Finite Group Databasebeta

← D3×#4803 #11857926

Subgroups — D3×#4803 #11857926

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×#239C211yesmaximal, characteristic
2C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3D32×C4⋊C4C211yesmaximal, characteristic, complemented
4#10592502C211yesmaximal, characteristic, complemented
5C3×#4803C211yesmaximal, characteristic, complemented
6C3×D3×#103C211yesmaximal, characteristic, complemented
7#10591554C211yesmaximal, characteristic, complemented
8#10591550C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10590957C211yesmaximal, characteristic, complemented
11D3×#821C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590612C211yesmaximal, characteristic, complemented
14#10590609C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16D3×#417—31nomaximal
17C2×#4803—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239—24no—
22D3×#239C418yescomplemented
23C2×D3×D12—21no—
24C2×D3×D12C2211yescharacteristic
25C2×C4×D32—21no—
26C2×C4×D32—21no—
27C2×C4×D32C2211yescharacteristic
28C2×#3799—21no—
29C2×#3799C2211yescharacteristic
30C2×#3796—21no—
31C2×#3796C2211yescharacteristic
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×#103C2211yescharacteristic, complemented
49#63662C2211yescharacteristic, complemented
50#63648C2211yescharacteristic, complemented
51#63636C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63562C2211yescharacteristic, complemented
64C2×D3×#41—31no—
65C22×#239—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×#103—31no—
72#5232—31no—
73C2×#835—31no—
74#5133—31no—
75C2×#821—31no—
76#4966—31no—
77C2×#809—31no—
78#4803—31no—
79#4803—31no—
80#4803—31no—
81#4803—31no—
82#4803—31no—
83#4803—31no—
84#4803—31no—
85#4803—31no—
86#4803—31no—
87#4803—61no—
88#4803D311yescharacteristic, direct product factor
89D3×#103—31no—
90D3×#103D311yescharacteristic, complemented
91#4771—31no—
92#4771—31no—
93D3×#102—31no—
94D3×#102—31no—
95C22×D32—21no—
96C22×D32D411yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98#3832—22no—
99#3832C2×C414yescomplemented
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C3×#239—22no—
106C3×#239C2×C414yescomplemented
107C3×D3×Q8—22no—
108C3×D3×Q8C2×C414yescomplemented
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#624—21no—
123C2×#624—21no—
124C2×#624D411yescharacteristic
125C2×D3×Dic3—21no—
126C2×D3×Dic3—21no—
127C2×D3×Dic3—21no—
128C2×D3×Dic3D411yescharacteristic
129C2×D3×Dic3D411yescharacteristic
130D3×D12—28no—
131D3×D12—22no—
132D3×D12C2×C414yescomplemented
133C4×D32—28no—
134C4×D32—44no—
135C4×D32C2×C414yes—
136C4×D32D414yes—
137#3799—22no—
138#3799—28no—
139#3799C2×C414yescomplemented
140#3796—22no—
141#3796—28no—
142#3796C2×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×Q8—31no—
166D3×#41—38no—
167D3×#41—64no—
168C2×#239—31no—
169C2×#239—31no—
170C2×#239—38no—
171C2×#239—31no—
172C2×#239—31no—
173C2×#239—61no—
174C2×#239—61no—
175C2×#239—61no—
176C2×#239—64no—
177C2×#239C2×D311yescharacteristic
178C2×D3×Q8C2×D311yescharacteristic
179C2×#237—31no—
180C2×#237—61no—
181C2×D3×D4—31no—
182C2×D3×D4—61no—
183C2×#235—31no—
184C2×#235—61no—
185C22×D12—31no—
186C22×D12—61no—
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—61no—
190C22×C4×D3—61no—
191C22×C4×D3—61no—
192C22×C4×D3—61no—
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—21no—
228C3×#103—31no—
229C3×#103—31no—
230C3×#103—31no—
231C3×#103—31no—
232C3×#103C2×D311yescharacteristic, complemented
233C3×#103C2×D311yescharacteristic, complemented
234C3×#102—31no—
235C3×#102—31no—
236#835—31no—
237#835—31no—
238#835—31no—
239#835—31no—
240#835—61no—
241#835C2×D311yescharacteristic, complemented
242#835C2×D311yescharacteristic, complemented
243#832—31no—
244#832—31no—
245#821—31no—
246#821—31no—
247#821—31no—
248#821—31no—
249#821—31no—
250#821—61no—
251#821C2×D311yescharacteristic, complemented
252#816—31no—
253#816C2×D311yescharacteristic, complemented
254#810—31no—
255#810C2×D311yescharacteristic, complemented
256#809—31no—
257#809—31no—
258#809—31no—
259#809—31no—
260#809—31no—
261#809—61no—
262#809C2×D311yescharacteristic, complemented
263C22×C3⋊D3—21no—
264C22×C3⋊D3C2×D411yescharacteristic
265C22×C3×D3—21no—
266C22×C3×D3C2×D411yescharacteristic
267C22×C3×D3C2×D411yescharacteristic
268C2×D32—22no—
269C2×D32—22no—
270C2×D32—24no—
271C2×D32—42no—
272C2×D32—42no—
273C2×D32C22⋊C414yes—
274C32×Q8—21no—
275C32×Q8C22×C412yescomplemented
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4C2411yescharacteristic
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3C2×D411yescharacteristic
281C4⋊(C3⋊D3)—24no—
282C4⋊(C3⋊D3)—21no—
283C4⋊(C3⋊D3)C22×C412yescomplemented
284C4×C3⋊D3—24no—
285C4×C3⋊D3—42no—
286C4×C3⋊D3C22×C412yes—
287C4×C3⋊D3C2×D412yes—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3C2×D411yescharacteristic
292C2×C3×Dic3C2×D411yescharacteristic
293C3×D12—24no—
294C3×D12—21no—
295C3×D12C22×C412yescomplemented
296C3×C4×D3—24no—
297C3×C4×D3—24no—
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×Dic6—24no—
306C3×Dic6C22×C412yescomplemented
307#626—24no—
308#626—24no—
309#626—24no—
310#624—24no—
311#624—42no—
312#624C22⋊C414yes—
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—31no—
334C2×#103—91no—
335C2×#102—91no—
336C2×#102—91no—
337C23×D3—31no—
338C23×D3—31no—
339C23×D3—61no—
340C23×D3—61no—
341C3×#41—34no—
342C3×#41—62no—
343C2×C3×Q8—21no—
344C2×C3×Q8—34no—
345C2×C3×Q8—31no—
346C2×C3×Q8—61no—
347C2×C3×Q8—62no—
348C2×C3×Q8C22×D311yescharacteristic
349C2×C3×Q8C22×D311yescharacteristic
350C2×C3×D4—31no—
351C2×C3×D4—61no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366#239—22no—
367#239—34no—
368#239—34no—
369#239—34no—
370#239—34no—
371#239—64no—
372#239—68no—
373#239—68no—
374#239—62no—
375#239—62no—
376#239—62no—
377#239—62no—
378#239—122no—
379#239C4×D314yescomplemented
380D3×Q8—22no—
381D3×Q8C4×D314yescomplemented
382#237—34no—
383#237—62no—
384#237—68no—
385D3×D4—34no—
386D3×D4—68no—
387D3×D4—62no—
388#235—34no—
389#235—68no—
390#235—62no—
391C2×D12—21no—
392C2×D12—31no—
393C2×D12—31no—
394C2×D12—34no—
395C2×D12—61no—
396C2×D12—62no—
397C2×D12—68no—
398C2×D12—61no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—61no—
402C2×D12—61no—
403C2×D12—121no—
404C2×D12C22×D311yescharacteristic
405C2×C4×D3—21no—
406C2×C4×D3—21no—
407C2×C4×D3—21no—
408C2×C4×D3—21no—
409C2×C4×D3—31no—
410C2×C4×D3—31no—
411C2×C4×D3—31no—
412C2×C4×D3—31no—
413C2×C4×D3—31no—
414C2×C4×D3—31no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—61no—
420C2×C4×D3—68no—
421C2×C4×D3—68no—
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—61no—
429C2×C4×D3—61no—
430C2×C4×D3—61no—
431C2×C4×D3—61no—
432C2×C4×D3—61no—
433C2×C4×D3—121no—
434C2×C4×D3—121no—
435C2×C4×D3—124no—
436C2×C4×D3—124no—
437C2×C4×D3C22×D311yescharacteristic
438C2×C4×D3C22×D311yescharacteristic
439C2×Dic6—21no—
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×C32C22×D411yescharacteristic
488C2×C3⋊D3—21no—
489C2×C3⋊D3—21no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—41no—
492C2×C3⋊D3—41no—
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×D3C2×C22⋊C412yes—
500C2×C3×D3C2×C22⋊C412yes—
501C2×C3×D3AGL(1,ℤ/8)12yes—
502C2×C3×D3#13712yes—
503D32—28no—
504D32—48no—
505C32×C4—22no—
506C32×C4—41no—
507C32×C4C23×C411yescharacteristic
508C32×C4C22×D411yescharacteristic
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—31no—
525C22×D4—91no—
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—31no—
549#103—31no—
550#103—91no—
551#103—91no—
552#103—91no—
553#103D3211yescharacteristic, complemented
554#102—31no—
555#102—31no—
556#102—91no—
557#102—91no—
558#102—91no—
559#102—91no—
560#102—91no—
561#102—91no—
562C23×C3—31no—
563C23×C3—31no—
564C23×C3—61no—
565C22×D3—21no—
566C22×D3—31no—
567C22×D3—31no—
568C22×D3—34no—
569C22×D3—34no—
570C22×D3—61no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—64no—
574C22×D3—62no—
575C22×D3—62no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—64no—
579C22×D3—121no—
580C22×D3—122no—
581C22×D3—122no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3D3×D411yescharacteristic
585C22×D3D3×D411yescharacteristic
586C3×Q8—21no—
587C3×Q8—21no—
588C3×Q8—22no—
589C3×Q8—32no—
590C3×Q8—41no—
591C3×Q8—64no—
592C3×Q8—61no—
593C3×Q8C2×C4×D312yescomplemented
594C3×Q8C2×C4×D312yescomplemented
595C3×D4—32no—
596C3×D4—64no—
597C3×D4—61no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—31no—
604C2×C3×C4—31no—
605C2×C3×C4—32no—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—64no—
612C2×C3×C4—64no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—122no—
617C2×C3×C4—122no—
618C2×C3×C4C23×D311yescharacteristic
619C2×C3×C4C23×D311yescharacteristic
620#67—64no—
621#67—64no—
622#67—64no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—31no—
627C2×Dic3—31no—
628C2×Dic3—34no—
629C2×Dic3—34no—
630C2×Dic3—61no—
631C2×Dic3—64no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—121no—
635C2×Dic3—122no—
636C2×Dic3—122no—
637C2×Dic3D3×D411yescharacteristic
638C2×Dic3D3×D411yescharacteristic
639D12—24no—
640D12—21no—
641D12—32no—
642D12—32no—
643D12—62no—
644D12—64no—
645D12—64no—
646D12—64no—
647D12—64no—
648D12—64no—
649D12—61no—
650D12—61no—
651D12—121no—
652D12—124no—
653D12C2×C4×D312yescomplemented
654C4×D3—24no—
655C4×D3—24no—
656C4×D3—34no—
657C4×D3—34no—
658C4×D3—32no—
659C4×D3—32no—
660C4×D3—32no—
661C4×D3—32no—
662C4×D3—34no—
663C4×D3—34no—
664C4×D3—42no—
665C4×D3—42no—
666C4×D3—62no—
667C4×D3—62no—
668C4×D3—64no—
669C4×D3—64no—
670C4×D3—64no—
671C4×D3—64no—
672C4×D3—64no—
673C4×D3—124no—
674C4×D3—122no—
675C4×D3—122no—
676C4×D3—122no—
677C4×D3—122no—
678C4×D3—122no—
679C4×D3—122no—
680C4×D3—242no—
681C4×D3C2×C4×D312yes—
682C4×D3C2×C4×D312yes—
683C4×D3D3×D412yes—
684C4×D3D3×D412yes—
685Dic6—21no—
686Dic6—24no—
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×C32C22×C22⋊C411yescharacteristic
699C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
700C2×C32C2×#13711yescharacteristic
701C3⋊D3—22no—
702C3⋊D3—42no—
703C3×D3—22no—
704C3×D3—42no—
705C3×D3#41714yescomplemented
706C24—91no—
707C24—181no—
708#41—34no—
709#41—62no—
710#41—94no—
711#41—94no—
712#41—94no—
713#41—182no—
714#41—188no—
715#41—188no—
716#41—182no—
717#41—182no—
718C2×Q8—34no—
719C2×Q8—31no—
720C2×Q8—61no—
721C2×Q8—62no—
722C2×Q8C2×D3211yescharacteristic
723C2×D4—31no—
724C2×D4—61no—
725C2×D4—94no—
726C2×D4—91no—
727C2×D4—181no—
728C2×D4—182no—
729C2×D4—181no—
730C2×D4—188no—
731C2×D4—181no—
732C2×D4—181no—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—61no—
736C22×C4—61no—
737C22×C4—61no—
738C22×C4—61no—
739C22×C4—91no—
740C22×C4—94no—
741C22×C4—94no—
742C22×C4—91no—
743C22×C4—91no—
744C22×C4—91no—
745C22×C4—181no—
746C22×C4—181no—
747C22×C4—181no—
748C22×C4—188no—
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—21no—
775C22×C3—32no—
776C22×C3—32no—
777C22×C3—32no—
778C22×C3—32no—
779C22×C3—61no—
780C22×C3—61no—
781C22×C3—62no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3C2×D3×D411yescharacteristic
785C22×C3C2×D3×D411yescharacteristic
786C2×D3—21no—
787C2×D3—21no—
788C2×D3—22no—
789C2×D3—32no—
790C2×D3—32no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—62no—
794C2×D3—68no—
795C2×D3—61no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—61no—
799C2×D3—68no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—122no—
805C2×D3—128no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—128no—
811C2×D3—241no—
812C2×D3—241no—
813C2×D3D3×C22⋊C412yes—
814C2×D3D3×C22⋊C412yes—
815C2×D3#91412yes—
816C2×D3#91812yes—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—32no—
822C3×C4—32no—
823C3×C4—42no—
824C3×C4—41no—
825C3×C4—41no—
826C3×C4—62no—
827C3×C4—81no—
828C3×C4—121no—
829C3×C4—121no—
830C3×C4C22×C4×D311yescharacteristic
831C3×C4C22×C4×D311yescharacteristic
832C3×C4C2×D3×D411yescharacteristic
833C3×C4C2×D3×D411yescharacteristic
834Dic3—22no—
835Dic3—32no—
836Dic3—32no—
837Dic3—41no—
838Dic3—41no—
839Dic3—62no—
840Dic3—121no—
841Dic3—121no—
842Dic3—241no—
843Dic3D3×C22⋊C412yes—
844Dic3D3×C22⋊C412yes—
845C32C2×#41711yescharacteristic, complemented, Sylow
846C23—31no—
847C23—31no—
848C23—61no—
849C23—94no—
850C23—91no—
851C23—182no—
852C23—182no—
853C23—184no—
854C23—181no—
855C23—362no—
856C23—362no—
857Q8—21no—
858Q8—32no—
859Q8—64no—
860Q8—61no—
861Q8C4×D3212yescomplemented
862D4—32no—
863D4—64no—
864D4—61no—
865D4—92no—
866D4—184no—
867D4—184no—
868D4—184no—
869D4—184no—
870D4—181no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—64no—
880C2×C4—64no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—94no—
885C2×C4—94no—
886C2×C4—94no—
887C2×C4—91no—
888C2×C4—92no—
889C2×C4—92no—
890C2×C4—122no—
891C2×C4—122no—
892C2×C4—184no—
893C2×C4—184no—
894C2×C4—184no—
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—62no—
910C2×C3—122no—
911C2×C3C2×D3×C22⋊C411yescharacteristic
912C2×C3C2×D3×C22⋊C411yescharacteristic
913C2×C3C2×#91411yescharacteristic
914C2×C3C2×#91811yescharacteristic
915C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
916C2×C3D3×#13711yescharacteristic
917D3—22no—
918D3—42no—
919D3—62no—
920D3—62no—
921D3—122no—
922D3—122no—
923D3—122no—
924D3—242no—
925D3#480314yesdirect product factor
926C22—32no—
927C22—32no—
928C22—32no—
929C22—32no—
930C22—61no—
931C22—61no—
932C22—62no—
933C22—92no—
934C22—121no—
935C22—121no—
936C22—188no—
937C22—181no—
938C22—181no—
939C22—182no—
940C22—368no—
941C22—361no—
942C22—361no—
943C22D32×D411yescharacteristic
944C4—22no—
945C4—32no—
946C4—32no—
947C4—41no—
948C4—62no—
949C4—92no—
950C4—121no—
951C4—121no—
952C4—361no—
953C4C2×C4×D3211yescharacteristic
954C4D32×D411yescharacteristic
955C3—21no—
956C3C2×#480311yescharacteristic, complemented
957C3D3×#41711yescharacteristic, complemented
958C2—34no—
959C2—62no—
960C2—122no—
961C2—182no—
962C2—362no—
963C2D32×C22⋊C411yescharacteristic
964C2D3×#91411yescharacteristic
965C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×#239C2
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C2×#417
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

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. #10592502C2semidirect
5. C3×#4803C2semidirect
6. C3×D3×#103C2semidirect
7. #10591554C2semidirect
8. #10591550C2semidirect
9. D3×#835C2semidirect
10. #10590957C2semidirect
11. D3×#821C2semidirect
12. #10590671C2semidirect
13. #10590612C2semidirect
14. #10590609C2semidirect
15. D3×#809C2semidirect
22. D3×#239C4semidirect
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×#103C22semidirect
49. #63662C22semidirect
50. #63648C22semidirect
51. #63636C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. #63566C22semidirect
59. #63565C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
63. #63562C22semidirect
88. #4803D3direct (N × H)
90. D3×#103D3semidirect
99. #3832C2×C4semidirect
106. C3×#239C2×C4semidirect
108. C3×D3×Q8C2×C4semidirect
132. D3×D12C2×C4semidirect
139. #3799C2×C4semidirect
142. #3796C2×C4semidirect
211. C2×ΓL(1,𝔽25)C2×D3semidirect
226. D3×C4⋊C4C2×D3semidirect
232. C3×#103C2×D3semidirect
233. C3×#103C2×D3semidirect
241. #835C2×D3semidirect
242. #835C2×D3semidirect
251. #821C2×D3semidirect
253. #816C2×D3semidirect
255. #810C2×D3semidirect
262. #809C2×D3semidirect
275. C32×Q8C22×C4semidirect
283. C4⋊(C3⋊D3)C22×C4semidirect
295. C3×D12C22×C4semidirect
306. C3×Dic6C22×C4semidirect
379. #239C4×D3semidirect
381. D3×Q8C4×D3semidirect
553. #103D32semidirect
593. C3×Q8C2×C4×D3semidirect
594. C3×Q8C2×C4×D3semidirect
653. D12C2×C4×D3semidirect
687. Dic6C2×C4×D3semidirect
705. C3×D3#417semidirect
845. C32C2×#417semidirect
861. Q8C4×D32semidirect
925. D3#4803direct (N × H)
956. C3C2×#4803semidirect
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×#2392
C2×D3×ΓL(1,𝔽25)2
D32×C4⋊C42
#105925022
C3×#48032
C3×D3×#1032
#105915542
#105915502
D3×#8352
#105909572
D3×#8212
#105906712
#105906122
#105906092
D3×#8092
D3×#4173
C2×#48033