Finite Group Databasebeta

← C2×#10594290 #11900972

Subgroups — C2×#10594290 #11900972

Order 1152.

4139 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C23×#625C211yesmaximal, characteristic, complemented
3C2×#64095C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic, complemented
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#63977C211yesmaximal, characteristic, complemented
7C2×#63962C211yesmaximal, characteristic, complemented
8C2×#63922C212yesmaximal, complemented
9C2×#63908C212yesmaximal, complemented
10C2×#63906C212yesmaximal, complemented
11C2×#63891C212yesmaximal, complemented
12#10594290C2116yesmaximal, direct product factor
13C2×#5589—31nomaximal
14C2×#5493—31nomaximal
15C24×C3×D3C2211yescharacteristic
16C24×C3×D3C2211yescharacteristic, complemented
17C23×D32C2211yescharacteristic, complemented
18C22×#638C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic, complemented
20C22×C3×#67C2211yescharacteristic
21C22×C3×D12C2212yescomplemented
22C22×C3×C4×D3C2212yescomplemented
23C2×D3×#67—28no—
24C2×D3×#67C2218yescomplemented
25C22×#626C2211yescharacteristic, complemented
26C22×#626C2212yescomplemented
27C22×#625—28no—
28C22×#625C2212yes—
29C22×#625C2212yescomplemented
30C22×#625C2211yescharacteristic, complemented
31C22×#625C2218yescomplemented
32C22×D3×Dic3C2211yescharacteristic, complemented
33C2×C32×C22⋊C4C2211yescharacteristic, complemented
34C2×#3752C2212yescomplemented
35C2×C4⋊(C3⋊Dic3)C2212yescomplemented
36#64095C2218yescomplemented
37C2×C3×#217C2211yescharacteristic, complemented
38C2×C3×(C2×D3)⋊C4C2212yescomplemented
39C2×C3×(C2×D3)⋊C4C2212yescomplemented
40C3×#882C2218yescomplemented
41C3×D3×C22⋊C4C2218yescomplemented
42#63977C2218yescomplemented
43C2×Dic3⋊Dic3C2212yescomplemented
44#63962C2218yescomplemented
45C2×(C2×D3)⋊Dic3C2212yescomplemented
46C2×(C2×D3)⋊Dic3C2212yescomplemented
47#63922C22116yescomplemented
48#63908C22116yescomplemented
49#63906C22116yescomplemented
50#63891C22116yescomplemented
51C23×#67—31no—
52C23×#67—31no—
53C23×#67—31no—
54C22×D3×D4—31no—
55C2×C3×#120—31no—
56C22×C3×C22⋊C4—31no—
57C2×#953—31no—
58C2×#938—32no—
59C2×#937—32no—
60C2×#935—31no—
61C2×#930—32no—
62C2×#930—32no—
63#5589—316no—
64#5493—316no—
65C2×#886—31no—
66C2×#886—31no—
67C2×#886—31no—
68C2×#886—32no—
69C2×#886—61no—
70C2×#884—32no—
71C2×#883—32no—
72C2×#882—31no—
73C2×#882—32no—
74C2×#882D311yescharacteristic, complemented
75C2×D3×C22⋊C4D311yescharacteristic, complemented
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3×D3—24no—
79C23×C3×D3—44no—
80C23×C3×D3—44no—
81C23×C3×D3D418yescomplemented
82C23×C3×D3C2312yes—
83C23×C3×D3C2311yescharacteristic
84C23×C3×D3C2311yescharacteristic
85C23×C3×D3C2311yescharacteristic
86C23×C3×D3C2314yes—
87C23×C3×D3C2314yescomplemented
88C22×D32—24no—
89C22×D32—44no—
90C22×D32C2314yescomplemented
91C22×C32×C4C2312yes—
92C2×#638—24no—
93C2×#638C2314yes—
94C22×C3⋊Dic3—24no—
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2312yes—
97C22×C3⋊Dic3C2314yescomplemented
98C2×C3×#67—24no—
99C2×C3×#67C2314yes—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2312yes—
102C2×C3×D12—44no—
103C2×C3×D12C2318yescomplemented
104C2×C3×C4×D3—44no—
105C2×C3×C4×D3C2318yescomplemented
106D3×#67—232no—
107C2×#626—24no—
108C2×#626—44no—
109C2×#626C2314yescomplemented
110C2×#626C2318yescomplemented
111C2×#625—28no—
112C2×#625—28no—
113C2×#625—24no—
114C2×#625—232no—
115C2×#625C2318yes—
116C2×#625C2318yescomplemented
117C2×#625C2314yescomplemented
118C2×D3×Dic3—24no—
119C2×D3×Dic3C2314yescomplemented
120C32×C22⋊C4C2314yescomplemented
121#3752C2318yescomplemented
122C4⋊(C3⋊Dic3)C2318yescomplemented
123C3×#217C2314yescomplemented
124C3×(C2×D3)⋊C4C2318yescomplemented
125C3×(C2×D3)⋊C4C2318yescomplemented
126Dic3⋊Dic3C2318yescomplemented
127(C2×D3)⋊Dic3C2318yescomplemented
128(C2×D3)⋊Dic3C2318yescomplemented
129C2×#534—91noSylow
130C25×C3—31no—
131C25×C3—31no—
132C24×D3—31no—
133C24×D3—31no—
134C24×D3C2×D311yescharacteristic
135C24×D3C2×D311yescharacteristic, complemented
136C22×C3×D4—31no—
137C22×C3×D4—32no—
138C23×C3×C4—32no—
139C22×#67—31no—
140C22×#67—31no—
141C22×#67—31no—
142C22×#67—32no—
143C22×#67—32no—
144C22×#67—32no—
145C22×#67—31no—
146C22×#67—32no—
147C22×#67—38no—
148C22×#67—38no—
149C22×#67—38no—
150C22×#67—31no—
151C22×#67—32no—
152C22×#67—61no—
153C22×#67—68no—
154C22×#67—68no—
155C22×#67—68no—
156C22×#67C2×D311yescharacteristic
157C23×Dic3—31no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C23×Dic3—61no—
161C2×D3×D4—38no—
162C2×D3×D4—68no—
163C22×D12—31no—
164C22×D12—32no—
165C22×D12C2×D312yescomplemented
166C22×C4×D3—31no—
167C22×C4×D3C2×D312yescomplemented
168C3×#120—38no—
169C2×C3×C22⋊C4—21no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—32no—
172C2×C3×C22⋊C4—32no—
173C2×C3×C22⋊C4—38no—
174C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
175C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
176#953—38no—
177C2×#217—32no—
178C2×#217—32no—
179C2×#217C2×D311yescharacteristic, complemented
180#938—316no—
181#937—316no—
182#935—38no—
183#930—316no—
184#930—316no—
185C2×(C2×D3)⋊C4—32no—
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4—62no—
190C2×(C2×D3)⋊C4C2×D312yescomplemented
191C2×(C2×D3)⋊C4C2×D312yescomplemented
192C2×C4⋊Dic3—32no—
193C2×C4⋊Dic3—32no—
194C2×C4⋊Dic3—32no—
195C2×C4⋊Dic3—62no—
196C2×Dic3⋊C4—32no—
197#886—38no—
198#886—38no—
199#886—38no—
200#886—316no—
201#886—68no—
202#884—316no—
203#883—316no—
204#882—38no—
205#882—316no—
206#882C2×D318yescomplemented
207D3×C22⋊C4C2×D318yescomplemented
208C23×C32—24no—
209C23×C32C2×D414yes—
210C23×C32C2412yes—
211C23×C32C2411yescharacteristic
212C22×C3⋊D3—22no—
213C22×C3⋊D3—24no—
214C22×C3⋊D3C2412yes—
215C22×C3×D3—24no—
216C22×C3×D3—24no—
217C22×C3×D3—22no—
218C22×C3×D3—24no—
219C22×C3×D3—28no—
220C22×C3×D3—24no—
221C22×C3×D3—24no—
222C22×C3×D3—24no—
223C22×C3×D3—416no—
224C22×C3×D3—48no—
225C22×C3×D3—48no—
226C22×C3×D3—416no—
227C22×C3×D3C2×D414yes—
228C22×C3×D3C2×D414yes—
229C22×C3×D3C2×D4116yescomplemented
230C22×C3×D3C2412yes—
231C22×C3×D3C2414yes—
232C22×C3×D3C2412yes—
233C22×C3×D3C2412yes—
234C2×D32—28no—
235C2×D32—48no—
236C2×D32—416no—
237C2×C32×C4—24no—
238C2×C32×C4C2414yes—
239#638—28no—
240C2×C3⋊Dic3—22no—
241C2×C3⋊Dic3—24no—
242C2×C3⋊Dic3—28no—
243C2×C3⋊Dic3C2412yes—
244C2×C3⋊Dic3C2414yes—
245C3×#67—28no—
246C2×C3×Dic3—22no—
247C2×C3×Dic3—24no—
248C2×C3×Dic3C2414yes—
249C2×C3×Dic3C2412yes—
250C3×D12—48no—
251C3×C4×D3—48no—
252#626—28no—
253#626—48no—
254#625—216no—
255#625—216no—
256#625—28no—
257D3×Dic3—28no—
258C23×D4—91no—
259C23×D4—91no—
260#534—916no—
261C2×#123—92no—
262C2×#123—91no—
263C2×#123—91no—
264C2×#121—92no—
265C2×#121—92no—
266C2×#120—31no—
267C2×#120—92no—
268C2×#120—91no—
269C22×C22⋊C4—31no—
270C24×C3—21no—
271C24×C3—31no—
272C24×C3—31no—
273C24×C3—38no—
274C24×C3—34no—
275C24×C3—32no—
276C24×C3—31no—
277C24×C3—34no—
278C24×C3—64no—
279C24×C3—124no—
280C24×C3—124no—
281C24×C3C22×D311yescharacteristic
282C24×C3C22×D311yescharacteristic
283C23×D3—24no—
284C23×D3—31no—
285C23×D3—31no—
286C23×D3—34no—
287C23×D3—34no—
288C23×D3—44no—
289C23×D3—44no—
290C23×D3—61no—
291C23×D3—64no—
292C23×D3—64no—
293C23×D3—124no—
294C23×D3—124no—
295C23×D3D1218yescomplemented
296C23×D3C22×D311yescharacteristic
297C23×D3C22×D312yes—
298C23×D3C22×D311yescharacteristic
299C23×D3C22×D311yescharacteristic
300C23×D3C22×D314yes—
301C23×D3C22×D314yescomplemented
302C2×C3×D4—34no—
303C2×C3×D4—38no—
304C2×C3×D4—64no—
305C2×C3×D4—124no—
306C22×C3×C4—22no—
307C22×C3×C4—31no—
308C22×C3×C4—32no—
309C22×C3×C4—38no—
310C22×C3×C4—124no—
311C22×C3×C4C22×D312yes—
312C22×C3×C4C22×D312yes—
313C2×#67—24no—
314C2×#67—34no—
315C2×#67—34no—
316C2×#67—38no—
317C2×#67—38no—
318C2×#67—38no—
319C2×#67—34no—
320C2×#67—38no—
321C2×#67—34no—
322C2×#67—34no—
323C2×#67—38no—
324C2×#67—64no—
325C2×#67—64no—
326C2×#67—632no—
327C2×#67—64no—
328C2×#67—68no—
329C2×#67—68no—
330C2×#67—632no—
331C2×#67—64no—
332C2×#67—64no—
333C2×#67—64no—
334C2×#67—68no—
335C2×#67—68no—
336C2×#67—632no—
337C2×#67—124no—
338C2×#67—124no—
339C2×#67C22×D314yes—
340C22×Dic3—34no—
341C22×Dic3—34no—
342C22×Dic3—32no—
343C22×Dic3—31no—
344C22×Dic3—32no—
345C22×Dic3—31no—
346C22×Dic3—34no—
347C22×Dic3—64no—
348C22×Dic3—61no—
349C22×Dic3—62no—
350C22×Dic3—64no—
351C22×Dic3—64no—
352C22×Dic3—64no—
353C22×Dic3—124no—
354C22×Dic3C22×D312yes—
355C22×Dic3C22×D311yescharacteristic
356D3×D4—632no—
357C2×D12—34no—
358C2×D12—38no—
359C2×D12—44no—
360C2×D12—64no—
361C2×D12—124no—
362C2×D12C22×D318yescomplemented
363C2×C4×D3—34no—
364C2×C4×D3—44no—
365C2×C4×D3—64no—
366C2×C4×D3C22×D318yescomplemented
367C3×C22⋊C4—24no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—38no—
370C3×C22⋊C4—38no—
371C3×C22⋊C4C22×D314yescomplemented
372C3×C22⋊C4C22×D314yescomplemented
373#217—38no—
374#217—38no—
375#217C22×D314yescomplemented
376(C2×D3)⋊C4—38no—
377(C2×D3)⋊C4—38no—
378(C2×D3)⋊C4—38no—
379(C2×D3)⋊C4—38no—
380(C2×D3)⋊C4—68no—
381(C2×D3)⋊C4C22×D318yescomplemented
382(C2×D3)⋊C4C22×D318yescomplemented
383C4⋊Dic3—38no—
384C4⋊Dic3—38no—
385C4⋊Dic3—38no—
386C4⋊Dic3—68no—
387Dic3⋊C4—38no—
388C22×C32—28no—
389C22×C32—24no—
390C22×C32C22×D414yes—
391C22×C32C22×D412yes—
392C22×C32H(5,𝔽2)14yes—
393C22×C32C2511yescharacteristic
394C2×C3⋊D3—22no—
395C2×C3⋊D3—24no—
396C2×C3⋊D3—44no—
397C2×C3×D3—28no—
398C2×C3×D3—28no—
399C2×C3×D3—24no—
400C2×C3×D3—24no—
401C2×C3×D3—24no—
402C2×C3×D3—22no—
403C2×C3×D3—24no—
404C2×C3×D3—24no—
405C2×C3×D3—24no—
406C2×C3×D3—416no—
407C2×C3×D3—416no—
408C2×C3×D3—44no—
409C2×C3×D3—48no—
410C2×C3×D3C22×D414yes—
411C2×C3×D3C22×D414yes—
412D32—416no—
413C32×C4—24no—
414C3⋊Dic3—22no—
415C3⋊Dic3—24no—
416C3×Dic3—22no—
417C3×Dic3—24no—
418C25—31no—
419C25—31no—
420C25—91no—
421C22×D4—31no—
422C22×D4—32no—
423C22×D4—91no—
424C22×D4—92no—
425C22×D4—98no—
426C22×D4—92no—
427C22×D4—92no—
428C22×D4—91no—
429C22×D4—98no—
430C22×D4—91no—
431C22×D4—188no—
432C22×D4—188no—
433C23×C4—32no—
434C23×C4—91no—
435C23×C4—91no—
436#123—916no—
437#123—98no—
438#123—98no—
439#121—916no—
440#121—916no—
441#120—38no—
442#120—916no—
443#120—98no—
444C2×C4⋊C4—92no—
445C2×C4⋊C4—92no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—32no—
448C2×C22⋊C4—32no—
449C2×C22⋊C4—38no—
450C2×C22⋊C4—92no—
451C2×C22⋊C4—92no—
452C2×C22⋊C4—92no—
453C2×C22⋊C4D3211yescharacteristic, complemented
454C23×C3—24no—
455C23×C3—24no—
456C23×C3—22no—
457C23×C3—21no—
458C23×C3—24no—
459C23×C3—34no—
460C23×C3—34no—
461C23×C3—32no—
462C23×C3—32no—
463C23×C3—316no—
464C23×C3—32no—
465C23×C3—34no—
466C23×C3—44no—
467C23×C3—64no—
468C23×C3—64no—
469C23×C3—68no—
470C23×C3—64no—
471C23×C3—62no—
472C23×C3—64no—
473C23×C3—64no—
474C23×C3—64no—
475C23×C3—128no—
476C23×C3—128no—
477C23×C3—1216no—
478C23×C3—1216no—
479C23×C3C2×D1214yes—
480C23×C3D3×D414yes—
481C23×C3C23×D312yes—
482C23×C3C23×D312yes—
483C23×C3C23×D311yescharacteristic
484C23×C3C23×D311yescharacteristic
485C22×D3—24no—
486C22×D3—24no—
487C22×D3—22no—
488C22×D3—24no—
489C22×D3—28no—
490C22×D3—24no—
491C22×D3—24no—
492C22×D3—24no—
493C22×D3—32no—
494C22×D3—32no—
495C22×D3—416no—
496C22×D3—48no—
497C22×D3—48no—
498C22×D3—416no—
499C22×D3—62no—
500C22×D3—68no—
501C22×D3—62no—
502C22×D3—62no—
503C22×D3—64no—
504C22×D3—64no—
505C22×D3—68no—
506C22×D3—122no—
507C22×D3—124no—
508C22×D3—128no—
509C22×D3—128no—
510C22×D3—1216no—
511C22×D3—1216no—
512C22×D3C2×D1214yes—
513C22×D3C2×D1214yes—
514C22×D3C2×D12116yescomplemented
515C22×D3C23×D312yes—
516C22×D3C23×D314yes—
517C22×D3C23×D312yes—
518C22×D3C23×D312yes—
519C3×D4—68no—
520C3×D4—128no—
521C2×C3×C4—24no—
522C2×C3×C4—24no—
523C2×C3×C4—24no—
524C2×C3×C4—32no—
525C2×C3×C4—34no—
526C2×C3×C4—44no—
527C2×C3×C4—62no—
528C2×C3×C4—64no—
529C2×C3×C4—128no—
530C2×C3×C4C23×D314yes—
531C2×C3×C4C23×D314yes—
532#67—28no—
533#67—68no—
534#67—68no—
535#67—616no—
536#67—616no—
537#67—68no—
538#67—68no—
539#67—68no—
540#67—616no—
541#67—616no—
542#67—128no—
543#67—128no—
544C2×Dic3—22no—
545C2×Dic3—24no—
546C2×Dic3—34no—
547C2×Dic3—32no—
548C2×Dic3—34no—
549C2×Dic3—32no—
550C2×Dic3—62no—
551C2×Dic3—64no—
552C2×Dic3—68no—
553C2×Dic3—62no—
554C2×Dic3—68no—
555C2×Dic3—64no—
556C2×Dic3—68no—
557C2×Dic3—62no—
558C2×Dic3—64no—
559C2×Dic3—124no—
560C2×Dic3—128no—
561C2×Dic3—122no—
562C2×Dic3C23×D314yes—
563C2×Dic3C23×D312yes—
564D12—48no—
565D12—68no—
566D12—128no—
567C4×D3—48no—
568C4×D3—68no—
569C2×C32—24no—
570C2×C32#53414yescomplemented
571C2×C32C23×D411yescharacteristic
572C2×C32C2×H(5,𝔽2)12yes—
573C3⋊D3—42no—
574C3×D3—24no—
575C3×D3—24no—
576C3×D3—42no—
577C3×D3—44no—
578C24—31no—
579C24—31no—
580C24—34no—
581C24—38no—
582C24—32no—
583C24—31no—
584C24—34no—
585C24—64no—
586C24—94no—
587C24—91no—
588C24—124no—
589C24—124no—
590C24—184no—
591C24—364no—
592C24C2×D3211yescharacteristic
593C2×D4—34no—
594C2×D4—38no—
595C2×D4—64no—
596C2×D4—94no—
597C2×D4—98no—
598C2×D4—98no—
599C2×D4—98no—
600C2×D4—94no—
601C2×D4—94no—
602C2×D4—124no—
603C2×D4—184no—
604C2×D4—1832no—
605C2×D4—188no—
606C2×D4—184no—
607C2×D4—188no—
608C2×D4—1832no—
609C2×D4—184no—
610C2×D4—364no—
611C22×C4—32no—
612C22×C4—31no—
613C22×C4—38no—
614C22×C4—94no—
615C22×C4—94no—
616C22×C4—91no—
617C22×C4—92no—
618C22×C4—124no—
619C22×C4—184no—
620C22×C4—184no—
621C22×C4C2×D3212yes—
622C4⋊C4—98no—
623C4⋊C4—98no—
624C22⋊C4—34no—
625C22⋊C4—38no—
626C22⋊C4—38no—
627C22⋊C4—98no—
628C22⋊C4—98no—
629C22⋊C4—98no—
630C22⋊C4C2×D3214yescomplemented
631C22×C3—24no—
632C22×C3—24no—
633C22×C3—28no—
634C22×C3—28no—
635C22×C3—22no—
636C22×C3—24no—
637C22×C3—24no—
638C22×C3—21no—
639C22×C3—34no—
640C22×C3—34no—
641C22×C3—44no—
642C22×C3—48no—
643C22×C3—64no—
644C22×C3—64no—
645C22×C3—68no—
646C22×C3—68no—
647C22×C3—64no—
648C22×C3—62no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—64no—
652C22×C3—1216no—
653C22×C3—1216no—
654C22×C3—124no—
655C22×C3—128no—
656C22×C3C22×D1214yes—
657C22×C3C22×D1212yes—
658C22×C3C2×D3×D414yes—
659C22×C3C2×D3×D412yes—
660C22×C3#100414yes—
661C22×C3#100414yes—
662C22×C3C24×D311yescharacteristic
663C22×C3C24×D311yescharacteristic
664C2×D3—24no—
665C2×D3—24no—
666C2×D3—28no—
667C2×D3—28no—
668C2×D3—22no—
669C2×D3—24no—
670C2×D3—24no—
671C2×D3—24no—
672C2×D3—24no—
673C2×D3—416no—
674C2×D3—416no—
675C2×D3—48no—
676C2×D3—44no—
677C2×D3—62no—
678C2×D3—62no—
679C2×D3—64no—
680C2×D3—64no—
681C2×D3—122no—
682C2×D3—124no—
683C2×D3—1216no—
684C2×D3—1216no—
685C2×D3—124no—
686C2×D3—124no—
687C2×D3—244no—
688C2×D3C22×D1214yes—
689C2×D3C22×D1214yes—
690C3×C4—24no—
691C3×C4—24no—
692C3×C4—44no—
693C3×C4—62no—
694C3×C4—64no—
695Dic3—22no—
696Dic3—24no—
697Dic3—62no—
698Dic3—64no—
699Dic3—62no—
700Dic3—64no—
701Dic3—124no—
702Dic3—122no—
703C32C2×#53411yescharacteristic, complemented, Sylow
704C23—24no—
705C23—34no—
706C23—34no—
707C23—32no—
708C23—32no—
709C23—316no—
710C23—34no—
711C23—32no—
712C23—64no—
713C23—64no—
714C23—62no—
715C23—68no—
716C23—64no—
717C23—64no—
718C23—64no—
719C23—64no—
720C23—92no—
721C23—128no—
722C23—128no—
723C23—1216no—
724C23—1216no—
725C23—188no—
726C23—182no—
727C23—184no—
728C23—368no—
729C23—3616no—
730C23D3×D1214yes—
731C23C22×D3212yes—
732C23C22×D3211yescharacteristic
733D4—68no—
734D4—128no—
735D4—188no—
736D4—1816no—
737D4—188no—
738D4—1816no—
739D4—188no—
740D4—368no—
741C2×C4—24no—
742C2×C4—34no—
743C2×C4—32no—
744C2×C4—62no—
745C2×C4—64no—
746C2×C4—92no—
747C2×C4—94no—
748C2×C4—128no—
749C2×C4—188no—
750C2×C4—188no—
751C2×C4—182no—
752C2×C4—184no—
753C2×C4C22×D3214yes—
754C2×C3—24no—
755C2×C3—24no—
756C2×C3—21no—
757C2×C3—22no—
758C2×C3—24no—
759C2×C3—44no—
760C2×C3—64no—
761C2×C3—64no—
762C2×C3—122no—
763C2×C3—124no—
764C2×C3#549314yescomplemented
765C2×C3#558914yescomplemented
766C2×C3C23×D1211yescharacteristic
767C2×C3C22×D3×D411yescharacteristic
768C2×C3C2×#100412yes—
769C2×C3C2×#100412yes—
770D3—24no—
771D3—24no—
772D3—44no—
773D3—42no—
774D3—122no—
775D3—122no—
776D3—242no—
777C22—24no—
778C22—28no—
779C22—34no—
780C22—34no—
781C22—64no—
782C22—64no—
783C22—68no—
784C22—68no—
785C22—62no—
786C22—64no—
787C22—64no—
788C22—64no—
789C22—64no—
790C22—1216no—
791C22—1216no—
792C22—128no—
793C22—124no—
794C22—182no—
795C22—184no—
796C22—3616no—
797C22—364no—
798C22C2×D3×D1214yes—
799C22C2×D3×D1212yes—
800C22#6431314yes—
801C22C23×D3211yescharacteristic
802C4—24no—
803C4—62no—
804C4—64no—
805C4—182no—
806C4—184no—
807C3—21no—
808C3C2×#549311yescharacteristic, complemented
809C3C2×#558911yescharacteristic, complemented
810C2—24no—
811C2—64no—
812C2—64no—
813C2—124no—
814C2—122no—
815C2—362no—
816C2#1059429014yesdirect product factor
817C2C22×D3×D1211yescharacteristic
818C2C2×#6431312yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C23×#625C2semidirect
3. C2×#64095C2semidirect
4. C2×C3×#882C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C2×#63977C2semidirect
7. C2×#63962C2semidirect
8. C2×#63922C2semidirect
9. C2×#63908C2semidirect
10. C2×#63906C2semidirect
11. C2×#63891C2semidirect
12. #10594290C2direct (N × H)
16. C24×C3×D3C22semidirect
17. C23×D32C22semidirect
19. C23×C3⋊Dic3C22semidirect
21. C22×C3×D12C22semidirect
22. C22×C3×C4×D3C22semidirect
24. C2×D3×#67C22semidirect
25. C22×#626C22semidirect
26. C22×#626C22semidirect
29. C22×#625C22semidirect
30. C22×#625C22semidirect
31. C22×#625C22semidirect
32. C22×D3×Dic3C22semidirect
33. C2×C32×C22⋊C4C22semidirect
34. C2×#3752C22semidirect
35. C2×C4⋊(C3⋊Dic3)C22semidirect
36. #64095C22semidirect
37. C2×C3×#217C22semidirect
38. C2×C3×(C2×D3)⋊C4C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C3×#882C22semidirect
41. C3×D3×C22⋊C4C22semidirect
42. #63977C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
44. #63962C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. #63922C22semidirect
48. #63908C22semidirect
49. #63906C22semidirect
50. #63891C22semidirect
74. C2×#882D3semidirect
75. C2×D3×C22⋊C4D3semidirect
81. C23×C3×D3D4semidirect
87. C23×C3×D3C23semidirect
90. C22×D32C23semidirect
97. C22×C3⋊Dic3C23semidirect
103. C2×C3×D12C23semidirect
105. C2×C3×C4×D3C23semidirect
109. C2×#626C23semidirect
110. C2×#626C23semidirect
116. C2×#625C23semidirect
117. C2×#625C23semidirect
119. C2×D3×Dic3C23semidirect
120. C32×C22⋊C4C23semidirect
121. #3752C23semidirect
122. C4⋊(C3⋊Dic3)C23semidirect
123. C3×#217C23semidirect
124. C3×(C2×D3)⋊C4C23semidirect
125. C3×(C2×D3)⋊C4C23semidirect
126. Dic3⋊Dic3C23semidirect
127. (C2×D3)⋊Dic3C23semidirect
128. (C2×D3)⋊Dic3C23semidirect
135. C24×D3C2×D3semidirect
165. C22×D12C2×D3semidirect
167. C22×C4×D3C2×D3semidirect
174. C2×C3×C22⋊C4C2×D3semidirect
175. C2×C3×C22⋊C4C2×D3semidirect
179. C2×#217C2×D3semidirect
190. C2×(C2×D3)⋊C4C2×D3semidirect
191. C2×(C2×D3)⋊C4C2×D3semidirect
206. #882C2×D3semidirect
207. D3×C22⋊C4C2×D3semidirect
229. C22×C3×D3C2×D4semidirect
295. C23×D3D12semidirect
301. C23×D3C22×D3semidirect
362. C2×D12C22×D3semidirect
366. C2×C4×D3C22×D3semidirect
371. C3×C22⋊C4C22×D3semidirect
372. C3×C22⋊C4C22×D3semidirect
375. #217C22×D3semidirect
381. (C2×D3)⋊C4C22×D3semidirect
382. (C2×D3)⋊C4C22×D3semidirect
453. C2×C22⋊C4D32semidirect
514. C22×D3C2×D12semidirect
570. C2×C32#534semidirect
630. C22⋊C4C2×D32semidirect
703. C32C2×#534semidirect
764. C2×C3#5493semidirect
765. C2×C3#5589semidirect
808. C3C2×#5493semidirect
809. C3C2×#5589semidirect
816. C2#10594290direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C23×#6252
C2×#640952
C2×C3×#8822
C2×C3×D3×C22⋊C42
C2×#639772
C2×#639622
C2×#639222
C2×#639082
C2×#639062
C2×#638912
#105942902
C2×#55893
C2×#54933