Finite Group Databasebeta

← #11904434

Subgroups — #11904434

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
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C2×#64330C211yesmaximal, characteristic, complemented
3#10596275C211yesmaximal, characteristic, complemented
4C3×#5804C211yesmaximal, characteristic, complemented
5#10595524C212yesmaximal, complemented
6#10595506C211yesmaximal, characteristic, complemented
7#10595498C212yesmaximal, complemented
8C2×#63966C211yesmaximal, characteristic, complemented
9C2×#63961C211yesmaximal, characteristic, complemented
10#10595305C214yesmaximal, complemented
11#10595304C214yesmaximal, complemented
12#10595151C214yesmaximal, complemented
13#10595149C214yesmaximal, complemented
14D3×#929C212yesmaximal, complemented
15#10594897C212yesmaximal, complemented
16#87273—31nomaximal
17#86296—31nomaximal
18C22×C32×D4C2211yescharacteristic, complemented
19C22×#638C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic, complemented
23C23×C3×Dic3C2211yescharacteristic, complemented
24C23×C3×Dic3C2211yescharacteristic, complemented
25C2×C3×#237—28no—
26C2×C3×#237C2214yescomplemented
27C2×C3×#237C2214yescomplemented
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
37#64162C2212yescomplemented
38C2×#3757C2211yescharacteristic, complemented
39#64148C2214yescomplemented
40#64146C2212yescomplemented
41#64144C2212yescomplemented
42#64138C2212yescomplemented
43C3×#953C2212yescomplemented
44C2×C3×#217C2211yescharacteristic, complemented
45C3×#939C2214yescomplemented
46C3×#937C2212yescomplemented
47C3×#935C2212yescomplemented
48C3×#929C2212yescomplemented
49#63983C2214yescomplemented
50#63978C2214yescomplemented
51#67⋊Dic3C2214yescomplemented
52Dic3×#67C2214yescomplemented
53Dic3×#67C2214yescomplemented
54#63971C2214yescomplemented
55#63970C2214yescomplemented
56#63969C2214yescomplemented
57D3×#217C2212yescomplemented
58C2×#3724C2212yescomplemented
59#63966C2214yescomplemented
60#63966C2212yescomplemented
61#63966C2212yescomplemented
62C2×Dic3⋊Dic3C2212yescomplemented
63#63964C2214yescomplemented
64C2×#3722C2212yescomplemented
65#63961C2214yescomplemented
66#63961C2212yescomplemented
67#63961C2212yescomplemented
68C2×(C2×D3)⋊Dic3C2212yescomplemented
69#63955C2212yescomplemented
70#63952C2214yescomplemented
71D3×(C2×D3)⋊C4C2214yescomplemented
72#63907C2214yescomplemented
73#63905C2214yescomplemented
74#63888C2214yescomplemented
75#63887C2214yescomplemented
76D3×Dic3⋊C4C2214yescomplemented
77#63850C2214yescomplemented
78#63839C2214yescomplemented
79C22×C3×#41—31no—
80C2×#1004—31no—
81C2×#1004—31no—
82C22×#237D311yescharacteristic, complemented
83C3×#534—31no—
84#5829—34no—
85#5829—34no—
86#5824—34no—
87#5824—34no—
88#5816—32no—
89#5804—31no—
90#5804—31no—
91#5804—32no—
92#5804—61no—
93#5804D311yescharacteristic, complemented
94#5798—31no—
95C2×#935—31no—
96#5791—32no—
97C2×#929—31no—
98C2×#929—31no—
99C2×#929—32no—
100#5655—34no—
101D3×#123—32no—
102#5648—32no—
103#5611—34no—
104#5610—34no—
105#5591—34no—
106#5589—32no—
107#5586—32no—
108C2×#886—31no—
109#5486—31no—
110C24×C32C2311yescharacteristic
111C24×C32C2311yescharacteristic
112C23×C3⋊D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2311yescharacteristic
115C22×D32C2312yes—
116C2×C32×D4—24no—
117C2×C32×D4C2312yes—
118C2×C32×D4C2312yes—
119C22×C32×C4C2311yescharacteristic
120C2×#638—24no—
121C2×#638C2312yes—
122C2×#638C2312yes—
123C2×#638C2314yes—
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×#67C2314yes—
132C2×C3×#67C2314yes—
133C2×C3×#67C2312yes—
134C2×C3×#67C2312yes—
135C22×C3×Dic3—24no—
136C22×C3×Dic3—24no—
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2314yes—
141C22×C3×Dic3C2312yes—
142C22×C3×Dic3C2312yes—
143C22×C3×Dic3C2312yes—
144C22×C3×Dic3C2311yescharacteristic
145C3×#237—216no—
146C3×#237—216no—
147C2×C3×C4×D3—24no—
148C2×C3×C4×D3C2314yes—
149C2×C3×Dic6—24no—
150C2×C3×Dic6C2314yes—
151#3811—28no—
152D3×#67—28no—
153D3×#67—28no—
154C2×#627C2312yes—
155C2×#626C2312yes—
156C2×#626C2312yes—
157C2×#625C2312yes—
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#3757C2314yes—
168#3752C2314yes—
169#3750C2314yes—
170C3×#217C2312yes—
171C3×#217C2312yes—
172C3×#217C2314yes—
173C3×(C2×D3)⋊C4C2314yes—
174C3×Dic3⋊C4C2314yes—
175#3724C2314yes—
176#3724C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180#3722C2314yes—
181#3722C2314yes—
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—21no—
192C22×C3×D4—31no—
193C22×C3×D4—31no—
194C22×C3×D4—31no—
195C22×C3×D4C2×D311yescharacteristic, complemented
196C22×C3×D4C2×D311yescharacteristic, complemented
197C23×C3×C4—31no—
198C23×C3×C4—31no—
199C23×C3×C4—31no—
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
208C23×Dic3C2×D311yescharacteristic, complemented
209C23×Dic3C2×D311yescharacteristic, complemented
210#1004—68no—
211#1004—68no—
212C2×#237—28no—
213C2×#237—32no—
214C2×#237—32no—
215C2×#237—32no—
216C2×#237—32no—
217C2×#237C2×D314yescomplemented
218C2×#237C2×D314yescomplemented
219C2×D3×D4—32no—
220C2×D3×D4—32no—
221C2×D3×D4—32no—
222C2×D3×D4—32no—
223C2×#235—32no—
224C2×#235—32no—
225C22×C4×D3C2×D311yescharacteristic, complemented
226C22×Dic6C2×D311yescharacteristic, complemented
227C3×#123—32no—
228C3×#123—32no—
229C3×#121—34no—
230C3×#120—32no—
231C3×#120—32no—
232C2×C3×C22⋊C4—31no—
233#953—32no—
234#953—32no—
235#953—62no—
236#953C2×D312yescomplemented
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—32no—
240C2×#217—32no—
241C2×#217—61no—
242C2×#217C2×D311yescharacteristic, complemented
243#947—34no—
244#946—34no—
245#946—34no—
246#944—34no—
247#939—34no—
248#939—34no—
249#939—34no—
250#939—34no—
251#939—34no—
252#939—64no—
253#939C2×D314yescomplemented
254#938—34no—
255#937—32no—
256#937—32no—
257#937—34no—
258#937—34no—
259#937—62no—
260#937C2×D312yescomplemented
261#935—32no—
262#935—32no—
263#935—32no—
264#935—32no—
265#935—34no—
266#935—34no—
267#935—62no—
268#935C2×D312yescomplemented
269D4×Dic3—34no—
270D4×Dic3—34no—
271D4×Dic3—34no—
272#930—34no—
273#929—32no—
274#929—32no—
275#929—32no—
276#929—32no—
277#929—34no—
278#929—32no—
279#929—32no—
280#929—34no—
281#929—34no—
282#929—34no—
283#929—62no—
284#929C2×D312yescomplemented
285C4×#67—34no—
286C4×#67—34no—
287C4×#67—34no—
288C2×(C2×D3)⋊C4—32no—
289C2×(C2×D3)⋊C4—32no—
290C2×(C2×D3)⋊C4—32no—
291C2×(C2×D3)⋊C4—34no—
292#926—32no—
293C2×C4⋊Dic3—32no—
294#924—34no—
295C2×Dic3⋊C4—32no—
296C2×Dic3⋊C4—32no—
297C2×Dic3⋊C4—32no—
298C2×Dic3⋊C4—34no—
299#896—34no—
300#894—34no—
301D3×C4⋊C4—34no—
302#888—34no—
303#886—32no—
304#886—32no—
305#886—34no—
306#885—34no—
307#884—34no—
308#883—34no—
309#883—34no—
310#67⋊C4—34no—
311#67⋊C4—34no—
312D3×C22⋊C4—32no—
313D3×C22⋊C4—34no—
314#878—34no—
315#878—34no—
316#877—32no—
317C23×C32—22no—
318C23×C32—42no—
319C23×C32—42no—
320C23×C32C2×D414yes—
321C23×C32C2412yes—
322C23×C32C2411yescharacteristic
323C23×C32C2411yescharacteristic
324C23×C32C2411yescharacteristic
325C22×C3⋊D3—22no—
326C22×C3⋊D3—42no—
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—
336C32×D4—24no—
337C32×D4—24no—
338C2×C32×C4—22no—
339C2×C32×C4C2412yes—
340#638—24no—
341#638—24no—
342#638—44no—
343C2×C3⋊Dic3—22no—
344C2×C3⋊Dic3—42no—
345C2×C3⋊Dic3C2414yes—
346C2×C3⋊Dic3C2412yes—
347C3×#67—24no—
348C3×#67—24no—
349C3×#67—28no—
350C3×#67—44no—
351C3×#67C2×D418yes—
352C3×#67C2×D418yes—
353C2×C3×Dic3—22no—
354C2×C3×Dic3—22no—
355C2×C3×Dic3—22no—
356C2×C3×Dic3—24no—
357C2×C3×Dic3—24no—
358C2×C3×Dic3—28no—
359C2×C3×Dic3—42no—
360C2×C3×Dic3C2×D414yes—
361C2×C3×Dic3C2414yes—
362C2×C3×Dic3C2412yes—
363C2×C3×Dic3C2412yes—
364C2×C3×Dic3C2412yes—
365C2×C3×Dic3C2412yes—
366C3×C4×D3—28no—
367C3×Dic6—28no—
368#627—24no—
369#626—24no—
370#626—24no—
371#625—24no—
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—31no—
384#534—92no—
385#534—91no—
386#525—92no—
387C2×#123—91no—
388C2×#123—92no—
389C2×#123—91no—
390#518—91no—
391C24×C3—21no—
392C24×C3—21no—
393C24×C3—31no—
394C24×C3—31no—
395C24×C3C22×D311yescharacteristic
396C24×C3C22×D311yescharacteristic
397C24×C3C22×D311yescharacteristic
398C24×C3C22×D311yescharacteristic
399C23×D3—31no—
400C23×D3—31no—
401C23×D3—32no—
402C23×D3—32no—
403C23×D3—61no—
404C23×D3C22×D311yescharacteristic
405C23×D3C22×D311yescharacteristic
406C3×#41—616no—
407C3×#41—616no—
408C2×C3×Q8—34no—
409C2×C3×Q8—64no—
410C2×C3×D4—24no—
411C2×C3×D4—24no—
412C2×C3×D4—22no—
413C2×C3×D4—22no—
414C2×C3×D4—38no—
415C2×C3×D4—32no—
416C2×C3×D4—32no—
417C2×C3×D4—32no—
418C2×C3×D4—32no—
419C2×C3×D4—34no—
420C2×C3×D4—34no—
421C2×C3×D4—44no—
422C2×C3×D4—64no—
423C2×C3×D4—64no—
424C2×C3×D4C22×D312yes—
425C2×C3×D4C22×D312yes—
426C2×C3×D4C22×D312yes—
427C2×C3×D4C22×D312yes—
428C22×C3×C4—21no—
429C22×C3×C4—31no—
430C22×C3×C4—31no—
431C22×C3×C4—32no—
432C22×C3×C4—32no—
433C22×C3×C4—34no—
434C22×C3×C4—31no—
435C22×C3×C4—31no—
436C22×C3×C4—32no—
437C22×C3×C4—34no—
438C22×C3×C4—64no—
439C22×C3×C4—64no—
440C22×C3×C4—64no—
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—62no—
456C2×#67—62no—
457C2×#67—64no—
458C2×#67—68no—
459C2×#67—64no—
460C2×#67—64no—
461C2×#67—68no—
462C2×#67—124no—
463C2×#67#6718yescomplemented
464C2×#67C22×D314yes—
465C2×#67C22×D312yes—
466C2×#67C22×D312yes—
467C2×#67C22×D314yes—
468C2×#67C22×D312yes—
469C2×#67C22×D312yes—
470C22×Dic3—24no—
471C22×Dic3—24no—
472C22×Dic3—31no—
473C22×Dic3—31no—
474C22×Dic3—32no—
475C22×Dic3—32no—
476C22×Dic3—32no—
477C22×Dic3—32no—
478C22×Dic3—34no—
479C22×Dic3—61no—
480C22×Dic3—62no—
481C22×Dic3C22×D314yes—
482C22×Dic3C22×D312yes—
483C22×Dic3C22×D311yescharacteristic
484C22×Dic3C22×D311yescharacteristic
485C22×Dic3C22×D311yescharacteristic
486C22×Dic3C22×D312yes—
487C22×Dic3C22×D312yes—
488C22×Dic3C22×D311yescharacteristic
489#237—216no—
490#237—216no—
491#237—68no—
492#237—68no—
493#237—68no—
494#237—68no—
495D3×D4—68no—
496D3×D4—68no—
497D3×D4—68no—
498D3×D4—68no—
499#235—68no—
500#235—68no—
501C2×D12—32no—
502C2×D12—32no—
503C2×C4×D3—24no—
504C2×C4×D3—32no—
505C2×C4×D3—32no—
506C2×C4×D3—32no—
507C2×C4×D3—32no—
508C2×C4×D3—34no—
509C2×C4×D3C22×D314yes—
510C2×Dic6—24no—
511C2×Dic6—32no—
512C2×Dic6—32no—
513C2×Dic6C22×D314yes—
514C3×C4⋊C4—34no—
515C3×C22⋊C4—32no—
516C3×C22⋊C4—34no—
517C3×C22⋊C4—32no—
518C3×C22⋊C4—34no—
519#217—32no—
520#217—34no—
521#217—34no—
522#217—32no—
523#217—32no—
524#217—32no—
525#217—34no—
526#217—34no—
527#217—34no—
528#217—62no—
529#217—62no—
530#217—64no—
531#217C22×D314yes—
532#217C22×D312yes—
533#217C22×D312yes—
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)⋊C4C22×D314yes—
545C4⋊Dic3—34no—
546C4⋊Dic3—34no—
547C4⋊Dic3—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—34no—
551Dic3⋊C4—34no—
552Dic3⋊C4—34no—
553Dic3⋊C4—34no—
554Dic3⋊C4—34no—
555Dic3⋊C4—34no—
556Dic3⋊C4—34no—
557Dic3⋊C4—64no—
558Dic3⋊C4C22×D314yes—
559C4×Dic3—34no—
560C4×Dic3—34no—
561C22×C32—22no—
562C22×C32—22no—
563C22×C32—22no—
564C22×C32—22no—
565C22×C32—24no—
566C22×C32—44no—
567C22×C32—44no—
568C22×C32C22×D412yes—
569C22×C32C22×D412yes—
570C22×C32C22×D412yes—
571C22×C32C2511yescharacteristic
572C2×C3⋊D3—22no—
573C2×C3⋊D3—24no—
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—22no—
583C3⋊Dic3—22no—
584C3⋊Dic3—24no—
585C3×Dic3—22no—
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—92no—
602C22×D4—92no—
603C22×D4—92no—
604C22×D4—91no—
605C22×D4D3211yescharacteristic, complemented
606C23×C4—31no—
607C23×C4—31no—
608C23×C4—31no—
609C4⋊Q8—94no—
610#124—94no—
611#123—32no—
612#123—32no—
613#123—92no—
614#123—92no—
615#123—94no—
616#123—94no—
617#123—94no—
618#123—94no—
619#123—92no—
620#123—92no—
621#123—94no—
622#123—92no—
623#123—92no—
624C22⋊Q8—94no—
625C22⋊Q8—94no—
626C22⋊Q8—94no—
627#121—34no—
628#121—94no—
629#121—94no—
630#121—94no—
631#121—94no—
632#120—32no—
633#120—32no—
634#120—94no—
635#120—92no—
636#120—92no—
637C4×D4—94no—
638C4×D4—94no—
639C4×D4—94no—
640C4×D4—94no—
641#117—92no—
642C2×C4⋊C4—94no—
643C2×C4⋊C4—92no—
644C2×C4⋊C4—92no—
645C2×C22⋊C4—31no—
646C2×C22⋊C4—94no—
647C2×C22⋊C4—92no—
648C2×C22⋊C4—92no—
649C2×C22⋊C4—92no—
650C2×C22⋊C4—91no—
651C23×C3—22no—
652C23×C3—22no—
653C23×C3—21no—
654C23×C3—21no—
655C23×C3—21no—
656C23×C3—22no—
657C23×C3—24no—
658C23×C3—32no—
659C23×C3—34no—
660C23×C3—32no—
661C23×C3—42no—
662C23×C3—42no—
663C23×C3—42no—
664C23×C3—42no—
665C23×C3—42no—
666C23×C3—62no—
667C23×C3—82no—
668C23×C3—82no—
669C23×C3—122no—
670C23×C3—122no—
671C23×C3D3×D414yes—
672C23×C3C2×#6714yes—
673C23×C3C23×D312yes—
674C23×C3C23×D312yes—
675C23×C3C23×D311yescharacteristic
676C23×C3C23×D311yescharacteristic
677C23×C3C23×D311yescharacteristic
678C23×C3C23×D311yescharacteristic
679C23×C3C23×D311yescharacteristic
680C23×C3C23×D311yescharacteristic
681C22×D3—22no—
682C22×D3—32no—
683C22×D3—32no—
684C22×D3—42no—
685C22×D3—42no—
686C22×D3—62no—
687C22×D3—64no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—64no—
691C22×D3—122no—
692C22×D3—124no—
693C22×D3—124no—
694C22×D3—122no—
695C22×D3—122no—
696C22×D3—242no—
697C22×D3C2×#6714yes—
698C22×D3C23×D312yes—
699C22×D3C23×D312yes—
700C3×Q8—68no—
701C3×D4—24no—
702C3×D4—24no—
703C3×D4—24no—
704C3×D4—24no—
705C3×D4—38no—
706C3×D4—38no—
707C3×D4—44no—
708C3×D4—44no—
709C3×D4—68no—
710C3×D4—64no—
711C3×D4—64no—
712C3×D4—124no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—34no—
717C2×C3×C4—32no—
718C2×C3×C4—34no—
719C2×C3×C4—32no—
720C2×C3×C4—32no—
721C2×C3×C4—32no—
722C2×C3×C4—42no—
723C2×C3×C4—68no—
724C2×C3×C4—68no—
725C2×C3×C4—62no—
726C2×C3×C4—62no—
727C2×C3×C4—64no—
728C2×C3×C4—64no—
729C2×C3×C4—62no—
730C2×C3×C4—122no—
731C2×C3×C4C23×D312yes—
732C2×C3×C4C23×D312yes—
733#67—24no—
734#67—24no—
735#67—28no—
736#67—44no—
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—244no—
750#67C2×#6718yes—
751#67C2×#6718yes—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—22no—
755C2×Dic3—24no—
756C2×Dic3—24no—
757C2×Dic3—28no—
758C2×Dic3—34no—
759C2×Dic3—34no—
760C2×Dic3—32no—
761C2×Dic3—32no—
762C2×Dic3—42no—
763C2×Dic3—62no—
764C2×Dic3—64no—
765C2×Dic3—64no—
766C2×Dic3—62no—
767C2×Dic3—62no—
768C2×Dic3—64no—
769C2×Dic3—122no—
770C2×Dic3—124no—
771C2×Dic3—122no—
772C2×Dic3—122no—
773C2×Dic3—242no—
774C2×Dic3C2×#6714yes—
775C2×Dic3C23×D314yes—
776C2×Dic3C23×D312yes—
777C2×Dic3C23×D312yes—
778C2×Dic3C23×D312yes—
779C2×Dic3C23×D312yes—
780D12—64no—
781D12—64no—
782C4×D3—28no—
783C4×D3—64no—
784C4×D3—64no—
785C4×D3—64no—
786C4×D3—64no—
787C4×D3—124no—
788Dic6—28no—
789Dic6—64no—
790Dic6—64no—
791C2×C32—22no—
792C2×C32—22no—
793C2×C32—22no—
794C2×C32—42no—
795C2×C32C23×D411yescharacteristic
796C2×C32#58512yes—
797C3⋊D3—42no—
798C3×D3—24no—
799C3×D3—42no—
800C24—31no—
801C24—31no—
802C24—92no—
803C24—91no—
804C24C2×D3211yescharacteristic
805C24C2×D3211yescharacteristic
806#41—616no—
807#41—616no—
808#41—188no—
809#41—188no—
810#41—188no—
811C2×Q8—34no—
812C2×Q8—64no—
813C2×Q8—92no—
814C2×D4—24no—
815C2×D4—32no—
816C2×D4—32no—
817C2×D4—38no—
818C2×D4—32no—
819C2×D4—34no—
820C2×D4—32no—
821C2×D4—34no—
822C2×D4—64no—
823C2×D4—64no—
824C2×D4—92no—
825C2×D4—92no—
826C2×D4—92no—
827C2×D4—92no—
828C2×D4—92no—
829C2×D4—94no—
830C2×D4—188no—
831C2×D4—188no—
832C2×D4—188no—
833C2×D4—184no—
834C2×D4C2×D3212yes—
835C2×D4C2×D3212yes—
836C22×C4—31no—
837C22×C4—32no—
838C22×C4—32no—
839C22×C4—31no—
840C22×C4—34no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—32no—
844C22×C4—34no—
845C22×C4—64no—
846C22×C4—64no—
847C22×C4—64no—
848C22×C4—92no—
849C22×C4—92no—
850C22×C4—92no—
851C22×C4—94no—
852C22×C4—91no—
853C22×C4—92no—
854C22×C4C2×D3211yescharacteristic
855C4⋊C4—34no—
856C4⋊C4—94no—
857C4⋊C4—94no—
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—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—92no—
872C22⋊C4—92no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C42—94no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—24no—
884C22×C3—24no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—21no—
890C22×C3—34no—
891C22×C3—42no—
892C22×C3—42no—
893C22×C3—42no—
894C22×C3—44no—
895C22×C3—42no—
896C22×C3—44no—
897C22×C3—44no—
898C22×C3—44no—
899C22×C3—44no—
900C22×C3—64no—
901C22×C3—64no—
902C22×C3—62no—
903C22×C3—84no—
904C22×C3—84no—
905C22×C3—124no—
906C22×C3—242no—
907C22×C3C2×D3×D412yes—
908C22×C3C2×D3×D412yes—
909C22×C3C2×D3×D412yes—
910C22×C3C22×#6712yes—
911C22×C3C22×#6712yes—
912C22×C3C22×#6712yes—
913C22×C3C24×D311yescharacteristic
914C22×C3C24×D311yescharacteristic
915C2×D3—24no—
916C2×D3—22no—
917C2×D3—24no—
918C2×D3—44no—
919C2×D3—62no—
920C2×D3—64no—
921C2×D3—64no—
922C2×D3—62no—
923C2×D3—82no—
924C2×D3—122no—
925C2×D3—124no—
926C2×D3—244no—
927C2×D3—244no—
928C2×D3—242no—
929C2×D3—242no—
930C2×D3—244no—
931C2×D3C22×#6714yes—
932C3×C4—22no—
933C3×C4—22no—
934C3×C4—34no—
935C3×C4—42no—
936C3×C4—62no—
937C3×C4—62no—
938C3×C4—64no—
939C3×C4—62no—
940Dic3—22no—
941Dic3—24no—
942Dic3—22no—
943Dic3—22no—
944Dic3—62no—
945Dic3—64no—
946Dic3—64no—
947Dic3—62no—
948Dic3—122no—
949Dic3—124no—
950Dic3C22×#6714yes—
951C32#348511yescharacteristic, complemented, Sylow
952C23—22no—
953C23—32no—
954C23—34no—
955C23—32no—
956C23—42no—
957C23—42no—
958C23—62no—
959C23—92no—
960C23—122no—
961C23—122no—
962C23—184no—
963C23—182no—
964C23—362no—
965C23—364no—
966C23D3×#6714yes—
967C23C22×D3212yes—
968C23C22×D3211yescharacteristic
969C23C22×D3211yescharacteristic
970C23C22×D3211yescharacteristic
971Q8—68no—
972Q8—184no—
973D4—24no—
974D4—24no—
975D4—38no—
976D4—38no—
977D4—68no—
978D4—64no—
979D4—64no—
980D4—124no—
981D4—184no—
982D4—184no—
983D4—184no—
984D4—184no—
985D4—184no—
986D4—364no—
987C2×C4—22no—
988C2×C4—34no—
989C2×C4—32no—
990C2×C4—34no—
991C2×C4—32no—
992C2×C4—32no—
993C2×C4—32no—
994C2×C4—68no—
995C2×C4—68no—
996C2×C4—62no—
997C2×C4—62no—
998C2×C4—64no—
999C2×C4—64no—
1000C2×C4—62no—
1001C2×C4—94no—
1002C2×C4—92no—
1003C2×C4—122no—
1004C2×C4—184no—
1005C2×C4—184no—
1006C2×C4—184no—
1007C2×C4—182no—
1008C2×C4—364no—
1009C2×C4—362no—
1010C2×C4C22×D3212yes—
1011C2×C3—22no—
1012C2×C3—22no—
1013C2×C3—22no—
1014C2×C3—22no—
1015C2×C3—22no—
1016C2×C3—22no—
1017C2×C3—22no—
1018C2×C3—21no—
1019C2×C3—42no—
1020C2×C3—42no—
1021C2×C3—42no—
1022C2×C3—42no—
1023C2×C3—42no—
1024C2×C3—64no—
1025C2×C3—82no—
1026C2×C3—122no—
1027C2×C3C22×D3×D411yescharacteristic
1028C2×C3#596412yes—
1029C2×C3#596612yes—
1030C2×C3C23×#6711yescharacteristic
1031D3—24no—
1032D3—42no—
1033D3—122no—
1034D3—122no—
1035D3—242no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—24no—
1040C22—22no—
1041C22—34no—
1042C22—44no—
1043C22—44no—
1044C22—64no—
1045C22—64no—
1046C22—62no—
1047C22—124no—
1048C22—184no—
1049C22—182no—
1050C22—242no—
1051C22—722no—
1052C22—724no—
1053C22C2×D3×#6712yes—
1054C22C2×D3×#6712yes—
1055C22C2×D3×#6712yes—
1056C22C23×D3211yescharacteristic
1057C4—22no—
1058C4—34no—
1059C4—64no—
1060C4—62no—
1061C4—62no—
1062C4—62no—
1063C4—184no—
1064C4—182no—
1065C3—21no—
1066C3#8629611yescharacteristic, complemented
1067C3#8727311yescharacteristic, complemented
1068C2—22no—
1069C2—22no—
1070C2—22no—
1071C2—42no—
1072C2—64no—
1073C2—122no—
1074C2—362no—
1075C2#1059667812yes—
1076C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×#64330C2semidirect
3. #10596275C2semidirect
4. C3×#5804C2semidirect
5. #10595524C2semidirect
6. #10595506C2semidirect
7. #10595498C2semidirect
8. C2×#63966C2semidirect
9. C2×#63961C2semidirect
10. #10595305C2semidirect
11. #10595304C2semidirect
12. #10595151C2semidirect
13. #10595149C2semidirect
14. D3×#929C2semidirect
15. #10594897C2semidirect
18. C22×C32×D4C22semidirect
22. C22×C3×#67C22semidirect
23. C23×C3×Dic3C22semidirect
24. C23×C3×Dic3C22semidirect
26. C2×C3×#237C22semidirect
27. C2×C3×#237C22semidirect
28. C22×C3×C4×D3C22semidirect
29. C22×C3×Dic6C22semidirect
31. C2×#3811C22semidirect
33. C2×D3×#67C22semidirect
34. C2×#3805C22semidirect
36. C2×#3804C22semidirect
37. #64162C22semidirect
38. C2×#3757C22semidirect
39. #64148C22semidirect
40. #64146C22semidirect
41. #64144C22semidirect
42. #64138C22semidirect
43. C3×#953C22semidirect
44. C2×C3×#217C22semidirect
45. C3×#939C22semidirect
46. C3×#937C22semidirect
47. C3×#935C22semidirect
48. C3×#929C22semidirect
49. #63983C22semidirect
50. #63978C22semidirect
51. #67⋊Dic3C22semidirect
52. Dic3×#67C22semidirect
53. Dic3×#67C22semidirect
54. #63971C22semidirect
55. #63970C22semidirect
56. #63969C22semidirect
57. D3×#217C22semidirect
58. C2×#3724C22semidirect
59. #63966C22semidirect
60. #63966C22semidirect
61. #63966C22semidirect
62. C2×Dic3⋊Dic3C22semidirect
63. #63964C22semidirect
64. C2×#3722C22semidirect
65. #63961C22semidirect
66. #63961C22semidirect
67. #63961C22semidirect
68. C2×(C2×D3)⋊Dic3C22semidirect
69. #63955C22semidirect
70. #63952C22semidirect
71. D3×(C2×D3)⋊C4C22semidirect
72. #63907C22semidirect
73. #63905C22semidirect
74. #63888C22semidirect
75. #63887C22semidirect
76. D3×Dic3⋊C4C22semidirect
77. #63850C22semidirect
78. #63839C22semidirect
82. C22×#237D3semidirect
93. #5804D3semidirect
128. C2×C3×#67D4semidirect
195. C22×C3×D4C2×D3semidirect
196. C22×C3×D4C2×D3semidirect
207. C22×#67C2×D3semidirect
208. C23×Dic3C2×D3semidirect
209. C23×Dic3C2×D3semidirect
217. C2×#237C2×D3semidirect
218. C2×#237C2×D3semidirect
225. C22×C4×D3C2×D3semidirect
226. C22×Dic6C2×D3semidirect
236. #953C2×D3semidirect
242. C2×#217C2×D3semidirect
253. #939C2×D3semidirect
260. #937C2×D3semidirect
268. #935C2×D3semidirect
284. #929C2×D3semidirect
463. C2×#67#67semidirect
605. C22×D4D32semidirect
951. C32#3485semidirect
1066. C3#86296semidirect
1067. C3#87273semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×#643302
#105962752
C3×#58042
#105955242
#105955062
#105954982
C2×#639662
C2×#639612
#105953052
#105953042
#105951512
#105951492
D3×#9292
#105948972
#872733
#862963