Finite Group Databasebeta

← #13177510

Subgroups — #13177510

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3#11723980C211yesmaximal, characteristic, complemented
4C3×#64146C211yesmaximal, characteristic, complemented
5C32×#938C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723626C211yesmaximal, characteristic, complemented
8#11723624C211yesmaximal, characteristic, complemented
9C3⋊D3×#217C211yesmaximal, characteristic, complemented
10#11723614C211yesmaximal, characteristic, complemented
11#11723592C211yesmaximal, characteristic, complemented
12D3×#3752C211yesmaximal, characteristic, complemented
13#11723506C211yesmaximal, characteristic, complemented
14#11723502C211yesmaximal, characteristic, complemented
15#11723493C211yesmaximal, characteristic, complemented
16#10596081—31nomaximal
17#10595290—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×C4×D3C2211yescharacteristic, complemented
29C3⋊D3×#67—24no—
30C2×#6293C2211yescharacteristic, complemented
31C2×#6292C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic
34C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
35C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
36#89029—24no—
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic, complemented
39#88859C2211yescharacteristic, complemented
40#88857C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic
43C3×#3752C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic
52#88803C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×#3830—31no—
56C2×D4×C3⋊D3—31no—
57C2×D3×#67—34no—
58C2×#3805—34no—
59C32×#121—31no—
60#64148—31no—
61#64148—34no—
62#64148—64no—
63#64146—31no—
64#64146D311yescharacteristic, complemented
65#64144—31no—
66C4×#638—31no—
67C2×#3752—31no—
68#64105—31no—
69#64103—31no—
70#64094—31no—
71#64093—31no—
72#64090—31no—
73C22⋊C4×C3⋊D3—31no—
74C3×#938D314yescomplemented
75C3×#937—34no—
76#63983—34no—
77#67⋊Dic3—34no—
78#63971—34no—
79#63969—34no—
80D3×#217—34no—
81#63953—34no—
82D3×(C2×D3)⋊C4—34no—
83#63899—34no—
84#63890—34no—
85#63879—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—22no—
91C22×C3×C3⋊D3—41no—
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C33×D4—41no—
99C2×C33×C4C2311yescharacteristic
100#6312—22no—
101#6312—41no—
102C2×C3⋊(C3⋊Dic3)—22no—
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C3×#638—22no—
107C3×#638—22no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C32×#67—22no—
111C32×#67—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C32×C4×D3—41no—
116#6293—22no—
117#6292—22no—
118#6290D414yescomplemented
119Dic3×C3⋊D3—22no—
120Dic3×C3⋊D3—22no—
121Dic3×C3⋊D3—41no—
122D3×C3⋊Dic3—22no—
123#5610—94no—
124#5591—91no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—34no—
128C22×D32—34no—
129C2×C32×D4—24no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×C32×D4C2×D314yescomplemented
133C2×C32×D4C2×D311yescharacteristic, complemented
134C22×C32×C4—31no—
135C2×#638—31no—
136C2×#638—31no—
137C2×#638—34no—
138C2×#638—31no—
139C2×#638—34no—
140C2×#638—64no—
141C2×#638—64no—
142C2×#638C2×D311yescharacteristic
143C2×#638C2×D311yescharacteristic, complemented
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—34no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3—64no—
148#3830—64no—
149D4×C3⋊D3—64no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C4×C3⋊D3—31no—
154C2×#634—31no—
155C2×C3×#67—34no—
156C2×C3×#67—34no—
157C2×C3×#67C2×D314yes—
158C2×C3×#67C2×D314yescomplemented
159C2×C3×C4×D3C2×D314yescomplemented
160D3×#67—616no—
161C2×#627—34no—
162C2×#626—34no—
163C2×#625—34no—
164#3805—616no—
165C2×D3×Dic3—34no—
166C2×D3×Dic3—34no—
167C2×D3×Dic3—34no—
168C2×D3×Dic3—34no—
169C32×C4⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172#3757—31no—
173#3757—34no—
174#3757—31no—
175#3757—64no—
176#3757C2×D311yescharacteristic, complemented
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—34no—
181#3752—31no—
182#3752—31no—
183#3752—64no—
184#3752C2×D311yescharacteristic
185#3752C2×D311yescharacteristic, complemented
186#3750—31no—
187#3750—34no—
188#3750—31no—
189#3750—31no—
190#3750—64no—
191C4×C3⋊Dic3—31no—
192C3×#217—34no—
193C3×#217C2×D314yescomplemented
194C3×#217C2×D314yescomplemented
195C3×(C2×D3)⋊C4—34no—
196C3×(C2×D3)⋊C4—34no—
197C3×C4⋊Dic3C2×D314yescomplemented
198#3724—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201#3722—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3×C3⋊D3—21no—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—21no—
220C2×C3×C3⋊D3—44no—
221C2×C3×C3⋊D3C2×D412yes—
222C2×C3×C3⋊D3#4112yescomplemented
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3C2×D412yes—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)C2×D412yes—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×#67—91no—
237C2×#237—94no—
238C2×#237—91no—
239C2×D3×D4—94no—
240C3×#121—34no—
241C3×#120—91no—
242C2×#217—91no—
243#939—94no—
244#939—91no—
245#939—91no—
246#939—184no—
247#938C3⋊D311yescharacteristic, complemented
248#937—34no—
249#937—94no—
250#937—91no—
251#935—94no—
252D4×Dic3—91no—
253C4×#67—94no—
254C2×(C2×D3)⋊C4—94no—
255#896—94no—
256#894—94no—
257#886—91no—
258#885—94no—
259#885—91no—
260#884—94no—
261#883—91no—
262#67⋊C4—94no—
263#67⋊C4—91no—
264D3×C22⋊C4—94no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32—24no—
268C23×C32—24no—
269C23×C32—31no—
270C23×C32C22×D314yes—
271C23×C32C22×D314yes—
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—22no—
275C22×C3⋊D3—22no—
276C22×C3⋊D3—31no—
277C22×C3⋊D3—34no—
278C22×C3⋊D3—41no—
279C22×C3⋊D3—64no—
280C22×C3⋊D3—62no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—121no—
283C22×C3⋊D3C22×D311yescharacteristic
284C22×C3⋊D3C22×D311yescharacteristic
285C22×C3×D3—34no—
286C22×C3×D3—34no—
287C22×C3×D3—68no—
288C22×C3×D3—68no—
289C22×C3×D3—124no—
290C22×C3×D3C22×D314yes—
291C2×D32—68no—
292C2×D32—68no—
293C2×D32—124no—
294C32×D4—41no—
295C32×D4—44no—
296C32×D4—48no—
297C32×D4—62no—
298C32×D4—62no—
299C2×C32×C4—24no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303C2×C32×C4—121no—
304C2×C32×C4C22×D314yes—
305C2×C32×C4C22×D311yescharacteristic
306#638—22no—
307#638—22no—
308#638—34no—
309#638—62no—
310#638—68no—
311#638—128no—
312#638—121no—
313#638—124no—
314#638—128no—
315C2×C3⋊Dic3—31no—
316C2×C3⋊Dic3—31no—
317C2×C3⋊Dic3—31no—
318C2×C3⋊Dic3—34no—
319C2×C3⋊Dic3—34no—
320C2×C3⋊Dic3—34no—
321C2×C3⋊Dic3—64no—
322C2×C3⋊Dic3—64no—
323C2×C3⋊Dic3—64no—
324C2×C3⋊Dic3—62no—
325C2×C3⋊Dic3—62no—
326C2×C3⋊Dic3—68no—
327C2×C3⋊Dic3—128no—
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4⋊(C3⋊D3)—62no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—121no—
334#634—62no—
335C3×#67—28no—
336C3×#67—28no—
337C3×#67—68no—
338C3×#67—68no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3—34no—
341C2×C3×Dic3C22×D314yes—
342C2×C3×Dic3C22×D314yes—
343C2×C3×Dic3C22×D314yes—
344C3×C4×D3—44no—
345#627—68no—
346#626—68no—
347#625—316no—
348D3×Dic3—68no—
349D3×Dic3—68no—
350D3×Dic3—68no—
351D3×Dic3—124no—
352#546—271noSylow
353C2×C33—41no—
354C2×C33—41no—
355C2×C33C22×D411yescharacteristic
356C2×C33C2×#4111yescharacteristic
357C2×C33H(5,𝔽2)11yescharacteristic
358C3⋊(C3⋊D3)—41no—
359C3×C3⋊D3—22no—
360C3×C3⋊D3—22no—
361C32×D3—22no—
362C24×C3—91no—
363C23×D3—34no—
364C23×D3—94no—
365C23×D3—91no—
366C2×C3×D4—24no—
367C2×C3×D4—34no—
368C2×C3×D4—34no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C2×C3×D4D3214yescomplemented
372C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
373C22×C3×C4—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—94no—
377C2×#67—91no—
378C2×#67—94no—
379C2×#67—91no—
380C2×#67—94no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—184no—
384C2×#67—184no—
385C2×#67—184no—
386C2×#67C2×C3⋊D311yescharacteristic
387C2×#67C2×C3⋊D311yescharacteristic, complemented
388C22×Dic3—94no—
389C22×Dic3—94no—
390C22×Dic3—91no—
391C22×Dic3—91no—
392C22×Dic3—91no—
393C22×Dic3—91no—
394C22×Dic3—184no—
395#237—184no—
396#237—1816no—
397D3×D4—1816no—
398C2×D12—94no—
399C2×C4×D3—94no—
400C2×C4×D3—94no—
401C2×C4×D3—91no—
402C2×C4×D3—94no—
403C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
404C2×Dic6—94no—
405C2×Dic6—91no—
406C3×C4⋊C4—34no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412#217—34no—
413#217—94no—
414#217—94no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—184no—
419#217C2×C3⋊D311yescharacteristic, complemented
420#217C2×C3⋊D311yescharacteristic, complemented
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—94no—
426(C2×D3)⋊C4—94no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—94no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—184no—
433C4⋊Dic3—91no—
434C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
435Dic3⋊C4—94no—
436Dic3⋊C4—94no—
437Dic3⋊C4—94no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—184no—
441C4×Dic3—94no—
442C4×Dic3—91no—
443C22×C32—28no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—24no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—24no—
452C22×C32—24no—
453C22×C32—24no—
454C22×C32—24no—
455C22×C32—24no—
456C22×C32—24no—
457C22×C32—32no—
458C22×C32—44no—
459C22×C32—44no—
460C22×C32—44no—
461C22×C32—44no—
462C22×C32—44no—
463C22×C32—61no—
464C22×C32—61no—
465C22×C32C23×D314yes—
466C22×C32C23×D311yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—44no—
472C2×C3⋊D3—61no—
473C2×C3⋊D3—61no—
474C2×C3⋊D3—61no—
475C2×C3⋊D3—64no—
476C2×C3⋊D3—64no—
477C2×C3⋊D3—64no—
478C2×C3⋊D3—124no—
479C2×C3⋊D3—124no—
480C2×C3⋊D3—124no—
481C2×C3⋊D3—124no—
482C2×C3⋊D3D3×D412yes—
483C2×C3⋊D3#23712yescomplemented
484C2×C3×D3—24no—
485C2×C3×D3—24no—
486C2×C3×D3—38no—
487C2×C3×D3—38no—
488C2×C3×D3—64no—
489C2×C3×D3—64no—
490C2×C3×D3—64no—
491C2×C3×D3—64no—
492C2×C3×D3—1216no—
493C2×C3×D3D3×D418yes—
494D32—1216no—
495C32×C4—21no—
496C32×C4—24no—
497C32×C4—44no—
498C32×C4—61no—
499C32×C4—61no—
500C32×C4—61no—
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—32no—
504C3⋊Dic3—38no—
505C3⋊Dic3—68no—
506C3⋊Dic3—61no—
507C3⋊Dic3—61no—
508C3⋊Dic3—64no—
509C3⋊Dic3—64no—
510C3⋊Dic3—124no—
511C3⋊Dic3—124no—
512C3×Dic3—24no—
513C3×Dic3—24no—
514C3×Dic3—24no—
515C3×Dic3—64no—
516C3×Dic3—64no—
517C2×#41—271no—
518C22×D4—271no—
519#124—271no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—31no—
524#121—271no—
525#121—271no—
526#120—91no—
527#120—271no—
528C4×D4—271no—
529C4×D4—271no—
530C2×C22⋊C4—271no—
531C2×C22⋊C4—271no—
532C33#54611yescharacteristic, complemented, Sylow
533C23×C3—24no—
534C23×C3—24no—
535C23×C3—34no—
536C23×C3—91no—
537C23×C3—91no—
538C23×C3—182no—
539C23×C3—182no—
540C23×C3—361no—
541C23×C3C2×D3214yes—
542C23×C3C2×D3214yes—
543C23×C3C22×C3⋊D311yescharacteristic
544C23×C3C22×C3⋊D311yescharacteristic
545C22×D3—34no—
546C22×D3—34no—
547C22×D3—68no—
548C22×D3—68no—
549C22×D3—94no—
550C22×D3—91no—
551C22×D3—124no—
552C22×D3—184no—
553C22×D3—182no—
554C22×D3—188no—
555C22×D3—188no—
556C22×D3—182no—
557C22×D3—361no—
558C22×D3—364no—
559C22×D3C22×C3⋊D311yescharacteristic
560C3×D4—44no—
561C3×D4—41no—
562C3×D4—48no—
563C3×D4—68no—
564C3×D4—68no—
565C3×D4—182no—
566C3×D4—182no—
567C2×C3×C4—24no—
568C2×C3×C4—34no—
569C2×C3×C4—34no—
570C2×C3×C4—34no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—124no—
574C2×C3×C4C2×D3214yes—
575C2×C3×C4C22×C3⋊D311yescharacteristic
576#67—22no—
577#67—22no—
578#67—68no—
579#67—68no—
580#67—916no—
581#67—94no—
582#67—182no—
583#67—182no—
584#67—188no—
585#67—368no—
586#67—364no—
587#67—361no—
588#67—368no—
589C2×Dic3—34no—
590C2×Dic3—34no—
591C2×Dic3—94no—
592C2×Dic3—91no—
593C2×Dic3—94no—
594C2×Dic3—94no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—184no—
598C2×Dic3—184no—
599C2×Dic3—184no—
600C2×Dic3—182no—
601C2×Dic3—182no—
602C2×Dic3—188no—
603C2×Dic3—182no—
604C2×Dic3—188no—
605C2×Dic3—368no—
606C2×Dic3—361no—
607C2×Dic3C22×C3⋊D311yescharacteristic
608C2×Dic3C22×C3⋊D311yescharacteristic
609C2×Dic3C22×C3⋊D311yescharacteristic
610D12—188no—
611C4×D3—41no—
612C4×D3—188no—
613C4×D3—188no—
614C4×D3—182no—
615C4×D3—364no—
616Dic6—182no—
617Dic6—188no—
618C2×C32—24no—
619C2×C32—24no—
620C2×C32—24no—
621C2×C32—48no—
622C2×C32—41no—
623C2×C32—41no—
624C2×C32—44no—
625C2×C32—44no—
626C2×C32—62no—
627C2×C32—84no—
628C2×C32C2×D3×D414yes—
629C2×C32C2×D3×D411yescharacteristic
630C2×C32C2×#23711yescharacteristic
631C2×C32#100414yes—
632C2×C32#100411yescharacteristic
633C2×C32D3×#4114yes—
634C3⋊D3—22no—
635C3⋊D3—22no—
636C3⋊D3—121no—
637C3⋊D3—124no—
638C3⋊D3—244no—
639C3×D3—28no—
640C3×D3—68no—
641C3×D3—68no—
642C24—91no—
643C24—271no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—91no—
649C2×D4—91no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—544no—
655C2×D4D3×C3⋊D311yescharacteristic, complemented
656C22×C4—31no—
657C22×C4—271no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C4⋊C4—31no—
663C4⋊C4—271no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—91no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C42—271no—
679C22×C3—28no—
680C22×C3—24no—
681C22×C3—24no—
682C22×C3—24no—
683C22×C3—24no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—24no—
693C22×C3—38no—
694C22×C3—44no—
695C22×C3—44no—
696C22×C3—44no—
697C22×C3—44no—
698C22×C3—44no—
699C22×C3—64no—
700C22×C3—64no—
701C22×C3—92no—
702C22×C3—92no—
703C22×C3—181no—
704C22×C3—181no—
705C22×C3—181no—
706C22×C3—181no—
707C22×C3—364no—
708C22×C3C22×D3214yes—
709C22×C3C23×C3⋊D311yescharacteristic
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—38no—
713C2×D3—38no—
714C2×D3—64no—
715C2×D3—64no—
716C2×D3—64no—
717C2×D3—64no—
718C2×D3—1216no—
719C2×D3—184no—
720C2×D3—184no—
721C2×D3—184no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—364no—
726C2×D3—364no—
727C2×D3—364no—
728C2×D3—364no—
729C2×D3—3616no—
730C2×D3D4×C3⋊D312yes—
731C3×C4—24no—
732C3×C4—21no—
733C3×C4—44no—
734C3×C4—64no—
735C3×C4—64no—
736C3×C4—64no—
737C3×C4—181no—
738C3×C4—181no—
739Dic3—21no—
740Dic3—21no—
741Dic3—21no—
742Dic3—64no—
743Dic3—64no—
744Dic3—98no—
745Dic3—92no—
746Dic3—188no—
747Dic3—184no—
748Dic3—184no—
749Dic3—181no—
750Dic3—181no—
751Dic3—364no—
752Dic3—364no—
753C32—24no—
754C32#559111yescharacteristic, complemented
755C32#561014yescomplemented
756C23—31no—
757C23—91no—
758C23—91no—
759C23—182no—
760C23—182no—
761C23—271no—
762C23—361no—
763C23—542no—
764C23—542no—
765C23—1081no—
766C23C2×D3×C3⋊D311yescharacteristic
767C23C2×D3×C3⋊D311yescharacteristic
768Q8—542no—
769D4—41no—
770D4—62no—
771D4—62no—
772D4—182no—
773D4—182no—
774D4—274no—
775D4—542no—
776D4—542no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—91no—
782C2×C4—91no—
783C2×C4—121no—
784C2×C4—271no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—542no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—542no—
791C2×C4—1081no—
792C2×C4C2×D3×C3⋊D311yescharacteristic
793C2×C3—24no—
794C2×C3—24no—
795C2×C3—24no—
796C2×C3—48no—
797C2×C3—44no—
798C2×C3—44no—
799C2×C3—41no—
800C2×C3—41no—
801C2×C3—68no—
802C2×C3—84no—
803C2×C3—182no—
804C2×C3—182no—
805C2×C3D32×D414yes—
806C2×C3D3×#23714yes—
807C2×C3#6433014yes—
808C2×C3C2×D4×C3⋊D311yescharacteristic
809C2×C3#6436111yescharacteristic
810C2×C3#41×C3⋊D311yescharacteristic
811D3—22no—
812D3—68no—
813D3—68no—
814D3—364no—
815D3—361no—
816D3—724no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—32no—
824C22—61no—
825C22—61no—
826C22—92no—
827C22—92no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—364no—
833C22—541no—
834C22—541no—
835C22—541no—
836C22—1084no—
837C22C22×D3×C3⋊D311yescharacteristic
838C4—21no—
839C4—61no—
840C4—61no—
841C4—61no—
842C4—181no—
843C4—181no—
844C4—272no—
845C4—541no—
846C4—541no—
847C3—24no—
848C3#1059529014yescomplemented
849C3#1059608111yescharacteristic, complemented
850C2—41no—
851C2—41no—
852C2—62no—
853C2—182no—
854C2—182no—
855C2—1081no—
856C2D3×D4×C3⋊D311yescharacteristic
857C2C3⋊D3×#23711yescharacteristic
858C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×#89029C2semidirect
3. #11723980C2semidirect
4. C3×#64146C2semidirect
5. C32×#938C2semidirect
6. #11723643C2semidirect
7. #11723626C2semidirect
8. #11723624C2semidirect
9. C3⋊D3×#217C2semidirect
10. #11723614C2semidirect
11. #11723592C2semidirect
12. D3×#3752C2semidirect
13. #11723506C2semidirect
14. #11723502C2semidirect
15. #11723493C2semidirect
20. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
23. C22×C3⋊(C3⋊Dic3)C22semidirect
25. C2×C3×#638C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×C4×D3C22semidirect
30. C2×#6293C22semidirect
34. C2×Dic3×C3⋊D3C22semidirect
35. C2×Dic3×C3⋊D3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. #88864C22semidirect
39. #88859C22semidirect
40. #88857C22semidirect
41. C3×#3757C22semidirect
43. C3×#3752C22semidirect
44. C32×#217C22semidirect
45. C32×#217C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
64. #64146D3semidirect
74. C3×#938D3semidirect
118. #6290D4semidirect
132. C2×C32×D4C2×D3semidirect
133. C2×C32×D4C2×D3semidirect
143. C2×#638C2×D3semidirect
158. C2×C3×#67C2×D3semidirect
159. C2×C3×C4×D3C2×D3semidirect
176. #3757C2×D3semidirect
185. #3752C2×D3semidirect
193. C3×#217C2×D3semidirect
194. C3×#217C2×D3semidirect
197. C3×C4⋊Dic3C2×D3semidirect
222. C2×C3×C3⋊D3#41semidirect
247. #938C3⋊D3semidirect
371. C2×C3×D4D32semidirect
372. C2×C3×D4C2×C3⋊D3semidirect
387. C2×#67C2×C3⋊D3semidirect
403. C2×C4×D3C2×C3⋊D3semidirect
419. #217C2×C3⋊D3semidirect
420. #217C2×C3⋊D3semidirect
434. C4⋊Dic3C2×C3⋊D3semidirect
483. C2×C3⋊D3#237semidirect
532. C33#546semidirect
655. C2×D4D3×C3⋊D3semidirect
754. C32#5591semidirect
755. C32#5610semidirect
848. C3#10595290semidirect
849. C3#10596081semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#890292
#117239802
C3×#641462
C32×#9382
#117236432
#117236262
#117236242
C3⋊D3×#2172
#117236142
#117235922
D3×#37522
#117235062
#117235022
#117234932
#105960813
#105952903