Finite Group Databasebeta

← #13168119

Subgroups — #13168119

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×#89014C211yesmaximal, characteristic, complemented
2C2×C3×#3802C211yesmaximal, characteristic, complemented
3C4×#6295C211yesmaximal, characteristic, complemented
4#11723431C211yesmaximal, characteristic, complemented
5#11723429C211yesmaximal, characteristic, complemented
6C3×#63916C211yesmaximal, characteristic, complemented
7C3×#63898C211yesmaximal, characteristic, complemented
8#11722989C212yesmaximal, complemented
9#11722956C212yesmaximal, complemented
10#11722947C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12#10595246—31nomaximal
13#10595228—31nomaximal
14#10594630—31nomaximal
15C22×C3×D32C2212yes—
16C2×#6308C2211yescharacteristic, complemented
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
19C2×C32×D12C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6290C2212yescomplemented
23C2×D3×C3⋊Dic3C2212yescomplemented
24#89014—24no—
25C2×C3×#626C2212yescomplemented
26C2×C3×#625C2212yes—
27C2×C3×D3×Dic3C2212yescomplemented
28C3×#3802—24no—
29C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C32×C4⋊Dic3C2211yescharacteristic, complemented
31#88815C2211yescharacteristic, complemented
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic, complemented
34Dic3⋊(C3⋊Dic3)C2212yescomplemented
35#88803C2212yes—
36(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×#3830—31no—
41C2×C3×D3×D4—31no—
42C2×C3×D3×D4—31no—
43C2×#3802D311yescharacteristic, complemented
44C2×#3795—31no—
45C2×#3795—31no—
46C2×#3795—61no—
47#64145—31no—
48#64106—31no—
49C3×#938—31no—
50C3×D4×Dic3—31no—
51C3×#895—31no—
52C3×#893—31no—
53#63978—32no—
54#63977—32no—
55#63976—32no—
56#63970—32no—
57#63969—32no—
58D3×#217—32no—
59#63962—32no—
60C2×(C2×D3)⋊Dic3—32no—
61#63922—32no—
62D3×(C2×D3)⋊C4—32no—
63#63916D311yescharacteristic, complemented
64#63908—32no—
65C4×#626—31no—
66C4×#626—31no—
67C4×#625—31no—
68#63898D311yescharacteristic, complemented
69#63891—32no—
70#63860—31no—
71#63860—31no—
72#63860—61no—
73#63857—31no—
74#63857—31no—
75#63857—61no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2312yes—
79C22×C32×D3C2312yes—
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⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊Dic3C2311yescharacteristic
90C3×C4×C3⋊D3—22no—
91C3×C4×C3⋊D3—22no—
92C2×C32×Dic3C2312yes—
93C32×D12—22no—
94C32×D12D414yescomplemented
95#6295—22no—
96#6290—24no—
97D3×C3⋊Dic3—24no—
98C3×#626—42no—
99C3×#625—24no—
100C3×D3×Dic3—42no—
101#5806—91no—
102#5612—91no—
103#5554—91no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C2×D312yes—
107C2×C32×D4—31no—
108C2×C32×D4—31no—
109C2×#638—32no—
110C22×C3⋊Dic3—32no—
111#3830—64no—
112C2×C4×C3⋊D3C2×D311yescharacteristic
113C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
114C2×#634—31no—
115C2×#634—31no—
116C2×#634—31no—
117C2×#634—61no—
118C2×#634—61no—
119C2×#634—61no—
120C2×#634—121no—
121C2×C3×#67—32no—
122C2×C3×#67—32no—
123C2×C3×#67—32no—
124C22×C3×Dic3—32no—
125C3×D3×D4—64no—
126C3×D3×D4—64no—
127C2×C3×D12—21no—
128C2×C3×D12—21no—
129C2×C3×D12—32no—
130C2×C3×D12C2×D311yescharacteristic
131C2×C3×D12C2×D311yescharacteristic
132C2×C3×D12C2×D311yescharacteristic
133C2×C3×D12C2×D311yescharacteristic
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—32no—
139C2×C3×C4×D3—61no—
140C2×C3×C4×D3—61no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#626C2×D312yescomplemented
144C2×#625—32no—
145C2×#625—32no—
146C2×#625—31no—
147C2×#625—62no—
148C2×#625C2×D312yes—
149C2×D3×Dic3—32no—
150C2×D3×Dic3—32no—
151C2×D3×Dic3—62no—
152C2×D3×Dic3C2×D312yescomplemented
153#3802—24no—
154#3795—68no—
155#3795—64no—
156#3795—64no—
157C32×C4⋊C4—31no—
158#3757—32no—
159#3757—32no—
160#3752—32no—
161C4⋊(C3⋊Dic3)—32no—
162C4×C3⋊Dic3C2×D311yescharacteristic, complemented
163C3×#217—32no—
164C3×#217—32no—
165C3×(C2×D3)⋊C4—32no—
166C3×(C2×D3)⋊C4—32no—
167C3×C4⋊Dic3—21no—
168C3×C4⋊Dic3C2×D311yescharacteristic, complemented
169C3×C4⋊Dic3C2×D311yescharacteristic, complemented
170C3×C4×Dic3—31no—
171C3×C4×Dic3—31no—
172C3×C4×Dic3—61no—
173#3724—31no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—32no—
177Dic3⋊Dic3—32no—
178Dic3⋊Dic3—62no—
179#3722—31no—
180#3722—31no—
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—62no—
192(C2×D3)⋊Dic3—62no—
193(C2×D3)⋊Dic3—62no—
194(C2×D3)⋊Dic3C2×D312yescomplemented
195(C2×D3)⋊Dic3C2×D312yescomplemented
196C22×C33C2411yescharacteristic
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3#4112yescomplemented
203C2×C32×D3—22no—
204C2×C32×D3—22no—
205C2×C32×D3—22no—
206C2×C32×D3—22no—
207C2×C32×D3—22no—
208C2×C32×D3C2×D414yes—
209C3×D32—48no—
210C33×C4C2×D412yes—
211C3⋊(C3⋊Dic3)—22no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C32×Dic3—22no—
217C22×C3×D4—91no—
218C2×#237—91no—
219C2×#237—91no—
220C2×#237—181no—
221C2×D3×D4—31no—
222C2×D3×D4—31no—
223C2×#235—91no—
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#936—91no—
233#936—91no—
234#936—181no—
235#935—92no—
236D4×Dic3—31no—
237#930—92no—
238C4×#67—91no—
239C4×#67—91no—
240C2×(C2×D3)⋊C4—92no—
241#924—91no—
242#897—91no—
243#897—91no—
244#897—181no—
245#895—31no—
246#893—31no—
247#886—92no—
248#883—92no—
249#882—92no—
250D3×C22⋊C4—92no—
251#875—91no—
252C4×D12—91no—
253C23×C32—32no—
254C23×C32—32no—
255C22×C3⋊D3C22×D311yescharacteristic
256C22×C3⋊D3C22×D311yescharacteristic
257C22×C3×D3—22no—
258C22×C3×D3—22no—
259C22×C3×D3—31no—
260C22×C3×D3—31no—
261C22×C3×D3—31no—
262C22×C3×D3—31no—
263C22×C3×D3—61no—
264C22×C3×D3—61no—
265C22×C3×D3—64no—
266C22×C3×D3—64no—
267C22×C3×D3—64no—
268C22×C3×D3—64no—
269C22×C3×D3—122no—
270C22×C3×D3—122no—
271C22×C3×D3C22×D312yes—
272C22×C3×D3C22×D312yes—
273C22×C3×D3C22×D312yes—
274C22×C3×D3C22×D312yes—
275C2×D32—24no—
276C2×D32—24no—
277C2×D32—42no—
278C32×D4—34no—
279C32×D4—62no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—32no—
284C2×C32×C4—41no—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288#638—64no—
289C2×C3⋊Dic3—32no—
290C2×C3⋊Dic3—32no—
291C2×C3⋊Dic3—32no—
292C2×C3⋊Dic3—62no—
293C2×C3⋊Dic3—62no—
294C2×C3⋊Dic3—62no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—122no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C4×C3⋊D3—22no—
302C4×C3⋊D3—22no—
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—64no—
312C3×#67—122no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—61no—
326C2×C3×Dic3—122no—
327C2×C3×Dic3C22×D312yes—
328C2×C3×Dic3C22×D312yes—
329C3×D12—22no—
330C3×D12—22no—
331C3×D12—24no—
332C3×D12—42no—
333C3×D12—122no—
334C3×D12D1214yescomplemented
335C3×D12#6714yescomplemented
336C3×C4×D3—64no—
337C3×C4×D3—62no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—62no—
341C3×C4×D3—122no—
342C3×C4×D3—122no—
343#626—42no—
344#626—62no—
345#626—62no—
346#625—24no—
347#625—62no—
348#625—68no—
349#625—64no—
350#625—64no—
351D3×Dic3—42no—
352D3×Dic3—68no—
353D3×Dic3—64no—
354D3×Dic3—64no—
355#546—271noSylow
356C2×C33C22×D411yescharacteristic
357C2×C33C2×#4111yescharacteristic
358C2×C33H(5,𝔽2)11yescharacteristic
359C3×C3⋊D3—22no—
360C3×C3⋊D3—41no—
361C32×D3—24no—
362C32×D3—42no—
363C24×C3—92no—
364C23×D3—32no—
365C23×D3—32no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—61no—
371C2×C3×D4—61no—
372C2×C3×D4—92no—
373C2×C3×D4—92no—
374C2×C3×D4—184no—
375C22×C3×C4—92no—
376C22×C3×C4—91no—
377C22×C3×C4—91no—
378C2×#67—32no—
379C2×#67—32no—
380C2×#67—32no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—92no—
384C2×#67—92no—
385C2×#67—92no—
386C2×#67—182no—
387C22×Dic3—32no—
388C22×Dic3—92no—
389C22×Dic3—92no—
390C22×Dic3—182no—
391#237—184no—
392#237—184no—
393#237—188no—
394D3×D4—64no—
395D3×D4—64no—
396#235—184no—
397C2×D12—32no—
398C2×D12—91no—
399C2×D12D3211yescharacteristic
400C2×D12D3211yescharacteristic
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—31no—
404C2×C4×D3—31no—
405C2×C4×D3—32no—
406C2×C4×D3—61no—
407C2×C4×D3—61no—
408C2×C4×D3—92no—
409C2×Dic6—91no—
410C2×Dic6—91no—
411C2×Dic6—91no—
412C2×Dic6—181no—
413C2×Dic6—181no—
414C2×Dic6—181no—
415C2×Dic6—361no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—61no—
419C3×C22⋊C4—92no—
420C3×C22⋊C4—92no—
421C3×C42—91no—
422#217—32no—
423#217—32no—
424#217—91no—
425#217—91no—
426#217—92no—
427#217—92no—
428#217—92no—
429#217—92no—
430#217—92no—
431#217—182no—
432#217—182no—
433(C2×D3)⋊C4—32no—
434(C2×D3)⋊C4—32no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—92no—
440(C2×D3)⋊C4—92no—
441(C2×D3)⋊C4—92no—
442(C2×D3)⋊C4—92no—
443(C2×D3)⋊C4—182no—
444C4⋊Dic3—91no—
445C4⋊Dic3—92no—
446C4⋊Dic3—92no—
447C4⋊Dic3—182no—
448C4⋊Dic3D3211yescharacteristic, complemented
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—92no—
452C4×Dic3—31no—
453C4×Dic3—31no—
454C4×Dic3—61no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—34no—
459C22×C32—41no—
460C22×C32—62no—
461C22×C32—62no—
462C22×C32—62no—
463C22×C32—62no—
464C22×C32—62no—
465C22×C32C23×D311yescharacteristic
466C22×C32C23×D311yescharacteristic
467C22×C32C23×D311yescharacteristic
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3#23712yescomplemented
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—24no—
485C2×C3×D3—32no—
486C2×C3×D3—32no—
487C2×C3×D3—42no—
488C2×C3×D3—42no—
489C2×C3×D3—42no—
490C2×C3×D3—42no—
491C2×C3×D3—42no—
492C2×C3×D3—62no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C2×C3×D3—61no—
496C2×C3×D3—61no—
497C2×C3×D3—62no—
498C2×C3×D3—61no—
499C2×C3×D3—61no—
500C2×C3×D3—61no—
501C2×C3×D3—61no—
502C2×C3×D3—61no—
503C2×C3×D3—61no—
504C2×C3×D3—121no—
505C2×C3×D3—121no—
506C2×C3×D3—121no—
507C2×C3×D3—121no—
508C2×C3×D3—128no—
509C2×C3×D3—128no—
510C2×C3×D3C2×D1214yes—
511C2×C3×D3C2×#6714yes—
512D32—48no—
513C32×C4—22no—
514C32×C4—22no—
515C32×C4—22no—
516C32×C4—42no—
517C32×C4—62no—
518C32×C4C2×D1212yes—
519C32×C4D3×D412yes—
520C32×C4C2×#6712yes—
521C3⋊Dic3—21no—
522C3⋊Dic3—21no—
523C3⋊Dic3—21no—
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—22no—
534C3×Dic3—42no—
535C3×Dic3—62no—
536C3×Dic3—61no—
537C3×Dic3—61no—
538C3×Dic3—61no—
539C3×Dic3—61no—
540C3×Dic3—61no—
541C3×Dic3—61no—
542C3×Dic3—61no—
543C3×Dic3—61no—
544C3×Dic3—121no—
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—32no—
560C23×C3—32no—
561C23×C3—32no—
562C23×C3—32no—
563C23×C3—62no—
564C23×C3—62no—
565C23×C3—91no—
566C23×C3—91no—
567C23×C3—184no—
568C23×C3—184no—
569C23×C3—362no—
570C22×D3—31no—
571C22×D3—31no—
572C22×D3—31no—
573C22×D3—31no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—64no—
577C22×D3—64no—
578C22×D3—64no—
579C22×D3—64no—
580C22×D3—122no—
581C22×D3—122no—
582C22×D3C2×D3212yes—
583C22×D3C2×D3212yes—
584C3×D4—34no—
585C3×D4—34no—
586C3×D4—64no—
587C3×D4—62no—
588C3×D4—62no—
589C3×D4—122no—
590C3×D4—184no—
591C3×D4—362no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—32no—
596C2×C3×C4—32no—
597C2×C3×C4—41no—
598C2×C3×C4—62no—
599C2×C3×C4—91no—
600C2×C3×C4—91no—
601C2×C3×C4—91no—
602C2×C3×C4—91no—
603C2×C3×C4—182no—
604C2×C3×C4—182no—
605C2×C3×C4—362no—
606C2×C3×C4C2×D3211yescharacteristic
607C2×C3×C4C2×D3211yescharacteristic
608C2×C3×C4C2×D3211yescharacteristic
609#67—64no—
610#67—64no—
611#67—122no—
612#67—182no—
613#67—182no—
614#67—184no—
615#67—184no—
616#67—188no—
617#67—184no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—31no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—92no—
631C2×Dic3—92no—
632C2×Dic3—92no—
633C2×Dic3—122no—
634C2×Dic3—182no—
635C2×Dic3—182no—
636C2×Dic3—182no—
637C2×Dic3—184no—
638C2×Dic3—184no—
639C2×Dic3—188no—
640C2×Dic3—362no—
641C2×Dic3C2×D3212yes—
642D12—22no—
643D12—122no—
644D12—182no—
645D12#62614yescomplemented
646C4×D3—64no—
647C4×D3—62no—
648C4×D3—62no—
649C4×D3—62no—
650C4×D3—62no—
651C4×D3—122no—
652C4×D3—122no—
653C4×D3—184no—
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—64no—
674C2×C32—122no—
675C2×C32C22×D1211yescharacteristic
676C2×C32C2×D3×D411yescharacteristic
677C2×C32C2×#23711yescharacteristic
678C2×C32#100411yescharacteristic
679C2×C32#100411yescharacteristic
680C2×C32#100411yescharacteristic
681C2×C32D3×#4111yescharacteristic
682C2×C32D3×#4111yescharacteristic
683C2×C32C22×#6711yescharacteristic
684C3⋊D3—22no—
685C3⋊D3—41no—
686C3×D3—24no—
687C3×D3—24no—
688C3×D3—44no—
689C3×D3—42no—
690C3×D3—42no—
691C3×D3—62no—
692C3×D3—62no—
693C3×D3—82no—
694C3×D3—122no—
695C3×D3—122no—
696C3×D3—121no—
697C3×D3—121no—
698C24—92no—
699#41—544no—
700C2×Q8—271no—
701C2×D4—31no—
702C2×D4—31no—
703C2×D4—92no—
704C2×D4—92no—
705C2×D4—184no—
706C2×D4—271no—
707C2×D4—272no—
708C22×C4—92no—
709C22×C4—91no—
710C22×C4—91no—
711C22×C4—272no—
712C4⋊C4—31no—
713C4⋊C4—272no—
714C4⋊C4—271no—
715C22⋊C4—92no—
716C22⋊C4—92no—
717C22⋊C4—272no—
718C22⋊C4—271no—
719C22⋊C4—271no—
720C22⋊C4—272no—
721C22⋊C4—272no—
722C42—91no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—34no—
727C22×C3—34no—
728C22×C3—41no—
729C22×C3—64no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—92no—
741C22×C3—122no—
742C22×C3—122no—
743C22×C3—122no—
744C22×C3—122no—
745C22×C3—122no—
746C22×C3—181no—
747C22×C3—181no—
748C22×C3—181no—
749C22×C3—181no—
750C22×C3—181no—
751C22×C3—368no—
752C22×C3C22×D3211yescharacteristic
753C22×C3C22×D3211yescharacteristic
754C22×C3C22×D3211yescharacteristic
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—32no—
761C2×D3—32no—
762C2×D3—62no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—62no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—128no—
779C2×D3—128no—
780C2×D3C2×#62614yes—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—42no—
785C3×C4—62no—
786C3×C4—62no—
787C3×C4—122no—
788C3×C4—181no—
789C3×C4—181no—
790C3×C4—181no—
791C3×C4—181no—
792C3×C4D3×D1212yes—
793C3×C4C2×#62612yes—
794C3×C4D3×#6712yes—
795Dic3—22no—
796Dic3—62no—
797Dic3—61no—
798Dic3—61no—
799Dic3—61no—
800Dic3—61no—
801Dic3—61no—
802Dic3—61no—
803Dic3—61no—
804Dic3—61no—
805Dic3—121no—
806Dic3—121no—
807Dic3—121no—
808Dic3—184no—
809Dic3—182no—
810Dic3—182no—
811Dic3—182no—
812Dic3—362no—
813Dic3—362no—
814Dic3—364no—
815C32—21no—
816C32—21no—
817C32—21no—
818C32—41no—
819C32#555411yescharacteristic, complemented
820C32#561211yescharacteristic, complemented
821C32#580611yescharacteristic, complemented
822C23—32no—
823C23—32no—
824C23—91no—
825C23—91no—
826C23—184no—
827C23—184no—
828C23—362no—
829Q8—542no—
830D4—34no—
831D4—62no—
832D4—184no—
833D4—362no—
834D4—542no—
835D4—544no—
836C2×C4—32no—
837C2×C4—91no—
838C2×C4—91no—
839C2×C4—91no—
840C2×C4—91no—
841C2×C4—182no—
842C2×C4—182no—
843C2×C4—272no—
844C2×C4—362no—
845C2×C4—544no—
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—64no—
860C2×C3—64no—
861C2×C3—124no—
862C2×C3—122no—
863C2×C3—122no—
864C2×C3—182no—
865C2×C3—242no—
866C2×C3—361no—
867C2×C3C2×D3×D1211yescharacteristic
868C2×C3D3×#23711yescharacteristic
869C2×C3D3×#23711yescharacteristic
870C2×C3#6431311yescharacteristic
871C2×C3#6431311yescharacteristic
872C2×C3#6431311yescharacteristic
873C2×C3#6431911yescharacteristic
874C2×C3C22×#62611yescharacteristic
875C2×C3C2×D3×#6711yescharacteristic
876D3—24no—
877D3—42no—
878D3—62no—
879D3—62no—
880D3—122no—
881D3—122no—
882D3—121no—
883D3—121no—
884C22—34no—
885C22—62no—
886C22—62no—
887C22—62no—
888C22—62no—
889C22—62no—
890C22—92no—
891C22—181no—
892C22—181no—
893C22—181no—
894C22—181no—
895C22—181no—
896C22—368no—
897C22C2×D3311yescharacteristic
898C4—62no—
899C4—181no—
900C4—181no—
901C4—181no—
902C4—181no—
903C4—542no—
904C4D3×#62612yes—
905C3—21no—
906C3—21no—
907C3—21no—
908C3—41no—
909C3#1059463011yescharacteristic, complemented
910C3#1059522811yescharacteristic, complemented
911C3#1059524611yescharacteristic, complemented
912C2—64no—
913C2—122no—
914C2—182no—
915C2—361no—
916C2#1172437411yescharacteristic
917C2#1172438211yescharacteristic
918C2C2×D3×#62611yescharacteristic
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×#89014C2semidirect
2. C2×C3×#3802C2semidirect
3. C4×#6295C2semidirect
4. #11723431C2semidirect
5. #11723429C2semidirect
6. C3×#63916C2semidirect
7. C3×#63898C2semidirect
8. #11722989C2semidirect
9. #11722956C2semidirect
10. #11722947C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
16. C2×#6308C22semidirect
18. C2×C3×C4×C3⋊D3C22semidirect
22. C2×#6290C22semidirect
23. C2×D3×C3⋊Dic3C22semidirect
25. C2×C3×#626C22semidirect
27. C2×C3×D3×Dic3C22semidirect
29. C3×C4×C3⋊Dic3C22semidirect
30. C32×C4⋊Dic3C22semidirect
31. #88815C22semidirect
33. #88814C22semidirect
34. Dic3⋊(C3⋊Dic3)C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
43. C2×#3802D3semidirect
63. #63916D3semidirect
68. #63898D3semidirect
94. C32×D12D4semidirect
113. C2×C4×C3⋊D3C2×D3semidirect
143. C2×#626C2×D3semidirect
152. C2×D3×Dic3C2×D3semidirect
162. C4×C3⋊Dic3C2×D3semidirect
168. C3×C4⋊Dic3C2×D3semidirect
169. C3×C4⋊Dic3C2×D3semidirect
194. (C2×D3)⋊Dic3C2×D3semidirect
195. (C2×D3)⋊Dic3C2×D3semidirect
202. C2×C3×C3⋊D3#41semidirect
334. C3×D12D12semidirect
335. C3×D12#67semidirect
448. C4⋊Dic3D32semidirect
473. C2×C3⋊D3#237semidirect
558. C33#546semidirect
645. D12#626semidirect
819. C32#5554semidirect
820. C32#5612semidirect
821. C32#5806semidirect
909. C3#10594630semidirect
910. C3#10595228semidirect
911. C3#10595246semidirect

Maximal subgroups

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

subgroupindex
C2×#890142
C2×C3×#38022
C4×#62952
#117234312
#117234292
C3×#639162
C3×#638982
#117229892
#117229562
#117229472
D3×(C2×D3)⋊Dic32
#105952463
#105952283
#105946303