Finite Group Databasebeta

← D3×#4670 #11801421

Subgroups — D3×#4670 #11801421

Order 1152.

1951 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
6#10592369C211yesmaximal, characteristic, complemented
7C3×#4670C211yesmaximal, characteristic, complemented
8C3×D3×#95C211yesmaximal, characteristic, complemented
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10#10591316C211yesmaximal, characteristic, complemented
11#10591287C211yesmaximal, characteristic, complemented
12#10591284C211yesmaximal, characteristic, complemented
13#10591266C211yesmaximal, characteristic, complemented
14#10591259C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16D3×#388—31nomaximal
17C2×#4670—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35C2×Dic3⋊Dic3C2211yescharacteristic, complemented
36C2×Dic3⋊Dic3C2211yescharacteristic, complemented
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic, complemented
44C2×Dic32C2211yescharacteristic, complemented
45D3×(C2×D3)⋊C4—24no—
46D3×(C2×D3)⋊C4—24no—
47D3×(C2×D3)⋊C4C418yescomplemented
48D3×C4⋊Dic3—24no—
49C4×D3×Dic3—24no—
50C32×#95C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57#63579C2211yescharacteristic, complemented
58C22×(C2×D3)⋊C4—31no—
59C22×(C2×D3)⋊C4—31no—
60C22×(C2×D3)⋊C4—31no—
61C22×C4⋊Dic3—31no—
62C22×C4×Dic3—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C22⋊C4—31no—
65C2×D3×C22⋊C4—31no—
66C2×D3×C22⋊C4—31no—
67C2×C42×D3—31no—
68C3×#388—31no—
69C2×C3×#95—31no—
70C2×C3⋊#95—31no—
71#4990—31no—
72#4951—31no—
73#4945—31no—
74#4944—31no—
75#4940—31no—
76#4670—31no—
77#4670—31no—
78#4670—31no—
79#4670—31no—
80#4670—31no—
81#4670—31no—
82#4670—31no—
83#4670—31no—
84#4670—61no—
85#4670D311yescharacteristic, direct product factor
86#4669—31no—
87D3×#95—31no—
88D3×#95D311yescharacteristic, complemented
89C23×C3⋊D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×D32—22no—
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—22no—
98C22×D32C2×C414yes—
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3C2×C414yes—
119C2×C3×C4×D3D414yes—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3C2×C414yes—
128C2×D3×Dic3D414yes—
129#3752—22no—
130#3752—22no—
131#3752C2×C414yescomplemented
132C4⋊(C3⋊Dic3)—22no—
133C4×C3⋊Dic3—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4C2×C414yescomplemented
137C3×C4⋊Dic3—22no—
138C3×C4×Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141#3722—22no—
142#3722—22no—
143#3722C2×C414yescomplemented
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3C2×C414yescomplemented
147Dic32—22no—
148Dic32—22no—
149C2×#388—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C23×C3×C4—31no—
153C23×C3×C4—31no—
154C23×C3×C4—31no—
155C23×Dic3—31no—
156C23×Dic3—31no—
157C23×Dic3—31no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3C2×D311yescharacteristic
162C22×C4×D3C2×D311yescharacteristic
163C22×C4×D3C2×D311yescharacteristic
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C42—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—38no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4—64no—
192C2×(C2×D3)⋊C4—64no—
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×(C2×D3)⋊C4C2×D311yescharacteristic
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3—61no—
201C2×C4⋊Dic3—64no—
202C2×C4⋊Dic3C2×D311yescharacteristic, complemented
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—61no—
212C2×C4×Dic3—64no—
213C2×C4×Dic3C2×D311yescharacteristic, complemented
214D3×C4⋊C4—64no—
215D3×C22⋊C4—38no—
216D3×C22⋊C4—64no—
217D3×C22⋊C4—64no—
218C42×D3—64no—
219C3×#95—21no—
220C3×#95—31no—
221C3×#95—31no—
222C3×#95—31no—
223C3×#95—31no—
224C3×#95C2×D311yescharacteristic, complemented
225C3×#95C2×D311yescharacteristic, complemented
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—61no—
233C3⋊#95C2×D311yescharacteristic, complemented
234C3⋊#95C2×D311yescharacteristic, complemented
235C3⋊#95C2×D311yescharacteristic, complemented
236C3⋊#95C2×D311yescharacteristic, complemented
237C23×C32C2411yescharacteristic
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3C22×C412yes—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3C22×C412yes—
252C22×C3×D3C22×C412yes—
253C22×C3×D3C2×D412yes—
254C22×C3×D3C2×D412yes—
255C22×C3×D3#4112yes—
256C22×C3×D3#4112yes—
257C22×C3×D3#4112yes—
258C22×C3×D3#4112yes—
259C2×D32—28no—
260C2×D32—28no—
261C2×D32—28no—
262C2×D32—44no—
263C2×D32—44no—
264C2×D32—44no—
265C2×D32—44no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C22×C412yes—
274C2×C32×C4C2×D412yes—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3C22×C412yes—
283C2×C3⋊Dic3C2×D412yes—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3C22×C412yes—
299C2×C3×Dic3C22×C412yes—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3C2×D412yes—
302C3×C4×D3—28no—
303C3×C4×D3—28no—
304C3×C4×D3—44no—
305D3×Dic3—28no—
306D3×Dic3—28no—
307D3×Dic3—44no—
308C22×C4⋊C4—91no—
309C22×C22⋊C4—91no—
310C22×C22⋊C4—91no—
311C22×C22⋊C4—91no—
312C22×C42—91no—
313#388—31no—
314#388—91no—
315#388—91no—
316#388—91no—
317#388—91no—
318#388—91no—
319#388—91no—
320#388—91no—
321C2×#95—31no—
322C2×#95—91no—
323C24×C3—31no—
324C24×C3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—34no—
328C23×D3—34no—
329C23×D3—61no—
330C23×D3—62no—
331C23×D3—62no—
332C23×D3—62no—
333C23×D3—62no—
334C23×D3—62no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3C22×D311yescharacteristic
343C23×D3C22×D311yescharacteristic
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—62no—
356C22×C3×C4—62no—
357C22×C3×C4—62no—
358C22×C3×C4—62no—
359C22×C3×C4—62no—
360C22×C3×C4—62no—
361C22×C3×C4—62no—
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—34no—
373C22×Dic3—34no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—62no—
380C22×Dic3—62no—
381C22×Dic3—62no—
382C22×Dic3—62no—
383C22×Dic3—62no—
384C22×Dic3—62no—
385C22×Dic3—62no—
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C2×C4×D3—22no—
393C2×C4×D3—22no—
394C2×C4×D3—22no—
395C2×C4×D3—22no—
396C2×C4×D3—22no—
397C2×C4×D3—22no—
398C2×C4×D3—22no—
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—62no—
408C2×C4×D3C4×D314yes—
409C2×C4×D3D1214yes—
410C3×C4⋊C4—62no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—62no—
413C3×C22⋊C4—62no—
414C3×C42—62no—
415#217—34no—
416#217—62no—
417#217—62no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—64no—
426(C2×D3)⋊C4—62no—
427(C2×D3)⋊C4—62no—
428(C2×D3)⋊C4—62no—
429(C2×D3)⋊C4—62no—
430(C2×D3)⋊C4—62no—
431(C2×D3)⋊C4—62no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—122no—
437(C2×D3)⋊C4—122no—
438(C2×D3)⋊C4C4×D314yescomplemented
439C4⋊Dic3—22no—
440C4⋊Dic3—62no—
441C4⋊Dic3—62no—
442C4⋊Dic3—62no—
443C4⋊Dic3—62no—
444C4⋊Dic3—122no—
445Dic3⋊C4—62no—
446Dic3⋊C4—62no—
447C4×Dic3—22no—
448C4×Dic3—62no—
449C4×Dic3—62no—
450C4×Dic3—62no—
451C4×Dic3—62no—
452C4×Dic3—62no—
453C4×Dic3—62no—
454C4×Dic3—122no—
455C22×C32C23×C411yescharacteristic
456C22×C32C22×D411yescharacteristic
457C22×C32C22×D411yescharacteristic
458C22×C32C2×#4111yescharacteristic
459C22×C32C2×#4111yescharacteristic
460C22×C32C2×#4111yescharacteristic
461C22×C32C2×#4111yescharacteristic
462C2×C3⋊D3—22no—
463C2×C3⋊D3—22no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3#11714yes—
477C2×C3×D3C4×D414yes—
478C2×C3×D3C4×D414yes—
479C2×C3×D3#12114yes—
480C2×C3×D3#12314yes—
481C2×C3×D3#12414yes—
482C2×C3×D3#12614yes—
483D32—416no—
484C32×C4—22no—
485C32×C4—22no—
486C32×C4—41no—
487C3⋊Dic3—22no—
488C3⋊Dic3—22no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C25—91no—
497C23×C4—31no—
498C23×C4—31no—
499C23×C4—31no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4—91no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—91no—
507C2×C4⋊C4—184no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—98no—
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—184no—
522C2×C22⋊C4—184no—
523C2×C42—31no—
524C2×C42—91no—
525C2×C42—91no—
526C2×C42—91no—
527C2×C42—184no—
528#95—31no—
529#95—31no—
530#95—31no—
531#95—31no—
532#95—91no—
533#95—91no—
534#95—91no—
535#95D3211yescharacteristic, complemented
536C23×C3—21no—
537C23×C3—32no—
538C23×C3—32no—
539C23×C3—32no—
540C23×C3—32no—
541C23×C3—32no—
542C23×C3—32no—
543C23×C3—32no—
544C23×C3—32no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3C23×D311yescharacteristic
552C23×C3C23×D311yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—32no—
560C22×D3—32no—
561C22×D3—62no—
562C22×D3—68no—
563C22×D3—68no—
564C22×D3—68no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—68no—
578C22×D3—68no—
579C22×D3—68no—
580C22×D3—121no—
581C22×D3—121no—
582C22×D3—121no—
583C22×D3—121no—
584C22×D3—121no—
585C22×D3—121no—
586C22×D3—124no—
587C22×D3—124no—
588C22×D3—124no—
589C22×D3—124no—
590C22×D3—124no—
591C22×D3—124no—
592C22×D3—124no—
593C22×D3—124no—
594C22×D3C2×C4×D312yes—
595C22×D3C2×C4×D312yes—
596C22×D3C2×D1212yes—
597C22×D3#23512yes—
598C22×D3D3×D412yes—
599C22×D3#23712yes—
600C22×D3#23712yes—
601C22×D3#23912yes—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—68no—
630C2×C3×C4—68no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—124no—
646C2×C3×C4C2×C4×D312yes—
647C2×C3×C4C2×C4×D312yes—
648C2×C3×C4C2×D1212yes—
649C2×C3×C4D3×D412yes—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—68no—
671C2×Dic3—68no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—121no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×Dic3—121no—
691C2×Dic3—121no—
692C2×Dic3—121no—
693C2×Dic3—124no—
694C2×Dic3C2×C4×D312yes—
695C2×Dic3C2×C4×D312yes—
696C2×Dic3C2×D1212yes—
697C2×Dic3D3×D412yes—
698C4×D3—28no—
699C4×D3—28no—
700C4×D3—44no—
701C4×D3—68no—
702C4×D3—68no—
703C4×D3—124no—
704C2×C32C2×#11711yescharacteristic
705C2×C32C2×C4×D411yescharacteristic
706C2×C32C2×C4×D411yescharacteristic
707C2×C32C2×#12111yescharacteristic
708C2×C32C2×#12311yescharacteristic
709C2×C32C2×#12411yescharacteristic
710C2×C32C2×#12611yescharacteristic
711C3⋊D3—42no—
712C3×D3—42no—
713C3×D3#38818yescomplemented
714C24—31no—
715C24—31no—
716C24—94no—
717C24—91no—
718C24—182no—
719C24—182no—
720C24—182no—
721C24—182no—
722C24—182no—
723C24—182no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—34no—
729C22×C4—34no—
730C22×C4—31no—
731C22×C4—31no—
732C22×C4—62no—
733C22×C4—62no—
734C22×C4—62no—
735C22×C4—62no—
736C22×C4—62no—
737C22×C4—62no—
738C22×C4—62no—
739C22×C4—94no—
740C22×C4—94no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—91no—
744C22×C4—182no—
745C22×C4—182no—
746C22×C4—182no—
747C22×C4—182no—
748C22×C4—182no—
749C22×C4—182no—
750C22×C4—182no—
751C22×C4C2×D3211yescharacteristic
752C22×C4C2×D3211yescharacteristic
753C22×C4C2×D3211yescharacteristic
754C4⋊C4—62no—
755C4⋊C4—182no—
756C4⋊C4—182no—
757C4⋊C4—182no—
758C22⋊C4—34no—
759C22⋊C4—62no—
760C22⋊C4—62no—
761C22⋊C4—94no—
762C22⋊C4—94no—
763C22⋊C4—94no—
764C22⋊C4—182no—
765C22⋊C4—182no—
766C22⋊C4—182no—
767C22⋊C4—182no—
768C22⋊C4—182no—
769C22⋊C4—182no—
770C42—62no—
771C42—182no—
772C42—182no—
773C42—182no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—34no—
782C22×C3—34no—
783C22×C3—34no—
784C22×C3—34no—
785C22×C3—34no—
786C22×C3—34no—
787C22×C3—34no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3C22×C4×D311yescharacteristic
796C22×C3C22×C4×D311yescharacteristic
797C22×C3C22×D1211yescharacteristic
798C22×C3C2×#23511yescharacteristic
799C22×C3C2×D3×D411yescharacteristic
800C22×C3C2×D3×D411yescharacteristic
801C22×C3C2×D3×D411yescharacteristic
802C22×C3C2×#23711yescharacteristic
803C22×C3C2×#23711yescharacteristic
804C22×C3C2×#23911yescharacteristic
805C22×C3D3×#4111yescharacteristic
806C22×C3D3×#4111yescharacteristic
807C22×C3D3×#4111yescharacteristic
808C22×C3D3×#4111yescharacteristic
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—62no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—122no—
823C2×D3—122no—
824C2×D3—122no—
825C2×D3—1216no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—121no—
834C2×D3—1216no—
835C2×D3—241no—
836C2×D3—241no—
837C2×D3—241no—
838C2×D3—241no—
839C2×D3C4×D1214yes—
840C2×D3#67⋊C414yes—
841C2×D3#88514yes—
842C2×D3#88614yes—
843C2×D3#89214yes—
844C2×D3#89514yes—
845C2×D3#89814yes—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—42no—
851C3×C4—42no—
852C3×C4—41no—
853C3×C4—41no—
854C3×C4—62no—
855C3×C4—62no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—81no—
859C3×C4—121no—
860C3×C4—121no—
861Dic3—22no—
862Dic3—22no—
863Dic3—22no—
864Dic3—22no—
865Dic3—41no—
866Dic3—41no—
867Dic3—62no—
868Dic3—62no—
869Dic3—62no—
870Dic3—62no—
871Dic3—122no—
872Dic3—122no—
873Dic3—121no—
874Dic3—121no—
875Dic3—241no—
876C32C2×#38811yescharacteristic, complemented, Sylow
877C23—32no—
878C23—32no—
879C23—32no—
880C23—32no—
881C23—32no—
882C23—32no—
883C23—32no—
884C23—32no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—92no—
892C23—188no—
893C23—188no—
894C23—188no—
895C23—181no—
896C23—181no—
897C23—181no—
898C23—181no—
899C23—181no—
900C23—181no—
901C23—364no—
902C23—364no—
903C23—364no—
904C23—364no—
905C23C22×D3211yescharacteristic
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—68no—
918C2×C4—68no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—92no—
934C2×C4—92no—
935C2×C4—124no—
936C2×C4—188no—
937C2×C4—188no—
938C2×C4—181no—
939C2×C4—181no—
940C2×C4—181no—
941C2×C4—181no—
942C2×C4—181no—
943C2×C4—181no—
944C2×C4—181no—
945C2×C4—364no—
946C2×C4C4×D3212yes—
947C2×C4D3×D1212yes—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—38no—
956C2×C3—122no—
957C2×C3C2×C4×D1211yescharacteristic
958C2×C3C2×#67⋊C411yescharacteristic
959C2×C3C2×#88511yescharacteristic
960C2×C3C2×#88611yescharacteristic
961C2×C3C2×#89211yescharacteristic
962C2×C3C2×#89511yescharacteristic
963C2×C3C2×#89811yescharacteristic
964C2×C3D3×#11711yescharacteristic
965C2×C3C4×D3×D411yescharacteristic
966C2×C3C4×D3×D411yescharacteristic
967C2×C3D3×#12111yescharacteristic
968C2×C3D3×#12311yescharacteristic
969C2×C3D3×#12411yescharacteristic
970C2×C3D3×#12611yescharacteristic
971D3—42no—
972D3—122no—
973D3—122no—
974D3—242no—
975D3#467018yesdirect product factor
976C22—34no—
977C22—34no—
978C22—34no—
979C22—34no—
980C22—34no—
981C22—34no—
982C22—34no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—182no—
991C22—182no—
992C22—182no—
993C22—3616no—
994C22—361no—
995C22—361no—
996C22—361no—
997C22—361no—
998C22C2×C4×D3211yescharacteristic
999C22C2×D3×D1211yescharacteristic
1000C22D3×#23511yescharacteristic
1001C22D32×D411yescharacteristic
1002C22D3×#23711yescharacteristic
1003C22D3×#23711yescharacteristic
1004C22D3×#23911yescharacteristic
1005C4—22no—
1006C4—22no—
1007C4—41no—
1008C4—62no—
1009C4—62no—
1010C4—62no—
1011C4—62no—
1012C4—121no—
1013C4—121no—
1014C4—182no—
1015C4—182no—
1016C4—361no—
1017C3—21no—
1018C3C2×#467011yescharacteristic, complemented
1019C3D3×#38811yescharacteristic, complemented
1020C2—38no—
1021C2—122no—
1022C2—362no—
1023C2C4×D3×D1211yescharacteristic
1024C2D3×#67⋊C411yescharacteristic
1025C2D3×#88511yescharacteristic
1026C2D3×#88611yescharacteristic
1027C2D3×#89211yescharacteristic
1028C2D3×#89511yescharacteristic
1029C2D3×#89811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenter#95D32
hypocenterC32C2×#388
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×D3×C4⋊Dic3C2semidirect
5. C2×C4×D3×Dic3C2semidirect
6. #10592369C2semidirect
7. C3×#4670C2semidirect
8. C3×D3×#95C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591316C2semidirect
11. #10591287C2semidirect
12. #10591284C2semidirect
13. #10591266C2semidirect
14. #10591259C2semidirect
15. #10591194C2semidirect
28. C2×C4⋊(C3⋊Dic3)C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C2×Dic3⋊Dic3C22semidirect
36. C2×Dic3⋊Dic3C22semidirect
43. C2×Dic32C22semidirect
44. C2×Dic32C22semidirect
47. D3×(C2×D3)⋊C4C4semidirect
50. C32×#95C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. #63579C22semidirect
57. #63579C22semidirect
85. #4670D3direct (N × H)
88. D3×#95D3semidirect
131. #3752C2×C4semidirect
136. C3×(C2×D3)⋊C4C2×C4semidirect
143. #3722C2×C4semidirect
146. (C2×D3)⋊Dic3C2×C4semidirect
202. C2×C4⋊Dic3C2×D3semidirect
213. C2×C4×Dic3C2×D3semidirect
224. C3×#95C2×D3semidirect
225. C3×#95C2×D3semidirect
233. C3⋊#95C2×D3semidirect
234. C3⋊#95C2×D3semidirect
235. C3⋊#95C2×D3semidirect
236. C3⋊#95C2×D3semidirect
438. (C2×D3)⋊C4C4×D3semidirect
535. #95D32semidirect
713. C3×D3#388semidirect
876. C32C2×#388semidirect
975. D3#4670direct (N × H)
1018. C3C2×#4670semidirect
1019. C3D3×#388semidirect

Maximal subgroups

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

subgroupindex
C2×D3×(C2×D3)⋊C42
C2×D3×C4⋊Dic32
C2×C4×D3×Dic32
#105923692
C3×#46702
C3×D3×#952
D3×C3⋊#952
#105913162
#105912872
#105912842
#105912662
#105912592
#105911942
D3×#3883
C2×#46703