Finite Group Databasebeta

← #11904427

Subgroups — #11904427

Order 1152.

3291 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×#64330C211yesmaximal, characteristic, complemented
3C2×#64138C211yesmaximal, characteristic, complemented
4C2×C3×#929C211yesmaximal, characteristic, complemented
5#10595519C211yesmaximal, characteristic, complemented
6#10595518C211yesmaximal, characteristic, complemented
7#10595506C211yesmaximal, characteristic, complemented
8#10595068C214yesmaximal, complemented
9#10595065C214yesmaximal, complemented
10#10595062C212yesmaximal, complemented
11D3×#929C212yesmaximal, complemented
12#10594897C212yesmaximal, complemented
13#10594896C212yesmaximal, complemented
14#10594888C214yesmaximal, complemented
15#10594885C214yesmaximal, complemented
16#87273—31nomaximal
17#86012—31nomaximal
18C23×C32×C4C2211yescharacteristic, complemented
19C22×#638C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic, complemented
23C2×C3×#235—28no—
24C2×C3×#235C2214yescomplemented
25C2×C3×#235C2214yescomplemented
26C22×C3×D12C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C22×C3×Dic6C2211yescharacteristic, complemented
30#64330—28no—
31C2×#3811C2212yescomplemented
32C2×D3×#67C2212yes—
33C2×D3×#67C2212yescomplemented
34C2×#3805C2212yescomplemented
35C2×#3804C2212yes—
36C2×#3804C2212yescomplemented
37C2×#3757C2211yescharacteristic, complemented
38#64138C2214yescomplemented
39#64138C2212yescomplemented
40#64138C2212yescomplemented
41C2×#3752C2212yescomplemented
42C2×#3750C2212yescomplemented
43C2×C3×#217C2211yescharacteristic, complemented
44C3×#929C2214yescomplemented
45C3×#929C2212yescomplemented
46C3×#929C2212yescomplemented
47C2×C3×(C2×D3)⋊C4C2212yescomplemented
48C2×C3×Dic3⋊C4C2212yescomplemented
49#63981C2212yescomplemented
50#63980C2214yescomplemented
51#63978C2214yescomplemented
52#63977C2212yescomplemented
53#63976C2212yescomplemented
54#63976C2212yescomplemented
55#67⋊Dic3C2214yescomplemented
56Dic3×#67C2214yescomplemented
57D3×#217C2212yescomplemented
58#63966C2212yescomplemented
59#63962C2212yescomplemented
60#63961C2212yescomplemented
61#63961C2212yescomplemented
62#63955C2212yescomplemented
63#63922C2214yescomplemented
64D3×(C2×D3)⋊C4C2214yescomplemented
65#63907C2214yescomplemented
66#63906C2214yescomplemented
67#63905C2214yescomplemented
68#63904C2214yescomplemented
69#63888C2214yescomplemented
70#63887C2214yescomplemented
71#63886C2214yescomplemented
72#63885C2214yescomplemented
73#63884C2214yescomplemented
74#63879C2214yescomplemented
75D3×Dic3⋊C4C2214yescomplemented
76#63851C2214yescomplemented
77#63850C2214yescomplemented
78#63839C2214yescomplemented
79C22×C3×#41—31no—
80C2×#1004—31no—
81C2×#1004—31no—
82C22×#235D311yescharacteristic, complemented
83C2×C3×#123—31no—
84#5829—34no—
85#5829—34no—
86#5824—34no—
87#5824—34no—
88#5816—32no—
89#5804—31no—
90#5804—31no—
91#5804—31no—
92#5804—32no—
93#5798—31no—
94#5791—32no—
95C2×#929—31no—
96C2×#929—31no—
97C2×#929—32no—
98C2×#929—61no—
99C2×#929D311yescharacteristic, complemented
100#5656—32no—
101#5655—34no—
102#5654—34no—
103#5653—32no—
104D3×#123—32no—
105#5648—32no—
106#5507—34no—
107#5493—31no—
108#5490—34no—
109#5486—31no—
110C24×C32C2311yescharacteristic
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2311yescharacteristic
115C22×D32C2312yes—
116C22×C32×C4—24no—
117C22×C32×C4C2312yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2312yes—
121C2×#638—24no—
122C2×#638C2312yes—
123C2×#638C2312yes—
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2312yes—
126C2×C3×#67—24no—
127C2×C3×#67—24no—
128C2×C3×#67D418yescomplemented
129C2×C3×#67C2312yes—
130C2×C3×#67C2312yes—
131C2×C3×#67C2312yes—
132C2×C3×#67C2312yes—
133C2×C3×#67C2312yes—
134C2×C3×#67C2312yes—
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2312yes—
138C22×C3×Dic3C2311yescharacteristic
139C3×#235—216no—
140C3×#235—216no—
141C2×C3×D12—24no—
142C2×C3×D12C2314yes—
143C2×C3×C4×D3—24no—
144C2×C3×C4×D3—24no—
145C2×C3×C4×D3C2314yes—
146C2×C3×C4×D3C2314yes—
147C2×C3×Dic6—24no—
148C2×C3×Dic6C2314yes—
149#3811—28no—
150D3×#67—28no—
151D3×#67—28no—
152C2×#627C2312yes—
153C2×#626C2312yes—
154C2×#626C2312yes—
155C2×#626C2314yes—
156C2×#625C2312yes—
157C2×#625C2314yes—
158C2×#624C2312yes—
159#3805—28no—
160#3804—28no—
161#3804—28no—
162C2×D3×Dic3C2312yes—
163C2×D3×Dic3C2312yes—
164C2×D3×Dic3C2314yes—
165#3757C2312yes—
166#3757C2312yes—
167#3752C2314yes—
168#3752C2314yes—
169#3750C2314yes—
170#3750C2314yes—
171C3×#217C2312yes—
172C3×#217C2312yes—
173C3×(C2×D3)⋊C4C2314yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×Dic3⋊C4C2314yes—
176C3×Dic3⋊C4C2314yes—
177#3724C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180#3722C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185Dic32C2314yes—
186#3485—91noSylow
187C2×C3×#41—34no—
188C2×C3×#41—34no—
189C2×C3×#41—68no—
190C22×C3×Q8—31no—
191C22×C3×D4—31no—
192C22×C3×D4—31no—
193C22×C3×D4—31no—
194C22×C3×D4—31no—
195C23×C3×C4—21no—
196C23×C3×C4—31no—
197C23×C3×C4—31no—
198C23×C3×C4C2×D311yescharacteristic, complemented
199C23×C3×C4C2×D311yescharacteristic, complemented
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—32no—
203C22×#67—32no—
204C22×#67—61no—
205C22×#67C2×D311yescharacteristic
206C22×#67C2×D311yescharacteristic
207C22×#67C2×D311yescharacteristic, complemented
208#1004—68no—
209#1004—68no—
210C2×#237—32no—
211C2×#237—32no—
212C2×#237—32no—
213C2×#237—32no—
214C2×D3×D4—32no—
215C2×D3×D4—32no—
216C2×D3×D4—32no—
217C2×D3×D4—32no—
218C2×#235—28no—
219C2×#235—32no—
220C2×#235—32no—
221C2×#235C2×D314yescomplemented
222C2×#235C2×D314yescomplemented
223C22×D12C2×D311yescharacteristic, complemented
224C22×C4×D3C2×D311yescharacteristic, complemented
225C22×C4×D3C2×D311yescharacteristic, complemented
226C22×Dic6C2×D311yescharacteristic, complemented
227C3×#123—32no—
228C3×#123—32no—
229C3×#123—34no—
230C2×C3×C4⋊C4—32no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—32no—
233#953—32no—
234#953—32no—
235#953—32no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—32no—
239C2×#217—61no—
240C2×#217C2×D311yescharacteristic, complemented
241#947—34no—
242#946—34no—
243#946—34no—
244#944—34no—
245#939—34no—
246#939—34no—
247#939—34no—
248#939—34no—
249#939—34no—
250#937—32no—
251#937—32no—
252#937—32no—
253#937—34no—
254#935—32no—
255#935—32no—
256#935—32no—
257#935—34no—
258D4×Dic3—34no—
259D4×Dic3—34no—
260#930—34no—
261#930—34no—
262#929—32no—
263#929—32no—
264#929—34no—
265#929—32no—
266#929—32no—
267#929—34no—
268#929—32no—
269#929—32no—
270#929—32no—
271#929—34no—
272#929—34no—
273#929—62no—
274#929—62no—
275#929—64no—
276#929C2×D312yescomplemented
277#929C2×D312yescomplemented
278#929C2×D314yescomplemented
279C4×#67—34no—
280C4×#67—34no—
281C4×#67—34no—
282C2×(C2×D3)⋊C4—32no—
283C2×(C2×D3)⋊C4—32no—
284C2×(C2×D3)⋊C4—34no—
285C2×(C2×D3)⋊C4—62no—
286C2×(C2×D3)⋊C4C2×D312yescomplemented
287#926—32no—
288#924—34no—
289C2×Dic3⋊C4—32no—
290C2×Dic3⋊C4—32no—
291C2×Dic3⋊C4—34no—
292C2×Dic3⋊C4—62no—
293C2×Dic3⋊C4C2×D312yescomplemented
294#896—34no—
295#896—34no—
296#895—34no—
297#894—34no—
298#894—34no—
299#893—34no—
300D3×C4⋊C4—34no—
301#888—34no—
302#886—32no—
303#886—32no—
304#885—34no—
305#884—34no—
306#884—34no—
307#883—34no—
308#882—32no—
309#882—32no—
310#882—34no—
311#67⋊C4—34no—
312#67⋊C4—34no—
313D3×C22⋊C4—32no—
314D3×C22⋊C4—34no—
315#878—34no—
316#877—32no—
317C23×C32—42no—
318C23×C32C2×D414yes—
319C23×C32C2411yescharacteristic
320C23×C32C2411yescharacteristic
321C23×C32C2411yescharacteristic
322C22×C3⋊D3—22no—
323C22×C3⋊D3—42no—
324C22×C3⋊D3C2412yes—
325C22×C3×D3—22no—
326C22×C3×D3—22no—
327C22×C3×D3—42no—
328C22×C3×D3—42no—
329C22×C3×D3—42no—
330C22×C3×D3C2×D414yes—
331C22×C3×D3C2412yes—
332C22×C3×D3C2412yes—
333C22×C3×D3C2412yes—
334C2×D32—24no—
335C2×D32—44no—
336C2×C32×C4—22no—
337C2×C32×C4—22no—
338C2×C32×C4—24no—
339C2×C32×C4—24no—
340C2×C32×C4C2412yes—
341C2×C32×C4C2412yes—
342#638—24no—
343#638—24no—
344C2×C3⋊Dic3—22no—
345C2×C3⋊Dic3—42no—
346C2×C3⋊Dic3C2414yes—
347C2×C3⋊Dic3C2412yes—
348C3×#67—24no—
349C3×#67—24no—
350C3×#67—24no—
351C3×#67—24no—
352C3×#67C2×D418yes—
353C3×#67C2×D418yes—
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—
362C3×D12—28no—
363C3×C4×D3—28no—
364C3×C4×D3—28no—
365C3×Dic6—28no—
366#627—24no—
367#626—24no—
368#626—24no—
369#626—44no—
370#625—24no—
371#625—44no—
372#624—24no—
373D3×Dic3—24no—
374D3×Dic3—24no—
375D3×Dic3—44no—
376C2×H(5,𝔽2)—91no—
377C22×#41—31no—
378#547—94no—
379#547—94no—
380#546—94no—
381#546—94no—
382#536—92no—
383#534—91no—
384#534—92no—
385#534—91no—
386#525—92no—
387C2×#123—31no—
388C2×#123—92no—
389C2×#123—91no—
390#518—91no—
391C24×C3—21no—
392C24×C3—31no—
393C24×C3—31no—
394C24×C3—31no—
395C24×C3C22×D311yescharacteristic
396C24×C3C22×D311yescharacteristic
397C23×D3—31no—
398C23×D3—31no—
399C23×D3—32no—
400C23×D3—32no—
401C23×D3—61no—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D311yescharacteristic
405C3×#41—616no—
406C3×#41—616no—
407C2×C3×Q8—34no—
408C2×C3×Q8—64no—
409C2×C3×D4—38no—
410C2×C3×D4—32no—
411C2×C3×D4—32no—
412C2×C3×D4—32no—
413C2×C3×D4—32no—
414C2×C3×D4—32no—
415C2×C3×D4—32no—
416C2×C3×D4—34no—
417C2×C3×D4—64no—
418C2×C3×D4—64no—
419C2×C3×D4—64no—
420C22×C3×C4—24no—
421C22×C3×C4—24no—
422C22×C3×C4—22no—
423C22×C3×C4—22no—
424C22×C3×C4—21no—
425C22×C3×C4—21no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—31no—
429C22×C3×C4—32no—
430C22×C3×C4—34no—
431C22×C3×C4—34no—
432C22×C3×C4—44no—
433C22×C3×C4—64no—
434C22×C3×C4—64no—
435C22×C3×C4C22×D312yes—
436C22×C3×C4C22×D312yes—
437C22×C3×C4C22×D312yes—
438C22×C3×C4C22×D311yescharacteristic
439C22×C3×C4C22×D311yescharacteristic
440C22×C3×C4C22×D312yes—
441C22×C3×C4C22×D311yescharacteristic
442C22×C3×C4C22×D311yescharacteristic
443C2×#67—24no—
444C2×#67—24no—
445C2×#67—32no—
446C2×#67—32no—
447C2×#67—32no—
448C2×#67—32no—
449C2×#67—32no—
450C2×#67—32no—
451C2×#67—34no—
452C2×#67—34no—
453C2×#67—32no—
454C2×#67—32no—
455C2×#67—34no—
456C2×#67—62no—
457C2×#67—62no—
458C2×#67—68no—
459C2×#67—64no—
460C2×#67—64no—
461C2×#67—68no—
462C2×#67—124no—
463C2×#67#6718yescomplemented
464C2×#67C22×D312yes—
465C2×#67C22×D312yes—
466C2×#67C22×D312yes—
467C2×#67C22×D312yes—
468C2×#67C22×D312yes—
469C2×#67C22×D312yes—
470C22×Dic3—31no—
471C22×Dic3—31no—
472C22×Dic3—32no—
473C22×Dic3—32no—
474C22×Dic3—32no—
475C22×Dic3—32no—
476C22×Dic3—34no—
477C22×Dic3—61no—
478C22×Dic3—62no—
479C22×Dic3C22×D311yescharacteristic
480C22×Dic3C22×D311yescharacteristic
481C22×Dic3C22×D312yes—
482C22×Dic3C22×D311yescharacteristic
483#237—68no—
484#237—68no—
485#237—68no—
486#237—68no—
487D3×D4—68no—
488D3×D4—68no—
489D3×D4—68no—
490D3×D4—68no—
491#235—216no—
492#235—216no—
493#235—68no—
494#235—68no—
495C2×D12—24no—
496C2×D12—32no—
497C2×D12—32no—
498C2×D12—34no—
499C2×D12C22×D314yes—
500C2×C4×D3—24no—
501C2×C4×D3—24no—
502C2×C4×D3—32no—
503C2×C4×D3—32no—
504C2×C4×D3—32no—
505C2×C4×D3—32no—
506C2×C4×D3—34no—
507C2×C4×D3C22×D314yes—
508C2×C4×D3C22×D314yes—
509C2×Dic6—24no—
510C2×Dic6—32no—
511C2×Dic6—32no—
512C2×Dic6C22×D314yes—
513C3×C4⋊C4—34no—
514C3×C4⋊C4—34no—
515C3×C22⋊C4—32no—
516C3×C22⋊C4—32no—
517C3×C22⋊C4—34no—
518C3×C22⋊C4—34no—
519#217—32no—
520#217—32no—
521#217—32no—
522#217—32no—
523#217—34no—
524#217—34no—
525#217—34no—
526#217—34no—
527#217—62no—
528#217—62no—
529#217C22×D312yes—
530#217C22×D312yes—
531(C2×D3)⋊C4—34no—
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—64no—
542(C2×D3)⋊C4—64no—
543(C2×D3)⋊C4C22×D314yes—
544(C2×D3)⋊C4C22×D314yes—
545C4⋊Dic3—34no—
546C4⋊Dic3—34no—
547Dic3⋊C4—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—34no—
551Dic3⋊C4—34no—
552Dic3⋊C4—34no—
553Dic3⋊C4—34no—
554Dic3⋊C4—34no—
555Dic3⋊C4—64no—
556Dic3⋊C4—64no—
557Dic3⋊C4C22×D314yes—
558Dic3⋊C4C22×D314yes—
559C4×Dic3—34no—
560C4×Dic3—34no—
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—24no—
571C2×C3⋊D3—82no—
572C2×C3×D3—24no—
573C2×C3×D3—22no—
574C2×C3×D3—22no—
575C2×C3×D3—24no—
576C2×C3×D3—24no—
577C2×C3×D3—44no—
578C2×C3×D3—44no—
579C2×C3×D3—82no—
580C2×C3×D3C22×D414yes—
581D32—84no—
582C32×C4—22no—
583C32×C4—22no—
584C3⋊Dic3—22no—
585C3⋊Dic3—24no—
586C3×Dic3—22no—
587C3×Dic3—22no—
588C3×Dic3—24no—
589C3×Dic3C22×D414yes—
590H(5,𝔽2)—188no—
591C2×#41—34no—
592C2×#41—34no—
593C2×#41—68no—
594C2×#41—92no—
595C2×#41—92no—
596C2×#41—92no—
597C22×Q8—31no—
598C22×D4—31no—
599C22×D4—31no—
600C22×D4—31no—
601C22×D4—31no—
602C22×D4—92no—
603C22×D4—92no—
604C22×D4—92no—
605C22×D4—91no—
606C23×C4—31no—
607C23×C4—31no—
608C23×C4D3211yescharacteristic, complemented
609C4⋊Q8—94no—
610#124—94no—
611#123—32no—
612#123—32no—
613#123—34no—
614#123—92no—
615#123—94no—
616#123—92no—
617#123—94no—
618#123—94no—
619#123—92no—
620#123—92no—
621#123—92no—
622#123—92no—
623#123—94no—
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—92no—
633#120—94no—
634#120—92no—
635#120—92no—
636#120—92no—
637C4×D4—94no—
638C4×D4—94no—
639C4×D4—94no—
640C4×D4—94no—
641#117—92no—
642C2×C4⋊C4—32no—
643C2×C4⋊C4—94no—
644C2×C4⋊C4—92no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—32no—
647C2×C22⋊C4—94no—
648C2×C22⋊C4—92no—
649C2×C22⋊C4—91no—
650C2×C22⋊C4—92no—
651C23×C3—21no—
652C23×C3—21no—
653C23×C3—21no—
654C23×C3—24no—
655C23×C3—32no—
656C23×C3—34no—
657C23×C3—32no—
658C23×C3—32no—
659C23×C3—42no—
660C23×C3—42no—
661C23×C3—44no—
662C23×C3—62no—
663C23×C3—62no—
664C23×C3—122no—
665C23×C3—122no—
666C23×C3—122no—
667C23×C3D3×D414yes—
668C23×C3C2×#6714yes—
669C23×C3C23×D311yescharacteristic
670C23×C3C23×D311yescharacteristic
671C23×C3C23×D311yescharacteristic
672C23×C3C23×D311yescharacteristic
673C23×C3C23×D311yescharacteristic
674C23×C3C23×D311yescharacteristic
675C22×D3—22no—
676C22×D3—22no—
677C22×D3—32no—
678C22×D3—32no—
679C22×D3—42no—
680C22×D3—42no—
681C22×D3—42no—
682C22×D3—62no—
683C22×D3—64no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—64no—
687C22×D3—122no—
688C22×D3—124no—
689C22×D3—124no—
690C22×D3—122no—
691C22×D3—122no—
692C22×D3—124no—
693C22×D3C2×#6714yes—
694C22×D3C23×D312yes—
695C22×D3C23×D312yes—
696C22×D3C23×D312yes—
697C3×Q8—68no—
698C3×D4—38no—
699C3×D4—38no—
700C3×D4—68no—
701C3×D4—64no—
702C3×D4—64no—
703C3×D4—64no—
704C3×D4—64no—
705C2×C3×C4—22no—
706C2×C3×C4—22no—
707C2×C3×C4—24no—
708C2×C3×C4—24no—
709C2×C3×C4—22no—
710C2×C3×C4—22no—
711C2×C3×C4—24no—
712C2×C3×C4—24no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—34no—
716C2×C3×C4—32no—
717C2×C3×C4—34no—
718C2×C3×C4—32no—
719C2×C3×C4—32no—
720C2×C3×C4—42no—
721C2×C3×C4—42no—
722C2×C3×C4—44no—
723C2×C3×C4—44no—
724C2×C3×C4—68no—
725C2×C3×C4—68no—
726C2×C3×C4—62no—
727C2×C3×C4—62no—
728C2×C3×C4—122no—
729C2×C3×C4C23×D312yes—
730C2×C3×C4C23×D312yes—
731C2×C3×C4C23×D312yes—
732C2×C3×C4C23×D312yes—
733#67—24no—
734#67—24no—
735#67—24no—
736#67—24no—
737#67—64no—
738#67—64no—
739#67—64no—
740#67—64no—
741#67—64no—
742#67—64no—
743#67—64no—
744#67—64no—
745#67—124no—
746#67—124no—
747#67—124no—
748#67—124no—
749#67—124no—
750#67C2×#6718yes—
751#67C2×#6718yes—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—34no—
755C2×Dic3—34no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—42no—
759C2×Dic3—62no—
760C2×Dic3—64no—
761C2×Dic3—64no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—64no—
765C2×Dic3—122no—
766C2×Dic3—124no—
767C2×Dic3—122no—
768C2×Dic3—122no—
769C2×Dic3—124no—
770C2×Dic3C2×#6714yes—
771C2×Dic3C23×D314yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775D12—28no—
776D12—64no—
777D12—64no—
778D12—124no—
779C4×D3—28no—
780C4×D3—28no—
781C4×D3—64no—
782C4×D3—64no—
783C4×D3—64no—
784C4×D3—64no—
785C4×D3—124no—
786Dic6—28no—
787Dic6—64no—
788Dic6—64no—
789C2×C32—22no—
790C2×C32—22no—
791C2×C32—22no—
792C2×C32C23×D411yescharacteristic
793C2×C32#58512yes—
794C3⋊D3—42no—
795C3×D3—24no—
796C3×D3—42no—
797C3×D3—42no—
798C24—31no—
799C24—31no—
800C24—31no—
801C24—92no—
802C24—91no—
803C24C2×D3211yescharacteristic
804#41—616no—
805#41—616no—
806#41—188no—
807#41—188no—
808#41—188no—
809C2×Q8—34no—
810C2×Q8—64no—
811C2×Q8—92no—
812C2×D4—32no—
813C2×D4—32no—
814C2×D4—38no—
815C2×D4—32no—
816C2×D4—32no—
817C2×D4—32no—
818C2×D4—32no—
819C2×D4—34no—
820C2×D4—64no—
821C2×D4—64no—
822C2×D4—64no—
823C2×D4—92no—
824C2×D4—92no—
825C2×D4—94no—
826C2×D4—92no—
827C2×D4—92no—
828C2×D4—92no—
829C2×D4—94no—
830C2×D4—188no—
831C2×D4—188no—
832C2×D4—188no—
833C2×D4—184no—
834C22×C4—24no—
835C22×C4—31no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—32no—
839C22×C4—34no—
840C22×C4—34no—
841C22×C4—64no—
842C22×C4—64no—
843C22×C4—92no—
844C22×C4—92no—
845C22×C4—92no—
846C22×C4—94no—
847C22×C4—91no—
848C22×C4—92no—
849C22×C4C2×D3212yes—
850C22×C4C2×D3212yes—
851C22×C4C2×D3211yescharacteristic
852C22×C4C2×D3211yescharacteristic
853C4⋊C4—34no—
854C4⋊C4—34no—
855C4⋊C4—94no—
856C4⋊C4—94no—
857C4⋊C4—94no—
858C4⋊C4—94no—
859C4⋊C4—94no—
860C22⋊C4—32no—
861C22⋊C4—32no—
862C22⋊C4—34no—
863C22⋊C4—34no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—92no—
870C22⋊C4—92no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C42—94no—
874C22×C3—24no—
875C22×C3—22no—
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—21no—
885C22×C3—34no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—44no—
889C22×C3—44no—
890C22×C3—48no—
891C22×C3—64no—
892C22×C3—62no—
893C22×C3—64no—
894C22×C3—64no—
895C22×C3—62no—
896C22×C3—124no—
897C22×C3—124no—
898C22×C3—242no—
899C22×C3C2×D3×D412yes—
900C22×C3C2×D3×D412yes—
901C22×C3C2×D3×D412yes—
902C22×C3C22×#6712yes—
903C22×C3C22×#6712yes—
904C22×C3C22×#6712yes—
905C22×C3C24×D311yescharacteristic
906C22×C3C24×D311yescharacteristic
907C2×D3—24no—
908C2×D3—22no—
909C2×D3—24no—
910C2×D3—24no—
911C2×D3—22no—
912C2×D3—44no—
913C2×D3—44no—
914C2×D3—62no—
915C2×D3—64no—
916C2×D3—64no—
917C2×D3—62no—
918C2×D3—82no—
919C2×D3—122no—
920C2×D3—124no—
921C2×D3—244no—
922C2×D3—244no—
923C2×D3—242no—
924C2×D3—242no—
925C2×D3—244no—
926C2×D3C22×#6714yes—
927C3×C4—22no—
928C3×C4—22no—
929C3×C4—22no—
930C3×C4—22no—
931C3×C4—34no—
932C3×C4—42no—
933C3×C4—42no—
934C3×C4—62no—
935C3×C4—64no—
936C3×C4—62no—
937Dic3—22no—
938Dic3—24no—
939Dic3—22no—
940Dic3—62no—
941Dic3—64no—
942Dic3—64no—
943Dic3—62no—
944Dic3—122no—
945Dic3—124no—
946Dic3C22×#6714yes—
947C32#348511yescharacteristic, complemented, Sylow
948C23—32no—
949C23—34no—
950C23—32no—
951C23—32no—
952C23—42no—
953C23—62no—
954C23—62no—
955C23—92no—
956C23—122no—
957C23—122no—
958C23—122no—
959C23—184no—
960C23—182no—
961C23—362no—
962C23—364no—
963C23D3×#6714yes—
964C23C22×D3211yescharacteristic
965C23C22×D3211yescharacteristic
966C23C22×D3211yescharacteristic
967Q8—68no—
968Q8—184no—
969D4—38no—
970D4—38no—
971D4—68no—
972D4—64no—
973D4—64no—
974D4—64no—
975D4—64no—
976D4—184no—
977D4—184no—
978D4—184no—
979D4—184no—
980D4—184no—
981D4—364no—
982D4—364no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—34no—
988C2×C4—32no—
989C2×C4—34no—
990C2×C4—32no—
991C2×C4—32no—
992C2×C4—68no—
993C2×C4—68no—
994C2×C4—62no—
995C2×C4—62no—
996C2×C4—94no—
997C2×C4—92no—
998C2×C4—122no—
999C2×C4—184no—
1000C2×C4—184no—
1001C2×C4—184no—
1002C2×C4—182no—
1003C2×C4—364no—
1004C2×C4—362no—
1005C2×C4C22×D3212yes—
1006C2×C4C22×D3212yes—
1007C2×C3—24no—
1008C2×C3—22no—
1009C2×C3—22no—
1010C2×C3—22no—
1011C2×C3—22no—
1012C2×C3—22no—
1013C2×C3—22no—
1014C2×C3—22no—
1015C2×C3—21no—
1016C2×C3—42no—
1017C2×C3—42no—
1018C2×C3—64no—
1019C2×C3—122no—
1020C2×C3—122no—
1021C2×C3C22×D3×D411yescharacteristic
1022C2×C3#596412yes—
1023C2×C3#596412yes—
1024C2×C3C23×#6711yescharacteristic
1025D3—24no—
1026D3—42no—
1027D3—42no—
1028D3—122no—
1029D3—122no—
1030D3—242no—
1031C22—22no—
1032C22—22no—
1033C22—22no—
1034C22—34no—
1035C22—44no—
1036C22—64no—
1037C22—64no—
1038C22—64no—
1039C22—62no—
1040C22—62no—
1041C22—124no—
1042C22—124no—
1043C22—184no—
1044C22—182no—
1045C22—242no—
1046C22—722no—
1047C22—724no—
1048C22C2×D3×#6712yes—
1049C22C2×D3×#6712yes—
1050C22C2×D3×#6712yes—
1051C22C23×D3211yescharacteristic
1052C4—22no—
1053C4—22no—
1054C4—34no—
1055C4—64no—
1056C4—62no—
1057C4—62no—
1058C4—184no—
1059C4—182no—
1060C3—21no—
1061C3#8601211yescharacteristic, complemented
1062C3#8727311yescharacteristic, complemented
1063C2—22no—
1064C2—22no—
1065C2—22no—
1066C2—64no—
1067C2—122no—
1068C2—122no—
1069C2—362no—
1070C2#1059666912yes—
1071C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C2×#64330C2semidirect
3. C2×#64138C2semidirect
4. C2×C3×#929C2semidirect
5. #10595519C2semidirect
6. #10595518C2semidirect
7. #10595506C2semidirect
8. #10595068C2semidirect
9. #10595065C2semidirect
10. #10595062C2semidirect
11. D3×#929C2semidirect
12. #10594897C2semidirect
13. #10594896C2semidirect
14. #10594888C2semidirect
15. #10594885C2semidirect
18. C23×C32×C4C22semidirect
22. C22×C3×#67C22semidirect
24. C2×C3×#235C22semidirect
25. C2×C3×#235C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×C4×D3C22semidirect
29. C22×C3×Dic6C22semidirect
31. C2×#3811C22semidirect
33. C2×D3×#67C22semidirect
34. C2×#3805C22semidirect
36. C2×#3804C22semidirect
37. C2×#3757C22semidirect
38. #64138C22semidirect
39. #64138C22semidirect
40. #64138C22semidirect
41. C2×#3752C22semidirect
42. C2×#3750C22semidirect
43. C2×C3×#217C22semidirect
44. C3×#929C22semidirect
45. C3×#929C22semidirect
46. C3×#929C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. #63981C22semidirect
50. #63980C22semidirect
51. #63978C22semidirect
52. #63977C22semidirect
53. #63976C22semidirect
54. #63976C22semidirect
55. #67⋊Dic3C22semidirect
56. Dic3×#67C22semidirect
57. D3×#217C22semidirect
58. #63966C22semidirect
59. #63962C22semidirect
60. #63961C22semidirect
61. #63961C22semidirect
62. #63955C22semidirect
63. #63922C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63907C22semidirect
66. #63906C22semidirect
67. #63905C22semidirect
68. #63904C22semidirect
69. #63888C22semidirect
70. #63887C22semidirect
71. #63886C22semidirect
72. #63885C22semidirect
73. #63884C22semidirect
74. #63879C22semidirect
75. D3×Dic3⋊C4C22semidirect
76. #63851C22semidirect
77. #63850C22semidirect
78. #63839C22semidirect
82. C22×#235D3semidirect
99. C2×#929D3semidirect
128. C2×C3×#67D4semidirect
198. C23×C3×C4C2×D3semidirect
199. C23×C3×C4C2×D3semidirect
207. C22×#67C2×D3semidirect
221. C2×#235C2×D3semidirect
222. C2×#235C2×D3semidirect
223. C22×D12C2×D3semidirect
224. C22×C4×D3C2×D3semidirect
225. C22×C4×D3C2×D3semidirect
226. C22×Dic6C2×D3semidirect
240. C2×#217C2×D3semidirect
276. #929C2×D3semidirect
277. #929C2×D3semidirect
278. #929C2×D3semidirect
286. C2×(C2×D3)⋊C4C2×D3semidirect
293. C2×Dic3⋊C4C2×D3semidirect
463. C2×#67#67semidirect
608. C23×C4D32semidirect
947. C32#3485semidirect
1061. C3#86012semidirect
1062. C3#87273semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#643302
C2×#641382
C2×C3×#9292
#105955192
#105955182
#105955062
#105950682
#105950652
#105950622
D3×#9292
#105948972
#105948962
#105948882
#105948852
#872733
#860123