Finite Group Databasebeta

← #13168268

Subgroups — #13168268

Order 1728.

1512 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89014C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3C4×#6295C211yesmaximal, characteristic, complemented
4#11723455C211yesmaximal, characteristic, complemented
5#11723431C211yesmaximal, characteristic, complemented
6C3×#63898C211yesmaximal, characteristic, complemented
7C3×#63871C211yesmaximal, characteristic, complemented
8#11722990C212yesmaximal, complemented
9#11722988C212yesmaximal, complemented
10#11722960C212yesmaximal, complemented
11D3×Dic3⋊Dic3C212yesmaximal, complemented
12#10595357—31nomaximal
13#10595248—31nomaximal
14#10594381—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×D12C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×#6295C2211yescharacteristic
21C2×#6290C2212yes—
22C2×D3×C3⋊Dic3C2212yes—
23#89014—24no—
24C2×C3×#626C2212yes—
25C2×C3×D3×Dic3C2212yes—
26C2×C3×D3×Dic3C2212yes—
27C3×#3796—24no—
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C32×C4⋊Dic3C2211yescharacteristic
30#88815C2211yescharacteristic
31#88814C2211yescharacteristic
32#88814C2211yescharacteristic
33#88807C2212yes—
34#88807C2212yes—
35Dic3⋊(C3⋊Dic3)C2212yes—
36#88803C2212yes—
37C3×Dic3⋊Dic3C2212yes—
38C3×#3722C2212yes—
39C3×(C2×D3)⋊Dic3C2212yes—
40C2×#3830—31no—
41C2×C3×#239—31no—
42C2×C3×#237—31no—
43C2×#3796D311yescharacteristic, complemented
44C2×#3795—31no—
45C2×#3795—31no—
46C2×#3795—61no—
47#64153—31no—
48#64106—31no—
49C3×#946—31no—
50C3×D4×Dic3—31no—
51C3×#897—31no—
52C3×#893—31no—
53#63978—32no—
54#63966—32no—
55C2×Dic3⋊Dic3—32no—
56#63962—32no—
57#63906—32no—
58#63905—32no—
59C4×#626—31no—
60C4×#626—31no—
61C4×#625—31no—
62#63898D311yescharacteristic, complemented
63#63891—32no—
64#63890—32no—
65D3×C4⋊Dic3—32no—
66#63885—32no—
67#63884—32no—
68D3×Dic3⋊C4—32no—
69#63871D311yescharacteristic, complemented
70#63866—31no—
71#63866—31no—
72#63866—61no—
73#63857—31no—
74#63857—31no—
75#63857—61no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2312yes—
79C2×C33×C4C2311yescharacteristic
80C2×C3⋊(C3⋊Dic3)C2312yes—
81#6308—22no—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C3×C4×C3⋊D3—22no—
87C3×C4×C3⋊D3—22no—
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2312yes—
90C32×D12D414yescomplemented
91C32×Dic6—22no—
92#6295—22no—
93#6290—24no—
94D3×C3⋊Dic3—24no—
95C3×#626—24no—
96C3×D3×Dic3—24no—
97C3×D3×Dic3—24no—
98#5824—91no—
99#5631—91no—
100#5555—91no—
101C2×C32×Q8—31no—
102C2×C32×D4—31no—
103C2×#638—32no—
104C22×C3⋊Dic3—32no—
105#3830—64no—
106C2×C4×C3⋊D3C2×D311yescharacteristic
107C2×C4×C3⋊D3C2×D311yescharacteristic
108C2×#634—31no—
109C2×#634—31no—
110C2×#634—31no—
111C2×#634—61no—
112C2×#634—61no—
113C2×#634—61no—
114C2×#634—121no—
115C2×C3×#67—32no—
116C22×C3×Dic3—32no—
117C22×C3×Dic3—32no—
118C3×#239—64no—
119C3×#237—64no—
120C2×C3×D12—21no—
121C2×C3×D12—32no—
122C2×C3×D12C2×D311yescharacteristic
123C2×C3×D12C2×D311yescharacteristic
124C2×C3×C4×D3—32no—
125C2×C3×C4×D3—32no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—61no—
131C2×C3×C4×D3—61no—
132C2×C3×Dic6—21no—
133C2×C3×Dic6C2×D311yescharacteristic
134C2×C3×Dic6C2×D311yescharacteristic
135C2×#626—31no—
136C2×#626—31no—
137C2×#626C2×D312yes—
138C2×#625—32no—
139C2×#625—32no—
140C2×#625—31no—
141C2×#625—62no—
142C2×D3×Dic3—32no—
143C2×D3×Dic3—32no—
144C2×D3×Dic3—62no—
145C2×D3×Dic3C2×D312yes—
146C2×D3×Dic3C2×D312yes—
147#3796—24no—
148#3795—68no—
149#3795—64no—
150#3795—64no—
151C32×C4⋊C4—31no—
152#3752—32no—
153C4⋊(C3⋊Dic3)—32no—
154#3750—32no—
155#3750—32no—
156C4×C3⋊Dic3C2×D311yescharacteristic
157C3×#217—32no—
158C3×(C2×D3)⋊C4—32no—
159C3×(C2×D3)⋊C4—32no—
160C3×(C2×D3)⋊C4—32no—
161C3×C4⋊Dic3—21no—
162C3×C4⋊Dic3—32no—
163C3×C4⋊Dic3C2×D311yescharacteristic
164C3×C4⋊Dic3C2×D311yescharacteristic
165C3×Dic3⋊C4—32no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—61no—
169#3724—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—32no—
173Dic3⋊Dic3—32no—
174Dic3⋊Dic3—32no—
175Dic3⋊Dic3—32no—
176Dic3⋊Dic3—32no—
177Dic3⋊Dic3—32no—
178Dic3⋊Dic3—62no—
179Dic3⋊Dic3—62no—
180Dic3⋊Dic3—62no—
181Dic3⋊Dic3C2×D312yes—
182#3722—31no—
183#3722—31no—
184#3722C2×D312yes—
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)⋊Dic3C2×D312yes—
193C22×C33C2411yescharacteristic
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C32×D3—22no—
201C2×C32×D3—22no—
202C2×C32×D3C2×D414yes—
203C33×C4C2×D412yes—
204C3⋊(C3⋊Dic3)—22no—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—21no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3#4112yescomplemented
209C32×Dic3—22no—
210C32×Dic3—22no—
211C2×C3×#41—91no—
212C2×#239—31no—
213C2×#237—31no—
214C2×#237—91no—
215C2×#237—91no—
216C2×#237—181no—
217C2×#235—91no—
218C3×C22⋊Q8—91no—
219C3×C4×D4—91no—
220#946—31no—
221#944—91no—
222#944—91no—
223#944—181no—
224#939—92no—
225#935—92no—
226D4×Dic3—31no—
227#930—92no—
228#929—92no—
229C4×#67—91no—
230C4×#67—91no—
231C2×C4⋊Dic3—92no—
232#924—91no—
233C2×Dic3⋊C4—92no—
234#897—31no—
235#897—91no—
236#897—91no—
237#897—181no—
238#894—92no—
239#893—31no—
240D3×C4⋊C4—92no—
241#886—92no—
242#886—92no—
243#884—92no—
244#883—92no—
245C4×D12—91no—
246#869—91no—
247C23×C32—32no—
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3⋊D3C22×D311yescharacteristic
250C22×C3×D3—22no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—61no—
256C22×C3×D3—61no—
257C22×C3×D3C22×D312yes—
258C22×C3×D3C22×D312yes—
259C32×Q8—62no—
260C32×D4—34no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—32no—
265C2×C32×C4—32no—
266C2×C32×C4—41no—
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270#638—64no—
271C2×C3⋊Dic3—32no—
272C2×C3⋊Dic3—32no—
273C2×C3⋊Dic3—32no—
274C2×C3⋊Dic3—62no—
275C2×C3⋊Dic3—62no—
276C2×C3⋊Dic3—62no—
277C2×C3⋊Dic3—64no—
278C2×C3⋊Dic3—122no—
279C2×C3⋊Dic3C22×D311yescharacteristic
280C2×C3⋊Dic3C22×D311yescharacteristic
281C2×C3⋊Dic3C22×D311yescharacteristic
282C2×C3⋊Dic3C22×D311yescharacteristic
283C4×C3⋊D3—22no—
284C4×C3⋊D3—22no—
285#634—62no—
286#634—64no—
287#634—62no—
288#634—62no—
289#634—122no—
290#634—122no—
291#634—124no—
292C3×#67—64no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—61no—
304C2×C3×Dic3—61no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—61no—
307C2×C3×Dic3—64no—
308C2×C3×Dic3—64no—
309C2×C3×Dic3C22×D312yes—
310C2×C3×Dic3C22×D312yes—
311C2×C3×Dic3C22×D312yes—
312C2×C3×Dic3C22×D312yes—
313C3×D12—24no—
314C3×D12—64no—
315C3×D12D1214yescomplemented
316C3×D12#6714yescomplemented
317C3×C4×D3—64no—
318C3×C4×D3—64no—
319C3×C4×D3—64no—
320C3×C4×D3—62no—
321C3×C4×D3—62no—
322C3×C4×D3—62no—
323C3×C4×D3—62no—
324C3×C4×D3—122no—
325C3×Dic6—22no—
326C3×Dic6—22no—
327C3×Dic6—42no—
328#626—24no—
329#626—62no—
330#626—62no—
331#625—68no—
332#625—64no—
333#625—64no—
334#625—62no—
335D3×Dic3—24no—
336D3×Dic3—24no—
337D3×Dic3—68no—
338D3×Dic3—64no—
339D3×Dic3—64no—
340#547—271noSylow
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C332−1+411yescharacteristic
344C3×C3⋊D3—41no—
345C3×C3⋊D3—41no—
346C32×D3—24no—
347C3×#41—184no—
348C2×C3×Q8—31no—
349C2×C3×Q8—31no—
350C2×C3×Q8—61no—
351C2×C3×D4—31no—
352C2×C3×D4—31no—
353C2×C3×D4—61no—
354C2×C3×D4—92no—
355C22×C3×C4—92no—
356C22×C3×C4—92no—
357C22×C3×C4—91no—
358C22×C3×C4—91no—
359C2×#67—32no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—92no—
363C2×#67—92no—
364C2×#67—92no—
365C2×#67—182no—
366C22×Dic3—32no—
367C22×Dic3—32no—
368C22×Dic3—92no—
369C22×Dic3—92no—
370C22×Dic3—182no—
371#239—64no—
372#237—64no—
373#237—184no—
374#237—184no—
375#237—188no—
376#235—184no—
377C2×D12—32no—
378C2×D12—91no—
379C2×D12D3211yescharacteristic
380C2×C4×D3—32no—
381C2×C4×D3—32no—
382C2×C4×D3—31no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—31no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—92no—
389C2×Dic6—91no—
390C2×Dic6—91no—
391C2×Dic6—91no—
392C2×Dic6—181no—
393C2×Dic6—181no—
394C2×Dic6—181no—
395C2×Dic6—361no—
396C2×Dic6D3211yescharacteristic
397C3×C4⋊C4—31no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—61no—
400C3×C4⋊C4—92no—
401C3×C22⋊C4—92no—
402C3×C22⋊C4—92no—
403C3×C42—91no—
404#217—32no—
405#217—91no—
406#217—91no—
407#217—92no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—32no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—92no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—182no—
418C4⋊Dic3—32no—
419C4⋊Dic3—91no—
420C4⋊Dic3—92no—
421C4⋊Dic3—92no—
422C4⋊Dic3—92no—
423C4⋊Dic3—92no—
424C4⋊Dic3—182no—
425C4⋊Dic3D3211yescharacteristic
426Dic3⋊C4—32no—
427Dic3⋊C4—91no—
428Dic3⋊C4—91no—
429Dic3⋊C4—92no—
430Dic3⋊C4—92no—
431Dic3⋊C4—92no—
432Dic3⋊C4—92no—
433Dic3⋊C4—92no—
434Dic3⋊C4—182no—
435Dic3⋊C4—182no—
436C4×Dic3—31no—
437C4×Dic3—31no—
438C4×Dic3—61no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—34no—
443C22×C32—41no—
444C22×C32—62no—
445C22×C32—62no—
446C22×C32C23×D311yescharacteristic
447C22×C32C23×D311yescharacteristic
448C22×C32C23×D311yescharacteristic
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—24no—
460C2×C3×D3—42no—
461C2×C3×D3—42no—
462C2×C3×D3—62no—
463C2×C3×D3—62no—
464C2×C3×D3—61no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—121no—
477C2×C3×D3—121no—
478C2×C3×D3—121no—
479C2×C3×D3—121no—
480C2×C3×D3C2×D1214yes—
481C2×C3×D3C2×#6714yes—
482C32×C4—22no—
483C32×C4—22no—
484C32×C4—22no—
485C32×C4—42no—
486C32×C4—62no—
487C32×C4—62no—
488C32×C4C2×D1212yes—
489C32×C4D3×D412yes—
490C32×C4C2×#6712yes—
491C3⋊Dic3—21no—
492C3⋊Dic3—21no—
493C3⋊Dic3—21no—
494C3⋊Dic3—62no—
495C3⋊Dic3—64no—
496C3⋊Dic3—62no—
497C3⋊Dic3—62no—
498C3⋊Dic3—122no—
499C3⋊Dic3—122no—
500C3⋊Dic3—124no—
501C3⋊Dic3#23712yescomplemented
502C3×Dic3—22no—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—32no—
507C3×Dic3—32no—
508C3×Dic3—42no—
509C3×Dic3—42no—
510C3×Dic3—62no—
511C3×Dic3—62no—
512C3×Dic3—62no—
513C3×Dic3—61no—
514C3×Dic3—61no—
515C3×Dic3—61no—
516C3×Dic3—61no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519C3×Dic3—121no—
520C2×#41—91no—
521C2×#41—271no—
522C4⋊Q8—271no—
523#123—272no—
524#123—272no—
525C22⋊Q8—91no—
526C22⋊Q8—271no—
527#121—272no—
528C4×D4—91no—
529C4×D4—271no—
530C2×C4⋊C4—272no—
531C33#54711yescharacteristic, complemented, Sylow
532C23×C3—32no—
533C23×C3—32no—
534C23×C3—62no—
535C23×C3—91no—
536C23×C3—91no—
537C22×D3—31no—
538C22×D3—31no—
539C22×D3—31no—
540C22×D3—31no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3C2×D3212yes—
544C3×Q8—62no—
545C3×Q8—62no—
546C3×Q8—122no—
547C3×D4—34no—
548C3×D4—34no—
549C3×D4—64no—
550C3×D4—184no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—41no—
559C2×C3×C4—62no—
560C2×C3×C4—62no—
561C2×C3×C4—91no—
562C2×C3×C4—91no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—184no—
566C2×C3×C4—184no—
567C2×C3×C4—182no—
568C2×C3×C4—182no—
569C2×C3×C4C2×D3211yescharacteristic
570C2×C3×C4C2×D3211yescharacteristic
571C2×C3×C4C2×D3211yescharacteristic
572#67—64no—
573#67—182no—
574#67—182no—
575#67—184no—
576#67—184no—
577#67—188no—
578#67—184no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—64no—
592C2×Dic3—64no—
593C2×Dic3—92no—
594C2×Dic3—92no—
595C2×Dic3—92no—
596C2×Dic3—182no—
597C2×Dic3—182no—
598C2×Dic3—182no—
599C2×Dic3—184no—
600C2×Dic3—184no—
601C2×Dic3—188no—
602C2×Dic3—362no—
603C2×Dic3C2×D3212yes—
604C2×Dic3C2×D3212yes—
605D12—64no—
606D12—182no—
607D12#62614yescomplemented
608C4×D3—64no—
609C4×D3—64no—
610C4×D3—64no—
611C4×D3—62no—
612C4×D3—62no—
613C4×D3—62no—
614C4×D3—62no—
615C4×D3—122no—
616C4×D3—184no—
617Dic6—22no—
618Dic6—184no—
619Dic6—182no—
620Dic6—182no—
621Dic6—182no—
622Dic6—362no—
623Dic6—362no—
624Dic6—364no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—41no—
635C2×C32—41no—
636C2×C32—41no—
637C2×C32—64no—
638C2×C32C22×D1211yescharacteristic
639C2×C32C2×D3×D411yescharacteristic
640C2×C32C2×#23711yescharacteristic
641C2×C32#100711yescharacteristic
642C2×C32D3×#4111yescharacteristic
643C2×C32D3×#4111yescharacteristic
644C2×C32#101011yescharacteristic
645C2×C32#101011yescharacteristic
646C2×C32C22×#6711yescharacteristic
647C3⋊D3—41no—
648C3⋊D3—41no—
649C3×D3—24no—
650C3×D3—24no—
651C3×D3—44no—
652C3×D3—122no—
653C3×D3—122no—
654C3×D3—121no—
655C3×D3—121no—
656C3×D3—121no—
657C3×D3—121no—
658#41—184no—
659#41—544no—
660C2×Q8—31no—
661C2×Q8—271no—
662C2×D4—31no—
663C2×D4—92no—
664C2×D4—271no—
665C2×D4—272no—
666C22×C4—92no—
667C22×C4—92no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—272no—
671C4⋊C4—31no—
672C4⋊C4—92no—
673C4⋊C4—272no—
674C4⋊C4—272no—
675C4⋊C4—272no—
676C4⋊C4—271no—
677C22⋊C4—92no—
678C22⋊C4—92no—
679C22⋊C4—272no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C42—91no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—34no—
687C22×C3—34no—
688C22×C3—41no—
689C22×C3—64no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—122no—
695C22×C3—122no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3C22×D3211yescharacteristic
703C22×C3C22×D3211yescharacteristic
704C22×C3C22×D3211yescharacteristic
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3C2×#62614yes—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—42no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—92no—
735C3×C4—122no—
736C3×C4—122no—
737C3×C4—181no—
738C3×C4—181no—
739C3×C4—181no—
740C3×C4D3×D1212yes—
741C3×C4C2×#62612yes—
742C3×C4D3×#6712yes—
743Dic3—22no—
744Dic3—22no—
745Dic3—32no—
746Dic3—32no—
747Dic3—62no—
748Dic3—62no—
749Dic3—62no—
750Dic3—61no—
751Dic3—61no—
752Dic3—61no—
753Dic3—61no—
754Dic3—61no—
755Dic3—61no—
756Dic3—121no—
757Dic3—184no—
758Dic3—182no—
759Dic3—182no—
760Dic3—182no—
761Dic3—362no—
762Dic3—362no—
763Dic3—364no—
764C32—21no—
765C32—21no—
766C32—21no—
767C32—41no—
768C32#555511yescharacteristic, complemented
769C32#563111yescharacteristic, complemented
770C32#582411yescharacteristic, complemented
771C23—32no—
772C23—91no—
773C23—91no—
774Q8—62no—
775Q8—542no—
776D4—34no—
777D4—184no—
778D4—542no—
779D4—544no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—91no—
785C2×C4—91no—
786C2×C4—184no—
787C2×C4—184no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—272no—
791C2×C4—544no—
792C2×C4D3311yescharacteristic
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—41no—
805C2×C3—64no—
806C2×C3—64no—
807C2×C3—124no—
808C2×C3—361no—
809C2×C3—361no—
810C2×C3C2×D3×D1211yescharacteristic
811C2×C3#6430911yescharacteristic
812C2×C3D3×#23711yescharacteristic
813C2×C3D3×#23711yescharacteristic
814C2×C3#6431511yescharacteristic
815C2×C3#6431511yescharacteristic
816C2×C3#6431911yescharacteristic
817C2×C3C22×#62611yescharacteristic
818C2×C3C2×D3×#6711yescharacteristic
819D3—24no—
820D3—122no—
821D3—122no—
822D3—121no—
823D3—121no—
824D3—121no—
825D3—121no—
826C22—34no—
827C22—62no—
828C22—62no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22C2×D3311yescharacteristic
836C4—62no—
837C4—62no—
838C4—92no—
839C4—181no—
840C4—181no—
841C4—181no—
842C4—542no—
843C4D3×#62612yes—
844C3—21no—
845C3—21no—
846C3—21no—
847C3—41no—
848C3#1059438111yescharacteristic, complemented
849C3#1059524811yescharacteristic, complemented
850C3#1059535711yescharacteristic, complemented
851C2—64no—
852C2—361no—
853C2—361no—
854C2#1172437411yescharacteristic
855C2#1172439411yescharacteristic
856C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#547
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×#3796C2semidirect
3. C4×#6295C2semidirect
4. #11723455C2semidirect
5. #11723431C2semidirect
6. C3×#63898C2semidirect
7. C3×#63871C2semidirect
8. #11722990C2semidirect
9. #11722988C2semidirect
10. #11722960C2semidirect
11. D3×Dic3⋊Dic3C2semidirect
43. C2×#3796D3semidirect
62. #63898D3semidirect
69. #63871D3semidirect
90. C32×D12D4semidirect
208. C3×C3⋊Dic3#41semidirect
315. C3×D12D12semidirect
316. C3×D12#67semidirect
501. C3⋊Dic3#237semidirect
531. C33#547semidirect
607. D12#626semidirect
768. C32#5555semidirect
769. C32#5631semidirect
770. C32#5824semidirect
848. C3#10594381semidirect
849. C3#10595248semidirect
850. C3#10595357semidirect

Maximal subgroups

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

subgroupindex
C2×#890142
C2×C3×#37962
C4×#62952
#117234552
#117234312
C3×#638982
C3×#638712
#117229902
#117229882
#117229602
D3×Dic3⋊Dic32
#105953573
#105952483
#105943813