Finite Group Databasebeta

← D3×#63815 #13170483

Subgroups — D3×#63815 #13170483

Order 1728.

1286 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#235C211yesmaximal, characteristic
2#11723657C211yesmaximal, characteristic, complemented
3#11723354C211yesmaximal, characteristic, complemented
4#11723350C211yesmaximal, characteristic, complemented
5C2×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#63815C211yesmaximal, characteristic, complemented
7C3×D3×#208C211yesmaximal, characteristic, complemented
8#11722823C212yesmaximal, complemented
9#11722822C212yesmaximal, complemented
10D3×#3711C212yesmaximal, complemented
11D32×C3⋊C8C212yesmaximal, complemented
12D3×#948—31nomaximal
13C2×#63815—31nomaximal
14D3×#907—31nomaximal
15C3×#3828C2211yescharacteristic
16C32×#235C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C3×D3×#67C412yes—
19C3×#3804C412yes—
20C3×D3×D12C411yescharacteristic
21C3×C4×D32C2212yes—
22C3×#3799C411yescharacteristic
23C3×#3798C2212yes—
24C3×#3795C411yescharacteristic
25C3×D3×Dic6C411yescharacteristic
26C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
27C3×#3748C2211yescharacteristic, complemented
28C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
29C32×#208C2211yescharacteristic, complemented
30#88809C2212yescomplemented
31#88808C2212yescomplemented
32#88787C2212yescomplemented
33#88786C2212yescomplemented
34C3⋊D3×C3⋊C8C2212yescomplemented
35D3×C3⋊(C3⋊C8)C2211yescharacteristic
36D3×C3⋊(C3⋊C8)C2211yescharacteristic
37D3×C3⋊(C3⋊C8)C2212yescomplemented
38D3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
39D3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
40C3×#3711C2212yescomplemented
41C3×#3711C2212yescomplemented
42C3×D3×C3⋊C8C2212yes—
43C3×D3×C3⋊C8C2212yescomplemented
44C3×D3×#41—31no—
45C2×C3×#235—31no—
46D3×#235D311yescharacteristic
47#64157—31no—
48C22×C3⋊(C3⋊C8)—31no—
49#64116—31no—
50C3×#948—31no—
51C2×C3×#208—31no—
52C3×#907—31no—
53C3×D3×M16—31no—
54C2×#3711—32no—
55#63817—31no—
56#63815—31no—
57#63815—31no—
58#63815—31no—
59#63815—31no—
60#63815—31no—
61#63815—32no—
62#63815—32no—
63#63815—32no—
64#63815—61no—
65#63815—61no—
66#63815D311yescharacteristic, direct product factor
67#63814—31no—
68#63814—32no—
69D3×#208—32no—
70D3×#208D311yescharacteristic, complemented
71C2×D3×C3⋊C8—31no—
72C2×D3×C3⋊C8—31no—
73C2×D3×C3⋊C8—32no—
74C2×D3×C3⋊C8—32no—
75C2×D3×C3⋊C8—61no—
76#63805—32no—
77#63804—32no—
78D3×ΓL(1,𝔽25)—32no—
79D32×C8—32no—
80C22×C32×D3C2×C411yescharacteristic
81C2×C3×D32C2×C412yes—
82C2×C33×C4C2311yescharacteristic
83C3×#638C2×C412yes—
84C3×C4⋊(C3⋊D3)C2×C411yescharacteristic
85C3×C4×C3⋊D3C2312yes—
86C3×#634C2×C411yescharacteristic
87C32×#67C2×C412yes—
88C2×C32×Dic3C2×C411yescharacteristic
89C32×D12C2×C411yescharacteristic
90C32×C4×D3C2×C411yescharacteristic
91C32×C4×D3C2×C411yescharacteristic
92C32×C4×D3C2311yescharacteristic
93C32×C4×D3C2312yes—
94C32×C4×D3C2311yescharacteristic
95C32×Dic6C2×C411yescharacteristic
96C3×#627C2×C412yes—
97C3×#626C2×C412yes—
98C3×#626C2×C412yes—
99C3×#625C2×C412yes—
100C3×#624C2×C412yes—
101C3×D3×Dic3C2×C412yes—
102C3×D3×Dic3C2×C412yes—
103C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
104C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
105C3×C3⋊(C3⋊C8)C2311yescharacteristic
106C3×C3⋊(C3⋊C8)C2311yescharacteristic
107C3×C3⋊(C3⋊C8)C2312yes—
108C32×C3⋊C8C2312yes—
109C2×#948—91no—
110D3×#131—91no—
111C2×#907—91no—
112C32×#41—31no—
113C22×C32×C4—31no—
114#3828C2×D311yescharacteristic
115C2×C3×#67—32no—
116C3×#239—31no—
117C3×D3×Q8—31no—
118C3×#237—32no—
119C3×#237—31no—
120C3×D3×D4—32no—
121C3×D3×D4—31no—
122C3×#235—21no—
123C3×#235—31no—
124C3×#235—31no—
125C3×#235—32no—
126C3×#235—31no—
127C3×#235—32no—
128C3×#235—32no—
129C3×#235—31no—
130C3×#235—61no—
131C3×#235C2×D311yescharacteristic
132C3×#235C2×D311yescharacteristic
133C2×C3×D12—31no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—32no—
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×C3×C4×D3C2×D311yescharacteristic
139C2×C3×Dic6—31no—
140D3×#67Dic312yes—
141#3804Dic312yes—
142D3×D12Dic311yescharacteristic
143C4×D32C2×D312yes—
144#3799Dic311yescharacteristic
145#3798C2×D312yes—
146#3795Dic311yescharacteristic
147D3×Dic6Dic311yescharacteristic
148C32×M16—31no—
149#3748—32no—
150#3748C2×D311yescharacteristic, complemented
151C2×C3⋊(C3⋊C8)—31no—
152C2×C3⋊(C3⋊C8)—31no—
153C2×C3⋊(C3⋊C8)—31no—
154C2×C3⋊(C3⋊C8)—31no—
155C2×C3⋊(C3⋊C8)—32no—
156C2×C3⋊(C3⋊C8)—31no—
157C2×C3⋊(C3⋊C8)—31no—
158C2×C3⋊(C3⋊C8)—31no—
159C2×C3⋊(C3⋊C8)—61no—
160C2×C3⋊(C3⋊C8)—61no—
161C2×C3⋊(C3⋊C8)—61no—
162C2×C3⋊(C3⋊C8)—121no—
163C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
164#3743—32no—
165C8×C3⋊D3—32no—
166C3×#208—21no—
167C3×#208—31no—
168C3×#208—31no—
169C3×#208—32no—
170C3×#208—32no—
171C3×#208—61no—
172C3×#208C2×D311yescharacteristic, complemented
173C3×#208C2×D311yescharacteristic, complemented
174C2×C3×C3⋊C8—31no—
175C2×C3×C3⋊C8—31no—
176C2×C3×C3⋊C8—32no—
177C2×C3×C3⋊C8—32no—
178C2×C3×C3⋊C8—61no—
179C3×ΓL(1,𝔽25)—32no—
180C3×ΓL(1,𝔽25)—32no—
181C3×D3×C8—32no—
182C3×D3×C8—32no—
183#3712—32no—
184#3711—32no—
185#3711—32no—
186#3711—32no—
187#3711—32no—
188#3711—32no—
189#3711—32no—
190#3711—62no—
191#3711—62no—
192#3711C2×D312yescomplemented
193#3711C2×D312yescomplemented
194#3710—32no—
195D3×C3⋊C8—31no—
196D3×C3⋊C8—32no—
197D3×C3⋊C8—31no—
198D3×C3⋊C8—31no—
199D3×C3⋊C8—31no—
200D3×C3⋊C8—31no—
201D3×C3⋊C8—31no—
202D3×C3⋊C8—31no—
203D3×C3⋊C8—31no—
204D3×C3⋊C8—32no—
205D3×C3⋊C8—32no—
206D3×C3⋊C8—32no—
207D3×C3⋊C8—32no—
208D3×C3⋊C8—32no—
209D3×C3⋊C8—62no—
210D3×C3⋊C8—61no—
211D3×C3⋊C8—61no—
212D3×C3⋊C8—61no—
213D3×C3⋊C8—61no—
214D3×C3⋊C8—62no—
215D3×C3⋊C8C2×D312yes—
216D3×C3⋊C8C2×D312yescomplemented
217C22×C33C22×C411yescharacteristic
218C2×C3×C3⋊D3C22×C412yes—
219C2×C32×D3—22no—
220C2×C32×D3C22×C412yes—
221C2×C32×D3C22×C411yescharacteristic
222C2×C32×D3C22×C411yescharacteristic
223C3×D32—24no—
224C33×C4C22×C411yescharacteristic
225C33×C4C2411yescharacteristic
226C3×C3⋊Dic3C22×C412yes—
227C32×Dic3C22×C411yescharacteristic
228C32×Dic3C22×C412yes—
229C32×Dic3C22×C411yescharacteristic
230C2×C3×#41—91no—
231D3×#41—31no—
232C2×#235—31no—
233C3×#131—91no—
234C2×C3×M16—91no—
235#948—31no—
236#948—91no—
237#948—92no—
238#948—92no—
239#948—91no—
240#948—91no—
241#948—91no—
242#948—181no—
243C2×#208—31no—
244C2×#208—92no—
245C22×C3⋊C8—92no—
246C22×C3⋊C8—91no—
247C22×C3⋊C8—91no—
248C22×C3⋊C8—181no—
249#907—31no—
250#907—92no—
251#907—92no—
252#907—92no—
253#907—91no—
254#907—91no—
255#907—91no—
256#907—91no—
257#907—181no—
258D3×M16—31no—
259D3×M16—92no—
260#901—92no—
261#901—91no—
262C2×ΓL(1,𝔽25)—92no—
263C2×D3×C8—92no—
264C2×D3×C8—92no—
265C2×D3×C8—91no—
266C23×C32—31no—
267C22×C3×D3—21no—
268C22×C3×D3—32no—
269C22×C3×D3—32no—
270C22×C3×D3C4×D311yescharacteristic
271C22×C3×D3C2×Dic311yescharacteristic
272C2×D32C2×Dic312yes—
273C32×Q8—31no—
274C32×D4—32no—
275C32×D4—31no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4—32no—
284C2×C32×C4—31no—
285C2×C32×C4—41no—
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289#638C2×Dic312yes—
290C4⋊(C3⋊D3)C2×Dic311yescharacteristic
291C4×C3⋊D3C22×D312yes—
292#634C2×Dic311yescharacteristic
293C3×#67—22no—
294C3×#67—32no—
295C3×#67—32no—
296C3×#67—32no—
297C3×#67—32no—
298C3×#67—32no—
299C3×#67—32no—
300C3×#67—62no—
301C3×#67C4×D312yes—
302C3×#67C2×Dic312yes—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—32no—
305C2×C3×Dic3—32no—
306C2×C3×Dic3C4×D311yescharacteristic
307C2×C3×Dic3C2×Dic311yescharacteristic
308C3×D12—21no—
309C3×D12—32no—
310C3×D12—32no—
311C3×D12—31no—
312C3×D12—31no—
313C3×D12—61no—
314C3×D12C4×D311yescharacteristic
315C3×D12C2×Dic311yescharacteristic
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—22no—
321C3×C4×D3—32no—
322C3×C4×D3—32no—
323C3×C4×D3—32no—
324C3×C4×D3—32no—
325C3×C4×D3—32no—
326C3×C4×D3—32no—
327C3×C4×D3—62no—
328C3×C4×D3C4×D311yescharacteristic
329C3×C4×D3C4×D311yescharacteristic
330C3×C4×D3C2×Dic311yescharacteristic
331C3×C4×D3C2×Dic311yescharacteristic
332C3×C4×D3C22×D311yescharacteristic
333C3×C4×D3C22×D311yescharacteristic
334C3×C4×D3C22×D312yes—
335C3×C4×D3C22×D311yescharacteristic
336C3×C4×D3C22×D311yescharacteristic
337C3×C4×D3C22×D312yes—
338C3×Dic6—21no—
339C3×Dic6—31no—
340C3×Dic6—31no—
341C3×Dic6—32no—
342C3×Dic6—32no—
343C3×Dic6—61no—
344C3×Dic6C4×D311yescharacteristic
345C3×Dic6C2×Dic311yescharacteristic
346#627C2×Dic312yes—
347#626C2×Dic312yes—
348#626C2×Dic312yes—
349#625C2×Dic312yes—
350#624C2×Dic312yes—
351D3×Dic3C2×Dic312yes—
352D3×Dic3C2×Dic312yes—
353C32×C8—32no—
354C3⋊(C3⋊C8)—31no—
355C3⋊(C3⋊C8)—31no—
356C3⋊(C3⋊C8)—31no—
357C3⋊(C3⋊C8)—31no—
358C3⋊(C3⋊C8)—31no—
359C3⋊(C3⋊C8)—31no—
360C3⋊(C3⋊C8)—61no—
361C3⋊(C3⋊C8)—61no—
362C3⋊(C3⋊C8)—61no—
363C3⋊(C3⋊C8)—61no—
364C3⋊(C3⋊C8)—61no—
365C3⋊(C3⋊C8)—61no—
366C3⋊(C3⋊C8)—121no—
367C3⋊(C3⋊C8)—121no—
368C3⋊(C3⋊C8)C22×D311yescharacteristic
369C3⋊(C3⋊C8)C22×D312yes—
370C3⋊(C3⋊C8)C22×D311yescharacteristic
371C3×C3⋊C8—22no—
372C3×C3⋊C8—31no—
373C3×C3⋊C8—31no—
374C3×C3⋊C8—31no—
375C3×C3⋊C8—32no—
376C3×C3⋊C8—31no—
377C3×C3⋊C8—32no—
378C3×C3⋊C8—61no—
379C3×C3⋊C8—61no—
380C3×C3⋊C8—62no—
381C3×C3⋊C8C22×D312yes—
382C3×C3⋊C8C22×D312yes—
383C2×#131—271noSylow
384C2×C33—21no—
385C2×C33C23×C411yescharacteristic
386C3×C3⋊D3—22no—
387C32×D3—21no—
388C32×D3—22no—
389C32×D3#13112yescomplemented
390C3×#41—31no—
391C3×#41—31no—
392C3×#41—61no—
393C3×#41—92no—
394C3×#41—92no—
395C3×#41—91no—
396C3×#41—91no—
397C3×#41—91no—
398C2×C3×Q8—91no—
399C2×C3×D4—91no—
400C2×C3×D4—92no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—61no—
404C22×C3×C4—92no—
405C2×#67—32no—
406#239—31no—
407D3×Q8—31no—
408#237—32no—
409#237—31no—
410D3×D4—32no—
411D3×D4—31no—
412#235—31no—
413#235—31no—
414#235—32no—
415#235—31no—
416#235—32no—
417#235—32no—
418#235—31no—
419#235—61no—
420#235D3211yescharacteristic
421C2×D12—31no—
422C2×C4×D3—32no—
423C2×C4×D3—32no—
424C2×C4×D3D3211yescharacteristic
425C2×Dic6—31no—
426C3×M16—31no—
427C3×M16—31no—
428C3×M16—61no—
429C3×M16—92no—
430C3×M16—92no—
431C3×M16—91no—
432C2×C3×C8—92no—
433C2×C3×C8—92no—
434C2×C3×C8—91no—
435#208—31no—
436#208—31no—
437#208—32no—
438#208—32no—
439#208—61no—
440#208—92no—
441#208—92no—
442#208—92no—
443#208—92no—
444#208—182no—
445#208D3211yescharacteristic, complemented
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—32no—
449C2×C3⋊C8—32no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8—92no—
452C2×C3⋊C8—91no—
453C2×C3⋊C8—92no—
454C2×C3⋊C8—91no—
455C2×C3⋊C8—91no—
456C2×C3⋊C8—91no—
457C2×C3⋊C8—91no—
458C2×C3⋊C8—91no—
459C2×C3⋊C8—91no—
460C2×C3⋊C8—92no—
461C2×C3⋊C8—91no—
462C2×C3⋊C8—91no—
463C2×C3⋊C8—91no—
464C2×C3⋊C8—91no—
465C2×C3⋊C8—92no—
466C2×C3⋊C8—181no—
467C2×C3⋊C8—181no—
468C2×C3⋊C8—181no—
469C2×C3⋊C8—181no—
470C2×C3⋊C8—182no—
471C2×C3⋊C8—181no—
472C2×C3⋊C8—181no—
473C2×C3⋊C8—181no—
474C2×C3⋊C8—361no—
475ΓL(1,𝔽25)—32no—
476ΓL(1,𝔽25)—32no—
477ΓL(1,𝔽25)—92no—
478ΓL(1,𝔽25)—92no—
479ΓL(1,𝔽25)—92no—
480ΓL(1,𝔽25)—92no—
481ΓL(1,𝔽25)—92no—
482ΓL(1,𝔽25)—182no—
483D3×C8—32no—
484D3×C8—32no—
485D3×C8—92no—
486D3×C8—92no—
487D3×C8—92no—
488D3×C8—92no—
489D3×C8—91no—
490D3×C8—91no—
491D3×C8—91no—
492D3×C8—92no—
493D3×C8—91no—
494D3×C8—182no—
495C22×C32—21no—
496C22×C32—21no—
497C22×C32—21no—
498C22×C32—31no—
499C22×C32—32no—
500C22×C32—31no—
501C22×C32—41no—
502C22×C32—62no—
503C22×C32C2×C4×D311yescharacteristic
504C22×C32C2×C4×D311yescharacteristic
505C22×C32C22×Dic311yescharacteristic
506C2×C3⋊D3C22×Dic312yes—
507C2×C3×D3—24no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—21no—
511C2×C3×D3—21no—
512C2×C3×D3—22no—
513C2×C3×D3—32no—
514C2×C3×D3—32no—
515C2×C3×D3—62no—
516C2×C3×D3—64no—
517C2×C3×D3—64no—
518C2×C3×D3C2×C4×D312yes—
519C2×C3×D3C2×C4×D311yescharacteristic
520C2×C3×D3C2×C4×D311yescharacteristic
521C2×C3×D3C22×Dic312yes—
522C2×C3×D3C22×Dic311yescharacteristic
523C2×C3×D3C22×Dic311yescharacteristic
524D32—24no—
525C32×C4—21no—
526C32×C4—21no—
527C32×C4—21no—
528C32×C4—21no—
529C32×C4—21no—
530C32×C4—21no—
531C32×C4—31no—
532C32×C4—32no—
533C32×C4—31no—
534C32×C4—41no—
535C32×C4—41no—
536C32×C4C2×C4×D311yescharacteristic
537C32×C4C2×C4×D311yescharacteristic
538C32×C4C22×Dic311yescharacteristic
539C32×C4C23×D311yescharacteristic
540C32×C4C23×D311yescharacteristic
541C32×C4C23×D311yescharacteristic
542C3⋊Dic3C22×Dic312yes—
543C3×Dic3—22no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—32no—
547C3×Dic3—32no—
548C3×Dic3—62no—
549C3×Dic3C2×C4×D311yescharacteristic
550C3×Dic3C2×C4×D312yes—
551C3×Dic3C2×C4×D311yescharacteristic
552C3×Dic3C22×Dic311yescharacteristic
553C3×Dic3C22×Dic312yes—
554C3×Dic3C22×Dic311yescharacteristic
555C2×#41—91no—
556#131—91no—
557#131—272no—
558#131—271no—
559#131—271no—
560#131—272no—
561#131—271no—
562C2×M16—91no—
563C2×M16—272no—
564C22×C8—272no—
565C22×C8—271no—
566C33C2×#13111yescharacteristic, complemented, Sylow
567C23×C3—31no—
568C23×C3—31no—
569C23×C3—61no—
570C23×C3—92no—
571C22×D3—32no—
572C22×D3—32no—
573C22×D3D3×Dic311yescharacteristic
574C3×Q8—31no—
575C3×Q8—31no—
576C3×Q8—61no—
577C3×Q8—92no—
578C3×Q8—91no—
579C3×D4—32no—
580C3×D4—32no—
581C3×D4—31no—
582C3×D4—31no—
583C3×D4—61no—
584C3×D4—62no—
585C3×D4—92no—
586C3×D4—92no—
587C3×D4—92no—
588C3×D4—92no—
589C3×D4—91no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—32no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—32no—
601C2×C3×C4—31no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—31no—
605C2×C3×C4—41no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—62no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—92no—
613C2×C3×C4—92no—
614C2×C3×C4—92no—
615C2×C3×C4—92no—
616C2×C3×C4C2×D3211yescharacteristic
617C2×C3×C4C2×D3211yescharacteristic
618C2×C3×C4C2×D3211yescharacteristic
619#67—32no—
620#67—32no—
621#67—32no—
622#67—32no—
623#67—32no—
624#67—32no—
625#67—62no—
626#67D3×Dic312yes—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3D3×Dic311yescharacteristic
630D12—32no—
631D12—32no—
632D12—31no—
633D12—31no—
634D12—61no—
635D12D3×Dic311yescharacteristic
636C4×D3—32no—
637C4×D3—32no—
638C4×D3—32no—
639C4×D3—32no—
640C4×D3—32no—
641C4×D3—32no—
642C4×D3—62no—
643C4×D3D3×Dic311yescharacteristic
644C4×D3D3×Dic311yescharacteristic
645C4×D3C2×D3211yescharacteristic
646C4×D3C2×D3212yes—
647C4×D3C2×D3211yescharacteristic
648Dic6—31no—
649Dic6—31no—
650Dic6—32no—
651Dic6—32no—
652Dic6—61no—
653Dic6D3×Dic311yescharacteristic
654C3×C8—32no—
655C3×C8—32no—
656C3×C8—62no—
657C3×C8—91no—
658C3×C8—91no—
659C3×C8—92no—
660C3⋊C8—31no—
661C3⋊C8—32no—
662C3⋊C8—31no—
663C3⋊C8—31no—
664C3⋊C8—32no—
665C3⋊C8—31no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C3⋊C8—62no—
669C3⋊C8—91no—
670C3⋊C8—91no—
671C3⋊C8—91no—
672C3⋊C8—91no—
673C3⋊C8—91no—
674C3⋊C8—91no—
675C3⋊C8—181no—
676C3⋊C8—181no—
677C3⋊C8—181no—
678C3⋊C8—181no—
679C3⋊C8—181no—
680C3⋊C8—181no—
681C3⋊C8—361no—
682C3⋊C8—361no—
683C3⋊C8C2×D3212yes—
684C2×C32—21no—
685C2×C32—22no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—32no—
692C2×C32—41no—
693C2×C32—41no—
694C2×C32—41no—
695C2×C32—42no—
696C2×C32—61no—
697C2×C32—62no—
698C2×C32C22×C4×D311yescharacteristic
699C2×C32C22×C4×D311yescharacteristic
700C2×C32C23×Dic311yescharacteristic
701C3⋊D3—22no—
702C3×D3—22no—
703C3×D3—21no—
704C3×D3—22no—
705C3×D3—22no—
706C3×D3—21no—
707C3×D3—22no—
708C3×D3—42no—
709C3×D3—62no—
710C3×D3—62no—
711C3×D3—122no—
712C3×D3#90712yescomplemented
713C3×D3#94812yescomplemented
714#41—31no—
715#41—92no—
716#41—92no—
717#41—91no—
718#41—91no—
719#41—91no—
720C2×Q8—91no—
721C2×D4—91no—
722C2×D4—92no—
723C22×C4—31no—
724C22×C4—92no—
725M16—31no—
726M16—92no—
727M16—92no—
728M16—91no—
729M16—272no—
730M16—272no—
731M16—272no—
732C2×C8—92no—
733C2×C8—92no—
734C2×C8—91no—
735C2×C8—272no—
736C2×C8—272no—
737C2×C8—271no—
738C2×C8—271no—
739C2×C8—271no—
740C2×C8—272no—
741C2×C8—271no—
742C2×C8—271no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—31no—
747C22×C3—31no—
748C22×C3—31no—
749C22×C3—32no—
750C22×C3—32no—
751C22×C3—31no—
752C22×C3—41no—
753C22×C3—61no—
754C22×C3—61no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—64no—
759C22×C3—92no—
760C22×C3—184no—
761C22×C3C4×D3211yescharacteristic
762C22×C3C2×D3×Dic311yescharacteristic
763C22×C3C2×D3×Dic311yescharacteristic
764C2×D3—22no—
765C2×D3—32no—
766C2×D3—32no—
767C2×D3—62no—
768C2×D3—64no—
769C2×D3—64no—
770C2×D3C2×D3×Dic312yes—
771C2×D3C2×D3×Dic311yescharacteristic
772C2×D3C2×D3×Dic311yescharacteristic
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—31no—
780C3×C4—31no—
781C3×C4—32no—
782C3×C4—31no—
783C3×C4—32no—
784C3×C4—31no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—61no—
788C3×C4—61no—
789C3×C4—62no—
790C3×C4—92no—
791C3×C4C4×D3211yescharacteristic
792C3×C4C2×D3×Dic311yescharacteristic
793C3×C4C2×D3×Dic311yescharacteristic
794C3×C4C22×D3211yescharacteristic
795C3×C4C22×D3211yescharacteristic
796C3×C4C22×D3211yescharacteristic
797Dic3—32no—
798Dic3—32no—
799Dic3—62no—
800Dic3C2×D3×Dic311yescharacteristic
801Dic3C2×D3×Dic312yes—
802Dic3C2×D3×Dic311yescharacteristic
803C32—21no—
804C32—21no—
805C32—21no—
806C32—41no—
807C32C2×#90711yescharacteristic, complemented
808C32D3×#13111yescharacteristic, complemented
809C32C2×#94811yescharacteristic, complemented
810C23—31no—
811C23—92no—
812Q8—31no—
813Q8—92no—
814Q8—91no—
815D4—32no—
816D4—31no—
817D4—92no—
818D4—92no—
819D4—92no—
820D4—92no—
821D4—91no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—32no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—31no—
828C2×C4—92no—
829C2×C4—92no—
830C2×C4—92no—
831C2×C4—92no—
832C2×C4D3311yescharacteristic
833C8—32no—
834C8—91no—
835C8—92no—
836C8—91no—
837C8—271no—
838C8—271no—
839C2×C3—22no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—32no—
847C2×C3—32no—
848C2×C3—41no—
849C2×C3—41no—
850C2×C3—42no—
851C2×C3—41no—
852C2×C3—62no—
853C2×C3—62no—
854C2×C3—61no—
855C2×C3—61no—
856C2×C3—62no—
857C2×C3—62no—
858C2×C3—122no—
859C2×C3—182no—
860C2×C3C2×C4×D3211yescharacteristic
861C2×C3C22×D3×Dic311yescharacteristic
862C2×C3C22×D3×Dic311yescharacteristic
863D3—22no—
864D3—21no—
865D3—62no—
866D3—62no—
867D3—122no—
868D3#6381512yesdirect product factor
869C22—31no—
870C22—31no—
871C22—32no—
872C22—62no—
873C22—92no—
874C22—184no—
875C22D32×Dic311yescharacteristic
876C4—31no—
877C4—31no—
878C4—32no—
879C4—92no—
880C4D32×Dic311yescharacteristic
881C4C2×D3311yescharacteristic
882C3—21no—
883C3—21no—
884C3—21no—
885C3—41no—
886C3D3×#90711yescharacteristic, complemented
887C3C2×#6381511yescharacteristic, complemented
888C3D3×#94811yescharacteristic, complemented
889C2—21no—
890C2—32no—
891C2—61no—
892C2—62no—
893C2—182no—
894C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC4C2×D33
commutator, socleC2×C33C23×C4
FittingC2×C33×C4C23
prime radicalC3×D3×#235C2
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. #11723354C2semidirect
4. #11723350C2semidirect
5. C2×D3×C3⋊(C3⋊C8)C2semidirect
6. C3×#63815C2semidirect
7. C3×D3×#208C2semidirect
8. #11722823C2semidirect
9. #11722822C2semidirect
10. D3×#3711C2semidirect
11. D32×C3⋊C8C2semidirect
26. C2×C3⋊(C3⋊(C3⋊C8))C22semidirect
27. C3×#3748C22semidirect
28. C2×C3×C3⋊(C3⋊C8)C22semidirect
29. C32×#208C22semidirect
30. #88809C22semidirect
31. #88808C22semidirect
32. #88787C22semidirect
33. #88786C22semidirect
34. C3⋊D3×C3⋊C8C22semidirect
37. D3×C3⋊(C3⋊C8)C22semidirect
38. D3×C3⋊(C3⋊C8)C22semidirect
39. D3×C3⋊(C3⋊C8)C22semidirect
40. C3×#3711C22semidirect
41. C3×#3711C22semidirect
43. C3×D3×C3⋊C8C22semidirect
66. #63815D3direct (N × H)
70. D3×#208D3semidirect
150. #3748C2×D3semidirect
163. C2×C3⋊(C3⋊C8)C2×D3semidirect
172. C3×#208C2×D3semidirect
173. C3×#208C2×D3semidirect
192. #3711C2×D3semidirect
193. #3711C2×D3semidirect
216. D3×C3⋊C8C2×D3semidirect
389. C32×D3#131semidirect
445. #208D32semidirect
566. C33C2×#131semidirect
712. C3×D3#907semidirect
713. C3×D3#948semidirect
807. C32C2×#907semidirect
808. C32D3×#131semidirect
809. C32C2×#948semidirect
868. D3#63815direct (N × H)
886. C3D3×#907semidirect
887. C3C2×#63815semidirect
888. C3D3×#948semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#2352
#117236572
#117233542
#117233502
C2×D3×C3⋊(C3⋊C8)2
C3×#638152
C3×D3×#2082
#117228232
#117228222
D3×#37112
D32×C3⋊C82
D3×#9483
C2×#638153
D3×#9073