Finite Group Databasebeta

← D3×#63846 #13167883

Subgroups — D3×#63846 #13167883

Order 1728.

1134 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2D3×#3750C211yesmaximal, characteristic
3#11723412C211yesmaximal, characteristic, complemented
4#11723401C211yesmaximal, characteristic, complemented
5C3×D3×C4⋊Dic3C211yesmaximal, characteristic
6C3×D3×Dic3⋊C4C211yesmaximal, characteristic
7C3×#63846C211yesmaximal, characteristic, complemented
8#11723017C211yesmaximal, characteristic, complemented
9#11723015C211yesmaximal, characteristic, complemented
10#11723013C211yesmaximal, characteristic, complemented
11#11723012C211yesmaximal, characteristic, complemented
12D3×Dic3⋊Dic3C211yesmaximal, characteristic
13D3×Dic3⋊Dic3C211yesmaximal, characteristic
14D3×Dic3⋊Dic3C211yesmaximal, characteristic
15D3×Dic32C211yesmaximal, characteristic
16C2×#63846—31nomaximal
17D3×#890—31nomaximal
18D3×#889—31nomaximal
19C2×C32×C4×D3C2211yescharacteristic
20C2×D3×C3⋊Dic3C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×C3×D3×Dic3C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26#88857C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88813C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39#88807C2211yescharacteristic
40#88806C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×Dic3⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C2×#3750—31no—
55#64099—31no—
56#64098—31no—
57C2×C3×C4⋊Dic3—31no—
58C2×C3×Dic3⋊C4—31no—
59C3×D3×C4⋊C4—31no—
60C3×D3×C4⋊C4—31no—
61C3×#890—31no—
62C3×#889—31no—
63C2×Dic3⋊Dic3—31no—
64C2×Dic3⋊Dic3—31no—
65C2×Dic3⋊Dic3—31no—
66C2×Dic32—31no—
67D3×C4⋊Dic3—31no—
68D3×C4⋊Dic3—31no—
69D3×C4⋊Dic3—31no—
70D3×C4⋊Dic3D311yescharacteristic
71D3×Dic3⋊C4—31no—
72D3×Dic3⋊C4—31no—
73D3×Dic3⋊C4—31no—
74D3×Dic3⋊C4—31no—
75D3×Dic3⋊C4—31no—
76D3×Dic3⋊C4—61no—
77D3×Dic3⋊C4D311yescharacteristic
78C4×D3×Dic3—31no—
79C4×D3×Dic3—31no—
80#63872—31no—
81#63870—31no—
82#63869—31no—
83#63867—31no—
84#63847—31no—
85#63847—31no—
86#63846—31no—
87#63846—31no—
88#63846—31no—
89#63846—31no—
90#63846—31no—
91#63846—31no—
92#63846—31no—
93#63846—31no—
94#63846—31no—
95#63846—31no—
96#63846—61no—
97#63846—61no—
98#63846D311yescharacteristic, direct product factor
99#63845—31no—
100#63845—31no—
101#63845—31no—
102C22×C32×D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×C4×D3—22no—
118D3×C3⋊Dic3—22no—
119D3×C3⋊Dic3—22no—
120C3×D3×Dic3—22no—
121C3×D3×Dic3—22no—
122C3×D3×Dic3—22no—
123C3×D3×Dic3Q814yes—
124D3×#125—91no—
125C2×#890—91no—
126C2×#889—91no—
127C22×C32×C4—31no—
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—31no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3—31no—
132C22×C3×Dic3—31no—
133C22×C3×Dic3—31no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3C2×D311yescharacteristic
140C2×C3×C4×D3C2×D311yescharacteristic
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—61no—
146C2×D3×Dic3—61no—
147C2×D3×Dic3C2×D311yescharacteristic
148C2×D3×Dic3C2×D311yescharacteristic
149C2×D3×Dic3C2×D311yescharacteristic
150C2×D3×Dic3C2×D311yescharacteristic
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—31no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)C2×D311yescharacteristic
157#3750—31no—
158#3750—31no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—61no—
166#3750—61no—
167#3750—61no—
168#3750—121no—
169#3750C2×D311yescharacteristic
170#3750C2×D311yescharacteristic
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3—31no—
173C3×C4⋊Dic3—21no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—61no—
183C3×C4⋊Dic3C2×D311yescharacteristic
184C3×C4⋊Dic3C2×D311yescharacteristic
185C3×Dic3⋊C4—21no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—61no—
199C3×Dic3⋊C4—61no—
200C3×Dic3⋊C4C2×D311yescharacteristic
201C3×Dic3⋊C4C2×D311yescharacteristic
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—61no—
210#3724C2×D311yescharacteristic
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3C2×D311yescharacteristic
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241Dic3⋊Dic3C2×D311yescharacteristic
242Dic3⋊Dic3C2×D311yescharacteristic
243Dic3⋊Dic3C2×D311yescharacteristic
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—61no—
252Dic32—61no—
253Dic32C2×D311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C32×D3C2×Q812yes—
256C2×C32×D3#4112yes—
257C2×C32×D3#4112yes—
258C33×C4—21no—
259C3⋊(C3⋊Dic3)—21no—
260C3⋊(C3⋊Dic3)—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3C2×Q812yes—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3C2×Q812yes—
272C3×#125—91no—
273C2×C3×C4⋊C4—91no—
274C2×C3×C4⋊C4—91no—
275C2×C4⋊Dic3—31no—
276C2×C4⋊Dic3—91no—
277C2×C4⋊Dic3—91no—
278C2×C4⋊Dic3—91no—
279C2×Dic3⋊C4—31no—
280C2×Dic3⋊C4—91no—
281C2×Dic3⋊C4—91no—
282C2×Dic3⋊C4—91no—
283C2×Dic3⋊C4—91no—
284C2×Dic3⋊C4—91no—
285C2×Dic3⋊C4—181no—
286C2×C4×Dic3—91no—
287C2×C4×Dic3—91no—
288D3×C4⋊C4—31no—
289D3×C4⋊C4—31no—
290D3×C4⋊C4—91no—
291D3×C4⋊C4—91no—
292D3×C4⋊C4—91no—
293D3×C4⋊C4—91no—
294#890—31no—
295#890—91no—
296#890—91no—
297#890—91no—
298#890—91no—
299#890—91no—
300#890—91no—
301#890—91no—
302#890—91no—
303#890—91no—
304#890—181no—
305#889—31no—
306#889—91no—
307#889—91no—
308#889—91no—
309#889—91no—
310#889—91no—
311#889—91no—
312#889—91no—
313#889—91no—
314#889—91no—
315#889—91no—
316#889—91no—
317#889—181no—
318C42×D3—91no—
319#870—91no—
320C23×C32—31no—
321C22×C3×D3—21no—
322C22×C3×D3C22×D311yescharacteristic
323C22×C3×D3C22×D311yescharacteristic
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—31no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—31no—
331C2×C32×C4—31no—
332C2×C32×C4—41no—
333C2×C32×C4—62no—
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C32×C4C22×D311yescharacteristic
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—31no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—62no—
350C2×C3⋊Dic3—62no—
351C2×C3⋊Dic3—121no—
352C2×C3⋊Dic3—121no—
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—34no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—62no—
384C2×C3×Dic3—62no—
385C2×C3×Dic3—62no—
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C3×C4×D3—22no—
397C3×C4×D3—22no—
398C3×C4×D3—34no—
399C3×C4×D3—42no—
400C3×C4×D3—62no—
401C3×C4×D3—62no—
402C3×C4×D3—62no—
403D3×Dic3—22no—
404D3×Dic3—22no—
405D3×Dic3—22no—
406D3×Dic3—64no—
407D3×Dic3—62no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411D3×Dic3—122no—
412D3×Dic3Dic614yes—
413C2×#125—271noSylow
414C2×C33C22×Q811yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C32×D3#12514yescomplemented
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—61no—
421C22×C3×C4—91no—
422C22×C3×C4—91no—
423C22×C3×C4—91no—
424C22×C3×C4—91no—
425C22×Dic3—31no—
426C22×Dic3—31no—
427C22×Dic3—31no—
428C22×Dic3—31no—
429C22×Dic3—91no—
430C22×Dic3—91no—
431C22×Dic3—91no—
432C22×Dic3—91no—
433C22×Dic3—181no—
434C22×Dic3—181no—
435C2×C4×D3—31no—
436C2×C4×D3—31no—
437C2×C4×D3—31no—
438C2×C4×D3—31no—
439C2×C4×D3—91no—
440C2×C4×D3—91no—
441C2×C4×D3D3211yescharacteristic
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—61no—
447C3×C4⋊C4—61no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C4⋊C4—91no—
458C3×C42—91no—
459C4⋊Dic3—31no—
460C4⋊Dic3—31no—
461C4⋊Dic3—31no—
462C4⋊Dic3—31no—
463C4⋊Dic3—31no—
464C4⋊Dic3—31no—
465C4⋊Dic3—31no—
466C4⋊Dic3—31no—
467C4⋊Dic3—61no—
468C4⋊Dic3—91no—
469C4⋊Dic3—91no—
470C4⋊Dic3—91no—
471C4⋊Dic3—91no—
472C4⋊Dic3—91no—
473C4⋊Dic3—91no—
474C4⋊Dic3—91no—
475C4⋊Dic3—91no—
476C4⋊Dic3—91no—
477C4⋊Dic3—91no—
478C4⋊Dic3—91no—
479C4⋊Dic3—91no—
480C4⋊Dic3—91no—
481C4⋊Dic3—181no—
482C4⋊Dic3—181no—
483C4⋊Dic3—181no—
484C4⋊Dic3D3211yescharacteristic
485Dic3⋊C4—31no—
486Dic3⋊C4—31no—
487Dic3⋊C4—31no—
488Dic3⋊C4—31no—
489Dic3⋊C4—31no—
490Dic3⋊C4—31no—
491Dic3⋊C4—31no—
492Dic3⋊C4—31no—
493Dic3⋊C4—31no—
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—31no—
497Dic3⋊C4—61no—
498Dic3⋊C4—61no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—91no—
503Dic3⋊C4—91no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—181no—
523Dic3⋊C4—181no—
524Dic3⋊C4—181no—
525Dic3⋊C4—181no—
526Dic3⋊C4—181no—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4—181no—
530Dic3⋊C4—361no—
531Dic3⋊C4D3211yescharacteristic
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—181no—
544C4×Dic3—181no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—32no—
549C22×C32—32no—
550C22×C32—32no—
551C22×C32—41no—
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3C2×Dic612yes—
559C2×C3×D3#23512yes—
560C2×C3×D3#23712yes—
561C2×C3×D3#23712yes—
562C2×C3×D3D3×Q812yes—
563C2×C3×D3#23912yes—
564C32×C4—21no—
565C32×C4—21no—
566C32×C4—21no—
567C32×C4—32no—
568C32×C4—41no—
569C32×C4—41no—
570C32×C4—41no—
571C32×C4—61no—
572C32×C4—61no—
573C32×C4—61no—
574C32×C4—61no—
575C32×C4—81no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—21no—
581C3⋊Dic3—61no—
582C3⋊Dic3—62no—
583C3⋊Dic3—61no—
584C3⋊Dic3—61no—
585C3⋊Dic3—61no—
586C3⋊Dic3—61no—
587C3⋊Dic3—61no—
588C3⋊Dic3—121no—
589C3⋊Dic3—121no—
590C3⋊Dic3—122no—
591C3⋊Dic3—121no—
592C3⋊Dic3—121no—
593C3⋊Dic3—121no—
594C3⋊Dic3—241no—
595C3⋊Dic3C2×Dic612yes—
596C3×Dic3—21no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—22no—
605C3×Dic3—32no—
606C3×Dic3—32no—
607C3×Dic3—41no—
608C3×Dic3—41no—
609C3×Dic3—41no—
610C3×Dic3—41no—
611C3×Dic3—62no—
612C3×Dic3—62no—
613C3×Dic3—61no—
614C3×Dic3—61no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—121no—
624C3×Dic3—121no—
625C3×Dic3—121no—
626C3×Dic3—121no—
627C3×Dic3C2×Dic612yes—
628C3×Dic3D3×Q812yes—
629#125—91no—
630#125—271no—
631#125—271no—
632#125—271no—
633#125—271no—
634#125—271no—
635#125—271no—
636#125—271no—
637C2×C4⋊C4—91no—
638C2×C4⋊C4—91no—
639C2×C4⋊C4—271no—
640C2×C4⋊C4—271no—
641C2×C4⋊C4—271no—
642C2×C4⋊C4—271no—
643C2×C42—271no—
644C33C2×#12511yescharacteristic, complemented, Sylow
645C23×C3—31no—
646C23×C3—31no—
647C23×C3—61no—
648C22×D3C2×D3211yescharacteristic
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—31no—
653C2×C3×C4—31no—
654C2×C3×C4—31no—
655C2×C3×C4—31no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—41no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—94no—
671C2×C3×C4—91no—
672C2×C3×C4—91no—
673C2×C3×C4—91no—
674C2×C3×C4—91no—
675C2×C3×C4—91no—
676C2×C3×C4—91no—
677C2×C3×C4—122no—
678C2×C3×C4—182no—
679C2×C3×C4—182no—
680C2×C3×C4—182no—
681C2×C3×C4C2×D3211yescharacteristic
682C2×C3×C4C2×D3211yescharacteristic
683C2×C3×C4C2×D3211yescharacteristic
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—34no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—31no—
696C2×Dic3—31no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—62no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—91no—
707C2×Dic3—91no—
708C2×Dic3—91no—
709C2×Dic3—91no—
710C2×Dic3—91no—
711C2×Dic3—91no—
712C2×Dic3—181no—
713C2×Dic3—181no—
714C2×Dic3—181no—
715C2×Dic3—181no—
716C2×Dic3—181no—
717C2×Dic3—181no—
718C2×Dic3—182no—
719C2×Dic3—182no—
720C2×Dic3—182no—
721C2×Dic3—182no—
722C2×Dic3—184no—
723C2×Dic3—361no—
724C2×Dic3—361no—
725C2×Dic3—362no—
726C2×Dic3C2×D3211yescharacteristic
727C2×Dic3C2×D3211yescharacteristic
728C2×Dic3C2×D3211yescharacteristic
729C2×Dic3C2×D3211yescharacteristic
730C2×Dic3C2×D3211yescharacteristic
731C4×D3—22no—
732C4×D3—34no—
733C4×D3—62no—
734C4×D3—62no—
735C4×D3—62no—
736C4×D3—182no—
737C4×D3—182no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—34no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—41no—
751C2×C32C22×Dic611yescharacteristic
752C2×C32C2×#23511yescharacteristic
753C2×C32C2×#23711yescharacteristic
754C2×C32C2×#23711yescharacteristic
755C2×C32C2×D3×Q811yescharacteristic
756C2×C32C2×D3×Q811yescharacteristic
757C2×C32C2×#23911yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C2×C32D3×#4111yescharacteristic
760C3×D3—24no—
761C3×D3#88914yescomplemented
762C3×D3#89014yescomplemented
763C22×C4—31no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—91no—
768C22×C4—271no—
769C22×C4—271no—
770C4⋊C4—31no—
771C4⋊C4—31no—
772C4⋊C4—91no—
773C4⋊C4—91no—
774C4⋊C4—91no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—271no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C4⋊C4—271no—
789C4⋊C4—271no—
790C4⋊C4—271no—
791C4⋊C4—271no—
792C4⋊C4—271no—
793C4⋊C4—271no—
794C42—91no—
795C42—271no—
796C42—271no—
797C42—271no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—32no—
802C22×C3—32no—
803C22×C3—32no—
804C22×C3—32no—
805C22×C3—32no—
806C22×C3—32no—
807C22×C3—41no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3C22×D3211yescharacteristic
812C22×C3C22×D3211yescharacteristic
813C22×C3C22×D3211yescharacteristic
814C2×D3D3×Dic612yes—
815C2×D3#379612yes—
816C2×D3#380412yes—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—32no—
821C3×C4—32no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—62no—
826C3×C4—61no—
827C3×C4—61no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—81no—
835C3×C4—92no—
836C3×C4—121no—
837C3×C4—121no—
838C3×C4—121no—
839C3×C4—121no—
840C3×C4—181no—
841C3×C4—181no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4—181no—
845Dic3—21no—
846Dic3—21no—
847Dic3—21no—
848Dic3—21no—
849Dic3—32no—
850Dic3—32no—
851Dic3—62no—
852Dic3—62no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—61no—
859Dic3—61no—
860Dic3—61no—
861Dic3—61no—
862Dic3—61no—
863Dic3—121no—
864Dic3—121no—
865Dic3—121no—
866Dic3—121no—
867Dic3—182no—
868Dic3—181no—
869Dic3—181no—
870Dic3—181no—
871Dic3—181no—
872Dic3—181no—
873Dic3—181no—
874Dic3—361no—
875Dic3—361no—
876Dic3—361no—
877Dic3—361no—
878Dic3—361no—
879Dic3—362no—
880Dic3—721no—
881Dic3D3×Dic612yes—
882C32—21no—
883C32—21no—
884C32—21no—
885C32—41no—
886C32C2×#88911yescharacteristic, complemented
887C32C2×#89011yescharacteristic, complemented
888C32D3×#12511yescharacteristic, complemented
889C23—31no—
890C2×C4—31no—
891C2×C4—31no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—62no—
896C2×C4—94no—
897C2×C4—91no—
898C2×C4—91no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—182no—
904C2×C4—182no—
905C2×C4—182no—
906C2×C4—271no—
907C2×C4—271no—
908C2×C4—542no—
909C2×C4—542no—
910C2×C4D3311yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—34no—
921C2×C3—34no—
922C2×C3—41no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—64no—
926C2×C3C2×D3×Dic611yescharacteristic
927C2×C3C2×D3×Dic611yescharacteristic
928C2×C3C2×#379611yescharacteristic
929C2×C3D3×#23511yescharacteristic
930C2×C3D3×#23711yescharacteristic
931C2×C3D3×#23711yescharacteristic
932C2×C3D32×Q811yescharacteristic
933C2×C3D3×#23911yescharacteristic
934C2×C3C2×#380411yescharacteristic
935D3#6384614yesdirect product factor
936C22—32no—
937C22—32no—
938C22—32no—
939C22C2×D3311yescharacteristic
940C4—21no—
941C4—32no—
942C4—61no—
943C4—61no—
944C4—61no—
945C4—61no—
946C4—92no—
947C4—181no—
948C4—181no—
949C4—181no—
950C4—181no—
951C4—181no—
952C4—541no—
953C4—541no—
954C3—21no—
955C3—21no—
956C3—21no—
957C3—41no—
958C3D3×#88911yescharacteristic, complemented
959C3D3×#89011yescharacteristic, complemented
960C3C2×#6384611yescharacteristic, complemented
961C2—34no—
962C2D32×Dic611yescharacteristic
963C2D3×#379611yescharacteristic
964C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33C2×#125
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723669C2semidirect
3. #11723412C2semidirect
4. #11723401C2semidirect
7. C3×#63846C2semidirect
8. #11723017C2semidirect
9. #11723015C2semidirect
10. #11723013C2semidirect
11. #11723012C2semidirect
98. #63846D3direct (N × H)
417. C32×D3#125semidirect
644. C33C2×#125semidirect
761. C3×D3#889semidirect
762. C3×D3#890semidirect
886. C32C2×#889semidirect
887. C32C2×#890semidirect
888. C32D3×#125semidirect
935. D3#63846direct (N × H)
958. C3D3×#889semidirect
959. C3D3×#890semidirect
960. C3C2×#63846semidirect

Maximal subgroups

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

subgroupindex
#117236692
D3×#37502
#117234122
#117234012
C3×D3×C4⋊Dic32
C3×D3×Dic3⋊C42
C3×#638462
#117230172
#117230152
#117230132
#117230122
D3×Dic3⋊Dic32
D3×Dic322
C2×#638463
D3×#8903
D3×#8893