Finite Group Databasebeta

← #13177298

Subgroups — #13177298

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×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3C4×#6312C211yesmaximal, characteristic, complemented
4C32×C4×#67C211yesmaximal, characteristic, complemented
5#11723643C211yesmaximal, characteristic, complemented
6#11723623C211yesmaximal, characteristic, complemented
7#11723621C211yesmaximal, characteristic, complemented
8#11723615C211yesmaximal, characteristic, complemented
9#11723541C211yesmaximal, characteristic, complemented
10C4×#6292C211yesmaximal, characteristic, complemented
11C4×#6290C211yesmaximal, characteristic, complemented
12#11723489C211yesmaximal, characteristic, complemented
13#11723488C211yesmaximal, characteristic, complemented
14#11723487C211yesmaximal, characteristic, complemented
15#11723437C211yesmaximal, characteristic, complemented
16#10596018—31nomaximal
17#10595060—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C3×#3828—24no—
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×#634C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic
30C2×C32×C4×D3C2211yescharacteristic
31C2×#6292C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×#6289C2211yescharacteristic
34C2×Dic3×C3⋊D3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic
36C4×D3×C3⋊D3—24no—
37#88864C2211yescharacteristic, complemented
38#88859C2211yescharacteristic
39#88857C2211yescharacteristic, complemented
40C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44C32×C4×Dic3C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88807C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic
52#88803C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
55C2×#3828D311yescharacteristic, complemented
56C22×C4×C3⋊D3—31no—
57C2×C3×#235—34no—
58C2×C4×D32—34no—
59C32×C4×D4—31no—
60#64148—31no—
61#64146—31no—
62C4×#638—31no—
63C4×#638—31no—
64C4×#638—34no—
65C4×#638—64no—
66#64105—31no—
67#64103—31no—
68#64093—31no—
69#64092—31no—
70#64091—31no—
71#64087—31no—
72C4×C4⋊(C3⋊D3)—31no—
73#64081—31no—
74C3×C4×#67D314yescomplemented
75#63983—34no—
76#63970—34no—
77#63969—34no—
78#63958—34no—
79#63922—34no—
80C4×#626—34no—
81C4×#625—34no—
82#63888—34no—
83#63887—34no—
84#63884—34no—
85#63855—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
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—
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C4×C3⋊(C3⋊D3)—22no—
102C3×#638—22no—
103C3×#638—22no—
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C3×C4⋊(C3⋊D3)—22no—
107C3×C4×C3⋊D3—22no—
108C3×C4×C3⋊D3D414yescomplemented
109C3×#634—22no—
110C32×#67—22no—
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C32×C4×D3—22no—
115#6292—22no—
116#6290—22no—
117#6289—22no—
118Dic3×C3⋊D3—22no—
119D3×C3⋊Dic3—22no—
120#5828—91no—
121#5547—94no—
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—34no—
131C2×#638—31no—
132C2×#638—64no—
133C2×#638C2×D311yescharacteristic
134C2×#638C2×D311yescharacteristic, complemented
135C22×C3⋊Dic3—31no—
136#3828—24no—
137C2×C4⋊(C3⋊D3)—31no—
138C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—34no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3—64no—
144C2×C4×C3⋊D3—64no—
145C2×C4×C3⋊D3C2×D311yescharacteristic
146C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
147C2×#634C2×D311yescharacteristic, complemented
148C2×C3×#67—34no—
149C2×C3×#67—34no—
150C2×C3×#67C2×D314yes—
151C3×#235—616no—
152C2×C3×D12—34no—
153C2×C3×C4×D3—34no—
154C2×C3×C4×D3—34no—
155C2×C3×C4×D3C2×D314yes—
156C2×C3×Dic6—34no—
157C2×#626—34no—
158C2×#625—34no—
159C2×#624—34no—
160C2×D3×Dic3—34no—
161C2×D3×Dic3—34no—
162C4×D32—616no—
163C32×C4⋊C4—31no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C42—31no—
167#3757—31no—
168#3757—34no—
169#3757—31no—
170#3757—64no—
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—34no—
177#3752—31no—
178#3752—64no—
179C4⋊(C3⋊Dic3)—31no—
180#3750—31no—
181#3750—34no—
182#3750—31no—
183#3750—31no—
184#3750—31no—
185#3750—64no—
186C4×C3⋊Dic3—31no—
187C4×C3⋊Dic3—34no—
188C4×C3⋊Dic3—64no—
189C3×#217C2×D314yescomplemented
190C3×(C2×D3)⋊C4C2×D314yes—
191C3×Dic3⋊C4C2×D314yescomplemented
192C3×C4×Dic3C2×D314yescomplemented
193#3724—34no—
194Dic3⋊Dic3—34no—
195Dic3⋊Dic3—34no—
196Dic3⋊Dic3—34no—
197#3722—34no—
198(C2×D3)⋊Dic3—34no—
199(C2×D3)⋊Dic3—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33C2411yescharacteristic
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⋊D3—21no—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3C2×D412yes—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3#4112yescomplemented
219D3×C3⋊D3—28no—
220C33×C4—21no—
221C33×C4C2×D412yes—
222C3⋊(C3⋊Dic3)—21no—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)—21no—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3C2×D412yes—
227C32×Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C2×C3×#41—91no—
231C2×#235—34no—
232C22×C4×D3—94no—
233C22×C4×D3—91no—
234C3×C4×D4—34no—
235#946—91no—
236#946—91no—
237#939—94no—
238#938—91no—
239#938—91no—
240#937—94no—
241#937—91no—
242#937—91no—
243#935—91no—
244#935—91no—
245C4×#67—94no—
246C4×#67—94no—
247C4×#67—91no—
248C4×#67—91no—
249C4×#67—91no—
250C4×#67—184no—
251C4×#67C3⋊D311yescharacteristic, complemented
252#926—91no—
253#896—94no—
254#894—94no—
255#884—94no—
256#883—94no—
257#882—94no—
258#878—94no—
259C4×D12—94no—
260#872—94no—
261C23×C32—24no—
262C23×C32—31no—
263C23×C32C22×D314yes—
264C23×C32C22×D311yescharacteristic
265C22×C3⋊D3—31no—
266C22×C3⋊D3—34no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—62no—
269C22×C3⋊D3—62no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3×D3—34no—
274C22×C3×D3—34no—
275C22×C3×D3C22×D314yes—
276C2×D32—68no—
277C2×D32—68no—
278C2×D32—68no—
279C32×D4—62no—
280C2×C32×C4—22no—
281C2×C32×C4—24no—
282C2×C32×C4—24no—
283C2×C32×C4—28no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4—48no—
288C2×C32×C4—62no—
289C2×C32×C4C22×D314yes—
290C2×C32×C4C22×D314yes—
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293#638—22no—
294#638—22no—
295#638—62no—
296#638—62no—
297#638—68no—
298#638—616no—
299C2×C3⋊Dic3—31no—
300C2×C3⋊Dic3—31no—
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—34no—
303C2×C3⋊Dic3—34no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—64no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—62no—
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C4⋊(C3⋊D3)—22no—
312C4⋊(C3⋊D3)—62no—
313C4×C3⋊D3—22no—
314C4×C3⋊D3—62no—
315C4×C3⋊D3—62no—
316C4×C3⋊D3—62no—
317C4×C3⋊D3—68no—
318C4×C3⋊D3—128no—
319C4×C3⋊D3#6714yescomplemented
320#634—22no—
321C3×#67—28no—
322C3×#67—68no—
323C3×#67—68no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3C22×D314yes—
327C2×C3×Dic3C22×D314yes—
328C2×C3×Dic3C22×D314yes—
329C3×D12—68no—
330C3×C4×D3—28no—
331C3×C4×D3—316no—
332C3×C4×D3—68no—
333C3×Dic6—68no—
334#626—68no—
335#625—68no—
336#624—68no—
337D3×Dic3—68no—
338D3×Dic3—68no—
339#525—271noSylow
340C2×C33—41no—
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C3⋊(C3⋊D3)—22no—
345C3×C3⋊D3—22no—
346C3×C3⋊D3—41no—
347C32×D3—22no—
348C23×D3—94no—
349C23×D3—91no—
350C3×#41—184no—
351C2×C3×Q8—91no—
352C2×C3×D4—34no—
353C2×C3×D4—91no—
354C2×C3×D4—91no—
355C2×C3×D4—91no—
356C22×C3×C4—24no—
357C22×C3×C4—34no—
358C22×C3×C4—91no—
359C22×C3×C4—91no—
360C22×C3×C4D3214yescomplemented
361C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—94no—
365C2×#67—94no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—184no—
370C2×#67C2×C3⋊D311yescharacteristic
371C22×Dic3—94no—
372C22×Dic3—91no—
373#235—616no—
374C2×D12—34no—
375C2×D12—94no—
376C2×C4×D3—34no—
377C2×C4×D3—34no—
378C2×C4×D3—94no—
379C2×C4×D3—94no—
380C2×C4×D3—91no—
381C2×C4×D3—94no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—184no—
385C2×C4×D3—184no—
386C2×C4×D3—1816no—
387C2×C4×D3C2×C3⋊D311yescharacteristic
388C2×Dic6—34no—
389C3×C4⋊C4—34no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—34no—
392C3×C42—34no—
393#217—94no—
394#217—94no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—184no—
401#217C2×C3⋊D311yescharacteristic, complemented
402(C2×D3)⋊C4—94no—
403(C2×D3)⋊C4—94no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—94no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—94no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—184no—
412(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
413C4⋊Dic3—94no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416Dic3⋊C4—94no—
417Dic3⋊C4—94no—
418Dic3⋊C4—94no—
419Dic3⋊C4—94no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—184no—
424Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
425C4×Dic3—94no—
426C4×Dic3—91no—
427C4×Dic3—184no—
428C4×Dic3C2×C3⋊D311yescharacteristic, complemented
429C22×C32—28no—
430C22×C32—24no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—24no—
435C22×C32—24no—
436C22×C32—24no—
437C22×C32—32no—
438C22×C32—44no—
439C22×C32—44no—
440C22×C32—61no—
441C22×C32—61no—
442C22×C32C23×D314yes—
443C22×C32C23×D311yescharacteristic
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—32no—
450C2×C3⋊D3—38no—
451C2×C3⋊D3—68no—
452C2×C3⋊D3—68no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—64no—
456C2×C3⋊D3—64no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3C2×#6712yes—
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—38no—
463C2×C3×D3—64no—
464C2×C3×D3—64no—
465C2×C3×D3—64no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3#23518yescomplemented
469D32—632no—
470C32×C4—21no—
471C32×C4—28no—
472C32×C4—24no—
473C32×C4—44no—
474C32×C4—61no—
475C32×C4—61no—
476C32×C4—61no—
477C32×C4D3×D418yes—
478C32×C4C2×#6712yes—
479C3⋊Dic3—21no—
480C3⋊Dic3—68no—
481C3⋊Dic3—64no—
482C3⋊Dic3—61no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3⋊Dic3—64no—
486C3⋊Dic3—64no—
487C3⋊Dic3—124no—
488C3⋊Dic3—124no—
489C3⋊Dic3C2×#6712yes—
490C3×Dic3—24no—
491C3×Dic3—24no—
492C3×Dic3—24no—
493C3×Dic3—38no—
494C3×Dic3—64no—
495C2×#41—91no—
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—271no—
510C33#52511yescharacteristic, complemented, Sylow
511C23×C3—24no—
512C23×C3—34no—
513C23×C3—91no—
514C23×C3—91no—
515C23×C3C2×D3214yes—
516C23×C3C22×C3⋊D311yescharacteristic
517C22×D3—34no—
518C22×D3—34no—
519C22×D3—94no—
520C22×D3—91no—
521C22×D3—184no—
522C22×D3—182no—
523C22×D3—182no—
524C22×D3—188no—
525C22×D3—188no—
526C22×D3—188no—
527C22×D3—182no—
528C22×D3C22×C3⋊D311yescharacteristic
529C3×Q8—182no—
530C3×D4—68no—
531C3×D4—182no—
532C3×D4—182no—
533C3×D4—182no—
534C2×C3×C4—28no—
535C2×C3×C4—22no—
536C2×C3×C4—24no—
537C2×C3×C4—24no—
538C2×C3×C4—34no—
539C2×C3×C4—34no—
540C2×C3×C4—34no—
541C2×C3×C4—48no—
542C2×C3×C4—68no—
543C2×C3×C4—91no—
544C2×C3×C4—94no—
545C2×C3×C4—91no—
546C2×C3×C4—182no—
547C2×C3×C4C2×D3214yes—
548C2×C3×C4C2×D3214yes—
549C2×C3×C4C22×C3⋊D311yescharacteristic
550C2×C3×C4C22×C3⋊D311yescharacteristic
551#67—22no—
552#67—68no—
553#67—68no—
554#67—182no—
555#67—188no—
556#67—188no—
557#67—182no—
558#67—1816no—
559#67—182no—
560C2×Dic3—34no—
561C2×Dic3—34no—
562C2×Dic3—94no—
563C2×Dic3—94no—
564C2×Dic3—94no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—184no—
569C2×Dic3—184no—
570C2×Dic3—184no—
571C2×Dic3—182no—
572C2×Dic3—188no—
573C2×Dic3C22×C3⋊D311yescharacteristic
574C2×Dic3C22×C3⋊D311yescharacteristic
575C2×Dic3C22×C3⋊D311yescharacteristic
576D12—68no—
577D12—188no—
578C4×D3—22no—
579C4×D3—316no—
580C4×D3—68no—
581C4×D3—182no—
582C4×D3—188no—
583C4×D3—188no—
584C4×D3—182no—
585C4×D3—188no—
586C4×D3—182no—
587C4×D3—368no—
588Dic6—68no—
589C2×C32—24no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—48no—
593C2×C32—44no—
594C2×C32—41no—
595C2×C32—62no—
596C2×C32C2×#23514yes—
597C2×C32C2×D3×D414yes—
598C2×C32D3×#4114yes—
599C2×C32D3×#4111yescharacteristic
600C2×C32D3×#4111yescharacteristic
601C2×C32C22×#6711yescharacteristic
602C3⋊D3—22no—
603C3⋊D3—41no—
604C3⋊D3—62no—
605C3⋊D3—68no—
606C3⋊D3—128no—
607C3×D3—28no—
608C3×D3—68no—
609C3×D3—124no—
610C24—271no—
611#41—184no—
612C2×Q8—91no—
613C2×D4—31no—
614C2×D4—91no—
615C2×D4—91no—
616C2×D4—91no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C22×C4—31no—
621C22×C4—91no—
622C22×C4—91no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—544no—
628C22×C4D3×C3⋊D311yescharacteristic, complemented
629C4⋊C4—31no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—31no—
646C42—271no—
647C22×C3—28no—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—24no—
655C22×C3—38no—
656C22×C3—44no—
657C22×C3—44no—
658C22×C3—64no—
659C22×C3—64no—
660C22×C3—92no—
661C22×C3—181no—
662C22×C3—181no—
663C22×C3—181no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3C22×D3214yes—
667C22×C3C23×C3⋊D311yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—38no—
671C2×D3—64no—
672C2×D3—64no—
673C2×D3—64no—
674C2×D3—64no—
675C2×D3—64no—
676C2×D3—98no—
677C2×D3—92no—
678C2×D3—188no—
679C2×D3—188no—
680C2×D3—1832no—
681C2×D3—184no—
682C2×D3—184no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—364no—
686C2×D3—364no—
687C2×D3#382812yescomplemented
688C3×C4—24no—
689C3×C4—21no—
690C3×C4—28no—
691C3×C4—44no—
692C3×C4—64no—
693C3×C4—64no—
694C3×C4—64no—
695C3×C4—92no—
696C3×C4—181no—
697C3×C4D3×#6718yes—
698C3×C4D4×C3⋊D312yes—
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—38no—
703Dic3—64no—
704Dic3—188no—
705Dic3—184no—
706Dic3—184no—
707Dic3—184no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—364no—
712Dic3—364no—
713C32—24no—
714C32#554714yescomplemented
715C32#582811yescharacteristic, complemented
716C23—31no—
717C23—91no—
718C23—91no—
719C23—271no—
720C23—542no—
721C23—542no—
722C23—542no—
723C23C2×D3×C3⋊D311yescharacteristic
724Q8—182no—
725D4—62no—
726D4—182no—
727D4—182no—
728D4—182no—
729D4—542no—
730D4—542no—
731D4—542no—
732C2×C4—22no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—62no—
737C2×C4—91no—
738C2×C4—94no—
739C2×C4—91no—
740C2×C4—182no—
741C2×C4—271no—
742C2×C4—271no—
743C2×C4—271no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4—542no—
748C2×C4C2×D3×C3⋊D311yescharacteristic
749C2×C4C2×D3×C3⋊D311yescharacteristic
750C2×C3—24no—
751C2×C3—24no—
752C2×C3—24no—
753C2×C3—48no—
754C2×C3—41no—
755C2×C3—44no—
756C2×C3—68no—
757C2×C3—182no—
758C2×C3—361no—
759C2×C3D3×#23514yes—
760C2×C3#6430614yes—
761C2×C3C2×D3×#6714yes—
762C2×C3C2×#382811yescharacteristic
763C2×C3C2×D4×C3⋊D311yescharacteristic
764C2×C3#41×C3⋊D311yescharacteristic
765D3—22no—
766D3—68no—
767D3—124no—
768D3—182no—
769D3—188no—
770D3—368no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—32no—
775C22—61no—
776C22—61no—
777C22—92no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—272no—
784C22—548no—
785C22—541no—
786C22—541no—
787C22C22×D3×C3⋊D311yescharacteristic
788C4—21no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—92no—
793C4—181no—
794C4—541no—
795C4—541no—
796C4—541no—
797C4C3⋊D3×#6712yes—
798C3—24no—
799C3#1059506014yescomplemented
800C3#1059601811yescharacteristic, complemented
801C2—41no—
802C2—62no—
803C2—182no—
804C2—361no—
805C2—542no—
806C2D3×#382811yescharacteristic
807C2#1172457811yescharacteristic
808C2C2×C3⋊D3×#6711yescharacteristic
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×C3×#3828C2semidirect
2. C2×C4×D3×C3⋊D3C2semidirect
3. C4×#6312C2semidirect
4. C32×C4×#67C2semidirect
5. #11723643C2semidirect
6. #11723623C2semidirect
7. #11723621C2semidirect
8. #11723615C2semidirect
9. #11723541C2semidirect
10. C4×#6292C2semidirect
11. C4×#6290C2semidirect
12. #11723489C2semidirect
13. #11723488C2semidirect
14. #11723487C2semidirect
15. #11723437C2semidirect
19. C22×C33×C4C22semidirect
23. C2×C3×#638C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C3×#634C22semidirect
37. #88864C22semidirect
39. #88857C22semidirect
40. C4×C3⋊(C3⋊Dic3)C22semidirect
41. C32×#217C22semidirect
43. C32×Dic3⋊C4C22semidirect
44. C32×C4×Dic3C22semidirect
45. #88807C22semidirect
46. #88807C22semidirect
47. #88806C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
55. C2×#3828D3semidirect
74. C3×C4×#67D3semidirect
108. C3×C4×C3⋊D3D4semidirect
127. C22×C32×C4C2×D3semidirect
128. C22×C32×C4C2×D3semidirect
134. C2×#638C2×D3semidirect
146. C2×C4×C3⋊D3C2×D3semidirect
147. C2×#634C2×D3semidirect
189. C3×#217C2×D3semidirect
191. C3×Dic3⋊C4C2×D3semidirect
192. C3×C4×Dic3C2×D3semidirect
209. C2×C3⋊(C3⋊D3)#41semidirect
218. C2×C32×D3#41semidirect
251. C4×#67C3⋊D3semidirect
319. C4×C3⋊D3#67semidirect
360. C22×C3×C4D32semidirect
361. C22×C3×C4C2×C3⋊D3semidirect
401. #217C2×C3⋊D3semidirect
424. Dic3⋊C4C2×C3⋊D3semidirect
428. C4×Dic3C2×C3⋊D3semidirect
468. C2×C3×D3#235semidirect
510. C33#525semidirect
628. C22×C4D3×C3⋊D3semidirect
687. C2×D3#3828semidirect
714. C32#5547semidirect
715. C32#5828semidirect
799. C3#10595060semidirect
800. C3#10596018semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C4×D3×C3⋊D32
C4×#63122
C32×C4×#672
#117236432
#117236232
#117236212
#117236152
#117235412
C4×#62922
C4×#62902
#117234892
#117234882
#117234872
#117234372
#105960183
#105950603