Finite Group Databasebeta

← #11864590

Subgroups — #11864590

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C3×#5608C211yesmaximal, characteristic, complemented
3C2×#63933C211yesmaximal, characteristic, complemented
4C2×#63925C211yesmaximal, characteristic, complemented
5#10592736C211yesmaximal, characteristic, complemented
6C3×#5036C211yesmaximal, characteristic, complemented
7#10591519C211yesmaximal, characteristic, complemented
8#10591515C211yesmaximal, characteristic, complemented
9#10591184C211yesmaximal, characteristic, complemented
10#10591169C211yesmaximal, characteristic, complemented
11#10591145C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590607C211yesmaximal, characteristic, complemented
14#10590596C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#83424—31nomaximal
17#80005—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C2×D3×#67—21no—
23C2×D3×#67—21no—
24#64307—24no—
25#64307—24no—
26C2×#3802—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×#3796—21no—
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C32×#121C2211yescharacteristic, complemented
33C2×#3754C2211yescharacteristic, complemented
34C2×#3753C2211yescharacteristic, complemented
35C3×#939—21no—
36C3×#938—21no—
37C3×#938C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C2×C3×#213C2211yescharacteristic, complemented
40C3×#924C2211yescharacteristic, complemented
41C3×#897C2211yescharacteristic, complemented
42C3×D3×C4⋊C4C2211yescharacteristic, complemented
43C3×#884—21no—
44C3×#878—21no—
45#63933—24no—
46#63925—24no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63657C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C3×#537—31no—
68C2×#950—31no—
69C2×#949—31no—
70C2×#912—31no—
71C2×#911—31no—
72#5608D311yescharacteristic, complemented
73C3×#447—31no—
74#5234—31no—
75#5218—31no—
76#5158—31no—
77#5156—31no—
78#5047—31no—
79#5047—31no—
80#5046—31no—
81#5046—31no—
82#5037—31no—
83#5037—31no—
84#5037—31no—
85#5037—61no—
86#5036—31no—
87#5036D311yescharacteristic, complemented
88#4966—31no—
89C2×#809—31no—
90#4783—31no—
91#4776—31no—
92#4771—31no—
93D3×#102—31no—
94#4733—31no—
95#4727—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×#638—21no—
103#3828—22no—
104#3828—22no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C2×C3×#67D411yescharacteristic
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237—22no—
115C3×#235—22no—
116C3×#235—22no—
117C2×C3×D12—21no—
118C2×C3×D12—22no—
119C2×C3×D12—22no—
120C2×C3×D12D411yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×Dic6D411yescharacteristic
127C2×C3×Dic6C2311yescharacteristic
128D3×#67—28no—
129D3×#67—28no—
130C2×#626—21no—
131C2×#626—21no—
132C2×#625—21no—
133C2×#625—21no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136#3802—28no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12D414yescomplemented
141#3796—28no—
142#3795—22no—
143#3795—22no—
144#3795—22no—
145#3795D414yescomplemented
146C32×C4⋊C4C2311yescharacteristic
147C32×C22⋊C4—21no—
148#3754—22no—
149#3753—22no—
150C2×C3⋊(C3⋊C8)C2311yescharacteristic
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C3×#217—21no—
153C3×#217—21no—
154C3×#213—22no—
155C3×#213—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3—21no—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×Dic3⋊C4—21no—
160C3×Dic3⋊C4—21no—
161C2×C3×C3⋊C8C2311yescharacteristic
162C2×C3×C3⋊C8C2311yescharacteristic
163#3719—22no—
164#3717—22no—
165#3715—22no—
166#3715—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C22×#67—61no—
175#1009—64no—
176#1009—64no—
177C2×#239—61no—
178#1004—64no—
179#1004—64no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—61no—
183C2×#237C2×D311yescharacteristic, complemented
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—61no—
195C2×#235C2×D311yescharacteristic
196C22×D12—31no—
197C22×D12—31no—
198C22×D12C2×D311yescharacteristic
199C2×C3×D8—31no—
200C2×C3×D8—31no—
201C3×C22⋊Q8—31no—
202C3×C22⋊Q8—31no—
203C3×C22⋊Q8—61no—
204C3×#121—21no—
205C3×#121—31no—
206C3×#121—61no—
207C3×#121—61no—
208C3×#121—61no—
209C3×#121C2×D311yescharacteristic, complemented
210C3×#121C2×D311yescharacteristic, complemented
211C2×C3×C4⋊C4—31no—
212#950—64no—
213#949—64no—
214C2×#216—31no—
215C2×#215—31no—
216C2×#215—31no—
217C2×#215—31no—
218#939—21no—
219#938—21no—
220#938C2×D311yescharacteristic, complemented
221C2×#214—31no—
222C2×#214—31no—
223C2×#214—31no—
224C2×#214—31no—
225C2×#214—61no—
226C2×#213—31no—
227C2×#213—31no—
228C2×#213—61no—
229C2×#213C2×D311yescharacteristic, complemented
230C2×#213C2×D311yescharacteristic, complemented
231#924C2×D311yescharacteristic, complemented
232C2×#208—31no—
233C22×C3⋊C8—31no—
234#912—64no—
235#911—64no—
236C2×Dic12—31no—
237C2×#204—31no—
238C2×ΓL(1,𝔽25)—31no—
239C2×D3×C8—31no—
240#897C2×D311yescharacteristic, complemented
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242#884—21no—
243#878—21no—
244C3×#102—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#832—31no—
248#832—31no—
249#830—31no—
250#830—31no—
251#830—31no—
252#830—31no—
253#830—61no—
254#830C2×D311yescharacteristic, complemented
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258#816—31no—
259#810—31no—
260#810—31no—
261#810—31no—
262#810—61no—
263#809—31no—
264#809—31no—
265#809—31no—
266#809—31no—
267#809—31no—
268#809—61no—
269#809C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3⋊D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—24no—
277C22×C3×D3—81no—
278C22×C3×D3—81no—
279C22×C3×D3C2×D411yescharacteristic
280C22×C3×D3C2×D411yescharacteristic
281C2×D32—24no—
282C2×D32—24no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C32×D4—21no—
288C32×D4—21no—
289C32×D4—81no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C2×D411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295#638—24no—
296C2×C3⋊Dic3—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)C2×D412yes—
299C4×C3⋊D3—24no—
300#634—21no—
301#634C2×D412yes—
302C3×#67—22no—
303C3×#67—22no—
304C3×#67—42no—
305C3×#67—81no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—42no—
309C2×C3×Dic3C2×D411yescharacteristic
310C2×C3×Dic3C2×D411yescharacteristic
311C3×D12—24no—
312C3×D12—22no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12C2×D412yes—
316C3×D12C2×D412yes—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—81no—
320C3×C4×D3C2×D412yes—
321C3×C4×D3C2×D412yes—
322C3×Dic6—22no—
323C3×Dic6—21no—
324C3×Dic6—21no—
325#626—24no—
326#626—24no—
327#625—24no—
328#625—24no—
329D3×Dic3—24no—
330D3×Dic3—24no—
331C3⋊(C3⋊C8)—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—31no—
339#452—91no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—31no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C24×C3—61no—
351C23×D3—21no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C3×#41—62no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C2×C3×Q8—31no—
361C2×C3×Q8—31no—
362C2×C3×D4—21no—
363C2×C3×D4—21no—
364C2×C3×D4—21no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—41no—
371C2×C3×D4—62no—
372C2×C3×D4—62no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D311yescharacteristic
378C22×C3×C4—21no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—61no—
382C22×C3×C4—61no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C2×#67—21no—
386C2×#67—21no—
387C2×#67—68no—
388C2×#67—68no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—61no—
393C2×#67—61no—
394C2×#67—61no—
395C2×#67—61no—
396C2×#67—61no—
397C2×#67—121no—
398C2×#67#6711yescharacteristic
399C2×#67#6711yescharacteristic
400C22×Dic3—21no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403#239—68no—
404#237—22no—
405#237—22no—
406#237—34no—
407#237—68no—
408#237—62no—
409#237—62no—
410#237—62no—
411D3×D4—34no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—68no—
415D3×D4—68no—
416D3×D4—68no—
417D3×D4—68no—
418D3×D4—62no—
419#235—22no—
420#235—22no—
421#235—34no—
422#235—62no—
423#235—62no—
424#235—62no—
425#235—62no—
426#235—62no—
427#235—62no—
428#235—62no—
429#235—122no—
430#235—122no—
431C2×D12—21no—
432C2×D12—22no—
433C2×D12—22no—
434C2×D12—31no—
435C2×D12—31no—
436C2×D12—34no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—62no—
440C2×D12—61no—
441C2×D12—61no—
442C2×D12—62no—
443C2×D12#6711yescharacteristic
444C2×D12C22×D311yescharacteristic
445C2×D12C22×D311yescharacteristic
446C2×C4×D3—21no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—121no—
452C2×C4×D3C22×D311yescharacteristic
453C2×C4×D3C22×D311yescharacteristic
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—61no—
457C2×Dic6#6711yescharacteristic
458C2×Dic6C22×D311yescharacteristic
459C3×D8—62no—
460C3×D8—62no—
461C2×C3×C8—31no—
462C2×C3×C8—31no—
463C3×C4⋊C4—21no—
464C3×C4⋊C4—31no—
465C3×C4⋊C4—61no—
466C3×C4⋊C4—61no—
467C3×C4⋊C4—61no—
468C3×C4⋊C4C22×D311yescharacteristic
469C3×C4⋊C4C22×D311yescharacteristic
470C3×C22⋊C4—21no—
471C3×C22⋊C4—21no—
472C3×C22⋊C4—41no—
473C3×C22⋊C4—61no—
474C3×C22⋊C4—61no—
475C3×C22⋊C4—61no—
476#217—21no—
477#217—21no—
478#216—62no—
479#215—62no—
480#215—62no—
481#215—62no—
482#214—62no—
483#214—62no—
484#214—62no—
485#214—62no—
486#214—122no—
487#213—22no—
488#213—22no—
489#213—62no—
490#213—62no—
491#213—122no—
492(C2×D3)⋊C4—21no—
493C4⋊Dic3—21no—
494C4⋊Dic3C22×D311yescharacteristic
495Dic3⋊C4—21no—
496Dic3⋊C4—21no—
497#208—62no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—62no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507Dic12—62no—
508#204—62no—
509ΓL(1,𝔽25)—62no—
510D3×C8—62no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32—41no—
515C22×C32—41no—
516C22×C32—41no—
517C22×C32C22×D411yescharacteristic
518C2×C3⋊D3—22no—
519C2×C3⋊D3—41no—
520C2×C3⋊D3—41no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—84no—
533C2×C3×D3#12012yes—
534D32—84no—
535D32—84no—
536C32×C4—21no—
537C32×C4—41no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
540C3⋊Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—41no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—31no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—91no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—31no—
567C2×D8—31no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—91no—
571C22⋊Q8—31no—
572C22⋊Q8—31no—
573C22⋊Q8—61no—
574#121—31no—
575#121—61no—
576#121—61no—
577#121—61no—
578#121D3211yescharacteristic, complemented
579C2×C4⋊C4—31no—
580#103—91no—
581#103—91no—
582#102—31no—
583#102—31no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—21no—
595C23×C3—31no—
596C23×C3—31no—
597C23×C3—41no—
598C23×C3—64no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—241no—
602C23×C3—241no—
603C23×C3D3×D411yescharacteristic
604C23×C3C2×#6711yescharacteristic
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—24no—
608C22×D3—64no—
609C22×D3—64no—
610C22×D3—64no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—64no—
614C22×D3—81no—
615C22×D3—81no—
616C22×D3—121no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3C2×#6711yescharacteristic
626C22×D3C2×#6711yescharacteristic
627C3×Q8—62no—
628C3×Q8—61no—
629C3×Q8—61no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—21no—
633C3×D4—21no—
634C3×D4—32no—
635C3×D4—32no—
636C3×D4—41no—
637C3×D4—41no—
638C3×D4—62no—
639C3×D4—64no—
640C3×D4—62no—
641C3×D4—62no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—81no—
645C3×D4—81no—
646C3×D4—82no—
647C3×D4—122no—
648C3×D4—241no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—31no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—31no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—122no—
669C2×C3×C4—241no—
670C2×C3×C4D3×D411yescharacteristic
671C2×C3×C4C2×#6711yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674#67—22no—
675#67—22no—
676#67—42no—
677#67—64no—
678#67—64no—
679#67—64no—
680#67—64no—
681#67—64no—
682#67—64no—
683#67—64no—
684#67—64no—
685#67—81no—
686#67—124no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—42no—
690C2×Dic3—64no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—64no—
694C2×Dic3—121no—
695C2×Dic3C2×#6711yescharacteristic
696C2×Dic3C2×#6711yescharacteristic
697D12—24no—
698D12—22no—
699D12—21no—
700D12—21no—
701D12—32no—
702D12—32no—
703D12—62no—
704D12—64no—
705D12—64no—
706D12—61no—
707D12—61no—
708D12—121no—
709D12D3×D412yes—
710D12D3×D412yes—
711C4×D3—21no—
712C4×D3—21no—
713C4×D3—64no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—81no—
718C4×D3—124no—
719C4×D3D3×D412yes—
720C4×D3D3×D412yes—
721Dic6—22no—
722Dic6—21no—
723Dic6—21no—
724Dic6—32no—
725Dic6—32no—
726Dic6—62no—
727Dic6—61no—
728Dic6—61no—
729Dic6—121no—
730C3×C8—61no—
731C3×C8—61no—
732C3⋊C8—21no—
733C3⋊C8—21no—
734C3⋊C8—61no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—121no—
739C3⋊C8—121no—
740C2×C32—41no—
741C2×C32—81no—
742C2×C32C2×#12011yescharacteristic
743C2×C32#57611yescharacteristic
744C2×C32#57711yescharacteristic
745C3⋊D3—42no—
746C3×D3—22no—
747C3×D3—41no—
748C3×D3—42no—
749C3×D3—42no—
750C24—61no—
751C24—181no—
752C24—181no—
753#41—62no—
754#41—62no—
755#41—62no—
756#41—62no—
757#41—94no—
758#41—182no—
759#41—182no—
760#41—182no—
761#41—182no—
762#41—182no—
763#41—188no—
764C2×Q8—31no—
765C2×Q8—31no—
766C2×Q8—91no—
767C2×D4—21no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—31no—
773C2×D4—62no—
774C2×D4—62no—
775C2×D4—61no—
776C2×D4—61no—
777C2×D4—61no—
778C2×D4—94no—
779C2×D4—91no—
780C2×D4—182no—
781C2×D4—181no—
782C2×D4—181no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—188no—
786C2×D4—188no—
787C2×D4—188no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4C2×D3211yescharacteristic
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4—181no—
799C22×C4C2×D3211yescharacteristic
800Q16—182no—
801SD16—182no—
802SD16—182no—
803SD16—182no—
804SD16—182no—
805D8—62no—
806D8—62no—
807D8—182no—
808M16—182no—
809C2×C8—31no—
810C2×C8—31no—
811C2×C8—91no—
812C2×C8—91no—
813C2×C8—182no—
814C4⋊C4—31no—
815C4⋊C4—61no—
816C4⋊C4—61no—
817C4⋊C4—61no—
818C4⋊C4C2×D3211yescharacteristic
819C22⋊C4—21no—
820C22⋊C4—61no—
821C22⋊C4—61no—
822C22⋊C4—61no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—32no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—61no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—61no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—244no—
855C22×C3C2×D3×D411yescharacteristic
856C22×C3C22×#6711yescharacteristic
857C2×D3—21no—
858C2×D3—21no—
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—21no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—84no—
871C2×D3—122no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—241no—
877C2×D3—241no—
878C2×D3—244no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3#93712yes—
883C3×C4—21no—
884C3×C4—21no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—32no—
888C3×C4—41no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—61no—
892C3×C4—81no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897C3×C4C2×D3×D411yescharacteristic
898C3×C4C2×D3×D411yescharacteristic
899Dic3—21no—
900Dic3—41no—
901Dic3—41no—
902Dic3—62no—
903Dic3—62no—
904Dic3—122no—
905Dic3#93712yes—
906C32#301211yescharacteristic, complemented, Sylow
907C23—21no—
908C23—31no—
909C23—31no—
910C23—64no—
911C23—61no—
912C23—61no—
913C23—184no—
914C23—184no—
915C23—181no—
916C23—241no—
917C23—241no—
918C23—721no—
919C23—721no—
920C23—721no—
921C23—721no—
922C23D3×#6711yescharacteristic
923Q8—62no—
924Q8—61no—
925Q8—61no—
926Q8—92no—
927Q8—181no—
928D4—21no—
929D4—21no—
930D4—32no—
931D4—32no—
932D4—62no—
933D4—64no—
934D4—62no—
935D4—62no—
936D4—61no—
937D4—61no—
938D4—81no—
939D4—92no—
940D4—122no—
941D4—184no—
942D4—184no—
943D4—184no—
944D4—184no—
945D4—184no—
946D4—181no—
947D4—241no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—31no—
952C2×C4—32no—
953C2×C4—32no—
954C2×C4—31no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—122no—
960C2×C4—184no—
961C2×C4—184no—
962C2×C4—184no—
963C2×C4—181no—
964C2×C4—241no—
965C2×C4D3×#6711yescharacteristic
966C2×C4C22×D3211yescharacteristic
967C8—61no—
968C8—61no—
969C8—181no—
970C8—181no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—41no—
975C2×C3—41no—
976C2×C3—62no—
977C2×C3—81no—
978C2×C3—81no—
979C2×C3—81no—
980C2×C3—121no—
981C2×C3—122no—
982C2×C3—122no—
983C2×C3—161no—
984C2×C3D3×#12011yescharacteristic
985C2×C3#575711yescharacteristic
986C2×C3#577511yescharacteristic
987C2×C3C2×#93711yescharacteristic
988C2×C3#583511yescharacteristic
989C2×C3#583711yescharacteristic
990D3—22no—
991D3—42no—
992D3—42no—
993D3—41no—
994D3—122no—
995D3—122no—
996D3—242no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—32no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—61no—
1005C22—61no—
1006C22—61no—
1007C22—61no—
1008C22—61no—
1009C22—62no—
1010C22—62no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—182no—
1016C22—244no—
1017C22—361no—
1018C22—361no—
1019C22—724no—
1020C22—724no—
1021C22C2×D3×#6711yescharacteristic
1022C4—21no—
1023C4—32no—
1024C4—41no—
1025C4—61no—
1026C4—121no—
1027C4—121no—
1028C4—182no—
1029C4D32×D411yescharacteristic
1030C4D32×D411yescharacteristic
1031C3—21no—
1032C3#8000511yescharacteristic, complemented
1033C3#8342411yescharacteristic, complemented
1034C2—41no—
1035C2—62no—
1036C2—81no—
1037C2—121no—
1038C2—122no—
1039C2—122no—
1040C2—362no—
1041C2#1059509611yescharacteristic
1042C2D3×#93711yescharacteristic
1043C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C3×#5608C2semidirect
3. C2×#63933C2semidirect
4. C2×#63925C2semidirect
5. #10592736C2semidirect
6. C3×#5036C2semidirect
7. #10591519C2semidirect
8. #10591515C2semidirect
9. #10591184C2semidirect
10. #10591169C2semidirect
11. #10591145C2semidirect
12. #10590614C2semidirect
13. #10590607C2semidirect
14. #10590596C2semidirect
15. D3×#809C2semidirect
19. C2×C3×#237C22semidirect
32. C32×#121C22semidirect
33. C2×#3754C22semidirect
34. C2×#3753C22semidirect
37. C3×#938C22semidirect
38. C2×C3×#213C22semidirect
39. C2×C3×#213C22semidirect
40. C3×#924C22semidirect
41. C3×#897C22semidirect
42. C3×D3×C4⋊C4C22semidirect
47. C2×#3719C22semidirect
48. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3715C22semidirect
51. C2×#3711C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63657C22semidirect
54. #63637C22semidirect
55. #63636C22semidirect
56. C3×#830C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
72. #5608D3semidirect
87. #5036D3semidirect
140. D3×D12D4semidirect
145. #3795D4semidirect
183. C2×#237C2×D3semidirect
209. C3×#121C2×D3semidirect
210. C3×#121C2×D3semidirect
220. #938C2×D3semidirect
229. C2×#213C2×D3semidirect
230. C2×#213C2×D3semidirect
231. #924C2×D3semidirect
240. #897C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
254. #830C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
578. #121D32semidirect
906. C32#3012semidirect
1032. C3#80005semidirect
1033. C3#83424semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C3×#56082
C2×#639332
C2×#639252
#105927362
C3×#50362
#105915192
#105915152
#105911842
#105911692
#105911452
#105906142
#105906072
#105905962
D3×#8092
#834243
#800053