Finite Group Databasebeta

← #11904439

Subgroups — #11904439

Order 1152.

3285 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3#10596299C211yesmaximal, characteristic, complemented
4C3×#5825C211yesmaximal, characteristic, complemented
5#10595358C214yesmaximal, complemented
6#10595234C214yesmaximal, complemented
7#10595229C214yesmaximal, complemented
8D3×#935C214yesmaximal, complemented
9#10595034C211yesmaximal, characteristic, complemented
10#10594982C211yesmaximal, characteristic, complemented
11#10594890C214yesmaximal, complemented
12#10594889C214yesmaximal, complemented
13#10594855C211yesmaximal, characteristic, complemented
14#87280—31nomaximal
15#86354—31nomaximal
16C2×C32×#41C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic, complemented
18C3×#1009—28no—
19C2×C3×#239C2212yescomplemented
20C2×C3×D3×D4C2214yes—
21C2×C3×D3×D4C2212yescomplemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2212yescomplemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×D12C2212yescomplemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C22×#626C2212yescomplemented
28C22×D3×Dic3C2212yescomplemented
29C2×#3796—28no—
30C2×#3796C2214yescomplemented
31C2×#3796C2214yescomplemented
32#64155C2212yescomplemented
33#64147C2212yescomplemented
34#64146C2212yescomplemented
35#64144C2212yescomplemented
36C4×#638C2214yescomplemented
37#64135C2211yescharacteristic, complemented
38C3×#944C2212yescomplemented
39C3×#936C2212yescomplemented
40C3×#935C2214yescomplemented
41C3×#926C2211yescharacteristic, complemented
42C3×#924C2214yescomplemented
43#63981C2212yescomplemented
44#63977C2218yescomplemented
45#63971C2218yescomplemented
46#63969C2218yescomplemented
47D3×#217C2218yescomplemented
48D3×#217C2214yescomplemented
49#63962C2212yescomplemented
50#63961C2214yescomplemented
51#63916C2212yescomplemented
52C4×#626C2214yescomplemented
53#63898C2214yescomplemented
54Dic3×D12C2214yescomplemented
55#63886C2218yescomplemented
56#63884C2218yescomplemented
57D3×Dic3⋊C4C2218yescomplemented
58#63873C2212yescomplemented
59#63871C2212yescomplemented
60#63863C2212yescomplemented
61#63856C2214yescomplemented
62#63850C2218yescomplemented
63C2×C3×H(5,𝔽2)—31no—
64C2×#1009D311yescharacteristic, complemented
65C22×#239—31no—
66C22×#237—31no—
67C3×#536—31no—
68#5828—31no—
69#5828—31no—
70#5828—31no—
71#5828—61no—
72#5825—31no—
73#5825D311yescharacteristic, complemented
74#5824—34no—
75#5824—34no—
76#5816—31no—
77#5806—34no—
78#5806—34no—
79#5804—34no—
80#5798—31no—
81C2×#935—34no—
82#5726—34no—
83#5676—34no—
84#5653—34no—
85D3×#123—34no—
86#5631—34no—
87#5630—34no—
88#5524—31no—
89#5521—31no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2314yes—
92C23×C3×D3C2312yes—
93C32×#41—24no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2312yes—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2312yes—
98C22×C32×C4C2311yescharacteristic
99C2×#638C2314yes—
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C4×C3⋊D3—24no—
102C2×C4×C3⋊D3C2312yes—
103C2×C4×C3⋊D3C2312yes—
104C2×C3×#67C2312yes—
105C2×C3×#67C2314yes—
106C22×C3×Dic3C2312yes—
107C3×#239—28no—
108C3×D3×D4—216no—
109C3×D3×D4—28no—
110C3×#235—24no—
111C3×#235—28no—
112C2×C3×D12—28no—
113C2×C3×D12D418yescomplemented
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2314yes—
116C2×C3×D12C2312yes—
117C2×C3×D12C2312yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2314yes—
120C2×C3×Dic6—24no—
121C2×C3×Dic6C2312yes—
122C2×C3×Dic6C2312yes—
123C2×C3×Dic6C2311yescharacteristic
124C2×#626—28no—
125C2×#626C2318yes—
126C2×#626C2314yes—
127C2×D3×Dic3—28no—
128C2×D3×Dic3C2318yes—
129C2×D3×Dic3C2318yes—
130#3796—216no—
131#3796—216no—
132#3757C2312yes—
133#3757C2314yes—
134#3752C2314yes—
135C4⋊(C3⋊Dic3)C2312yes—
136#3750C2314yes—
137C4×C3⋊Dic3C2312yes—
138C3×#217C2318yes—
139C3×#217C2312yes—
140C3×C4⋊Dic3C2312yes—
141C3×Dic3⋊C4C2318yes—
142C3×C4×Dic3C2312yes—
143#3724C2318yes—
144Dic3⋊Dic3C2314yes—
145#3722C2314yes—
146(C2×D3)⋊Dic3C2318yes—
147(C2×D3)⋊Dic3C2318yes—
148(C2×D3)⋊Dic3C2314yes—
149#3485—91noSylow
150C3×H(5,𝔽2)—68no—
151C2×C3×#41—21no—
152C2×C3×#41—32no—
153C2×C3×#41—31no—
154C2×C3×#41—32no—
155C2×C3×#41C2×D311yescharacteristic
156C2×C3×#41C2×D311yescharacteristic
157C22×C3×Q8—31no—
158C22×C3×D4—34no—
159C22×C3×D4—32no—
160C22×C3×D4—31no—
161C22×C3×D4—32no—
162C22×#67—32no—
163C23×Dic3—32no—
164#1009—28no—
165C2×#239—34no—
166C2×#239—34no—
167C2×#239—68no—
168C2×#239C2×D312yescomplemented
169C2×#237—34no—
170C2×#237—34no—
171C2×#237—68no—
172C2×D3×D4C2×D314yes—
173C2×D3×D4C2×D312yescomplemented
174C2×#235C2×D311yescharacteristic
175C2×#235C2×D312yescomplemented
176C22×D12—32no—
177C22×D12C2×D311yescharacteristic
178C22×D12C2×D312yescomplemented
179C22×C4×D3—32no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—61no—
183C22×Dic6C2×D311yescharacteristic, complemented
184C3×C4⋊Q8—32no—
185C3×#124—32no—
186C3×#123—34no—
187C3×C22⋊Q8—34no—
188C3×#117—31no—
189#953—38no—
190C2×#217—34no—
191C2×#217—38no—
192#947—32no—
193#946—32no—
194#946—32no—
195#946—34no—
196#946—32no—
197#946—62no—
198#944—32no—
199#944—32no—
200#944C2×D312yescomplemented
201#939—38no—
202#939—38no—
203#938—32no—
204#938—32no—
205#938—32no—
206#938—62no—
207#937—32no—
208#937—32no—
209#937—32no—
210#937—62no—
211#936—32no—
212#936C2×D312yescomplemented
213#935—32no—
214#935—32no—
215#935—34no—
216#935—32no—
217#935—38no—
218#935—38no—
219#935—62no—
220#935C2×D314yescomplemented
221D4×Dic3—34no—
222D4×Dic3—34no—
223#929—34no—
224#929—38no—
225C4×#67—34no—
226C4×#67—34no—
227C4×#67—34no—
228C4×#67—64no—
229#926—31no—
230#926—31no—
231#926—61no—
232#926C2×D311yescharacteristic, complemented
233#924—34no—
234#924C2×D314yescomplemented
235C2×Dic3⋊C4—38no—
236#897—32no—
237#895—38no—
238#895—32no—
239#894—38no—
240#894—38no—
241#893—34no—
242D3×C4⋊C4—38no—
243#886—32no—
244#884—38no—
245#883—38no—
246#882—38no—
247#882—32no—
248D3×C22⋊C4—34no—
249D3×C22⋊C4—38no—
250C4×D12—34no—
251C4×D12—34no—
252C23×C32C2412yes—
253C23×C32C2411yescharacteristic
254C22×C3⋊D3—22no—
255C22×C3⋊D3—42no—
256C22×C3⋊D3C2412yes—
257C22×C3×D3—28no—
258C22×C3×D3—44no—
259C22×C3×D3—48no—
260C22×C3×D3C2×D418yes—
261C22×C3×D3C2412yes—
262C22×C3×D3C2414yes—
263C32×Q8—22no—
264C32×D4—24no—
265C32×D4—22no—
266C2×C32×C4—24no—
267C2×C32×C4C2×D414yes—
268C2×C32×C4C2412yes—
269C2×C32×C4C2411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271#638—44no—
272C2×C3⋊Dic3—22no—
273C2×C3⋊Dic3C2414yes—
274C2×C3⋊Dic3C2412yes—
275C4×C3⋊D3—24no—
276C4×C3⋊D3—24no—
277C3×#67—24no—
278C3×#67—28no—
279C2×C3×Dic3—24no—
280C2×C3×Dic3C2414yes—
281C2×C3×Dic3C2414yes—
282C2×C3×Dic3C2412yes—
283C3×D12—28no—
284C3×D12—22no—
285C3×D12C2×D418yes—
286C3×D12C2×D418yes—
287C3×C4×D3—28no—
288C3×C4×D3—24no—
289C3×Dic6—24no—
290C3×Dic6—24no—
291C3×Dic6—22no—
292#626—216no—
293#626—44no—
294D3×Dic3—216no—
295D3×Dic3—48no—
296C2×H(5,𝔽2)—31no—
297C22×#41—91no—
298#547—94no—
299#547—94no—
300#546—94no—
301#546—94no—
302#536—31no—
303#536—91no—
304#534—94no—
305#525—91no—
306#525—91no—
307C2×#123—94no—
308#518—91no—
309C24×C3—32no—
310C24×C3—34no—
311C23×D3—31no—
312C23×D3—31no—
313C23×D3—61no—
314C23×D3C22×D314yes—
315C23×D3C22×D312yes—
316C3×#41—24no—
317C3×#41—24no—
318C3×#41—44no—
319C3×#41—68no—
320C3×#41—68no—
321C3×#41—64no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—32no—
325C2×C3×Q8—32no—
326C2×C3×Q8—64no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—22no—
330C2×C3×D4—21no—
331C2×C3×D4—32no—
332C2×C3×D4—34no—
333C2×C3×D4—38no—
334C2×C3×D4—32no—
335C2×C3×D4—32no—
336C2×C3×D4—34no—
337C2×C3×D4—31no—
338C2×C3×D4—68no—
339C2×C3×D4—68no—
340C2×C3×D4—616no—
341C2×C3×D4C22×D312yes—
342C2×C3×D4C22×D312yes—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C22×D311yescharacteristic
345C22×C3×C4—21no—
346C22×C3×C4—22no—
347C22×C3×C4—32no—
348C22×C3×C4—34no—
349C22×C3×C4—32no—
350C22×C3×C4C22×D312yes—
351C22×C3×C4C22×D312yes—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—38no—
357C2×#67—34no—
358C2×#67—64no—
359C2×#67—68no—
360C2×#67C22×D312yes—
361C2×#67C22×D314yes—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—38no—
365C22×Dic3—38no—
366C22×Dic3—61no—
367C22×Dic3—68no—
368C22×Dic3C22×D312yes—
369#239—28no—
370#239—616no—
371#239—616no—
372#237—616no—
373#237—616no—
374D3×D4—216no—
375D3×D4—28no—
376#235—24no—
377#235—28no—
378C2×D12—28no—
379C2×D12—38no—
380C2×D12—34no—
381C2×D12—68no—
382C2×D12#6718yescomplemented
383C2×D12C22×D314yes—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D312yes—
386C2×D12C22×D312yes—
387C2×C4×D3—38no—
388C2×C4×D3—32no—
389C2×C4×D3—32no—
390C2×C4×D3—32no—
391C2×C4×D3—32no—
392C2×C4×D3—38no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—68no—
396C2×C4×D3—64no—
397C2×C4×D3—64no—
398C2×C4×D3—124no—
399C2×C4×D3C22×D312yes—
400C2×C4×D3C22×D314yes—
401C2×Dic6—24no—
402C2×Dic6C22×D311yescharacteristic
403C2×Dic6C22×D312yes—
404C2×Dic6C22×D312yes—
405C3×C4⋊C4—38no—
406C3×C4⋊C4—32no—
407C3×C22⋊C4—32no—
408C3×C22⋊C4—38no—
409C3×C42—32no—
410#217—34no—
411#217—32no—
412#217—32no—
413#217—34no—
414#217—38no—
415#217—34no—
416#217—38no—
417#217—62no—
418#217—64no—
419#217C22×D318yes—
420#217C22×D312yes—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—38no—
423(C2×D3)⋊C4—38no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—64no—
429C4⋊Dic3—32no—
430C4⋊Dic3—32no—
431C4⋊Dic3—34no—
432C4⋊Dic3—62no—
433C4⋊Dic3C22×D312yes—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—38no—
437Dic3⋊C4—34no—
438Dic3⋊C4—38no—
439Dic3⋊C4—64no—
440Dic3⋊C4C22×D318yes—
441C4×Dic3—32no—
442C4×Dic3—32no—
443C4×Dic3—62no—
444C4×Dic3C22×D312yes—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—24no—
448C22×C32C22×D412yes—
449C22×C32C2511yescharacteristic
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—44no—
454C2×C3×D3—28no—
455C2×C3×D3—22no—
456C2×C3×D3—24no—
457C2×C3×D3—48no—
458C2×C3×D3—88no—
459C2×C3×D3C22×D418yes—
460C32×C4—22no—
461C32×C4C22×D412yes—
462C32×C4C22×D412yes—
463C3⋊Dic3—22no—
464C3⋊Dic3—24no—
465C3×Dic3—24no—
466C3×Dic3—22no—
467C3×Dic3—24no—
468H(5,𝔽2)—68no—
469C2×#41—32no—
470C2×#41—31no—
471C2×#41—32no—
472C2×#41—94no—
473C2×#41—94no—
474C2×#41—188no—
475C2×#41D3211yescharacteristic
476C22×Q8—31no—
477C22×D4—34no—
478C22×D4—32no—
479C22×D4—31no—
480C22×D4—32no—
481C22×D4—92no—
482C23×C4—92no—
483C23×C4—91no—
484C4⋊Q8—32no—
485C4⋊Q8—92no—
486#124—32no—
487#124—92no—
488#123—34no—
489#123—92no—
490#123—98no—
491#123—98no—
492#123—98no—
493#123—94no—
494#123—92no—
495C22⋊Q8—34no—
496C22⋊Q8—92no—
497C22⋊Q8—94no—
498C22⋊Q8—92no—
499#121—98no—
500#121—92no—
501#121—98no—
502#121—92no—
503#120—92no—
504#120—98no—
505#120—92no—
506C4×D4—94no—
507C4×D4—94no—
508C4×D4—94no—
509C4×D4—94no—
510#117—31no—
511#117—91no—
512C2×C4⋊C4—98no—
513C2×C22⋊C4—94no—
514C2×C22⋊C4—98no—
515C23×C3—21no—
516C23×C3—22no—
517C23×C3—34no—
518C23×C3—38no—
519C23×C3—32no—
520C23×C3—68no—
521C23×C3—124no—
522C23×C3—128no—
523C23×C3C23×D312yes—
524C23×C3C23×D312yes—
525C23×C3C23×D311yescharacteristic
526C23×C3C23×D311yescharacteristic
527C22×D3—28no—
528C22×D3—32no—
529C22×D3—32no—
530C22×D3—44no—
531C22×D3—48no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—122no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—124no—
539C22×D3C2×#6718yes—
540C22×D3C23×D312yes—
541C22×D3C23×D314yes—
542C3×Q8—22no—
543C3×Q8—22no—
544C3×Q8—42no—
545C3×Q8—62no—
546C3×Q8—64no—
547C3×Q8—64no—
548C3×D4—24no—
549C3×D4—24no—
550C3×D4—22no—
551C3×D4—22no—
552C3×D4—38no—
553C3×D4—38no—
554C3×D4—42no—
555C3×D4—44no—
556C3×D4—68no—
557C3×D4—68no—
558C3×D4—64no—
559C3×D4—62no—
560C2×C3×C4—24no—
561C2×C3×C4—24no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—22no—
565C2×C3×C4—24no—
566C2×C3×C4—32no—
567C2×C3×C4—34no—
568C2×C3×C4—34no—
569C2×C3×C4—44no—
570C2×C3×C4—68no—
571C2×C3×C4—64no—
572C2×C3×C4—64no—
573C2×C3×C4D3×D414yes—
574C2×C3×C4C2×#6714yes—
575C2×C3×C4C23×D312yes—
576C2×C3×C4C23×D312yes—
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—24no—
582#67—28no—
583#67—616no—
584#67—124no—
585#67—124no—
586#67—124no—
587#67—128no—
588C2×Dic3—24no—
589C2×Dic3—34no—
590C2×Dic3—34no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—64no—
594C2×Dic3—62no—
595C2×Dic3—616no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—122no—
599C2×Dic3—128no—
600C2×Dic3C23×D314yes—
601C2×Dic3C23×D312yes—
602C2×Dic3C23×D314yes—
603D12—28no—
604D12—22no—
605D12—616no—
606D12—124no—
607D12C2×#6718yes—
608D12C2×#6718yes—
609C4×D3—28no—
610C4×D3—24no—
611C4×D3—616no—
612C4×D3—64no—
613C4×D3—64no—
614C4×D3—64no—
615C4×D3—64no—
616C4×D3—124no—
617C4×D3—124no—
618C4×D3—128no—
619Dic6—24no—
620Dic6—24no—
621Dic6—22no—
622C2×C32—22no—
623C2×C32—42no—
624C2×C32C23×D411yescharacteristic
625C2×C32#58512yes—
626C3⋊D3—42no—
627C3×D3—28no—
628C3×D3—42no—
629C24—32no—
630C24—34no—
631C24—91no—
632#41—24no—
633#41—68no—
634#41—68no—
635#41—64no—
636#41—1816no—
637#41—1816no—
638C2×Q8—32no—
639C2×Q8—32no—
640C2×Q8—31no—
641C2×Q8—64no—
642C2×Q8C2×D3211yescharacteristic
643C2×D4—32no—
644C2×D4—34no—
645C2×D4—32no—
646C2×D4—32no—
647C2×D4—34no—
648C2×D4—31no—
649C2×D4—38no—
650C2×D4—68no—
651C2×D4—68no—
652C2×D4—616no—
653C2×D4—98no—
654C2×D4—94no—
655C2×D4—94no—
656C2×D4—188no—
657C2×D4C2×D3212yes—
658C2×D4C2×D3211yescharacteristic
659C22×C4—32no—
660C22×C4—34no—
661C22×C4—32no—
662C22×C4—98no—
663C22×C4—98no—
664C22×C4—91no—
665C22×C4—92no—
666C22×C4—92no—
667C22×C4—188no—
668C22×C4—184no—
669C22×C4C2×D3212yes—
670C22×C4C2×D3211yescharacteristic
671C4⋊C4—38no—
672C4⋊C4—32no—
673C4⋊C4—94no—
674C4⋊C4—98no—
675C4⋊C4—94no—
676C4⋊C4—92no—
677C22⋊C4—32no—
678C22⋊C4—38no—
679C22⋊C4—94no—
680C22⋊C4—94no—
681C22⋊C4—98no—
682C22⋊C4—98no—
683C22⋊C4—92no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C42—32no—
687C42—92no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—24no—
692C22×C3—24no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—21no—
696C22×C3—38no—
697C22×C3—42no—
698C22×C3—44no—
699C22×C3—42no—
700C22×C3—68no—
701C22×C3—62no—
702C22×C3—64no—
703C22×C3—128no—
704C22×C3—248no—
705C22×C3C2×D3×D412yes—
706C22×C3C22×#6712yes—
707C22×C3C24×D311yescharacteristic
708C22×C3C24×D311yescharacteristic
709C2×D3—28no—
710C2×D3—24no—
711C2×D3—22no—
712C2×D3—48no—
713C2×D3—64no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—88no—
721C2×D3—122no—
722C2×D3—122no—
723C2×D3—124no—
724C2×D3—124no—
725C2×D3—128no—
726C2×D3C22×#6718yes—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—42no—
732C3×C4—62no—
733C3×C4—64no—
734C3×C4—64no—
735C3×C4C2×D3×D412yes—
736C3×C4C2×D3×D412yes—
737C3×C4C22×#6712yes—
738C3×C4C22×#6712yes—
739Dic3—24no—
740Dic3—24no—
741Dic3—22no—
742Dic3—62no—
743Dic3—64no—
744Dic3—64no—
745Dic3—62no—
746Dic3—122no—
747Dic3—124no—
748C32#348511yescharacteristic, complemented, Sylow
749C23—34no—
750C23—38no—
751C23—32no—
752C23—68no—
753C23—92no—
754C23—124no—
755C23—128no—
756C23—182no—
757C23—362no—
758C23C22×D3212yes—
759C23C22×D3211yescharacteristic
760Q8—22no—
761Q8—64no—
762Q8—64no—
763Q8—62no—
764D4—24no—
765D4—22no—
766D4—38no—
767D4—38no—
768D4—68no—
769D4—68no—
770D4—64no—
771D4—62no—
772D4—1816no—
773D4—364no—
774D4—364no—
775C2×C4—24no—
776C2×C4—34no—
777C2×C4—34no—
778C2×C4—32no—
779C2×C4—68no—
780C2×C4—64no—
781C2×C4—64no—
782C2×C4—94no—
783C2×C4—92no—
784C2×C4—1816no—
785C2×C4—182no—
786C2×C4—184no—
787C2×C4—184no—
788C2×C4—368no—
789C2×C4D3×#6714yes—
790C2×C4C22×D3212yes—
791C2×C4C22×D3211yescharacteristic
792C2×C4C22×D3211yescharacteristic
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—22no—
796C2×C3—21no—
797C2×C3—42no—
798C2×C3—42no—
799C2×C3—42no—
800C2×C3—68no—
801C2×C3—82no—
802C2×C3—122no—
803C2×C3C22×D3×D411yescharacteristic
804C2×C3#596612yes—
805C2×C3#596812yes—
806C2×C3C23×#6711yescharacteristic
807D3—28no—
808D3—42no—
809D3—124no—
810D3—122no—
811D3—122no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—38no—
816C22—68no—
817C22—64no—
818C22—62no—
819C22—128no—
820C22—182no—
821C22—182no—
822C22—182no—
823C22—248no—
824C22—364no—
825C22C2×D3×#6712yes—
826C22C23×D3211yescharacteristic
827C4—22no—
828C4—64no—
829C4—62no—
830C4—64no—
831C4—184no—
832C4—182no—
833C4C2×D3×#6712yes—
834C4C2×D3×#6712yes—
835C3—21no—
836C3#8635411yescharacteristic, complemented
837C3#8728011yescharacteristic, complemented
838C2—22no—
839C2—42no—
840C2—68no—
841C2—122no—
842C2—362no—
843C2#1059669812yes—
844C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C22×#3796C2semidirect
3. #10596299C2semidirect
4. C3×#5825C2semidirect
5. #10595358C2semidirect
6. #10595234C2semidirect
7. #10595229C2semidirect
8. D3×#935C2semidirect
9. #10595034C2semidirect
10. #10594982C2semidirect
11. #10594890C2semidirect
12. #10594889C2semidirect
13. #10594855C2semidirect
17. C22×C4×C3⋊D3C22semidirect
19. C2×C3×#239C22semidirect
21. C2×C3×D3×D4C22semidirect
23. C2×C3×#235C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×Dic6C22semidirect
27. C22×#626C22semidirect
28. C22×D3×Dic3C22semidirect
30. C2×#3796C22semidirect
31. C2×#3796C22semidirect
32. #64155C22semidirect
33. #64147C22semidirect
34. #64146C22semidirect
35. #64144C22semidirect
36. C4×#638C22semidirect
37. #64135C22semidirect
38. C3×#944C22semidirect
39. C3×#936C22semidirect
40. C3×#935C22semidirect
41. C3×#926C22semidirect
42. C3×#924C22semidirect
43. #63981C22semidirect
44. #63977C22semidirect
45. #63971C22semidirect
46. #63969C22semidirect
47. D3×#217C22semidirect
48. D3×#217C22semidirect
49. #63962C22semidirect
50. #63961C22semidirect
51. #63916C22semidirect
52. C4×#626C22semidirect
53. #63898C22semidirect
54. Dic3×D12C22semidirect
55. #63886C22semidirect
56. #63884C22semidirect
57. D3×Dic3⋊C4C22semidirect
58. #63873C22semidirect
59. #63871C22semidirect
60. #63863C22semidirect
61. #63856C22semidirect
62. #63850C22semidirect
64. C2×#1009D3semidirect
73. #5825D3semidirect
113. C2×C3×D12D4semidirect
168. C2×#239C2×D3semidirect
173. C2×D3×D4C2×D3semidirect
175. C2×#235C2×D3semidirect
178. C22×D12C2×D3semidirect
183. C22×Dic6C2×D3semidirect
200. #944C2×D3semidirect
212. #936C2×D3semidirect
220. #935C2×D3semidirect
232. #926C2×D3semidirect
234. #924C2×D3semidirect
382. C2×D12#67semidirect
748. C32#3485semidirect
836. C3#86354semidirect
837. C3#87280semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C22×#37962
#105962992
C3×#58252
#105953582
#105952342
#105952292
D3×#9352
#105950342
#105949822
#105948902
#105948892
#105948552
#872803
#863543