Finite Group Databasebeta

← #11864385

Subgroups — #11864385

Order 1152.

1580 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic
2C2×C3×#918C211yesmaximal, characteristic, complemented
3#10595397C211yesmaximal, characteristic, complemented
4C2×D3×#215C211yesmaximal, characteristic, complemented
5#10592886C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7#10591652C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591602C211yesmaximal, characteristic, complemented
10#10591597C211yesmaximal, characteristic, complemented
11#10591556C211yesmaximal, characteristic, complemented
12#10590955C211yesmaximal, characteristic, complemented
13#10590943C211yesmaximal, characteristic, complemented
14#10590942C211yesmaximal, characteristic, complemented
15#10590939C211yesmaximal, characteristic, complemented
16#83982—31nomaximal
17#80229—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic, complemented
22#64320—24no—
23#64320—24no—
24C2×#3802—21no—
25C2×#3802C2211yescharacteristic
26C2×D3×D12—21no—
27C2×D3×D12—21no—
28C2×D3×D12C2211yescharacteristic
29C2×D3×D12C2211yescharacteristic
30C2×#3798—21no—
31C2×#3798C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33#64155C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C2×C3×#215C2211yescharacteristic, complemented
39C3×#918—24no—
40C2×C3×#204C2211yescharacteristic, complemented
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42D3×#215—24no—
43#63907—21no—
44#63905—21no—
45#63871C2211yescharacteristic, complemented
46#63856C2211yescharacteristic, complemented
47#63850—21no—
48#63841C2211yescharacteristic, complemented
49#63839—21no—
50C2×#3717C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1009—31no—
67C2×C3×#137—31no—
68#5816—31no—
69C22×#215—31no—
70C2×#918D311yescharacteristic, complemented
71C2×D3×SD16—31no—
72#5628—31no—
73C3×#452—31no—
74#5239—31no—
75#5233—31no—
76#5187—31no—
77#5187—31no—
78#5187—31no—
79#5187—31no—
80#5187—61no—
81#5187D311yescharacteristic, complemented
82#5169—31no—
83#5169—31no—
84#5169—31no—
85#5169—31no—
86#5169—31no—
87#5131—31no—
88#5129—31no—
89#5046—31no—
90#4808—31no—
91#4804—31no—
92#4776—31no—
93#4770—31no—
94#4731—31no—
95#4727—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101#3832—22no—
102#3832—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3C2311yescharacteristic
107C3×#239—22no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239D414yes—
111C3×D3×Q8—22no—
112C3×D3×Q8—22no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6—21no—
123C2×C3×Dic6C2311yescharacteristic
124C2×#627D411yescharacteristic
125C2×#626—21no—
126C2×#626—21no—
127C2×#626D411yescharacteristic
128C2×#626D411yescharacteristic
129C2×#625—21no—
130C2×#625D411yescharacteristic
131#3802—28no—
132#3802—22no—
133#3802—22no—
134D3×D12—28no—
135D3×D12—28no—
136D3×D12—22no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12D414yes—
140#3798—28no—
141#3798—22no—
142#3798—22no—
143C32×Q16—22no—
144C2×C32×C8C2311yescharacteristic
145#3755—22no—
146#3752—21no—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148#3750—21no—
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150C3×#216—22no—
151C3×#215—22no—
152C3×#215—22no—
153C3×(C2×D3)⋊C4—21no—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×Dic3⋊C4—21no—
156C2×C3×C3⋊C8C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C3×#204—22no—
159C3×ΓL(1,𝔽25)—22no—
160#3724—21no—
161Dic3⋊Dic3—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165Dic32—21no—
166#3717—22no—
167#3715—22no—
168D3×C3⋊C8—22no—
169#3009—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×Q8—31no—
173#1009—64no—
174#1009—64no—
175#1009—64no—
176#1009—64no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—61no—
180C2×#239C2×D311yescharacteristic
181C2×#239C2×D311yescharacteristic
182C2×D3×Q8C2×D311yescharacteristic, complemented
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×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—61no—
198C22×D12—61no—
199C3×#137—64no—
200C2×C3×Q16—21no—
201C2×C3×Q16—31no—
202C2×C3×Q16C2×D311yescharacteristic, complemented
203C2×C3×Q16C2×D311yescharacteristic, complemented
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×SD16—31no—
207C2×C3×M16—31no—
208C3×C22⋊Q8—31no—
209#947—61no—
210#946—31no—
211#946—31no—
212#946—31no—
213#946—31no—
214#946—61no—
215#946C2×D311yescharacteristic, complemented
216#944—61no—
217C2×#216C2×D311yescharacteristic, complemented
218C2×#215—31no—
219C2×#215—31no—
220C2×#215—31no—
221C2×#215—31no—
222C2×#215—61no—
223C2×#215—64no—
224C2×#215C2×D311yescharacteristic, complemented
225C2×#215C2×D311yescharacteristic, complemented
226C2×#214—31no—
227#929—61no—
228#929—61no—
229#926—31no—
230#924—31no—
231C22×C3⋊C8—31no—
232#918—24no—
233D3×SD16—64no—
234C2×#204—31no—
235C2×#204C2×D311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
237C2×D3×C8—31no—
238#897—31no—
239#894—61no—
240#892—31no—
241#888—61no—
242#885—61no—
243#883—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—61no—
250#835C2×D311yescharacteristic, complemented
251#832—31no—
252#832—31no—
253#832—31no—
254#830—31no—
255#821—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261#821C2×D311yescharacteristic, complemented
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—61no—
268(C2×D3)⋊C8C2×D311yescharacteristic, complemented
269#809—31no—
270#809—31no—
271C22×C3⋊D3—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—24no—
278C2×D32—24no—
279C2×D32—24no—
280C2×D32—81no—
281C2×D32—81no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C32×Q8—21no—
287C32×Q8—21no—
288C32×Q8—21no—
289C32×Q8C2×D412yes—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4C2411yescharacteristic
293C2×C3⋊Dic3—21no—
294C2×C3⋊Dic3C2×D411yescharacteristic
295C4⋊(C3⋊D3)—24no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)C2×D412yes—
298C4×C3⋊D3—24no—
299C4×C3⋊D3—21no—
300C4×C3⋊D3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3C2×D411yescharacteristic
304C2×C3×Dic3C2×D411yescharacteristic
305C3×D12—24no—
306C3×D12—24no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12C2×D412yes—
310C3×D12C2×D412yes—
311C3×C4×D3—24no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—24no—
315C3×C4×D3—42no—
316C3×C4×D3C2×D412yes—
317C3×C4×D3C2×D412yes—
318C3×Dic6—21no—
319C3×Dic6—21no—
320C3×Dic6—42no—
321#627—22no—
322#626—24no—
323#626—22no—
324#626—22no—
325#626—24no—
326#625—24no—
327#625—22no—
328C32×C8—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C2×H(5,𝔽2)—91no—
333C2×#137—31no—
334C22×SD16—91no—
335#536—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#450—91no—
341#450—91no—
342#450—91no—
343#450—91no—
344#418—91no—
345#416—91no—
346#408—91no—
347C23×D3—61no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C3×#41—34no—
354C3×#41—62no—
355C3×#41—62no—
356C3×#41—62no—
357C2×C3×Q8—21no—
358C2×C3×Q8—21no—
359C2×C3×Q8—31no—
360C2×C3×Q8—61no—
361C2×C3×Q8—62no—
362C2×C3×Q8—62no—
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×Q8C22×D311yescharacteristic
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—61no—
370C2×C3×D4—61no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—61no—
374C22×C3×C4—61no—
375C22×C3×C4—61no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384#239—22no—
385#239—22no—
386#239—22no—
387#239—62no—
388#239—62no—
389#239—62no—
390#239—62no—
391#239—122no—
392#239—122no—
393#239#6714yes—
394D3×Q8—22no—
395D3×Q8—22no—
396D3×D4—34no—
397D3×D4—62no—
398D3×D4—62no—
399D3×D4—68no—
400D3×D4—68no—
401D3×D4—62no—
402D3×D4—62no—
403D3×D4—68no—
404D3×D4—68no—
405D3×D4—62no—
406D3×D4—62no—
407D3×D4—62no—
408#235—62no—
409#235—62no—
410#235—68no—
411#235—68no—
412#235—62no—
413#235—62no—
414C2×D12—21no—
415C2×D12—21no—
416C2×D12—31no—
417C2×D12—31no—
418C2×D12—34no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—61no—
422C2×D12—62no—
423C2×D12—62no—
424C2×D12—68no—
425C2×D12—68no—
426C2×D12—61no—
427C2×D12—61no—
428C2×D12—61no—
429C2×D12—61no—
430C2×D12—62no—
431C2×D12—121no—
432C2×D12C22×D311yescharacteristic
433C2×D12C22×D311yescharacteristic
434C2×C4×D3—21no—
435C2×C4×D3—21no—
436C2×C4×D3—21no—
437C2×C4×D3—31no—
438C2×C4×D3—31no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—61no—
442C2×C4×D3—121no—
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D311yescharacteristic
445C2×Dic6—21no—
446C2×Dic6—31no—
447C2×Dic6—31no—
448C2×Dic6C22×D311yescharacteristic
449C3×Q16—22no—
450C3×Q16—22no—
451C3×Q16—42no—
452C3×Q16—62no—
453C3×SD16—62no—
454C3×SD16—62no—
455C3×SD16—62no—
456C3×M16—62no—
457C2×C3×C8—21no—
458C2×C3×C8—31no—
459C2×C3×C8—31no—
460C2×C3×C8C22×D311yescharacteristic
461C2×C3×C8C22×D311yescharacteristic
462C3×C4⋊C4—31no—
463C3×C4⋊C4—61no—
464C3×C22⋊C4—61no—
465#217—61no—
466#217—61no—
467#216—22no—
468#215—22no—
469#215—22no—
470#215—62no—
471#215—62no—
472#215—62no—
473#215—62no—
474#215—122no—
475#214—62no—
476(C2×D3)⋊C4—21no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—121no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—61no—
487C4⋊Dic3—61no—
488C4⋊Dic3C22×D311yescharacteristic
489Dic3⋊C4—21no—
490Dic3⋊C4—61no—
491Dic3⋊C4—61no—
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—121no—
496C4×Dic3—61no—
497C4×Dic3—61no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8—62no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504#204—22no—
505#204—62no—
506ΓL(1,𝔽25)—22no—
507D3×C8—62no—
508C22×C32C22×D411yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
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#12012yes—
527D32—84no—
528D32—84no—
529D32—84no—
530C32×C4—22no—
531C32×C4—41no—
532C32×C4C22×D411yescharacteristic
533C32×C4C22×D411yescharacteristic
534C3⋊Dic3—21no—
535C3⋊Dic3—41no—
536C3×Dic3—21no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C3×Dic3#12012yes—
540H(5,𝔽2)—184no—
541H(5,𝔽2)—184no—
542C2×#41—31no—
543C2×#41—31no—
544C2×#41—91no—
545C2×#41—91no—
546C2×#41—181no—
547C22×Q8—31no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C22×D4—181no—
552C22×D4—181no—
553C22×D4—181no—
554#137—64no—
555C2×Q16—31no—
556C2×Q16D3211yescharacteristic, complemented
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16—31no—
560C2×SD16—91no—
561C2×SD16—91no—
562C2×SD16—91no—
563C2×SD16—184no—
564C2×M16—31no—
565C22×C8—91no—
566C4⋊Q8—181no—
567#124—181no—
568#123—181no—
569#123—181no—
570C22⋊Q8—31no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—91no—
574#117—91no—
575#103—31no—
576#103—91no—
577#102—31no—
578#102—91no—
579#102—91no—
580#102—91no—
581#102—91no—
582#102—91no—
583C22⋊C8—31no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C22⋊C8—91no—
587C23×C3—31no—
588C23×C3—31no—
589C23×C3—61no—
590C23×C3—61no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—31no—
594C22×D3—31no—
595C22×D3—61no—
596C22×D3—64no—
597C22×D3—64no—
598C22×D3—64no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—64no—
604C22×D3—121no—
605C22×D3—241no—
606C22×D3—241no—
607C22×D3—241no—
608C22×D3—241no—
609C22×D3—241no—
610C22×D3—241no—
611C22×D3—241no—
612C22×D3—241no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3D3×D411yescharacteristic
618C22×D3D3×D411yescharacteristic
619C3×Q8—21no—
620C3×Q8—21no—
621C3×Q8—21no—
622C3×Q8—21no—
623C3×Q8—21no—
624C3×Q8—21no—
625C3×Q8—22no—
626C3×Q8—41no—
627C3×Q8—41no—
628C3×Q8—41no—
629C3×Q8—61no—
630C3×Q8—61no—
631C3×Q8—122no—
632C3×Q8D3×D412yes—
633C3×Q8C2×#6712yes—
634C3×D4—32no—
635C3×D4—32no—
636C3×D4—64no—
637C3×D4—64no—
638C3×D4—61no—
639C3×D4—61no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—31no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—31no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—64no—
652C2×C3×C4—64no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—122no—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660#67—62no—
661#67—64no—
662#67—62no—
663#67—64no—
664#67—64no—
665#67—62no—
666#67—64no—
667#67—62no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—121no—
676C2×Dic3D3×D411yescharacteristic
677C2×Dic3D3×D411yescharacteristic
678D12—24no—
679D12—24no—
680D12—21no—
681D12—21no—
682D12—32no—
683D12—32no—
684D12—62no—
685D12—64no—
686D12—64no—
687D12—62no—
688D12—64no—
689D12—64no—
690D12—62no—
691D12—61no—
692D12—61no—
693D12—121no—
694D12—124no—
695D12D3×D412yes—
696D12C2×#6712yes—
697C4×D3—24no—
698C4×D3—21no—
699C4×D3—21no—
700C4×D3—24no—
701C4×D3—42no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—61no—
705C4×D3—61no—
706C4×D3—61no—
707C4×D3—61no—
708C4×D3—121no—
709C4×D3—121no—
710C4×D3—124no—
711C4×D3D3×D412yes—
712C4×D3C2×#6712yes—
713Dic6—21no—
714Dic6—21no—
715Dic6—42no—
716Dic6—62no—
717Dic6—62no—
718C3×C8—21no—
719C3×C8—21no—
720C3×C8—41no—
721C3×C8—61no—
722C3×C8—61no—
723C3⋊C8—21no—
724C3⋊C8—21no—
725C3⋊C8—61no—
726C3⋊C8—61no—
727C3⋊C8—121no—
728C2×C32C2×#12011yescharacteristic
729C2×C32#57711yescharacteristic
730C2×C32#57711yescharacteristic
731C3⋊D3—41no—
732C3⋊D3—42no—
733C3×D3—22no—
734C3×D3—41no—
735C3×D3—42no—
736C3×D3—42no—
737C24—181no—
738C24—181no—
739C24—181no—
740#41—34no—
741#41—62no—
742#41—62no—
743#41—62no—
744#41—182no—
745#41—182no—
746#41—188no—
747#41—182no—
748#41—182no—
749C2×Q8—31no—
750C2×Q8—61no—
751C2×Q8—62no—
752C2×Q8—62no—
753C2×Q8—91no—
754C2×Q8C2×D3211yescharacteristic
755C2×Q8C2×D3211yescharacteristic
756C2×D4—31no—
757C2×D4—31no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—94no—
761C2×D4—91no—
762C2×D4—91no—
763C2×D4—91no—
764C2×D4—91no—
765C2×D4—181no—
766C2×D4—182no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—182no—
770C2×D4—182no—
771C2×D4—188no—
772C2×D4—188no—
773C2×D4—181no—
774C2×D4—182no—
775C2×D4—182no—
776C2×D4—188no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—91no—
783C22×C4—181no—
784Q16—22no—
785Q16—62no—
786SD16—62no—
787SD16—62no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792M16—62no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—91no—
796C2×C8—182no—
797C2×C8C2×D3211yescharacteristic
798C4⋊C4—31no—
799C4⋊C4—61no—
800C4⋊C4—91no—
801C4⋊C4—181no—
802C4⋊C4—181no—
803C4⋊C4—181no—
804C22⋊C4—61no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C42—181no—
810C22×C3—21no—
811C22×C3—32no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—62no—
817C22×C3—61no—
818C22×C3—62no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—22no—
830C2×D3—21no—
831C2×D3—22no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—61no—
839C2×D3—61no—
840C2×D3—62no—
841C2×D3—61no—
842C2×D3—62no—
843C2×D3—61no—
844C2×D3—122no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—241no—
853C2×D3—241no—
854C2×D3—244no—
855C2×D3—244no—
856C2×D3—244no—
857C2×D3—244no—
858C2×D3—244no—
859C2×D3—244no—
860C2×D3#93712yes—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—21no—
864C3×C4—21no—
865C3×C4—32no—
866C3×C4—42no—
867C3×C4—41no—
868C3×C4—41no—
869C3×C4—61no—
870C3×C4—81no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875C3×C4C2×D3×D411yescharacteristic
876C3×C4C22×#6711yescharacteristic
877Dic3—21no—
878Dic3—41no—
879Dic3—41no—
880Dic3—61no—
881Dic3—61no—
882Dic3—121no—
883Dic3—121no—
884Dic3—121no—
885Dic3—241no—
886Dic3#93712yes—
887C32#300911yescharacteristic, complemented, Sylow
888C23—31no—
889C23—31no—
890C23—61no—
891C23—61no—
892C23—91no—
893C23—184no—
894C23—184no—
895C23—184no—
896C23—181no—
897C23—721no—
898C23—721no—
899C23—721no—
900C23—721no—
901C23—721no—
902C23—721no—
903Q8—21no—
904Q8—21no—
905Q8—21no—
906Q8—61no—
907Q8—61no—
908Q8—122no—
909Q8—182no—
910Q8D3×#6712yes—
911D4—32no—
912D4—32no—
913D4—64no—
914D4—64no—
915D4—61no—
916D4—61no—
917D4—92no—
918D4—184no—
919D4—184no—
920D4—182no—
921D4—182no—
922D4—184no—
923D4—182no—
924D4—184no—
925D4—181no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—31no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—31no—
932C2×C4—64no—
933C2×C4—64no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—91no—
939C2×C4—122no—
940C2×C4—184no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—181no—
944C2×C4C22×D3211yescharacteristic
945C8—21no—
946C8—61no—
947C8—61no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—62no—
953C2×C3—121no—
954C2×C3—122no—
955C2×C3—122no—
956C2×C3D3×#12011yescharacteristic
957C2×C3#577011yescharacteristic
958C2×C3#577811yescharacteristic
959C2×C3#577811yescharacteristic
960C2×C3#577811yescharacteristic
961C2×C3C2×#93711yescharacteristic
962D3—22no—
963D3—42no—
964D3—41no—
965D3—42no—
966D3—121no—
967D3—122no—
968D3—121no—
969D3—122no—
970D3—241no—
971D3—242no—
972C22—32no—
973C22—61no—
974C22—61no—
975C22—62no—
976C22—62no—
977C22—61no—
978C22—61no—
979C22—61no—
980C22—121no—
981C22—121no—
982C22—121no—
983C22—121no—
984C22—182no—
985C22—181no—
986C22—181no—
987C22—181no—
988C22—361no—
989C22—361no—
990C22—724no—
991C22—724no—
992C22—724no—
993C22D32×D411yescharacteristic
994C4—22no—
995C4—32no—
996C4—41no—
997C4—61no—
998C4—121no—
999C4—121no—
1000C4—181no—
1001C4—361no—
1002C4D32×D411yescharacteristic
1003C4C2×D3×#6711yescharacteristic
1004C3—21no—
1005C3#8022911yescharacteristic, complemented
1006C3#8398211yescharacteristic, complemented
1007C2—62no—
1008C2—121no—
1009C2—122no—
1010C2—122no—
1011C2—361no—
1012C2—362no—
1013C2#1059476711yescharacteristic
1014C2#1059477011yescharacteristic
1015C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#64320C2
hypercenterC2×Q16D32
hypocenterC32#3009
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
2. C2×C3×#918C2semidirect
3. #10595397C2semidirect
4. C2×D3×#215C2semidirect
5. #10592886C2semidirect
6. C3×#5187C2semidirect
7. #10591652C2semidirect
8. #10591651C2semidirect
9. #10591602C2semidirect
10. #10591597C2semidirect
11. #10591556C2semidirect
12. #10590955C2semidirect
13. #10590943C2semidirect
14. #10590942C2semidirect
15. #10590939C2semidirect
21. C2×C3×D3×Q8C22semidirect
32. C2×C32×Q16C22semidirect
33. #64155C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#215C22semidirect
40. C2×C3×#204C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
45. #63871C22semidirect
46. #63856C22semidirect
48. #63841C22semidirect
50. C2×#3717C22semidirect
51. C2×#3715C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63662C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63564C22semidirect
60. #63563C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
70. C2×#918D3semidirect
81. #5187D3semidirect
182. C2×D3×Q8C2×D3semidirect
202. C2×C3×Q16C2×D3semidirect
203. C2×C3×Q16C2×D3semidirect
215. #946C2×D3semidirect
217. C2×#216C2×D3semidirect
224. C2×#215C2×D3semidirect
225. C2×#215C2×D3semidirect
235. C2×#204C2×D3semidirect
236. C2×ΓL(1,𝔽25)C2×D3semidirect
250. #835C2×D3semidirect
261. #821C2×D3semidirect
268. (C2×D3)⋊C8C2×D3semidirect
556. C2×Q16D32semidirect
887. C32#3009semidirect
1005. C3#80229semidirect
1006. C3#83982semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×C3×#9182
#105953972
C2×D3×#2152
#105928862
C3×#51872
#105916522
#105916512
#105916022
#105915972
#105915562
#105909552
#105909432
#105909422
#105909392
#839823
#802293