Finite Group Databasebeta

← #11905963

Subgroups — #11905963

Order 1152.

3945 conjugacy classes of subgroups.

The subgroup lattice has 1097 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic, complemented
2C2×#64313C211yesmaximal, characteristic, complemented
3C3×D4×#67C212yesmaximal, complemented
4#10595526C214yesmaximal, complemented
5C2×#63979C212yesmaximal, complemented
6#10595502C212yesmaximal, complemented
7#10595300C211yesmaximal, characteristic, complemented
8#10595292C214yesmaximal, complemented
9#10595241C211yesmaximal, characteristic, complemented
10#10595239C212yesmaximal, complemented
11D4×#626C212yesmaximal, complemented
12#10595190C211yesmaximal, characteristic, complemented
13#10595165C212yesmaximal, complemented
14#10595164C212yesmaximal, complemented
15#10595082C211yesmaximal, characteristic, complemented
16#10595017C211yesmaximal, characteristic, complemented
17#10594919C212yesmaximal, complemented
18#86608—32nomaximal
19C22×C32×D4C2211yescharacteristic, complemented
20C22×#638C2212yescomplemented
21C22×#638C2212yescomplemented
22#64361—28no—
23C2×#3830C2211yescharacteristic
24C2×#3830C2211yescharacteristic, complemented
25C2×#3830C2212yescomplemented
26C2×D4×C3⋊D3C2211yescharacteristic, complemented
27C2×D4×C3⋊D3C2211yescharacteristic, complemented
28C2×D4×C3⋊D3C2212yescomplemented
29C2×#3828C2211yescharacteristic, complemented
30C2×#3828C2211yescharacteristic, complemented
31C22×C3×#67C2214yescomplemented
32C2×C3×D3×D4C2212yescomplemented
33C2×#3811C2214yescomplemented
34C2×D3×#67C2214yescomplemented
35C22×#626C2214yescomplemented
36C22×#625C2212yescomplemented
37C2×#3805C2212yescomplemented
38#64313—28no—
39C2×#3802C2211yescharacteristic, complemented
40C2×#3798C2211yescharacteristic, complemented
41C2×#3795C2212yescomplemented
42C3×#953C2214yescomplemented
43C3×#940C2212yescomplemented
44C3×#939C2214yescomplemented
45C3×#938C2212yescomplemented
46C3×#937C2214yescomplemented
47C3×D4×Dic3C2212yescomplemented
48C3×#930C2212yescomplemented
49C3×C4×#67C2212yescomplemented
50#63983C2212yescomplemented
51#63981C2214yescomplemented
52#63981C2214yescomplemented
53#63980C2214yescomplemented
54#63979C2212yescomplemented
55#63979C2214yescomplemented
56#63979C2212yescomplemented
57#63979C2214yescomplemented
58#63979C2212yescomplemented
59#63979C2212yescomplemented
60#63979C2211yescharacteristic, complemented
61#63978C2214yescomplemented
62#63977C2214yescomplemented
63#67⋊Dic3C2214yescomplemented
64#63971C2214yescomplemented
65#63971C2214yescomplemented
66#63958C2212yescomplemented
67#63957C2212yescomplemented
68C2×Dic32C2212yescomplemented
69#63953C2212yescomplemented
70#63953C2211yescharacteristic, complemented
71#63952C2214yescomplemented
72#63923C2212yescomplemented
73#63916C2212yescomplemented
74#63913C2212yescomplemented
75#63913C2211yescharacteristic, complemented
76#63912C2214yescomplemented
77#63911C2212yescomplemented
78#63910C2212yescomplemented
79#63909C2212yescomplemented
80C4×#626C2212yescomplemented
81C4×#624C2211yescharacteristic, complemented
82#63881C2214yescomplemented
83#63849C2211yescharacteristic, complemented
84#63844C2212yescomplemented
85#63840C2211yescharacteristic, complemented
86C2×#1004—32no—
87C2×#1004—32no—
88C2×#1004—61no—
89C3×D42—32no—
90C2×#940—34no—
91D4×#67—34no—
92D4×#67—32no—
93D4×#67D312yescomplemented
94#5718—32no—
95D3×#127—32no—
96#5609—34no—
97#5607—32no—
98#5607—32no—
99#5599—32no—
100#5599—32no—
101#5596—34no—
102#5592—34no—
103#5592—34no—
104#5590—34no—
105#5590—34no—
106#5553—32no—
107D4×D12—32no—
108#5548—32no—
109C4×#237—32no—
110C24×C32C2312yes—
111C23×C3⋊D3C2312yes—
112C23×C3⋊D3C2312yes—
113C23×C3×D3C2314yes—
114C22×D32C2312yes—
115C2×C32×D4—24no—
116C2×C32×D4C2312yes—
117C2×C32×D4C2311yescharacteristic
118C2×C32×D4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C2×#638—28no—
121C2×#638—28no—
122C2×#638C2311yescharacteristic
123C2×#638C2311yescharacteristic
124C2×#638C2312yes—
125C2×#638C2312yes—
126C2×#638C2312yes—
127C2×#638C2312yes—
128C2×#638C2312yes—
129C22×C3⋊Dic3C2312yes—
130C22×C3⋊Dic3C2312yes—
131#3830—28no—
132#3830—24no—
133#3830D418yescomplemented
134D4×C3⋊D3—24no—
135D4×C3⋊D3—28no—
136D4×C3⋊D3—24no—
137#3828—24no—
138#3828—24no—
139C2×C4⋊(C3⋊D3)C2311yescharacteristic
140C2×C4⋊(C3⋊D3)C2311yescharacteristic
141C2×C4×C3⋊D3C2312yes—
142C2×C4×C3⋊D3C2311yescharacteristic
143C2×C4×C3⋊D3C2311yescharacteristic
144C2×#634C2311yescharacteristic
145C2×#634C2311yescharacteristic
146C2×C3×#67—48no—
147C2×C3×#67C2312yes—
148C2×C3×#67C2314yes—
149C2×C3×#67C2314yes—
150C2×C3×#67C2314yes—
151C2×C3×#67C2314yes—
152C2×C3×#67C2314yes—
153C22×C3×Dic3C2314yes—
154C3×D3×D4—28no—
155C2×C3×D12C2312yes—
156C2×C3×C4×D3C2312yes—
157#3811—48no—
158D3×#67—216no—
159C2×#627C2311yescharacteristic
160C2×#626—48no—
161C2×#626C2312yes—
162C2×#626C2312yes—
163C2×#626C2314yes—
164C2×#626C2314yes—
165C2×#626C2314yes—
166C2×#626C2314yes—
167C2×#625—28no—
168C2×#625C2314yes—
169C2×#625C2311yescharacteristic
170C2×#625C2312yes—
171C2×#624C2312yes—
172#3805—28no—
173C2×D3×Dic3C2314yes—
174#3802—24no—
175#3798—24no—
176#3795—28no—
177C3×#217C2312yes—
178C3×#217C2314yes—
179C3×#217C2314yes—
180C3×(C2×D3)⋊C4C2312yes—
181C3×(C2×D3)⋊C4C2314yes—
182C3×C4⋊Dic3C2312yes—
183C3×Dic3⋊C4C2312yes—
184C3×C4×Dic3C2312yes—
185#3724C2314yes—
186Dic3⋊Dic3C2312yes—
187#3722C2312yes—
188#3722C2314yes—
189#3722C2312yes—
190(C2×D3)⋊Dic3C2312yes—
191(C2×D3)⋊Dic3C2314yes—
192Dic32C2311yescharacteristic
193Dic32C2314yes—
194Dic32C2312yes—
195Dic32C2311yescharacteristic
196#3498—91noSylow
197C22×C3×D4—21no—
198C22×C3×D4—34no—
199C22×C3×D4—32no—
200C22×C3×D4C2×D312yescomplemented
201C22×#67—34no—
202C22×#67—34no—
203C22×#67—34no—
204C22×#67—34no—
205C22×#67—34no—
206C22×#67—62no—
207C22×#67—62no—
208C22×#67C2×D314yescomplemented
209#1004—616no—
210#1004—616no—
211#1004—616no—
212C2×#237—32no—
213C2×#237—32no—
214C2×#237—34no—
215C2×#237—34no—
216C2×#237—32no—
217C2×#237—61no—
218C2×#237—62no—
219C2×#237—61no—
220C2×D3×D4—34no—
221C2×D3×D4—32no—
222C2×D3×D4—32no—
223C2×D3×D4—34no—
224C2×D3×D4—34no—
225C2×D3×D4—34no—
226C2×D3×D4—32no—
227C2×D3×D4—61no—
228C2×D3×D4—61no—
229C2×D3×D4—62no—
230C2×D3×D4C2×D312yescomplemented
231C2×#235—32no—
232C2×#235—32no—
233C2×#235—32no—
234C2×#235—32no—
235C2×#235—61no—
236C2×#235—61no—
237C22×D12—34no—
238C3×#127—32no—
239C3×#121—32no—
240C3×#121—34no—
241C3×#121—32no—
242C3×#120—34no—
243C3×#120—34no—
244C3×C4×D4—32no—
245C3×C4×D4—32no—
246#953—34no—
247#953C2×D314yescomplemented
248#940—34no—
249#940—34no—
250#940—34no—
251#940—34no—
252#940—32no—
253#940—34no—
254#940—34no—
255#940—34no—
256#940—34no—
257#940—32no—
258#940C2×D312yescomplemented
259#939—34no—
260#939—34no—
261#939—34no—
262#939—34no—
263#939—34no—
264#939C2×D314yescomplemented
265#938—32no—
266#938—32no—
267#938C2×D312yescomplemented
268#937—34no—
269#937—34no—
270#937—34no—
271#937C2×D314yescomplemented
272D4×Dic3—34no—
273D4×Dic3C2×D312yescomplemented
274#930—34no—
275#930—32no—
276#930C2×D312yescomplemented
277C4×#67—34no—
278C4×#67—32no—
279C4×#67C2×D312yescomplemented
280C2×C4×Dic3—34no—
281#895—32no—
282#895—32no—
283#895—32no—
284#893—34no—
285#892—32no—
286#888—32no—
287#887—32no—
288#885—32no—
289#885—34no—
290#885—32no—
291#885—34no—
292#884—32no—
293#884—34no—
294#884—34no—
295#884—34no—
296#884—34no—
297#884—32no—
298#882—34no—
299#882—34no—
300#882—34no—
301#882—34no—
302#67⋊C4—34no—
303#67⋊C4—34no—
304#67⋊C4—34no—
305#877—34no—
306#874—32no—
307C4×D12—32no—
308C42×D3—32no—
309C4×Dic6—32no—
310C23×C32—24no—
311C23×C32—44no—
312C23×C32C2412yes—
313C23×C32C2411yescharacteristic
314C23×C32C2412yes—
315C22×C3⋊D3—24no—
316C22×C3⋊D3—24no—
317C22×C3⋊D3—44no—
318C22×C3⋊D3—44no—
319C22×C3⋊D3C2411yescharacteristic
320C22×C3⋊D3C2412yes—
321C22×C3⋊D3C2411yescharacteristic
322C22×C3×D3—28no—
323C22×C3×D3—44no—
324C22×C3×D3—44no—
325C22×C3×D3C2414yes—
326C22×C3×D3C2412yes—
327C2×D32—24no—
328C2×D32—44no—
329C32×D4—24no—
330C32×D4—22no—
331C32×D4C2×D414yescomplemented
332C2×C32×C4—22no—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335#638—24no—
336#638—22no—
337#638—24no—
338#638—22no—
339#638—24no—
340#638—24no—
341#638C2×D418yescomplemented
342C2×C3⋊Dic3—24no—
343C2×C3⋊Dic3C2×D418yescomplemented
344C2×C3⋊Dic3C2411yescharacteristic
345C2×C3⋊Dic3C2411yescharacteristic
346C2×C3⋊Dic3C2412yes—
347C4⋊(C3⋊D3)—22no—
348C4⋊(C3⋊D3)—22no—
349C4×C3⋊D3—22no—
350C4×C3⋊D3—24no—
351C4×C3⋊D3C2×D414yescomplemented
352#634—22no—
353#634C2×D414yescomplemented
354C3×#67—28no—
355C3×#67—28no—
356C3×#67—24no—
357C3×#67—44no—
358C3×#67—44no—
359C3×#67—44no—
360C2×C3×Dic3—28no—
361C2×C3×Dic3C2414yes—
362C2×C3×Dic3C2412yes—
363C2×C3×Dic3C2412yes—
364C2×C3×Dic3C2412yes—
365C3×D12—24no—
366C3×C4×D3—24no—
367#627—22no—
368#626—24no—
369#626—24no—
370#626—28no—
371#626—44no—
372#626—44no—
373#626—44no—
374#625—28no—
375#625—22no—
376#625—24no—
377#624—24no—
378D3×Dic3—28no—
379C2×H(5,𝔽2)—91no—
380C2×H(5,𝔽2)—91no—
381#550—92no—
382#550—92no—
383D42—32no—
384D42—92no—
385D42—94no—
386D42—94no—
387#535—92no—
388#535—92no—
389#535—91no—
390#535—91no—
391#532—91no—
392#532—92no—
393C2×#127—91no—
394C2×#127—92no—
395C4×#41—91no—
396C24×C3—22no—
397C24×C3—34no—
398C24×C3C22×D314yes—
399C23×D3—34no—
400C23×D3—34no—
401C23×D3—34no—
402C23×D3—62no—
403C23×D3—62no—
404C23×D3C22×D314yes—
405C2×C3×D4—28no—
406C2×C3×D4—28no—
407C2×C3×D4—22no—
408C2×C3×D4—21no—
409C2×C3×D4—21no—
410C2×C3×D4—34no—
411C2×C3×D4—34no—
412C2×C3×D4—32no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—34no—
416C2×C3×D4—32no—
417C2×C3×D4—68no—
418C2×C3×D4—128no—
419C2×C3×D4C22×D314yes—
420C2×C3×D4C22×D312yes—
421C2×C3×D4C22×D312yes—
422C22×C3×C4—21no—
423C22×C3×C4—34no—
424C22×C3×C4—32no—
425C22×C3×C4C22×D312yes—
426C2×#67—34no—
427C2×#67—34no—
428C2×#67—32no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—32no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—32no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—32no—
439C2×#67—32no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—34no—
443C2×#67—48no—
444C2×#67—61no—
445C2×#67—62no—
446C2×#67—61no—
447C2×#67—62no—
448C2×#67—62no—
449C2×#67—62no—
450C2×#67—62no—
451C2×#67—616no—
452C2×#67—616no—
453C2×#67—616no—
454C2×#67—616no—
455C2×#67—616no—
456C2×#67—616no—
457C2×#67—128no—
458C2×#67C22×D314yes—
459C2×#67C22×D314yes—
460C2×#67C22×D312yes—
461C2×#67C22×D314yes—
462C2×#67C22×D314yes—
463C2×#67C22×D314yes—
464C22×Dic3—34no—
465C22×Dic3—34no—
466C22×Dic3—34no—
467C22×Dic3—62no—
468C22×Dic3—62no—
469C22×Dic3C22×D314yes—
470#237—316no—
471#237—68no—
472#237—68no—
473#237—68no—
474#237—616no—
475#237—616no—
476#237—616no—
477#237—68no—
478D3×D4—28no—
479D3×D4—68no—
480D3×D4—68no—
481D3×D4—616no—
482D3×D4—616no—
483D3×D4—68no—
484D3×D4—616no—
485D3×D4—68no—
486D3×D4—68no—
487D3×D4—128no—
488D3×D4—128no—
489#235—68no—
490#235—68no—
491#235—68no—
492#235—68no—
493#235—68no—
494#235—68no—
495C2×D12—32no—
496C2×D12—34no—
497C2×D12—32no—
498C2×D12—32no—
499C2×D12—32no—
500C2×D12—34no—
501C2×D12—34no—
502C2×D12—34no—
503C2×D12—61no—
504C2×D12—61no—
505C2×D12—128no—
506C2×D12C22×D312yes—
507C2×C4×D3—32no—
508C2×C4×D3—34no—
509C2×C4×D3—32no—
510C2×C4×D3—34no—
511C2×C4×D3—32no—
512C2×C4×D3—32no—
513C2×C4×D3—61no—
514C2×C4×D3—62no—
515C2×C4×D3—61no—
516C2×C4×D3C22×D312yes—
517C2×Dic6—32no—
518C2×Dic6—32no—
519C2×Dic6—32no—
520C2×Dic6—61no—
521C2×Dic6—61no—
522C3×C4⋊C4—32no—
523C3×C4⋊C4—32no—
524C3×C22⋊C4—34no—
525C3×C22⋊C4—34no—
526C3×C22⋊C4—32no—
527C3×C22⋊C4—34no—
528C3×C22⋊C4—32no—
529C3×C42—32no—
530#217—32no—
531#217—34no—
532#217C22×D314yes—
533#217C22×D312yes—
534#217C22×D314yes—
535(C2×D3)⋊C4—32no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—32no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—34no—
540(C2×D3)⋊C4—34no—
541(C2×D3)⋊C4—32no—
542(C2×D3)⋊C4C22×D314yes—
543(C2×D3)⋊C4C22×D312yes—
544C4⋊Dic3—32no—
545C4⋊Dic3C22×D312yes—
546Dic3⋊C4—34no—
547Dic3⋊C4—34no—
548Dic3⋊C4—32no—
549Dic3⋊C4C22×D312yes—
550C4×Dic3—34no—
551C4×Dic3—32no—
552C4×Dic3—32no—
553C4×Dic3—34no—
554C4×Dic3—34no—
555C4×Dic3C22×D312yes—
556C22×C32—22no—
557C22×C32—21no—
558C22×C32—24no—
559C22×C32—24no—
560C22×C32—22no—
561C22×C32—84no—
562C22×C32C22×D414yes—
563C22×C32C2511yescharacteristic
564C2×C3⋊D3—21no—
565C2×C3⋊D3—22no—
566C2×C3⋊D3—22no—
567C2×C3⋊D3—24no—
568C2×C3⋊D3—22no—
569C2×C3⋊D3—84no—
570C2×C3⋊D3—84no—
571C2×C3⋊D3C22×D412yes—
572C2×C3×D3—24no—
573C2×C3×D3—22no—
574C2×C3×D3—22no—
575C2×C3×D3—24no—
576C2×C3×D3—24no—
577C2×C3×D3—22no—
578C2×C3×D3—88no—
579D32—84no—
580C32×C4—21no—
581C32×C4C22×D412yes—
582C3⋊Dic3—21no—
583C3⋊Dic3C22×D414yes—
584C3⋊Dic3C22×D412yes—
585C3×Dic3—22no—
586C3×Dic3—22no—
587C3×Dic3—24no—
588C3×Dic3H(5,𝔽2)14yescomplemented
589H(5,𝔽2)—188no—
590H(5,𝔽2)—188no—
591C2×#41—91no—
592C2×#41—92no—
593C2×#41—92no—
594C2×#41—91no—
595C2×#41—92no—
596C2×#41—91no—
597C2×#41—91no—
598C2×#41—91no—
599C22×D4—34no—
600C22×D4—32no—
601C22×D4—94no—
602C22×D4—91no—
603C22×D4—94no—
604C22×D4—94no—
605C22×D4—92no—
606C22×D4—92no—
607C22×D4—92no—
608C22×D4—91no—
609C22×D4—92no—
610C22×D4—91no—
611C22×D4D3211yescharacteristic, complemented
612C4⋊Q8—91no—
613#127—32no—
614#127—92no—
615#127—91no—
616#127—92no—
617#127—92no—
618#127—92no—
619#127—92no—
620#127—94no—
621#127—94no—
622#124—91no—
623#124—92no—
624#124—91no—
625#124—92no—
626#121—34no—
627#121—32no—
628#121—32no—
629#121—94no—
630#121—92no—
631#121—92no—
632#121—94no—
633#121—94no—
634#121—92no—
635#121—92no—
636#121—94no—
637#121—94no—
638#120—34no—
639#120—34no—
640#120—92no—
641#120—94no—
642#120—94no—
643#120—94no—
644#120—92no—
645C4×Q8—92no—
646C4×D4—32no—
647C4×D4—32no—
648C4×D4—92no—
649C4×D4—94no—
650C4×D4—94no—
651C4×D4—94no—
652#117—92no—
653#117—91no—
654C2×C42—91no—
655C2×C42—92no—
656C23×C3—28no—
657C23×C3—28no—
658C23×C3—22no—
659C23×C3—22no—
660C23×C3—21no—
661C23×C3—34no—
662C23×C3—32no—
663C23×C3—44no—
664C23×C3—44no—
665C23×C3—68no—
666C23×C3—84no—
667C23×C3—124no—
668C23×C3—124no—
669C23×C3C23×D314yes—
670C23×C3C23×D312yes—
671C23×C3C23×D314yes—
672C22×D3—28no—
673C22×D3—32no—
674C22×D3—34no—
675C22×D3—32no—
676C22×D3—44no—
677C22×D3—44no—
678C22×D3—61no—
679C22×D3—62no—
680C22×D3—61no—
681C22×D3—68no—
682C22×D3—68no—
683C22×D3—68no—
684C22×D3—68no—
685C22×D3—68no—
686C22×D3—124no—
687C22×D3—124no—
688C22×D3—124no—
689C22×D3—124no—
690C22×D3—124no—
691C22×D3—124no—
692C22×D3—244no—
693C22×D3—244no—
694C22×D3C23×D314yes—
695C22×D3C23×D312yes—
696C3×D4—28no—
697C3×D4—24no—
698C3×D4—28no—
699C3×D4—24no—
700C3×D4—24no—
701C3×D4—68no—
702C3×D4—64no—
703C3×D4—68no—
704C3×D4—64no—
705C3×D4—124no—
706C3×D4—124no—
707C3×D4—124no—
708C3×D4D3×D418yescomplemented
709C2×C3×C4—24no—
710C2×C3×C4—24no—
711C2×C3×C4—21no—
712C2×C3×C4—21no—
713C2×C3×C4—32no—
714C2×C3×C4—34no—
715C2×C3×C4—32no—
716C2×C3×C4—32no—
717C2×C3×C4—68no—
718C2×C3×C4—64no—
719C2×C3×C4C23×D312yes—
720C2×C3×C4C23×D312yes—
721#67—28no—
722#67—28no—
723#67—24no—
724#67—316no—
725#67—44no—
726#67—44no—
727#67—44no—
728#67—68no—
729#67—64no—
730#67—68no—
731#67—64no—
732#67—68no—
733#67—68no—
734#67—68no—
735#67—64no—
736#67—68no—
737#67—68no—
738#67—64no—
739#67—64no—
740#67—68no—
741#67—64no—
742#67—68no—
743#67—68no—
744#67—68no—
745#67—68no—
746#67—68no—
747#67—64no—
748#67—124no—
749#67—124no—
750#67—124no—
751C2×Dic3—28no—
752C2×Dic3—316no—
753C2×Dic3—32no—
754C2×Dic3—34no—
755C2×Dic3—32no—
756C2×Dic3—68no—
757C2×Dic3—61no—
758C2×Dic3—62no—
759C2×Dic3—61no—
760C2×Dic3—68no—
761C2×Dic3—68no—
762C2×Dic3—68no—
763C2×Dic3C23×D314yes—
764C2×Dic3C23×D312yes—
765C2×Dic3C23×D312yes—
766C2×Dic3C23×D312yes—
767D12—24no—
768D12—64no—
769D12—64no—
770D12—64no—
771D12—64no—
772D12—68no—
773D12—64no—
774D12—64no—
775D12—124no—
776D12—124no—
777D12—124no—
778C4×D3—24no—
779C4×D3—38no—
780C4×D3—64no—
781C4×D3—64no—
782C4×D3—68no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—64no—
786C4×D3—64no—
787C4×D3—64no—
788Dic6—38no—
789Dic6—64no—
790Dic6—64no—
791Dic6—64no—
792Dic6—64no—
793C2×C32—24no—
794C2×C32—42no—
795C2×C32—41no—
796C2×C32C23×D411yescharacteristic
797C2×C32C2×H(5,𝔽2)12yes—
798C3⋊D3—22no—
799C3⋊D3—42no—
800C3⋊D3—41no—
801C3×D3—44no—
802C3×D3—42no—
803C24—34no—
804C24—92no—
805C24—92no—
806C24—92no—
807C24C2×D3212yes—
808#41—98no—
809#41—184no—
810#41—184no—
811#41—184no—
812#41—188no—
813#41—188no—
814#41—188no—
815#41—184no—
816C2×Q8—91no—
817C2×Q8—91no—
818C2×Q8—91no—
819C2×D4—24no—
820C2×D4—32no—
821C2×D4—34no—
822C2×D4—34no—
823C2×D4—34no—
824C2×D4—34no—
825C2×D4—34no—
826C2×D4—32no—
827C2×D4—68no—
828C2×D4—92no—
829C2×D4—94no—
830C2×D4—92no—
831C2×D4—94no—
832C2×D4—94no—
833C2×D4—94no—
834C2×D4—92no—
835C2×D4—94no—
836C2×D4—91no—
837C2×D4—92no—
838C2×D4—91no—
839C2×D4—92no—
840C2×D4—92no—
841C2×D4—92no—
842C2×D4—92no—
843C2×D4—91no—
844C2×D4—91no—
845C2×D4—91no—
846C2×D4—128no—
847C2×D4—184no—
848C2×D4—184no—
849C2×D4—188no—
850C2×D4—188no—
851C2×D4—188no—
852C2×D4—1816no—
853C2×D4—188no—
854C2×D4—184no—
855C2×D4—368no—
856C2×D4—368no—
857C2×D4C2×D3212yes—
858C2×D4C2×D3211yescharacteristic
859C2×D4C2×D3211yescharacteristic
860C22×C4—34no—
861C22×C4—32no—
862C22×C4—92no—
863C22×C4—94no—
864C22×C4—92no—
865C22×C4—91no—
866C22×C4—92no—
867C22×C4—92no—
868C22×C4—91no—
869C22×C4C2×D3211yescharacteristic
870C4⋊C4—32no—
871C4⋊C4—32no—
872C4⋊C4—94no—
873C4⋊C4—92no—
874C22⋊C4—34no—
875C22⋊C4—32no—
876C22⋊C4—34no—
877C22⋊C4—32no—
878C22⋊C4—34no—
879C22⋊C4—92no—
880C22⋊C4—92no—
881C22⋊C4—94no—
882C22⋊C4—92no—
883C22⋊C4—94no—
884C42—32no—
885C42—91no—
886C42—91no—
887C42—92no—
888C42—94no—
889C22×C3—24no—
890C22×C3—24no—
891C22×C3—24no—
892C22×C3—22no—
893C22×C3—24no—
894C22×C3—22no—
895C22×C3—22no—
896C22×C3—24no—
897C22×C3—24no—
898C22×C3—22no—
899C22×C3—24no—
900C22×C3—21no—
901C22×C3—44no—
902C22×C3—44no—
903C22×C3—42no—
904C22×C3—64no—
905C22×C3—62no—
906C22×C3—62no—
907C22×C3—64no—
908C22×C3—64no—
909C22×C3—62no—
910C22×C3—88no—
911C22×C3—88no—
912C22×C3—248no—
913C22×C3C2×D3×D418yes—
914C22×C3C24×D312yes—
915C2×D3—22no—
916C2×D3—24no—
917C2×D3—24no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—24no—
921C2×D3—34no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—64no—
926C2×D3—62no—
927C2×D3—64no—
928C2×D3—62no—
929C2×D3—64no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—64no—
933C2×D3—88no—
934C2×D3—122no—
935C2×D3—124no—
936C2×D3—122no—
937C2×D3—248no—
938C2×D3—248no—
939C2×D3—248no—
940C2×D3—248no—
941C2×D3—248no—
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—22no—
945C3×C4—34no—
946C3×C4—62no—
947C3×C4—62no—
948C3×C4—64no—
949C3×C4C2×D3×D414yes—
950Dic3—22no—
951Dic3—24no—
952Dic3—22no—
953Dic3—38no—
954Dic3—34no—
955Dic3—62no—
956Dic3—64no—
957Dic3—62no—
958Dic3—62no—
959Dic3#100414yescomplemented
960C32#349811yescharacteristic, complemented, Sylow
961C23—24no—
962C23—32no—
963C23—34no—
964C23—44no—
965C23—68no—
966C23—91no—
967C23—92no—
968C23—91no—
969C23—124no—
970C23—124no—
971C23—184no—
972C23—184no—
973C23—184no—
974C23—364no—
975C23—364no—
976C23—364no—
977C23C22×D3212yes—
978C23C22×D3211yescharacteristic
979C23C22×D3212yes—
980Q8—94no—
981Q8—182no—
982Q8—182no—
983D4—24no—
984D4—22no—
985D4—64no—
986D4—68no—
987D4—68no—
988D4—64no—
989D4—98no—
990D4—124no—
991D4—124no—
992D4—124no—
993D4—182no—
994D4—188no—
995D4—184no—
996D4—184no—
997D4—182no—
998D4—184no—
999D4—184no—
1000D4—184no—
1001D4—182no—
1002D4—184no—
1003D4—188no—
1004D4—182no—
1005D4—184no—
1006D4—182no—
1007D4—364no—
1008D4—364no—
1009D4—364no—
1010D4#381114yescomplemented
1011C2×C4—22no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—34no—
1015C2×C4—32no—
1016C2×C4—68no—
1017C2×C4—64no—
1018C2×C4—98no—
1019C2×C4—91no—
1020C2×C4—92no—
1021C2×C4—94no—
1022C2×C4—91no—
1023C2×C4—184no—
1024C2×C4—184no—
1025C2×C4—188no—
1026C2×C4—184no—
1027C2×C4—182no—
1028C2×C4C22×D3211yescharacteristic
1029C2×C4C22×D3211yescharacteristic
1030C2×C3—28no—
1031C2×C3—22no—
1032C2×C3—21no—
1033C2×C3—44no—
1034C2×C3—44no—
1035C2×C3—42no—
1036C2×C3—44no—
1037C2×C3—42no—
1038C2×C3—124no—
1039C2×C3—122no—
1040C2×C3C22×D3×D412yes—
1041C2×C3C2×#100412yes—
1042C2×C3D3×H(5,𝔽2)12yes—
1043D3—42no—
1044D3—44no—
1045D3—64no—
1046D3—122no—
1047D3—122no—
1048D3—124no—
1049D3—124no—
1050D3—122no—
1051C22—24no—
1052C22—22no—
1053C22—24no—
1054C22—21no—
1055C22—22no—
1056C22—62no—
1057C22—64no—
1058C22—64no—
1059C22—62no—
1060C22—62no—
1061C22—64no—
1062C22—84no—
1063C22—92no—
1064C22—182no—
1065C22—184no—
1066C22—182no—
1067C22—182no—
1068C22—181no—
1069C22—248no—
1070C22—724no—
1071C22—724no—
1072C22—724no—
1073C22C2×#381114yes—
1074C22C23×D3211yescharacteristic
1075C4—21no—
1076C4—34no—
1077C4—64no—
1078C4—62no—
1079C4—62no—
1080C4—92no—
1081C4—94no—
1082C4—181no—
1083C4C2×#381112yes—
1084C3—21no—
1085C3#8660812yescomplemented
1086C2—24no—
1087C2—41no—
1088C2—42no—
1089C2—122no—
1090C2—124no—
1091C2—182no—
1092C2—361no—
1093C2—362no—
1094C2D3×#100412yes—
1095C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3498
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C2×#64313C2semidirect
3. C3×D4×#67C2semidirect
4. #10595526C2semidirect
5. C2×#63979C2semidirect
6. #10595502C2semidirect
7. #10595300C2semidirect
8. #10595292C2semidirect
9. #10595241C2semidirect
10. #10595239C2semidirect
11. D4×#626C2semidirect
12. #10595190C2semidirect
13. #10595165C2semidirect
14. #10595164C2semidirect
15. #10595082C2semidirect
16. #10595017C2semidirect
17. #10594919C2semidirect
19. C22×C32×D4C22semidirect
20. C22×#638C22semidirect
21. C22×#638C22semidirect
24. C2×#3830C22semidirect
25. C2×#3830C22semidirect
26. C2×D4×C3⋊D3C22semidirect
27. C2×D4×C3⋊D3C22semidirect
28. C2×D4×C3⋊D3C22semidirect
29. C2×#3828C22semidirect
30. C2×#3828C22semidirect
31. C22×C3×#67C22semidirect
32. C2×C3×D3×D4C22semidirect
33. C2×#3811C22semidirect
34. C2×D3×#67C22semidirect
35. C22×#626C22semidirect
36. C22×#625C22semidirect
37. C2×#3805C22semidirect
39. C2×#3802C22semidirect
40. C2×#3798C22semidirect
41. C2×#3795C22semidirect
42. C3×#953C22semidirect
43. C3×#940C22semidirect
44. C3×#939C22semidirect
45. C3×#938C22semidirect
46. C3×#937C22semidirect
47. C3×D4×Dic3C22semidirect
48. C3×#930C22semidirect
49. C3×C4×#67C22semidirect
50. #63983C22semidirect
51. #63981C22semidirect
52. #63981C22semidirect
53. #63980C22semidirect
54. #63979C22semidirect
55. #63979C22semidirect
56. #63979C22semidirect
57. #63979C22semidirect
58. #63979C22semidirect
59. #63979C22semidirect
60. #63979C22semidirect
61. #63978C22semidirect
62. #63977C22semidirect
63. #67⋊Dic3C22semidirect
64. #63971C22semidirect
65. #63971C22semidirect
66. #63958C22semidirect
67. #63957C22semidirect
68. C2×Dic32C22semidirect
69. #63953C22semidirect
70. #63953C22semidirect
71. #63952C22semidirect
72. #63923C22semidirect
73. #63916C22semidirect
74. #63913C22semidirect
75. #63913C22semidirect
76. #63912C22semidirect
77. #63911C22semidirect
78. #63910C22semidirect
79. #63909C22semidirect
80. C4×#626C22semidirect
81. C4×#624C22semidirect
82. #63881C22semidirect
83. #63849C22semidirect
84. #63844C22semidirect
85. #63840C22semidirect
93. D4×#67D3semidirect
133. #3830D4semidirect
200. C22×C3×D4C2×D3semidirect
208. C22×#67C2×D3semidirect
230. C2×D3×D4C2×D3semidirect
247. #953C2×D3semidirect
258. #940C2×D3semidirect
264. #939C2×D3semidirect
267. #938C2×D3semidirect
271. #937C2×D3semidirect
273. D4×Dic3C2×D3semidirect
276. #930C2×D3semidirect
279. C4×#67C2×D3semidirect
331. C32×D4C2×D4semidirect
341. #638C2×D4semidirect
343. C2×C3⋊Dic3C2×D4semidirect
351. C4×C3⋊D3C2×D4semidirect
353. #634C2×D4semidirect
588. C3×Dic3H(5,𝔽2)semidirect
611. C22×D4D32semidirect
708. C3×D4D3×D4semidirect
959. Dic3#1004semidirect
960. C32#3498semidirect
1010. D4#3811semidirect
1085. C3#86608semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C2×#643132
C3×D4×#672
#105955262
C2×#639792
#105955022
#105953002
#105952922
#105952412
#105952392
D4×#6262
#105951902
#105951652
#105951642
#105950822
#105950172
#105949192
#866083