Finite Group Databasebeta

← D3×#4782 #11866983

Subgroups — D3×#4782 #11866983

Order 1152.

1257 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#938C211yesmaximal, characteristic, complemented
2C2×D3×#213C211yesmaximal, characteristic, complemented
3C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592481C211yesmaximal, characteristic, complemented
6C3×#4782C211yesmaximal, characteristic, complemented
7C3×D3×#102C211yesmaximal, characteristic, complemented
8#10591454C211yesmaximal, characteristic, complemented
9#10591453C211yesmaximal, characteristic, complemented
10D3×#821C211yesmaximal, characteristic, complemented
11#10590840C211yesmaximal, characteristic, complemented
12#10590827C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590508C211yesmaximal, characteristic, complemented
15#10590504C211yesmaximal, characteristic, complemented
16D3×#469—31nomaximal
17C2×#4782—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12—21no—
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32C2211yescharacteristic
23#64147C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25C2×#3743C2211yescharacteristic, complemented
26#64104C2211yescharacteristic, complemented
27C3×#938C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic, complemented
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
30C2×C3×D3×C8C2211yescharacteristic
31C3×#895C2211yescharacteristic, complemented
32C3×D3×C4⋊C4C2211yescharacteristic
33#63970—21no—
34D3×#217—21no—
35#63958—21no—
36D3×#213—24no—
37D3×(C2×D3)⋊C4—21no—
38#63916C2211yescharacteristic, complemented
39#63916C2211yescharacteristic, complemented
40#63910—21no—
41#63909C2211yescharacteristic, complemented
42#63908C2211yescharacteristic, complemented
43D3×C4⋊Dic3C2211yescharacteristic
44#63886—21no—
45C2×#3714C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic, complemented
47C2×#3712C2211yescharacteristic, complemented
48C2×#3711C2211yescharacteristic, complemented
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×ΓL(1,𝔽25)—24no—
51C32×#102C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59#63574C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#938—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C2×D3×M16—31no—
67C22×ΓL(1,𝔽25)—31no—
68D3×#121—31no—
69D3×#121—31no—
70C2×#895—31no—
71C3×#469—31no—
72C2×C3×#102—31no—
73#5159—31no—
74#5135—31no—
75C2×#821—31no—
76#5039—31no—
77#5039—31no—
78C2×#808—31no—
79#4865—31no—
80D3×#106—31no—
81#4782—31no—
82#4782—31no—
83#4782—31no—
84#4782—31no—
85#4782—31no—
86#4782—31no—
87#4782—31no—
88#4782—31no—
89#4782—31no—
90#4782—61no—
91#4782D311yescharacteristic, direct product factor
92D3×#102—31no—
93D3×#102D311yescharacteristic, complemented
94C23×C3×D3—21no—
95C22×D32—21no—
96C22×D32D411yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C3×D3×D4—22no—
105C3×D3×D4—22no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112D3×#67—44no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×#624D411yescharacteristic
119C2×D3×Dic3—21no—
120C2×D3×Dic3D411yescharacteristic
121C2×D3×Dic3D411yescharacteristic
122D3×D12—22no—
123D3×D12—22no—
124D3×D12—44no—
125C4×D32—22no—
126C4×D32—22no—
127C2×C32×C8C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129#3757—21no—
130#3753—22no—
131#3752—21no—
132C4⋊(C3⋊Dic3)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3743—22no—
135C3×#217—21no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×ΓL(1,𝔽25)—22no—
144C3×D3×C8—22no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150#3714—22no—
151#3713—22no—
152#3712—22no—
153#3711—22no—
154D3×C3⋊C8D414yescomplemented
155C2×#469—91noSylow
156C22×C3×D4—31no—
157C22×#67—61no—
158C2×D3×D4—31no—
159C2×D3×D4—61no—
160C2×D3×D4—61no—
161C2×D3×D4C2×D311yescharacteristic
162C22×D12—31no—
163C22×D12—61no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C2×C3×D8—31no—
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×#121—31no—
170C3×#121—31no—
171C2×C3×C4⋊C4—31no—
172C2×#217—61no—
173#939—61no—
174#939—61no—
175#938—31no—
176#938—31no—
177#938—31no—
178#938—31no—
179#938—31no—
180#938—61no—
181#938—61no—
182#938—61no—
183#938C2×D311yescharacteristic, complemented
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—61no—
190C2×#213—64no—
191C2×#213C2×D311yescharacteristic, complemented
192#930—31no—
193#930—31no—
194C2×(C2×D3)⋊C4—61no—
195C2×C4⋊Dic3—31no—
196C2×#208—31no—
197C22×C3⋊C8—31no—
198D3×D8—64no—
199D3×M16—64no—
200C2×D24—31no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×ΓL(1,𝔽25)—31no—
206C2×ΓL(1,𝔽25)—61no—
207C2×ΓL(1,𝔽25)—64no—
208C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
209C2×D3×C8—31no—
210C2×D3×C8C2×D311yescharacteristic
211#895—31no—
212#895—31no—
213#895—31no—
214#895—31no—
215#895—31no—
216#895—61no—
217#895—61no—
218#895—61no—
219#895C2×D311yescharacteristic, complemented
220D3×C4⋊C4—31no—
221D3×C4⋊C4C2×D311yescharacteristic
222#884—61no—
223#884—61no—
224D3×C22⋊C4—61no—
225D3×C22⋊C4—61no—
226C3×#106—31no—
227C3×#102—21no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#102C2×D311yescharacteristic, complemented
233C3×#102C2×D311yescharacteristic, complemented
234#832—31no—
235#832C2×D311yescharacteristic, complemented
236#821—31no—
237#821—31no—
238#821—31no—
239#821—31no—
240#821—61no—
241#821C2×D311yescharacteristic, complemented
242#821C2×D311yescharacteristic, complemented
243#817—31no—
244#809—31no—
245#809C2×D311yescharacteristic, complemented
246#808—31no—
247#808—31no—
248#808—31no—
249#808—31no—
250#808—31no—
251#808—61no—
252#808C2×D311yescharacteristic, complemented
253C23×C32—21no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—22no—
264C2×D32—22no—
265C2×D32—22no—
266C2×D32—42no—
267C2×D32—42no—
268C2×D32—42no—
269C32×D4—21no—
270C32×D4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—42no—
279C4×C3⋊D3—21no—
280C4×C3⋊D3—21no—
281C3×#67—42no—
282C3×#67—42no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—42no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×C4×D3C2×D412yes—
296C3×C4×D3#4112yes—
297#626—42no—
298#626—42no—
299#626—42no—
300#626—42no—
301#625—42no—
302#624—22no—
303D3×Dic3—22no—
304D3×Dic3—22no—
305D3×Dic3—42no—
306C32×C8—21no—
307C3⋊(C3⋊C8)C2×D412yescomplemented
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yescomplemented
310C22×D8—91no—
311C22×M16—91no—
312C2×#121—91no—
313C2×#121—91no—
314#469—31no—
315#469—91no—
316#469—91no—
317#469—91no—
318#469—91no—
319#469—91no—
320#469—91no—
321#469—91no—
322C2×#106—91no—
323C2×#102—31no—
324C2×#102—91no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—61no—
330C23×D3—61no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—62no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—121no—
355C2×#67—124no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—61no—
359D3×D4—22no—
360D3×D4—22no—
361D3×D4—62no—
362D3×D4—62no—
363D3×D4—124no—
364D3×D4—124no—
365C2×D12—21no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—61no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12—124no—
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—31no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—31no—
388C2×C4×D3—61no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3—61no—
394C2×C4×D3C22×D311yescharacteristic
395C2×C4×D3C22×D311yescharacteristic
396C3×D8—62no—
397C3×M16—62no—
398C2×C3×C8—21no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C2×C3×C8—62no—
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C3×C4⋊C4—21no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4C22×D311yescharacteristic
409C3×C4⋊C4C22×D311yescharacteristic
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412#217—21no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—121no—
419#213—22no—
420#213—62no—
421#213—62no—
422#213—62no—
423#213—62no—
424#213—62no—
425#213—122no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—121no—
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—61no—
443#208—62no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—34no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450D24—62no—
451ΓL(1,𝔽25)—22no—
452ΓL(1,𝔽25)—62no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—62no—
455ΓL(1,𝔽25)—62no—
456ΓL(1,𝔽25)—62no—
457ΓL(1,𝔽25)—122no—
458D3×C8—22no—
459D3×C8—34no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C2×C3×D3#12112yes—
481C2×C3×D3AGL(1,ℤ/8)12yes—
482C2×C3×D3AGL(1,ℤ/8)12yes—
483D32—44no—
484D32—84no—
485C32×C4—41no—
486C32×C4C22×D411yescharacteristic
487C32×C4C2×#4111yescharacteristic
488C3⋊Dic3—21no—
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—41no—
492C3×Dic3—41no—
493C3×Dic3#12112yes—
494C22×D4—31no—
495C22×D4—91no—
496C22×D4—181no—
497C22×D4—181no—
498C23×C4—91no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—184no—
504C2×M16—31no—
505C2×M16—91no—
506C2×M16—91no—
507C2×M16—91no—
508C2×M16—184no—
509C22×C8—31no—
510C22×C8—91no—
511#121—31no—
512#121—31no—
513#121—91no—
514#121—91no—
515#121—91no—
516#121—91no—
517#121—91no—
518#121—91no—
519#121—181no—
520#121—181no—
521#121—181no—
522#121—181no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—91no—
525C2×C22⋊C4—181no—
526C2×C22⋊C4—181no—
527#106—31no—
528#106—91no—
529#106—91no—
530#106—91no—
531#102—31no—
532#102—31no—
533#102—31no—
534#102—31no—
535#102—91no—
536#102—91no—
537#102—91no—
538#102D3211yescharacteristic, complemented
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—122no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—31no—
552C22×D3—31no—
553C22×D3—42no—
554C22×D3—42no—
555C22×D3—42no—
556C22×D3—61no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—121no—
566C22×D3—122no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—122no—
572C22×D3D3×D411yescharacteristic
573C22×D3D3×D411yescharacteristic
574C3×D4—21no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—122no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—31no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—31no—
594C2×C3×C4—41no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—122no—
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602#67—42no—
603#67—42no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—242no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—61no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—121no—
623C2×Dic3—122no—
624C2×Dic3D3×D411yescharacteristic
625C2×Dic3D3×D411yescharacteristic
626D12—21no—
627D12—21no—
628D12—21no—
629D12—21no—
630D12—42no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—121no—
636D12—121no—
637D12—122no—
638D12—122no—
639D12—122no—
640D12—122no—
641D12—122no—
642D12—122no—
643D12—242no—
644C4×D3—21no—
645C4×D3—21no—
646C4×D3—42no—
647C4×D3—62no—
648C4×D3—62no—
649C4×D3—62no—
650C4×D3—61no—
651C4×D3—61no—
652C4×D3—61no—
653C4×D3—61no—
654C4×D3—62no—
655C4×D3—121no—
656C4×D3—121no—
657C4×D3—122no—
658C4×D3#23512yes—
659C4×D3D3×D412yes—
660C3×C8—21no—
661C3×C8—21no—
662C3×C8—32no—
663C3×C8—41no—
664C3×C8—61no—
665C3⋊C8—21no—
666C3⋊C8—32no—
667C3⋊C8—32no—
668C3⋊C8—62no—
669C3⋊C8D3×D412yescomplemented
670C2×C32—81no—
671C2×C32C2×#12111yescharacteristic
672C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
673C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
674C3⋊D3—41no—
675C3⋊D3—81no—
676C3×D3—41no—
677C3×D3—81no—
678C3×D3—81no—
679C3×D3#46914yescomplemented
680C24—61no—
681C24—91no—
682C24—181no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—61no—
686C2×D4—62no—
687C2×D4—62no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—91no—
691C2×D4—181no—
692C2×D4—182no—
693C2×D4—182no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—364no—
701C2×D4—364no—
702C2×D4C2×D3211yescharacteristic
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—61no—
706C22×C4—91no—
707C22×C4—91no—
708C22×C4—91no—
709C22×C4—91no—
710C22×C4—182no—
711C22×C4—182no—
712C22×C4—181no—
713D8—62no—
714D8—182no—
715D8—182no—
716D8—182no—
717M16—62no—
718M16—182no—
719M16—182no—
720M16—182no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—62no—
724C2×C8—94no—
725C2×C8—91no—
726C2×C8C2×D3211yescharacteristic
727C4⋊C4—31no—
728C4⋊C4—31no—
729C4⋊C4—61no—
730C4⋊C4—91no—
731C4⋊C4—181no—
732C4⋊C4C2×D3211yescharacteristic
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C22⋊C4—181no—
741C22×C3—21no—
742C22×C3—32no—
743C22×C3—32no—
744C22×C3—32no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—61no—
752C22×C3—61no—
753C22×C3—61no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—244no—
764C22×C3C2×D3×D411yescharacteristic
765C22×C3C2×D3×D411yescharacteristic
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—21no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—61no—
780C2×D3—61no—
781C2×D3—84no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—124no—
786C2×D3—124no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—241no—
794C2×D3—241no—
795C2×D3—241no—
796C2×D3—244no—
797C2×D3—244no—
798C2×D3#88412yes—
799C2×D3#91112yes—
800C2×D3#91412yes—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—32no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—61no—
807C3×C4—81no—
808C3×C4—121no—
809C3×C4—121no—
810C3×C4C2×#23511yescharacteristic
811C3×C4C2×D3×D411yescharacteristic
812C3×C4C2×D3×D411yescharacteristic
813C3×C4D3×#4111yescharacteristic
814Dic3—21no—
815Dic3—41no—
816Dic3—41no—
817Dic3—61no—
818Dic3—61no—
819Dic3—121no—
820Dic3—121no—
821Dic3—121no—
822Dic3—241no—
823Dic3#88412yes—
824C32C2×#46911yescharacteristic, complemented, Sylow
825C23—21no—
826C23—31no—
827C23—31no—
828C23—61no—
829C23—61no—
830C23—91no—
831C23—122no—
832C23—122no—
833C23—122no—
834C23—182no—
835C23—182no—
836C23—182no—
837C23—181no—
838C23—362no—
839C23—362no—
840C23—362no—
841D4—21no—
842D4—21no—
843D4—61no—
844D4—61no—
845D4—61no—
846D4—61no—
847D4—122no—
848D4—122no—
849D4—122no—
850D4—181no—
851D4—181no—
852D4—362no—
853D4—362no—
854D4—362no—
855D4—362no—
856D4—362no—
857D4—362no—
858D4—362no—
859C2×C4—21no—
860C2×C4—31no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—31no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—91no—
869C2×C4—122no—
870C2×C4—182no—
871C2×C4—182no—
872C2×C4—182no—
873C2×C4—181no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—362no—
877C2×C4C22×D3211yescharacteristic
878C8—21no—
879C8—32no—
880C8—61no—
881C8—92no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—34no—
886C2×C3—81no—
887C2×C3—81no—
888C2×C3—121no—
889C2×C3—161no—
890C2×C3—241no—
891C2×C3—241no—
892C2×C3C2×#88411yescharacteristic
893C2×C3D3×#12111yescharacteristic
894C2×C3C2×#91111yescharacteristic
895C2×C3C2×#91411yescharacteristic
896C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
897C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
898D3—41no—
899D3—81no—
900D3—81no—
901D3—121no—
902D3—121no—
903D3—241no—
904D3—241no—
905D3—241no—
906D3—481no—
907D3#478214yesdirect product factor
908C22—32no—
909C22—32no—
910C22—32no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—61no—
915C22—61no—
916C22—61no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—181no—
924C22—181no—
925C22—181no—
926C22—244no—
927C22—364no—
928C22—361no—
929C22—361no—
930C22—361no—
931C22—724no—
932C22D32×D411yescharacteristic
933C4—32no—
934C4—41no—
935C4—61no—
936C4—121no—
937C4—121no—
938C4—181no—
939C4—361no—
940C4D3×#23511yescharacteristic
941C4D32×D411yescharacteristic
942C3—21no—
943C3C2×#478211yescharacteristic, complemented
944C3D3×#46911yescharacteristic, complemented
945C2—34no—
946C2—81no—
947C2—121no—
948C2—241no—
949C2—241no—
950C2—361no—
951C2—721no—
952C2D3×#88411yescharacteristic
953C2D3×#91111yescharacteristic
954C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32C2×#469
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. D3×#938C2semidirect
2. C2×D3×#213C2semidirect
3. C2×D3×ΓL(1,𝔽25)C2semidirect
4. D3×#895C2semidirect
5. #10592481C2semidirect
6. C3×#4782C2semidirect
7. C3×D3×#102C2semidirect
8. #10591454C2semidirect
9. #10591453C2semidirect
10. D3×#821C2semidirect
11. #10590840C2semidirect
12. #10590827C2semidirect
13. D3×#808C2semidirect
14. #10590508C2semidirect
15. #10590504C2semidirect
23. #64147C22semidirect
24. C2×#3753C22semidirect
25. C2×#3743C22semidirect
26. #64104C22semidirect
27. C3×#938C22semidirect
28. C2×C3×#213C22semidirect
29. C2×C3×ΓL(1,𝔽25)C22semidirect
31. C3×#895C22semidirect
38. #63916C22semidirect
39. #63916C22semidirect
41. #63909C22semidirect
42. #63908C22semidirect
45. C2×#3714C22semidirect
46. C2×#3713C22semidirect
47. C2×#3712C22semidirect
48. C2×#3711C22semidirect
51. C32×#102C22semidirect
52. #63648C22semidirect
53. #63635C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×#821C22semidirect
57. C3×#809C22semidirect
58. C3×#808C22semidirect
59. #63574C22semidirect
60. #63573C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
91. #4782D3direct (N × H)
93. D3×#102D3semidirect
154. D3×C3⋊C8D4semidirect
183. #938C2×D3semidirect
191. C2×#213C2×D3semidirect
208. C2×ΓL(1,𝔽25)C2×D3semidirect
219. #895C2×D3semidirect
232. C3×#102C2×D3semidirect
233. C3×#102C2×D3semidirect
235. #832C2×D3semidirect
241. #821C2×D3semidirect
242. #821C2×D3semidirect
245. #809C2×D3semidirect
252. #808C2×D3semidirect
307. C3⋊(C3⋊C8)C2×D4semidirect
309. C3×C3⋊C8C2×D4semidirect
538. #102D32semidirect
669. C3⋊C8D3×D4semidirect
679. C3×D3#469semidirect
824. C32C2×#469semidirect
907. D3#4782direct (N × H)
943. C3C2×#4782semidirect
944. C3D3×#469semidirect

Maximal subgroups

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

subgroupindex
D3×#9382
C2×D3×#2132
C2×D3×ΓL(1,𝔽25)2
D3×#8952
#105924812
C3×#47822
C3×D3×#1022
#105914542
#105914532
D3×#8212
#105908402
#105908272
D3×#8082
#105905082
#105905042
D3×#4693
C2×#47823