Finite Group Databasebeta

← #13175397

Subgroups — #13175397

Order 1728.

2356 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89020C211yesmaximal, characteristic, complemented
3C4×C4⋊(C3⋊(C3⋊D3))C211yesmaximal, characteristic, complemented
4C3×#64081C211yesmaximal, characteristic, complemented
5C32×C4×D12C211yesmaximal, characteristic, complemented
6#11723542C211yesmaximal, characteristic, complemented
7#11723540C211yesmaximal, characteristic, complemented
8#11723525C211yesmaximal, characteristic, complemented
9#11723523C211yesmaximal, characteristic, complemented
10C4×#6291C211yesmaximal, characteristic, complemented
11C4×#6291C211yesmaximal, characteristic, complemented
12#11723495C211yesmaximal, characteristic, complemented
13#11723493C211yesmaximal, characteristic, complemented
14#11723491C211yesmaximal, characteristic, complemented
15#11723475C211yesmaximal, characteristic, complemented
16#10596018—31nomaximal
17#10593997—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×D12C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic, complemented
26C2×#6293C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic
30C2×#6291C2211yescharacteristic, complemented
31C2×#6290C2211yescharacteristic
32C2×#6289C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C4×D3×C3⋊D3—24no—
36#89020—24no—
37C33×C42C2211yescharacteristic, complemented
38#88859C2211yescharacteristic
39#88859C2211yescharacteristic, complemented
40C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic
42C3×#3752C2211yescharacteristic
43C3×#3750C2211yescharacteristic, complemented
44C3×#3750C2211yescharacteristic, complemented
45C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×C4⋊Dic3C2211yescharacteristic, complemented
49#88807C2211yescharacteristic, complemented
50#88807C2211yescharacteristic, complemented
51#88804C2211yescharacteristic
52#88804C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×#3828—31no—
56C22×C4×C3⋊D3—31no—
57C2×C4×D32—34no—
58C2×#3798—34no—
59C32×C4×D4—31no—
60#64148—31no—
61#64146—31no—
62C4×#638—31no—
63C4×#638—31no—
64#64105—31no—
65#64103—31no—
66#64093—31no—
67#64092—31no—
68#64091—31no—
69#64087—31no—
70C4×C4⋊(C3⋊D3)—31no—
71C4×C4⋊(C3⋊D3)—34no—
72C4×C4⋊(C3⋊D3)—64no—
73#64081D311yescharacteristic, complemented
74C3×C4×D12D314yescomplemented
75C3×#872—34no—
76#63923—34no—
77#63922—34no—
78#63910—34no—
79C4×#626—34no—
80C4×#626—34no—
81#63895—34no—
82#63893—34no—
83#63891—34no—
84#63890—34no—
85#63886—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C2×D3×C3⋊D3—22no—
92C2×D3×C3⋊D3—22no—
93C2×D3×C3⋊D3—22no—
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C4⋊(C3⋊(C3⋊D3))—22no—
100C4×C3⋊(C3⋊D3)—22no—
101C4×C3⋊(C3⋊D3)—22no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C3×C4×C3⋊D3D414yescomplemented
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C32×D12—22no—
109C32×C4×D3—22no—
110C32×C4×D3—22no—
111#6293—22no—
112#6292—22no—
113#6291—22no—
114#6291—22no—
115#6291—22no—
116#6290—22no—
117#6289—22no—
118Dic3×C3⋊D3—22no—
119D3×C3⋊Dic3—22no—
120#5547—94no—
121#5524—91no—
122C23×C3⋊D3—31no—
123C22×D32—34no—
124C2×C32×D4—31no—
125C22×C32×C4—31no—
126C22×C32×C4—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—31no—
131C22×C3⋊Dic3—31no—
132#3828—64no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4⋊(C3⋊D3)—34no—
136C2×C4⋊(C3⋊D3)—64no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—34no—
141C2×C4×C3⋊D3—34no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3—64no—
144C2×C4×C3⋊D3—64no—
145C2×C4×C3⋊D3—64no—
146C2×C4×C3⋊D3C2×D311yescharacteristic
147C2×#634—31no—
148C2×C3×D12C2×D314yes—
149C2×C3×C4×D3—34no—
150C2×C3×C4×D3C2×D314yes—
151C2×C3×C4×D3C2×D314yescomplemented
152C2×#627—34no—
153C2×#626—34no—
154C2×#626—34no—
155C2×#626—34no—
156C2×#626—34no—
157C2×#625—34no—
158C2×#624—34no—
159C2×D3×Dic3—34no—
160C2×D3×Dic3—34no—
161C4×D32—616no—
162#3798—616no—
163C32×C4⋊C4—31no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C42—24no—
167C32×C42C2×D314yescomplemented
168C32×C42C2×D311yescharacteristic, complemented
169#3757—31no—
170#3757—31no—
171#3752—31no—
172#3752—31no—
173#3752—34no—
174#3752—34no—
175#3752—31no—
176#3752—31no—
177#3752—64no—
178#3752—64no—
179#3752C2×D311yescharacteristic
180#3752C2×D311yescharacteristic
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)—34no—
183C4⋊(C3⋊Dic3)—64no—
184#3750—31no—
185#3750—31no—
186#3750C2×D311yescharacteristic, complemented
187#3750C2×D311yescharacteristic, complemented
188C4×C3⋊Dic3C2×D311yescharacteristic, complemented
189C3×(C2×D3)⋊C4—34no—
190C3×(C2×D3)⋊C4—34no—
191C3×(C2×D3)⋊C4C2×D314yes—
192C3×(C2×D3)⋊C4C2×D314yescomplemented
193C3×C4⋊Dic3C2×D314yescomplemented
194C3×Dic3⋊C4—34no—
195C3×Dic3⋊C4—34no—
196C3×C4×Dic3—34no—
197Dic3⋊Dic3—34no—
198Dic3⋊Dic3—34no—
199#3722—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203C22×C33C2411yescharacteristic
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)—21no—
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)#4112yescomplemented
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3C2×D412yes—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3#4112yescomplemented
219D3×C3⋊D3—28no—
220C33×C4—21no—
221C33×C4—21no—
222C33×C4C2×D412yes—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)—21no—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3C2×D412yes—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C2×#235—94no—
231C2×#235—91no—
232C22×C4×D3—94no—
233C22×C4×D3—91no—
234C3×C4×D4—34no—
235C3×#117—91no—
236#939—94no—
237#937—94no—
238C4×#67—94no—
239C4×#67—94no—
240#897—91no—
241#897—91no—
242#896—94no—
243#895—91no—
244#895—91no—
245#894—94no—
246#886—91no—
247#886—91no—
248#884—94no—
249#883—94no—
250#882—94no—
251#882—91no—
252#882—91no—
253#878—94no—
254C4×D12—91no—
255C4×D12—91no—
256C4×D12—94no—
257C4×D12—91no—
258C4×D12—184no—
259C4×D12C3⋊D311yescharacteristic, complemented
260#872—34no—
261C23×C32—31no—
262C23×C32—31no—
263C22×C3⋊D3—31no—
264C22×C3⋊D3—31no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—34no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—64no—
269C22×C3⋊D3—62no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3×D3—34no—
274C22×C3×D3C22×D314yes—
275C22×C3×D3C22×D314yes—
276C2×D32—68no—
277C2×D32—68no—
278C2×D32—68no—
279C32×D4—62no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—24no—
283C2×C32×C4—31no—
284C2×C32×C4—31no—
285C2×C32×C4—62no—
286C2×C32×C4—62no—
287C2×C32×C4C22×D314yes—
288C2×C32×C4C22×D314yes—
289C2×C32×C4C22×D314yes—
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293#638—62no—
294#638—62no—
295#638—62no—
296#638—62no—
297C2×C3⋊Dic3—31no—
298C2×C3⋊Dic3—31no—
299C2×C3⋊Dic3—34no—
300C2×C3⋊Dic3—34no—
301C2×C3⋊Dic3—64no—
302C2×C3⋊Dic3—64no—
303C2×C3⋊Dic3—62no—
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D311yescharacteristic
306C2×C3⋊Dic3C22×D311yescharacteristic
307C4⋊(C3⋊D3)—62no—
308C4⋊(C3⋊D3)—68no—
309C4⋊(C3⋊D3)—616no—
310C4⋊(C3⋊D3)—62no—
311C4×C3⋊D3—62no—
312C4×C3⋊D3—62no—
313C4×C3⋊D3—62no—
314C4×C3⋊D3—62no—
315C4×C3⋊D3—68no—
316C4×C3⋊D3—68no—
317C4×C3⋊D3—128no—
318C4×C3⋊D3—128no—
319C4×C3⋊D3D1214yescomplemented
320#634—62no—
321C2×C3×Dic3—34no—
322C2×C3×Dic3—34no—
323C2×C3×Dic3—34no—
324C2×C3×Dic3C22×D314yes—
325C2×C3×Dic3C22×D314yes—
326C3×D12—28no—
327C3×C4×D3—28no—
328C3×C4×D3—28no—
329C3×C4×D3—316no—
330#627—68no—
331#626—68no—
332#626—68no—
333#626—68no—
334#626—68no—
335#625—68no—
336#624—68no—
337D3×Dic3—68no—
338D3×Dic3—68no—
339#525—271noSylow
340C2×C33C22×D411yescharacteristic
341C2×C33C2×#4111yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C3⋊(C3⋊D3)—22no—
344C3⋊(C3⋊D3)—41no—
345C3×C3⋊D3—22no—
346C32×D3—22no—
347C32×D3—41no—
348C23×D3—94no—
349C23×D3—91no—
350C2×C3×D4—34no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—91no—
354C2×#67—94no—
355C2×#67—94no—
356C2×#67—94no—
357C2×#67—94no—
358C2×#67—91no—
359C2×#67—91no—
360C22×Dic3—94no—
361C22×Dic3—91no—
362#235—184no—
363#235—1816no—
364C2×D12—94no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—94no—
369C2×D12—91no—
370C2×D12—184no—
371C2×D12C2×C3⋊D311yescharacteristic
372C2×C4×D3—34no—
373C2×C4×D3—94no—
374C2×C4×D3—94no—
375C2×C4×D3—91no—
376C2×C4×D3—94no—
377C2×C4×D3—94no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—184no—
382C2×C4×D3—184no—
383C2×C4×D3—184no—
384C2×C4×D3—1816no—
385C2×C4×D3C2×C3⋊D311yescharacteristic
386C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
387C2×Dic6—94no—
388C2×Dic6—91no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C42—24no—
397C3×C42—91no—
398C3×C42D3214yescomplemented
399C3×C42C2×C3⋊D311yescharacteristic, complemented
400#217—94no—
401#217—94no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—94no—
409(C2×D3)⋊C4—94no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—184no—
415(C2×D3)⋊C4—184no—
416(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
417(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
418C4⋊Dic3—94no—
419C4⋊Dic3—91no—
420C4⋊Dic3—91no—
421C4⋊Dic3—91no—
422C4⋊Dic3—184no—
423C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—94no—
427Dic3⋊C4—94no—
428C4×Dic3—34no—
429C22×C32—24no—
430C22×C32—32no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32—61no—
435C22×C32—61no—
436C22×C32C23×D314yes—
437C22×C32C23×D311yescharacteristic
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—32no—
441C2×C3⋊D3—38no—
442C2×C3⋊D3—68no—
443C2×C3⋊D3—68no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—68no—
447C2×C3⋊D3—61no—
448C2×C3⋊D3—64no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—64no—
452C2×C3⋊D3—64no—
453C2×C3⋊D3—64no—
454C2×C3⋊D3—64no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3—124no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3C2×D1212yes—
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—24no—
465C2×C3×D3—38no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3#23518yescomplemented
469D32—632no—
470C32×C4—28no—
471C32×C4—24no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—28no—
475C32×C4—24no—
476C32×C4—44no—
477C32×C4—61no—
478C32×C4—61no—
479C32×C4C2×D1212yes—
480C32×C4D3×D418yes—
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3⋊Dic3—64no—
486C3⋊Dic3—64no—
487C3⋊Dic3—124no—
488C3⋊Dic3—124no—
489C3⋊Dic3C2×D1212yes—
490C3×Dic3—24no—
491C3×Dic3—24no—
492C3×Dic3—38no—
493C3×Dic3—64no—
494C3×Dic3—64no—
495C2×#41—271no—
496C23×C4—271no—
497#123—271no—
498#123—271no—
499C22⋊Q8—271no—
500C22⋊Q8—271no—
501#121—271no—
502#121—271no—
503#120—271no—
504#120—271no—
505C4×D4—31no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509#117—91no—
510C33#52511yescharacteristic, complemented, Sylow
511C23×C3—34no—
512C23×C3—34no—
513C23×C3—91no—
514C22×D3—34no—
515C22×D3—94no—
516C22×D3—91no—
517C22×D3—94no—
518C22×D3—91no—
519C22×D3—184no—
520C22×D3—184no—
521C22×D3—182no—
522C22×D3—182no—
523C22×D3—188no—
524C22×D3—188no—
525C22×D3—188no—
526C22×D3—182no—
527C22×D3C22×C3⋊D311yescharacteristic
528C22×D3C22×C3⋊D311yescharacteristic
529C3×D4—68no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—24no—
533C2×C3×C4—34no—
534C2×C3×C4—34no—
535C2×C3×C4—68no—
536C2×C3×C4—68no—
537C2×C3×C4—91no—
538C2×C3×C4—94no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4C2×D3214yes—
542C2×C3×C4C2×D3214yes—
543C2×C3×C4C2×D3214yes—
544C2×C3×C4C22×C3⋊D311yescharacteristic
545C2×C3×C4C22×C3⋊D311yescharacteristic
546C2×C3×C4C22×C3⋊D311yescharacteristic
547#67—182no—
548#67—188no—
549#67—188no—
550#67—188no—
551#67—182no—
552#67—188no—
553C2×Dic3—34no—
554C2×Dic3—34no—
555C2×Dic3—34no—
556C2×Dic3—94no—
557C2×Dic3—94no—
558C2×Dic3—91no—
559C2×Dic3—91no—
560C2×Dic3—184no—
561C2×Dic3—184no—
562C2×Dic3—182no—
563C2×Dic3—188no—
564C2×Dic3C22×C3⋊D311yescharacteristic
565C2×Dic3C22×C3⋊D311yescharacteristic
566D12—22no—
567D12—188no—
568D12—182no—
569D12—1816no—
570D12—188no—
571D12—182no—
572D12—182no—
573D12—182no—
574C4×D3—22no—
575C4×D3—22no—
576C4×D3—316no—
577C4×D3—182no—
578C4×D3—188no—
579C4×D3—188no—
580C4×D3—182no—
581C4×D3—188no—
582C4×D3—188no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—368no—
586C4×D3—368no—
587Dic6—182no—
588Dic6—188no—
589C2×C32—24no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—62no—
593C2×C32—121no—
594C2×C32C22×D1211yescharacteristic
595C2×C32C2×#23514yes—
596C2×C32C2×D3×D414yes—
597C2×C32D3×#4114yes—
598C2×C32D3×#4111yescharacteristic
599C2×C32D3×#4111yescharacteristic
600C3⋊D3—22no—
601C3⋊D3—62no—
602C3⋊D3—68no—
603C3⋊D3—128no—
604C3⋊D3—128no—
605C3⋊D3—121no—
606C3⋊D3—124no—
607C3×D3—28no—
608C3×D3—44no—
609C3×D3—68no—
610C24—271no—
611#41—544no—
612C2×Q8—271no—
613C2×D4—31no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—91no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—271no—
628C22×C4—544no—
629C4⋊C4—31no—
630C4⋊C4—91no—
631C4⋊C4—91no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—91no—
646C42D3×C3⋊D311yescharacteristic, complemented
647C22×C3—24no—
648C22×C3—38no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—64no—
652C22×C3—64no—
653C22×C3—64no—
654C22×C3—92no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3C22×D3214yes—
658C22×C3C23×C3⋊D311yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—38no—
665C2×D3—64no—
666C2×D3—64no—
667C2×D3—98no—
668C2×D3—92no—
669C2×D3—188no—
670C2×D3—188no—
671C2×D3—1832no—
672C2×D3—184no—
673C2×D3—184no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—188no—
677C2×D3—184no—
678C2×D3—184no—
679C2×D3—184no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—364no—
684C2×D3—364no—
685C2×D3—364no—
686C2×D3—364no—
687C2×D3#382812yescomplemented
688C3×C4—28no—
689C3×C4—24no—
690C3×C4—24no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—28no—
694C3×C4—44no—
695C3×C4—64no—
696C3×C4—64no—
697C3×C4—92no—
698C3×C4—181no—
699C3×C4—181no—
700C3×C4D3×D1218yes—
701C3×C4D4×C3⋊D312yes—
702Dic3—21no—
703Dic3—21no—
704Dic3—38no—
705Dic3—64no—
706Dic3—64no—
707Dic3—184no—
708Dic3—184no—
709Dic3—181no—
710Dic3—181no—
711Dic3—364no—
712Dic3—364no—
713C32—24no—
714C32#552411yescharacteristic, complemented
715C32#554714yescomplemented
716C23—31no—
717C23—31no—
718C23—91no—
719C23—271no—
720C23—271no—
721C23—542no—
722C23—542no—
723C23—542no—
724Q8—542no—
725D4—62no—
726D4—542no—
727D4—542no—
728D4—542no—
729D4—542no—
730D4—542no—
731D4—542no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—91no—
737C2×C4—94no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—271no—
741C2×C4—271no—
742C2×C4—542no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4C2×D3×C3⋊D311yescharacteristic
748C2×C4C2×D3×C3⋊D311yescharacteristic
749C2×C4C2×D3×C3⋊D311yescharacteristic
750C2×C3—24no—
751C2×C3—24no—
752C2×C3—24no—
753C2×C3—68no—
754C2×C3—124no—
755C2×C3—182no—
756C2×C3C2×D3×D1214yes—
757C2×C3D3×#23514yes—
758C2×C3#6430614yes—
759C2×C3C2×#382811yescharacteristic
760C2×C3C2×D4×C3⋊D311yescharacteristic
761C2×C3#41×C3⋊D311yescharacteristic
762D3—22no—
763D3—41no—
764D3—68no—
765D3—182no—
766D3—188no—
767D3—368no—
768D3—368no—
769D3—361no—
770D3—364no—
771C22—32no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—92no—
778C22—181no—
779C22—181no—
780C22—272no—
781C22—548no—
782C22—541no—
783C22—541no—
784C22—541no—
785C22—541no—
786C22—541no—
787C22C22×D3×C3⋊D311yescharacteristic
788C4—21no—
789C4—21no—
790C4—61no—
791C4—61no—
792C4—92no—
793C4—181no—
794C4—181no—
795C4—541no—
796C4—541no—
797C4C3⋊D3×D1212yes—
798C3—24no—
799C3#1059399714yescomplemented
800C3#1059601811yescharacteristic, complemented
801C2—62no—
802C2—121no—
803C2—182no—
804C2—542no—
805C2—1081no—
806C2C2×C3⋊D3×D1211yescharacteristic
807C2D3×#382811yescharacteristic
808C2#1172457811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FrattiniC22C22×D3×C3⋊D3
FittingC33×C42C22
hypercenterC42D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×C3⋊D3C2semidirect
2. C2×#89020C2semidirect
3. C4×C4⋊(C3⋊(C3⋊D3))C2semidirect
4. C3×#64081C2semidirect
5. C32×C4×D12C2semidirect
6. #11723542C2semidirect
7. #11723540C2semidirect
8. #11723525C2semidirect
9. #11723523C2semidirect
10. C4×#6291C2semidirect
11. C4×#6291C2semidirect
12. #11723495C2semidirect
13. #11723493C2semidirect
14. #11723491C2semidirect
15. #11723475C2semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
25. C2×C32×C4×D3C22semidirect
26. C2×#6293C22semidirect
30. C2×#6291C22semidirect
37. C33×C42C22semidirect
39. #88859C22semidirect
40. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
43. C3×#3750C22semidirect
44. C3×#3750C22semidirect
45. C3×C4×C3⋊Dic3C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×C4⋊Dic3C22semidirect
49. #88807C22semidirect
50. #88807C22semidirect
52. #88804C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
73. #64081D3semidirect
74. C3×C4×D12D3semidirect
105. C3×C4×C3⋊D3D4semidirect
151. C2×C3×C4×D3C2×D3semidirect
167. C32×C42C2×D3semidirect
168. C32×C42C2×D3semidirect
186. #3750C2×D3semidirect
187. #3750C2×D3semidirect
188. C4×C3⋊Dic3C2×D3semidirect
192. C3×(C2×D3)⋊C4C2×D3semidirect
193. C3×C4⋊Dic3C2×D3semidirect
209. C2×C3⋊(C3⋊D3)#41semidirect
218. C2×C32×D3#41semidirect
259. C4×D12C3⋊D3semidirect
319. C4×C3⋊D3D12semidirect
386. C2×C4×D3C2×C3⋊D3semidirect
398. C3×C42D32semidirect
399. C3×C42C2×C3⋊D3semidirect
417. (C2×D3)⋊C4C2×C3⋊D3semidirect
423. C4⋊Dic3C2×C3⋊D3semidirect
468. C2×C3×D3#235semidirect
510. C33#525semidirect
646. C42D3×C3⋊D3semidirect
687. C2×D3#3828semidirect
714. C32#5524semidirect
715. C32#5547semidirect
799. C3#10593997semidirect
800. C3#10596018semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×C3⋊D32
C2×#890202
C4×C4⋊(C3⋊(C3⋊D3))2
C3×#640812
C32×C4×D122
#117235422
#117235402
#117235252
#117235232
C4×#62912
#117234952
#117234932
#117234912
#117234752
#105960183
#105939973