Finite Group Databasebeta

← #13177330

Subgroups — #13177330

Order 1728.

2636 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89076C211yesmaximal, characteristic, complemented
2C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×C4×#638C211yesmaximal, characteristic, complemented
4C32×C4×#67C211yesmaximal, characteristic, complemented
5#11723643C211yesmaximal, characteristic, complemented
6#11723628C211yesmaximal, characteristic, complemented
7#11723624C211yesmaximal, characteristic, complemented
8#11723616C211yesmaximal, characteristic, complemented
9#11723542C211yesmaximal, characteristic, complemented
10C4×#6292C211yesmaximal, characteristic, complemented
11C4×#6291C211yesmaximal, characteristic, complemented
12#11723498C211yesmaximal, characteristic, complemented
13#11723497C211yesmaximal, characteristic, complemented
14#11723496C211yesmaximal, characteristic, complemented
15#11723452C211yesmaximal, characteristic, complemented
16#10596018—31nomaximal
17#10595076—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22#89076—24no—
23C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
24C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
25C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×#6308C2211yescharacteristic, complemented
27C2×C3×#638C2211yescharacteristic
28C2×C3×C4×C3⋊D3C2211yescharacteristic
29C2×C32×#67C2211yescharacteristic
30C2×C32×C4×D3C2211yescharacteristic
31C2×#6292C2211yescharacteristic
32C2×#6291C2211yescharacteristic
33C2×#6289C2211yescharacteristic
34C2×Dic3×C3⋊D3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic
36C4×D3×C3⋊D3—24no—
37C3×#3757C2211yescharacteristic, complemented
38C3×#3752C2211yescharacteristic
39C3×#3750C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44C32×C4×Dic3C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
55C2×#3828—31no—
56C2×#3828—34no—
57C2×#3828—64no—
58C22×C4×C3⋊D3—31no—
59C2×C4×D32—34no—
60C32×C4×D4—31no—
61#64148—31no—
62#64146—31no—
63C4×#638—31no—
64C4×#638D311yescharacteristic, complemented
65#64105—31no—
66#64103—31no—
67#64093—31no—
68#64092—31no—
69#64091—31no—
70#64087—31no—
71C4×C4⋊(C3⋊D3)—31no—
72#64081—31no—
73C3×C4×#67—34no—
74C3×C4×#67D314yescomplemented
75#63983—34no—
76#63975—34no—
77#63971—34no—
78#63971—34no—
79#63923—34no—
80C4×#626—34no—
81C4×#626—34no—
82#63897—34no—
83#63896—34no—
84#63896—34no—
85#63874—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C2×D3×C3⋊D3—22no—
92C2×D3×C3⋊D3—22no—
93C2×D3×C3⋊D3—22no—
94C2×C33×C4—22no—
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97#6312—22no—
98#6312—22no—
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C4⋊(C3⋊(C3⋊D3))—22no—
102C4×C3⋊(C3⋊D3)—22no—
103C4×C3⋊(C3⋊D3)D414yescomplemented
104#6308—22no—
105C3×#638—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×C4×C3⋊D3—22no—
110C32×#67—22no—
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C32×C4×D3—22no—
115#6292—22no—
116#6291—22no—
117#6289—22no—
118Dic3×C3⋊D3—22no—
119D3×C3⋊Dic3—22no—
120#5547—94no—
121#5547—91no—
122C23×C3⋊D3—31no—
123C22×D32—34no—
124C2×C32×D4—31no—
125C22×C32×C4—24no—
126C22×C32×C4—31no—
127C22×C32×C4C2×D314yescomplemented
128C22×C32×C4C2×D311yescharacteristic, complemented
129C2×#638—31no—
130C2×#638—31no—
131C2×#638—34no—
132C2×#638—34no—
133C2×#638—31no—
134C2×#638—64no—
135C2×#638—64no—
136C2×#638C2×D311yescharacteristic
137C22×C3⋊Dic3—31no—
138#3828—64no—
139#3828—616no—
140#3828—632no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)—34no—
144C2×C4⋊(C3⋊D3)—64no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—34no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—34no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—64no—
152C2×C4×C3⋊D3—64no—
153C2×C4×C3⋊D3—64no—
154C2×C4×C3⋊D3C2×D311yescharacteristic
155C2×#634—31no—
156C2×#634—34no—
157C2×#634—64no—
158C2×C3×#67—34no—
159C2×C3×#67C2×D314yes—
160C2×C3×C4×D3—34no—
161C2×C3×C4×D3C2×D314yes—
162C2×#626—34no—
163C2×#626—34no—
164C2×#624—34no—
165C2×D3×Dic3—34no—
166C2×D3×Dic3—34no—
167C4×D32—616no—
168C32×C4⋊C4—31no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C42—31no—
172#3757—31no—
173#3757C2×D311yescharacteristic, complemented
174#3752—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752C2×D311yescharacteristic
180C4⋊(C3⋊Dic3)—31no—
181#3750—31no—
182#3750—31no—
183#3750—31no—
184#3750C2×D311yescharacteristic, complemented
185C4×C3⋊Dic3C2×D311yescharacteristic, complemented
186C3×#217—34no—
187C3×#217C2×D314yescomplemented
188C3×(C2×D3)⋊C4—34no—
189C3×(C2×D3)⋊C4C2×D314yes—
190C3×Dic3⋊C4—34no—
191C3×Dic3⋊C4C2×D314yescomplemented
192C3×C4×Dic3—34no—
193C3×C4×Dic3C2×D314yescomplemented
194#3724—34no—
195#3724—34no—
196Dic3⋊Dic3—34no—
197Dic3⋊Dic3—34no—
198#3722—34no—
199#3722—34no—
200#3722—34no—
201#3722—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33—21no—
207C22×C33C2411yescharacteristic
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)—21no—
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3⋊(C3⋊D3)C2×D412yes—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C3×C3⋊D3#4112yescomplemented
217C2×C32×D3—21no—
218C2×C32×D3—21no—
219C2×C32×D3#4112yescomplemented
220D3×C3⋊D3—28no—
221C33×C4—21no—
222C33×C4C2×D412yes—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)C2×D412yes—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C32×Dic3—21no—
231C2×#235—94no—
232C2×#235—91no—
233C2×#235—184no—
234C22×C4×D3—94no—
235C22×C4×D3—91no—
236C3×C4×D4—34no—
237C3×C4×D4—91no—
238#939—94no—
239#939—91no—
240#937—94no—
241#937—91no—
242C4×#67—34no—
243C4×#67—94no—
244C4×#67—91no—
245C4×#67C3⋊D311yescharacteristic, complemented
246#896—94no—
247#896—91no—
248#894—94no—
249#894—91no—
250#884—94no—
251#884—91no—
252#883—94no—
253#883—91no—
254#882—94no—
255#882—91no—
256#878—94no—
257#878—91no—
258C4×D12—94no—
259C4×D12—91no—
260#872—94no—
261#872—91no—
262C23×C32—24no—
263C23×C32—31no—
264C23×C32C22×D314yes—
265C23×C32C22×D311yescharacteristic
266C22×C3⋊D3—31no—
267C22×C3⋊D3—31no—
268C22×C3⋊D3—34no—
269C22×C3⋊D3—34no—
270C22×C3⋊D3—64no—
271C22×C3⋊D3—64no—
272C22×C3⋊D3—62no—
273C22×C3⋊D3—62no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3C22×D311yescharacteristic
276C22×C3×D3—34no—
277C22×C3×D3C22×D314yes—
278C2×D32—68no—
279C2×D32—68no—
280C2×D32—68no—
281C32×D4—62no—
282C2×C32×C4—216no—
283C2×C32×C4—28no—
284C2×C32×C4—22no—
285C2×C32×C4—24no—
286C2×C32×C4—24no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—31no—
290C2×C32×C4—62no—
291C2×C32×C4C22×D314yes—
292C2×C32×C4C22×D314yes—
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295#638—22no—
296#638—62no—
297#638—62no—
298#638—68no—
299#638—62no—
300#638—68no—
301#638—616no—
302#638—616no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—31no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—34no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—64no—
309C2×C3⋊Dic3—62no—
310C2×C3⋊Dic3C22×D311yescharacteristic
311C2×C3⋊Dic3C22×D311yescharacteristic
312C2×C3⋊Dic3C22×D311yescharacteristic
313C4⋊(C3⋊D3)—62no—
314C4⋊(C3⋊D3)—68no—
315C4⋊(C3⋊D3)—616no—
316C4⋊(C3⋊D3)—62no—
317C4×C3⋊D3—22no—
318C4×C3⋊D3—34no—
319C4×C3⋊D3—316no—
320C4×C3⋊D3—616no—
321C4×C3⋊D3—62no—
322C4×C3⋊D3—62no—
323C4×C3⋊D3—616no—
324C4×C3⋊D3—68no—
325C4×C3⋊D3—62no—
326#634—62no—
327#634—68no—
328#634—616no—
329C3×#67—28no—
330C3×#67—68no—
331C2×C3×Dic3—34no—
332C2×C3×Dic3—34no—
333C2×C3×Dic3—34no—
334C2×C3×Dic3C22×D314yes—
335C2×C3×Dic3C22×D314yes—
336C2×C3×Dic3C22×D314yes—
337C3×C4×D3—28no—
338C3×C4×D3—68no—
339#626—68no—
340#626—68no—
341#624—68no—
342D3×Dic3—68no—
343D3×Dic3—68no—
344#525—271noSylow
345C2×C33—41no—
346C2×C33C22×D411yescharacteristic
347C2×C33C2×#4111yescharacteristic
348C2×C33C2×#4111yescharacteristic
349C3⋊(C3⋊D3)—22no—
350C3⋊(C3⋊D3)—41no—
351C3×C3⋊D3—22no—
352C32×D3—22no—
353C23×D3—94no—
354C23×D3—91no—
355C2×C3×D4—34no—
356C2×C3×D4—91no—
357C22×C3×C4—24no—
358C22×C3×C4—34no—
359C22×C3×C4—91no—
360C22×C3×C4D3214yescomplemented
361C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
362C2×#67—34no—
363C2×#67—94no—
364C2×#67—94no—
365C2×#67—94no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—184no—
370C2×#67—184no—
371C2×#67C2×C3⋊D311yescharacteristic
372C22×Dic3—94no—
373C22×Dic3—91no—
374#235—1816no—
375#235—184no—
376#235—1832no—
377C2×D12—94no—
378C2×D12—91no—
379C2×D12—94no—
380C2×D12—91no—
381C2×D12—184no—
382C2×C4×D3—34no—
383C2×C4×D3—94no—
384C2×C4×D3—91no—
385C2×C4×D3—94no—
386C2×C4×D3—94no—
387C2×C4×D3—91no—
388C2×C4×D3—94no—
389C2×C4×D3—91no—
390C2×C4×D3—91no—
391C2×C4×D3—184no—
392C2×C4×D3—184no—
393C2×C4×D3—184no—
394C2×C4×D3—1816no—
395C2×C4×D3C2×C3⋊D311yescharacteristic
396C2×Dic6—94no—
397C2×Dic6—91no—
398C2×Dic6—184no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4—91no—
401C3×C22⋊C4—34no—
402C3×C22⋊C4—34no—
403C3×C22⋊C4—91no—
404C3×C22⋊C4—91no—
405C3×C42—34no—
406C3×C42—91no—
407#217—34no—
408#217—94no—
409#217—91no—
410#217C2×C3⋊D311yescharacteristic, complemented
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—94no—
413(C2×D3)⋊C4—94no—
414(C2×D3)⋊C4—94no—
415(C2×D3)⋊C4—94no—
416(C2×D3)⋊C4—94no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
423C4⋊Dic3—94no—
424C4⋊Dic3—91no—
425Dic3⋊C4—34no—
426Dic3⋊C4—94no—
427Dic3⋊C4—94no—
428Dic3⋊C4—94no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
433C4×Dic3—34no—
434C4×Dic3C2×C3⋊D311yescharacteristic, complemented
435C22×C32—28no—
436C22×C32—21no—
437C22×C32—24no—
438C22×C32—21no—
439C22×C32—21no—
440C22×C32—24no—
441C22×C32—24no—
442C22×C32—24no—
443C22×C32—32no—
444C22×C32—44no—
445C22×C32—44no—
446C22×C32—61no—
447C22×C32—61no—
448C22×C32C23×D314yes—
449C22×C32C23×D311yescharacteristic
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—32no—
453C2×C3⋊D3—38no—
454C2×C3⋊D3—68no—
455C2×C3⋊D3—68no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—68no—
459C2×C3⋊D3—61no—
460C2×C3⋊D3—64no—
461C2×C3⋊D3—61no—
462C2×C3⋊D3—61no—
463C2×C3⋊D3—64no—
464C2×C3⋊D3—64no—
465C2×C3⋊D3—64no—
466C2×C3⋊D3—64no—
467C2×C3⋊D3—124no—
468C2×C3⋊D3—124no—
469C2×C3⋊D3—124no—
470C2×C3⋊D3—124no—
471C2×C3⋊D3#23512yescomplemented
472C2×C3×D3—24no—
473C2×C3×D3—24no—
474C2×C3×D3—38no—
475C2×C3×D3—64no—
476C2×C3×D3—64no—
477C2×C3×D3#23518yescomplemented
478D32—632no—
479C32×C4—28no—
480C32×C4—24no—
481C32×C4—21no—
482C32×C4—28no—
483C32×C4—61no—
484C32×C4—61no—
485C32×C4—61no—
486C32×C4D3×D418yes—
487C32×C4D3×D412yes—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3⋊Dic3—21no—
491C3⋊Dic3—32no—
492C3⋊Dic3—38no—
493C3⋊Dic3—68no—
494C3⋊Dic3—68no—
495C3⋊Dic3—64no—
496C3⋊Dic3—61no—
497C3×Dic3—24no—
498C3×Dic3—24no—
499C3×Dic3—24no—
500C3×Dic3—64no—
501C3×Dic3—64no—
502C3×Dic3—64no—
503C2×#41—271no—
504C23×C4—271no—
505#123—271no—
506#123—271no—
507C22⋊Q8—271no—
508C22⋊Q8—271no—
509#121—271no—
510#121—271no—
511#120—271no—
512#120—271no—
513C4×D4—31no—
514C4×D4—91no—
515C4×D4—271no—
516C4×D4—271no—
517#117—271no—
518C33#52511yescharacteristic, complemented, Sylow
519C23×C3—24no—
520C23×C3—34no—
521C23×C3—91no—
522C23×C3C2×D3214yes—
523C23×C3C22×C3⋊D311yescharacteristic
524C22×D3—34no—
525C22×D3—94no—
526C22×D3—91no—
527C22×D3—94no—
528C22×D3—91no—
529C22×D3—184no—
530C22×D3—184no—
531C22×D3—182no—
532C22×D3—182no—
533C22×D3—188no—
534C22×D3—188no—
535C22×D3—188no—
536C22×D3—182no—
537C22×D3C22×C3⋊D311yescharacteristic
538C3×D4—68no—
539C3×D4—182no—
540C2×C3×C4—216no—
541C2×C3×C4—28no—
542C2×C3×C4—22no—
543C2×C3×C4—24no—
544C2×C3×C4—24no—
545C2×C3×C4—34no—
546C2×C3×C4—34no—
547C2×C3×C4—34no—
548C2×C3×C4—68no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—91no—
552C2×C3×C4—182no—
553C2×C3×C4C2×D3214yes—
554C2×C3×C4C2×D3214yes—
555C2×C3×C4C22×C3⋊D311yescharacteristic
556C2×C3×C4C22×C3⋊D311yescharacteristic
557#67—22no—
558#67—68no—
559#67—182no—
560#67—188no—
561#67—188no—
562#67—182no—
563#67—188no—
564#67—182no—
565#67—1816no—
566#67—1816no—
567C2×Dic3—34no—
568C2×Dic3—34no—
569C2×Dic3—34no—
570C2×Dic3—94no—
571C2×Dic3—91no—
572C2×Dic3—94no—
573C2×Dic3—91no—
574C2×Dic3—184no—
575C2×Dic3—184no—
576C2×Dic3—182no—
577C2×Dic3—188no—
578C2×Dic3C22×C3⋊D311yescharacteristic
579C2×Dic3C22×C3⋊D311yescharacteristic
580C2×Dic3C22×C3⋊D311yescharacteristic
581D12—188no—
582D12—182no—
583D12—1816no—
584D12—188no—
585D12—182no—
586C4×D3—22no—
587C4×D3—68no—
588C4×D3—916no—
589C4×D3—94no—
590C4×D3—1816no—
591C4×D3—182no—
592C4×D3—188no—
593C4×D3—188no—
594C4×D3—182no—
595C4×D3—1816no—
596C4×D3—188no—
597C4×D3—182no—
598Dic6—188no—
599Dic6—182no—
600Dic6—1816no—
601C2×C32—24no—
602C2×C32—24no—
603C2×C32—24no—
604C2×C32—48no—
605C2×C32—44no—
606C2×C32—41no—
607C2×C32—62no—
608C2×C32C2×#23514yes—
609C2×C32C2×#23511yescharacteristic
610C2×C32C2×D3×D414yes—
611C2×C32C2×D3×D411yescharacteristic
612C2×C32D3×#4114yes—
613C2×C32D3×#4111yescharacteristic
614C3⋊D3—22no—
615C3⋊D3—62no—
616C3⋊D3—68no—
617C3⋊D3—128no—
618C3⋊D3—128no—
619C3⋊D3—124no—
620C3⋊D3—121no—
621C3×D3—28no—
622C3×D3—68no—
623C24—271no—
624#41—544no—
625C2×Q8—271no—
626C2×D4—31no—
627C2×D4—91no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4—271no—
633C22×C4—31no—
634C22×C4—91no—
635C22×C4—271no—
636C22×C4—271no—
637C22×C4—271no—
638C22×C4—271no—
639C22×C4—271no—
640C22×C4—544no—
641C22×C4D3×C3⋊D311yescharacteristic, complemented
642C4⋊C4—31no—
643C4⋊C4—91no—
644C4⋊C4—271no—
645C4⋊C4—271no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C22⋊C4—31no—
649C22⋊C4—31no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C42—31no—
659C42—91no—
660C22×C3—28no—
661C22×C3—24no—
662C22×C3—24no—
663C22×C3—24no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—24no—
668C22×C3—38no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3—64no—
672C22×C3—64no—
673C22×C3—92no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3C22×D3214yes—
677C22×C3C23×C3⋊D311yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—38no—
681C2×D3—64no—
682C2×D3—64no—
683C2×D3—98no—
684C2×D3—92no—
685C2×D3—188no—
686C2×D3—188no—
687C2×D3—1832no—
688C2×D3—184no—
689C2×D3—184no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—188no—
693C2×D3—184no—
694C2×D3—184no—
695C2×D3—184no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—364no—
700C2×D3—364no—
701C2×D3—364no—
702C2×D3—364no—
703C2×D3#382812yescomplemented
704C3×C4—28no—
705C3×C4—24no—
706C3×C4—21no—
707C3×C4—28no—
708C3×C4—64no—
709C3×C4—64no—
710C3×C4—64no—
711C3×C4—181no—
712C3×C4—181no—
713C3×C4—181no—
714C3×C4#381118yes—
715C3×C4D4×C3⋊D312yes—
716Dic3—21no—
717Dic3—21no—
718Dic3—21no—
719Dic3—64no—
720Dic3—64no—
721Dic3—64no—
722Dic3—98no—
723Dic3—92no—
724Dic3—188no—
725Dic3—188no—
726Dic3—184no—
727Dic3—181no—
728C32—24no—
729C32#554714yescomplemented
730C32#554711yescharacteristic, complemented
731C23—31no—
732C23—91no—
733C23—271no—
734C23—271no—
735C23—542no—
736C23—542no—
737C23—542no—
738C23C2×D3×C3⋊D311yescharacteristic
739Q8—542no—
740D4—62no—
741D4—182no—
742D4—542no—
743D4—542no—
744D4—542no—
745D4—542no—
746D4—542no—
747C2×C4—22no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—31no—
751C2×C4—62no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—182no—
756C2×C4—271no—
757C2×C4—274no—
758C2×C4—271no—
759C2×C4—542no—
760C2×C4—542no—
761C2×C4—542no—
762C2×C4—542no—
763C2×C4C2×D3×C3⋊D311yescharacteristic
764C2×C4C2×D3×C3⋊D311yescharacteristic
765C2×C3—24no—
766C2×C3—24no—
767C2×C3—24no—
768C2×C3—48no—
769C2×C3—44no—
770C2×C3—41no—
771C2×C3—68no—
772C2×C3—182no—
773C2×C3D3×#23514yes—
774C2×C3D3×#23514yes—
775C2×C3C2×#381114yes—
776C2×C3C2×#382811yescharacteristic
777C2×C3C2×D4×C3⋊D311yescharacteristic
778C2×C3#41×C3⋊D311yescharacteristic
779D3—22no—
780D3—68no—
781D3—188no—
782D3—182no—
783D3—368no—
784D3—368no—
785D3—364no—
786D3—361no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—32no—
791C22—61no—
792C22—61no—
793C22—92no—
794C22—181no—
795C22—181no—
796C22—272no—
797C22—548no—
798C22—541no—
799C22—541no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22C22×D3×C3⋊D311yescharacteristic
804C4—21no—
805C4—61no—
806C4—61no—
807C4—61no—
808C4—181no—
809C4—181no—
810C4—181no—
811C4—272no—
812C4—541no—
813C4#8903912yes—
814C3—24no—
815C3#1059507614yescomplemented
816C3#1059601811yescharacteristic, complemented
817C2—41no—
818C2—62no—
819C2—182no—
820C2—542no—
821C2—1081no—
822C2D3×#382811yescharacteristic
823C2C3⋊D3×#23511yescharacteristic
824C2C2×#8903911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FrattiniC22C22×D3×C3⋊D3
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89076C2semidirect
2. C2×C4×D3×C3⋊D3C2semidirect
3. C3×C4×#638C2semidirect
4. C32×C4×#67C2semidirect
5. #11723643C2semidirect
6. #11723628C2semidirect
7. #11723624C2semidirect
8. #11723616C2semidirect
9. #11723542C2semidirect
10. C4×#6292C2semidirect
11. C4×#6291C2semidirect
12. #11723498C2semidirect
13. #11723497C2semidirect
14. #11723496C2semidirect
15. #11723452C2semidirect
19. C22×C33×C4C22semidirect
21. C2×#6312C22semidirect
25. C2×C4×C3⋊(C3⋊D3)C22semidirect
26. C2×#6308C22semidirect
37. C3×#3757C22semidirect
39. C3×#3750C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
41. C32×#217C22semidirect
43. C32×Dic3⋊C4C22semidirect
44. C32×C4×Dic3C22semidirect
45. #88807C22semidirect
46. #88806C22semidirect
47. #88806C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
64. C4×#638D3semidirect
74. C3×C4×#67D3semidirect
103. C4×C3⋊(C3⋊D3)D4semidirect
127. C22×C32×C4C2×D3semidirect
128. C22×C32×C4C2×D3semidirect
173. #3757C2×D3semidirect
184. #3750C2×D3semidirect
185. C4×C3⋊Dic3C2×D3semidirect
187. C3×#217C2×D3semidirect
191. C3×Dic3⋊C4C2×D3semidirect
193. C3×C4×Dic3C2×D3semidirect
216. C2×C3×C3⋊D3#41semidirect
219. C2×C32×D3#41semidirect
245. C4×#67C3⋊D3semidirect
360. C22×C3×C4D32semidirect
361. C22×C3×C4C2×C3⋊D3semidirect
410. #217C2×C3⋊D3semidirect
432. Dic3⋊C4C2×C3⋊D3semidirect
434. C4×Dic3C2×C3⋊D3semidirect
471. C2×C3⋊D3#235semidirect
477. C2×C3×D3#235semidirect
518. C33#525semidirect
641. C22×C4D3×C3⋊D3semidirect
703. C2×D3#3828semidirect
729. C32#5547semidirect
730. C32#5547semidirect
815. C3#10595076semidirect
816. C3#10596018semidirect

Maximal subgroups

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

subgroupindex
C2×#890762
C2×C4×D3×C3⋊D32
C3×C4×#6382
C32×C4×#672
#117236432
#117236282
#117236242
#117236162
#117235422
C4×#62922
C4×#62912
#117234982
#117234972
#117234962
#117234522
#105960183
#105950763