Finite Group Databasebeta

← #11904424

Subgroups — #11904424

Order 1152.

3293 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3#10595964C211yesmaximal, characteristic, complemented
4C2×C3×#886C211yesmaximal, characteristic, complemented
5C3×#5486C211yesmaximal, characteristic, complemented
6#10595519C211yesmaximal, characteristic, complemented
7C2×#63966C211yesmaximal, characteristic, complemented
8#10595073C214yesmaximal, complemented
9#10594906C214yesmaximal, complemented
10#10594293C214yesmaximal, complemented
11#10594291C212yesmaximal, complemented
12D3×#886C212yesmaximal, complemented
13#10594081C212yesmaximal, complemented
14#10594079C212yesmaximal, complemented
15#10594077C214yesmaximal, complemented
16#86012—31nomaximal
17#85858—31nomaximal
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic, complemented
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23#64330—28no—
24C2×#3811C2212yescomplemented
25C2×D3×#67C2212yes—
26C2×D3×#67C2212yescomplemented
27C22×#627C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic, complemented
29C22×#624C2211yescharacteristic, complemented
30C2×#3805C2212yescomplemented
31C2×#3804—28no—
32C2×#3804C2212yes—
33C2×#3804C2214yescomplemented
34C2×#3804C2214yescomplemented
35C2×#3804C2212yescomplemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C2×C32×C22⋊C4C2211yescharacteristic, complemented
38#64139C2214yescomplemented
39#64095C2212yescomplemented
40#64095C2212yescomplemented
41#64091C2212yescomplemented
42#64091C2212yescomplemented
43C2×C3×#217C2211yescharacteristic, complemented
44C3×C4×#67C2214yescomplemented
45C2×C3×(C2×D3)⋊C4C2212yescomplemented
46C2×C3×C4⋊Dic3C2212yescomplemented
47C3×#886C2214yescomplemented
48C3×#886C2212yescomplemented
49C3×#886C2212yescomplemented
50C3×#67⋊C4C2214yescomplemented
51C3×D3×C22⋊C4C2212yescomplemented
52C3×#877C2212yescomplemented
53#63981C2212yescomplemented
54#63978C2214yescomplemented
55#63977C2212yescomplemented
56#63966C2214yescomplemented
57#63966C2212yescomplemented
58#63966C2212yescomplemented
59#63966C2212yescomplemented
60C2×Dic3⋊Dic3C2212yescomplemented
61C2×#3722C2212yescomplemented
62#63962C2212yescomplemented
63#63923C2214yescomplemented
64D3×(C2×D3)⋊C4C2214yescomplemented
65#63918C2214yescomplemented
66#63910C2214yescomplemented
67#63909C2214yescomplemented
68#63906C2214yescomplemented
69#63895C2214yescomplemented
70#63895C2214yescomplemented
71#63894C2214yescomplemented
72#63893C2214yescomplemented
73#63891C2214yescomplemented
74#63890C2214yescomplemented
75#63890C2214yescomplemented
76D3×C4⋊Dic3C2214yescomplemented
77#63880C2214yescomplemented
78#63852C2214yescomplemented
79C2×#1004—31no—
80C2×#1004—31no—
81C22×#237—31no—
82C22×#235—31no—
83C2×C3×#123—31no—
84C3×#518—31no—
85#5804—31no—
86C2×#929—31no—
87#5656—32no—
88#5655—34no—
89#5654—34no—
90#5653—32no—
91D3×#123—32no—
92#5648—32no—
93#5555—34no—
94#5555—34no—
95#5554—34no—
96#5554—34no—
97#5526—32no—
98#5524—32no—
99#5507—34no—
100#5493—31no—
101#5493—31no—
102#5493—31no—
103#5493—32no—
104#5493—61no—
105C2×#886—31no—
106C2×#886—32no—
107C2×#886D311yescharacteristic, complemented
108#5490—34no—
109#5486D311yescharacteristic, complemented
110C24×C32C2311yescharacteristic
111C23×C3⋊D3C2311yescharacteristic
112C23×C3⋊D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2311yescharacteristic
115C22×D32C2312yes—
116C22×C32×C4C2312yes—
117C2×#638—24no—
118C2×#638—24no—
119C2×#638C2312yes—
120C2×#638C2312yes—
121C2×#638C2312yes—
122C2×#638C2312yes—
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C2×C4⋊(C3⋊D3)C2314yes—
126C2×C3×#67—24no—
127C2×C3×#67D418yescomplemented
128C2×C3×#67C2312yes—
129C2×C3×#67C2312yes—
130C2×C3×#67C2312yes—
131C2×C3×#67C2312yes—
132C22×C3×Dic3—24no—
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2312yes—
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2312yes—
138C22×C3×Dic3C2312yes—
139C22×C3×Dic3C2311yescharacteristic
140C2×C3×C4×D3C2314yes—
141#3811—28no—
142D3×#67—28no—
143D3×#67—28no—
144C2×#627—24no—
145C2×#627C2312yes—
146C2×#627C2314yes—
147C2×#626—24no—
148C2×#626C2312yes—
149C2×#626C2314yes—
150C2×#626C2312yes—
151C2×#626C2314yes—
152C2×#625C2312yes—
153C2×#624—24no—
154C2×#624C2312yes—
155C2×#624C2314yes—
156#3805—28no—
157#3804—216no—
158#3804—216no—
159#3804—28no—
160#3804—28no—
161C2×D3×Dic3—24no—
162C2×D3×Dic3C2314yes—
163C2×D3×Dic3C2312yes—
164C2×D3×Dic3C2312yes—
165C32×C22⋊C4C2312yes—
166C32×C22⋊C4C2312yes—
167#3752C2314yes—
168#3752C2314yes—
169C4⋊(C3⋊Dic3)C2314yes—
170C3×#217C2312yes—
171C3×#217C2312yes—
172C3×(C2×D3)⋊C4C2314yes—
173C3×(C2×D3)⋊C4C2314yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×C4⋊Dic3C2314yes—
176C3×C4⋊Dic3C2314yes—
177C3×Dic3⋊C4C2314yes—
178C3×C4×Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182#3722C2314yes—
183#3722C2314yes—
184#3722C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186#3485—91noSylow
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C23×C3×C4—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—32no—
195C22×#67—32no—
196C22×#67—31no—
197C22×#67—61no—
198C22×#67—61no—
199C22×#67C2×D311yescharacteristic
200C22×#67C2×D311yescharacteristic
201C23×Dic3—31no—
202C23×Dic3C2×D311yescharacteristic, complemented
203#1004—68no—
204#1004—68no—
205C2×#237—32no—
206C2×#237—32no—
207C2×#237—32no—
208C2×#237—34no—
209C2×#237—34no—
210C2×#237—32no—
211C2×#237—68no—
212C2×D3×D4—32no—
213C2×D3×D4—32no—
214C2×D3×D4—32no—
215C2×D3×D4—32no—
216C2×#235—34no—
217C2×#235—34no—
218C2×#235—32no—
219C2×#235—32no—
220C2×#235—68no—
221C22×D12—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×#123—32no—
228C3×#123—32no—
229C3×#123—34no—
230C3×C4×D4—34no—
231C3×C4×D4—34no—
232C3×#117—32no—
233C2×C3×C4⋊C4—32no—
234C2×C3×C22⋊C4—21no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—32no—
237C2×C3×C22⋊C4—32no—
238C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
239C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
240#953—32no—
241C2×#217C2×D311yescharacteristic, complemented
242#939—34no—
243#937—32no—
244#935—32no—
245#930—34no—
246#930—34no—
247#930—34no—
248#930—34no—
249#930—34no—
250#930—64no—
251#929—32no—
252#929—32no—
253#929—34no—
254#929—32no—
255C4×#67C2×D314yescomplemented
256C2×(C2×D3)⋊C4—32no—
257C2×(C2×D3)⋊C4—32no—
258C2×(C2×D3)⋊C4—34no—
259C2×(C2×D3)⋊C4C2×D312yescomplemented
260C2×C4⋊Dic3—32no—
261C2×C4⋊Dic3—34no—
262C2×C4⋊Dic3C2×D312yescomplemented
263C2×Dic3⋊C4—32no—
264#897—34no—
265#897—34no—
266#897—34no—
267#896—34no—
268#896—34no—
269#895—34no—
270#895—34no—
271#894—34no—
272#894—34no—
273#893—34no—
274D3×C4⋊C4—34no—
275#888—34no—
276#886—32no—
277#886—32no—
278#886—32no—
279#886—34no—
280#886—32no—
281#886—32no—
282#886—32no—
283#886—32no—
284#886—32no—
285#886—34no—
286#886—34no—
287#886—34no—
288#886—62no—
289#886—62no—
290#886C2×D312yescomplemented
291#886C2×D312yescomplemented
292#886C2×D314yescomplemented
293#885—34no—
294#884—34no—
295#884—34no—
296#883—34no—
297#882—32no—
298#882—32no—
299#882—32no—
300#882—32no—
301#882—32no—
302#882—32no—
303#882—34no—
304#882—34no—
305#882—62no—
306#882—62no—
307#67⋊C4—34no—
308#67⋊C4C2×D314yescomplemented
309D3×C22⋊C4—34no—
310D3×C22⋊C4C2×D312yescomplemented
311#878—34no—
312#877C2×D312yescomplemented
313#875—34no—
314C4×D12—34no—
315C4×D12—34no—
316#869—34no—
317C23×C32—42no—
318C23×C32C2×D414yes—
319C23×C32C2411yescharacteristic
320C23×C32C2411yescharacteristic
321C23×C32C2411yescharacteristic
322C22×C3⋊D3—22no—
323C22×C3⋊D3—22no—
324C22×C3⋊D3—42no—
325C22×C3⋊D3—42no—
326C22×C3⋊D3C2412yes—
327C22×C3⋊D3C2412yes—
328C22×C3×D3—22no—
329C22×C3×D3—42no—
330C22×C3×D3—42no—
331C22×C3×D3C2×D414yes—
332C22×C3×D3C2412yes—
333C22×C3×D3C2412yes—
334C2×D32—24no—
335C2×D32—44no—
336C2×C32×C4—42no—
337C2×C32×C4C2414yes—
338#638—24no—
339#638—24no—
340#638—24no—
341#638—24no—
342C2×C3⋊Dic3—22no—
343C2×C3⋊Dic3—22no—
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2412yes—
346C4⋊(C3⋊D3)—44no—
347C3×#67—24no—
348C3×#67—24no—
349C3×#67C2×D418yes—
350C3×#67C2×D418yes—
351C2×C3×Dic3—22no—
352C2×C3×Dic3—24no—
353C2×C3×Dic3—24no—
354C2×C3×Dic3—22no—
355C2×C3×Dic3—22no—
356C2×C3×Dic3—42no—
357C2×C3×Dic3C2×D414yes—
358C2×C3×Dic3C2414yes—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2412yes—
361C2×C3×Dic3C2412yes—
362C2×C3×Dic3C2412yes—
363C3×C4×D3—44no—
364#627—24no—
365#627—28no—
366#626—28no—
367#626—24no—
368#626—24no—
369#626—44no—
370#625—24no—
371#624—28no—
372#624—24no—
373D3×Dic3—28no—
374D3×Dic3—24no—
375D3×Dic3—24no—
376C2×H(5,𝔽2)—91no—
377C22×#41—91no—
378#547—94no—
379#547—94no—
380#546—94no—
381#546—94no—
382#536—92no—
383#534—92no—
384#534—91no—
385#534—91no—
386#525—92no—
387C2×#123—31no—
388C2×#123—92no—
389C2×#123—91no—
390#518—31no—
391C24×C3—21no—
392C24×C3—31no—
393C24×C3—31no—
394C24×C3C22×D311yescharacteristic
395C24×C3C22×D311yescharacteristic
396C23×D3—31no—
397C23×D3—31no—
398C23×D3—31no—
399C23×D3—31no—
400C23×D3—32no—
401C23×D3—32no—
402C23×D3—61no—
403C23×D3—61no—
404C23×D3C22×D311yescharacteristic
405C23×D3C22×D311yescharacteristic
406C2×C3×D4—38no—
407C2×C3×D4—32no—
408C2×C3×D4—32no—
409C2×C3×D4—32no—
410C2×C3×D4—32no—
411C2×C3×D4—64no—
412C22×C3×C4—22no—
413C22×C3×C4—31no—
414C22×C3×C4—32no—
415C22×C3×C4—32no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—31no—
419C22×C3×C4—32no—
420C22×C3×C4—34no—
421C22×C3×C4—64no—
422C22×C3×C4C22×D312yes—
423C22×C3×C4C22×D312yes—
424C2×#67—24no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—32no—
428C2×#67—32no—
429C2×#67—32no—
430C2×#67—32no—
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—34no—
436C2×#67—32no—
437C2×#67—32no—
438C2×#67—34no—
439C2×#67—62no—
440C2×#67—62no—
441C2×#67—62no—
442C2×#67—62no—
443C2×#67—64no—
444C2×#67—68no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—68no—
450C2×#67—124no—
451C2×#67—124no—
452C2×#67D1218yescomplemented
453C2×#67C22×D312yes—
454C2×#67C22×D312yes—
455C2×#67C22×D312yes—
456C2×#67C22×D312yes—
457C22×Dic3—24no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—31no—
461C22×Dic3—31no—
462C22×Dic3—32no—
463C22×Dic3—32no—
464C22×Dic3—34no—
465C22×Dic3—61no—
466C22×Dic3—61no—
467C22×Dic3—64no—
468C22×Dic3C22×D311yescharacteristic
469C22×Dic3C22×D311yescharacteristic
470C22×Dic3C22×D311yescharacteristic
471C22×Dic3C22×D312yes—
472C22×Dic3C22×D312yes—
473C22×Dic3C22×D312yes—
474C22×Dic3C22×D311yescharacteristic
475#237—616no—
476#237—616no—
477#237—68no—
478#237—68no—
479#237—68no—
480#237—68no—
481D3×D4—68no—
482D3×D4—68no—
483D3×D4—68no—
484D3×D4—68no—
485#235—68no—
486#235—616no—
487#235—616no—
488#235—68no—
489C2×D12—32no—
490C2×D12—34no—
491C2×D12—32no—
492C2×D12—34no—
493C2×D12—34no—
494C2×D12—34no—
495C2×D12—64no—
496C2×D12—64no—
497C2×C4×D3—32no—
498C2×C4×D3—34no—
499C2×C4×D3—32no—
500C2×C4×D3—34no—
501C2×C4×D3—32no—
502C2×C4×D3—34no—
503C2×C4×D3—32no—
504C2×C4×D3—64no—
505C2×C4×D3—64no—
506C2×C4×D3—64no—
507C2×C4×D3C22×D314yes—
508C2×Dic6—32no—
509C2×Dic6—34no—
510C2×Dic6—34no—
511C2×Dic6—32no—
512C2×Dic6—64no—
513C2×Dic6—64no—
514C3×C4⋊C4—34no—
515C3×C4⋊C4—34no—
516C3×C4⋊C4—34no—
517C3×C22⋊C4—22no—
518C3×C22⋊C4—22no—
519C3×C22⋊C4—32no—
520C3×C22⋊C4—32no—
521C3×C22⋊C4—34no—
522C3×C22⋊C4—34no—
523C3×C22⋊C4—34no—
524C3×C22⋊C4C22×D312yes—
525C3×C22⋊C4C22×D312yes—
526C3×C22⋊C4C22×D312yes—
527C3×C22⋊C4C22×D312yes—
528C3×C42—34no—
529#217—34no—
530#217C22×D312yes—
531#217C22×D312yes—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—34no—
540(C2×D3)⋊C4—34no—
541(C2×D3)⋊C4—34no—
542(C2×D3)⋊C4—34no—
543(C2×D3)⋊C4—64no—
544(C2×D3)⋊C4—64no—
545(C2×D3)⋊C4C22×D314yes—
546(C2×D3)⋊C4C22×D314yes—
547(C2×D3)⋊C4C22×D314yes—
548C4⋊Dic3—34no—
549C4⋊Dic3—34no—
550C4⋊Dic3—34no—
551C4⋊Dic3—34no—
552C4⋊Dic3—34no—
553C4⋊Dic3—64no—
554C4⋊Dic3C22×D314yes—
555C4⋊Dic3C22×D314yes—
556Dic3⋊C4—34no—
557Dic3⋊C4—34no—
558Dic3⋊C4—34no—
559Dic3⋊C4C22×D314yes—
560C4×Dic3C22×D314yes—
561C22×C32—22no—
562C22×C32—22no—
563C22×C32—22no—
564C22×C32—44no—
565C22×C32C22×D412yes—
566C22×C32C22×D412yes—
567C22×C32C22×D412yes—
568C22×C32C2511yescharacteristic
569C2×C3⋊D3—22no—
570C2×C3⋊D3—22no—
571C2×C3⋊D3—24no—
572C2×C3⋊D3—24no—
573C2×C3⋊D3—44no—
574C2×C3⋊D3—82no—
575C2×C3×D3—24no—
576C2×C3×D3—22no—
577C2×C3×D3—24no—
578C2×C3×D3—44no—
579C2×C3×D3—82no—
580C2×C3×D3C22×D414yes—
581D32—84no—
582C32×C4—24no—
583C3⋊Dic3—22no—
584C3⋊Dic3—22no—
585C3×Dic3—22no—
586C3×Dic3—22no—
587C3×Dic3—22no—
588C3×Dic3—24no—
589C3×Dic3C22×D414yes—
590H(5,𝔽2)—188no—
591C2×#41—92no—
592C2×#41—94no—
593C2×#41—94no—
594C2×#41—92no—
595C2×#41—92no—
596C2×#41—188no—
597C22×Q8—91no—
598C22×D4—31no—
599C22×D4—31no—
600C22×D4—91no—
601C22×D4—92no—
602C22×D4—92no—
603C22×D4—92no—
604C22×D4—91no—
605C22×D4—91no—
606C23×C4—31no—
607C23×C4—91no—
608C23×C4—91no—
609C4⋊Q8—94no—
610#124—94no—
611#123—32no—
612#123—32no—
613#123—34no—
614#123—94no—
615#123—94no—
616#123—94no—
617#123—92no—
618#123—92no—
619#123—94no—
620#123—92no—
621#123—92no—
622#123—92no—
623#123—92no—
624C22⋊Q8—94no—
625C22⋊Q8—94no—
626C22⋊Q8—94no—
627#121—94no—
628#121—94no—
629#121—94no—
630#121—94no—
631#121—94no—
632#120—94no—
633#120—92no—
634#120—92no—
635#120—92no—
636#120—92no—
637C4×D4—34no—
638C4×D4—34no—
639C4×D4—94no—
640C4×D4—94no—
641#117—32no—
642C2×C4⋊C4—32no—
643C2×C4⋊C4—94no—
644C2×C4⋊C4—92no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—32no—
647C2×C22⋊C4—32no—
648C2×C22⋊C4—94no—
649C2×C22⋊C4—92no—
650C2×C22⋊C4D3211yescharacteristic, complemented
651C23×C3—21no—
652C23×C3—21no—
653C23×C3—21no—
654C23×C3—24no—
655C23×C3—32no—
656C23×C3—34no—
657C23×C3—32no—
658C23×C3—42no—
659C23×C3—42no—
660C23×C3—62no—
661C23×C3—82no—
662C23×C3—122no—
663C23×C3—122no—
664C23×C3C2×D1214yes—
665C23×C3D3×D414yes—
666C23×C3C23×D311yescharacteristic
667C23×C3C23×D311yescharacteristic
668C23×C3C23×D311yescharacteristic
669C23×C3C23×D311yescharacteristic
670C23×C3C23×D311yescharacteristic
671C23×C3C23×D311yescharacteristic
672C22×D3—22no—
673C22×D3—32no—
674C22×D3—32no—
675C22×D3—32no—
676C22×D3—32no—
677C22×D3—42no—
678C22×D3—42no—
679C22×D3—62no—
680C22×D3—62no—
681C22×D3—64no—
682C22×D3—62no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—64no—
687C22×D3—122no—
688C22×D3—122no—
689C22×D3—124no—
690C22×D3—124no—
691C22×D3—122no—
692C22×D3—122no—
693C22×D3—122no—
694C22×D3—122no—
695C22×D3—242no—
696C22×D3—242no—
697C22×D3C2×D1214yes—
698C22×D3C23×D312yes—
699C22×D3C23×D312yes—
700C3×D4—38no—
701C3×D4—38no—
702C3×D4—64no—
703C3×D4—64no—
704C2×C3×C4—24no—
705C2×C3×C4—34no—
706C2×C3×C4—32no—
707C2×C3×C4—32no—
708C2×C3×C4—32no—
709C2×C3×C4—32no—
710C2×C3×C4—34no—
711C2×C3×C4—42no—
712C2×C3×C4—42no—
713C2×C3×C4—62no—
714C2×C3×C4—62no—
715C2×C3×C4—64no—
716C2×C3×C4—64no—
717C2×C3×C4—62no—
718C2×C3×C4—82no—
719C2×C3×C4—124no—
720C2×C3×C4—122no—
721C2×C3×C4C23×D314yes—
722C2×C3×C4C23×D314yes—
723#67—24no—
724#67—24no—
725#67—64no—
726#67—68no—
727#67—64no—
728#67—64no—
729#67—64no—
730#67—64no—
731#67—64no—
732#67—64no—
733#67—64no—
734#67—64no—
735#67—64no—
736#67—64no—
737#67—64no—
738#67—124no—
739#67—124no—
740#67—124no—
741#67—124no—
742#67—124no—
743#67C2×D1218yes—
744#67C2×D1218yes—
745C2×Dic3—22no—
746C2×Dic3—22no—
747C2×Dic3—24no—
748C2×Dic3—24no—
749C2×Dic3—22no—
750C2×Dic3—32no—
751C2×Dic3—32no—
752C2×Dic3—32no—
753C2×Dic3—32no—
754C2×Dic3—42no—
755C2×Dic3—62no—
756C2×Dic3—62no—
757C2×Dic3—68no—
758C2×Dic3—64no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—64no—
764C2×Dic3—122no—
765C2×Dic3—122no—
766C2×Dic3C2×D1214yes—
767C2×Dic3C23×D314yes—
768C2×Dic3C23×D312yes—
769C2×Dic3C23×D312yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772D12—64no—
773D12—68no—
774D12—64no—
775D12—124no—
776D12—124no—
777D12—124no—
778D12—244no—
779C4×D3—44no—
780C4×D3—68no—
781C4×D3—64no—
782C4×D3—64no—
783C4×D3—68no—
784C4×D3—64no—
785C4×D3—68no—
786C4×D3—64no—
787Dic6—68no—
788Dic6—64no—
789Dic6—68no—
790Dic6—64no—
791C2×C32—22no—
792C2×C32—22no—
793C2×C32—22no—
794C2×C32C23×D411yescharacteristic
795C2×C32#58512yes—
796C3⋊D3—42no—
797C3⋊D3—42no—
798C3×D3—24no—
799C3×D3—42no—
800C24—31no—
801C24—31no—
802C24—92no—
803C24—91no—
804C24—91no—
805C24C2×D3211yescharacteristic
806#41—188no—
807#41—1816no—
808#41—1816no—
809#41—188no—
810#41—188no—
811C2×Q8—94no—
812C2×Q8—92no—
813C2×Q8—184no—
814C2×D4—32no—
815C2×D4—32no—
816C2×D4—38no—
817C2×D4—32no—
818C2×D4—32no—
819C2×D4—64no—
820C2×D4—94no—
821C2×D4—92no—
822C2×D4—92no—
823C2×D4—94no—
824C2×D4—92no—
825C2×D4—92no—
826C2×D4—92no—
827C2×D4—92no—
828C2×D4—92no—
829C2×D4—94no—
830C2×D4—184no—
831C2×D4—188no—
832C2×D4—188no—
833C2×D4—188no—
834C2×D4—184no—
835C2×D4—184no—
836C22×C4—31no—
837C22×C4—32no—
838C22×C4—32no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—32no—
843C22×C4—34no—
844C22×C4—64no—
845C22×C4—94no—
846C22×C4—92no—
847C22×C4—94no—
848C22×C4—92no—
849C22×C4—92no—
850C22×C4—91no—
851C22×C4—91no—
852C22×C4—184no—
853C22×C4—184no—
854C22×C4C2×D3212yes—
855C4⋊C4—34no—
856C4⋊C4—34no—
857C4⋊C4—34no—
858C4⋊C4—94no—
859C4⋊C4—94no—
860C4⋊C4—94no—
861C4⋊C4—94no—
862C22⋊C4—32no—
863C22⋊C4—32no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—34no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C22⋊C4C2×D3212yes—
874C22⋊C4C2×D3212yes—
875C42—34no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—21no—
886C22×C3—34no—
887C22×C3—42no—
888C22×C3—42no—
889C22×C3—42no—
890C22×C3—44no—
891C22×C3—44no—
892C22×C3—64no—
893C22×C3—62no—
894C22×C3—64no—
895C22×C3—84no—
896C22×C3—124no—
897C22×C3—242no—
898C22×C3C22×D1212yes—
899C22×C3C22×D1212yes—
900C22×C3C22×D1212yes—
901C22×C3C2×D3×D412yes—
902C22×C3C2×D3×D412yes—
903C22×C3C2×D3×D412yes—
904C22×C3C24×D311yescharacteristic
905C22×C3C24×D311yescharacteristic
906C2×D3—24no—
907C2×D3—22no—
908C2×D3—24no—
909C2×D3—44no—
910C2×D3—62no—
911C2×D3—62no—
912C2×D3—62no—
913C2×D3—62no—
914C2×D3—64no—
915C2×D3—64no—
916C2×D3—64no—
917C2×D3—64no—
918C2×D3—82no—
919C2×D3—124no—
920C2×D3—124no—
921C2×D3—122no—
922C2×D3—122no—
923C2×D3—124no—
924C2×D3—124no—
925C2×D3—244no—
926C2×D3—244no—
927C2×D3—244no—
928C2×D3—242no—
929C2×D3—242no—
930C2×D3—244no—
931C2×D3C22×D1214yes—
932C3×C4—24no—
933C3×C4—24no—
934C3×C4—34no—
935C3×C4—44no—
936C3×C4—62no—
937C3×C4—62no—
938C3×C4—62no—
939C3×C4—64no—
940Dic3—22no—
941Dic3—22no—
942Dic3—22no—
943Dic3—24no—
944Dic3—62no—
945Dic3—62no—
946Dic3—62no—
947Dic3—62no—
948Dic3—122no—
949Dic3—122no—
950Dic3C22×D1214yes—
951C32#348511yescharacteristic, complemented, Sylow
952C23—32no—
953C23—34no—
954C23—32no—
955C23—42no—
956C23—62no—
957C23—92no—
958C23—92no—
959C23—122no—
960C23—122no—
961C23—184no—
962C23—182no—
963C23—182no—
964C23—362no—
965C23—362no—
966C23—364no—
967C23D3×D1214yes—
968C23C22×D3211yescharacteristic
969C23C22×D3211yescharacteristic
970C23C22×D3211yescharacteristic
971Q8—188no—
972Q8—184no—
973D4—38no—
974D4—38no—
975D4—64no—
976D4—64no—
977D4—184no—
978D4—184no—
979D4—188no—
980D4—184no—
981D4—184no—
982D4—184no—
983D4—184no—
984D4—184no—
985D4—364no—
986D4—364no—
987C2×C4—34no—
988C2×C4—32no—
989C2×C4—34no—
990C2×C4—32no—
991C2×C4—32no—
992C2×C4—32no—
993C2×C4—42no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—64no—
997C2×C4—64no—
998C2×C4—62no—
999C2×C4—92no—
1000C2×C4—92no—
1001C2×C4—124no—
1002C2×C4—122no—
1003C2×C4—188no—
1004C2×C4—184no—
1005C2×C4—184no—
1006C2×C4—188no—
1007C2×C4—184no—
1008C2×C4—182no—
1009C2×C4—182no—
1010C2×C4C22×D3214yes—
1011C2×C3—22no—
1012C2×C3—22no—
1013C2×C3—22no—
1014C2×C3—22no—
1015C2×C3—22no—
1016C2×C3—22no—
1017C2×C3—21no—
1018C2×C3—22no—
1019C2×C3—42no—
1020C2×C3—42no—
1021C2×C3—42no—
1022C2×C3—64no—
1023C2×C3—122no—
1024C2×C3C23×D1211yescharacteristic
1025C2×C3C22×D3×D411yescharacteristic
1026C2×C3#596412yes—
1027C2×C3#596612yes—
1028D3—24no—
1029D3—42no—
1030D3—122no—
1031D3—122no—
1032D3—122no—
1033D3—122no—
1034D3—242no—
1035D3—242no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—34no—
1040C22—44no—
1041C22—64no—
1042C22—62no—
1043C22—64no—
1044C22—124no—
1045C22—182no—
1046C22—182no—
1047C22—184no—
1048C22—184no—
1049C22—242no—
1050C22—364no—
1051C22—722no—
1052C22—724no—
1053C22C2×D3×D1212yes—
1054C22C2×D3×D1212yes—
1055C22C2×D3×D1212yes—
1056C22C23×D3211yescharacteristic
1057C4—24no—
1058C4—34no—
1059C4—62no—
1060C4—62no—
1061C4—62no—
1062C4—64no—
1063C4—182no—
1064C4—182no—
1065C3—21no—
1066C3#8585811yescharacteristic, complemented
1067C3#8601211yescharacteristic, complemented
1068C2—22no—
1069C2—22no—
1070C2—22no—
1071C2—64no—
1072C2—122no—
1073C2—362no—
1074C2—362no—
1075C2C22×D3×D1211yescharacteristic
1076C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
hypercenterC2×C22⋊C4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64330C2semidirect
2. C22×#3804C2semidirect
3. #10595964C2semidirect
4. C2×C3×#886C2semidirect
5. C3×#5486C2semidirect
6. #10595519C2semidirect
7. C2×#63966C2semidirect
8. #10595073C2semidirect
9. #10594906C2semidirect
10. #10594293C2semidirect
11. #10594291C2semidirect
12. D3×#886C2semidirect
13. #10594081C2semidirect
14. #10594079C2semidirect
15. #10594077C2semidirect
19. C22×#638C22semidirect
22. C23×C3×Dic3C22semidirect
24. C2×#3811C22semidirect
26. C2×D3×#67C22semidirect
27. C22×#627C22semidirect
28. C22×#626C22semidirect
29. C22×#624C22semidirect
30. C2×#3805C22semidirect
33. C2×#3804C22semidirect
34. C2×#3804C22semidirect
35. C2×#3804C22semidirect
36. C22×D3×Dic3C22semidirect
37. C2×C32×C22⋊C4C22semidirect
38. #64139C22semidirect
39. #64095C22semidirect
40. #64095C22semidirect
41. #64091C22semidirect
42. #64091C22semidirect
43. C2×C3×#217C22semidirect
44. C3×C4×#67C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×C4⋊Dic3C22semidirect
47. C3×#886C22semidirect
48. C3×#886C22semidirect
49. C3×#886C22semidirect
50. C3×#67⋊C4C22semidirect
51. C3×D3×C22⋊C4C22semidirect
52. C3×#877C22semidirect
53. #63981C22semidirect
54. #63978C22semidirect
55. #63977C22semidirect
56. #63966C22semidirect
57. #63966C22semidirect
58. #63966C22semidirect
59. #63966C22semidirect
60. C2×Dic3⋊Dic3C22semidirect
61. C2×#3722C22semidirect
62. #63962C22semidirect
63. #63923C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63918C22semidirect
66. #63910C22semidirect
67. #63909C22semidirect
68. #63906C22semidirect
69. #63895C22semidirect
70. #63895C22semidirect
71. #63894C22semidirect
72. #63893C22semidirect
73. #63891C22semidirect
74. #63890C22semidirect
75. #63890C22semidirect
76. D3×C4⋊Dic3C22semidirect
77. #63880C22semidirect
78. #63852C22semidirect
107. C2×#886D3semidirect
109. #5486D3semidirect
127. C2×C3×#67D4semidirect
202. C23×Dic3C2×D3semidirect
238. C2×C3×C22⋊C4C2×D3semidirect
239. C2×C3×C22⋊C4C2×D3semidirect
241. C2×#217C2×D3semidirect
255. C4×#67C2×D3semidirect
259. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×C4⋊Dic3C2×D3semidirect
290. #886C2×D3semidirect
291. #886C2×D3semidirect
292. #886C2×D3semidirect
308. #67⋊C4C2×D3semidirect
310. D3×C22⋊C4C2×D3semidirect
312. #877C2×D3semidirect
452. C2×#67D12semidirect
650. C2×C22⋊C4D32semidirect
951. C32#3485semidirect
1066. C3#85858semidirect
1067. C3#86012semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
C22×#38042
#105959642
C2×C3×#8862
C3×#54862
#105955192
C2×#639662
#105950732
#105949062
#105942932
#105942912
D3×#8862
#105940812
#105940792
#105940772
#860123
#858583