Finite Group Databasebeta

← #11866340

Subgroups — #11866340

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×D3×SD16C211yesmaximal, characteristic, complemented
2#10595347C211yesmaximal, characteristic, complemented
3C2×#63946C211yesmaximal, characteristic, complemented
4#10595233C211yesmaximal, characteristic
5#10592865C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic, complemented
7#10591622C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10591443C211yesmaximal, characteristic, complemented
10#10591438C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10590954C211yesmaximal, characteristic, complemented
13#10590876C211yesmaximal, characteristic, complemented
14#10590859C211yesmaximal, characteristic, complemented
15#10590694C211yesmaximal, characteristic, complemented
16#83849—31nomaximal
17#80385—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24#64145C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#940C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×D3×SD16—24no—
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33#63976—21no—
34#63976—21no—
35#63970—21no—
36#63970—21no—
37#63946—24no—
38#63914C2211yescharacteristic
39#63860C2211yescharacteristic
40#63855—21no—
41#63855C2211yescharacteristic
42#63843—21no—
43#63843C2211yescharacteristic, complemented
44Dic3×Dic6—21no—
45Dic3×Dic6C2211yescharacteristic, complemented
46#63841—21no—
47#63841C2211yescharacteristic
48C2×#3719C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic
51#63659C2211yescharacteristic
52#63643C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×#821C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57#63572C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic
63C22×C3×SD16—31no—
64#5812—31no—
65C2×#942—31no—
66#5805—31no—
67C2×#915—31no—
68C2×D3×SD16D311yescharacteristic, complemented
69#5715—31no—
70#5572—31no—
71C3×#460—31no—
72#5215—31no—
73#5166—31no—
74#5166—31no—
75#5166—31no—
76#5166—31no—
77#5166—31no—
78#5166—61no—
79#5163—31no—
80#5163—31no—
81#5163—31no—
82#5163—31no—
83#5163D311yescharacteristic, complemented
84#5113—31no—
85#5102—31no—
86#5075—31no—
87#5028—31no—
88#4845—31no—
89#4839—31no—
90#4772—31no—
91#4770—31no—
92#4767—31no—
93#4762—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×Q8—22no—
102C3×D3×Q8D414yescomplemented
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×#625—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115#3795—22no—
116#3795—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×#215—22no—
128C3×#215—22no—
129C3×#214—22no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—22no—
137C3×D3×C8—22no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3D411yescharacteristic
141Dic3⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3D411yescharacteristic
146(C2×D3)⋊Dic3D411yescharacteristic
147Dic32—21no—
148Dic32—21no—
149Dic32—21no—
150#3719—22no—
151#3715—22no—
152#3711—22no—
153#3043—91noSylow
154C22×C3×Q8—31no—
155C22×C3×D4—31no—
156C2×D3×Q8C2×D311yescharacteristic
157C2×#237—31no—
158C2×D3×D4C2×D311yescharacteristic
159C2×#235—31no—
160C2×C3×SD16—21no—
161C2×C3×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16—64no—
166C2×C3×SD16C2×D311yescharacteristic
167C2×C3×SD16C2×D311yescharacteristic
168C22×C3×C8—31no—
169C3×#127—31no—
170C3×C4×Q8—31no—
171#953—61no—
172#953—61no—
173Q8×Dic3—31no—
174Q8×Dic3—31no—
175Q8×Dic3—31no—
176Q8×Dic3—31no—
177Q8×Dic3—61no—
178Q8×Dic3—61no—
179Q8×Dic3—61no—
180Q8×Dic3C2×D311yescharacteristic, complemented
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—61no—
185#942—64no—
186C2×#215—31no—
187C2×#215C2×D311yescharacteristic
188C2×#215C2×D311yescharacteristic, complemented
189#940—31no—
190#940—31no—
191#940C2×D311yescharacteristic
192#939—61no—
193#939—61no—
194#938—61no—
195#938—61no—
196#937—61no—
197#937—61no—
198#936—31no—
199#936—31no—
200#936—31no—
201#936—61no—
202C2×#214—31no—
203C2×#214C2×D311yescharacteristic
204#926—31no—
205#926—31no—
206#926—61no—
207#926—61no—
208C2×#208—31no—
209#915—64no—
210D3×SD16—24no—
211C2×Dic12—31no—
212C2×#204C2×D311yescharacteristic
213C2×ΓL(1,𝔽25)—31no—
214C2×D3×C8C2×D311yescharacteristic
215#892—31no—
216#892—61no—
217#887—31no—
218#887—61no—
219#875—31no—
220#872—31no—
221#872—61no—
222C4×Dic6—31no—
223C4×Dic6—61no—
224C3×C4⋊C8—31no—
225C3×#102—31no—
226C3×#102—31no—
227#832—31no—
228#832—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic
234#821—31no—
235#821—31no—
236#821C2×D311yescharacteristic, complemented
237#816—31no—
238#816—31no—
239#816—31no—
240#816—61no—
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—81no—
256C22×C3×D3—81no—
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—
271C3×#67—81no—
272C3×#67—81no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×C4×D3—24no—
283C3×C4×D3C2×D412yes—
284C3×C4×D3#4112yes—
285C3×Dic6—21no—
286C3×Dic6—24no—
287C3×Dic6C2×D412yes—
288#625—42no—
289#625—81no—
290#625—81no—
291D3×Dic3—42no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#137—91no—
297C22×SD16—31no—
298#535—91no—
299#519—91no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#460—31no—
305#460—91no—
306#460—91no—
307#460—91no—
308#424—91no—
309#418—91no—
310#416—91no—
311C24×C3—61no—
312C23×D3—21no—
313C2×C3×Q8—21no—
314C2×C3×Q8—34no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×D4—21no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—62no—
324C2×C3×D4—62no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C2×#67—21no—
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C22×Dic3—61no—
342D3×Q8—22no—
343D3×Q8#6714yescomplemented
344#237—62no—
345#237—62no—
346D3×D4—22no—
347D3×D4—22no—
348#235—62no—
349#235—62no—
350C2×D12C22×D311yescharacteristic
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3C22×D311yescharacteristic
355C2×Dic6—21no—
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C2×Dic6C22×D311yescharacteristic
360C3×SD16—22no—
361C3×SD16—22no—
362C3×SD16—42no—
363C3×SD16—62no—
364C3×SD16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C2×C3×C8—21no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—62no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—31no—
374C3×C4⋊C4—61no—
375C3×C42—31no—
376C3×C42—61no—
377#217—31no—
378#217—31no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—121no—
387#217—121no—
388#216—62no—
389#216—62no—
390#216—62no—
391#216—122no—
392#215—22no—
393#215—22no—
394#215—62no—
395#214—22no—
396#214—62no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
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
432#208—62no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—61no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438Dic12—62no—
439#204—22no—
440ΓL(1,𝔽25)—62no—
441D3×C8—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
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—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—22no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—31no—
470C22×D4—31no—
471#137—184no—
472C2×Q16—91no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—31no—
478C2×SD16—64no—
479C2×SD16—91no—
480C2×SD16D3211yescharacteristic
481C2×M16—91no—
482C22×C8—31no—
483#127—31no—
484#127—91no—
485#124—91no—
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—91no—
506#103—91no—
507#102—31no—
508#102—31no—
509#102—91no—
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—241no—
521C23×C3—241no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—42no—
525C22×D3—81no—
526C22×D3—81no—
527C22×D3D3×D411yescharacteristic
528C3×Q8—21no—
529C3×Q8—21no—
530C3×Q8—22no—
531C3×Q8—32no—
532C3×Q8—41no—
533C3×Q8—64no—
534C3×Q8—61no—
535C3×Q8D3×D412yes—
536C3×Q8C2×#6712yes—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—41no—
542C3×D4—41no—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—61no—
546C3×D4—61no—
547C3×D4—122no—
548C3×D4—241no—
549C3×D4—241no—
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—64no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4C23×D311yescharacteristic
563C2×C3×C4C23×D311yescharacteristic
564#67—42no—
565#67—81no—
566#67—81no—
567#67—122no—
568#67—122no—
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—61no—
584C2×Dic3—61no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588C2×Dic3D3×D411yescharacteristic
589C2×Dic3D3×D411yescharacteristic
590C2×Dic3D3×D411yescharacteristic
591D12—21no—
592D12—21no—
593D12—21no—
594D12—21no—
595C4×D3—24no—
596C4×D3—122no—
597C4×D3#23712yes—
598C4×D3C2×#6712yes—
599Dic6—21no—
600Dic6—24no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6—121no—
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×C32—81no—
619C2×C32C2×#12111yescharacteristic
620C2×C32#57711yescharacteristic
621C2×C32#57711yescharacteristic
622C3×D3—22no—
623C3×D3—81no—
624C3×D3—81no—
625C24—61no—
626#41—182no—
627#41—182no—
628C2×Q8—34no—
629C2×Q8—31no—
630C2×Q8—61no—
631C2×Q8—62no—
632C2×Q8—91no—
633C2×Q8C2×D3211yescharacteristic
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—62no—
637C2×D4—62no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4C2×D3211yescharacteristic
645C22×C4—31no—
646C22×C4—61no—
647C22×C4—181no—
648Q16—182no—
649Q16—182no—
650SD16—22no—
651SD16—62no—
652SD16—62no—
653SD16—62no—
654SD16—62no—
655SD16—182no—
656M16—182no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—62no—
660C2×C8—91no—
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—91no—
671C22⋊C4—91no—
672C22⋊C4—181no—
673C22⋊C4—181no—
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—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
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—41no—
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—62no—
725C3×C4—121no—
726C3×C4C2×D3×D411yescharacteristic
727C3×C4C2×#23711yescharacteristic
728C3×C4D3×#4111yescharacteristic
729C3×C4C22×#6711yescharacteristic
730Dic3—21no—
731Dic3—21no—
732Dic3—22no—
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#304311yescharacteristic, complemented, Sylow
748C23—21no—
749C23—31no—
750C23—61no—
751C23—61no—
752C23—122no—
753C23—241no—
754C23—241no—
755Q8—21no—
756Q8—32no—
757Q8—64no—
758Q8—61no—
759Q8—181no—
760Q8—181no—
761Q8D3×#6712yes—
762D4—21no—
763D4—21no—
764D4—61no—
765D4—61no—
766D4—61no—
767D4—61no—
768D4—122no—
769D4—241no—
770D4—241no—
771D4—362no—
772D4—721no—
773D4—721no—
774C2×C4—21no—
775C2×C4—31no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—64no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—91no—
784C2×C4—91no—
785C2×C4—181no—
786C2×C4—181no—
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—161no—
800C2×C3—241no—
801C2×C3—241no—
802C2×C3D3×#12111yescharacteristic
803C2×C3#576211yescharacteristic
804C2×C3#576211yescharacteristic
805C2×C3#576211yescharacteristic
806C2×C3#577511yescharacteristic
807C2×C3C2×#93911yescharacteristic
808D3—22no—
809D3—81no—
810D3—81no—
811C22—32no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—61no—
816C22—61no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—244no—
824C22D32×D411yescharacteristic
825C4—22no—
826C4—32no—
827C4—61no—
828C4—61no—
829C4—62no—
830C4—121no—
831C4—181no—
832C4—181no—
833C4—361no—
834C4—361no—
835C4D3×#23711yescharacteristic
836C4C2×D3×#6711yescharacteristic
837C3—21no—
838C3#8038511yescharacteristic, complemented
839C3#8384911yescharacteristic, complemented
840C2—62no—
841C2—81no—
842C2—241no—
843C2—241no—
844C2#1059474811yescharacteristic
845C2#1059474911yescharacteristic
846C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595233C2
hypercenterC2×SD16D32
hypocenterC32#3043
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
1. C2×C3×D3×SD16C2semidirect
2. #10595347C2semidirect
3. C2×#63946C2semidirect
5. #10592865C2semidirect
6. C3×#5163C2semidirect
7. #10591622C2semidirect
8. #10591604C2semidirect
9. #10591443C2semidirect
10. #10591438C2semidirect
11. #10591421C2semidirect
12. #10590954C2semidirect
13. #10590876C2semidirect
14. #10590859C2semidirect
15. #10590694C2semidirect
22. Q8×C3⋊Dic3C22semidirect
23. C2×#3756C22semidirect
25. C3×Q8×Dic3C22semidirect
27. C2×C3×#215C22semidirect
43. #63843C22semidirect
45. Dic3×Dic6C22semidirect
48. C2×#3719C22semidirect
49. C2×#3715C22semidirect
52. #63643C22semidirect
53. #63641C22semidirect
55. C3×#821C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. #63572C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
61. #63563C22semidirect
68. C2×D3×SD16D3semidirect
83. #5163D3semidirect
102. C3×D3×Q8D4semidirect
180. Q8×Dic3C2×D3semidirect
188. C2×#215C2×D3semidirect
236. #821C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
343. D3×Q8#67semidirect
747. C32#3043semidirect
838. C3#80385semidirect
839. C3#83849semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
#105953472
C2×#639462
#105952332
#105928652
C3×#51632
#105916222
#105916042
#105914432
#105914382
#105914212
#105909542
#105908762
#105908592
#105906942
#838493
#803853