Finite Group Databasebeta

← #11866144

Subgroups — #11866144

Order 1152.

1056 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×#914C211yesmaximal, characteristic
2Dic3×#239C211yesmaximal, characteristic, complemented
3C2×#63943C211yesmaximal, characteristic, complemented
4D3×#936C211yesmaximal, characteristic, complemented
5#10592865C211yesmaximal, characteristic, complemented
6C3×#5166C211yesmaximal, characteristic, complemented
7#10591612C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10591434C211yesmaximal, characteristic, complemented
10#10591431C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590948C211yesmaximal, characteristic, complemented
13#10590755C211yesmaximal, characteristic, complemented
14#10590751C211yesmaximal, characteristic, complemented
15#10590663C211yesmaximal, characteristic, complemented
16#83933—31nomaximal
17#80599—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24#64145C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#936C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#914—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33D3×#217—21no—
34D3×#217—21no—
35#63959—21no—
36#63959—21no—
37#63943—24no—
38#63898—21no—
39#63898C2211yescharacteristic, complemented
40Dic3×D12—21no—
41Dic3×D12C2211yescharacteristic, complemented
42C4×D3×Dic3—21no—
43C4×D3×Dic3C2211yescharacteristic
44#63863C2211yescharacteristic
45#63860C2211yescharacteristic
46#63841—21no—
47#63841C2211yescharacteristic
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic
51#63659C2211yescharacteristic
52#63643C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63562C2211yescharacteristic
63C2×C3×AGL(1,ℤ/8)—31no—
64Dic3×#41—31no—
65C2×#951—31no—
66C2×#936—31no—
67C2×#918—31no—
68C2×#914D311yescharacteristic
69D3×#124—31no—
70C4×#239—31no—
71C3×#464—31no—
72#5215—31no—
73#5185—31no—
74#5166—31no—
75#5166—31no—
76#5166—31no—
77#5166—31no—
78#5166—61no—
79#5166D311yescharacteristic, complemented
80#5153—31no—
81#5153—31no—
82#5153—31no—
83#5153—31no—
84#5120—31no—
85#5118—31no—
86#5057—31no—
87#5028—31no—
88#4844—31no—
89#4837—31no—
90#4819—31no—
91#4802—31no—
92#4787—31no—
93#4770—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C3×#239—22no—
100C3×#239D414yes—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3D411yescharacteristic
114C2×D3×Dic3D411yescharacteristic
115D3×Dic6—22no—
116D3×Dic6—22no—
117C32×SD16—22no—
118C2×C32×C8C2311yescharacteristic
119#3757—21no—
120#3757—21no—
121#3756—22no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217—21no—
128C3×#217—21no—
129C3×#216—22no—
130C3×#215—22no—
131C3×#213—22no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—22no—
139C3×ΓL(1,𝔽25)—22no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32—21no—
148Dic32D411yescharacteristic
149Dic32D411yescharacteristic
150#3716—22no—
151#3715—22no—
152#3711—22no—
153#3040—91noSylow
154C2×C3×#41—31no—
155C22×C3×D4—31no—
156C2×#239C2×D311yescharacteristic
157C2×D3×Q8—31no—
158C2×D3×D4C2×D311yescharacteristic
159C22×Dic6—31no—
160C3×AGL(1,ℤ/8)—64no—
161C2×C3×Q16—31no—
162C2×C3×SD16—21no—
163C2×C3×SD16—31no—
164C2×C3×SD16C2×D311yescharacteristic
165C2×C3×SD16C2×D311yescharacteristic
166C2×C3×D8—31no—
167C2×C3×D8—31no—
168C2×C3×M16—31no—
169C3×#124—31no—
170C3×C4×Q8—31no—
171C2×#217—61no—
172C2×#217—61no—
173#951—64no—
174#947—31no—
175Q8×Dic3—31no—
176Q8×Dic3—31no—
177Q8×Dic3—61no—
178Q8×Dic3C2×D311yescharacteristic, complemented
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—61no—
182C2×#216C2×D311yescharacteristic, complemented
183C2×#215—31no—
184C2×#215C2×D311yescharacteristic
185#936—31no—
186#936—31no—
187#936—31no—
188#936—31no—
189#936—61no—
190#936—61no—
191#936—61no—
192#936C2×D311yescharacteristic
193D4×Dic3—31no—
194D4×Dic3—31no—
195D4×Dic3—61no—
196D4×Dic3—61no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#213C2×D311yescharacteristic
200#926—31no—
201#926—61no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—61no—
204C2×#208—31no—
205#918—64no—
206#914—24no—
207C2×D24C2×D311yescharacteristic
208C2×#204—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×ΓL(1,𝔽25)C2×D311yescharacteristic
211#893—31no—
212#893—61no—
213#892—31no—
214#892—61no—
215#885—61no—
216#885—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#875—31no—
220C4×D12—31no—
221C4×D12—61no—
222C42×D3—31no—
223C42×D3—61no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—31no—
227#835—31no—
228#832—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic
234#821—31no—
235#816—31no—
236#816—31no—
237#816—31no—
238#816—31no—
239#816—61no—
240#816C2×D311yescharacteristic, complemented
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—42no—
255C22×C3×D3—42no—
256C22×C3×D3—42no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8C2×D412yes—
260C32×D4—21no—
261C32×D4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2411yescharacteristic
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268#634—21no—
269#634—21no—
270C3×#67—42no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—24no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12C2×D412yes—
281C3×C4×D3—24no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—21no—
285C3×Dic6—21no—
286#627—42no—
287D3×Dic3—41no—
288D3×Dic3—41no—
289D3×Dic3—42no—
290D3×Dic3—42no—
291D3×Dic3—42no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—91no—
297C2×AGL(1,ℤ/8)—31no—
298C2×#124—91no—
299C4×#41—91no—
300#464—31no—
301#464—91no—
302#464—91no—
303#464—91no—
304#463—91no—
305#463—91no—
306#463—91no—
307#463—91no—
308#423—91no—
309#419—91no—
310#418—91no—
311C24×C3—61no—
312C23×D3—21no—
313C3×#41—34no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×D4—21no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4—62no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C2×#67—21no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336#239—22no—
337#239#6714yes—
338D3×Q8—62no—
339D3×Q8—62no—
340D3×D4—22no—
341D3×D4—22no—
342C2×D12—21no—
343C2×D12C22×D311yescharacteristic
344C2×D12C22×D311yescharacteristic
345C2×C4×D3—21no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—62no—
356C2×Dic6—62no—
357C2×Dic6—61no—
358C2×Dic6—61no—
359C2×Dic6C22×D311yescharacteristic
360C3×Q16—62no—
361C3×SD16—22no—
362C3×SD16—22no—
363C3×SD16—42no—
364C3×SD16—62no—
365C3×D8—62no—
366C3×D8—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—21no—
380#217—21no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—61no—
390#217—61no—
391#217—61no—
392#217—121no—
393#217—121no—
394#216—22no—
395#216—62no—
396#216—62no—
397#216—122no—
398#215—22no—
399#215—62no—
400#214—62no—
401#214—62no—
402#213—22no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410C4⋊Dic3—21no—
411C4⋊Dic3—31no—
412C4⋊Dic3—31no—
413C4⋊Dic3—61no—
414C4⋊Dic3—61no—
415C4⋊Dic3—61no—
416C4⋊Dic3—121no—
417C4⋊Dic3C22×D311yescharacteristic
418C4×Dic3—21no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—31no—
424C4×Dic3—31no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3—121no—
431C4×Dic3C22×D311yescharacteristic
432#208—62no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—61no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438D24—22no—
439#204—62no—
440ΓL(1,𝔽25)—22no—
441ΓL(1,𝔽25)—62no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—84no—
455C2×C3×D3#12112yes—
456C32×C4—22no—
457C32×C4C22×D411yescharacteristic
458C32×C4C2×#4111yescharacteristic
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—41no—
462C3⋊Dic3—41no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—91no—
470C22×D4—31no—
471#137—184no—
472AGL(1,ℤ/8)—64no—
473C2×Q16—31no—
474C2×Q16—91no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16D3211yescharacteristic
479C2×D8—31no—
480C2×D8—31no—
481C2×M16—31no—
482C2×M16—91no—
483#124—31no—
484#124—91no—
485#124—91no—
486#124—91no—
487#124—181no—
488#124—181no—
489C4×Q8—31no—
490C4×Q8—91no—
491C4×D4—91no—
492C4×D4—91no—
493C4×D4—181no—
494C4×D4—181no—
495#117—91no—
496#117—181no—
497C2×C22⋊C4—181no—
498C2×C22⋊C4—181no—
499C2×C42—91no—
500C2×C42—181no—
501C4⋊C8—31no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8—91no—
505#103—31no—
506#103—91no—
507#103—91no—
508#103—91no—
509#102—31no—
510#102—91no—
511#102—91no—
512#102—91no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—31no—
516C23×C3—41no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—122no—
520C23×C3—122no—
521C23×C3—122no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—42no—
525C22×D3—42no—
526C22×D3—42no—
527C22×D3D3×D411yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—22no—
531C3×Q8—41no—
532C3×Q8—61no—
533C3×Q8—61no—
534C3×Q8D3×D412yes—
535C3×Q8C2×#6712yes—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—21no—
540C3×D4—32no—
541C3×D4—41no—
542C3×D4—41no—
543C3×D4—64no—
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—31no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—41no—
557C2×C3×C4—64no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—42no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3—122no—
580C2×Dic3—122no—
581C2×Dic3—122no—
582C2×Dic3D3×D411yescharacteristic
583C2×Dic3D3×D411yescharacteristic
584C2×Dic3D3×D411yescharacteristic
585D12—24no—
586D12—21no—
587D12—21no—
588D12—21no—
589D12C2×#6712yes—
590C4×D3—24no—
591C4×D3—121no—
592C4×D3—121no—
593C4×D3—122no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3#23712yes—
597C4×D3C2×#6712yes—
598Dic6—21no—
599Dic6—21no—
600Dic6—61no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—121no—
605Dic6—121no—
606Dic6—122no—
607Dic6—122no—
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×C32—81no—
619C2×C32C2×#12111yescharacteristic
620C2×C32#57511yescharacteristic
621C2×C32#57511yescharacteristic
622C3×D3—22no—
623C3×D3—42no—
624C3×D3—81no—
625C24—61no—
626#41—34no—
627#41—62no—
628C2×Q8—31no—
629C2×Q8—91no—
630C2×Q8—181no—
631C2×Q8—182no—
632C2×Q8—182no—
633C2×Q8C2×D3211yescharacteristic
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—61no—
637C2×D4—62no—
638C2×D4—62no—
639C2×D4—61no—
640C2×D4C2×D3211yescharacteristic
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—91no—
644C22×C4—91no—
645C22×C4—181no—
646C22×C4—181no—
647C22×C4—181no—
648Q16—62no—
649Q16—182no—
650SD16—22no—
651SD16—62no—
652SD16—182no—
653SD16—182no—
654D8—62no—
655D8—62no—
656M16—62no—
657M16—182no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—91no—
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—181no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C42—31no—
678C42—61no—
679C42—91no—
680C42—91no—
681C42—91no—
682C42—181no—
683C42—181no—
684C22×C3—21no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—62no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—244no—
704C22×C3C2×D3×D411yescharacteristic
705C22×C3C2×D3×D411yescharacteristic
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—22no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—84no—
715C2×D3#93912yes—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—32no—
721C3×C4—42no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4C2×D3×D411yescharacteristic
727C3×C4C2×#23711yescharacteristic
728C3×C4D3×#4111yescharacteristic
729C3×C4C22×#6711yescharacteristic
730Dic3—21no—
731Dic3—21no—
732Dic3—41no—
733Dic3—41no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3—241no—
746Dic3#93912yes—
747C32#304011yescharacteristic, complemented, Sylow
748C23—21no—
749C23—31no—
750C23—61no—
751C23—61no—
752C23—122no—
753C23—122no—
754C23—122no—
755Q8—21no—
756Q8—61no—
757Q8—61no—
758Q8—181no—
759Q8—181no—
760Q8—362no—
761Q8D3×#6712yes—
762D4—21no—
763D4—21no—
764D4—32no—
765D4—64no—
766D4—61no—
767D4—61no—
768D4—61no—
769D4—122no—
770C2×C4—21no—
771C2×C4—31no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—64no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—91no—
780C2×C4—91no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—361no—
784C2×C4—361no—
785C2×C4—362no—
786C2×C4—362no—
787C2×C4—362no—
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—81no—
798C2×C3—81no—
799C2×C3—122no—
800C2×C3—161no—
801C2×C3—241no—
802C2×C3D3×#12111yescharacteristic
803C2×C3#576811yescharacteristic
804C2×C3#577311yescharacteristic
805C2×C3#577311yescharacteristic
806C2×C3#577711yescharacteristic
807C2×C3C2×#93911yescharacteristic
808D3—22no—
809D3—42no—
810D3—81no—
811C22—32no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—61no—
816C22—61no—
817C22—62no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—244no—
824C22D32×D411yescharacteristic
825C4—22no—
826C4—32no—
827C4—61no—
828C4—61no—
829C4—121no—
830C4—121no—
831C4—181no—
832C4—181no—
833C4—361no—
834C4—361no—
835C4D3×#23711yescharacteristic
836C4C2×D3×#6711yescharacteristic
837C3—21no—
838C3#8059911yescharacteristic, complemented
839C3#8393311yescharacteristic, complemented
840C2—62no—
841C2—81no—
842C2—122no—
843C2—241no—
844C2#1059474411yescharacteristic
845C2#1059474511yescharacteristic
846C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×#914C2
hypercenterC2×SD16D32
hypocenterC32#3040
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. Dic3×#239C2semidirect
3. C2×#63943C2semidirect
4. D3×#936C2semidirect
5. #10592865C2semidirect
6. C3×#5166C2semidirect
7. #10591612C2semidirect
8. #10591604C2semidirect
9. #10591434C2semidirect
10. #10591431C2semidirect
11. #10591421C2semidirect
12. #10590948C2semidirect
13. #10590755C2semidirect
14. #10590751C2semidirect
15. #10590663C2semidirect
22. Q8×C3⋊Dic3C22semidirect
23. C2×#3756C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
39. #63898C22semidirect
41. Dic3×D12C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
52. #63643C22semidirect
53. #63641C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
79. #5166D3semidirect
178. Q8×Dic3C2×D3semidirect
182. C2×#216C2×D3semidirect
240. #816C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
747. C32#3040semidirect
838. C3#80599semidirect
839. C3#83933semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
Dic3×#2392
C2×#639432
D3×#9362
#105928652
C3×#51662
#105916122
#105916042
#105914342
#105914312
#105914212
#105909482
#105907552
#105907512
#105906632
#839333
#805993