Finite Group Databasebeta

← #13167950

Subgroups — #13167950

Order 1728.

1642 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89015C211yesmaximal, characteristic
2#11723668C211yesmaximal, characteristic, complemented
3C4×#6289C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63898C211yesmaximal, characteristic, complemented
6C3×Dic3×D12C211yesmaximal, characteristic, complemented
7C3×#63844C211yesmaximal, characteristic, complemented
8#11722935C212yesmaximal, complemented
9#11722932C212yesmaximal, complemented
10#11722917C212yesmaximal, complemented
11D3×Dic32C212yesmaximal, complemented
12#10595190—31nomaximal
13#10594360—31nomaximal
14C4×#3796—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×#6291C2212yes—
19C2×#6289C2211yescharacteristic
20C2×#6289C2211yescharacteristic
21C2×D3×C3⋊Dic3C2212yes—
22#89015C418yescomplemented
23C2×C3×D3×Dic3C2212yes—
24C2×C3×D3×Dic3C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C32×C4⋊Dic3C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29#88815C2212yes—
30#88813C2212yes—
31#88804C2212yes—
32Dic3×C3⋊Dic3C2211yescharacteristic
33Dic3×C3⋊Dic3C2212yes—
34Dic3×C3⋊Dic3C2211yescharacteristic
35C3×#3724C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×Dic32C2212yes—
39C2×#3830—31no—
40C2×#3796—31no—
41C2×#3796—31no—
42C2×#3796—61no—
43#64101—31no—
44C42×C3⋊D3—31no—
45C3×D4×Dic3—31no—
46C3×D4×Dic3—31no—
47C3×#893—31no—
48C3×#887—31no—
49C3×C4×D12—31no—
50C3×C4×Dic6—31no—
51#63957—32no—
52C2×Dic32—32no—
53#63952—32no—
54#63952—32no—
55#63904—32no—
56C4×#626—32no—
57#63898D311yescharacteristic, complemented
58Dic3×D12D311yescharacteristic, complemented
59C4×#624—31no—
60C4×#624—31no—
61C4×#624—61no—
62#63881—32no—
63#63880—32no—
64#63878—32no—
65#63878—32no—
66C4×D3×Dic3—32no—
67C4×D3×Dic3—32no—
68#63849—31no—
69#63849—31no—
70#63849—61no—
71#63844—31no—
72#63844D311yescharacteristic, complemented
73#63843—31no—
74Dic3×Dic6—31no—
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C22×C32×D3C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C4×C3⋊(C3⋊D3)C2×C414yescomplemented
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×#634C2×C414yescomplemented
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C32×D12C2×C414yescomplemented
89#6291C2×C418yescomplemented
90#6289—22no—
91#6289—22no—
92D3×C3⋊Dic3C2×C418yescomplemented
93C3×D3×Dic3—24no—
94C3×D3×Dic3—24no—
95C4×#239—91no—
96C4×#237—91no—
97C4×#237—91no—
98C2×C32×D4—31no—
99C2×#638—32no—
100C22×C3⋊Dic3—32no—
101#3830—38no—
102C2×C4×C3⋊D3—31no—
103C2×C4×C3⋊D3—31no—
104C2×C4×C3⋊D3—31no—
105C2×C4×C3⋊D3—31no—
106C2×C4×C3⋊D3—31no—
107C2×C4×C3⋊D3—61no—
108C2×C4×C3⋊D3—61no—
109C2×C4×C3⋊D3—61no—
110C2×C4×C3⋊D3—121no—
111C2×#634C2×D311yescharacteristic
112C22×C3×Dic3—32no—
113C22×C3×Dic3—32no—
114C2×C3×D12—21no—
115C2×C3×D12C2×D311yescharacteristic
116C2×C3×D12C2×D311yescharacteristic
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—32no—
119C2×C3×Dic6—31no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—61no—
122C2×#626—32no—
123C2×#626—32no—
124C2×#626—62no—
125C2×#624—31no—
126C2×#624—31no—
127C2×#624—31no—
128C2×#624—31no—
129C2×#624—61no—
130C2×#624—61no—
131C2×D3×Dic3—32no—
132C2×D3×Dic3—32no—
133C2×D3×Dic3—62no—
134C2×D3×Dic3C2×D312yes—
135C2×D3×Dic3C2×D312yes—
136#3796—38no—
137#3796—38no—
138#3796—68no—
139C32×C4⋊C4—31no—
140C32×C42—31no—
141#3752—32no—
142C4⋊(C3⋊Dic3)C2×D311yescharacteristic
143C4×C3⋊Dic3—31no—
144C4×C3⋊Dic3—31no—
145C4×C3⋊Dic3—32no—
146C4×C3⋊Dic3C2×D311yescharacteristic
147C3×#217—32no—
148C3×#217—32no—
149C3×(C2×D3)⋊C4—32no—
150C3×(C2×D3)⋊C4—32no—
151C3×C4⋊Dic3—21no—
152C3×C4⋊Dic3—31no—
153C3×C4⋊Dic3—31no—
154C3×C4⋊Dic3—61no—
155C3×C4⋊Dic3C2×D311yescharacteristic
156C3×C4⋊Dic3C2×D311yescharacteristic
157C3×Dic3⋊C4—32no—
158C3×Dic3⋊C4—32no—
159C3×C4×Dic3—21no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—32no—
163C3×C4×Dic3—32no—
164C3×C4×Dic3—61no—
165C3×C4×Dic3C2×D311yescharacteristic
166C3×C4×Dic3C2×D311yescharacteristic
167#3724—32no—
168#3724C2×D312yes—
169Dic3⋊Dic3—32no—
170Dic3⋊Dic3—32no—
171#3722—32no—
172#3722—32no—
173#3722—62no—
174(C2×D3)⋊Dic3C2×D312yes—
175(C2×D3)⋊Dic3C2×D312yes—
176Dic32—32no—
177Dic32—32no—
178Dic32—32no—
179Dic32—32no—
180Dic32—32no—
181Dic32—31no—
182Dic32—31no—
183Dic32—31no—
184Dic32—31no—
185Dic32—62no—
186Dic32—61no—
187Dic32—61no—
188Dic32C2×D312yes—
189C22×C33C2411yescharacteristic
190C2×C3⋊(C3⋊D3)—21no—
191C2×C3⋊(C3⋊D3)—21no—
192C2×C3⋊(C3⋊D3)C22×C412yes—
193C2×C32×D3—22no—
194C2×C32×D3—22no—
195C2×C32×D3C22×C414yes—
196C33×C4C22×C412yes—
197C3⋊(C3⋊Dic3)C22×C412yes—
198C3×C3⋊Dic3—21no—
199C3×C3⋊Dic3—22no—
200C3×C3⋊Dic3C22×C414yes—
201C3×C3⋊Dic3#4112yescomplemented
202C32×Dic3—21no—
203C32×Dic3—22no—
204C32×Dic3#4112yescomplemented
205C2×#239—91no—
206C2×#237—91no—
207C2×#237—91no—
208C2×#237—181no—
209C3×C4×Q8—91no—
210C3×C4×D4—91no—
211C3×C4×D4—91no—
212Q8×Dic3—91no—
213D4×Dic3—31no—
214D4×Dic3—31no—
215C4×#67—92no—
216C4×#67—92no—
217C2×C4×Dic3—92no—
218C2×C4×Dic3—92no—
219#893—31no—
220#893—92no—
221#892—91no—
222#892—91no—
223#892—92no—
224#892—91no—
225#892—181no—
226#887—31no—
227#887—91no—
228#67⋊C4—92no—
229#67⋊C4—92no—
230#877—92no—
231#877—92no—
232C4×D12—31no—
233C4×D12—92no—
234C42×D3—91no—
235C42×D3—91no—
236C42×D3—92no—
237C42×D3—91no—
238C42×D3—181no—
239C4×Dic6—31no—
240C4×Dic6—91no—
241C23×C32—32no—
242C22×C3⋊D3—31no—
243C22×C3⋊D3—31no—
244C22×C3⋊D3—31no—
245C22×C3⋊D3—61no—
246C22×C3⋊D3—61no—
247C22×C3⋊D3—61no—
248C22×C3⋊D3—121no—
249C22×C3×D3—22no—
250C22×C3×D3C22×D312yes—
251C22×C3×D3C22×D312yes—
252C32×D4—34no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—31no—
257C2×C32×C4—32no—
258C2×C32×C4—31no—
259C2×C32×C4—41no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263#638—38no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—31no—
267C2×C3⋊Dic3—38no—
268C2×C3⋊Dic3—61no—
269C2×C3⋊Dic3—61no—
270C2×C3⋊Dic3—61no—
271C2×C3⋊Dic3—121no—
272C2×C3⋊Dic3C22×D312yes—
273C2×C3⋊Dic3C22×D311yescharacteristic
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D311yescharacteristic
276C4×C3⋊D3—34no—
277C4×C3⋊D3—34no—
278C4×C3⋊D3—34no—
279C4×C3⋊D3—64no—
280C4×C3⋊D3—64no—
281C4×C3⋊D3—64no—
282C4×C3⋊D3—62no—
283C4×C3⋊D3—62no—
284C4×C3⋊D3—124no—
285#634C4×D314yescomplemented
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—32no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—32no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—61no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—62no—
301C2×C3×Dic3—64no—
302C2×C3×Dic3—64no—
303C2×C3×Dic3C22×D312yes—
304C2×C3×Dic3C22×D311yescharacteristic
305C2×C3×Dic3C22×D312yes—
306C2×C3×Dic3C22×D311yescharacteristic
307C2×C3×Dic3C22×D311yescharacteristic
308C2×C3×Dic3C22×D311yescharacteristic
309C3×D12—24no—
310C3×D12C4×D314yescomplemented
311C3×D12C4×D314yescomplemented
312C3×C4×D3—64no—
313C3×C4×D3—64no—
314C3×Dic6—34no—
315C3×Dic6—34no—
316C3×Dic6—64no—
317#626—38no—
318#626—38no—
319#626—68no—
320#624—62no—
321#624—62no—
322#624—64no—
323#624—64no—
324#624—62no—
325#624—62no—
326D3×Dic3—24no—
327D3×Dic3—24no—
328D3×Dic3—38no—
329D3×Dic3—38no—
330D3×Dic3—68no—
331C4×#41—271noSylow
332C2×C33C23×C411yescharacteristic
333C2×C33C2×#4111yescharacteristic
334C2×C33C2×#4111yescharacteristic
335C3⋊(C3⋊D3)—22no—
336C32×D3—24no—
337C2×C3×Q8—91no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—61no—
341C22×C3×C4—92no—
342C22×C3×C4—92no—
343C2×#67—92no—
344C2×#67—92no—
345C2×#67—182no—
346C22×Dic3—32no—
347C22×Dic3—32no—
348C22×Dic3—92no—
349C22×Dic3—92no—
350C22×Dic3—182no—
351#239—98no—
352#237—98no—
353#237—98no—
354#237—188no—
355C2×D12—92no—
356C2×D12D3211yescharacteristic
357C2×C4×D3—32no—
358C2×C4×D3—32no—
359C2×C4×D3—92no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×C4×D3—181no—
370C2×C4×D3—181no—
371C2×C4×D3—181no—
372C2×C4×D3—181no—
373C2×C4×D3—181no—
374C2×C4×D3—361no—
375C2×Dic6—31no—
376C2×Dic6—31no—
377C2×Dic6—61no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—92no—
382C3×C4⋊C4—91no—
383C3×C22⋊C4—92no—
384C3×C22⋊C4—92no—
385C3×C42—31no—
386C3×C42—31no—
387C3×C42—61no—
388C3×C42—92no—
389C3×C42—91no—
390#217—32no—
391#217—32no—
392(C2×D3)⋊C4—32no—
393(C2×D3)⋊C4—32no—
394(C2×D3)⋊C4—92no—
395(C2×D3)⋊C4—92no—
396(C2×D3)⋊C4—92no—
397(C2×D3)⋊C4—182no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—61no—
401C4⋊Dic3—92no—
402C4⋊Dic3D3211yescharacteristic
403Dic3⋊C4—32no—
404Dic3⋊C4—32no—
405Dic3⋊C4—92no—
406Dic3⋊C4—92no—
407C4×Dic3—31no—
408C4×Dic3—31no—
409C4×Dic3—32no—
410C4×Dic3—32no—
411C4×Dic3—61no—
412C4×Dic3—92no—
413C4×Dic3—92no—
414C4×Dic3—92no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—92no—
419C4×Dic3—91no—
420C4×Dic3—92no—
421C4×Dic3—91no—
422C4×Dic3—91no—
423C4×Dic3—92no—
424C4×Dic3—181no—
425C4×Dic3—181no—
426C4×Dic3—182no—
427C4×Dic3D3211yescharacteristic
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—34no—
432C22×C32—41no—
433C22×C32—62no—
434C22×C32—62no—
435C22×C32C23×D311yescharacteristic
436C22×C32C23×D311yescharacteristic
437C22×C32C23×D311yescharacteristic
438C2×C3⋊D3—32no—
439C2×C3⋊D3—32no—
440C2×C3⋊D3—32no—
441C2×C3⋊D3—62no—
442C2×C3⋊D3—62no—
443C2×C3⋊D3—62no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—62no—
447C2×C3⋊D3—62no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—122no—
453C2×C3⋊D3—121no—
454C2×C3⋊D3—121no—
455C2×C3⋊D3—121no—
456C2×C3⋊D3—121no—
457C2×C3⋊D3—122no—
458C2×C3⋊D3—122no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—24no—
464C2×C3×D3—42no—
465C2×C3×D3—42no—
466C2×C3×D3C2×C4×D314yes—
467C2×C3×D3C2×C4×D314yes—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4—22no—
471C32×C4—32no—
472C32×C4—42no—
473C32×C4—61no—
474C32×C4—62no—
475C32×C4C2×C4×D312yes—
476C32×C4C2×C4×D312yes—
477C32×C4C2×C4×D312yes—
478C3⋊Dic3—21no—
479C3⋊Dic3—22no—
480C3⋊Dic3—32no—
481C3⋊Dic3—32no—
482C3⋊Dic3—32no—
483C3⋊Dic3—62no—
484C3⋊Dic3—62no—
485C3⋊Dic3—62no—
486C3⋊Dic3—122no—
487C3⋊Dic3C2×C4×D314yes—
488C3⋊Dic3#23712yescomplemented
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3—34no—
496C3×Dic3—34no—
497C3×Dic3—32no—
498C3×Dic3—32no—
499C3×Dic3—42no—
500C3×Dic3—64no—
501C3×Dic3—62no—
502C3×Dic3—62no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—62no—
506C3×Dic3—62no—
507C3×Dic3—122no—
508C3×Dic3#23712yescomplemented
509C3×Dic3#23912yescomplemented
510C2×#41—271no—
511C4×Q8—91no—
512C4×Q8—271no—
513C4×D4—91no—
514C4×D4—91no—
515C4×D4—272no—
516C4×D4—272no—
517#117—272no—
518#117—271no—
519C2×C42—271no—
520C2×C42—272no—
521C33C4×#4111yescharacteristic, complemented, Sylow
522C23×C3—32no—
523C23×C3—32no—
524C23×C3—62no—
525C22×D3—91no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—181no—
529C22×D3—181no—
530C22×D3—181no—
531C22×D3—361no—
532C22×D3C2×D3212yes—
533C3×Q8—94no—
534C3×D4—34no—
535C3×D4—34no—
536C3×D4—64no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—32no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—32no—
546C2×C3×C4—41no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—62no—
550C2×C3×C4—91no—
551C2×C3×C4—92no—
552C2×C3×C4—92no—
553C2×C3×C4—91no—
554C2×C3×C4—184no—
555C2×C3×C4—184no—
556C2×C3×C4C2×D3211yescharacteristic
557C2×C3×C4C2×D3211yescharacteristic
558C2×C3×C4C2×D3211yescharacteristic
559#67—98no—
560#67—98no—
561#67—188no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—64no—
575C2×Dic3—64no—
576C2×Dic3—98no—
577C2×Dic3—98no—
578C2×Dic3—91no—
579C2×Dic3—91no—
580C2×Dic3—91no—
581C2×Dic3—188no—
582C2×Dic3—181no—
583C2×Dic3—181no—
584C2×Dic3—181no—
585C2×Dic3—361no—
586C2×Dic3C2×D3212yes—
587C2×Dic3C2×D3211yescharacteristic
588C2×Dic3C2×D3211yescharacteristic
589D12—98no—
590D12#62414yescomplemented
591C4×D3—64no—
592C4×D3—64no—
593C4×D3—98no—
594C4×D3—94no—
595C4×D3—94no—
596C4×D3—94no—
597C4×D3—184no—
598C4×D3—184no—
599C4×D3—184no—
600C4×D3—182no—
601C4×D3—182no—
602C4×D3—182no—
603C4×D3—182no—
604C4×D3—182no—
605C4×D3—184no—
606C4×D3—184no—
607C4×D3—182no—
608C4×D3—364no—
609Dic6—34no—
610Dic6—34no—
611Dic6—64no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—41no—
622C2×C32—41no—
623C2×C32—41no—
624C2×C32—64no—
625C2×C32C22×C4×D311yescharacteristic
626C2×C32C22×C4×D311yescharacteristic
627C2×C32C22×C4×D311yescharacteristic
628C2×C32C2×#23711yescharacteristic
629C2×C32C2×#23711yescharacteristic
630C2×C32C2×#23911yescharacteristic
631C2×C32D3×#4111yescharacteristic
632C2×C32D3×#4111yescharacteristic
633C2×C32D3×#4111yescharacteristic
634C3⋊D3—62no—
635C3⋊D3—64no—
636C3⋊D3—62no—
637C3⋊D3—62no—
638C3⋊D3—122no—
639C3⋊D3—122no—
640C3⋊D3—124no—
641C3×D3—24no—
642C3×D3—24no—
643C3×D3—44no—
644#41—278no—
645C2×Q8—91no—
646C2×D4—31no—
647C2×D4—272no—
648C22×C4—92no—
649C22×C4—92no—
650C22×C4—271no—
651C22×C4—271no—
652C22×C4—272no—
653C22×C4—271no—
654C4⋊C4—31no—
655C4⋊C4—92no—
656C4⋊C4—91no—
657C4⋊C4—272no—
658C22⋊C4—92no—
659C22⋊C4—92no—
660C22⋊C4—272no—
661C42—31no—
662C42—92no—
663C42—91no—
664C42—271no—
665C42—271no—
666C42—272no—
667C42—272no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—34no—
672C22×C3—34no—
673C22×C3—41no—
674C22×C3—64no—
675C22×C3—62no—
676C22×C3—62no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—122no—
680C22×C3—122no—
681C22×C3C22×D3211yescharacteristic
682C22×C3C22×D3211yescharacteristic
683C22×C3C22×D3211yescharacteristic
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—92no—
687C2×D3—92no—
688C2×D3—92no—
689C2×D3—182no—
690C2×D3—182no—
691C2×D3—182no—
692C2×D3—182no—
693C2×D3—182no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—362no—
701C2×D3—361no—
702C2×D3—361no—
703C2×D3—361no—
704C2×D3—361no—
705C2×D3—362no—
706C2×D3—362no—
707C2×D3C2×#62414yes—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—22no—
711C3×C4—32no—
712C3×C4—32no—
713C3×C4—42no—
714C3×C4—62no—
715C3×C4—62no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—92no—
721C3×C4—94no—
722C3×C4—122no—
723C3×C4—181no—
724C3×C4—182no—
725C3×C4C4×D3212yes—
726C3×C4C4×D3212yes—
727C3×C4C2×#62412yes—
728Dic3—21no—
729Dic3—22no—
730Dic3—34no—
731Dic3—34no—
732Dic3—32no—
733Dic3—32no—
734Dic3—64no—
735Dic3—62no—
736Dic3—62no—
737Dic3—62no—
738Dic3—62no—
739Dic3—61no—
740Dic3—61no—
741Dic3—92no—
742Dic3—92no—
743Dic3—92no—
744Dic3—122no—
745Dic3—182no—
746Dic3—182no—
747Dic3—182no—
748Dic3—362no—
749Dic3#379612yescomplemented
750C32—21no—
751C32—21no—
752C32—21no—
753C32—41no—
754C32C4×#23711yescharacteristic, complemented
755C32C4×#23711yescharacteristic, complemented
756C32C4×#23911yescharacteristic, complemented
757C23—32no—
758C23—271no—
759Q8—94no—
760D4—34no—
761D4—278no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—32no—
765C2×C4—91no—
766C2×C4—92no—
767C2×C4—91no—
768C2×C4—92no—
769C2×C4—184no—
770C2×C4—184no—
771C2×C4—278no—
772C2×C4—271no—
773C2×C4—274no—
774C2×C4—542no—
775C2×C4—542no—
776C2×C4D3311yescharacteristic
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—41no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—64no—
790C2×C3—64no—
791C2×C3—124no—
792C2×C3C2×#379611yescharacteristic
793C2×C3C2×C4×D3211yescharacteristic
794C2×C3C2×C4×D3211yescharacteristic
795C2×C3#6430611yescharacteristic
796C2×C3D3×#23711yescharacteristic
797C2×C3D3×#23711yescharacteristic
798C2×C3D3×#23711yescharacteristic
799C2×C3D3×#23911yescharacteristic
800C2×C3C22×#62411yescharacteristic
801D3—24no—
802D3—184no—
803D3—182no—
804D3—182no—
805D3—182no—
806D3—362no—
807D3—362no—
808D3—364no—
809C22—34no—
810C22—62no—
811C22—62no—
812C22—272no—
813C22—541no—
814C22—541no—
815C22C2×D3311yescharacteristic
816C4—32no—
817C4—62no—
818C4—61no—
819C4—92no—
820C4—94no—
821C4—182no—
822C4—181no—
823C4—272no—
824C4D3×#62412yes—
825C3—21no—
826C3—21no—
827C3—21no—
828C3—41no—
829C3C4×#379611yescharacteristic, complemented
830C3#1059436011yescharacteristic, complemented
831C3#1059519011yescharacteristic, complemented
832C2—64no—
833C2—542no—
834C2D3×#379611yescharacteristic
835C2#1172437311yescharacteristic
836C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89015C2
hypercenterC2×C4D33
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723668C2semidirect
3. C4×#6289C2semidirect
4. #11723413C2semidirect
5. C3×#63898C2semidirect
6. C3×Dic3×D12C2semidirect
7. C3×#63844C2semidirect
8. #11722935C2semidirect
9. #11722932C2semidirect
10. #11722917C2semidirect
11. D3×Dic32C2semidirect
22. #89015C4semidirect
57. #63898D3semidirect
58. Dic3×D12D3semidirect
72. #63844D3semidirect
79. C4×C3⋊(C3⋊D3)C2×C4semidirect
84. C3×#634C2×C4semidirect
88. C32×D12C2×C4semidirect
89. #6291C2×C4semidirect
92. D3×C3⋊Dic3C2×C4semidirect
201. C3×C3⋊Dic3#41semidirect
204. C32×Dic3#41semidirect
285. #634C4×D3semidirect
310. C3×D12C4×D3semidirect
311. C3×D12C4×D3semidirect
488. C3⋊Dic3#237semidirect
508. C3×Dic3#237semidirect
509. C3×Dic3#239semidirect
521. C33C4×#41semidirect
590. D12#624semidirect
749. Dic3#3796semidirect
754. C32C4×#237semidirect
755. C32C4×#237semidirect
756. C32C4×#239semidirect
829. C3C4×#3796semidirect
830. C3#10594360semidirect
831. C3#10595190semidirect

Maximal subgroups

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

subgroupindex
C2×#890152
#117236682
C4×#62892
#117234132
C3×#638982
C3×Dic3×D122
C3×#638442
#117229352
#117229322
#117229172
D3×Dic322
#105951903
#105943603
C4×#37963