Finite Group Databasebeta

← #11864643

Subgroups — #11864643

Order 1152.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4#10594522C211yesmaximal, characteristic, complemented
5#10592507C211yesmaximal, characteristic, complemented
6C3×#4810C211yesmaximal, characteristic, complemented
7C3×#4803C211yesmaximal, characteristic, complemented
8#10591599C211yesmaximal, characteristic, complemented
9#10591593C211yesmaximal, characteristic, complemented
10#10590955C211yesmaximal, characteristic, complemented
11#10590946C211yesmaximal, characteristic, complemented
12#10590945C211yesmaximal, characteristic, complemented
13#10590597C211yesmaximal, characteristic, complemented
14#10590595C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#80087—31nomaximal
17#78886—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21#64320—24no—
22#64320—24no—
23C2×#3802—21no—
24C2×#3802C2211yescharacteristic
25C2×D3×D12—21no—
26C2×D3×D12—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×#3798—21no—
30C2×#3798C2211yescharacteristic
31C2×#3795C2211yescharacteristic, complemented
32C2×#3756C2211yescharacteristic, complemented
33C2×#3744C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35C2×C3×#215C2211yescharacteristic, complemented
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C3×#895C2211yescharacteristic, complemented
39C3×D3×C4⋊C4C2211yescharacteristic, complemented
40#63947—24no—
41#63916C2211yescharacteristic, complemented
42#63908—21no—
43#63906—21no—
44#63893—21no—
45#63886—21no—
46#63857C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63795—24no—
53C32×#103C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1009—31no—
67C2×#950—31no—
68C2×#916—31no—
69C2×#911—31no—
70C2×#908—31no—
71#5608—31no—
72#5510—31no—
73C3×#449—31no—
74C3×#417—31no—
75#5239—31no—
76#5172—31no—
77#5156—31no—
78#5129—31no—
79#5036—31no—
80C2×#809—31no—
81#4810—31no—
82#4810D311yescharacteristic, complemented
83#4808—31no—
84#4808—31no—
85#4808—31no—
86#4808—61no—
87#4803D311yescharacteristic, complemented
88#4776—31no—
89#4776—31no—
90#4776—31no—
91#4773—31no—
92#4773—31no—
93D3×#102—31no—
94#4731—31no—
95#4727—31no—
96C22×D32—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100#3832—22no—
101#3832—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C3×#239—22no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239D414yescomplemented
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
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×#627D411yescharacteristic
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626D411yescharacteristic
127C2×#626D411yescharacteristic
128C2×#625—21no—
129C2×#625—21no—
130C2×#625D411yescharacteristic
131C2×D3×Dic3—21no—
132#3802—28no—
133#3802—22no—
134#3802—22no—
135D3×D12—28no—
136D3×D12—28no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12D414yescomplemented
141#3798—28no—
142#3798—22no—
143#3798—22no—
144#3795—22no—
145#3795—22no—
146C2×C32×C8C2311yescharacteristic
147C32×C4⋊C4C2311yescharacteristic
148#3756—22no—
149#3752—21no—
150C4⋊(C3⋊Dic3)—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152#3744—22no—
153C3×#215—22no—
154C3×(C2×D3)⋊C4—21no—
155C3×C4⋊Dic3C2311yescharacteristic
156C3×Dic3⋊C4—21no—
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×D24—22no—
160C3×ΓL(1,𝔽25)—22no—
161Dic3⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163(C2×D3)⋊Dic3—21no—
164#3716—22no—
165#3716—22no—
166#3714—22no—
167#3713—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172#1009—64no—
173#1009—64no—
174#1009—64no—
175#1009—64no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—61no—
179C2×#239C2×D311yescharacteristic
180C2×#239C2×D311yescharacteristic
181C2×#237—31no—
182C2×D3×D4—31no—
183C2×D3×D4—31no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—61no—
194C2×#235—61no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—61no—
198C22×D12—61no—
199C2×C3×SD16—31no—
200C2×C3×D8—31no—
201C2×C3×M16—31no—
202C3×#121—31no—
203C2×C3×C4⋊C4—31no—
204#950—64no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#216—61no—
208C2×#215C2×D311yescharacteristic, complemented
209#939—61no—
210#938—31no—
211#938—61no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217#930—61no—
218#930—61no—
219#924—31no—
220C22×C3⋊C8—31no—
221#916—64no—
222#911—64no—
223#908—64no—
224C2×D24—31no—
225C2×D24C2×D311yescharacteristic, complemented
226C2×#204—31no—
227C2×#204—31no—
228C2×#204—31no—
229C2×#204—31no—
230C2×#204—61no—
231C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
232C2×D3×C8—31no—
233#897—31no—
234#897—31no—
235#897—31no—
236#897—61no—
237#897—61no—
238#895—31no—
239#895—61no—
240#895C2×D311yescharacteristic, complemented
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242#884—61no—
243#878—61no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103C2×D311yescharacteristic, complemented
247C3×#103C2×D311yescharacteristic, complemented
248C3×#102—31no—
249C3×#102—31no—
250C3×#102—31no—
251C3×C22⋊C8—31no—
252#835C2×D311yescharacteristic, complemented
253#832—31no—
254#830—31no—
255#821—31no—
256#821C2×D311yescharacteristic, complemented
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—61no—
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264#809—31no—
265#809—31no—
266#809—31no—
267#809—31no—
268#809—61no—
269#809C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C22×C3⋊D3—21no—
272C22×C3⋊D3C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3C2×D411yescharacteristic
277C22×C3×D3C2×D411yescharacteristic
278C2×D32—24no—
279C2×D32—24no—
280C2×D32—24no—
281C2×D32—81no—
282C2×D32—81no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C32×Q8—21no—
288C32×Q8C2×D412yes—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4C2411yescharacteristic
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3C2×D411yescharacteristic
294C4⋊(C3⋊D3)—24no—
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)C2×D412yes—
297C4×C3⋊D3—24no—
298C4×C3⋊D3—21no—
299C4×C3⋊D3—21no—
300#634—21no—
301#634—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×D12—21no—
310C3×D12—21no—
311C3×D12—81no—
312C3×D12C2×D412yes—
313C3×D12C2×D412yes—
314C3×C4×D3—24no—
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—24no—
318C3×C4×D3—81no—
319C3×C4×D3C2×D412yes—
320C3×C4×D3C2×D412yes—
321#627—22no—
322#626—24no—
323#626—22no—
324#626—22no—
325#626—24no—
326#626—81no—
327#625—24no—
328#625—22no—
329#625—42no—
330D3×Dic3—42no—
331C32×C8—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—91no—
339#452—91no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—31no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—31no—
348C2×#102—91no—
349#408—91no—
350C23×D3—61no—
351C23×D3—61no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C3×#41—34no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C2×C3×Q8—21no—
361C2×C3×Q8C22×D311yescharacteristic
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—61no—
372C22×C3×C4—61no—
373C22×C3×C4—61no—
374C2×#67—31no—
375C2×#67—31no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C22×Dic3—61no—
386#239—22no—
387#239—22no—
388#239—22no—
389#239—62no—
390#239—62no—
391#239—62no—
392#239—62no—
393#239—122no—
394#239—122no—
395#239D1214yescomplemented
396#237—62no—
397#237—62no—
398D3×D4—34no—
399D3×D4—62no—
400D3×D4—62no—
401D3×D4—68no—
402D3×D4—68no—
403D3×D4—62no—
404D3×D4—62no—
405D3×D4—68no—
406D3×D4—68no—
407D3×D4—62no—
408D3×D4—62no—
409D3×D4—62no—
410#235—62no—
411#235—62no—
412#235—68no—
413#235—68no—
414#235—62no—
415#235—62no—
416#235—62no—
417#235—62no—
418C2×D12—21no—
419C2×D12—21no—
420C2×D12—21no—
421C2×D12—31no—
422C2×D12—31no—
423C2×D12—34no—
424C2×D12—31no—
425C2×D12—31no—
426C2×D12—61no—
427C2×D12—62no—
428C2×D12—62no—
429C2×D12—68no—
430C2×D12—68no—
431C2×D12—61no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—62no—
436C2×D12—61no—
437C2×D12—121no—
438C2×D12C22×D311yescharacteristic
439C2×D12C22×D311yescharacteristic
440C2×D12C22×D311yescharacteristic
441C2×C4×D3—21no—
442C2×C4×D3—21no—
443C2×C4×D3—21no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—121no—
451C2×C4×D3C22×D311yescharacteristic
452C2×C4×D3C22×D311yescharacteristic
453C2×Dic6—31no—
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6—61no—
458C3×SD16—62no—
459C3×D8—62no—
460C3×M16—62no—
461C2×C3×C8—21no—
462C2×C3×C8—31no—
463C2×C3×C8—31no—
464C2×C3×C8C22×D311yescharacteristic
465C2×C3×C8C22×D311yescharacteristic
466C3×C4⋊C4—21no—
467C3×C4⋊C4—31no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4C22×D311yescharacteristic
470C3×C4⋊C4C22×D311yescharacteristic
471C3×C22⋊C4—61no—
472#217—61no—
473#217—61no—
474#216—62no—
475#216—62no—
476#216—122no—
477#215—22no—
478#214—62no—
479#214—62no—
480#213—62no—
481#213—62no—
482#213—62no—
483(C2×D3)⋊C4—21no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—61no—
488(C2×D3)⋊C4—121no—
489C4⋊Dic3—61no—
490C4⋊Dic3—61no—
491C4⋊Dic3—61no—
492C4⋊Dic3—121no—
493C4⋊Dic3C22×D311yescharacteristic
494Dic3⋊C4—21no—
495Dic3⋊C4—61no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—61no—
499C2×C3⋊C8—62no—
500C2×C3⋊C8C22×D311yescharacteristic
501C2×C3⋊C8C22×D311yescharacteristic
502D24—22no—
503D24—62no—
504#204—62no—
505#204—62no—
506#204—62no—
507#204—62no—
508#204—122no—
509ΓL(1,𝔽25)—22no—
510D3×C8—62no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—21no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3#12012yes—
533D32—84no—
534D32—84no—
535D32—84no—
536C32×C4—22no—
537C32×C4—41no—
538C32×C4C22×D411yescharacteristic
539C32×C4C22×D411yescharacteristic
540C3⋊Dic3—21no—
541C3⋊Dic3—41no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—31no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—31no—
570C22×C8—91no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—31no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—31no—
580#103—31no—
581#103D3211yescharacteristic, complemented
582#102—31no—
583#102—31no—
584#102—31no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—31no—
593C23×C3—31no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—31no—
601C22×D3—31no—
602C22×D3—61no—
603C22×D3—64no—
604C22×D3—64no—
605C22×D3—64no—
606C22×D3—64no—
607C22×D3—64no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—64no—
611C22×D3—121no—
612C22×D3—241no—
613C22×D3—241no—
614C22×D3—241no—
615C22×D3—241no—
616C22×D3—241no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3D3×D411yescharacteristic
625C22×D3D3×D411yescharacteristic
626C3×Q8—21no—
627C3×Q8—21no—
628C3×Q8—22no—
629C3×Q8—41no—
630C3×Q8C2×D1212yes—
631C3×Q8D3×D412yes—
632C3×D4—32no—
633C3×D4—32no—
634C3×D4—64no—
635C3×D4—64no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—241no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—31no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—31no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—64no—
653C2×C3×C4—64no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—241no—
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—
668#67—122no—
669#67—122no—
670#67—241no—
671C2×Dic3—21no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—121no—
678C2×Dic3—122no—
679C2×Dic3D3×D411yescharacteristic
680C2×Dic3D3×D411yescharacteristic
681D12—24no—
682D12—24no—
683D12—21no—
684D12—21no—
685D12—21no—
686D12—21no—
687D12—32no—
688D12—32no—
689D12—62no—
690D12—64no—
691D12—64no—
692D12—62no—
693D12—64no—
694D12—64no—
695D12—62no—
696D12—61no—
697D12—61no—
698D12—81no—
699D12—121no—
700D12—124no—
701D12—241no—
702D12C2×D1212yes—
703D12D3×D412yes—
704C4×D3—24no—
705C4×D3—21no—
706C4×D3—21no—
707C4×D3—24no—
708C4×D3—64no—
709C4×D3—64no—
710C4×D3—61no—
711C4×D3—61no—
712C4×D3—61no—
713C4×D3—61no—
714C4×D3—81no—
715C4×D3—121no—
716C4×D3—121no—
717C4×D3—124no—
718C4×D3—122no—
719C4×D3C2×D1212yes—
720C4×D3D3×D412yes—
721Dic6—62no—
722Dic6—62no—
723Dic6—61no—
724Dic6—61no—
725Dic6—61no—
726Dic6—61no—
727Dic6—121no—
728Dic6—121no—
729C3×C8—21no—
730C3×C8—21no—
731C3×C8—41no—
732C3×C8—61no—
733C3×C8—61no—
734C3⋊C8—21no—
735C3⋊C8—21no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—121no—
739C2×C32C2×#12011yescharacteristic
740C2×C32#57611yescharacteristic
741C2×C32#57711yescharacteristic
742C3⋊D3—41no—
743C3⋊D3—42no—
744C3×D3—22no—
745C3×D3—41no—
746C3×D3—42no—
747C3×D3—42no—
748C3×D3—81no—
749C24—181no—
750C24—181no—
751C24—181no—
752#41—34no—
753#41—62no—
754#41—62no—
755#41—62no—
756#41—182no—
757#41—182no—
758#41—182no—
759#41—182no—
760#41—188no—
761#41—182no—
762#41—182no—
763C2×Q8—91no—
764C2×Q8—91no—
765C2×Q8C2×D3211yescharacteristic
766C2×D4—31no—
767C2×D4—31no—
768C2×D4—31no—
769C2×D4—61no—
770C2×D4—61no—
771C2×D4—61no—
772C2×D4—94no—
773C2×D4—91no—
774C2×D4—91no—
775C2×D4—91no—
776C2×D4—91no—
777C2×D4—181no—
778C2×D4—182no—
779C2×D4—181no—
780C2×D4—181no—
781C2×D4—182no—
782C2×D4—182no—
783C2×D4—188no—
784C2×D4—188no—
785C2×D4—181no—
786C2×D4—181no—
787C2×D4—182no—
788C2×D4—182no—
789C2×D4—188no—
790C2×D4—181no—
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—91no—
797C22×C4—181no—
798C22×C4—181no—
799Q16—182no—
800SD16—62no—
801SD16—182no—
802SD16—182no—
803SD16—182no—
804D8—62no—
805D8—182no—
806D8—182no—
807M16—62no—
808C2×C8—31no—
809C2×C8—31no—
810C2×C8—91no—
811C2×C8—182no—
812C2×C8C2×D3211yescharacteristic
813C4⋊C4—31no—
814C4⋊C4—61no—
815C4⋊C4—181no—
816C4⋊C4—181no—
817C4⋊C4C2×D3211yescharacteristic
818C22⋊C4—61no—
819C22⋊C4—181no—
820C22⋊C4—181no—
821C22⋊C4—181no—
822C22×C3—21no—
823C22×C3—32no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—62no—
827C22×C3—61no—
828C22×C3—61no—
829C22×C3—61no—
830C22×C3—62no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3—121no—
837C22×C3—121no—
838C22×C3C2×D3×D411yescharacteristic
839C22×C3C2×D3×D411yescharacteristic
840C2×D3—21no—
841C2×D3—21no—
842C2×D3—22no—
843C2×D3—21no—
844C2×D3—21no—
845C2×D3—21no—
846C2×D3—22no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—62no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—61no—
858C2×D3—61no—
859C2×D3—61no—
860C2×D3—62no—
861C2×D3—61no—
862C2×D3—122no—
863C2×D3—121no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—241no—
871C2×D3—241no—
872C2×D3—244no—
873C2×D3—244no—
874C2×D3—244no—
875C2×D3—244no—
876C2×D3—244no—
877C2×D3—244no—
878C2×D3#88212yes—
879C3×C4—22no—
880C3×C4—22no—
881C3×C4—21no—
882C3×C4—21no—
883C3×C4—32no—
884C3×C4—42no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—61no—
888C3×C4—81no—
889C3×C4—121no—
890C3×C4C22×D1211yescharacteristic
891C3×C4C2×D3×D411yescharacteristic
892C3×C4C2×D3×D411yescharacteristic
893C3×C4C2×D3×D411yescharacteristic
894Dic3—21no—
895Dic3—41no—
896Dic3—61no—
897Dic3—61no—
898Dic3—121no—
899Dic3—121no—
900Dic3—121no—
901Dic3—241no—
902Dic3#88212yes—
903C32#301211yescharacteristic, complemented, Sylow
904C23—31no—
905C23—31no—
906C23—61no—
907C23—61no—
908C23—61no—
909C23—91no—
910C23—184no—
911C23—184no—
912C23—184no—
913C23—181no—
914C23—721no—
915C23—721no—
916C23—721no—
917C23—721no—
918C23—721no—
919C23—721no—
920Q8—21no—
921Q8—182no—
922Q8—181no—
923Q8—181no—
924Q8D3×D1212yes—
925D4—32no—
926D4—32no—
927D4—64no—
928D4—64no—
929D4—61no—
930D4—61no—
931D4—61no—
932D4—61no—
933D4—92no—
934D4—184no—
935D4—184no—
936D4—182no—
937D4—182no—
938D4—184no—
939D4—182no—
940D4—184no—
941D4—181no—
942D4—241no—
943D4—362no—
944D4—721no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—31no—
948C2×C4—32no—
949C2×C4—32no—
950C2×C4—31no—
951C2×C4—64no—
952C2×C4—64no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—91no—
957C2×C4—184no—
958C2×C4—181no—
959C2×C4—181no—
960C2×C4—181no—
961C2×C4—241no—
962C2×C4—362no—
963C2×C4C22×D3211yescharacteristic
964C8—21no—
965C8—61no—
966C8—61no—
967C8—181no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—62no—
972C2×C3—121no—
973C2×C3—122no—
974C2×C3—122no—
975C2×C3—241no—
976C2×C3C2×#88211yescharacteristic
977C2×C3D3×#12011yescharacteristic
978C2×C3#577011yescharacteristic
979C2×C3#577411yescharacteristic
980C2×C3#577411yescharacteristic
981C2×C3#577811yescharacteristic
982D3—22no—
983D3—42no—
984D3—41no—
985D3—42no—
986D3—81no—
987D3—121no—
988D3—122no—
989D3—121no—
990D3—122no—
991D3—241no—
992D3—242no—
993C22—32no—
994C22—61no—
995C22—61no—
996C22—61no—
997C22—62no—
998C22—62no—
999C22—61no—
1000C22—61no—
1001C22—121no—
1002C22—121no—
1003C22—121no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—181no—
1009C22—182no—
1010C22—181no—
1011C22—181no—
1012C22—361no—
1013C22—361no—
1014C22—724no—
1015C22—724no—
1016C22—724no—
1017C22D32×D411yescharacteristic
1018C4—22no—
1019C4—32no—
1020C4—41no—
1021C4—61no—
1022C4—121no—
1023C4—181no—
1024C4—361no—
1025C4C2×D3×D1211yescharacteristic
1026C4D32×D411yescharacteristic
1027C3—21no—
1028C3#7888611yescharacteristic, complemented
1029C3#8008711yescharacteristic, complemented
1030C2—62no—
1031C2—121no—
1032C2—122no—
1033C2—122no—
1034C2—241no—
1035C2—361no—
1036C2—362no—
1037C2D3×#88211yescharacteristic
1038C2#1059475011yescharacteristic
1039C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. C2×#64320C2semidirect
2. C2×#63947C2semidirect
3. C2×#63795C2semidirect
4. #10594522C2semidirect
5. #10592507C2semidirect
6. C3×#4810C2semidirect
7. C3×#4803C2semidirect
8. #10591599C2semidirect
9. #10591593C2semidirect
10. #10590955C2semidirect
11. #10590946C2semidirect
12. #10590945C2semidirect
13. #10590597C2semidirect
14. #10590595C2semidirect
15. D3×#809C2semidirect
31. C2×#3795C22semidirect
32. C2×#3756C22semidirect
33. C2×#3744C22semidirect
34. #64106C22semidirect
35. C2×C3×#215C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C3×#895C22semidirect
39. C3×D3×C4⋊C4C22semidirect
41. #63916C22semidirect
46. #63857C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. C32×#103C22semidirect
54. #63647C22semidirect
55. #63636C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
82. #4810D3semidirect
87. #4803D3semidirect
110. C3×#239D4semidirect
140. D3×D12D4semidirect
208. C2×#215C2×D3semidirect
225. C2×D24C2×D3semidirect
231. C2×ΓL(1,𝔽25)C2×D3semidirect
240. #895C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
246. C3×#103C2×D3semidirect
247. C3×#103C2×D3semidirect
252. #835C2×D3semidirect
256. #821C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
395. #239D12semidirect
581. #103D32semidirect
903. C32#3012semidirect
1028. C3#78886semidirect
1029. C3#80087semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#639472
C2×#637952
#105945222
#105925072
C3×#48102
C3×#48032
#105915992
#105915932
#105909552
#105909462
#105909452
#105905972
#105905952
D3×#8092
#800873
#788863