Finite Group Databasebeta

← #11866346

Subgroups — #11866346

Order 1152.

1036 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic, complemented
2#10595426C211yesmaximal, characteristic
3#10595347C211yesmaximal, characteristic, complemented
4C2×D3×#215C211yesmaximal, characteristic, complemented
5#10592884C211yesmaximal, characteristic, complemented
6C3×#5185C211yesmaximal, characteristic, complemented
7#10591622C211yesmaximal, characteristic, complemented
8#10591617C211yesmaximal, characteristic, complemented
9#10591579C211yesmaximal, characteristic, complemented
10#10591578C211yesmaximal, characteristic, complemented
11#10591556C211yesmaximal, characteristic, complemented
12#10590939C211yesmaximal, characteristic, complemented
13#10590876C211yesmaximal, characteristic, complemented
14#10590799C211yesmaximal, characteristic, complemented
15#10590695C211yesmaximal, characteristic, complemented
16#83969—31nomaximal
17#80600—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic, complemented
22#64156C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C3×#947C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#918—24no—
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33D3×#215—24no—
34#63922—21no—
35#63922—21no—
36#63914C2211yescharacteristic
37#63911C2211yescharacteristic
38#63906—21no—
39#63906—21no—
40#63855—21no—
41#63855C2211yescharacteristic
42#63843—21no—
43#63843C2211yescharacteristic, complemented
44Dic3×Dic6—21no—
45Dic3×Dic6C2211yescharacteristic, complemented
46#63841—21no—
47#63841C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63648C2211yescharacteristic
53#63641C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64#5830—31no—
65#5812—31no—
66C22×#215—31no—
67C2×#918D311yescharacteristic, complemented
68C2×D3×SD16—31no—
69#5674—31no—
70#5572—31no—
71C3×#464—31no—
72#5233—31no—
73#5185—31no—
74#5185—31no—
75#5185—31no—
76#5185—31no—
77#5185—61no—
78#5185D311yescharacteristic, complemented
79#5163—31no—
80#5163—31no—
81#5163—31no—
82#5163—31no—
83#5163—31no—
84#5131—31no—
85#5119—31no—
86#5054—31no—
87#5027—31no—
88#4848—31no—
89#4839—31no—
90#4804—31no—
91#4798—31no—
92#4770—31no—
93#4762—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C3×#239—22no—
99C3×#239—22no—
100C3×D3×Q8—22no—
101C3×D3×Q8D414yescomplemented
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#625—21no—
114C2×#625—21no—
115D3×D12—22no—
116D3×D12—22no—
117C32×Q16—22no—
118C2×C32×C8C2311yescharacteristic
119#3755—22no—
120#3752—21no—
121#3752—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#216—22no—
128C3×#215—22no—
129C3×#215—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139C3×ΓL(1,𝔽25)—22no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3D411yescharacteristic
143Dic3⋊Dic3D411yescharacteristic
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3D411yescharacteristic
146(C2×D3)⋊Dic3D411yescharacteristic
147Dic32—21no—
148Dic32—21no—
149Dic32—21no—
150#3717—22no—
151#3715—22no—
152D3×C3⋊C8—22no—
153#3043—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×D4—31no—
159C22×D12—31no—
160C3×#137—64no—
161C2×C3×Q16—21no—
162C2×C3×Q16—31no—
163C2×C3×Q16C2×D311yescharacteristic, complemented
164C2×C3×Q16C2×D311yescharacteristic, complemented
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×M16—31no—
169C3×#124—31no—
170C3×C4×Q8—31no—
171#947—31no—
172#947—31no—
173#947—61no—
174#947C2×D311yescharacteristic
175Q8×Dic3—31no—
176Q8×Dic3—31no—
177Q8×Dic3—31no—
178Q8×Dic3—31no—
179Q8×Dic3—61no—
180Q8×Dic3—61no—
181Q8×Dic3—61no—
182Q8×Dic3C2×D311yescharacteristic, complemented
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—61no—
189C2×#215—64no—
190C2×#215C2×D311yescharacteristic
191C2×#215C2×D311yescharacteristic, complemented
192#940—31no—
193#940—31no—
194#940—31no—
195#937—61no—
196#937—61no—
197C2×#214—31no—
198#930—61no—
199#930—61no—
200#926—31no—
201#926—31no—
202#926—61no—
203#926—61no—
204C22×C3⋊C8—31no—
205#918—24no—
206D3×SD16—64no—
207C2×#204—31no—
208C2×#204C2×D311yescharacteristic, complemented
209C2×ΓL(1,𝔽25)C2×D311yescharacteristic
210C2×D3×C8—31no—
211#892—31no—
212#892—61no—
213#887—31no—
214#887—61no—
215#884—61no—
216#884—61no—
217#882—61no—
218#882—61no—
219#874—31no—
220#872—31no—
221#872—61no—
222C4×Dic6—31no—
223C4×Dic6—61no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#835—61no—
230#835C2×D311yescharacteristic, complemented
231#832—31no—
232#832—31no—
233#832—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—61no—
240#821C2×D311yescharacteristic
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#809—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—42no—
256C2×D32—81no—
257C2×D32—81no—
258C32×Q8—21no—
259C32×Q8—21no—
260C32×Q8—21no—
261C32×Q8C2×D412yes—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—42no—
280C3×C4×D3—24no—
281C3×C4×D3—42no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—21no—
285C3×Dic6—24no—
286C3×Dic6C2×D412yes—
287#626—42no—
288#626—81no—
289#626—81no—
290#625—81no—
291#625—81no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—31no—
297C22×SD16—91no—
298#535—91no—
299#519—91no—
300#464—31no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—91no—
305#460—91no—
306#460—91no—
307#460—91no—
308#424—91no—
309#418—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—21no—
317C2×C3×Q8—34no—
318C2×C3×Q8—31no—
319C2×C3×Q8—61no—
320C2×C3×Q8—62no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×D4—31no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338#239—22no—
339#239—22no—
340D3×Q8—22no—
341D3×Q8#6714yescomplemented
342D3×D4—62no—
343D3×D4—62no—
344C2×D12—21no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—61no—
348C2×D12—62no—
349C2×D12—62no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12C22×D311yescharacteristic
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—21no—
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6—21no—
359C2×Dic6C22×D311yescharacteristic
360C3×Q16—22no—
361C3×Q16—22no—
362C3×Q16—42no—
363C3×Q16—62no—
364C3×SD16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×M16—62no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—31no—
374C3×C4⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C42—31no—
378C3×C42—61no—
379#217—31no—
380#217—31no—
381#217—61no—
382#216—22no—
383#215—22no—
384#215—22no—
385#215—62no—
386#215—62no—
387#215—62no—
388#215—62no—
389#215—122no—
390#214—62no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—121no—
401(C2×D3)⋊C4—121no—
402C4⋊Dic3—21no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—121no—
413C4⋊Dic3C22×D311yescharacteristic
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418C4×Dic3—21no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3—121no—
431C4×Dic3C22×D311yescharacteristic
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438#204—22no—
439#204—62no—
440ΓL(1,𝔽25)—22no—
441D3×C8—62no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—22no—
457C32×C4—41no—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—41no—
463C3×Dic3—22no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—31no—
470C22×D4—91no—
471#137—64no—
472C2×Q16—31no—
473C2×Q16D3211yescharacteristic, complemented
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—184no—
481C2×M16—31no—
482C22×C8—91no—
483#127—91no—
484#127—91no—
485#124—31no—
486#124—91no—
487#121—181no—
488#121—181no—
489#120—181no—
490#120—181no—
491C4×Q8—31no—
492C4×Q8—91no—
493C4×Q8—91no—
494C4×Q8—91no—
495C4×Q8—181no—
496C4×Q8—181no—
497#117—91no—
498#117—91no—
499#117—181no—
500#117—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—91no—
507#102—31no—
508#102—91no—
509#102—91no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—121no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3D3×D411yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—21no—
534C3×Q8—22no—
535C3×Q8—32no—
536C3×Q8—41no—
537C3×Q8—41no—
538C3×Q8—41no—
539C3×Q8—64no—
540C3×Q8—61no—
541C3×Q8D3×D412yes—
542C3×Q8C2×#6712yes—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—61no—
547C3×D4—122no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—31no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—64no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—122no—
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—122no—
567#67—241no—
568#67—241no—
569#67—241no—
570#67—241no—
571#67—241no—
572#67—241no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—121no—
584C2×Dic3D3×D411yescharacteristic
585C2×Dic3D3×D411yescharacteristic
586C2×Dic3D3×D411yescharacteristic
587D12—21no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—42no—
592D12—61no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—121no—
597D12—121no—
598D12—122no—
599D12—241no—
600D12—241no—
601C4×D3—24no—
602C4×D3—42no—
603C4×D3#23712yes—
604C4×D3C2×#6712yes—
605Dic6—21no—
606Dic6—24no—
607Dic6C2×#6712yes—
608C3×C8—21no—
609C3×C8—21no—
610C3×C8—41no—
611C3×C8—61no—
612C3×C8—61no—
613C3⋊C8—21no—
614C3⋊C8—21no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—121no—
618C2×C32C2×#12111yescharacteristic
619C2×C32#57711yescharacteristic
620C2×C32#57711yescharacteristic
621C3⋊D3—81no—
622C3×D3—22no—
623C3×D3—81no—
624C3×D3—81no—
625C24—181no—
626#41—62no—
627#41—62no—
628C2×Q8—34no—
629C2×Q8—31no—
630C2×Q8—61no—
631C2×Q8—62no—
632C2×Q8C2×D3211yescharacteristic
633C2×Q8C2×D3211yescharacteristic
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—91no—
638C2×D4—182no—
639C2×D4—182no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C22×C4—31no—
646C22×C4—61no—
647C22×C4—61no—
648Q16—22no—
649Q16—62no—
650SD16—62no—
651SD16—62no—
652SD16—62no—
653SD16—182no—
654SD16—182no—
655SD16—182no—
656M16—62no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—91no—
660C2×C8—182no—
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—91no—
673C22⋊C4—91no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C42—31no—
678C42—61no—
679C42—91no—
680C42—181no—
681C42—181no—
682C42—181no—
683C42—181no—
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C2×D3×D411yescharacteristic
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3—244no—
714C2×D3—244no—
715C2×D3#93912yes—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—32no—
721C3×C4—42no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—62no—
727C3×C4—81no—
728C3×C4—121no—
729C3×C4C2×D3×D411yescharacteristic
730C3×C4C2×#23711yescharacteristic
731C3×C4D3×#4111yescharacteristic
732C3×C4C22×#6711yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—22no—
736Dic3—41no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—121no—
745Dic3—241no—
746Dic3#93912yes—
747C32#304311yescharacteristic, complemented, Sylow
748C23—31no—
749C23—61no—
750C23—61no—
751C23—181no—
752C23—362no—
753C23—721no—
754C23—721no—
755Q8—21no—
756Q8—21no—
757Q8—21no—
758Q8—32no—
759Q8—64no—
760Q8—61no—
761Q8D3×#6712yes—
762D4—61no—
763D4—61no—
764D4—61no—
765D4—61no—
766D4—122no—
767D4—181no—
768D4—181no—
769D4—362no—
770D4—721no—
771D4—721no—
772D4—721no—
773D4—721no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—31no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—64no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—91no—
785C2×C4—91no—
786C2×C4—122no—
787C2×C4—181no—
788C2×C4C22×D3211yescharacteristic
789C8—21no—
790C8—61no—
791C8—61no—
792C8—181no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—62no—
797C2×C3—241no—
798C2×C3—241no—
799C2×C3D3×#12111yescharacteristic
800C2×C3#577011yescharacteristic
801C2×C3#577811yescharacteristic
802C2×C3#577811yescharacteristic
803C2×C3#577811yescharacteristic
804C2×C3C2×#93911yescharacteristic
805D3—22no—
806D3—81no—
807D3—81no—
808D3—241no—
809D3—241no—
810D3—481no—
811C22—32no—
812C22—61no—
813C22—61no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—361no—
821C22—361no—
822C22—361no—
823C22—724no—
824C22D32×D411yescharacteristic
825C4—22no—
826C4—32no—
827C4—41no—
828C4—61no—
829C4—61no—
830C4—62no—
831C4—121no—
832C4—181no—
833C4—181no—
834C4—361no—
835C4D3×#23711yescharacteristic
836C4C2×D3×#6711yescharacteristic
837C3—21no—
838C3#8060011yescharacteristic, complemented
839C3#8396911yescharacteristic, complemented
840C2—62no—
841C2—241no—
842C2—241no—
843C2—721no—
844C2#1059476711yescharacteristic
845C2#1059477011yescharacteristic
846C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595426C2
hypercenterC2×Q16D32
hypocenterC32#3043
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#918C2semidirect
3. #10595347C2semidirect
4. C2×D3×#215C2semidirect
5. #10592884C2semidirect
6. C3×#5185C2semidirect
7. #10591622C2semidirect
8. #10591617C2semidirect
9. #10591579C2semidirect
10. #10591578C2semidirect
11. #10591556C2semidirect
12. #10590939C2semidirect
13. #10590876C2semidirect
14. #10590799C2semidirect
15. #10590695C2semidirect
21. C2×C32×Q16C22semidirect
23. Q8×C3⋊Dic3C22semidirect
26. C3×Q8×Dic3C22semidirect
27. C2×C3×#216C22semidirect
29. C2×C3×#215C22semidirect
31. C2×C3×#204C22semidirect
43. #63843C22semidirect
45. Dic3×Dic6C22semidirect
51. #63662C22semidirect
53. #63641C22semidirect
54. C3×#835C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
67. C2×#918D3semidirect
78. #5185D3semidirect
101. C3×D3×Q8D4semidirect
163. C2×C3×Q16C2×D3semidirect
164. C2×C3×Q16C2×D3semidirect
182. Q8×Dic3C2×D3semidirect
183. C2×#216C2×D3semidirect
191. C2×#215C2×D3semidirect
208. C2×#204C2×D3semidirect
230. #835C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
341. D3×Q8#67semidirect
473. C2×Q16D32semidirect
747. C32#3043semidirect
838. C3#80600semidirect
839. C3#83969semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
#105954262
#105953472
C2×D3×#2152
#105928842
C3×#51852
#105916222
#105916172
#105915792
#105915782
#105915562
#105909392
#105908762
#105907992
#105906952
#839693
#806003