Finite Group Databasebeta

← #13167951

Subgroups — #13167951

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×#89017C211yesmaximal, characteristic
2#11723691C211yesmaximal, characteristic, complemented
3C4×#6289C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×#63843C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11722937C212yesmaximal, complemented
9#11722933C212yesmaximal, complemented
10#11722921C212yesmaximal, complemented
11Dic3×#624C212yesmaximal, complemented
12#10595386—31nomaximal
13#10594360—31nomaximal
14C4×#3796—31nomaximal
15C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6294C2212yes—
19C2×#6292C2212yes—
20C2×#6289C2211yescharacteristic
21C2×#6289C2211yescharacteristic
22C2×Dic3×C3⋊D3C2212yes—
23#89017C418yescomplemented
24C2×C3×#624C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C32×C4⋊Dic3C2211yescharacteristic
28C32×C4×Dic3C2211yescharacteristic
29#88814C2212yes—
30#88804C2212yes—
31Dic3×C3⋊Dic3C2211yescharacteristic
32Dic3×C3⋊Dic3C2212yes—
33Dic3×C3⋊Dic3C2211yescharacteristic
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×#3722C2212yes—
37C3×Dic32C2212yes—
38C3×Dic32C2212yes—
39C2×#3832—31no—
40C2×#3796—31no—
41C2×#3796—31no—
42C2×#3796—61no—
43#64101—31no—
44C42×C3⋊D3—31no—
45C3×Q8×Dic3—31no—
46C3×Q8×Dic3—31no—
47C3×#893—31no—
48C3×#887—31no—
49C3×C4×D12—31no—
50C3×C4×Dic6—31no—
51#63904—32no—
52C4×#626—32no—
53#63898—31no—
54#63894—31no—
55#63894—32no—
56#63894—32no—
57#63894D311yescharacteristic, complemented
58Dic3×D12—31no—
59C4×#624—32no—
60C4×#624—31no—
61C4×#624—31no—
62C4×#624—61no—
63#63881—32no—
64#63880—32no—
65#63878—32no—
66#63878—32no—
67C4×D3×Dic3—32no—
68C4×D3×Dic3—32no—
69#63849—31no—
70#63849—31no—
71#63849—32no—
72#63849—61no—
73#63843D311yescharacteristic, complemented
74Dic3×Dic6D311yescharacteristic, complemented
75C22×C3⋊(C3⋊D3)C2311yescharacteristic
76C22×C3×C3⋊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⋊Dic3C2311yescharacteristic
83C3×C4⋊(C3⋊D3)C2×C414yescomplemented
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C32×Dic6C2×C414yescomplemented
89#6294—24no—
90#6292C2×C418yescomplemented
91#6289—22no—
92#6289—22no—
93Dic3×C3⋊D3C2×C418yescomplemented
94C3×#624—24no—
95C4×#239—91no—
96C4×#239—91no—
97C4×#237—91no—
98C2×C32×Q8—31no—
99#3832—38no—
100C2×C4⋊(C3⋊D3)—32no—
101C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
102C2×C4×C3⋊D3—32no—
103C2×C4×C3⋊D3—31no—
104C2×C4×C3⋊D3—31no—
105C2×C4×C3⋊D3—31no—
106C2×C4×C3⋊D3—31no—
107C2×C4×C3⋊D3—31no—
108C2×C4×C3⋊D3—61no—
109C2×C4×C3⋊D3—61no—
110C2×C4×C3⋊D3—61no—
111C2×C4×C3⋊D3—121no—
112C2×C3×D12—31no—
113C2×C3×D12—31no—
114C2×C3×D12—61no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—32no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6C2×D311yescharacteristic
119C2×C3×Dic6C2×D311yescharacteristic
120C2×#626—32no—
121C2×#626—32no—
122C2×#626—62no—
123C2×#624—32no—
124C2×#624—31no—
125C2×#624—31no—
126C2×#624—31no—
127C2×#624—31no—
128C2×#624—61no—
129C2×#624—61no—
130C2×#624C2×D312yes—
131C2×D3×Dic3—32no—
132C2×D3×Dic3—32no—
133C2×D3×Dic3—32no—
134C2×D3×Dic3—32no—
135C2×D3×Dic3—62no—
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×(C2×D3)⋊C4—32no—
148C3×(C2×D3)⋊C4—32no—
149C3×C4⋊Dic3—21no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—31no—
152C3×C4⋊Dic3—32no—
153C3×C4⋊Dic3—32no—
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—32no—
165C3×C4×Dic3—32no—
166C3×C4×Dic3—61no—
167C3×C4×Dic3C2×D311yescharacteristic
168C3×C4×Dic3C2×D311yescharacteristic
169Dic3⋊Dic3C2×D312yes—
170Dic3⋊Dic3C2×D312yes—
171#3722—32no—
172#3722—32no—
173#3722—32no—
174#3722—62no—
175#3722C2×D312yes—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178Dic32—32no—
179Dic32—31no—
180Dic32—32no—
181Dic32—31no—
182Dic32—31no—
183Dic32—31no—
184Dic32—62no—
185Dic32—61no—
186Dic32—61no—
187Dic32C2×D312yes—
188Dic32C2×D312yes—
189C22×C33C2411yescharacteristic
190C2×C3⋊(C3⋊D3)—21no—
191C2×C3⋊(C3⋊D3)—21no—
192C2×C3⋊(C3⋊D3)C22×C412yes—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3C22×C414yes—
196C33×C4C22×C412yes—
197C3⋊(C3⋊Dic3)C22×C412yes—
198C3×C3⋊Dic3—21no—
199C3×C3⋊Dic3—22no—
200C3×C3⋊Dic3#4112yescomplemented
201C32×Dic3—21no—
202C32×Dic3—22no—
203C32×Dic3C22×C414yes—
204C32×Dic3#4112yescomplemented
205C2×#239—91no—
206C2×#239—91no—
207C2×#239—181no—
208C2×#237—91no—
209C3×C4×Q8—91no—
210C3×C4×Q8—91no—
211C3×C4×D4—91no—
212Q8×Dic3—31no—
213Q8×Dic3—31no—
214D4×Dic3—91no—
215C4×#67—92no—
216C2×C4×Dic3—92no—
217#893—31no—
218#893—92no—
219#893—92no—
220#893—91no—
221#892—92no—
222#892—92no—
223#892—91no—
224#892—91no—
225#892—91no—
226#892—181no—
227#887—31no—
228#67⋊C4—92no—
229#877—92no—
230C4×D12—31no—
231C4×D12—92no—
232C4×D12—92no—
233C4×D12—91no—
234C42×D3—91no—
235C42×D3—91no—
236C42×D3—92no—
237C42×D3—92no—
238C42×D3—91no—
239C42×D3—181no—
240C4×Dic6—31no—
241C22×C3⋊D3—31no—
242C22×C3⋊D3—31no—
243C22×C3⋊D3—31no—
244C22×C3⋊D3—61no—
245C22×C3⋊D3—61no—
246C22×C3⋊D3—61no—
247C22×C3⋊D3—121no—
248C22×C3⋊D3C22×D312yes—
249C22×C3×D3—32no—
250C22×C3×D3—32no—
251C22×C3×D3—62no—
252C32×Q8—34no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—32no—
257C2×C32×C4—31no—
258C2×C32×C4—32no—
259C2×C32×C4—31no—
260C2×C32×C4—41no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—31no—
267C2×C3⋊Dic3—61no—
268C2×C3⋊Dic3—61no—
269C2×C3⋊Dic3—61no—
270C2×C3⋊Dic3—121no—
271C2×C3⋊Dic3C22×D312yes—
272C2×C3⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D311yescharacteristic
274C4⋊(C3⋊D3)—38no—
275C4⋊(C3⋊D3)C4×D314yescomplemented
276C4×C3⋊D3—38no—
277C4×C3⋊D3—34no—
278C4×C3⋊D3—34no—
279C4×C3⋊D3—34no—
280C4×C3⋊D3—64no—
281C4×C3⋊D3—64no—
282C4×C3⋊D3—64no—
283C4×C3⋊D3—62no—
284C4×C3⋊D3—62no—
285C4×C3⋊D3—124no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—32no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3C22×D312yes—
300C2×C3×Dic3C22×D312yes—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C2×C3×Dic3C22×D312yes—
304C2×C3×Dic3C22×D312yes—
305C2×C3×Dic3C22×D311yescharacteristic
306C2×C3×Dic3C22×D311yescharacteristic
307C3×D12—34no—
308C3×D12—34no—
309C3×D12—64no—
310C3×C4×D3—64no—
311C3×C4×D3—64no—
312C3×Dic6—24no—
313C3×Dic6C4×D314yescomplemented
314C3×Dic6C4×D314yescomplemented
315#626—38no—
316#626—38no—
317#626—68no—
318#624—24no—
319#624—62no—
320#624—62no—
321#624—64no—
322#624—64no—
323#624—64no—
324#624—62no—
325#624—62no—
326D3×Dic3—38no—
327D3×Dic3—38no—
328D3×Dic3—68no—
329D3×Dic3—64no—
330D3×Dic3—64no—
331C4×#41—271noSylow
332C2×C33C23×C411yescharacteristic
333C2×C33C2×#4111yescharacteristic
334C2×C33C2×#4111yescharacteristic
335C3⋊(C3⋊D3)—22no—
336C3×C3⋊D3—24no—
337C2×C3×Q8—31no—
338C2×C3×Q8—31no—
339C2×C3×Q8—61no—
340C2×C3×D4—91no—
341C22×C3×C4—92no—
342C2×#67—92no—
343C22×Dic3—92no—
344C22×Dic3—92no—
345#239—98no—
346#239—98no—
347#239—188no—
348#237—98no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—61no—
352C2×D12—92no—
353C2×D12—92no—
354C2×D12—182no—
355C2×C4×D3—32no—
356C2×C4×D3—32no—
357C2×C4×D3—92no—
358C2×C4×D3—92no—
359C2×C4×D3—91no—
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—92no—
367C2×C4×D3—92no—
368C2×C4×D3—91no—
369C2×C4×D3—91no—
370C2×C4×D3—181no—
371C2×C4×D3—181no—
372C2×C4×D3—181no—
373C2×C4×D3—181no—
374C2×C4×D3—181no—
375C2×C4×D3—182no—
376C2×C4×D3—361no—
377C2×Dic6D3211yescharacteristic
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—92no—
382C3×C4⋊C4—92no—
383C3×C4⋊C4—91no—
384C3×C22⋊C4—92no—
385C3×C42—31no—
386C3×C42—31no—
387C3×C42—61no—
388C3×C42—92no—
389C3×C42—92no—
390C3×C42—91no—
391#217—92no—
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—92no—
398(C2×D3)⋊C4—92no—
399(C2×D3)⋊C4—182no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—32no—
403C4⋊Dic3—32no—
404C4⋊Dic3—61no—
405C4⋊Dic3D3211yescharacteristic
406Dic3⋊C4—32no—
407Dic3⋊C4—32no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—32no—
411C4×Dic3—32no—
412C4×Dic3—32no—
413C4×Dic3—32no—
414C4×Dic3—61no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—92no—
419C4×Dic3—91no—
420C4×Dic3—92no—
421C4×Dic3—91no—
422C4×Dic3—92no—
423C4×Dic3—91no—
424C4×Dic3—181no—
425C4×Dic3—181no—
426C4×Dic3—182no—
427C4×Dic3D3211yescharacteristic
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—41no—
432C22×C32C23×D311yescharacteristic
433C22×C32C23×D311yescharacteristic
434C22×C32C23×D311yescharacteristic
435C2×C3⋊D3—22no—
436C2×C3⋊D3—22no—
437C2×C3⋊D3—32no—
438C2×C3⋊D3—32no—
439C2×C3⋊D3—32no—
440C2×C3⋊D3—62no—
441C2×C3⋊D3—62no—
442C2×C3⋊D3—62no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—62no—
446C2×C3⋊D3—62no—
447C2×C3⋊D3—61no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—122no—
452C2×C3⋊D3—121no—
453C2×C3⋊D3—121no—
454C2×C3⋊D3—121no—
455C2×C3⋊D3—121no—
456C2×C3⋊D3—122no—
457C2×C3⋊D3—122no—
458C2×C3⋊D3C2×C4×D314yes—
459C2×C3×D3—34no—
460C2×C3×D3—34no—
461C2×C3×D3—64no—
462C2×C3×D3—62no—
463C2×C3×D3—62no—
464C2×C3×D3—62no—
465C2×C3×D3—62no—
466C2×C3×D3—122no—
467C2×C3×D3—122no—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4—22no—
471C32×C4—34no—
472C32×C4—32no—
473C32×C4—42no—
474C32×C4—61no—
475C32×C4—62no—
476C32×C4C2×C4×D312yes—
477C32×C4C2×C4×D312yes—
478C32×C4C2×C4×D312yes—
479C3⋊Dic3—21no—
480C3⋊Dic3—22no—
481C3⋊Dic3—32no—
482C3⋊Dic3—32no—
483C3⋊Dic3—32no—
484C3⋊Dic3—62no—
485C3⋊Dic3—62no—
486C3⋊Dic3—62no—
487C3⋊Dic3—122no—
488C3⋊Dic3#23912yescomplemented
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3—24no—
496C3×Dic3—32no—
497C3×Dic3—32no—
498C3×Dic3—42no—
499C3×Dic3—62no—
500C3×Dic3—62no—
501C3×Dic3—61no—
502C3×Dic3—62no—
503C3×Dic3—61no—
504C3×Dic3—62no—
505C3×Dic3—122no—
506C3×Dic3C2×C4×D314yes—
507C3×Dic3C2×C4×D314yes—
508C3×Dic3#23712yescomplemented
509C3×Dic3#23912yescomplemented
510C2×#41—271no—
511C4×Q8—91no—
512C4×Q8—91no—
513C4×D4—91no—
514C4×D4—272no—
515C4×D4—272no—
516C4×D4—271no—
517#117—272no—
518#117—271no—
519C2×C42—271no—
520C2×C42—272no—
521C33C4×#4111yescharacteristic, complemented, Sylow
522C23×C3—92no—
523C22×D3—32no—
524C22×D3—32no—
525C22×D3—62no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—91no—
529C22×D3—181no—
530C22×D3—181no—
531C22×D3—181no—
532C22×D3—361no—
533C3×Q8—34no—
534C3×Q8—34no—
535C3×Q8—64no—
536C3×D4—94no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—31no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—31no—
544C2×C3×C4—32no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—32no—
548C2×C3×C4—41no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—92no—
556C2×C3×C4—184no—
557C2×C3×C4C2×D3211yescharacteristic
558C2×C3×C4C2×D3211yescharacteristic
559C2×C3×C4C2×D3211yescharacteristic
560#67—98no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—31no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—62no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—91no—
573C2×Dic3—98no—
574C2×Dic3—181no—
575C2×Dic3—181no—
576C2×Dic3—181no—
577C2×Dic3—184no—
578C2×Dic3—361no—
579C2×Dic3C2×D3212yes—
580C2×Dic3C2×D3211yescharacteristic
581C2×Dic3C2×D3211yescharacteristic
582C2×Dic3C2×D3212yes—
583D12—34no—
584D12—34no—
585D12—64no—
586D12—98no—
587D12—98no—
588D12—188no—
589C4×D3—64no—
590C4×D3—64no—
591C4×D3—98no—
592C4×D3—98no—
593C4×D3—94no—
594C4×D3—94no—
595C4×D3—94no—
596C4×D3—184no—
597C4×D3—184no—
598C4×D3—184no—
599C4×D3—188no—
600C4×D3—182no—
601C4×D3—182no—
602C4×D3—182no—
603C4×D3—184no—
604C4×D3—182no—
605C4×D3—182no—
606C4×D3—184no—
607C4×D3—184no—
608C4×D3—184no—
609C4×D3—182no—
610C4×D3—364no—
611Dic6#62414yescomplemented
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×C32C22×C4×D311yescharacteristic
625C2×C32C22×C4×D311yescharacteristic
626C2×C32C22×C4×D311yescharacteristic
627C2×C32C2×#23711yescharacteristic
628C2×C32C2×#23911yescharacteristic
629C2×C32C2×#23911yescharacteristic
630C2×C32D3×#4111yescharacteristic
631C2×C32D3×#4111yescharacteristic
632C2×C32D3×#4111yescharacteristic
633C3⋊D3—24no—
634C3⋊D3—62no—
635C3⋊D3—64no—
636C3⋊D3—62no—
637C3⋊D3—62no—
638C3⋊D3—122no—
639C3⋊D3—122no—
640C3⋊D3—124no—
641C3×D3—64no—
642C3×D3—64no—
643C3×D3—124no—
644#41—278no—
645C2×Q8—31no—
646C2×D4—91no—
647C2×D4—272no—
648C22×C4—92no—
649C22×C4—271no—
650C22×C4—271no—
651C22×C4—272no—
652C22×C4—272no—
653C22×C4—271no—
654C4⋊C4—31no—
655C4⋊C4—92no—
656C4⋊C4—92no—
657C4⋊C4—91no—
658C22⋊C4—92no—
659C22⋊C4—272no—
660C22⋊C4—272no—
661C42—31no—
662C42—92no—
663C42—92no—
664C42—91no—
665C42—271no—
666C42—271no—
667C42—272no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—41no—
672C22×C3—94no—
673C22×C3—182no—
674C22×C3—182no—
675C22×C3C22×D3211yescharacteristic
676C22×C3C22×D3211yescharacteristic
677C22×C3C22×D3211yescharacteristic
678C2×D3—34no—
679C2×D3—34no—
680C2×D3—64no—
681C2×D3—62no—
682C2×D3—62no—
683C2×D3—62no—
684C2×D3—62no—
685C2×D3—92no—
686C2×D3—92no—
687C2×D3—92no—
688C2×D3—122no—
689C2×D3—122no—
690C2×D3—182no—
691C2×D3—182no—
692C2×D3—182no—
693C2×D3—182no—
694C2×D3—182no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—362no—
702C2×D3—361no—
703C2×D3—361no—
704C2×D3—361no—
705C2×D3—361no—
706C2×D3—362no—
707C2×D3—362no—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—22no—
711C3×C4—34no—
712C3×C4—34no—
713C3×C4—32no—
714C3×C4—32no—
715C3×C4—42no—
716C3×C4—64no—
717C3×C4—62no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—62no—
723C3×C4—92no—
724C3×C4—122no—
725C3×C4—181no—
726C3×C4—182no—
727C3×C4C4×D3212yes—
728C3×C4C4×D3212yes—
729C3×C4C2×#62412yes—
730Dic3—21no—
731Dic3—22no—
732Dic3—32no—
733Dic3—32no—
734Dic3—62no—
735Dic3—62no—
736Dic3—62no—
737Dic3—61no—
738Dic3—61no—
739Dic3—62no—
740Dic3—92no—
741Dic3—92no—
742Dic3—92no—
743Dic3—122no—
744Dic3—182no—
745Dic3—182no—
746Dic3—182no—
747Dic3—362no—
748Dic3#379612yescomplemented
749Dic3C2×#62414yes—
750C32—21no—
751C32—21no—
752C32—21no—
753C32—41no—
754C32C4×#23711yescharacteristic, complemented
755C32C4×#23911yescharacteristic, complemented
756C32C4×#23911yescharacteristic, complemented
757C23—92no—
758C23—271no—
759Q8—34no—
760D4—94no—
761D4—278no—
762C2×C4—31no—
763C2×C4—32no—
764C2×C4—31no—
765C2×C4—32no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—92no—
769C2×C4—184no—
770C2×C4—278no—
771C2×C4—271no—
772C2×C4—274no—
773C2×C4—542no—
774C2×C4—542no—
775C2×C4—544no—
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—184no—
790C2×C3C2×#379611yescharacteristic
791C2×C3C2×C4×D3211yescharacteristic
792C2×C3C2×C4×D3211yescharacteristic
793C2×C3#6430611yescharacteristic
794C2×C3D3×#23711yescharacteristic
795C2×C3D3×#23911yescharacteristic
796C2×C3D3×#23911yescharacteristic
797C2×C3D3×#23911yescharacteristic
798C2×C3C22×#62411yescharacteristic
799D3—64no—
800D3—64no—
801D3—124no—
802D3—184no—
803D3—182no—
804D3—182no—
805D3—182no—
806D3—362no—
807D3—362no—
808D3—364no—
809C22—94no—
810C22—182no—
811C22—182no—
812C22—272no—
813C22—541no—
814C22—541no—
815C22C2×D3311yescharacteristic
816C4—32no—
817C4—34no—
818C4—62no—
819C4—61no—
820C4—92no—
821C4—181no—
822C4—182no—
823C4—272no—
824C4D3×#62412yes—
825C3—21no—
826C3—21no—
827C3—21no—
828C3—41no—
829C3C4×#379611yescharacteristic, complemented
830C3#1059436011yescharacteristic, complemented
831C3#1059538611yescharacteristic, complemented
832C2—184no—
833C2—542no—
834C2D3×#379611yescharacteristic
835C2#1172439111yescharacteristic
836C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89017C2
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. #11723691C2semidirect
3. C4×#6289C2semidirect
4. #11723413C2semidirect
5. C3×#63894C2semidirect
6. C3×#63843C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11722937C2semidirect
9. #11722933C2semidirect
10. #11722921C2semidirect
11. Dic3×#624C2semidirect
23. #89017C4semidirect
57. #63894D3semidirect
73. #63843D3semidirect
74. Dic3×Dic6D3semidirect
79. C4×C3⋊(C3⋊D3)C2×C4semidirect
83. C3×C4⋊(C3⋊D3)C2×C4semidirect
88. C32×Dic6C2×C4semidirect
90. #6292C2×C4semidirect
93. Dic3×C3⋊D3C2×C4semidirect
200. C3×C3⋊Dic3#41semidirect
204. C32×Dic3#41semidirect
275. C4⋊(C3⋊D3)C4×D3semidirect
313. C3×Dic6C4×D3semidirect
314. C3×Dic6C4×D3semidirect
488. C3⋊Dic3#239semidirect
508. C3×Dic3#237semidirect
509. C3×Dic3#239semidirect
521. C33C4×#41semidirect
611. Dic6#624semidirect
748. Dic3#3796semidirect
754. C32C4×#237semidirect
755. C32C4×#239semidirect
756. C32C4×#239semidirect
829. C3C4×#3796semidirect
830. C3#10594360semidirect
831. C3#10595386semidirect

Maximal subgroups

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

subgroupindex
C2×#890172
#117236912
C4×#62892
#117234132
C3×#638942
C3×#638432
C3×Dic3×Dic62
#117229372
#117229332
#117229212
Dic3×#6242
#105953863
#105943603
C4×#37963