Finite Group Databasebeta

← #13168153

Subgroups — #13168153

Order 1728.

1446 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3796C211yesmaximal, characteristic
2#11723689C211yesmaximal, characteristic, complemented
3#11723499C211yesmaximal, characteristic, complemented
4#11723437C211yesmaximal, characteristic, complemented
5#11723397C211yesmaximal, characteristic, complemented
6C3×Dic3×D12C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
8#11722928C212yesmaximal, complemented
9#11722927C212yesmaximal, complemented
10#11722913C212yesmaximal, complemented
11D3×Dic3⋊Dic3C212yesmaximal, complemented
12#10595394—31nomaximal
13#10595222—31nomaximal
14#10593889—31nomaximal
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C32×D12C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×#6294C2212yes—
19C2×D3×C3⋊Dic3C2212yes—
20C2×C3×#626C2212yes—
21C2×C3×D3×Dic3C2212yes—
22C2×C3×D3×Dic3C2212yes—
23C3×#3796C418yescomplemented
24C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C32×C4×Dic3C2211yescharacteristic
28#88815C2212yes—
29#88807C2211yescharacteristic
30#88807C2211yescharacteristic
31Dic3⋊(C3⋊Dic3)C2212yes—
32#88803C2211yescharacteristic
33#88803C2211yescharacteristic
34(C2×D3)⋊(C3⋊Dic3)C2212yes—
35Dic3×C3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×Dic32C2212yes—
39C2×C3×#239—31no—
40C2×C3×#237—31no—
41C2×#3796D311yescharacteristic
42Q8×C3⋊Dic3—31no—
43D4×C3⋊Dic3—31no—
44#64081—31no—
45C3×Q8×Dic3—31no—
46C3×D4×Dic3—31no—
47C3×C4×D12—31no—
48C3×C4×Dic6—31no—
49#67⋊Dic3—32no—
50Dic3×#67—32no—
51C2×Dic3⋊Dic3—32no—
52#63955—32no—
53#63904—32no—
54#63900—31no—
55#63898—31no—
56#63898—31no—
57#63898—32no—
58#63898—61no—
59Dic3×D12—32no—
60Dic3×D12D311yescharacteristic, complemented
61D3×C4⋊Dic3—32no—
62D3×C4⋊Dic3—31no—
63D3×C4⋊Dic3—31no—
64#63880—32no—
65#63877—32no—
66D3×Dic3⋊C4—32no—
67#63855—31no—
68#63855—31no—
69#63855—32no—
70#63855—61no—
71#63843—31no—
72#63843—31no—
73#63843—61no—
74Dic3×Dic6D311yescharacteristic, complemented
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C32×D3C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C3×C4×C3⋊D3C2×C414yescomplemented
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2312yes—
87C32×D12C2×C414yescomplemented
88C32×Dic6C2×C414yescomplemented
89#6294—42no—
90D3×C3⋊Dic3—42no—
91C3×#626C2×C418yescomplemented
92C3×D3×Dic3—42no—
93C3×D3×Dic3C2×C418yescomplemented
94#5827—91no—
95#5574—91no—
96#5546—91no—
97C2×C32×Q8—31no—
98C2×C32×D4—31no—
99C22×C3⋊Dic3—32no—
100C2×C4×C3⋊D3C2×D311yescharacteristic
101C2×C3×#67—32no—
102C22×C3×Dic3—32no—
103C22×C3×Dic3—32no—
104C3×#239—38no—
105C3×#237—38no—
106C2×C3×D12—21no—
107C2×C3×D12—32no—
108C2×C3×D12C2×D311yescharacteristic
109C2×C3×D12C2×D311yescharacteristic
110C2×C3×C4×D3—32no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—61no—
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2×D311yescharacteristic
117C2×C3×Dic6C2×D311yescharacteristic
118C2×#626C2×D312yes—
119C2×#624—32no—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122C2×D3×Dic3—32no—
123C2×D3×Dic3—32no—
124C2×D3×Dic3—62no—
125C2×D3×Dic3C2×D312yes—
126C2×D3×Dic3C2×D312yes—
127#3796Dic318yescomplemented
128C32×C42—31no—
129#3757—32no—
130#3752—31no—
131#3752—31no—
132C4⋊(C3⋊Dic3)—32no—
133C4⋊(C3⋊Dic3)C2×D311yescharacteristic
134C4⋊(C3⋊Dic3)C2×D311yescharacteristic
135#3750—31no—
136#3750—31no—
137C4×C3⋊Dic3—31no—
138C4×C3⋊Dic3—31no—
139C4×C3⋊Dic3—31no—
140C4×C3⋊Dic3—32no—
141C4×C3⋊Dic3—61no—
142C4×C3⋊Dic3—61no—
143C4×C3⋊Dic3—61no—
144C4×C3⋊Dic3—121no—
145C3×#217—32no—
146C3×(C2×D3)⋊C4—32no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—32no—
152C3×C4⋊Dic3—61no—
153C3×C4⋊Dic3—61no—
154C3×Dic3⋊C4—32no—
155C3×C4×Dic3—21no—
156C3×C4×Dic3—32no—
157C3×C4×Dic3—32no—
158C3×C4×Dic3C2×D311yescharacteristic
159C3×C4×Dic3C2×D311yescharacteristic
160#3724—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—62no—
170Dic3⋊Dic3—61no—
171Dic3⋊Dic3—61no—
172Dic3⋊Dic3C2×D312yes—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179(C2×D3)⋊Dic3—61no—
180(C2×D3)⋊Dic3—61no—
181(C2×D3)⋊Dic3—62no—
182(C2×D3)⋊Dic3C2×D312yes—
183Dic32—32no—
184Dic32—32no—
185Dic32—62no—
186Dic32C2×D312yes—
187C22×C33C2411yescharacteristic
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—21no—
190C2×C3×C3⋊D3C22×C412yes—
191C2×C32×D3—22no—
192C2×C32×D3—22no—
193C2×C32×D3C22×C414yes—
194C33×C4C22×C412yes—
195C3⋊(C3⋊Dic3)—21no—
196C3⋊(C3⋊Dic3)—21no—
197C3×C3⋊Dic3—22no—
198C3×C3⋊Dic3—22no—
199C3×C3⋊Dic3C22×C412yes—
200C32×Dic3—21no—
201C32×Dic3—21no—
202C32×Dic3C22×C414yes—
203C2×C3×#41—91no—
204C2×#239—31no—
205C2×#237—31no—
206C3×C4×Q8—91no—
207C3×C4×D4—91no—
208Q8×Dic3—31no—
209Q8×Dic3—91no—
210Q8×Dic3—91no—
211Q8×Dic3—181no—
212D4×Dic3—31no—
213D4×Dic3—92no—
214D4×Dic3—92no—
215D4×Dic3—91no—
216D4×Dic3—91no—
217D4×Dic3—181no—
218C4×#67—92no—
219#926—92no—
220#926—91no—
221C2×C4⋊Dic3—91no—
222C2×C4⋊Dic3—92no—
223C2×Dic3⋊C4—92no—
224#893—92no—
225#893—91no—
226D3×C4⋊C4—91no—
227D3×C4⋊C4—91no—
228D3×C4⋊C4—92no—
229#887—91no—
230#67⋊C4—92no—
231#877—92no—
232C4×D12—31no—
233C4×D12—92no—
234#872—92no—
235#872—91no—
236#872—91no—
237#872—181no—
238C4×Dic6—31no—
239C23×C32—32no—
240C22×C3⋊D3C22×D311yescharacteristic
241C22×C3×D3—22no—
242C22×C3×D3—31no—
243C22×C3×D3—31no—
244C22×C3×D3—61no—
245C22×C3×D3C22×D312yes—
246C22×C3×D3C22×D312yes—
247C32×Q8—34no—
248C32×D4—34no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—32no—
253C2×C32×C4—31no—
254C2×C32×C4—31no—
255C2×C32×C4—41no—
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—61no—
266C2×C3⋊Dic3—61no—
267C2×C3⋊Dic3—61no—
268C2×C3⋊Dic3—61no—
269C2×C3⋊Dic3—61no—
270C2×C3⋊Dic3—61no—
271C2×C3⋊Dic3—121no—
272C2×C3⋊Dic3—121no—
273C2×C3⋊Dic3—122no—
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D312yes—
276C2×C3⋊Dic3C22×D311yescharacteristic
277C4×C3⋊D3C2×Dic314yescomplemented
278C3×#67—38no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—38no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—32no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—62no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3—122no—
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D312yes—
298C2×C3×Dic3C22×D312yes—
299C3×D12—24no—
300C3×D12—38no—
301C3×D12C4×D314yescomplemented
302C3×D12C2×Dic314yescomplemented
303C3×C4×D3—38no—
304C3×C4×D3—34no—
305C3×C4×D3—34no—
306C3×C4×D3—64no—
307C3×C4×D3—122no—
308C3×Dic6—24no—
309C3×Dic6C4×D314yescomplemented
310C3×Dic6C2×Dic314yescomplemented
311#626C2×Dic318yescomplemented
312#624—122no—
313D3×Dic3—42no—
314D3×Dic3—122no—
315D3×Dic3—122no—
316D3×Dic3—122no—
317D3×Dic3—122no—
318D3×Dic3—124no—
319D3×Dic3C2×Dic318yescomplemented
320#520—271noSylow
321C2×C33C23×C411yescharacteristic
322C2×C33H(5,𝔽2)11yescharacteristic
323C2×C332−1+411yescharacteristic
324C3×C3⋊D3—22no—
325C32×D3—24no—
326C3×#41—98no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×Q8—61no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—92no—
334C22×C3×C4—92no—
335C22×C3×C4—92no—
336C22×C3×C4—91no—
337C2×#67—32no—
338C22×Dic3—32no—
339C22×Dic3—32no—
340C22×Dic3—92no—
341C22×Dic3—92no—
342C22×Dic3—92no—
343C22×Dic3—182no—
344#239—38no—
345#237—38no—
346C2×D12—32no—
347C2×D12D3211yescharacteristic
348C2×C4×D3—32no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—32no—
352C2×C4×D3—61no—
353C2×C4×D3—92no—
354C2×C4×D3—92no—
355C2×C4×D3—92no—
356C2×Dic6D3211yescharacteristic
357C3×C4⋊C4—92no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C22⋊C4—92no—
361C3×C42—31no—
362C3×C42—31no—
363C3×C42—61no—
364C3×C42—92no—
365#217—32no—
366#217—92no—
367#217—92no—
368#217—91no—
369#217—91no—
370#217—182no—
371(C2×D3)⋊C4—32no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—92no—
377(C2×D3)⋊C4—181no—
378(C2×D3)⋊C4—181no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—32no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—92no—
387C4⋊Dic3—92no—
388C4⋊Dic3—92no—
389C4⋊Dic3—91no—
390C4⋊Dic3—91no—
391C4⋊Dic3—182no—
392Dic3⋊C4—32no—
393Dic3⋊C4—92no—
394Dic3⋊C4—92no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—92no—
400Dic3⋊C4—181no—
401Dic3⋊C4—181no—
402C4×Dic3—32no—
403C4×Dic3—32no—
404C4×Dic3—92no—
405C4×Dic3—92no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C4×Dic3—91no—
409C4×Dic3—92no—
410C4×Dic3—182no—
411C4×Dic3—181no—
412C4×Dic3—181no—
413C4×Dic3—181no—
414C4×Dic3—361no—
415C4×Dic3D3211yescharacteristic
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—34no—
420C22×C32—41no—
421C22×C32—62no—
422C22×C32—62no—
423C22×C32C23×D311yescharacteristic
424C22×C32C23×D311yescharacteristic
425C22×C32C23×D311yescharacteristic
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3C22×Dic312yes—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—24no—
434C2×C3×D3—32no—
435C2×C3×D3—32no—
436C2×C3×D3—42no—
437C2×C3×D3—42no—
438C2×C3×D3—62no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—121no—
444C2×C3×D3—121no—
445C2×C3×D3C2×C4×D314yes—
446C2×C3×D3C22×Dic314yes—
447C32×C4—22no—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—34no—
451C32×C4—42no—
452C32×C4—61no—
453C32×C4—61no—
454C32×C4C2×C4×D312yes—
455C32×C4C2×C4×D312yes—
456C32×C4C22×Dic312yes—
457C3⋊Dic3—22no—
458C3⋊Dic3—22no—
459C3⋊Dic3—61no—
460C3⋊Dic3—61no—
461C3⋊Dic3—62no—
462C3⋊Dic3—62no—
463C3⋊Dic3—61no—
464C3⋊Dic3—61no—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3⋊Dic3—121no—
468C3⋊Dic3—121no—
469C3⋊Dic3—121no—
470C3⋊Dic3—121no—
471C3⋊Dic3—122no—
472C3⋊Dic3—122no—
473C3⋊Dic3C22×Dic312yes—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—24no—
479C3×Dic3—32no—
480C3×Dic3—32no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C3×Dic3—62no—
484C3×Dic3—62no—
485C3×Dic3—62no—
486C3×Dic3—62no—
487C3×Dic3—62no—
488C3×Dic3—122no—
489C3×Dic3—122no—
490C3×Dic3C2×C4×D314yes—
491C3×Dic3C22×Dic314yes—
492C2×#41—91no—
493C4×Q8—91no—
494C4×Q8—271no—
495C4×D4—91no—
496C4×D4—272no—
497C4×D4—272no—
498C4×D4—271no—
499#117—271no—
500#117—272no—
501C2×C4⋊C4—271no—
502C2×C4⋊C4—272no—
503C33#52011yescharacteristic, complemented, Sylow
504C23×C3—32no—
505C23×C3—32no—
506C23×C3—62no—
507C23×C3—91no—
508C22×D3—31no—
509C22×D3—31no—
510C22×D3—61no—
511C22×D3C2×D3212yes—
512C3×Q8—34no—
513C3×Q8—34no—
514C3×Q8—64no—
515C3×D4—34no—
516C3×D4—34no—
517C3×D4—64no—
518C3×D4—98no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—32no—
523C2×C3×C4—32no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—62no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—98no—
533C2×C3×C4—91no—
534C2×C3×C4—94no—
535C2×C3×C4—92no—
536C2×C3×C4—92no—
537C2×C3×C4—362no—
538C2×C3×C4C2×D3211yescharacteristic
539C2×C3×C4C2×D3211yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541#67—38no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—38no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—61no—
550C2×Dic3—62no—
551C2×Dic3—62no—
552C2×Dic3—91no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—122no—
559C2×Dic3—181no—
560C2×Dic3—181no—
561C2×Dic3—181no—
562C2×Dic3—181no—
563C2×Dic3—181no—
564C2×Dic3—181no—
565C2×Dic3—361no—
566C2×Dic3—361no—
567C2×Dic3—362no—
568C2×Dic3—362no—
569C2×Dic3—362no—
570C2×Dic3—364no—
571C2×Dic3C2×D3211yescharacteristic
572C2×Dic3C2×D3211yescharacteristic
573C2×Dic3C2×D3212yes—
574D12—38no—
575D12D3×Dic314yescomplemented
576C4×D3—38no—
577C4×D3—34no—
578C4×D3—34no—
579C4×D3—64no—
580C4×D3—122no—
581C4×D3—362no—
582C4×D3—362no—
583C4×D3—362no—
584Dic6D3×Dic314yescomplemented
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—21no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—41no—
595C2×C32—41no—
596C2×C32—41no—
597C2×C32—64no—
598C2×C32C22×C4×D311yescharacteristic
599C2×C32C22×C4×D311yescharacteristic
600C2×C32#100411yescharacteristic
601C2×C32#100711yescharacteristic
602C2×C32#100911yescharacteristic
603C2×C32#100911yescharacteristic
604C2×C32#101011yescharacteristic
605C2×C32#101011yescharacteristic
606C2×C32C23×Dic311yescharacteristic
607C3⋊D3—22no—
608C3×D3—24no—
609C3×D3—24no—
610C3×D3—44no—
611C3×D3—62no—
612C3×D3—62no—
613C3×D3—122no—
614#41—98no—
615C2×Q8—31no—
616C2×D4—31no—
617C2×D4—92no—
618C22×C4—92no—
619C22×C4—92no—
620C22×C4—91no—
621C22×C4—272no—
622C22×C4—272no—
623C4⋊C4—92no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—271no—
627C4⋊C4—272no—
628C4⋊C4—271no—
629C4⋊C4—272no—
630C22⋊C4—92no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—272no—
634C42—31no—
635C42—92no—
636C42—272no—
637C42—271no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—34no—
642C22×C3—34no—
643C22×C3—41no—
644C22×C3—64no—
645C22×C3—62no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—62no—
649C22×C3—92no—
650C22×C3—122no—
651C22×C3—122no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3C22×D3211yescharacteristic
655C22×C3C22×D3211yescharacteristic
656C22×C3C22×D3211yescharacteristic
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—32no—
660C2×D3—32no—
661C2×D3—62no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3C2×D3×Dic314yes—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—34no—
673C3×C4—34no—
674C3×C4—42no—
675C3×C4—64no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—92no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—182no—
684C3×C4—182no—
685C3×C4C4×D3212yes—
686C3×C4C2×D3×Dic312yes—
687C3×C4C2×D3×Dic312yes—
688Dic3—21no—
689Dic3—21no—
690Dic3—32no—
691Dic3—32no—
692Dic3—62no—
693Dic3—62no—
694Dic3—62no—
695Dic3—62no—
696Dic3—62no—
697Dic3—122no—
698Dic3—122no—
699Dic3—182no—
700Dic3—182no—
701Dic3—181no—
702Dic3—181no—
703Dic3—181no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—361no—
708Dic3—361no—
709Dic3—361no—
710Dic3—361no—
711Dic3—362no—
712Dic3—362no—
713Dic3C2×D3×Dic314yes—
714C32—21no—
715C32—21no—
716C32—21no—
717C32—41no—
718C32#554611yescharacteristic, complemented
719C32#557411yescharacteristic, complemented
720C32#582711yescharacteristic, complemented
721C23—32no—
722C23—91no—
723Q8—34no—
724D4—34no—
725D4—98no—
726C2×C4—32no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—98no—
730C2×C4—91no—
731C2×C4—94no—
732C2×C4—92no—
733C2×C4—92no—
734C2×C4—271no—
735C2×C4—271no—
736C2×C4—362no—
737C2×C4—1082no—
738C2×C4—1082no—
739C2×C4D3311yescharacteristic
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—41no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—64no—
753C2×C3—64no—
754C2×C3—124no—
755C2×C3—182no—
756C2×C3#6429711yescharacteristic
757C2×C3C2×C4×D3211yescharacteristic
758C2×C3#6430711yescharacteristic
759C2×C3#6430911yescharacteristic
760C2×C3#6431411yescharacteristic
761C2×C3#6431511yescharacteristic
762C2×C3#6432011yescharacteristic
763C2×C3C22×D3×Dic311yescharacteristic
764C2×C3C22×D3×Dic311yescharacteristic
765D3—24no—
766D3—62no—
767D3—62no—
768D3—122no—
769C22—34no—
770C22—62no—
771C22—62no—
772C22—92no—
773C22—181no—
774C22—181no—
775C22C2×D3311yescharacteristic
776C4—34no—
777C4—61no—
778C4—61no—
779C4—92no—
780C4—182no—
781C4—182no—
782C4—541no—
783C4—541no—
784C4D32×Dic312yes—
785C3—21no—
786C3—21no—
787C3—21no—
788C3—41no—
789C3#1059388911yescharacteristic, complemented
790C3#1059522211yescharacteristic, complemented
791C3#1059539411yescharacteristic, complemented
792C2—64no—
793C2—182no—
794C2#1172438511yescharacteristic
795C2#1172439311yescharacteristic
796C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3796C2
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. #11723689C2semidirect
3. #11723499C2semidirect
4. #11723437C2semidirect
5. #11723397C2semidirect
6. C3×Dic3×D12C2semidirect
7. C3×Dic3×Dic6C2semidirect
8. #11722928C2semidirect
9. #11722927C2semidirect
10. #11722913C2semidirect
11. D3×Dic3⋊Dic3C2semidirect
23. C3×#3796C4semidirect
60. Dic3×D12D3semidirect
74. Dic3×Dic6D3semidirect
83. C3×C4×C3⋊D3C2×C4semidirect
87. C32×D12C2×C4semidirect
88. C32×Dic6C2×C4semidirect
91. C3×#626C2×C4semidirect
93. C3×D3×Dic3C2×C4semidirect
127. #3796Dic3semidirect
277. C4×C3⋊D3C2×Dic3semidirect
301. C3×D12C4×D3semidirect
302. C3×D12C2×Dic3semidirect
309. C3×Dic6C4×D3semidirect
310. C3×Dic6C2×Dic3semidirect
311. #626C2×Dic3semidirect
319. D3×Dic3C2×Dic3semidirect
503. C33#520semidirect
575. D12D3×Dic3semidirect
584. Dic6D3×Dic3semidirect
718. C32#5546semidirect
719. C32#5574semidirect
720. C32#5827semidirect
789. C3#10593889semidirect
790. C3#10595222semidirect
791. C3#10595394semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37962
#117236892
#117234992
#117234372
#117233972
C3×Dic3×D122
C3×Dic3×Dic62
#117229282
#117229272
#117229132
D3×Dic3⋊Dic32
#105953943
#105952223
#105938893