Finite Group Databasebeta

← D3×#4771 #11857905

Subgroups — D3×#4771 #11857905

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 967 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3D32×C4⋊C4C211yesmaximal, characteristic, complemented
4#10592470C211yesmaximal, characteristic, complemented
5C3×#4771C211yesmaximal, characteristic, complemented
6C3×D3×#102C211yesmaximal, characteristic, complemented
7#10591418C211yesmaximal, characteristic, complemented
8#10591414C211yesmaximal, characteristic, complemented
9D3×#832C211yesmaximal, characteristic, complemented
10#10590957C211yesmaximal, characteristic, complemented
11#10590670C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13#10590612C211yesmaximal, characteristic, complemented
14#10590607C211yesmaximal, characteristic, complemented
15D3×#810C211yesmaximal, characteristic, complemented
16D3×#417—31nomaximal
17C2×#4771—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C22×D3×Dic3—21no—
25D3×#237—24no—
26D3×#237C418yescomplemented
27C2×C4×D32—21no—
28C2×C4×D32C2211yescharacteristic
29C2×#3796C2211yescharacteristic
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic
32C2×#3743C2211yescharacteristic, complemented
33C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
35C2×C3×D3×C8C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic, complemented
38#63900C2211yescharacteristic, complemented
39D3×C4⋊Dic3C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic, complemented
41#63883—21no—
42D3×Dic3⋊C4—21no—
43D3×Dic3⋊C4—21no—
44C2×#3712C2211yescharacteristic, complemented
45C2×#3711C2211yescharacteristic, complemented
46C2×D3×C3⋊C8C2211yescharacteristic
47D3×ΓL(1,𝔽25)—24no—
48C32×#102C2211yescharacteristic, complemented
49#63659C2211yescharacteristic, complemented
50#63643C2211yescharacteristic, complemented
51#63637C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64C2×D3×#41—31no—
65C22×#237—31no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68C2×D3×C4⋊C4—31no—
69C2×D3×C4⋊C4—31no—
70C3×#417—31no—
71C2×C3×#102—31no—
72#5232—31no—
73C2×#832—31no—
74#5133—31no—
75C2×#816—31no—
76C2×#810—31no—
77#4966—31no—
78#4803—31no—
79#4803—31no—
80D3×#103—31no—
81D3×#103—31no—
82#4771—31no—
83#4771—31no—
84#4771—31no—
85#4771—31no—
86#4771—31no—
87#4771—31no—
88#4771—31no—
89#4771—31no—
90#4771—31no—
91#4771—61no—
92#4771D311yescharacteristic, direct product factor
93D3×#102—31no—
94D3×#102D311yescharacteristic, complemented
95C23×C3×D3—21no—
96C22×D32D411yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C22×C3⋊Dic3—21no—
100#3830—22no—
101#3830C2×C414yescomplemented
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C3×#237—22no—
109C3×#237C2×C414yescomplemented
110C3×D3×D4—22no—
111C3×D3×D4C2×C414yescomplemented
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118D3×#67—28no—
119C2×#627—21no—
120C2×#626—21no—
121C2×#625—21no—
122C2×#624—21no—
123C2×#624D411yescharacteristic
124#3805—28no—
125#3804—28no—
126C2×D3×Dic3—21no—
127C2×D3×Dic3—21no—
128C2×D3×Dic3—21no—
129C2×D3×Dic3—28no—
130C2×D3×Dic3—21no—
131C2×D3×Dic3—21no—
132C2×D3×Dic3D411yescharacteristic
133C2×D3×Dic3D411yescharacteristic
134C4×D32—44no—
135C4×D32C2×C414yes—
136C4×D32D414yes—
137#3796—22no—
138#3796C2×C414yescomplemented
139#3795—22no—
140#3795C2×C414yescomplemented
141D3×Dic6—22no—
142D3×Dic6C2×C414yescomplemented
143C2×C32×C8C2311yescharacteristic
144C32×C4⋊C4C2311yescharacteristic
145C4⋊(C3⋊Dic3)C2311yescharacteristic
146#3750—21no—
147C2×C3⋊(C3⋊C8)C2311yescharacteristic
148#3743—22no—
149C3×C4⋊Dic3C2311yescharacteristic
150C3×C4⋊Dic3C2311yescharacteristic
151C3×Dic3⋊C4—21no—
152C3×Dic3⋊C4—21no—
153C2×C3×C3⋊C8C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C3×ΓL(1,𝔽25)—22no—
156C3×D3×C8—22no—
157#3724—21no—
158Dic3⋊Dic3—21no—
159Dic3⋊Dic3—21no—
160#3712—22no—
161#3711—22no—
162D3×C3⋊C8—22no—
163C2×#417—91noSylow
164C2×C3×#41—31no—
165C22×C3×D4—31no—
166C22×#67—61no—
167C23×Dic3—61no—
168D3×#41—38no—
169D3×#41—64no—
170C2×#239—31no—
171C2×D3×Q8—31no—
172C2×#237—31no—
173C2×#237—31no—
174C2×#237—38no—
175C2×#237—31no—
176C2×#237—31no—
177C2×#237—61no—
178C2×#237—64no—
179C2×#237—61no—
180C2×#237—61no—
181C2×#237—61no—
182C2×#237C2×D311yescharacteristic
183C2×D3×D4—61no—
184C2×D3×D4C2×D311yescharacteristic
185C2×#235—31no—
186C2×#235—61no—
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—61no—
190C22×C4×D3—61no—
191C22×C4×D3—61no—
192C22×Dic6—31no—
193C2×C3×M16—31no—
194C22×C3×C8—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×Dic3⋊C4—61no—
200C2×Dic3⋊C4—61no—
201C2×#208—31no—
202C22×C3⋊C8—31no—
203D3×M16—64no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—31no—
207C2×ΓL(1,𝔽25)—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—61no—
210C2×ΓL(1,𝔽25)—64no—
211C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
212C2×D3×C8—31no—
213C2×D3×C8C2×D311yescharacteristic
214D3×C4⋊C4—31no—
215D3×C4⋊C4—31no—
216D3×C4⋊C4—31no—
217D3×C4⋊C4—31no—
218D3×C4⋊C4—31no—
219D3×C4⋊C4—31no—
220D3×C4⋊C4—61no—
221D3×C4⋊C4—61no—
222D3×C4⋊C4—61no—
223D3×C4⋊C4—61no—
224D3×C4⋊C4—61no—
225D3×C4⋊C4C2×D311yescharacteristic
226D3×C4⋊C4C2×D311yescharacteristic, complemented
227C3×#103—31no—
228C3×#103—31no—
229C3×#102—21no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#102—31no—
233C3×#102—31no—
234C3×#102C2×D311yescharacteristic, complemented
235C3×#102C2×D311yescharacteristic, complemented
236#835—31no—
237#835—31no—
238#832—31no—
239#832—31no—
240#832—31no—
241#832—31no—
242#832—61no—
243#832C2×D311yescharacteristic, complemented
244#832C2×D311yescharacteristic, complemented
245#821—31no—
246#821C2×D311yescharacteristic, complemented
247#816—31no—
248#816—31no—
249#816—31no—
250#816—31no—
251#816—31no—
252#816—61no—
253#816C2×D311yescharacteristic, complemented
254#810—31no—
255#810—31no—
256#810—31no—
257#810—31no—
258#810—31no—
259#810—61no—
260#810C2×D311yescharacteristic, complemented
261#809—31no—
262#809C2×D311yescharacteristic, complemented
263C23×C32—21no—
264C22×C3⋊D3C2×D411yescharacteristic
265C22×C3×D3—21no—
266C22×C3×D3—24no—
267C22×C3×D3—42no—
268C22×C3×D3—42no—
269C22×C3×D3C2×D411yescharacteristic
270C22×C3×D3C2×D411yescharacteristic
271C2×D32—22no—
272C2×D32—22no—
273C2×D32C22⋊C414yes—
274C32×D4—21no—
275C32×D4C22×C412yescomplemented
276C2×C32×C4—21no—
277C2×C32×C4C2411yescharacteristic
278#638—24no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—24no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3C2×D411yescharacteristic
283C4×C3⋊D3—42no—
284C4×C3⋊D3C22×C412yes—
285C4×C3⋊D3C2×D412yes—
286#634—21no—
287#634C22×C412yescomplemented
288C3×#67—24no—
289C3×#67—24no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—24no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3C2×D411yescharacteristic
295C2×C3×Dic3C2×D411yescharacteristic
296C3×D12—21no—
297C3×D12C22×C412yescomplemented
298C3×C4×D3—42no—
299C3×C4×D3—42no—
300C3×C4×D3C22×C412yes—
301C3×C4×D3C22×C412yes—
302C3×C4×D3C2×D412yes—
303C3×C4×D3C2×D412yes—
304C3×Dic6—21no—
305C3×Dic6C22×C412yescomplemented
306#627—24no—
307#626—24no—
308#625—24no—
309#624—42no—
310#624C22⋊C414yes—
311D3×Dic3—24no—
312D3×Dic3—24no—
313D3×Dic3—24no—
314D3×Dic3—42no—
315D3×Dic3—42no—
316D3×Dic3C22⋊C414yes—
317D3×Dic3C22⋊C414yes—
318C32×C8—21no—
319C3⋊(C3⋊C8)—21no—
320C3×C3⋊C8—21no—
321C3×C3⋊C8—21no—
322C22×#41—91no—
323C22×M16—91no—
324C22×C4⋊C4—91no—
325#417—31no—
326#417—91no—
327#417—91no—
328#417—91no—
329#417—91no—
330#417—91no—
331#417—91no—
332#417—91no—
333C2×#103—91no—
334C2×#103—91no—
335C2×#102—31no—
336C2×#102—91no—
337C24×C3—61no—
338C23×D3—21no—
339C23×D3—31no—
340C23×D3—31no—
341C3×#41—34no—
342C3×#41—62no—
343C2×C3×Q8—31no—
344C2×C3×D4—21no—
345C2×C3×D4—34no—
346C2×C3×D4—31no—
347C2×C3×D4—62no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4C22×D311yescharacteristic
351C2×C3×D4C22×D311yescharacteristic
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—61no—
360C2×#67—68no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—121no—
366C22×Dic3—21no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—61no—
370C22×Dic3—68no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3—61no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—121no—
378#239—34no—
379#239—62no—
380D3×Q8—34no—
381D3×Q8—62no—
382#237—22no—
383#237—34no—
384#237—34no—
385#237—34no—
386#237—34no—
387#237—64no—
388#237—62no—
389#237—68no—
390#237—68no—
391#237—62no—
392#237—62no—
393#237—68no—
394#237—62no—
395#237—122no—
396#237C4×D314yescomplemented
397D3×D4—22no—
398D3×D4—68no—
399D3×D4C4×D314yescomplemented
400#235—34no—
401#235—68no—
402#235—62no—
403C2×D12—61no—
404C2×D12C22×D311yescharacteristic
405C2×C4×D3—21no—
406C2×C4×D3—21no—
407C2×C4×D3—31no—
408C2×C4×D3—31no—
409C2×C4×D3—31no—
410C2×C4×D3—31no—
411C2×C4×D3—31no—
412C2×C4×D3—31no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—61no—
418C2×C4×D3—68no—
419C2×C4×D3—61no—
420C2×C4×D3—61no—
421C2×C4×D3—61no—
422C2×C4×D3—61no—
423C2×C4×D3—61no—
424C2×C4×D3—61no—
425C2×C4×D3—61no—
426C2×C4×D3—61no—
427C2×C4×D3—61no—
428C2×C4×D3—121no—
429C2×C4×D3—124no—
430C2×C4×D3—124no—
431C2×C4×D3C22×D311yescharacteristic
432C2×C4×D3C22×D311yescharacteristic
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—34no—
436C2×Dic6—61no—
437C2×Dic6—62no—
438C2×Dic6—61no—
439C2×Dic6—61no—
440C2×Dic6C22×D311yescharacteristic
441C3×M16—62no—
442C2×C3×C8—21no—
443C2×C3×C8—31no—
444C2×C3×C8—31no—
445C2×C3×C8—62no—
446C2×C3×C8C22×D311yescharacteristic
447C2×C3×C8C22×D311yescharacteristic
448C3×C4⋊C4—21no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—61no—
452C3×C4⋊C4—61no—
453C3×C4⋊C4C22×D311yescharacteristic
454C3×C4⋊C4C22×D311yescharacteristic
455C4⋊Dic3—31no—
456C4⋊Dic3—31no—
457C4⋊Dic3—61no—
458C4⋊Dic3—61no—
459C4⋊Dic3—61no—
460C4⋊Dic3C22×D311yescharacteristic
461C4⋊Dic3C22×D311yescharacteristic
462Dic3⋊C4—21no—
463Dic3⋊C4—21no—
464Dic3⋊C4—61no—
465Dic3⋊C4—61no—
466Dic3⋊C4—61no—
467Dic3⋊C4—61no—
468Dic3⋊C4—61no—
469Dic3⋊C4—61no—
470Dic3⋊C4—121no—
471#208—62no—
472C2×C3⋊C8—31no—
473C2×C3⋊C8—31no—
474C2×C3⋊C8—61no—
475C2×C3⋊C8—62no—
476C2×C3⋊C8C22×D311yescharacteristic
477C2×C3⋊C8C22×D311yescharacteristic
478ΓL(1,𝔽25)—22no—
479ΓL(1,𝔽25)—62no—
480ΓL(1,𝔽25)—62no—
481ΓL(1,𝔽25)—62no—
482ΓL(1,𝔽25)—62no—
483ΓL(1,𝔽25)—62no—
484ΓL(1,𝔽25)—122no—
485D3×C8—22no—
486D3×C8—62no—
487C22×C32—22no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32C22×D411yescharacteristic
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3C2×C22⋊C412yes—
494C2×C3×D3—21no—
495C2×C3×D3—21no—
496C2×C3×D3—22no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—48no—
500C2×C3×D3C2×C22⋊C412yes—
501C2×C3×D3C2×C22⋊C412yes—
502C2×C3×D3AGL(1,ℤ/8)12yes—
503C2×C3×D3#13712yes—
504D32—28no—
505C32×C4—41no—
506C32×C4C23×C411yescharacteristic
507C32×C4C22×D411yescharacteristic
508C3⋊Dic3—22no—
509C3⋊Dic3—41no—
510C3⋊Dic3C2×C22⋊C412yes—
511C3×Dic3—22no—
512C3×Dic3—41no—
513C3×Dic3—41no—
514C3×Dic3C2×C22⋊C412yes—
515C3×Dic3C2×C22⋊C412yes—
516C2×#41—31no—
517C2×#41—91no—
518C2×#41—91no—
519C2×#41—98no—
520C2×#41—91no—
521C2×#41—181no—
522C2×#41—181no—
523C2×#41—184no—
524C22×Q8—91no—
525C22×D4—31no—
526C22×D4—181no—
527C23×C4—91no—
528C23×C4—181no—
529C23×C4—181no—
530C2×M16—31no—
531C2×M16—91no—
532C2×M16—91no—
533C2×M16—91no—
534C2×M16—184no—
535C22×C8—31no—
536C22×C8—91no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—181no—
544C2×C4⋊C4—181no—
545C2×C4⋊C4—181no—
546#103—31no—
547#103—31no—
548#103—91no—
549#103—91no—
550#103—91no—
551#103—91no—
552#103—91no—
553#103—91no—
554#102—31no—
555#102—31no—
556#102—31no—
557#102—31no—
558#102—91no—
559#102—91no—
560#102—91no—
561#102D3211yescharacteristic, complemented
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—31no—
565C23×C3—31no—
566C23×C3—41no—
567C23×C3—64no—
568C23×C3—61no—
569C23×C3—122no—
570C23×C3—122no—
571C22×D3—21no—
572C22×D3—24no—
573C22×D3—31no—
574C22×D3—31no—
575C22×D3—34no—
576C22×D3—34no—
577C22×D3—42no—
578C22×D3—42no—
579C22×D3—61no—
580C22×D3—62no—
581C22×D3—62no—
582C22×D3—62no—
583C22×D3—62no—
584C22×D3D3×D411yescharacteristic
585C22×D3D3×D411yescharacteristic
586C3×Q8—32no—
587C3×Q8—61no—
588C3×D4—21no—
589C3×D4—21no—
590C3×D4—22no—
591C3×D4—32no—
592C3×D4—41no—
593C3×D4—64no—
594C3×D4—64no—
595C3×D4—61no—
596C3×D4C2×C4×D312yescomplemented
597C3×D4C2×C4×D312yescomplemented
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—31no—
602C2×C3×C4—31no—
603C2×C3×C4—32no—
604C2×C3×C4—32no—
605C2×C3×C4—32no—
606C2×C3×C4—32no—
607C2×C3×C4—41no—
608C2×C3×C4—64no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—122no—
613C2×C3×C4—122no—
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C23×D311yescharacteristic
616#67—24no—
617#67—24no—
618#67—64no—
619#67—64no—
620#67—64no—
621#67—64no—
622#67—64no—
623#67—124no—
624C2×Dic3—21no—
625C2×Dic3—24no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—31no—
629C2×Dic3—31no—
630C2×Dic3—34no—
631C2×Dic3—34no—
632C2×Dic3—61no—
633C2×Dic3—64no—
634C2×Dic3—64no—
635C2×Dic3—64no—
636C2×Dic3—64no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—64no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—124no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—122no—
646C2×Dic3—122no—
647C2×Dic3D3×D411yescharacteristic
648C2×Dic3D3×D411yescharacteristic
649D12—21no—
650D12—64no—
651D12C2×C4×D312yescomplemented
652C4×D3—34no—
653C4×D3—34no—
654C4×D3—32no—
655C4×D3—32no—
656C4×D3—32no—
657C4×D3—32no—
658C4×D3—34no—
659C4×D3—34no—
660C4×D3—42no—
661C4×D3—42no—
662C4×D3—62no—
663C4×D3—62no—
664C4×D3—64no—
665C4×D3—64no—
666C4×D3—64no—
667C4×D3—122no—
668C4×D3—122no—
669C4×D3—122no—
670C4×D3—122no—
671C4×D3—122no—
672C4×D3—122no—
673C4×D3—242no—
674C4×D3C2×C4×D312yes—
675C4×D3C2×C4×D312yes—
676C4×D3D3×D412yes—
677C4×D3D3×D412yes—
678Dic6—21no—
679Dic6—32no—
680Dic6—32no—
681Dic6—62no—
682Dic6—64no—
683Dic6—61no—
684Dic6—61no—
685Dic6—64no—
686Dic6—121no—
687Dic6C2×C4×D312yescomplemented
688C3×C8—21no—
689C3×C8—21no—
690C3×C8—41no—
691C3×C8—61no—
692C3×C8—61no—
693C3⋊C8—21no—
694C3⋊C8—21no—
695C3⋊C8—61no—
696C3⋊C8—61no—
697C3⋊C8—121no—
698C2×C32—42no—
699C2×C32C22×C22⋊C411yescharacteristic
700C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
701C2×C32C2×#13711yescharacteristic
702C3⋊D3—22no—
703C3×D3—22no—
704C3×D3—42no—
705C3×D3#41714yescomplemented
706C24—61no—
707C24—91no—
708#41—34no—
709#41—62no—
710#41—94no—
711#41—94no—
712#41—94no—
713#41—182no—
714#41—188no—
715#41—182no—
716#41—188no—
717#41—182no—
718C2×Q8—31no—
719C2×Q8—94no—
720C2×Q8—91no—
721C2×Q8—181no—
722C2×Q8—182no—
723C2×D4—34no—
724C2×D4—31no—
725C2×D4—62no—
726C2×D4—61no—
727C2×D4—61no—
728C2×D4—181no—
729C2×D4—188no—
730C2×D4—181no—
731C2×D4—181no—
732C2×D4C2×D3211yescharacteristic
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—91no—
739C22×C4—94no—
740C22×C4—94no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—91no—
744C22×C4—181no—
745C22×C4—181no—
746C22×C4—181no—
747C22×C4—188no—
748C22×C4—181no—
749C22×C4—181no—
750C22×C4—181no—
751C22×C4—181no—
752C22×C4—181no—
753C22×C4—364no—
754M16—62no—
755M16—182no—
756M16—182no—
757M16—182no—
758C2×C8—31no—
759C2×C8—31no—
760C2×C8—62no—
761C2×C8—91no—
762C2×C8—182no—
763C2×C8C2×D3211yescharacteristic
764C4⋊C4—31no—
765C4⋊C4—31no—
766C4⋊C4—61no—
767C4⋊C4—61no—
768C4⋊C4—91no—
769C4⋊C4—181no—
770C4⋊C4—181no—
771C4⋊C4—181no—
772C4⋊C4—181no—
773C4⋊C4C2×D3211yescharacteristic
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—21no—
777C22×C3—32no—
778C22×C3—32no—
779C22×C3—32no—
780C22×C3—32no—
781C22×C3—42no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—62no—
789C22×C3—81no—
790C22×C3—81no—
791C22×C3—128no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3C2×D3×D411yescharacteristic
795C22×C3C2×D3×D411yescharacteristic
796C2×D3—21no—
797C2×D3—21no—
798C2×D3—22no—
799C2×D3—32no—
800C2×D3—32no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3—48no—
804C2×D3—62no—
805C2×D3—68no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—68no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3D3×C22⋊C412yes—
814C2×D3D3×C22⋊C412yes—
815C2×D3#91112yes—
816C2×D3#91512yes—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—32no—
820C3×C4—32no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—62no—
824C3×C4—81no—
825C3×C4—121no—
826C3×C4—121no—
827C3×C4C22×C4×D311yescharacteristic
828C3×C4C22×C4×D311yescharacteristic
829C3×C4C2×D3×D411yescharacteristic
830C3×C4C2×D3×D411yescharacteristic
831Dic3—22no—
832Dic3—32no—
833Dic3—32no—
834Dic3—41no—
835Dic3—41no—
836Dic3—62no—
837Dic3—62no—
838Dic3—62no—
839Dic3—122no—
840Dic3—121no—
841Dic3—121no—
842Dic3—241no—
843Dic3D3×C22⋊C412yes—
844Dic3D3×C22⋊C412yes—
845C32C2×#41711yescharacteristic, complemented, Sylow
846C23—21no—
847C23—31no—
848C23—31no—
849C23—64no—
850C23—61no—
851C23—94no—
852C23—91no—
853C23—122no—
854C23—122no—
855C23—182no—
856C23—182no—
857Q8—32no—
858Q8—61no—
859Q8—92no—
860Q8—184no—
861Q8—181no—
862D4—21no—
863D4—32no—
864D4—64no—
865D4—64no—
866D4—61no—
867D4—184no—
868D4—184no—
869D4—184no—
870D4C4×D3212yescomplemented
871C2×C4—21no—
872C2×C4—31no—
873C2×C4—31no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—64no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—94no—
883C2×C4—94no—
884C2×C4—94no—
885C2×C4—91no—
886C2×C4—92no—
887C2×C4—92no—
888C2×C4—122no—
889C2×C4—122no—
890C2×C4—184no—
891C2×C4—184no—
892C2×C4—184no—
893C2×C4—184no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—362no—
897C2×C4—362no—
898C2×C4—362no—
899C2×C4—362no—
900C2×C4C22×D3211yescharacteristic
901C8—21no—
902C8—61no—
903C8—61no—
904C8—181no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—34no—
909C2×C3—42no—
910C2×C3—42no—
911C2×C3—62no—
912C2×C3—82no—
913C2×C3—122no—
914C2×C3C2×D3×C22⋊C411yescharacteristic
915C2×C3C2×D3×C22⋊C411yescharacteristic
916C2×C3C2×#91111yescharacteristic
917C2×C3C2×#91511yescharacteristic
918C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
919C2×C3D3×#13711yescharacteristic
920D3—22no—
921D3—42no—
922D3—62no—
923D3—62no—
924D3—122no—
925D3#477114yesdirect product factor
926C22—22no—
927C22—32no—
928C22—32no—
929C22—32no—
930C22—32no—
931C22—41no—
932C22—41no—
933C22—61no—
934C22—61no—
935C22—62no—
936C22—92no—
937C22—128no—
938C22—121no—
939C22—121no—
940C22—188no—
941C22—181no—
942C22—181no—
943C22D32×D411yescharacteristic
944C4—32no—
945C4—32no—
946C4—41no—
947C4—62no—
948C4—92no—
949C4—121no—
950C4—121no—
951C4—182no—
952C4—361no—
953C4C2×C4×D3211yescharacteristic
954C4D32×D411yescharacteristic
955C3—21no—
956C3C2×#477111yescharacteristic, complemented
957C3D3×#41711yescharacteristic, complemented
958C2—34no—
959C2—42no—
960C2—62no—
961C2—122no—
962C2—182no—
963C2D32×C22⋊C411yescharacteristic
964C2D3×#91111yescharacteristic
965C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D3×#237C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32C2×#417
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×D3×ΓL(1,𝔽25)C2semidirect
3. D32×C4⋊C4C2semidirect
4. #10592470C2semidirect
5. C3×#4771C2semidirect
6. C3×D3×#102C2semidirect
7. #10591418C2semidirect
8. #10591414C2semidirect
9. D3×#832C2semidirect
10. #10590957C2semidirect
11. #10590670C2semidirect
12. D3×#816C2semidirect
13. #10590612C2semidirect
14. #10590607C2semidirect
15. D3×#810C2semidirect
26. D3×#237C4semidirect
32. C2×#3743C22semidirect
33. C4⋊C4×C3⋊D3C22semidirect
34. C2×C3×ΓL(1,𝔽25)C22semidirect
37. C3×D3×C4⋊C4C22semidirect
38. #63900C22semidirect
40. D3×C4⋊Dic3C22semidirect
44. C2×#3712C22semidirect
45. C2×#3711C22semidirect
48. C32×#102C22semidirect
49. #63659C22semidirect
50. #63643C22semidirect
51. #63637C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. #63567C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63565C22semidirect
62. #63563C22semidirect
63. #63562C22semidirect
92. #4771D3direct (N × H)
94. D3×#102D3semidirect
101. #3830C2×C4semidirect
109. C3×#237C2×C4semidirect
111. C3×D3×D4C2×C4semidirect
138. #3796C2×C4semidirect
140. #3795C2×C4semidirect
142. D3×Dic6C2×C4semidirect
211. C2×ΓL(1,𝔽25)C2×D3semidirect
226. D3×C4⋊C4C2×D3semidirect
234. C3×#102C2×D3semidirect
235. C3×#102C2×D3semidirect
243. #832C2×D3semidirect
244. #832C2×D3semidirect
246. #821C2×D3semidirect
253. #816C2×D3semidirect
260. #810C2×D3semidirect
262. #809C2×D3semidirect
275. C32×D4C22×C4semidirect
287. #634C22×C4semidirect
297. C3×D12C22×C4semidirect
305. C3×Dic6C22×C4semidirect
396. #237C4×D3semidirect
399. D3×D4C4×D3semidirect
561. #102D32semidirect
596. C3×D4C2×C4×D3semidirect
597. C3×D4C2×C4×D3semidirect
651. D12C2×C4×D3semidirect
687. Dic6C2×C4×D3semidirect
705. C3×D3#417semidirect
845. C32C2×#417semidirect
870. D4C4×D32semidirect
925. D3#4771direct (N × H)
956. C3C2×#4771semidirect
957. C3D3×#417semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×D3×ΓL(1,𝔽25)2
D32×C4⋊C42
#105924702
C3×#47712
C3×D3×#1022
#105914182
#105914142
D3×#8322
#105909572
#105906702
D3×#8162
#105906122
#105906072
D3×#8102
D3×#4173
C2×#47713