Finite Group Databasebeta

← D3×C3⋊D3×#106 #72244812

Subgroups — D3×C3⋊D3×#106 #72244812

Order 3456.

4120 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C8×C3⋊D3C211yesmaximal, characteristic
2D3×C4⋊C4×C3⋊D3C212yesmaximal
3#106×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×C3⋊D3×#106C211yesmaximal, characteristic, complemented
5C32×D3×#106C211yesmaximal, characteristic, complemented
6#13159550C211yesmaximal, characteristic, complemented
7D3×#63644C211yesmaximal, characteristic, complemented
8C3⋊D3×#817C211yesmaximal, characteristic, complemented
9#13159326C212yesmaximal, complemented
10D3×#63635C212yesmaximal, complemented
11C3⋊D3×#808C212yesmaximal, complemented
12D32×#106—34nomaximal
13C2×C3⋊D3×#106—31nomaximal
14C2×C4×D3×C3⋊D3—22no—
15C2×C4×D3×C3⋊D3C2211yescharacteristic
16C2×C8×C3⋊(C3⋊D3)C2211yescharacteristic
17C4⋊C4×C3⋊(C3⋊D3)C2212yes—
18C2×C3×C8×C3⋊D3C2211yescharacteristic
19C3×C4⋊C4×C3⋊D3C2212yes—
20C2×C32×D3×C8C2211yescharacteristic
21C32×D3×C4⋊C4C2212yes—
22#11723503C2212yes—
23C3⋊D3×C4⋊Dic3C2212yes—
24D3×C4⋊(C3⋊Dic3)C2212yes—
25#11723470—22no—
26C3⋊D3×Dic3⋊C4—22no—
27D3×#3750—22no—
28C2×#88785C2211yescharacteristic
29C2×C3⋊D3×C3⋊C8C2211yescharacteristic
30C2×D3×C3⋊(C3⋊C8)C2211yescharacteristic
31D3×C8×C3⋊D3C418yescomplemented
32C33×#106C2211yescharacteristic, complemented
33#11722187C2211yescharacteristic, complemented
34#11722178C2212yescomplemented
35C3×#63644C2211yescharacteristic, complemented
36C3×#63635C2212yescomplemented
37C32×#817C2211yescharacteristic, complemented
38C32×#808C2212yescomplemented
39#11722054C2212yescomplemented
40#11722053C2212yescomplemented
41#11722052C2212yescomplemented
42C22×C8×C3⋊D3—31no—
43C2×C4⋊C4×C3⋊D3—32no—
44C2×D32×C8—34no—
45D32×C4⋊C4—38no—
46C2×C32×#106—31no—
47C2×#63644—31no—
48C2×#63635—32no—
49C3⋊D3×#106—31no—
50C3⋊D3×#106—34no—
51C3⋊D3×#106—31no—
52C3⋊D3×#106—32no—
53C3⋊D3×#106—31no—
54C3⋊D3×#106—32no—
55C3⋊D3×#106—64no—
56C3⋊D3×#106D311yescharacteristic, direct product factor
57C3×D3×#106—34no—
58C3×D3×#106D314yescomplemented
59#10590685—34no—
60D3×#817—34no—
61D3×#817—34no—
62#10590575—38no—
63D3×#808—38no—
64D3×#808—38no—
65C22×D3×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊(C3⋊D3)—22no—
67C2×C4×C3⋊(C3⋊D3)C2311yescharacteristic
68C2×C3×C4×C3⋊D3—22no—
69C2×C3×C4×C3⋊D3C2311yescharacteristic
70C2×C32×C4×D3—22no—
71C2×C32×C4×D3C2311yescharacteristic
72C2×#6289—22no—
73C2×#6289D411yescharacteristic
74C2×Dic3×C3⋊D3—22no—
75C2×Dic3×C3⋊D3D411yescharacteristic
76C2×D3×C3⋊Dic3—22no—
77C2×D3×C3⋊Dic3D411yescharacteristic
78C4×D3×C3⋊D3—48no—
79C4×D3×C3⋊D3C2×C414yes—
80C4×D3×C3⋊D3Q814yes—
81C2×C33×C8C2311yescharacteristic
82C33×C4⋊C4C2312yes—
83C4⋊(C3⋊(C3⋊Dic3))C2312yes—
84#88857—22no—
85C2×C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
86C8×C3⋊(C3⋊D3)C2×C414yescomplemented
87C3×C4⋊(C3⋊Dic3)C2312yes—
88C3×#3750—22no—
89C2×C3×C3⋊(C3⋊C8)C2311yescharacteristic
90C3×C8×C3⋊D3C2×C414yescomplemented
91C32×C4⋊Dic3C2312yes—
92C32×Dic3⋊C4—22no—
93C2×C32×C3⋊C8C2311yescharacteristic
94C32×D3×C8C2×C414yescomplemented
95#88807—22no—
96#88806—22no—
97Dic3⋊(C3⋊Dic3)—22no—
98#88785C2×C414yescomplemented
99C3⋊D3×C3⋊C8C2×C414yescomplemented
100D3×C3⋊(C3⋊C8)C2×C414yescomplemented
101C2×D3×#106—94no—
102C2×D3×#106—91no—
103C22×C4×C3⋊D3—31no—
104C22×C4×C3⋊D3—62no—
105C2×C4×D32—34no—
106C2×C4×D32—68no—
107C22×C32×C8—31no—
108C2×C32×C4⋊C4—32no—
109C2×C4⋊(C3⋊Dic3)—32no—
110C2×#3750—62no—
111C22×C3⋊(C3⋊C8)—31no—
112C2×C8×C3⋊D3—31no—
113C2×C8×C3⋊D3—31no—
114C2×C8×C3⋊D3—31no—
115C2×C8×C3⋊D3—38no—
116C2×C8×C3⋊D3—34no—
117C2×C8×C3⋊D3—64no—
118C2×C8×C3⋊D3C2×D311yescharacteristic
119C4⋊C4×C3⋊D3—32no—
120C4⋊C4×C3⋊D3—32no—
121C4⋊C4×C3⋊D3—32no—
122C4⋊C4×C3⋊D3—38no—
123C4⋊C4×C3⋊D3—68no—
124C4⋊C4×C3⋊D3—62no—
125C4⋊C4×C3⋊D3—62no—
126C4⋊C4×C3⋊D3C2×D312yes—
127C2×C3×D3×C8—34no—
128C2×C3×D3×C8C2×D314yes—
129C3×D3×C4⋊C4—38no—
130C3×D3×C4⋊C4C2×D318yes—
131#63900—38no—
132D3×C4⋊Dic3—38no—
133D3×C4⋊Dic3—38no—
134#63883—68no—
135D3×Dic3⋊C4—68no—
136D3×Dic3⋊C4—68no—
137C2×#3710—34no—
138C2×D3×C3⋊C8—34no—
139C2×D3×C3⋊C8—34no—
140D32×C8—332no—
141C32×#106—24no—
142C32×#106—31no—
143C32×#106—32no—
144C32×#106C2×D314yescomplemented
145C32×#106C2×D311yescharacteristic, complemented
146#63644—31no—
147#63644—32no—
148#63644—34no—
149#63644—64no—
150#63644C2×D311yescharacteristic, complemented
151#63635—32no—
152#63635—32no—
153#63635—32no—
154#63635—38no—
155#63635—68no—
156#63635C2×D312yescomplemented
157C3×#817—34no—
158C3×#817C2×D314yescomplemented
159C3×#808—38no—
160C3×#808C2×D318yescomplemented
161#63574—38no—
162#63573—38no—
163#63573—38no—
164C22×C3⋊(C3⋊D3)C2×D411yescharacteristic
165C22×C3×C3⋊D3C2×D411yescharacteristic
166C22×C32×D3C2×D411yescharacteristic
167C2×D3×C3⋊D3C4⋊C414yes—
168C2×D3×C3⋊D3SD1618yes—
169C2×C33×C4—22no—
170C2×C33×C4C2411yescharacteristic
171C2×C3⋊(C3⋊Dic3)—22no—
172C2×C3⋊(C3⋊Dic3)C2×D411yescharacteristic
173C4×C3⋊(C3⋊D3)—44no—
174C4×C3⋊(C3⋊D3)C22×C412yes—
175C4×C3⋊(C3⋊D3)C2×Q812yes—
176C2×C3×C3⋊Dic3—22no—
177C2×C3×C3⋊Dic3C2×D411yescharacteristic
178C3×C4×C3⋊D3—44no—
179C3×C4×C3⋊D3C22×C412yes—
180C3×C4×C3⋊D3C2×Q812yes—
181C2×C32×Dic3—22no—
182C2×C32×Dic3C2×D411yescharacteristic
183C32×C4×D3—44no—
184C32×C4×D3C22×C412yes—
185C32×C4×D3C2×Q812yes—
186#6289—44no—
187#6289C4⋊C414yes—
188Dic3×C3⋊D3—44no—
189Dic3×C3⋊D3C4⋊C414yes—
190D3×C3⋊Dic3—44no—
191D3×C3⋊Dic3C4⋊C414yes—
192C33×C8C22×C412yescomplemented
193C3⋊(C3⋊(C3⋊C8))C22×C412yescomplemented
194C3×C3⋊(C3⋊C8)C22×C412yescomplemented
195C32×C3⋊C8C22×C412yescomplemented
196C22×D3×C8—94no—
197C22×D3×C8—91no—
198C2×D3×C4⋊C4—98no—
199C2×D3×C4⋊C4—92no—
200C2×C3×#106—34no—
201C2×C3×#106—91no—
202C2×#817—94no—
203C2×#817—91no—
204C2×#808—98no—
205C2×#808—92no—
206D3×#106—34no—
207D3×#106—98no—
208D3×#106—94no—
209D3×#106—98no—
210D3×#106—94no—
211D3×#106—91no—
212D3×#106—92no—
213D3×#106—94no—
214D3×#106—91no—
215D3×#106—91no—
216D3×#106—92no—
217D3×#106—184no—
218D3×#106C3⋊D311yescharacteristic, direct product factor
219C23×C3⋊D3—31no—
220C22×D32—34no—
221C22×C32×C4—31no—
222C22×C32×C4—62no—
223C22×C3⋊Dic3—31no—
224C22×C3⋊Dic3—62no—
225C2×C4×C3⋊D3—22no—
226C2×C4×C3⋊D3—31no—
227C2×C4×C3⋊D3—31no—
228C2×C4×C3⋊D3—34no—
229C2×C4×C3⋊D3—31no—
230C2×C4×C3⋊D3—34no—
231C2×C4×C3⋊D3—34no—
232C2×C4×C3⋊D3—64no—
233C2×C4×C3⋊D3—62no—
234C2×C4×C3⋊D3—62no—
235C2×C4×C3⋊D3—68no—
236C2×C4×C3⋊D3—62no—
237C2×C4×C3⋊D3—128no—
238C2×C4×C3⋊D3—128no—
239C2×C4×C3⋊D3C22×D311yescharacteristic
240C2×C3×C4×D3—28no—
241C2×C3×C4×D3—34no—
242C2×C3×C4×D3—68no—
243C2×C3×C4×D3C22×D314yes—
244C2×#624—34no—
245C2×#624—68no—
246C2×D3×Dic3—34no—
247C2×D3×Dic3—34no—
248C2×D3×Dic3—68no—
249C2×D3×Dic3—68no—
250C4×D32—316no—
251C4×D32—316no—
252C4×D32—1232no—
253C2×C32×C8—24no—
254C2×C32×C8—31no—
255C2×C32×C8—34no—
256C2×C32×C8C22×D314yes—
257C2×C32×C8C22×D311yescharacteristic
258C32×C4⋊C4—28no—
259C32×C4⋊C4—32no—
260C32×C4⋊C4—62no—
261C32×C4⋊C4C22×D318yes—
262C32×C4⋊C4C22×D312yes—
263C4⋊(C3⋊Dic3)—32no—
264C4⋊(C3⋊Dic3)—38no—
265C4⋊(C3⋊Dic3)—62no—
266C4⋊(C3⋊Dic3)—68no—
267C4⋊(C3⋊Dic3)C22×D312yes—
268#3750—22no—
269#3750—62no—
270#3750—62no—
271#3750—68no—
272#3750—62no—
273#3750—128no—
274C2×C3⋊(C3⋊C8)—31no—
275C2×C3⋊(C3⋊C8)—34no—
276C2×C3⋊(C3⋊C8)—34no—
277C2×C3⋊(C3⋊C8)—64no—
278C2×C3⋊(C3⋊C8)C22×D311yescharacteristic
279C8×C3⋊D3—34no—
280C8×C3⋊D3—34no—
281C8×C3⋊D3—316no—
282C8×C3⋊D3—34no—
283C8×C3⋊D3—616no—
284C8×C3⋊D3C4×D314yescomplemented
285C3×C4⋊Dic3—38no—
286C3×C4⋊Dic3C22×D318yes—
287C3×Dic3⋊C4—28no—
288C3×Dic3⋊C4—68no—
289C2×C3×C3⋊C8—34no—
290C2×C3×C3⋊C8C22×D314yes—
291C3×D3×C8—316no—
292C3×D3×C8C4×D3116yescomplemented
293#3724—68no—
294Dic3⋊Dic3—68no—
295Dic3⋊Dic3—68no—
296#3710—316no—
297D3×C3⋊C8—316no—
298D3×C3⋊C8—316no—
299C22×#106—271noSylow
300C22×C33C22×D411yescharacteristic
301C2×C3⋊(C3⋊D3)C2×C4⋊C412yes—
302C2×C3⋊(C3⋊D3)C2×SD1614yes—
303C2×C3×C3⋊D3C2×C4⋊C412yes—
304C2×C3×C3⋊D3C2×SD1614yes—
305C2×C32×D3C2×C4⋊C412yes—
306C2×C32×D3C2×SD1614yes—
307D3×C3⋊D3#106116yesdirect product factor
308C33×C4—42no—
309C33×C4C23×C411yescharacteristic
310C33×C4C22×Q811yescharacteristic
311C3⋊(C3⋊Dic3)—42no—
312C3⋊(C3⋊Dic3)C2×C4⋊C412yes—
313C3×C3⋊Dic3—42no—
314C3×C3⋊Dic3C2×C4⋊C412yes—
315C32×Dic3—42no—
316C32×Dic3C2×C4⋊C412yes—
317C22×C4×D3—94no—
318C22×C4×D3—91no—
319C22×C4×D3—182no—
320C22×C4×D3—188no—
321C22×C3×C8—34no—
322C22×C3×C8—91no—
323C2×C3×C4⋊C4—38no—
324C2×C3×C4⋊C4—92no—
325C2×C4⋊Dic3—98no—
326C2×C4⋊Dic3—92no—
327C2×Dic3⋊C4—182no—
328C2×Dic3⋊C4—188no—
329C22×C3⋊C8—94no—
330C22×C3⋊C8—91no—
331C2×D3×C8—34no—
332C2×D3×C8—932no—
333C2×D3×C8—94no—
334C2×D3×C8—94no—
335C2×D3×C8—91no—
336C2×D3×C8—94no—
337C2×D3×C8—91no—
338C2×D3×C8—91no—
339C2×D3×C8—98no—
340C2×D3×C8—184no—
341C2×D3×C8C2×C3⋊D311yescharacteristic
342D3×C4⋊C4—38no—
343D3×C4⋊C4—98no—
344D3×C4⋊C4—98no—
345D3×C4⋊C4—92no—
346D3×C4⋊C4—98no—
347D3×C4⋊C4—92no—
348D3×C4⋊C4—92no—
349D3×C4⋊C4—188no—
350D3×C4⋊C4—182no—
351D3×C4⋊C4—188no—
352D3×C4⋊C4—188no—
353D3×C4⋊C4—182no—
354D3×C4⋊C4C2×C3⋊D312yes—
355C3×#106—24no—
356C3×#106—34no—
357C3×#106—38no—
358C3×#106—91no—
359C3×#106—92no—
360C3×#106D3214yescomplemented
361C3×#106C2×C3⋊D311yescharacteristic, complemented
362#817—34no—
363#817—98no—
364#817—94no—
365#817—91no—
366#817—92no—
367#817—184no—
368#817C2×C3⋊D311yescharacteristic, complemented
369#808—38no—
370#808—98no—
371#808—98no—
372#808—98no—
373#808—92no—
374#808—92no—
375#808—92no—
376#808—188no—
377#808C2×C3⋊D312yescomplemented
378C23×C32—31no—
379C22×C3⋊D3—31no—
380C22×C3⋊D3—34no—
381C22×C3⋊D3—38no—
382C22×C3⋊D3—34no—
383C22×C3⋊D3—64no—
384C22×C3⋊D3D3×D411yescharacteristic
385C22×C3×D3—34no—
386C22×C3×D3D3×D414yes—
387C2×D32—316no—
388C2×D32—332no—
389C2×C32×C4—22no—
390C2×C32×C4—24no—
391C2×C32×C4—28no—
392C2×C32×C4—31no—
393C2×C32×C4—32no—
394C2×C32×C4—32no—
395C2×C32×C4—48no—
396C2×C32×C4—62no—
397C2×C32×C4—124no—
398C2×C32×C4C23×D314yes—
399C2×C32×C4C23×D311yescharacteristic
400C2×C3⋊Dic3—22no—
401C2×C3⋊Dic3—31no—
402C2×C3⋊Dic3—34no—
403C2×C3⋊Dic3—34no—
404C2×C3⋊Dic3—64no—
405C2×C3⋊Dic3—62no—
406C2×C3⋊Dic3—68no—
407C2×C3⋊Dic3—128no—
408C2×C3⋊Dic3—124no—
409C2×C3⋊Dic3D3×D411yescharacteristic
410C4×C3⋊D3—34no—
411C4×C3⋊D3—32no—
412C4×C3⋊D3—32no—
413C4×C3⋊D3—34no—
414C4×C3⋊D3—38no—
415C4×C3⋊D3—38no—
416C4×C3⋊D3—44no—
417C4×C3⋊D3—68no—
418C4×C3⋊D3—68no—
419C4×C3⋊D3—124no—
420C4×C3⋊D3—124no—
421C4×C3⋊D3—124no—
422C4×C3⋊D3—1216no—
423C4×C3⋊D3—2416no—
424C4×C3⋊D3C2×C4×D312yes—
425C4×C3⋊D3D3×Q812yes—
426C2×C3×Dic3—28no—
427C2×C3×Dic3—34no—
428C2×C3×Dic3—68no—
429C2×C3×Dic3D3×D414yes—
430C3×C4×D3—38no—
431C3×C4×D3—38no—
432C3×C4×D3—416no—
433C3×C4×D3—1216no—
434C3×C4×D3C2×C4×D318yes—
435C3×C4×D3D3×Q818yes—
436#624—316no—
437#624—1216no—
438D3×Dic3—316no—
439D3×Dic3—316no—
440D3×Dic3—1216no—
441D3×Dic3—1216no—
442C32×C8—28no—
443C32×C8—32no—
444C32×C8C2×C4×D318yescomplemented
445C32×C8C2×C4×D312yescomplemented
446C3⋊(C3⋊C8)—32no—
447C3⋊(C3⋊C8)—38no—
448C3⋊(C3⋊C8)—68no—
449C3⋊(C3⋊C8)C2×C4×D312yescomplemented
450C3×C3⋊C8—38no—
451C3×C3⋊C8C2×C4×D318yescomplemented
452C23×C8—271no—
453C22×C4⋊C4—272no—
454C2×#106—31no—
455C2×#106—91no—
456C2×#106—271no—
457C2×#106—272no—
458C2×#106—272no—
459C2×#106—271no—
460C2×#106—272no—
461C2×#106—271no—
462C2×#106—271no—
463C2×C33C22×C4⋊C411yescharacteristic
464C2×C33C22×SD1612yes—
465C3⋊(C3⋊D3)C2×#10614yescomplemented
466C3×C3⋊D3C2×#10614yescomplemented
467C32×D3C2×#10614yescomplemented
468C23×D3—94no—
469C23×D3—91no—
470C22×C3×C4—34no—
471C22×C3×C4—68no—
472C22×C3×C4—91no—
473C22×C3×C4—182no—
474C22×Dic3—94no—
475C22×Dic3—91no—
476C22×Dic3—182no—
477C22×Dic3—188no—
478C2×C4×D3—22no—
479C2×C4×D3—34no—
480C2×C4×D3—68no—
481C2×C4×D3—916no—
482C2×C4×D3—916no—
483C2×C4×D3—94no—
484C2×C4×D3—94no—
485C2×C4×D3—91no—
486C2×C4×D3—94no—
487C2×C4×D3—91no—
488C2×C4×D3—91no—
489C2×C4×D3—94no—
490C2×C4×D3—94no—
491C2×C4×D3—184no—
492C2×C4×D3—182no—
493C2×C4×D3—188no—
494C2×C4×D3—182no—
495C2×C4×D3—188no—
496C2×C4×D3—188no—
497C2×C4×D3—182no—
498C2×C4×D3—368no—
499C2×C4×D3—368no—
500C2×C4×D3—3632no—
501C2×C4×D3C22×C3⋊D311yescharacteristic
502C2×C3×C8—24no—
503C2×C3×C8—34no—
504C2×C3×C8—316no—
505C2×C3×C8—91no—
506C2×C3×C8—94no—
507C2×C3×C8C2×D3214yes—
508C2×C3×C8C22×C3⋊D311yescharacteristic
509C3×C4⋊C4—28no—
510C3×C4⋊C4—38no—
511C3×C4⋊C4—68no—
512C3×C4⋊C4—92no—
513C3×C4⋊C4—182no—
514C3×C4⋊C4C2×D3218yes—
515C3×C4⋊C4C22×C3⋊D312yes—
516C4⋊Dic3—38no—
517C4⋊Dic3—98no—
518C4⋊Dic3—92no—
519C4⋊Dic3—188no—
520C4⋊Dic3—182no—
521C4⋊Dic3—188no—
522C4⋊Dic3C22×C3⋊D312yes—
523Dic3⋊C4—22no—
524Dic3⋊C4—68no—
525Dic3⋊C4—182no—
526Dic3⋊C4—188no—
527Dic3⋊C4—188no—
528Dic3⋊C4—182no—
529Dic3⋊C4—188no—
530Dic3⋊C4—182no—
531Dic3⋊C4—368no—
532C2×C3⋊C8—34no—
533C2×C3⋊C8—916no—
534C2×C3⋊C8—94no—
535C2×C3⋊C8—91no—
536C2×C3⋊C8—94no—
537C2×C3⋊C8—184no—
538C2×C3⋊C8C22×C3⋊D311yescharacteristic
539D3×C8—316no—
540D3×C8—916no—
541D3×C8—916no—
542D3×C8—94no—
543D3×C8—916no—
544D3×C8—94no—
545D3×C8—94no—
546D3×C8—1816no—
547D3×C8C4×C3⋊D314yescomplemented
548C22×C32—24no—
549C22×C32—32no—
550C22×C32—34no—
551C22×C32C2×D3×D414yes—
552C22×C32C2×D3×D411yescharacteristic
553C2×C3⋊D3—32no—
554C2×C3⋊D3—34no—
555C2×C3⋊D3—316no—
556C2×C3⋊D3—38no—
557C2×C3⋊D3—316no—
558C2×C3⋊D3—68no—
559C2×C3⋊D3—616no—
560C2×C3⋊D3D3×C4⋊C412yes—
561C2×C3⋊D3D3×SD1614yes—
562C2×C3×D3—38no—
563C2×C3×D3—316no—
564C2×C3×D3D3×C4⋊C418yes—
565C2×C3×D3D3×SD16116yes—
566D32—364no—
567C32×C4—24no—
568C32×C4—24no—
569C32×C4—32no—
570C32×C4—42no—
571C32×C4—48no—
572C32×C4—88no—
573C32×C4—122no—
574C32×C4C22×C4×D314yes—
575C32×C4C22×C4×D311yescharacteristic
576C32×C4C2×D3×Q814yes—
577C32×C4C2×D3×Q811yescharacteristic
578C3⋊Dic3—32no—
579C3⋊Dic3—38no—
580C3⋊Dic3—42no—
581C3⋊Dic3—68no—
582C3⋊Dic3—122no—
583C3⋊Dic3—128no—
584C3⋊Dic3—248no—
585C3⋊Dic3D3×C4⋊C412yes—
586C3×Dic3—38no—
587C3×Dic3—48no—
588C3×Dic3—128no—
589C3×Dic3D3×C4⋊C418yes—
590C23×C4—271no—
591C23×C4—542no—
592C22×C8—31no—
593C22×C8—91no—
594C22×C8—278no—
595C22×C8—271no—
596C22×C8—271no—
597C22×C8—271no—
598C22×C8—271no—
599C2×C4⋊C4—32no—
600C2×C4⋊C4—92no—
601C2×C4⋊C4—272no—
602C2×C4⋊C4—272no—
603C2×C4⋊C4—272no—
604C2×C4⋊C4—272no—
605C2×C4⋊C4—542no—
606C2×C4⋊C4—542no—
607C2×C4⋊C4—542no—
608#106—31no—
609#106—32no—
610#106—91no—
611#106—92no—
612#106—272no—
613#106—272no—
614#106—272no—
615#106—271no—
616#106—272no—
617#106D3×C3⋊D311yescharacteristic, direct product factor
618C33C22×#10611yescharacteristic, complemented, Sylow
619C23×C3—34no—
620C23×C3—91no—
621C22×D3—34no—
622C22×D3—916no—
623C22×D3—932no—
624C22×D3—94no—
625C22×D3—91no—
626C22×D3—94no—
627C22×D3—98no—
628C22×D3—184no—
629C22×D3D4×C3⋊D311yescharacteristic
630C2×C3×C4—28no—
631C2×C3×C4—22no—
632C2×C3×C4—24no—
633C2×C3×C4—34no—
634C2×C3×C4—38no—
635C2×C3×C4—38no—
636C2×C3×C4—48no—
637C2×C3×C4—68no—
638C2×C3×C4—91no—
639C2×C3×C4—92no—
640C2×C3×C4—92no—
641C2×C3×C4—1216no—
642C2×C3×C4—182no—
643C2×C3×C4—364no—
644C2×C3×C4C22×D3214yes—
645C2×C3×C4C23×C3⋊D311yescharacteristic
646C2×Dic3—22no—
647C2×Dic3—34no—
648C2×Dic3—68no—
649C2×Dic3—916no—
650C2×Dic3—94no—
651C2×Dic3—91no—
652C2×Dic3—94no—
653C2×Dic3—184no—
654C2×Dic3—188no—
655C2×Dic3—182no—
656C2×Dic3—368no—
657C2×Dic3—364no—
658C2×Dic3—3616no—
659C2×Dic3D4×C3⋊D311yescharacteristic
660C4×D3—38no—
661C4×D3—38no—
662C4×D3—44no—
663C4×D3—916no—
664C4×D3—916no—
665C4×D3—94no—
666C4×D3—98no—
667C4×D3—98no—
668C4×D3—92no—
669C4×D3—92no—
670C4×D3—94no—
671C4×D3—1216no—
672C4×D3—188no—
673C4×D3—188no—
674C4×D3—364no—
675C4×D3—3616no—
676C4×D3—364no—
677C4×D3—3616no—
678C4×D3—3616no—
679C4×D3—364no—
680C4×D3—7216no—
681C4×D3C2×C4×C3⋊D312yes—
682C4×D3Q8×C3⋊D312yes—
683C3×C8—28no—
684C3×C8—38no—
685C3×C8—92no—
686C3×C8C4×D3218yescomplemented
687C3×C8C2×C4×C3⋊D312yescomplemented
688C3⋊C8—38no—
689C3⋊C8—98no—
690C3⋊C8—92no—
691C3⋊C8—188no—
692C3⋊C8C2×C4×C3⋊D312yescomplemented
693C2×C32—24no—
694C2×C32—28no—
695C2×C32—34no—
696C2×C32C2×D3×C4⋊C414yes—
697C2×C32C2×D3×C4⋊C411yescharacteristic
698C2×C32C2×D3×SD1618yes—
699C2×C32C2×D3×SD1612yes—
700C3⋊D3—34no—
701C3⋊D3—316no—
702C3⋊D3—616no—
703C3⋊D3D3×#10614yesdirect product factor
704C3×D3—316no—
705C3×D3D3×#106116yescomplemented
706C24—271no—
707C22×C4—31no—
708C22×C4—62no—
709C22×C4—91no—
710C22×C4—182no—
711C22×C4—271no—
712C22×C4—274no—
713C22×C4—274no—
714C22×C4—271no—
715C22×C4—271no—
716C22×C4—271no—
717C22×C4—542no—
718C22×C4—542no—
719C22×C4—542no—
720C22×C4—542no—
721C22×C4—1088no—
722C2×C8—31no—
723C2×C8—34no—
724C2×C8—91no—
725C2×C8—94no—
726C2×C8—274no—
727C2×C8—274no—
728C2×C8—274no—
729C2×C8—271no—
730C2×C8—274no—
731C2×C8C2×D3×C3⋊D311yescharacteristic
732C4⋊C4—32no—
733C4⋊C4—62no—
734C4⋊C4—92no—
735C4⋊C4—182no—
736C4⋊C4—272no—
737C4⋊C4—542no—
738C4⋊C4—542no—
739C4⋊C4—542no—
740C4⋊C4—542no—
741C4⋊C4C2×D3×C3⋊D312yes—
742C22×C3—24no—
743C22×C3—38no—
744C22×C3—316no—
745C22×C3—92no—
746C22×C3—94no—
747C22×C3D32×D414yes—
748C22×C3C2×D4×C3⋊D311yescharacteristic
749C2×D3—38no—
750C2×D3—316no—
751C2×D3—964no—
752C2×D3—98no—
753C2×D3—92no—
754C2×D3—94no—
755C2×D3—916no—
756C2×D3—916no—
757C2×D3—188no—
758C2×D3—1816no—
759C2×D3C4⋊C4×C3⋊D312yes—
760C2×D3SD16×C3⋊D314yes—
761C3×C4—24no—
762C3×C4—24no—
763C3×C4—38no—
764C3×C4—42no—
765C3×C4—48no—
766C3×C4—88no—
767C3×C4—92no—
768C3×C4—128no—
769C3×C4—362no—
770C3×C4C2×C4×D3214yes—
771C3×C4D32×Q814yes—
772C3×C4C22×C4×C3⋊D311yescharacteristic
773C3×C4C2×Q8×C3⋊D311yescharacteristic
774Dic3—38no—
775Dic3—42no—
776Dic3—98no—
777Dic3—92no—
778Dic3—128no—
779Dic3—188no—
780Dic3—362no—
781Dic3—368no—
782Dic3—728no—
783Dic3C4⋊C4×C3⋊D312yes—
784C32—24no—
785C32C2×D3×#10614yescomplemented
786C32C2×D3×#10611yescharacteristic, complemented
787C23—31no—
788C23—91no—
789C23—274no—
790C23—278no—
791C23—271no—
792C2×C4—22no—
793C2×C4—31no—
794C2×C4—32no—
795C2×C4—32no—
796C2×C4—62no—
797C2×C4—91no—
798C2×C4—92no—
799C2×C4—92no—
800C2×C4—124no—
801C2×C4—182no—
802C2×C4—274no—
803C2×C4—274no—
804C2×C4—274no—
805C2×C4—271no—
806C2×C4—272no—
807C2×C4—272no—
808C2×C4—364no—
809C2×C4—542no—
810C2×C4—1084no—
811C2×C4—1084no—
812C2×C4—1084no—
813C2×C4—1084no—
814C2×C4C22×D3×C3⋊D311yescharacteristic
815C8—32no—
816C8—92no—
817C8—272no—
818C8C4×D3×C3⋊D312yescomplemented
819C2×C3—28no—
820C2×C3—24no—
821C2×C3—316no—
822C2×C3—94no—
823C2×C3D32×C4⋊C414yes—
824C2×C3D32×SD1618yes—
825C2×C3C2×C4⋊C4×C3⋊D311yescharacteristic
826C2×C3C2×SD16×C3⋊D312yes—
827D3—316no—
828D3—94no—
829D3—916no—
830D3—1816no—
831D3C3⋊D3×#10614yesdirect product factor
832C22—34no—
833C22—32no—
834C22—94no—
835C22—92no—
836C22—2716no—
837C22—274no—
838C22—272no—
839C22D3×D4×C3⋊D311yescharacteristic
840C4—32no—
841C4—42no—
842C4—92no—
843C4—122no—
844C4—272no—
845C4—362no—
846C4—1082no—
847C4C2×C4×D3×C3⋊D311yescharacteristic
848C4D3×Q8×C3⋊D311yescharacteristic
849C3—24no—
850C3C2×C3⋊D3×#10611yescharacteristic, complemented
851C3D32×#10614yescomplemented
852C2—34no—
853C2—94no—
854C2—274no—
855C2D3×C4⋊C4×C3⋊D311yescharacteristic
856C2D3×SD16×C3⋊D312yes—
subgroupG/H
centerC22D3×D4×C3⋊D3
commutatorC33×C4C23×C4
FrattiniC2×C4C22×D3×C3⋊D3
FittingC33×#106C22
socleC22×C33C22×D4
prime radicalC22×D3×C3⋊D3D4
cosocleC2×C33×C4C24
hypercenter#106D3×C3⋊D3
hypocenterC33C22×#106
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #106×C3⋊(C3⋊D3)C2semidirect
4. C3×C3⋊D3×#106C2semidirect
5. C32×D3×#106C2semidirect
6. #13159550C2semidirect
7. D3×#63644C2semidirect
8. C3⋊D3×#817C2semidirect
9. #13159326C2semidirect
10. D3×#63635C2semidirect
11. C3⋊D3×#808C2semidirect
31. D3×C8×C3⋊D3C4semidirect
32. C33×#106C22semidirect
33. #11722187C22semidirect
34. #11722178C22semidirect
35. C3×#63644C22semidirect
36. C3×#63635C22semidirect
37. C32×#817C22semidirect
38. C32×#808C22semidirect
39. #11722054C22semidirect
40. #11722053C22semidirect
41. #11722052C22semidirect
56. C3⋊D3×#106D3direct (N × H)
58. C3×D3×#106D3semidirect
86. C8×C3⋊(C3⋊D3)C2×C4semidirect
90. C3×C8×C3⋊D3C2×C4semidirect
94. C32×D3×C8C2×C4semidirect
98. #88785C2×C4semidirect
99. C3⋊D3×C3⋊C8C2×C4semidirect
100. D3×C3⋊(C3⋊C8)C2×C4semidirect
144. C32×#106C2×D3semidirect
145. C32×#106C2×D3semidirect
150. #63644C2×D3semidirect
156. #63635C2×D3semidirect
158. C3×#817C2×D3semidirect
160. C3×#808C2×D3semidirect
192. C33×C8C22×C4semidirect
193. C3⋊(C3⋊(C3⋊C8))C22×C4semidirect
194. C3×C3⋊(C3⋊C8)C22×C4semidirect
195. C32×C3⋊C8C22×C4semidirect
218. D3×#106C3⋊D3direct (N × H)
284. C8×C3⋊D3C4×D3semidirect
292. C3×D3×C8C4×D3semidirect
307. D3×C3⋊D3#106direct (N × H)
360. C3×#106D32semidirect
361. C3×#106C2×C3⋊D3semidirect
368. #817C2×C3⋊D3semidirect
377. #808C2×C3⋊D3semidirect
444. C32×C8C2×C4×D3semidirect
445. C32×C8C2×C4×D3semidirect
449. C3⋊(C3⋊C8)C2×C4×D3semidirect
451. C3×C3⋊C8C2×C4×D3semidirect
465. C3⋊(C3⋊D3)C2×#106semidirect
466. C3×C3⋊D3C2×#106semidirect
467. C32×D3C2×#106semidirect
547. D3×C8C4×C3⋊D3semidirect
617. #106D3×C3⋊D3direct (N × H)
618. C33C22×#106semidirect
686. C3×C8C4×D32semidirect
687. C3×C8C2×C4×C3⋊D3semidirect
692. C3⋊C8C2×C4×C3⋊D3semidirect
703. C3⋊D3D3×#106direct (N × H)
705. C3×D3D3×#106semidirect
785. C32C2×D3×#106semidirect
786. C32C2×D3×#106semidirect
818. C8C4×D3×C3⋊D3semidirect
831. D3C3⋊D3×#106direct (N × H)
850. C3C2×C3⋊D3×#106semidirect
851. C3D32×#106semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C8×C3⋊D32
D3×C4⋊C4×C3⋊D32
#106×C3⋊(C3⋊D3)2
C3×C3⋊D3×#1062
C32×D3×#1062
#131595502
D3×#636442
C3⋊D3×#8172
#131593262
D3×#636352
C3⋊D3×#8082
D32×#1063
C2×C3⋊D3×#1063