Finite Group Databasebeta

← #13168042

Subgroups — #13168042

Order 1728.

1688 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89021C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3#11723691C211yesmaximal, characteristic, complemented
4#11723429C211yesmaximal, characteristic, complemented
5#11723426C211yesmaximal, characteristic, complemented
6C3×#63908C211yesmaximal, characteristic, complemented
7C3×C4×#625C211yesmaximal, characteristic, complemented
8#11722991C212yesmaximal, complemented
9#11722965C212yesmaximal, complemented
10#11722946C212yesmaximal, complemented
11#11722902C212yesmaximal, complemented
12#10595228—31nomaximal
13#10595078—31nomaximal
14#10594886—31nomaximal
15C22×C3×D32C2212yes—
16C2×#6308C2211yescharacteristic, complemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C32×D12C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic, complemented
21C2×#6294C2212yescomplemented
22C2×#6290C2212yescomplemented
23C2×Dic3×C3⋊D3C2212yescomplemented
24#89021—24no—
25C2×C3×#626C2212yes—
26C2×C3×#625C2211yescharacteristic
27C2×C3×#625C2212yescomplemented
28C3×D3×D12—24no—
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
31#88814C2212yescomplemented
32#88807C2212yescomplemented
33(C2×D3)⋊(C3⋊Dic3)C2212yes—
34(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
35(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
36C3×#3724C2211yescharacteristic, complemented
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
40C2×#3828—31no—
41C2×C3×D3×D4—31no—
42C22×C3×D12—31no—
43C2×D3×D12D311yescharacteristic, complemented
44C2×#3795—31no—
45C2×#3795—31no—
46C2×#3795—61no—
47#64145—31no—
48#64133—31no—
49C3×#938—31no—
50C3×#930—31no—
51C3×C4×#67—31no—
52C3×C4×#67—31no—
53#63983—32no—
54#63976—32no—
55#63976—32no—
56#63970—32no—
57#63969—32no—
58D3×#217—32no—
59D3×#217—32no—
60#63958—32no—
61#63921—32no—
62#63908D311yescharacteristic, complemented
63C4×#625D311yescharacteristic, complemented
64#63898—31no—
65#63894—31no—
66Dic3×D12—31no—
67#63885—32no—
68#63884—32no—
69#63860—31no—
70#63860—31no—
71#63860—61no—
72#63857—31no—
73#63857—31no—
74#63857—61no—
75#63853—32no—
76C22×C3×C3⋊D3C2312yes—
77C22×C32×D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C22×C32×D3C2311yescharacteristic
80C2×C3×D32—24no—
81C2×C3×D32—24no—
82C2×C3×D32—42no—
83C2×C33×C4C2311yescharacteristic
84C2×C3⋊(C3⋊Dic3)C2312yes—
85#6308—22no—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2312yes—
89C3×C4⋊(C3⋊D3)D414yescomplemented
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2311yescharacteristic
92C32×D12—22no—
93C32×C4×D3—22no—
94C32×C4×D3—22no—
95#6294—42no—
96#6290—24no—
97Dic3×C3⋊D3—24no—
98C3×#626—24no—
99C3×#625—22no—
100C3×#625—42no—
101#5806—91no—
102#5612—91no—
103#5550—91no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C2×D312yes—
107C2×C32×D4—31no—
108C22×C32×C4—31no—
109C22×C32×C4—31no—
110C2×#638—32no—
111#3828—64no—
112C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
113C2×C4×C3⋊D3—32no—
114C2×#634—31no—
115C2×#634—31no—
116C2×#634—31no—
117C2×#634—61no—
118C2×#634—61no—
119C2×#634—61no—
120C2×#634—121no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67—32no—
124C2×C3×#67—32no—
125C2×C3×#67—32no—
126C3×D3×D4—64no—
127C2×C3×D12—21no—
128C2×C3×D12—31no—
129C2×C3×D12—31no—
130C2×C3×D12—32no—
131C2×C3×D12—64no—
132C2×C3×D12—61no—
133C2×C3×D12C2×D311yescharacteristic
134C2×C3×D12C2×D311yescharacteristic
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3—21no—
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×C3×C4×D3C2×D311yescharacteristic
139C2×C3×C4×D3C2×D311yescharacteristic, complemented
140C2×C3×C4×D3C2×D311yescharacteristic, complemented
141C2×#626C2×D312yes—
142C2×#625—32no—
143C2×#625—32no—
144C2×#625—62no—
145C2×#625C2×D311yescharacteristic
146C2×#625C2×D312yescomplemented
147C2×#624—32no—
148C2×D3×Dic3—32no—
149C2×D3×Dic3—32no—
150C2×D3×Dic3—32no—
151C2×D3×Dic3—32no—
152C2×D3×Dic3—62no—
153D3×D12—24no—
154#3795—64no—
155#3795—64no—
156#3795—68no—
157#3757—32no—
158#3757—32no—
159#3757—32no—
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
161#3750—32no—
162C4×C3⋊Dic3C2×D311yescharacteristic, complemented
163C3×#217—31no—
164C3×#217—31no—
165C3×#217—32no—
166C3×(C2×D3)⋊C4—31no—
167C3×(C2×D3)⋊C4—31no—
168C3×(C2×D3)⋊C4—32no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—61no—
172C3×Dic3⋊C4—31no—
173C3×Dic3⋊C4—31no—
174C3×C4×Dic3—31no—
175C3×C4×Dic3—31no—
176C3×C4×Dic3—61no—
177#3724C2×D311yescharacteristic, complemented
178Dic3⋊Dic3—32no—
179Dic3⋊Dic3—32no—
180Dic3⋊Dic3—62no—
181#3722—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—62no—
191(C2×D3)⋊Dic3—62no—
192(C2×D3)⋊Dic3—62no—
193(C2×D3)⋊Dic3C2×D311yescharacteristic
194(C2×D3)⋊Dic3C2×D312yescomplemented
195(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
196C22×C33C2411yescharacteristic
197C2×C3×C3⋊D3—22no—
198C2×C3×C3⋊D3—22no—
199C2×C3×C3⋊D3C2×D414yes—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C2×C32×D3—22no—
204C2×C32×D3—21no—
205C2×C32×D3—22no—
206C2×C32×D3—21no—
207C2×C32×D3—22no—
208C2×C32×D3#4112yescomplemented
209C3×D32—48no—
210C33×C4C2×D412yes—
211C3⋊(C3⋊Dic3)—22no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3—22no—
214C3×C3⋊Dic3—21no—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C22×C3×D4—91no—
218C2×#237—91no—
219C2×D3×D4—31no—
220C2×#235—91no—
221C2×#235—91no—
222C2×#235—181no—
223C22×D12—31no—
224C3×#121—91no—
225C3×C4×D4—91no—
226#953—92no—
227C2×#217—92no—
228#939—92no—
229#938—31no—
230#938—92no—
231#937—92no—
232#937—92no—
233#936—91no—
234#936—91no—
235#936—181no—
236#935—92no—
237D4×Dic3—91no—
238#930—31no—
239C4×#67—31no—
240C4×#67—31no—
241#924—91no—
242#924—91no—
243#924—181no—
244#897—91no—
245#894—92no—
246#893—91no—
247#884—92no—
248#883—92no—
249D3×C22⋊C4—92no—
250D3×C22⋊C4—92no—
251#875—91no—
252C4×D12—91no—
253C23×C32—31no—
254C23×C32—32no—
255C23×C32—31no—
256C22×C3⋊D3C22×D312yes—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—22no—
260C22×C3×D3—32no—
261C22×C3×D3—32no—
262C22×C3×D3—62no—
263C22×C3×D3—64no—
264C22×C3×D3—64no—
265C22×C3×D3—64no—
266C22×C3×D3—64no—
267C22×C3×D3—122no—
268C22×C3×D3—122no—
269C22×C3×D3C22×D312yes—
270C22×C3×D3C22×D312yes—
271C22×C3×D3C22×D311yescharacteristic
272C22×C3×D3C22×D311yescharacteristic
273C22×C3×D3C22×D311yescharacteristic
274C22×C3×D3C22×D311yescharacteristic
275C2×D32—24no—
276C2×D32—24no—
277C2×D32—42no—
278C32×D4—62no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—31no—
283C2×C32×C4—31no—
284C2×C32×C4—41no—
285C2×C32×C4—62no—
286C2×C32×C4—62no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290#638—64no—
291C2×C3⋊Dic3—32no—
292C2×C3⋊Dic3—32no—
293C2×C3⋊Dic3—32no—
294C2×C3⋊Dic3—62no—
295C2×C3⋊Dic3—62no—
296C2×C3⋊Dic3—62no—
297C2×C3⋊Dic3—122no—
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D312yes—
300C2×C3⋊Dic3C22×D311yescharacteristic
301C4⋊(C3⋊D3)#6714yescomplemented
302C4×C3⋊D3—64no—
303#634—62no—
304#634—64no—
305#634—62no—
306#634—62no—
307#634—122no—
308#634—122no—
309#634—124no—
310C3×#67—64no—
311C3×#67—62no—
312C3×#67—62no—
313C3×#67—122no—
314C3×#67—122no—
315C2×C3×Dic3—21no—
316C2×C3×Dic3—21no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—32no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—32no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—62no—
326C2×C3×Dic3C22×D311yescharacteristic
327C2×C3×Dic3C22×D311yescharacteristic
328C2×C3×Dic3C22×D311yescharacteristic
329C2×C3×Dic3C22×D311yescharacteristic
330C3×D12—22no—
331C3×D12—22no—
332C3×D12—34no—
333C3×D12—34no—
334C3×D12—42no—
335C3×D12—64no—
336C3×D12—64no—
337C3×C4×D3—24no—
338C3×C4×D3—22no—
339C3×C4×D3—22no—
340C3×C4×D3—22no—
341C3×C4×D3—22no—
342C3×C4×D3—42no—
343#626—24no—
344#625—22no—
345#625—42no—
346#625—64no—
347#625—64no—
348#625—68no—
349#624—122no—
350D3×Dic3—64no—
351D3×Dic3—64no—
352D3×Dic3—68no—
353D3×Dic3—122no—
354D3×Dic3—122no—
355#546—271noSylow
356C2×C33C22×D411yescharacteristic
357C2×C33C2×#4111yescharacteristic
358C2×C33H(5,𝔽2)11yescharacteristic
359C3×C3⋊D3—24no—
360C32×D3—22no—
361C32×D3—41no—
362C32×D3—42no—
363C24×C3—92no—
364C23×D3—32no—
365C23×D3—32no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—61no—
369C2×C3×D4—92no—
370C2×C3×D4—91no—
371C2×C3×D4—92no—
372C2×C3×D4—91no—
373C2×C3×D4—184no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—61no—
379C22×C3×C4—61no—
380C2×#67—31no—
381C2×#67—31no—
382C2×#67—32no—
383C2×#67—32no—
384C2×#67—32no—
385C2×#67—92no—
386C2×#67—92no—
387C2×#67—92no—
388C2×#67—182no—
389C22×Dic3—92no—
390C22×Dic3—92no—
391#237—184no—
392D3×D4—64no—
393#235—184no—
394#235—184no—
395#235—188no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—32no—
399C2×D12—61no—
400C2×D12—64no—
401C2×D12D3211yescharacteristic
402C2×C4×D3—92no—
403C2×C4×D3—92no—
404C2×C4×D3—92no—
405C2×C4×D3—92no—
406C2×C4×D3—182no—
407C2×C4×D3D3211yescharacteristic
408C2×C4×D3D3211yescharacteristic, complemented
409C2×Dic6—91no—
410C2×Dic6—91no—
411C2×Dic6—91no—
412C2×Dic6—181no—
413C2×Dic6—181no—
414C2×Dic6—181no—
415C2×Dic6—361no—
416C3×C4⋊C4—91no—
417C3×C4⋊C4—91no—
418C3×C22⋊C4—91no—
419C3×C22⋊C4—92no—
420C3×C22⋊C4—91no—
421C3×C42—91no—
422#217—31no—
423#217—31no—
424#217—32no—
425#217—92no—
426#217—92no—
427#217—92no—
428#217—92no—
429#217—92no—
430#217—92no—
431#217—92no—
432#217—182no—
433#217—182no—
434#217—182no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—32no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—92no—
439(C2×D3)⋊C4—92no—
440(C2×D3)⋊C4—92no—
441(C2×D3)⋊C4—92no—
442(C2×D3)⋊C4—92no—
443C4⋊Dic3—31no—
444C4⋊Dic3—31no—
445C4⋊Dic3—61no—
446C4⋊Dic3—92no—
447Dic3⋊C4—31no—
448Dic3⋊C4—31no—
449Dic3⋊C4—92no—
450Dic3⋊C4—92no—
451Dic3⋊C4—182no—
452C4×Dic3—31no—
453C4×Dic3—31no—
454C4×Dic3—61no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—32no—
459C22×C32—41no—
460C22×C32—61no—
461C22×C32—61no—
462C22×C32—61no—
463C22×C32—62no—
464C22×C32—62no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—62no—
468C22×C32C23×D311yescharacteristic
469C22×C32C23×D311yescharacteristic
470C22×C32C23×D311yescharacteristic
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3C2×#6714yes—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—22no—
479C2×C3×D3—21no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—21no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—21no—
488C2×C3×D3—22no—
489C2×C3×D3—21no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—34no—
493C2×C3×D3—34no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—42no—
499C2×C3×D3—42no—
500C2×C3×D3—42no—
501C2×C3×D3—64no—
502C2×C3×D3—62no—
503C2×C3×D3—62no—
504C2×C3×D3—62no—
505C2×C3×D3—62no—
506C2×C3×D3—122no—
507C2×C3×D3—122no—
508C2×C3×D3—128no—
509C2×C3×D3—128no—
510C2×C3×D3#23512yescomplemented
511C2×C3×D3#23712yescomplemented
512D32—48no—
513C32×C4—22no—
514C32×C4—22no—
515C32×C4—22no—
516C32×C4—42no—
517C32×C4—61no—
518C32×C4—61no—
519C32×C4D3×D412yes—
520C32×C4D3×D412yes—
521C32×C4C2×#6712yes—
522C3⋊Dic3—21no—
523C3⋊Dic3—22no—
524C3⋊Dic3—21no—
525C3⋊Dic3—62no—
526C3⋊Dic3—64no—
527C3⋊Dic3—62no—
528C3⋊Dic3—62no—
529C3⋊Dic3—122no—
530C3⋊Dic3—122no—
531C3⋊Dic3—124no—
532C3×Dic3—22no—
533C3×Dic3—21no—
534C3×Dic3—21no—
535C3×Dic3—21no—
536C3×Dic3—21no—
537C3×Dic3—41no—
538C3×Dic3—61no—
539C3×Dic3—61no—
540C3×Dic3—61no—
541C3×Dic3—62no—
542C3×Dic3—61no—
543C3×Dic3—62no—
544C3×Dic3—122no—
545C3×Dic3—121no—
546C3×Dic3—121no—
547C2×#41—271no—
548C22×D4—91no—
549#124—271no—
550#123—272no—
551C22⋊Q8—271no—
552#121—91no—
553#121—272no—
554#120—272no—
555C4×D4—91no—
556C4×D4—271no—
557C2×C22⋊C4—272no—
558C33#54611yescharacteristic, complemented, Sylow
559C23×C3—31no—
560C23×C3—31no—
561C23×C3—32no—
562C23×C3—31no—
563C23×C3—32no—
564C23×C3—31no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—62no—
568C23×C3—92no—
569C23×C3—184no—
570C23×C3—184no—
571C23×C3—362no—
572C22×D3—32no—
573C22×D3—32no—
574C22×D3—62no—
575C22×D3—64no—
576C22×D3—64no—
577C22×D3—64no—
578C22×D3—64no—
579C22×D3—122no—
580C22×D3—122no—
581C22×D3C2×D3212yes—
582C22×D3C2×D3211yescharacteristic
583C22×D3C2×D3211yescharacteristic
584C3×D4—62no—
585C3×D4—62no—
586C3×D4—94no—
587C3×D4—122no—
588C3×D4—184no—
589C3×D4—182no—
590C3×D4—362no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—41no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—64no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—62no—
605C2×C3×C4—62no—
606C2×C3×C4—92no—
607C2×C3×C4—91no—
608C2×C3×C4—91no—
609C2×C3×C4—122no—
610C2×C3×C4C2×D3211yescharacteristic
611C2×C3×C4C2×D3211yescharacteristic
612C2×C3×C4C2×D3211yescharacteristic
613#67—64no—
614#67—62no—
615#67—62no—
616#67—122no—
617#67—122no—
618#67—184no—
619#67—184no—
620#67—184no—
621#67—188no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—62no—
631C2×Dic3—92no—
632C2×Dic3—92no—
633C2×Dic3—92no—
634C2×Dic3—182no—
635C2×Dic3—182no—
636C2×Dic3—182no—
637C2×Dic3—184no—
638C2×Dic3—362no—
639C2×Dic3—362no—
640C2×Dic3C2×D3211yescharacteristic
641C2×Dic3C2×D3211yescharacteristic
642D12—22no—
643D12—34no—
644D12—34no—
645D12—64no—
646D12—64no—
647C4×D3—22no—
648C4×D3—22no—
649C4×D3—184no—
650C4×D3—184no—
651C4×D3—188no—
652C4×D3—362no—
653C4×D3—362no—
654Dic6—184no—
655Dic6—182no—
656Dic6—182no—
657Dic6—182no—
658Dic6—362no—
659Dic6—362no—
660Dic6—364no—
661C2×C32—21no—
662C2×C32—21no—
663C2×C32—21no—
664C2×C32—21no—
665C2×C32—21no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—41no—
671C2×C32—41no—
672C2×C32—41no—
673C2×C32—62no—
674C2×C32—121no—
675C2×C32—122no—
676C2×C32C2×#23511yescharacteristic
677C2×C32C2×D3×D411yescharacteristic
678C2×C32C2×D3×D411yescharacteristic
679C2×C32C2×#23711yescharacteristic
680C2×C32#100411yescharacteristic
681C2×C32#100411yescharacteristic
682C2×C32D3×#4111yescharacteristic
683C2×C32#100911yescharacteristic
684C2×C32C22×#6711yescharacteristic
685C3⋊D3—24no—
686C3×D3—22no—
687C3×D3—22no—
688C3×D3—42no—
689C3×D3—42no—
690C3×D3—41no—
691C3×D3—42no—
692C3×D3—41no—
693C3×D3—42no—
694C3×D3—64no—
695C3×D3—64no—
696C3×D3—82no—
697C3×D3—124no—
698C24—92no—
699#41—544no—
700C2×Q8—271no—
701C2×D4—31no—
702C2×D4—92no—
703C2×D4—91no—
704C2×D4—92no—
705C2×D4—91no—
706C2×D4—184no—
707C2×D4—272no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—272no—
711C22×C4—272no—
712C4⋊C4—91no—
713C4⋊C4—91no—
714C4⋊C4—272no—
715C22⋊C4—91no—
716C22⋊C4—92no—
717C22⋊C4—91no—
718C22⋊C4—272no—
719C22⋊C4—272no—
720C22⋊C4—272no—
721C22⋊C4—272no—
722C42—91no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—32no—
727C22×C3—32no—
728C22×C3—41no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—61no—
740C22×C3—62no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—62no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—62no—
747C22×C3—94no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—122no—
753C22×C3—122no—
754C22×C3—122no—
755C22×C3—182no—
756C22×C3—182no—
757C22×C3—368no—
758C22×C3C22×D3211yescharacteristic
759C22×C3C22×D3211yescharacteristic
760C22×C3C22×D3211yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—22no—
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—21no—
769C2×D3—34no—
770C2×D3—34no—
771C2×D3—64no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—122no—
777C2×D3—122no—
778C2×D3—128no—
779C2×D3—128no—
780C2×D3#379512yescomplemented
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—42no—
785C3×C4—62no—
786C3×C4—61no—
787C3×C4—61no—
788C3×C4—61no—
789C3×C4—61no—
790C3×C4—121no—
791C3×C4—182no—
792C3×C4—181no—
793C3×C4—181no—
794C3×C4D3×#6712yes—
795C3×C4D3×#6712yes—
796C3×C4#381112yes—
797Dic3—21no—
798Dic3—21no—
799Dic3—61no—
800Dic3—61no—
801Dic3—61no—
802Dic3—61no—
803Dic3—62no—
804Dic3—62no—
805Dic3—121no—
806Dic3—121no—
807Dic3—122no—
808Dic3—184no—
809Dic3—182no—
810Dic3—182no—
811Dic3—182no—
812Dic3—362no—
813Dic3—362no—
814Dic3—364no—
815C32—21no—
816C32—21no—
817C32—21no—
818C32—41no—
819C32#555011yescharacteristic, complemented
820C32#561211yescharacteristic, complemented
821C32#580611yescharacteristic, complemented
822C23—31no—
823C23—32no—
824C23—31no—
825C23—92no—
826C23—184no—
827C23—184no—
828C23—362no—
829Q8—542no—
830D4—62no—
831D4—94no—
832D4—184no—
833D4—182no—
834D4—362no—
835D4—544no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—91no—
841C2×C4—91no—
842C2×C4—92no—
843C2×C4—272no—
844C2×C4—544no—
845C2×C4—1082no—
846C2×C4D3311yescharacteristic
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—41no—
857C2×C3—41no—
858C2×C3—41no—
859C2×C3—62no—
860C2×C3—62no—
861C2×C3—122no—
862C2×C3—122no—
863C2×C3—122no—
864C2×C3—122no—
865C2×C3—121no—
866C2×C3—121no—
867C2×C3—184no—
868C2×C3—242no—
869C2×C3C2×#379511yescharacteristic
870C2×C3D3×#23511yescharacteristic
871C2×C3#6430711yescharacteristic
872C2×C3#6430711yescharacteristic
873C2×C3D3×#23711yescharacteristic
874C2×C3#6431311yescharacteristic
875C2×C3C2×D3×#6711yescharacteristic
876C2×C3C2×D3×#6711yescharacteristic
877C2×C3C2×#381111yescharacteristic
878D3—22no—
879D3—41no—
880D3—42no—
881D3—64no—
882D3—64no—
883D3—124no—
884C22—32no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—62no—
889C22—61no—
890C22—62no—
891C22—61no—
892C22—62no—
893C22—94no—
894C22—182no—
895C22—182no—
896C22—368no—
897C22C2×D3311yescharacteristic
898C4—61no—
899C4—61no—
900C4—181no—
901C4—181no—
902C4—182no—
903C4—542no—
904C4#8895212yes—
905C3—21no—
906C3—21no—
907C3—21no—
908C3—41no—
909C3#1059488611yescharacteristic, complemented
910C3#1059507811yescharacteristic, complemented
911C3#1059522811yescharacteristic, complemented
912C2—62no—
913C2—122no—
914C2—121no—
915C2—184no—
916C2D3×#379511yescharacteristic
917C2#1172438011yescharacteristic
918C2C2×#8895211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89021C2semidirect
2. C2×C3×D3×D12C2semidirect
3. #11723691C2semidirect
4. #11723429C2semidirect
5. #11723426C2semidirect
6. C3×#63908C2semidirect
7. C3×C4×#625C2semidirect
8. #11722991C2semidirect
9. #11722965C2semidirect
10. #11722946C2semidirect
11. #11722902C2semidirect
16. C2×#6308C22semidirect
20. C2×C32×C4×D3C22semidirect
21. C2×#6294C22semidirect
22. C2×#6290C22semidirect
23. C2×Dic3×C3⋊D3C22semidirect
27. C2×C3×#625C22semidirect
29. C3×C4⋊(C3⋊Dic3)C22semidirect
30. C3×C4×C3⋊Dic3C22semidirect
31. #88814C22semidirect
32. #88807C22semidirect
34. (C2×D3)⋊(C3⋊Dic3)C22semidirect
35. (C2×D3)⋊(C3⋊Dic3)C22semidirect
36. C3×#3724C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
43. C2×D3×D12D3semidirect
62. #63908D3semidirect
63. C4×#625D3semidirect
89. C3×C4⋊(C3⋊D3)D4semidirect
139. C2×C3×C4×D3C2×D3semidirect
140. C2×C3×C4×D3C2×D3semidirect
146. C2×#625C2×D3semidirect
160. C4⋊(C3⋊Dic3)C2×D3semidirect
162. C4×C3⋊Dic3C2×D3semidirect
177. #3724C2×D3semidirect
194. (C2×D3)⋊Dic3C2×D3semidirect
195. (C2×D3)⋊Dic3C2×D3semidirect
208. C2×C32×D3#41semidirect
301. C4⋊(C3⋊D3)#67semidirect
408. C2×C4×D3D32semidirect
510. C2×C3×D3#235semidirect
511. C2×C3×D3#237semidirect
558. C33#546semidirect
780. C2×D3#3795semidirect
819. C32#5550semidirect
820. C32#5612semidirect
821. C32#5806semidirect
909. C3#10594886semidirect
910. C3#10595078semidirect
911. C3#10595228semidirect

Maximal subgroups

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

subgroupindex
C2×#890212
C2×C3×D3×D122
#117236912
#117234292
#117234262
C3×#639082
C3×C4×#6252
#117229912
#117229652
#117229462
#117229022
#105952283
#105950783
#105948863