Finite Group Databasebeta

← D3×#63817 #13170487

Subgroups — D3×#63817 #13170487

Order 1728.

1392 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3828C211yesmaximal, characteristic
2#11723657C211yesmaximal, characteristic, complemented
3#11723357C211yesmaximal, characteristic, complemented
4#11723356C211yesmaximal, characteristic, complemented
5C3×#63817C211yesmaximal, characteristic, complemented
6C3×D3×#208C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8#11722825C212yesmaximal, complemented
9#11722824C212yesmaximal, complemented
10D3×#3712C212yesmaximal, complemented
11D3×#3710C212yesmaximal, complemented
12C2×#63817—31nomaximal
13D3×#907—31nomaximal
14D3×#901—31nomaximal
15#89076C2211yescharacteristic
16C3×#3828C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18D3×#638C412yes—
19#89031C412yes—
20D3×C4⋊(C3⋊D3)C411yescharacteristic
21C4×D3×C3⋊D3C2212yes—
22#89022C411yescharacteristic
23#89021C411yescharacteristic
24#89020C2212yes—
25D3×#634C411yescharacteristic
26C3×#3748C2211yescharacteristic, complemented
27C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C32×#208C2211yescharacteristic, complemented
29C2×C32×C3⋊C8C2211yescharacteristic, complemented
30#88809C2212yescomplemented
31#88808C2212yescomplemented
32#88788C2212yescomplemented
33#88788C2212yescomplemented
34#88785C2212yescomplemented
35#88785C2212yescomplemented
36C3×#3712C2212yescomplemented
37C3×#3711C2212yescomplemented
38C3×#3710C2212yescomplemented
39C3×D3×C3⋊C8C2211yescharacteristic
40C3×D3×C3⋊C8C2212yes—
41C3×D3×C3⋊C8C2211yescharacteristic
42C3×D3×C3⋊C8C2211yescharacteristic, complemented
43C3×D3×C3⋊C8C2211yescharacteristic, complemented
44C2×#3828—31no—
45D3×#235—31no—
46D3×#235—31no—
47D3×#235—61no—
48#64116—31no—
49#64110—31no—
50C2×C3×#208—31no—
51C22×C3×C3⋊C8—31no—
52C3×#907—31no—
53C3×D3×M16—31no—
54C3×#901—31no—
55C2×C3×D3×C8—31no—
56C2×#3712—32no—
57#63817—31no—
58#63817—31no—
59#63817—31no—
60#63817—31no—
61#63817—31no—
62#63817—32no—
63#63817—32no—
64#63817—61no—
65#63817—61no—
66#63817D311yescharacteristic, direct product factor
67C2×#3710—32no—
68#63815—31no—
69#63814—31no—
70D3×#208D311yescharacteristic, complemented
71C2×D3×C3⋊C8D311yescharacteristic, complemented
72#63805—32no—
73#63804—32no—
74#63804—32no—
75#63803—32no—
76D3×ΓL(1,𝔽25)—32no—
77D3×ΓL(1,𝔽25)—32no—
78D32×C8—32no—
79D32×C8—32no—
80C22×C32×D3C2×C411yescharacteristic
81C2×D3×C3⋊D3C2×C412yes—
82C2×C33×C4C2311yescharacteristic
83#6312C2×C412yes—
84C4⋊(C3⋊(C3⋊D3))C2×C411yescharacteristic
85C4×C3⋊(C3⋊D3)C2312yes—
86#6308C2×C411yescharacteristic
87C3×#638C2×C412yes—
88C3×C4⋊(C3⋊D3)C2×C411yescharacteristic
89C3×C4×C3⋊D3C2312yes—
90C3×#634C2×C411yescharacteristic
91C2×C32×Dic3C2×C411yescharacteristic
92C32×C4×D3C2×C411yescharacteristic
93C32×C4×D3C2×C411yescharacteristic
94C32×C4×D3C2311yescharacteristic
95C32×C4×D3C2311yescharacteristic
96#6293C2×C412yes—
97#6292C2×C412yes—
98#6291C2×C412yes—
99#6290C2×C412yes—
100#6289C2×C412yes—
101Dic3×C3⋊D3C2×C412yes—
102D3×C3⋊Dic3C2×C412yes—
103C3×C3⋊(C3⋊C8)C2311yescharacteristic
104C3×C3⋊(C3⋊C8)C2311yescharacteristic
105C3×C3⋊(C3⋊C8)C2312yes—
106C32×C3⋊C8C2311yescharacteristic
107C32×C3⋊C8C2311yescharacteristic
108C32×C3⋊C8C2312yes—
109D3×#131—91no—
110C2×#907—91no—
111C2×#901—91no—
112C22×C32×C4—31no—
113C2×#638—32no—
114#3828—31no—
115#3828—31no—
116#3828—31no—
117#3828—32no—
118#3828—31no—
119#3828—32no—
120#3828—31no—
121#3828—61no—
122#3828—61no—
123#3828—61no—
124#3828—121no—
125#3828C2×D311yescharacteristic
126C2×C4⋊(C3⋊D3)—31no—
127C2×C4×C3⋊D3—32no—
128C2×#634—31no—
129C3×#235—31no—
130C3×#235—31no—
131C3×#235—61no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×C3×C4×D3C2×D311yescharacteristic
135D3×#67—32no—
136D3×#67—32no—
137D3×#67—62no—
138#3804—32no—
139#3804—32no—
140#3804—62no—
141D3×D12—31no—
142D3×D12—31no—
143D3×D12—61no—
144C4×D32—32no—
145C4×D32—32no—
146C4×D32—62no—
147#3799—31no—
148#3799—31no—
149#3799—61no—
150#3798—32no—
151#3798—32no—
152#3798—62no—
153#3795—31no—
154#3795—31no—
155#3795—61no—
156D3×Dic6—31no—
157D3×Dic6—31no—
158D3×Dic6—61no—
159C32×M16—31no—
160C2×C32×C8—31no—
161#3748C2×D311yescharacteristic, complemented
162C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
163#3743—32no—
164#3743—32no—
165C8×C3⋊D3—32no—
166C8×C3⋊D3—32no—
167C3×#208—21no—
168C3×#208—31no—
169C3×#208—31no—
170C3×#208—32no—
171C3×#208—61no—
172C3×#208C2×D311yescharacteristic, complemented
173C3×#208C2×D311yescharacteristic, complemented
174C2×C3×C3⋊C8—21no—
175C2×C3×C3⋊C8—31no—
176C2×C3×C3⋊C8—31no—
177C2×C3×C3⋊C8—31no—
178C2×C3×C3⋊C8—31no—
179C2×C3×C3⋊C8—31no—
180C2×C3×C3⋊C8—31no—
181C2×C3×C3⋊C8—32no—
182C2×C3×C3⋊C8—61no—
183C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
184C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
185C3×ΓL(1,𝔽25)—32no—
186C3×ΓL(1,𝔽25)—32no—
187C3×ΓL(1,𝔽25)—32no—
188C3×D3×C8—31no—
189C3×D3×C8—31no—
190C3×D3×C8—31no—
191C3×D3×C8—31no—
192C3×D3×C8—32no—
193C3×D3×C8—32no—
194C3×D3×C8—32no—
195#3712—32no—
196#3712—32no—
197#3712—32no—
198#3712—32no—
199#3712—32no—
200#3712—62no—
201#3712—62no—
202#3712C2×D312yescomplemented
203#3711—32no—
204#3711—32no—
205#3711C2×D312yescomplemented
206#3710—32no—
207#3710—32no—
208#3710—32no—
209#3710—32no—
210#3710—32no—
211#3710—62no—
212#3710—62no—
213#3710C2×D312yescomplemented
214D3×C3⋊C8—32no—
215D3×C3⋊C8—32no—
216D3×C3⋊C8C2×D311yescharacteristic
217D3×C3⋊C8C2×D312yes—
218D3×C3⋊C8C2×D311yescharacteristic
219D3×C3⋊C8C2×D311yescharacteristic, complemented
220D3×C3⋊C8C2×D311yescharacteristic, complemented
221C22×C33C22×C411yescharacteristic
222C2×C3⋊(C3⋊D3)C22×C412yes—
223C2×C3×C3⋊D3C22×C412yes—
224C2×C32×D3—22no—
225C2×C32×D3C22×C411yescharacteristic
226C2×C32×D3C22×C411yescharacteristic
227D3×C3⋊D3—24no—
228C33×C4C22×C411yescharacteristic
229C33×C4C2411yescharacteristic
230C3⋊(C3⋊Dic3)C22×C412yes—
231C3×C3⋊Dic3C22×C412yes—
232C32×Dic3C22×C411yescharacteristic
233C32×Dic3C22×C411yescharacteristic
234D3×#41—91no—
235C2×#235—91no—
236C2×#235—91no—
237C2×#235—181no—
238C3×#131—91no—
239C2×C3×M16—91no—
240C22×C3×C8—91no—
241#948—91no—
242C2×#208—31no—
243C22×C3⋊C8—31no—
244#907—31no—
245#907—92no—
246#907—92no—
247#907—92no—
248#907—91no—
249#907—91no—
250#907—91no—
251#907—91no—
252#907—181no—
253D3×M16—31no—
254D3×M16—92no—
255#901—31no—
256#901—92no—
257#901—92no—
258#901—92no—
259#901—91no—
260#901—91no—
261#901—91no—
262#901—91no—
263#901—181no—
264C2×ΓL(1,𝔽25)—92no—
265C2×ΓL(1,𝔽25)—92no—
266C2×D3×C8—31no—
267C2×D3×C8—92no—
268C2×D3×C8—92no—
269C2×D3×C8—92no—
270C23×C32—31no—
271C22×C3⋊D3—32no—
272C22×C3×D3—21no—
273C22×C3×D3C4×D311yescharacteristic
274C22×C3×D3C4×D311yescharacteristic
275C2×D32—32no—
276C2×D32—32no—
277C2×D32—62no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4—31no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—41no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290#638—32no—
291#638—32no—
292#638—32no—
293#638—32no—
294#638—32no—
295#638—62no—
296#638—62no—
297#638—62no—
298#638—122no—
299#638C4×D312yes—
300C2×C3⋊Dic3—32no—
301C4⋊(C3⋊D3)—32no—
302C4⋊(C3⋊D3)—31no—
303C4⋊(C3⋊D3)—31no—
304C4⋊(C3⋊D3)—31no—
305C4⋊(C3⋊D3)—61no—
306C4⋊(C3⋊D3)—61no—
307C4⋊(C3⋊D3)—61no—
308C4⋊(C3⋊D3)—121no—
309C4⋊(C3⋊D3)C4×D311yescharacteristic
310C4×C3⋊D3—32no—
311C4×C3⋊D3—32no—
312C4×C3⋊D3—32no—
313C4×C3⋊D3—32no—
314C4×C3⋊D3—32no—
315C4×C3⋊D3—62no—
316C4×C3⋊D3—62no—
317C4×C3⋊D3—62no—
318C4×C3⋊D3—122no—
319C4×C3⋊D3C22×D312yes—
320#634—31no—
321#634—31no—
322#634—31no—
323#634—32no—
324#634—61no—
325#634—61no—
326#634—61no—
327#634—121no—
328#634C4×D311yescharacteristic
329C3×#67—32no—
330C3×#67—32no—
331C3×#67—62no—
332C2×C3×Dic3—21no—
333C2×C3×Dic3C4×D311yescharacteristic
334C2×C3×Dic3C4×D311yescharacteristic
335C3×D12—31no—
336C3×D12—31no—
337C3×D12—61no—
338C3×C4×D3—21no—
339C3×C4×D3—21no—
340C3×C4×D3—21no—
341C3×C4×D3—21no—
342C3×C4×D3—32no—
343C3×C4×D3—32no—
344C3×C4×D3—62no—
345C3×C4×D3C4×D311yescharacteristic
346C3×C4×D3C4×D311yescharacteristic
347C3×C4×D3C4×D311yescharacteristic
348C3×C4×D3C4×D311yescharacteristic
349C3×C4×D3C22×D311yescharacteristic
350C3×C4×D3C22×D311yescharacteristic
351C3×C4×D3C22×D311yescharacteristic
352C3×C4×D3C22×D311yescharacteristic
353C3×Dic6—31no—
354C3×Dic6—31no—
355C3×Dic6—61no—
356#627—32no—
357#627—32no—
358#627—62no—
359#626—32no—
360#626—32no—
361#626—32no—
362#626—32no—
363#626—62no—
364#626—62no—
365#625—32no—
366#625—32no—
367#625—62no—
368#624—32no—
369#624—32no—
370#624—62no—
371D3×Dic3—32no—
372D3×Dic3—32no—
373D3×Dic3—32no—
374D3×Dic3—32no—
375D3×Dic3—62no—
376D3×Dic3—62no—
377C32×C8—31no—
378C32×C8—32no—
379C32×C8—31no—
380C3⋊(C3⋊C8)C22×D311yescharacteristic
381C3⋊(C3⋊C8)C22×D312yes—
382C3⋊(C3⋊C8)C22×D311yescharacteristic
383C3×C3⋊C8—21no—
384C3×C3⋊C8—22no—
385C3×C3⋊C8—21no—
386C3×C3⋊C8—31no—
387C3×C3⋊C8—32no—
388C3×C3⋊C8—31no—
389C3×C3⋊C8—32no—
390C3×C3⋊C8—31no—
391C3×C3⋊C8—31no—
392C3×C3⋊C8—61no—
393C3×C3⋊C8—62no—
394C3×C3⋊C8—61no—
395C3×C3⋊C8C22×D311yescharacteristic
396C3×C3⋊C8C22×D311yescharacteristic
397C3×C3⋊C8C22×D312yes—
398C3×C3⋊C8C22×D311yescharacteristic
399C3×C3⋊C8C22×D312yes—
400C3×C3⋊C8C22×D311yescharacteristic
401C2×#131—271noSylow
402C2×C33—21no—
403C2×C33C23×C411yescharacteristic
404C3⋊(C3⋊D3)—22no—
405C3×C3⋊D3—22no—
406C32×D3—21no—
407C32×D3#13112yescomplemented
408C3×#41—91no—
409C22×C3×C4—31no—
410C22×C3×C4—31no—
411C22×C3×C4—61no—
412C2×#67—92no—
413C2×#67—92no—
414C2×#67—182no—
415#239—91no—
416D3×Q8—91no—
417#237—92no—
418#237—91no—
419D3×D4—92no—
420D3×D4—91no—
421#235—31no—
422#235—31no—
423#235—61no—
424#235—91no—
425#235—91no—
426#235—92no—
427#235—92no—
428#235—91no—
429#235—91no—
430#235—92no—
431#235—92no—
432#235—91no—
433#235—91no—
434#235—91no—
435#235—92no—
436#235—181no—
437#235—182no—
438#235—181no—
439#235—182no—
440#235—181no—
441#235—181no—
442#235—181no—
443#235—361no—
444C2×D12—91no—
445C2×D12—91no—
446C2×D12—181no—
447C2×C4×D3—92no—
448C2×C4×D3—92no—
449C2×C4×D3—92no—
450C2×C4×D3—182no—
451C2×C4×D3D3211yescharacteristic
452C2×Dic6—91no—
453C2×Dic6—91no—
454C2×Dic6—181no—
455C3×M16—31no—
456C3×M16—31no—
457C3×M16—61no—
458C3×M16—92no—
459C3×M16—92no—
460C3×M16—91no—
461C2×C3×C8—31no—
462C2×C3×C8—31no—
463C2×C3×C8—61no—
464C2×C3×C8—92no—
465C2×C3×C8—91no—
466C2×C3×C8—92no—
467C2×C3×C8—91no—
468C2×C3×C8—91no—
469C2×C3×C8—91no—
470C2×C3×C8—91no—
471#208—31no—
472#208—31no—
473#208—32no—
474#208—61no—
475#208—92no—
476#208D3211yescharacteristic, complemented
477C2×C3⋊C8—31no—
478C2×C3⋊C8—31no—
479C2×C3⋊C8—31no—
480C2×C3⋊C8—32no—
481C2×C3⋊C8—31no—
482C2×C3⋊C8—31no—
483C2×C3⋊C8—31no—
484C2×C3⋊C8—61no—
485C2×C3⋊C8—92no—
486C2×C3⋊C8D3211yescharacteristic, complemented
487ΓL(1,𝔽25)—32no—
488ΓL(1,𝔽25)—32no—
489ΓL(1,𝔽25)—32no—
490ΓL(1,𝔽25)—92no—
491ΓL(1,𝔽25)—92no—
492ΓL(1,𝔽25)—92no—
493ΓL(1,𝔽25)—92no—
494ΓL(1,𝔽25)—92no—
495ΓL(1,𝔽25)—92no—
496ΓL(1,𝔽25)—92no—
497ΓL(1,𝔽25)—92no—
498ΓL(1,𝔽25)—182no—
499ΓL(1,𝔽25)—182no—
500D3×C8—31no—
501D3×C8—31no—
502D3×C8—32no—
503D3×C8—31no—
504D3×C8—31no—
505D3×C8—32no—
506D3×C8—32no—
507D3×C8—92no—
508D3×C8—92no—
509D3×C8—92no—
510D3×C8—92no—
511D3×C8—92no—
512D3×C8—92no—
513D3×C8—92no—
514D3×C8—92no—
515D3×C8—182no—
516D3×C8—182no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—31no—
521C22×C32—31no—
522C22×C32—41no—
523C22×C32—62no—
524C22×C32C2×C4×D311yescharacteristic
525C22×C32C2×C4×D311yescharacteristic
526C22×C32C2×C4×D311yescharacteristic
527C2×C3⋊D3—32no—
528C2×C3⋊D3—32no—
529C2×C3⋊D3—32no—
530C2×C3⋊D3—62no—
531C2×C3⋊D3—62no—
532C2×C3⋊D3—62no—
533C2×C3⋊D3—64no—
534C2×C3⋊D3—122no—
535C2×C3⋊D3C2×C4×D312yes—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—21no—
539C2×C3×D3—21no—
540C2×C3×D3—32no—
541C2×C3×D3—32no—
542C2×C3×D3—42no—
543C2×C3×D3—62no—
544C2×C3×D3C2×C4×D311yescharacteristic
545C2×C3×D3C2×C4×D311yescharacteristic
546C2×C3×D3C2×C4×D311yescharacteristic
547C2×C3×D3C2×C4×D311yescharacteristic
548D32—64no—
549D32—64no—
550D32—124no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—31no—
558C32×C4—31no—
559C32×C4—41no—
560C32×C4—41no—
561C32×C4C2×C4×D311yescharacteristic
562C32×C4C2×C4×D311yescharacteristic
563C32×C4C2×C4×D311yescharacteristic
564C32×C4C23×D311yescharacteristic
565C32×C4C23×D311yescharacteristic
566C32×C4C23×D311yescharacteristic
567C3⋊Dic3—32no—
568C3⋊Dic3—32no—
569C3⋊Dic3—32no—
570C3⋊Dic3—62no—
571C3⋊Dic3—62no—
572C3⋊Dic3—62no—
573C3⋊Dic3—122no—
574C3⋊Dic3C2×C4×D312yes—
575C3×Dic3—21no—
576C3×Dic3—21no—
577C3×Dic3—32no—
578C3×Dic3—32no—
579C3×Dic3—62no—
580C3×Dic3C2×C4×D311yescharacteristic
581C3×Dic3C2×C4×D311yescharacteristic
582C3×Dic3C2×C4×D311yescharacteristic
583C3×Dic3C2×C4×D311yescharacteristic
584C2×#41—271no—
585#131—91no—
586#131—271no—
587#131—272no—
588#131—271no—
589#131—272no—
590#131—271no—
591C2×M16—91no—
592C2×M16—272no—
593C22×C8—91no—
594C22×C8—272no—
595C33C2×#13111yescharacteristic, complemented, Sylow
596C23×C3—31no—
597C23×C3—31no—
598C23×C3—61no—
599C22×D3—92no—
600C22×D3—92no—
601C22×D3—92no—
602C22×D3—182no—
603C22×D3#62411yescharacteristic
604C3×Q8—91no—
605C3×D4—92no—
606C3×D4—91no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—31no—
613C2×C3×C4—31no—
614C2×C3×C4—31no—
615C2×C3×C4—31no—
616C2×C3×C4—31no—
617C2×C3×C4—31no—
618C2×C3×C4—31no—
619C2×C3×C4—31no—
620C2×C3×C4—41no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—92no—
627C2×C3×C4C2×D3211yescharacteristic
628C2×C3×C4C2×D3211yescharacteristic
629C2×C3×C4C2×D3211yescharacteristic
630#67—32no—
631#67—32no—
632#67—62no—
633#67—92no—
634#67—92no—
635#67—92no—
636#67—92no—
637#67—92no—
638#67—92no—
639#67—92no—
640#67—92no—
641#67—92no—
642#67—182no—
643#67—182no—
644#67—182no—
645#67—182no—
646#67—182no—
647#67—362no—
648C2×Dic3—92no—
649C2×Dic3—92no—
650C2×Dic3—92no—
651C2×Dic3—182no—
652C2×Dic3#62411yescharacteristic
653D12—31no—
654D12—31no—
655D12—61no—
656D12—92no—
657D12—92no—
658D12—92no—
659D12—91no—
660D12—91no—
661D12—91no—
662D12—181no—
663D12—181no—
664D12—181no—
665D12—182no—
666D12—361no—
667C4×D3—32no—
668C4×D3—32no—
669C4×D3—62no—
670C4×D3—92no—
671C4×D3—92no—
672C4×D3—92no—
673C4×D3—92no—
674C4×D3—92no—
675C4×D3—92no—
676C4×D3—92no—
677C4×D3—92no—
678C4×D3—92no—
679C4×D3—182no—
680C4×D3—182no—
681C4×D3—182no—
682C4×D3—182no—
683C4×D3—182no—
684C4×D3—362no—
685C4×D3#62411yescharacteristic
686C4×D3#62411yescharacteristic
687C4×D3C2×D3211yescharacteristic
688C4×D3C2×D3211yescharacteristic
689Dic6—31no—
690Dic6—31no—
691Dic6—61no—
692Dic6—92no—
693Dic6—92no—
694Dic6—91no—
695Dic6—91no—
696Dic6—91no—
697Dic6—92no—
698Dic6—182no—
699Dic6—181no—
700Dic6—181no—
701Dic6—181no—
702Dic6—361no—
703C3×C8—31no—
704C3×C8—31no—
705C3×C8—31no—
706C3×C8—32no—
707C3×C8—32no—
708C3×C8—31no—
709C3×C8—61no—
710C3×C8—62no—
711C3×C8—61no—
712C3×C8—91no—
713C3×C8—92no—
714C3×C8—91no—
715C3⋊C8—31no—
716C3⋊C8—31no—
717C3⋊C8—32no—
718C3⋊C8—31no—
719C3⋊C8—32no—
720C3⋊C8—31no—
721C3⋊C8—61no—
722C3⋊C8—62no—
723C3⋊C8—61no—
724C3⋊C8C2×D3211yescharacteristic
725C3⋊C8C2×D3212yes—
726C3⋊C8C2×D3211yescharacteristic
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—21no—
730C2×C32—21no—
731C2×C32—21no—
732C2×C32—21no—
733C2×C32—32no—
734C2×C32—41no—
735C2×C32—41no—
736C2×C32—41no—
737C2×C32—41no—
738C2×C32—61no—
739C2×C32—81no—
740C2×C32C22×C4×D311yescharacteristic
741C2×C32C22×C4×D311yescharacteristic
742C2×C32C22×C4×D311yescharacteristic
743C3⋊D3—22no—
744C3⋊D3—62no—
745C3⋊D3—62no—
746C3⋊D3—62no—
747C3⋊D3—122no—
748C3⋊D3—122no—
749C3⋊D3—122no—
750C3⋊D3—242no—
751C3×D3—21no—
752C3×D3—21no—
753C3×D3—22no—
754C3×D3—41no—
755C3×D3—62no—
756C3×D3—62no—
757C3×D3—122no—
758C3×D3#90112yescomplemented
759C3×D3#90712yescomplemented
760#41—91no—
761#41—272no—
762#41—272no—
763#41—271no—
764#41—271no—
765#41—271no—
766C2×Q8—271no—
767C2×D4—271no—
768C2×D4—272no—
769C22×C4—31no—
770C22×C4—272no—
771M16—31no—
772M16—92no—
773M16—92no—
774M16—91no—
775M16—272no—
776M16—272no—
777M16—272no—
778C2×C8—31no—
779C2×C8—92no—
780C2×C8—91no—
781C2×C8—91no—
782C2×C8—91no—
783C2×C8—91no—
784C2×C8—92no—
785C2×C8—91no—
786C2×C8—272no—
787C2×C8—272no—
788C2×C8—272no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—31no—
793C22×C3—31no—
794C22×C3—31no—
795C22×C3—31no—
796C22×C3—41no—
797C22×C3—61no—
798C22×C3—61no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—92no—
802C22×C3—122no—
803C22×C3C4×D3211yescharacteristic
804C22×C3C4×D3211yescharacteristic
805C22×C3C2×#62411yescharacteristic
806C2×D3—22no—
807C2×D3—32no—
808C2×D3—32no—
809C2×D3—62no—
810C2×D3—92no—
811C2×D3—92no—
812C2×D3—92no—
813C2×D3—182no—
814C2×D3—182no—
815C2×D3—182no—
816C2×D3—184no—
817C2×D3—184no—
818C2×D3—184no—
819C2×D3—362no—
820C2×D3—364no—
821C2×D3C2×#62411yescharacteristic
822C2×D3C2×#62411yescharacteristic
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—31no—
830C3×C4—31no—
831C3×C4—31no—
832C3×C4—31no—
833C3×C4—41no—
834C3×C4—41no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—92no—
838C3×C4C4×D3211yescharacteristic
839C3×C4C4×D3211yescharacteristic
840C3×C4C2×#62411yescharacteristic
841C3×C4C22×D3211yescharacteristic
842C3×C4C22×D3211yescharacteristic
843C3×C4C22×D3211yescharacteristic
844Dic3—32no—
845Dic3—32no—
846Dic3—62no—
847Dic3—92no—
848Dic3—92no—
849Dic3—92no—
850Dic3—182no—
851Dic3—182no—
852Dic3—182no—
853Dic3—362no—
854Dic3C2×#62411yescharacteristic
855Dic3C2×#62411yescharacteristic
856C32—21no—
857C32—21no—
858C32—21no—
859C32—41no—
860C32C2×#90111yescharacteristic, complemented
861C32C2×#90711yescharacteristic, complemented
862C32D3×#13111yescharacteristic, complemented
863C23—31no—
864C23—272no—
865Q8—91no—
866Q8—272no—
867Q8—271no—
868D4—92no—
869D4—91no—
870D4—272no—
871D4—272no—
872D4—272no—
873D4—272no—
874D4—271no—
875C2×C4—31no—
876C2×C4—31no—
877C2×C4—31no—
878C2×C4—31no—
879C2×C4—31no—
880C2×C4—92no—
881C2×C4—272no—
882C2×C4—272no—
883C2×C4—272no—
884C2×C4—272no—
885C2×C4D3311yescharacteristic
886C8—31no—
887C8—31no—
888C8—32no—
889C8—91no—
890C8—91no—
891C8—92no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—32no—
899C2×C3—32no—
900C2×C3—41no—
901C2×C3—41no—
902C2×C3—41no—
903C2×C3—41no—
904C2×C3—62no—
905C2×C3—61no—
906C2×C3—61no—
907C2×C3—81no—
908C2×C3—121no—
909C2×C3—182no—
910C2×C3C2×C4×D3211yescharacteristic
911C2×C3C2×C4×D3211yescharacteristic
912C2×C3C22×#62411yescharacteristic
913D3—21no—
914D3—62no—
915D3—62no—
916D3—122no—
917D3—182no—
918D3—182no—
919D3—182no—
920D3—362no—
921D3—362no—
922D3—362no—
923D3—722no—
924D3#6381712yesdirect product factor
925C22—31no—
926C22—31no—
927C22—62no—
928C22—92no—
929C22—272no—
930C22—544no—
931C22D3×#62411yescharacteristic
932C4—31no—
933C4—31no—
934C4—92no—
935C4—272no—
936C4D3×#62411yescharacteristic
937C4C2×D3311yescharacteristic
938C3—21no—
939C3—21no—
940C3—21no—
941C3—41no—
942C3D3×#90111yescharacteristic, complemented
943C3D3×#90711yescharacteristic, complemented
944C3C2×#6381711yescharacteristic, complemented
945C2—21no—
946C2—32no—
947C2—61no—
948C2—182no—
949C2—542no—
950C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC4C2×D33
commutator, socleC2×C33C23×C4
FittingC2×C33×C4C23
prime radicalD3×#3828C2
cosocleC33×C4C24
hypercenterC2×C4D33
hypocenterC33C2×#131
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723657C2semidirect
3. #11723357C2semidirect
4. #11723356C2semidirect
5. C3×#63817C2semidirect
6. C3×D3×#208C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. #11722825C2semidirect
9. #11722824C2semidirect
10. D3×#3712C2semidirect
11. D3×#3710C2semidirect
26. C3×#3748C22semidirect
27. C2×C3×C3⋊(C3⋊C8)C22semidirect
28. C32×#208C22semidirect
29. C2×C32×C3⋊C8C22semidirect
30. #88809C22semidirect
31. #88808C22semidirect
32. #88788C22semidirect
33. #88788C22semidirect
34. #88785C22semidirect
35. #88785C22semidirect
36. C3×#3712C22semidirect
37. C3×#3711C22semidirect
38. C3×#3710C22semidirect
42. C3×D3×C3⋊C8C22semidirect
43. C3×D3×C3⋊C8C22semidirect
66. #63817D3direct (N × H)
70. D3×#208D3semidirect
71. C2×D3×C3⋊C8D3semidirect
161. #3748C2×D3semidirect
162. C2×C3⋊(C3⋊C8)C2×D3semidirect
172. C3×#208C2×D3semidirect
173. C3×#208C2×D3semidirect
183. C2×C3×C3⋊C8C2×D3semidirect
184. C2×C3×C3⋊C8C2×D3semidirect
202. #3712C2×D3semidirect
205. #3711C2×D3semidirect
213. #3710C2×D3semidirect
219. D3×C3⋊C8C2×D3semidirect
220. D3×C3⋊C8C2×D3semidirect
407. C32×D3#131semidirect
476. #208D32semidirect
486. C2×C3⋊C8D32semidirect
595. C33C2×#131semidirect
758. C3×D3#901semidirect
759. C3×D3#907semidirect
860. C32C2×#901semidirect
861. C32C2×#907semidirect
862. C32D3×#131semidirect
924. D3#63817direct (N × H)
942. C3D3×#901semidirect
943. C3D3×#907semidirect
944. C3C2×#63817semidirect

Maximal subgroups

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

subgroupindex
D3×#38282
#117236572
#117233572
#117233562
C3×#638172
C3×D3×#2082
C2×C3×D3×C3⋊C82
#117228252
#117228242
D3×#37122
D3×#37102
C2×#638173
D3×#9073
D3×#9013