Finite Group Databasebeta

← #11864306

Subgroups — #11864306

Order 1152.

1667 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64314C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4#10594628C211yesmaximal, characteristic, complemented
5#10592472C211yesmaximal, characteristic, complemented
6C3×#4773C211yesmaximal, characteristic, complemented
7C3×#4772C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10#10590967C211yesmaximal, characteristic, complemented
11#10590963C211yesmaximal, characteristic, complemented
12#10590953C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590615C211yesmaximal, characteristic, complemented
15#10590592C211yesmaximal, characteristic, complemented
16#80004—31nomaximal
17#78834—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C2×#3811—21no—
22C2×D3×#67—21no—
23C22×#626—21no—
24C2×#3804—21no—
25#64314—24no—
26#64314—24no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic, complemented
29C2×#3799C2211yescharacteristic, complemented
30C2×#3798C2211yescharacteristic
31C2×#3796C2211yescharacteristic, complemented
32C2×#3753C2211yescharacteristic, complemented
33C2×#3745C2211yescharacteristic, complemented
34#64104C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic, complemented
38C3×#895C2211yescharacteristic, complemented
39C3×#892C2211yescharacteristic, complemented
40#63925—24no—
41#63923—21no—
42#63922—21no—
43#63916C2211yescharacteristic, complemented
44#63911—21no—
45#63909C2211yescharacteristic, complemented
46#63852—21no—
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52D3×D24—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C2×#949—31no—
68C2×#911—31no—
69C2×D3×D8—31no—
70C22×D24—31no—
71#5607—31no—
72#5525—31no—
73C3×#447—31no—
74C3×#416—31no—
75#5217—31no—
76#5158—31no—
77#5156—31no—
78#5110—31no—
79#5037—31no—
80#5001—31no—
81#4810—31no—
82#4810—31no—
83#4810—31no—
84#4810—31no—
85#4781—31no—
86#4773—31no—
87#4773—31no—
88#4773—31no—
89#4773—31no—
90#4773—61no—
91#4773D311yescharacteristic, complemented
92#4772D311yescharacteristic, complemented
93#4770—31no—
94#4734—31no—
95#4727—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C22×D32—21no—
99C22×D32—21no—
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102D4×C3⋊D3—22no—
103D4×C3⋊D3—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C3×#237—22no—
112C3×#237D414yescomplemented
113C3×D3×D4—22no—
114C3×D3×D4—22no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121#3811—28no—
122D3×#67—28no—
123C2×#627D411yescharacteristic
124C2×#626—28no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#626—21no—
131C2×#626D411yescharacteristic
132C2×#626D411yescharacteristic
133C2×#625D411yescharacteristic
134C2×#624—21no—
135#3804—28no—
136C2×D3×Dic3—21no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12D414yescomplemented
141#3799—22no—
142#3799—22no—
143#3798—22no—
144#3798—22no—
145#3796—22no—
146#3796—22no—
147C2×C32×C8C2311yescharacteristic
148C32×C4⋊C4C2311yescharacteristic
149#3753—22no—
150#3752—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152#3745—22no—
153C3×#213—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4×Dic3—21no—
158C2×C3×C3⋊C8C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C3×D24—22no—
161C3×D3×C8—22no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164#3717—22no—
165#3715—22no—
166#3714—22no—
167#3714—22no—
168#3711—22no—
169#3008—91noSylow
170C2×C3×#41—31no—
171C22×C3×D4—31no—
172C22×#67—61no—
173C22×#67—61no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178#1004—64no—
179#1004—64no—
180C2×#237—31no—
181C2×#237—61no—
182C2×#237C2×D311yescharacteristic
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—31no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4C2×D311yescharacteristic, complemented
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—31no—
195C2×#235—61no—
196C22×D12—31no—
197C22×D12—31no—
198C22×D12—61no—
199C2×C3×D8—31no—
200C2×C3×D8—31no—
201C22×C3×C8—31no—
202C3×#121—31no—
203C3×#117—31no—
204#949—64no—
205C2×#215—31no—
206C2×#215—31no—
207#940—61no—
208#938—31no—
209#937—61no—
210C2×#214—31no—
211C2×#213—31no—
212C2×#213—31no—
213C2×#213—31no—
214C2×#213—31no—
215C2×#213—61no—
216C2×#213C2×D311yescharacteristic, complemented
217#930—31no—
218C2×#208—31no—
219#911—64no—
220D3×D8—64no—
221C2×D24—31no—
222C2×D24—31no—
223C2×D24—31no—
224C2×D24—31no—
225C2×D24—61no—
226C2×D24—64no—
227C2×D24C2×D311yescharacteristic, complemented
228C2×#204—31no—
229C2×ΓL(1,𝔽25)—31no—
230C2×D3×C8C2×D311yescharacteristic, complemented
231#895—31no—
232#895—31no—
233#895—31no—
234#895—31no—
235#895—61no—
236#895C2×D311yescharacteristic, complemented
237#892C2×D311yescharacteristic, complemented
238#885—61no—
239#882—61no—
240#882—61no—
241#882—61no—
242#875—61no—
243#874—61no—
244C3×#103—31no—
245C3×#103—31no—
246C3×#102—21no—
247C3×#102—31no—
248C3×#102—31no—
249C3×#102C2×D311yescharacteristic, complemented
250C3×#102C2×D311yescharacteristic, complemented
251C3×C22⋊C8—31no—
252#832—31no—
253#832C2×D311yescharacteristic, complemented
254#830—31no—
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816C2×D311yescharacteristic, complemented
264#810C2×D311yescharacteristic, complemented
265#809—31no—
266#809—31no—
267#809—31no—
268#809—31no—
269#809—61no—
270#809C2×D311yescharacteristic, complemented
271C23×C32—21no—
272C22×C3⋊D3—21no—
273C22×C3⋊D3—24no—
274C22×C3⋊D3—21no—
275C22×C3⋊D3—81no—
276C22×C3⋊D3—81no—
277C22×C3⋊D3C2×D411yescharacteristic
278C22×C3×D3—21no—
279C22×C3×D3—24no—
280C22×C3×D3—21no—
281C22×C3×D3—81no—
282C22×C3×D3—81no—
283C22×C3×D3C2×D411yescharacteristic
284C22×C3×D3C2×D411yescharacteristic
285C2×D32—24no—
286C2×D32—42no—
287C2×D32—81no—
288C2×D32—81no—
289C2×D32—81no—
290C2×D32—81no—
291C32×D4—21no—
292C32×D4C2×D412yes—
293C2×C32×C4—21no—
294C2×C32×C4C2411yescharacteristic
295#638—24no—
296C2×C3⋊Dic3C2×D411yescharacteristic
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)—21no—
300C4⋊(C3⋊D3)—81no—
301C4⋊(C3⋊D3)C2×D412yes—
302C4×C3⋊D3—21no—
303C4×C3⋊D3—21no—
304C3×#67—24no—
305C3×#67—24no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—24no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3C2×D411yescharacteristic
310C2×C3×Dic3C2×D411yescharacteristic
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—81no—
315C3×D12C2×D412yes—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—21no—
321C3×Dic6C2×D412yes—
322#627—22no—
323#626—24no—
324#626—24no—
325#626—22no—
326#626—22no—
327#626—24no—
328#626—42no—
329#626—81no—
330#626—81no—
331#625—22no—
332#624—24no—
333D3×Dic3—24no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C2×H(5,𝔽2)—91no—
339C2×AGL(1,ℤ/8)—91no—
340C22×D8—91no—
341#535—91no—
342#449—91no—
343#449—91no—
344#449—91no—
345#449—91no—
346#447—31no—
347#447—91no—
348#447—91no—
349#447—91no—
350#418—91no—
351#416—31no—
352#408—91no—
353C24×C3—61no—
354C23×D3—21no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3—61no—
360C23×D3—61no—
361C23×D3—121no—
362C3×#41—34no—
363C3×#41—62no—
364C2×C3×Q8—31no—
365C2×C3×D4—21no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—61no—
369C2×C3×D4—61no—
370C2×C3×D4—62no—
371C2×C3×D4—61no—
372C2×C3×D4—62no—
373C2×C3×D4C22×D311yescharacteristic
374C2×C3×D4C22×D311yescharacteristic
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—61no—
378C2×#67—21no—
379C2×#67—21no—
380C2×#67—31no—
381C2×#67—31no—
382C2×#67—31no—
383C2×#67—31no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—68no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—68no—
392C2×#67—61no—
393C2×#67—61no—
394C2×#67—121no—
395C22×Dic3—21no—
396C22×Dic3—61no—
397#239—62no—
398#239—62no—
399#239—62no—
400#239—62no—
401#237—22no—
402#237—62no—
403#237—68no—
404#237—62no—
405#237D1214yescomplemented
406D3×D4—22no—
407D3×D4—22no—
408D3×D4—34no—
409D3×D4—62no—
410D3×D4—62no—
411D3×D4—68no—
412D3×D4—68no—
413D3×D4—68no—
414D3×D4—62no—
415D3×D4—62no—
416D3×D4—62no—
417D3×D4—62no—
418D3×D4—62no—
419D3×D4—122no—
420D3×D4—122no—
421#235—62no—
422#235—62no—
423#235—62no—
424#235—68no—
425#235—62no—
426#235—62no—
427#235—62no—
428C2×D12—21no—
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—34no—
432C2×D12—31no—
433C2×D12—31no—
434C2×D12—31no—
435C2×D12—31no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—62no—
439C2×D12—62no—
440C2×D12—62no—
441C2×D12—61no—
442C2×D12—61no—
443C2×D12—68no—
444C2×D12—61no—
445C2×D12—61no—
446C2×D12—61no—
447C2×D12—61no—
448C2×D12—61no—
449C2×D12—61no—
450C2×D12—121no—
451C2×D12C22×D311yescharacteristic
452C2×D12C22×D311yescharacteristic
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—61no—
456C2×C4×D3—61no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3C22×D311yescharacteristic
460C2×C4×D3C22×D311yescharacteristic
461C2×Dic6—31no—
462C2×Dic6—31no—
463C2×Dic6C22×D311yescharacteristic
464C3×D8—62no—
465C3×D8—62no—
466C2×C3×C8—21no—
467C2×C3×C8—31no—
468C2×C3×C8—31no—
469C2×C3×C8—62no—
470C2×C3×C8C22×D311yescharacteristic
471C2×C3×C8C22×D311yescharacteristic
472C3×C4⋊C4—21no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4C22×D311yescharacteristic
475C3×C4⋊C4C22×D311yescharacteristic
476C3×C22⋊C4—61no—
477C3×C22⋊C4—61no—
478C3×C42—61no—
479#217—61no—
480#215—62no—
481#215—62no—
482#214—62no—
483#213—22no—
484#213—62no—
485#213—62no—
486#213—62no—
487#213—62no—
488#213—122no—
489(C2×D3)⋊C4—21no—
490(C2×D3)⋊C4—21no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—61no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—121no—
497C4⋊Dic3C22×D311yescharacteristic
498C4×Dic3—21no—
499#208—62no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8C22×D311yescharacteristic
504C2×C3⋊C8C22×D311yescharacteristic
505D24—22no—
506D24—62no—
507D24—62no—
508D24—62no—
509D24—62no—
510D24—122no—
511#204—62no—
512ΓL(1,𝔽25)—62no—
513D3×C8—22no—
514C22×C32—22no—
515C22×C32—41no—
516C22×C32—41no—
517C22×C32C22×D411yescharacteristic
518C2×C3⋊D3—21no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3—21no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3⋊D3—41no—
527C2×C3⋊D3—84no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—21no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3—41no—
539C2×C3×D3—84no—
540C2×C3×D3#12012yes—
541D32—84no—
542D32—84no—
543C32×C4—41no—
544C32×C4C22×D411yescharacteristic
545C32×C4C22×D411yescharacteristic
546C3⋊Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—21no—
549C3×Dic3—41no—
550C3×Dic3#12012yes—
551H(5,𝔽2)—184no—
552H(5,𝔽2)—184no—
553C2×#41—31no—
554C2×#41—91no—
555C2×#41—91no—
556C2×#41—91no—
557C2×#41—181no—
558C22×D4—31no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—91no—
562C22×D4—181no—
563C22×D4—181no—
564C22×D4—181no—
565AGL(1,ℤ/8)—184no—
566C2×SD16—91no—
567C2×SD16—91no—
568C2×D8—31no—
569C2×D8—31no—
570C2×D8—91no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—184no—
575C2×M16—91no—
576C22×C8—31no—
577#127—181no—
578#124—181no—
579#121—31no—
580#121—91no—
581#121—91no—
582#121—91no—
583#120—181no—
584#120—181no—
585#117—31no—
586#103—31no—
587#103—31no—
588#102—31no—
589#102—31no—
590#102—91no—
591#102—91no—
592#102—91no—
593#102D3211yescharacteristic, complemented
594C22⋊C8—31no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C22⋊C8—91no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—31no—
601C23×C3—31no—
602C23×C3—41no—
603C23×C3—64no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—241no—
607C23×C3—241no—
608C22×D3—21no—
609C22×D3—24no—
610C22×D3—21no—
611C22×D3—31no—
612C22×D3—31no—
613C22×D3—61no—
614C22×D3—64no—
615C22×D3—61no—
616C22×D3—61no—
617C22×D3—64no—
618C22×D3—64no—
619C22×D3—64no—
620C22×D3—61no—
621C22×D3—61no—
622C22×D3—81no—
623C22×D3—81no—
624C22×D3—121no—
625C22×D3—124no—
626C22×D3—121no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—241no—
630C22×D3—241no—
631C22×D3—241no—
632C22×D3—241no—
633C22×D3—241no—
634C22×D3—241no—
635C22×D3—241no—
636C22×D3—241no—
637C22×D3—241no—
638C22×D3—241no—
639C22×D3—241no—
640C22×D3—241no—
641C22×D3—242no—
642C22×D3—242no—
643C22×D3D3×D411yescharacteristic
644C22×D3D3×D411yescharacteristic
645C3×Q8—32no—
646C3×Q8—61no—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—22no—
650C3×D4—32no—
651C3×D4—41no—
652C3×D4—64no—
653C3×D4—64no—
654C3×D4—61no—
655C3×D4—61no—
656C3×D4—61no—
657C3×D4—241no—
658C3×D4C2×D1212yes—
659C3×D4D3×D412yes—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—31no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—31no—
667C2×C3×C4—41no—
668C2×C3×C4—64no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675#67—24no—
676#67—24no—
677#67—62no—
678#67—64no—
679#67—64no—
680#67—62no—
681#67—64no—
682#67—64no—
683#67—62no—
684#67—62no—
685#67—64no—
686#67—124no—
687#67—122no—
688#67—241no—
689#67—241no—
690C2×Dic3—21no—
691C2×Dic3—24no—
692C2×Dic3—21no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—61no—
696C2×Dic3—64no—
697C2×Dic3D3×D411yescharacteristic
698C2×Dic3D3×D411yescharacteristic
699D12—21no—
700D12—21no—
701D12—21no—
702D12—32no—
703D12—32no—
704D12—62no—
705D12—62no—
706D12—64no—
707D12—64no—
708D12—64no—
709D12—62no—
710D12—61no—
711D12—61no—
712D12—61no—
713D12—61no—
714D12—61no—
715D12—61no—
716D12—81no—
717D12—121no—
718D12—121no—
719D12—121no—
720D12—122no—
721D12—241no—
722D12—241no—
723D12—242no—
724D12—241no—
725D12—241no—
726D12D3×D412yes—
727C4×D3—21no—
728C4×D3—21no—
729C4×D3—64no—
730C4×D3—64no—
731C4×D3—64no—
732C4×D3—61no—
733C4×D3—61no—
734C4×D3—61no—
735C4×D3—61no—
736C4×D3—121no—
737C4×D3—121no—
738C4×D3C2×D1212yes—
739C4×D3D3×D412yes—
740Dic6—21no—
741Dic6—62no—
742Dic6—62no—
743Dic6C2×D1212yes—
744C3×C8—21no—
745C3×C8—21no—
746C3×C8—41no—
747C3×C8—61no—
748C3×C8—61no—
749C3⋊C8—21no—
750C3⋊C8—21no—
751C3⋊C8—61no—
752C3⋊C8—61no—
753C3⋊C8—121no—
754C2×C32—42no—
755C2×C32C2×#12011yescharacteristic
756C2×C32#57611yescharacteristic
757C2×C32#57611yescharacteristic
758C3⋊D3—41no—
759C3⋊D3—42no—
760C3⋊D3—81no—
761C3×D3—22no—
762C3×D3—42no—
763C3×D3—41no—
764C3×D3—81no—
765C24—61no—
766C24—181no—
767C24—181no—
768C24—181no—
769#41—34no—
770#41—62no—
771#41—182no—
772#41—182no—
773#41—188no—
774#41—182no—
775#41—182no—
776#41—182no—
777#41—182no—
778C2×Q8—31no—
779C2×Q8—91no—
780C2×D4—31no—
781C2×D4—31no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—62no—
785C2×D4—61no—
786C2×D4—62no—
787C2×D4—94no—
788C2×D4—91no—
789C2×D4—91no—
790C2×D4—91no—
791C2×D4—91no—
792C2×D4—91no—
793C2×D4—181no—
794C2×D4—182no—
795C2×D4—182no—
796C2×D4—182no—
797C2×D4—181no—
798C2×D4—181no—
799C2×D4—181no—
800C2×D4—181no—
801C2×D4—188no—
802C2×D4—181no—
803C2×D4—181no—
804C2×D4—181no—
805C2×D4—182no—
806C2×D4—188no—
807C2×D4—188no—
808C2×D4—182no—
809C2×D4C2×D3211yescharacteristic
810C22×C4—31no—
811C22×C4—31no—
812C22×C4—61no—
813C22×C4—91no—
814C22×C4—181no—
815C22×C4—181no—
816SD16—182no—
817SD16—182no—
818D8—62no—
819D8—62no—
820D8—182no—
821D8—182no—
822D8—182no—
823D8—182no—
824M16—182no—
825C2×C8—31no—
826C2×C8—31no—
827C2×C8—62no—
828C2×C8—91no—
829C2×C8C2×D3211yescharacteristic
830C4⋊C4—31no—
831C4⋊C4C2×D3211yescharacteristic
832C22⋊C4—61no—
833C22⋊C4—61no—
834C22⋊C4—181no—
835C22⋊C4—181no—
836C22⋊C4—181no—
837C42—61no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—21no—
841C22×C3—32no—
842C22×C3—42no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—62no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—81no—
854C22×C3—81no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—244no—
861C22×C3C2×D3×D411yescharacteristic
862C22×C3C2×D3×D411yescharacteristic
863C2×D3—21no—
864C2×D3—21no—
865C2×D3—21no—
866C2×D3—21no—
867C2×D3—21no—
868C2×D3—22no—
869C2×D3—41no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—62no—
882C2×D3—61no—
883C2×D3—84no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—122no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—121no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—121no—
894C2×D3—121no—
895C2×D3—121no—
896C2×D3—121no—
897C2×D3—241no—
898C2×D3—241no—
899C2×D3—241no—
900C2×D3—241no—
901C2×D3—241no—
902C2×D3—244no—
903C2×D3—244no—
904C2×D3—244no—
905C2×D3—244no—
906C2×D3—244no—
907C2×D3—244no—
908C2×D3—248no—
909C2×D3#88212yes—
910C3×C4—21no—
911C3×C4—21no—
912C3×C4—32no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—61no—
916C3×C4—62no—
917C3×C4—81no—
918C3×C4—121no—
919C3×C4C22×D1211yescharacteristic
920C3×C4C2×D3×D411yescharacteristic
921C3×C4C2×D3×D411yescharacteristic
922C3×C4C2×D3×D411yescharacteristic
923Dic3—22no—
924Dic3—21no—
925Dic3—41no—
926Dic3—61no—
927Dic3—61no—
928Dic3—121no—
929Dic3#88212yes—
930C32#300811yescharacteristic, complemented, Sylow
931C23—21no—
932C23—31no—
933C23—31no—
934C23—64no—
935C23—61no—
936C23—61no—
937C23—91no—
938C23—184no—
939C23—184no—
940C23—181no—
941C23—181no—
942C23—241no—
943C23—241no—
944C23—362no—
945C23—721no—
946C23—721no—
947C23—721no—
948C23—721no—
949C23—721no—
950C23—721no—
951Q8—32no—
952Q8—61no—
953Q8—182no—
954D4—21no—
955D4—32no—
956D4—64no—
957D4—64no—
958D4—61no—
959D4—61no—
960D4—61no—
961D4—92no—
962D4—182no—
963D4—184no—
964D4—182no—
965D4—184no—
966D4—184no—
967D4—184no—
968D4—182no—
969D4—181no—
970D4—181no—
971D4—181no—
972D4—241no—
973D4—362no—
974D4—721no—
975D4—721no—
976D4—721no—
977D4D3×D1212yes—
978C2×C4—21no—
979C2×C4—31no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—31no—
983C2×C4—64no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—61no—
988C2×C4—91no—
989C2×C4—184no—
990C2×C4—184no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4C22×D3211yescharacteristic
994C8—21no—
995C8—61no—
996C8—61no—
997C8—181no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—42no—
1002C2×C3—42no—
1003C2×C3—62no—
1004C2×C3—82no—
1005C2×C3—122no—
1006C2×C3—121no—
1007C2×C3—241no—
1008C2×C3C2×#88211yescharacteristic
1009C2×C3D3×#12011yescharacteristic
1010C2×C3#575711yescharacteristic
1011C2×C3#576911yescharacteristic
1012C2×C3#576911yescharacteristic
1013C2×C3#577411yescharacteristic
1014D3—22no—
1015D3—41no—
1016D3—42no—
1017D3—81no—
1018D3—122no—
1019D3—121no—
1020D3—122no—
1021D3—121no—
1022D3—122no—
1023D3—242no—
1024D3—241no—
1025D3—241no—
1026D3—481no—
1027C22—22no—
1028C22—32no—
1029C22—41no—
1030C22—41no—
1031C22—61no—
1032C22—61no—
1033C22—61no—
1034C22—61no—
1035C22—61no—
1036C22—62no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—181no—
1043C22—181no—
1044C22—182no—
1045C22—181no—
1046C22—244no—
1047C22—361no—
1048C22—361no—
1049C22—361no—
1050C22—361no—
1051C22—361no—
1052C22—724no—
1053C22—724no—
1054C22—724no—
1055C22D32×D411yescharacteristic
1056C4—32no—
1057C4—41no—
1058C4—61no—
1059C4—62no—
1060C4—121no—
1061C4—181no—
1062C4C2×D3×D1211yescharacteristic
1063C4D32×D411yescharacteristic
1064C3—21no—
1065C3#7883411yescharacteristic, complemented
1066C3#8000411yescharacteristic, complemented
1067C2—42no—
1068C2—62no—
1069C2—121no—
1070C2—122no—
1071C2—241no—
1072C2—361no—
1073C2—362no—
1074C2—721no—
1075C2D3×#88211yescharacteristic
1076C2#1059473411yescharacteristic
1077C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3008
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#64314C2semidirect
2. C2×#63925C2semidirect
3. C2×D3×D24C2semidirect
4. #10594628C2semidirect
5. #10592472C2semidirect
6. C3×#4773C2semidirect
7. C3×#4772C2semidirect
8. #10591456C2semidirect
9. #10591448C2semidirect
10. #10590967C2semidirect
11. #10590963C2semidirect
12. #10590953C2semidirect
13. #10590617C2semidirect
14. #10590615C2semidirect
15. #10590592C2semidirect
18. C2×D4×C3⋊D3C22semidirect
20. C2×C3×D3×D4C22semidirect
28. C2×D3×D12C22semidirect
29. C2×#3799C22semidirect
31. C2×#3796C22semidirect
32. C2×#3753C22semidirect
33. C2×#3745C22semidirect
34. #64104C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×D3×C8C22semidirect
38. C3×#895C22semidirect
39. C3×#892C22semidirect
43. #63916C22semidirect
45. #63909C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
51. C2×#3711C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
91. #4773D3semidirect
92. #4772D3semidirect
112. C3×#237D4semidirect
140. D3×D12D4semidirect
191. C2×D3×D4C2×D3semidirect
216. C2×#213C2×D3semidirect
227. C2×D24C2×D3semidirect
230. C2×D3×C8C2×D3semidirect
236. #895C2×D3semidirect
237. #892C2×D3semidirect
249. C3×#102C2×D3semidirect
250. C3×#102C2×D3semidirect
253. #832C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
263. #816C2×D3semidirect
264. #810C2×D3semidirect
270. #809C2×D3semidirect
405. #237D12semidirect
593. #102D32semidirect
930. C32#3008semidirect
1065. C3#78834semidirect
1066. C3#80004semidirect

Maximal subgroups

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

subgroupindex
C2×#643142
C2×#639252
C2×D3×D242
#105946282
#105924722
C3×#47732
C3×#47722
#105914562
#105914482
#105909672
#105909632
#105909532
#105906172
#105906152
#105905922
#800043
#788343