
640C22×C3—24no—
641C22×C3—28no—
642C22×C3—22no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—22no—
646C22×C3—24no—
647C22×C3—22no—
648C22×C3—24no—
649C22×C3—21no—
650C22×C3—34no—
651C22×C3—34no—
652C22×C3—44no—
653C22×C3—48no—
654C22×C3—44no—
655C22×C3—42no—
656C22×C3—44no—
657C22×C3—44no—
658C22×C3—68no—
659C22×C3—68no—
660C22×C3—64no—
661C22×C3—64no—
662C22×C3—62no—
663C22×C3—64no—
664C22×C3—84no—
665C22×C3—1216no—
666C22×C3—1216no—
667C22×C3—124no—
668C22×C3C2×D3×D414yes—
669C22×C3C2×D3×D412yes—
670C22×C3#100414yes—
671C22×C3#100914yes—
672C22×C3C22×#6714yes—
673C22×C3C22×#6712yes—
674C22×C3C24×D311yescharacteristic
675C22×C3C24×D311yescharacteristic
676C2×D3—24no—
677C2×D3—24no—
678C2×D3—28no—
679C2×D3—28no—
680C2×D3—24no—
681C2×D3—22no—
682C2×D3—416no—
683C2×D3—416no—
684C2×D3—44no—
685C2×D3—68no—
686C2×D3—64no—
687C2×D3—64no—
688C2×D3—64no—
689C2×D3—64no—
690C2×D3—64no—
691C2×D3—64no—
692C2×D3—124no—
693C2×D3—124no—
694C2×D3—1216no—
695C2×D3—1216no—
696C2×D3—1216no—
697C2×D3—1232no—
698C2×D3—128no—
699C2×D3—128no—
700C2×D3C22×#6714yes—
701C2×D3C22×#6714yes—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—42no—
705C3×C4—62no—
706C3×C4—64no—
707C3×C4—64no—
708Dic3—24no—
709Dic3—24no—
710Dic3—22no—
711Dic3—64no—
712Dic3—64no—
713Dic3—124no—
714C32C2×#53411yescharacteristic, complemented, Sylow
715C23—24no—
716C23—24no—
717C23—22no—
718C23—34no—
719C23—34no—
720C23—32no—
721C23—32no—
722C23—316no—
723C23—32no—
724C23—68no—
725C23—64no—
726C23—64no—
727C23—64no—
728C23—62no—
729C23—94no—
730C23—128no—
731C23—1216no—
732C23—128no—
733C23—1216no—
734C23—184no—
735C23—184no—
736C23—188no—
737C23—184no—
738C23—368no—
739C23—3616no—
740C23D3×#6714yes—
741C23C22×D3212yes—
742C23C22×D3212yes—
743C23C22×D3211yescharacteristic
744D4—28no—
745D4—68no—
746D4—68no—
747D4—68no—
748D4—1816no—
749D4—1816no—
750D4—368no—
751D4—368no—
752C2×C4—22no—
753C2×C4—34no—
754C2×C4—34no—
755C2×C4—32no—
756C2×C4—68no—
757C2×C4—64no—
758C2×C4—62no—
759C2×C4—68no—
760C2×C4—64no—
761C2×C4—94no—
762C2×C4—184no—
763C2×C4—368no—
764C2×C4C22×D3212yes—
765C2×C3—24no—
766C2×C3—24no—
767C2×C3—22no—
768C2×C3—21no—
769C2×C3—24no—
770C2×C3—44no—
771C2×C3—42no—
772C2×C3—42no—
773C2×C3—64no—
774C2×C3—64no—
775C2×C3—82no—
776C2×C3—122no—
777C2×C3#565314yescomplemented
778C2×C3#580414yescomplemented
779C2×C3C22×D3×D411yescharacteristic
780C2×C3C2×#100412yes—
781C2×C3C2×#100912yes—
782C2×C3C23×#6711yescharacteristic
783D3—24no—
784D3—24no—
785D3—42no—
786D3—128no—
787D3—124no—
788D3—124no—
789C22—24no—
790C22—28no—
791C22—24no—
792C22—22no—
793C22—34no—
794C22—34no—
795C22—44no—
796C22—64no—
797C22—64no—
798C22—68no—
799C22—68no—
800C22—64no—
801C22—62no—
802C22—1216no—
803C22—1216no—
804C22—124no—
805C22—184no—
806C22—184no—
807C22—184no—
808C22—3616no—
809C22—368no—
810C22#6431414yes—
811C22C2×D3×#6714yes—
812C22C2×D3×#6712yes—
813C22C23×D3211yescharacteristic
814C4—22no—
815C4—64no—
816C4—62no—
817C4—64no—
818C4—184no—
819C3—21no—
820C3C2×#565311yescharacteristic, complemented
821C3C2×#580411yescharacteristic, complemented
822C2—24no—
823C2—42no—
824C2—64no—
825C2—64no—
826C2—122no—
827C2—364no—
828C2#1059523414yesdirect product factor
829C2C2×#6431412yes—
830C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C23×#626C2semidirect
3. C2×#64146C2semidirect
4. C2×C3×#935C2semidirect
5. C2×#63981C2semidirect
6. C2×#63977C2semidirect
7. C2×#63971C2semidirect
8. C2×D3×#217C2semidirect
9. C2×#63961C2semidirect
10. #10595234C2direct (N × H)
11. C2×#63886C2semidirect
12. C2×#63850C2semidirect
15. C24×C3⋊D3C22semidirect
17. C24×C3×D3C22semidirect
19. C22×#638C22semidirect
21. C22×C3×#67C22semidirect
22. C23×C3×Dic3C22semidirect
24. C2×C3×D3×D4C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
29. C22×#626C22semidirect
30. C22×#626C22semidirect
31. C22×#626C22semidirect
32. C22×D3×Dic3C22semidirect
33. C2×#3757C22semidirect
34. #64146C22semidirect
35. C2×#3752C22semidirect
36. C2×C3×#217C22semidirect
37. C2×C3×#217C22semidirect
38. C3×#935C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
40. #63981C22semidirect
41. #63977C22semidirect
42. #63971C22semidirect
43. D3×#217C22semidirect
44. C2×#3724C22semidirect
45. C2×#3722C22semidirect
46. #63961C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. #63886C22semidirect
50. #63850C22semidirect
53. C22×D3×D4D3semidirect
66. C2×#935D3semidirect
81. C23×C3⋊D3C23semidirect
85. C23×C3×D3D4semidirect
90. C23×C3×D3C23semidirect
95. C2×#638C23semidirect
100. C2×C3×#67C23semidirect
105. C22×C3×Dic3C23semidirect
108. C2×C3×D12C23semidirect
110. C2×C3×C4×D3C23semidirect
116. C2×#626C23semidirect
117. C2×#626C23semidirect
119. C2×D3×Dic3C23semidirect
120. #3757C23semidirect
121. #3752C23semidirect
122. C3×#217C23semidirect
123. C3×#217C23semidirect
124. C3×Dic3⋊C4C23semidirect
125. #3724C23semidirect
126. #3722C23semidirect
127. (C2×D3)⋊Dic3C23semidirect
128. (C2×D3)⋊Dic3C23semidirect
136. C24×D3C2×D3semidirect
156. C22×#67C2×D3semidirect
158. C23×Dic3C2×D3semidirect
160. C2×D3×D4C2×D3semidirect
166. C22×D12C2×D3semidirect
168. C22×C4×D3C2×D3semidirect
180. C2×#217C2×D3semidirect
181. C2×#217C2×D3semidirect
189. #935C2×D3semidirect
201. C2×Dic3⋊C4C2×D3semidirect
233. C22×C3×D3C2×D4semidirect
300. C23×D3#67semidirect
305. C23×D3C22×D3semidirect
345. C2×#67C22×D3semidirect
355. C22×Dic3C22×D3semidirect
365. C2×D12C22×D3semidirect
369. C2×C4×D3C22×D3semidirect
378. #217C22×D3semidirect
379. #217C22×D3semidirect
389. Dic3⋊C4C22×D3semidirect
524. C22×D3C2×#67semidirect
578. C2×C32#534semidirect
714. C32C2×#534semidirect
777. C2×C3#5653semidirect
778. C2×C3#5804semidirect
820. C3C2×#5653semidirect
821. C3C2×#5804semidirect
828. C2#10595234direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C23×#6262
C2×#641462
C2×C3×#9352
C2×#639812
C2×#639772
C2×#639712
C2×D3×#2172
C2×#639612
#105952342
C2×#638862
C2×#638502
C2×#58043
C2×#56533