Finite Group Databasebeta

← #13168151

Subgroups — #13168151

Order 1728.

1458 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3795C211yesmaximal, characteristic
2#11723668C211yesmaximal, characteristic, complemented
3D12×C3⋊Dic3C211yesmaximal, characteristic, complemented
4D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5Dic3×#634C211yesmaximal, characteristic, complemented
6C3×Dic3×D12C211yesmaximal, characteristic, complemented
7C3×#63855C211yesmaximal, characteristic, complemented
8#11722925C212yesmaximal, complemented
9#11722924C212yesmaximal, complemented
10#11722914C212yesmaximal, complemented
11D3×Dic3⋊Dic3C212yesmaximal, complemented
12#10595222—31nomaximal
13#10594992—31nomaximal
14#10593887—31nomaximal
15C2×C3×#634C2211yescharacteristic
16C2×C32×D12C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×D3×C3⋊Dic3C2212yes—
19C2×D3×C3⋊Dic3C2212yes—
20C2×C3×#625C2212yes—
21C2×C3×D3×Dic3C2212yes—
22C2×C3×D3×Dic3C2212yes—
23C3×#3795C418yescomplemented
24C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88815C2212yes—
29#88813C2212yes—
30#88807C2212yes—
31Dic3⋊(C3⋊Dic3)C2212yes—
32(C2×D3)⋊(C3⋊Dic3)C2212yes—
33Dic3×C3⋊Dic3C2212yes—
34C3×Dic3⋊Dic3C2211yescharacteristic
35C3×Dic3⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×C3×#237—31no—
40C2×C3×#235—31no—
41C2×#3795D311yescharacteristic
42D4×C3⋊Dic3—31no—
43C2×C4⋊(C3⋊Dic3)—31no—
44C4×#634—31no—
45C3×D4×Dic3—31no—
46C3×#926—31no—
47C3×C4×D12—31no—
48C3×#872—31no—
49#67⋊Dic3—32no—
50#67⋊Dic3—32no—
51#67⋊Dic3—32no—
52Dic3×#67—32no—
53C2×Dic3⋊Dic3—32no—
54#63955—32no—
55#63902—32no—
56Dic3×D12—31no—
57Dic3×D12—31no—
58Dic3×D12—61no—
59Dic3×D12D311yescharacteristic, complemented
60D3×C4⋊Dic3—31no—
61D3×C4⋊Dic3—31no—
62D3×C4⋊Dic3—32no—
63D3×C4⋊Dic3—61no—
64#63879—32no—
65#63878—32no—
66D3×Dic3⋊C4—32no—
67#63855D311yescharacteristic, complemented
68#63844—31no—
69#63843—31no—
70Dic3×Dic6—31no—
71Dic3×Dic6—31no—
72Dic3×Dic6—31no—
73Dic3×Dic6—61no—
74#63841—32no—
75C22×C32×D3C2312yes—
76C22×C32×D3C2311yescharacteristic
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2312yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C3×#634C2×C414yescomplemented
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C32×D12C2×C414yescomplemented
88C32×C4×D3C2×C414yescomplemented
89D3×C3⋊Dic3—42no—
90D3×C3⋊Dic3—42no—
91C3×#625C2×C418yescomplemented
92C3×D3×Dic3—42no—
93C3×D3×Dic3C2×C418yescomplemented
94#5827—91no—
95#5546—91no—
96#5523—91no—
97C2×C32×D4—31no—
98C22×C32×C4—31no—
99C22×C3⋊Dic3—32no—
100C22×C3⋊Dic3—32no—
101C2×#634C2×D311yescharacteristic
102C2×C3×#67—32no—
103C2×C3×#67—32no—
104C22×C3×Dic3—32no—
105C22×C3×Dic3—32no—
106C3×#237—38no—
107C3×#235—38no—
108C2×C3×D12—21no—
109C2×C3×D12C2×D311yescharacteristic
110C2×C3×D12C2×D311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3C2×D311yescharacteristic
115C2×C3×C4×D3C2×D311yescharacteristic
116C2×C3×Dic6—31no—
117C2×C3×Dic6—31no—
118C2×C3×Dic6—61no—
119C2×#625C2×D312yes—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—62no—
125C2×D3×Dic3—62no—
126C2×D3×Dic3C2×D312yes—
127C2×D3×Dic3C2×D312yes—
128#3795Dic318yescomplemented
129C32×C42—31no—
130#3757—32no—
131C4⋊(C3⋊Dic3)—31no—
132C4⋊(C3⋊Dic3)—31no—
133C4⋊(C3⋊Dic3)—31no—
134C4⋊(C3⋊Dic3)—32no—
135C4⋊(C3⋊Dic3)—61no—
136C4⋊(C3⋊Dic3)—61no—
137C4⋊(C3⋊Dic3)—61no—
138C4⋊(C3⋊Dic3)—121no—
139C4⋊(C3⋊Dic3)C2×D311yescharacteristic
140#3750—32no—
141C4×C3⋊Dic3—32no—
142C4×C3⋊Dic3C2×D311yescharacteristic
143C3×#217—31no—
144C3×#217—31no—
145C3×#217—32no—
146C3×(C2×D3)⋊C4—32no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—31no—
152C3×C4⋊Dic3—31no—
153C3×C4⋊Dic3—61no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4—31no—
156C3×C4×Dic3—21no—
157C3×C4×Dic3—31no—
158C3×C4×Dic3—31no—
159C3×C4×Dic3—61no—
160C3×C4×Dic3C2×D311yescharacteristic
161C3×C4×Dic3C2×D311yescharacteristic
162#3724—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—62no—
170Dic3⋊Dic3—62no—
171Dic3⋊Dic3C2×D311yescharacteristic
172Dic3⋊Dic3C2×D311yescharacteristic
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—62no—
176(C2×D3)⋊Dic3C2×D312yes—
177(C2×D3)⋊Dic3C2×D311yescharacteristic
178(C2×D3)⋊Dic3C2×D311yescharacteristic
179Dic32—32no—
180Dic32—32no—
181Dic32—32no—
182Dic32—32no—
183Dic32—32no—
184Dic32—62no—
185C22×C33C2411yescharacteristic
186C2×C32×D3—21no—
187C2×C32×D3—22no—
188C2×C32×D3—21no—
189C2×C32×D3—22no—
190C2×C32×D3C22×C414yes—
191C2×C32×D3C22×C412yes—
192C33×C4C22×C412yes—
193C3⋊(C3⋊Dic3)—22no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3—21no—
197C3×C3⋊Dic3C22×C414yes—
198C32×Dic3—21no—
199C32×Dic3—21no—
200C32×Dic3C22×C412yes—
201C2×C3×#41—91no—
202C2×#237—31no—
203C2×#235—31no—
204C3×C4×D4—91no—
205C3×#117—91no—
206Q8×Dic3—91no—
207Q8×Dic3—91no—
208D4×Dic3—31no—
209D4×Dic3—91no—
210D4×Dic3—91no—
211D4×Dic3—92no—
212D4×Dic3—92no—
213D4×Dic3—181no—
214C4×#67—92no—
215#926—31no—
216#926—92no—
217C2×C4⋊Dic3—92no—
218C2×C4⋊Dic3—91no—
219C2×C4⋊Dic3—91no—
220C2×C4⋊Dic3—181no—
221C2×Dic3⋊C4—92no—
222#892—92no—
223D3×C4⋊C4—92no—
224D3×C4⋊C4—91no—
225#887—91no—
226#67⋊C4—92no—
227#67⋊C4—92no—
228#67⋊C4—92no—
229#877—92no—
230C4×D12—31no—
231C4×D12—91no—
232#872—31no—
233C4×Dic6—91no—
234C4×Dic6—91no—
235C4×Dic6—91no—
236C4×Dic6—181no—
237C23×C32—31no—
238C23×C32—32no—
239C22×C3×D3—21no—
240C22×C3×D3—22no—
241C22×C3×D3C22×D312yes—
242C22×C3×D3C22×D311yescharacteristic
243C22×C3×D3C22×D312yes—
244C22×C3×D3C22×D311yescharacteristic
245C32×D4—34no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—31no—
250C2×C32×C4—34no—
251C2×C32×C4—31no—
252C2×C32×C4—31no—
253C2×C32×C4—41no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C3⋊Dic3—32no—
258C2×C3⋊Dic3—32no—
259C2×C3⋊Dic3—32no—
260C2×C3⋊Dic3—62no—
261C2×C3⋊Dic3—62no—
262C2×C3⋊Dic3—62no—
263C2×C3⋊Dic3—122no—
264C2×C3⋊Dic3—122no—
265C2×C3⋊Dic3—122no—
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D312yes—
268C2×C3⋊Dic3C22×D311yescharacteristic
269C2×C3⋊Dic3C22×D312yes—
270#634C2×Dic314yescomplemented
271C3×#67—38no—
272C3×#67—38no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—38no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—62no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—122no—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C3×D12—24no—
297C3×D12C4×D314yescomplemented
298C3×D12C2×Dic314yescomplemented
299C3×C4×D3—24no—
300C3×C4×D3—38no—
301C3×C4×D3—122no—
302C3×C4×D3C4×D314yescomplemented
303C3×C4×D3C2×Dic314yescomplemented
304C3×Dic6—34no—
305C3×Dic6—34no—
306C3×Dic6—64no—
307#625C2×Dic318yescomplemented
308D3×Dic3—42no—
309D3×Dic3—122no—
310D3×Dic3—122no—
311D3×Dic3—122no—
312D3×Dic3—122no—
313D3×Dic3—124no—
314D3×Dic3—124no—
315D3×Dic3C2×Dic318yescomplemented
316#520—271noSylow
317C2×C33C23×C411yescharacteristic
318C2×C33H(5,𝔽2)11yescharacteristic
319C2×C332−1+411yescharacteristic
320C32×D3—22no—
321C32×D3—24no—
322C3×#41—98no—
323C2×C3×Q8—91no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C2×C3×D4—92no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C22×C3×C4—92no—
332C22×C3×C4—92no—
333C2×#67—32no—
334C2×#67—32no—
335C22×Dic3—32no—
336C22×Dic3—32no—
337C22×Dic3—92no—
338C22×Dic3—92no—
339C22×Dic3—92no—
340C22×Dic3—92no—
341C22×Dic3—182no—
342C22×Dic3—182no—
343#237—38no—
344#235—38no—
345C2×D12D3211yescharacteristic
346C2×C4×D3—32no—
347C2×C4×D3—32no—
348C2×C4×D3—92no—
349C2×C4×D3—92no—
350C2×C4×D3D3211yescharacteristic
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—61no—
354C3×C4⋊C4—91no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—91no—
357C3×C22⋊C4—92no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4—91no—
360C3×C42—31no—
361C3×C42—31no—
362C3×C42—61no—
363C3×C42—91no—
364#217—31no—
365#217—31no—
366#217—32no—
367#217—92no—
368#217—92no—
369#217—182no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—32no—
373(C2×D3)⋊C4—92no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—92no—
380C4⋊Dic3—92no—
381C4⋊Dic3—92no—
382C4⋊Dic3—91no—
383C4⋊Dic3—91no—
384C4⋊Dic3—91no—
385C4⋊Dic3—92no—
386C4⋊Dic3—182no—
387C4⋊Dic3—181no—
388C4⋊Dic3—181no—
389C4⋊Dic3—181no—
390C4⋊Dic3—361no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—92no—
394Dic3⋊C4—92no—
395Dic3⋊C4—92no—
396Dic3⋊C4—92no—
397Dic3⋊C4—92no—
398Dic3⋊C4—182no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C4×Dic3—92no—
403C4×Dic3—92no—
404C4×Dic3—92no—
405C4×Dic3—92no—
406C4×Dic3—92no—
407C4×Dic3—92no—
408C4×Dic3—182no—
409C4×Dic3D3211yescharacteristic
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—34no—
414C22×C32—32no—
415C22×C32—41no—
416C22×C32—61no—
417C22×C32—61no—
418C22×C32—62no—
419C22×C32—62no—
420C22×C32C23×D311yescharacteristic
421C22×C32C23×D311yescharacteristic
422C22×C32C23×D311yescharacteristic
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—24no—
435C2×C3×D3—42no—
436C2×C3×D3—42no—
437C2×C3×D3C2×C4×D314yes—
438C2×C3×D3C2×C4×D312yes—
439C2×C3×D3C22×Dic314yes—
440C2×C3×D3C22×Dic312yes—
441C32×C4—22no—
442C32×C4—22no—
443C32×C4—22no—
444C32×C4—32no—
445C32×C4—42no—
446C32×C4—61no—
447C32×C4—61no—
448C32×C4C2×C4×D312yes—
449C32×C4C2×C4×D312yes—
450C32×C4C22×Dic312yes—
451C3⋊Dic3—21no—
452C3⋊Dic3—22no—
453C3⋊Dic3—21no—
454C3⋊Dic3—62no—
455C3⋊Dic3—62no—
456C3⋊Dic3—62no—
457C3⋊Dic3—122no—
458C3⋊Dic3—122no—
459C3⋊Dic3—122no—
460C3⋊Dic3—242no—
461C3⋊Dic3C22×Dic314yes—
462C3×Dic3—22no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—21no—
466C3×Dic3—21no—
467C3×Dic3—22no—
468C3×Dic3—34no—
469C3×Dic3—34no—
470C3×Dic3—41no—
471C3×Dic3—64no—
472C3×Dic3—62no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C3×Dic3—62no—
476C3×Dic3—62no—
477C3×Dic3—61no—
478C3×Dic3—61no—
479C3×Dic3—122no—
480C3×Dic3—121no—
481C3×Dic3C2×C4×D312yes—
482C3×Dic3C22×Dic312yes—
483C2×#41—91no—
484C4×Q8—271no—
485C4×Q8—271no—
486C4×D4—91no—
487C4×D4—271no—
488C4×D4—272no—
489C4×D4—272no—
490#117—91no—
491#117—272no—
492C2×C4⋊C4—271no—
493C2×C4⋊C4—272no—
494C33#52011yescharacteristic, complemented, Sylow
495C23×C3—31no—
496C23×C3—32no—
497C23×C3—32no—
498C23×C3—31no—
499C23×C3—61no—
500C23×C3—62no—
501C22×D3C2×D3211yescharacteristic
502C22×D3C2×D3212yes—
503C3×Q8—94no—
504C3×D4—34no—
505C3×D4—34no—
506C3×D4—64no—
507C3×D4—98no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—34no—
514C2×C3×C4—34no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—64no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—98no—
525C2×C3×C4—92no—
526C2×C3×C4—91no—
527C2×C3×C4—92no—
528C2×C3×C4—91no—
529C2×C3×C4—362no—
530C2×C3×C4C2×D3211yescharacteristic
531C2×C3×C4C2×D3211yescharacteristic
532C2×C3×C4C2×D3211yescharacteristic
533#67—38no—
534#67—38no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—38no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—61no—
545C2×Dic3—62no—
546C2×Dic3—61no—
547C2×Dic3—62no—
548C2×Dic3—92no—
549C2×Dic3—92no—
550C2×Dic3—92no—
551C2×Dic3—122no—
552C2×Dic3—182no—
553C2×Dic3—182no—
554C2×Dic3—182no—
555C2×Dic3—362no—
556C2×Dic3—362no—
557C2×Dic3—362no—
558C2×Dic3—362no—
559C2×Dic3—362no—
560C2×Dic3—364no—
561C2×Dic3—364no—
562C2×Dic3C2×D3211yescharacteristic
563C2×Dic3C2×D3211yescharacteristic
564C2×Dic3C2×D3211yescharacteristic
565D12D3×Dic314yescomplemented
566C4×D3—38no—
567C4×D3—122no—
568C4×D3—362no—
569C4×D3—362no—
570C4×D3D3×Dic314yescomplemented
571Dic6—34no—
572Dic6—34no—
573Dic6—64no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32—41no—
586C2×C32—62no—
587C2×C32—64no—
588C2×C32C22×C4×D311yescharacteristic
589C2×C32C22×C4×D311yescharacteristic
590C2×C32#100411yescharacteristic
591C2×C32#100911yescharacteristic
592C2×C32#100911yescharacteristic
593C2×C32#101011yescharacteristic
594C2×C32#101011yescharacteristic
595C2×C32#101011yescharacteristic
596C2×C32C23×Dic311yescharacteristic
597C3×D3—24no—
598C3×D3—22no—
599C3×D3—24no—
600C3×D3—24no—
601C3×D3—22no—
602C3×D3—44no—
603#41—98no—
604C2×Q8—91no—
605C2×D4—31no—
606C2×D4—92no—
607C22×C4—31no—
608C22×C4—92no—
609C22×C4—92no—
610C22×C4—272no—
611C22×C4—272no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—272no—
616C4⋊C4—272no—
617C4⋊C4—272no—
618C4⋊C4—271no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—92no—
622C22⋊C4—272no—
623C42—31no—
624C42—91no—
625C42—272no—
626C42—272no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—32no—
631C22×C3—34no—
632C22×C3—34no—
633C22×C3—32no—
634C22×C3—41no—
635C22×C3—62no—
636C22×C3—64no—
637C22×C3—62no—
638C22×C3—62no—
639C22×C3—61no—
640C22×C3—62no—
641C22×C3—62no—
642C22×C3—62no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—122no—
648C22×C3—122no—
649C22×C3C22×D3211yescharacteristic
650C22×C3C22×D3211yescharacteristic
651C22×C3C22×D3211yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3C2×D3×Dic314yes—
657C2×D3C2×D3×Dic312yes—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—32no—
662C3×C4—32no—
663C3×C4—42no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—94no—
671C3×C4—121no—
672C3×C4—182no—
673C3×C4—181no—
674C3×C4—181no—
675C3×C4C4×D3212yes—
676C3×C4C2×D3×Dic312yes—
677C3×C4C2×D3×Dic312yes—
678Dic3—21no—
679Dic3—21no—
680Dic3—34no—
681Dic3—34no—
682Dic3—64no—
683Dic3—62no—
684Dic3—61no—
685Dic3—61no—
686Dic3—62no—
687Dic3—61no—
688Dic3—61no—
689Dic3—62no—
690Dic3—122no—
691Dic3—121no—
692Dic3—182no—
693Dic3—182no—
694Dic3—182no—
695Dic3—362no—
696Dic3—362no—
697Dic3—362no—
698Dic3—722no—
699Dic3C2×D3×Dic312yes—
700C32—21no—
701C32—21no—
702C32—21no—
703C32—41no—
704C32#552311yescharacteristic, complemented
705C32#554611yescharacteristic, complemented
706C32#582711yescharacteristic, complemented
707C23—31no—
708C23—32no—
709Q8—94no—
710D4—34no—
711D4—98no—
712C2×C4—31no—
713C2×C4—34no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—98no—
717C2×C4—92no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—92no—
721C2×C4—272no—
722C2×C4—362no—
723C2×C4—1082no—
724C2×C4—1082no—
725C2×C4D3311yescharacteristic
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—41no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—64no—
739C2×C3—62no—
740C2×C3—64no—
741C2×C3—62no—
742C2×C3—64no—
743C2×C3—124no—
744C2×C3#6429811yescharacteristic
745C2×C3#6429811yescharacteristic
746C2×C3C2×C4×D3211yescharacteristic
747C2×C3#6430711yescharacteristic
748C2×C3#6430811yescharacteristic
749C2×C3#6430911yescharacteristic
750C2×C3#6431411yescharacteristic
751C2×C3C22×D3×Dic311yescharacteristic
752C2×C3C22×D3×Dic311yescharacteristic
753D3—24no—
754D3—22no—
755C22—32no—
756C22—34no—
757C22—62no—
758C22—61no—
759C22—61no—
760C22—62no—
761C22C2×D3311yescharacteristic
762C4—32no—
763C4—61no—
764C4—61no—
765C4—94no—
766C4—182no—
767C4—181no—
768C4—181no—
769C4—542no—
770C4D32×Dic312yes—
771C3—21no—
772C3—21no—
773C3—21no—
774C3—41no—
775C3#1059388711yescharacteristic, complemented
776C3#1059499211yescharacteristic, complemented
777C3#1059522211yescharacteristic, complemented
778C2—62no—
779C2—64no—
780C2#1172438411yescharacteristic
781C2#1172439211yescharacteristic
782C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3795C2
hypercenterC2×C4D33
hypocenterC33#520
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. D12×C3⋊Dic3C2semidirect
4. D3×C4⋊(C3⋊Dic3)C2semidirect
5. Dic3×#634C2semidirect
6. C3×Dic3×D12C2semidirect
7. C3×#63855C2semidirect
8. #11722925C2semidirect
9. #11722924C2semidirect
10. #11722914C2semidirect
11. D3×Dic3⋊Dic3C2semidirect
23. C3×#3795C4semidirect
59. Dic3×D12D3semidirect
67. #63855D3semidirect
83. C3×#634C2×C4semidirect
87. C32×D12C2×C4semidirect
88. C32×C4×D3C2×C4semidirect
91. C3×#625C2×C4semidirect
93. C3×D3×Dic3C2×C4semidirect
128. #3795Dic3semidirect
270. #634C2×Dic3semidirect
297. C3×D12C4×D3semidirect
298. C3×D12C2×Dic3semidirect
302. C3×C4×D3C4×D3semidirect
303. C3×C4×D3C2×Dic3semidirect
307. #625C2×Dic3semidirect
315. D3×Dic3C2×Dic3semidirect
494. C33#520semidirect
565. D12D3×Dic3semidirect
570. C4×D3D3×Dic3semidirect
704. C32#5523semidirect
705. C32#5546semidirect
706. C32#5827semidirect
775. C3#10593887semidirect
776. C3#10594992semidirect
777. C3#10595222semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37952
#117236682
D12×C3⋊Dic32
D3×C4⋊(C3⋊Dic3)2
Dic3×#6342
C3×Dic3×D122
C3×#638552
#117229252
#117229242
#117229142
D3×Dic3⋊Dic32
#105952223
#105949923
#105938873