Finite Group Databasebeta

← #13168332

Subgroups — #13168332

Order 1728.

1310 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Dic6C211yesmaximal, characteristic
2#11723668C211yesmaximal, characteristic, complemented
3#11723423C211yesmaximal, characteristic
4#11723410C211yesmaximal, characteristic, complemented
5#11723397C211yesmaximal, characteristic, complemented
6C3×#63843C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic
8#11722940C212yesmaximal, complemented
9Dic3×#627C212yesmaximal, complemented
10#11722914C212yesmaximal
11#11722913C212yesmaximal
12#10595347—31nomaximal
13#10594818—31nomaximal
14#10594357—31nomaximal
15C2×C3×#634C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×C3×#627C2212yes—
19C2×C3×D3×Dic3C2212yes—
20C3×D3×Dic6C418yescomplemented
21C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×C4×C3⋊Dic3C2211yescharacteristic
24C32×C4⋊Dic3C2211yescharacteristic
25#88815C2212yes—
26#88813C2212yes—
27#88807C2212yes—
28Dic3⋊(C3⋊Dic3)C2212yes—
29Dic3⋊(C3⋊Dic3)C2211yescharacteristic
30Dic3⋊(C3⋊Dic3)C2211yescharacteristic
31(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
32(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
33Dic3×C3⋊Dic3C2212yes—
34Dic3×C3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×Dic32C2212yes—
38C3×Dic32C2212yes—
39C2×C3×D3×Q8—31no—
40C22×C3×Dic6—31no—
41C2×D3×Dic6D311yescharacteristic
42Q8×C3⋊Dic3—31no—
43#64135—31no—
44#64096—31no—
45C3×Q8×Dic3—31no—
46C3×#926—31no—
47C3×#892—31no—
48C3×#887—31no—
49#63955—32no—
50#63955—32no—
51C4×#627—32no—
52#63878—32no—
53#63877—32no—
54#63855—31no—
55#63855—31no—
56#63855—32no—
57#63855—61no—
58#63844—31no—
59#63843—31no—
60#63843—31no—
61#63843—31no—
62#63843—31no—
63#63843—31no—
64#63843—32no—
65#63843—61no—
66#63843—61no—
67#63843D311yescharacteristic, complemented
68Dic3×Dic6—31no—
69Dic3×Dic6—32no—
70Dic3×Dic6—32no—
71Dic3×Dic6—32no—
72#63841—32no—
73#63841D311yescharacteristic
74#63837—32no—
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
78C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C3×#634C2×C414yes—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C32×C4×D3C2×C414yes—
88C32×Dic6C2×C414yes—
89C3×#627C2×C418yes—
90C3×D3×Dic3C2×C418yes—
91#5812—91no—
92#5572—91no—
93#5516—91no—
94C2×C32×Q8—31no—
95C22×C32×C4—31no—
96C2×#634C2×D311yescharacteristic
97C22×C3×Dic3—32no—
98C3×D3×Q8—38no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—32no—
101C2×C3×C4×D3C2×D311yescharacteristic
102C2×C3×C4×D3C2×D311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—31no—
106C2×C3×Dic6—32no—
107C2×C3×Dic6—32no—
108C2×C3×Dic6—38no—
109C2×C3×Dic6—61no—
110C2×C3×Dic6C2×D311yescharacteristic
111C2×C3×Dic6C2×D311yescharacteristic
112C2×#627C2×D312yes—
113C2×D3×Dic3C2×D312yes—
114D3×Dic6Dic318yescomplemented
115C32×C4⋊C4—31no—
116#3757—31no—
117#3757—31no—
118C4⋊(C3⋊Dic3)—32no—
119C4⋊(C3⋊Dic3)—31no—
120C4⋊(C3⋊Dic3)—31no—
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic
122#3750—32no—
123C4×C3⋊Dic3—31no—
124C4×C3⋊Dic3—31no—
125C4×C3⋊Dic3—31no—
126C4×C3⋊Dic3—32no—
127C4×C3⋊Dic3—32no—
128C4×C3⋊Dic3—61no—
129C4×C3⋊Dic3—61no—
130C4×C3⋊Dic3—61no—
131C4×C3⋊Dic3—121no—
132C4×C3⋊Dic3C2×D311yescharacteristic
133C3×#217—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—61no—
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×Dic3⋊C4—32no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3—32no—
147C3×C4×Dic3—32no—
148C3×C4×Dic3—32no—
149C3×C4×Dic3—61no—
150#3724—32no—
151Dic3⋊Dic3—32no—
152Dic3⋊Dic3—32no—
153Dic3⋊Dic3—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—32no—
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—62no—
162Dic3⋊Dic3—61no—
163Dic3⋊Dic3—61no—
164Dic3⋊Dic3—62no—
165Dic3⋊Dic3C2×D312yes—
166(C2×D3)⋊Dic3—31no—
167(C2×D3)⋊Dic3—31no—
168(C2×D3)⋊Dic3—31no—
169(C2×D3)⋊Dic3—31no—
170(C2×D3)⋊Dic3—61no—
171(C2×D3)⋊Dic3—61no—
172(C2×D3)⋊Dic3C2×D312yes—
173Dic32—32no—
174Dic32—32no—
175Dic32—32no—
176Dic32—32no—
177Dic32—32no—
178Dic32—32no—
179Dic32—32no—
180Dic32—62no—
181Dic32—62no—
182Dic32C2×D312yes—
183Dic32C2×D312yes—
184C22×C33C2411yescharacteristic
185C2×C32×D3—21no—
186C2×C32×D3—21no—
187C2×C32×D3C22×C412yes—
188C33×C4C22×C412yes—
189C3⋊(C3⋊Dic3)—21no—
190C3⋊(C3⋊Dic3)—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3C22×C414yes—
195C32×Dic3—22no—
196C32×Dic3C22×C414yes—
197C32×Dic3C22×C412yes—
198C22×C3×Q8—91no—
199C2×D3×Q8—31no—
200C22×Dic6—31no—
201C3×C4×Q8—91no—
202C3×#117—91no—
203Q8×Dic3—31no—
204Q8×Dic3—92no—
205Q8×Dic3—91no—
206Q8×Dic3—92no—
207Q8×Dic3—91no—
208Q8×Dic3—91no—
209Q8×Dic3—91no—
210Q8×Dic3—181no—
211#926—31no—
212#926—92no—
213#926—91no—
214#926—91no—
215#926—92no—
216#926—181no—
217#892—31no—
218#892—92no—
219#887—31no—
220#887—92no—
221#887—91no—
222#887—91no—
223#887—91no—
224#887—91no—
225#887—181no—
226#877—92no—
227#877—92no—
228#872—92no—
229#872—91no—
230C4×Dic6—92no—
231C4×Dic6—92no—
232C4×Dic6—92no—
233C4×Dic6—91no—
234C23×C32—31no—
235C22×C3×D3—21no—
236C22×C3×D3C22×D311yescharacteristic
237C22×C3×D3C22×D311yescharacteristic
238C32×Q8—34no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—31no—
243C2×C32×C4—32no—
244C2×C32×C4—34no—
245C2×C32×C4—32no—
246C2×C32×C4—41no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—31no—
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—61no—
257C2×C3⋊Dic3—61no—
258C2×C3⋊Dic3—61no—
259C2×C3⋊Dic3—61no—
260C2×C3⋊Dic3—61no—
261C2×C3⋊Dic3—61no—
262C2×C3⋊Dic3—121no—
263C2×C3⋊Dic3—121no—
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D312yes—
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D312yes—
268#634C2×Dic314yes—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—38no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3C22×D312yes—
286C2×C3×Dic3C22×D312yes—
287C2×C3×Dic3C22×D312yes—
288C2×C3×Dic3C22×D311yescharacteristic
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D311yescharacteristic
291C3×C4×D3—24no—
292C3×C4×D3—38no—
293C3×C4×D3C4×D314yes—
294C3×C4×D3C2×Dic314yes—
295C3×Dic6—24no—
296C3×Dic6—34no—
297C3×Dic6—34no—
298C3×Dic6—38no—
299C3×Dic6—38no—
300C3×Dic6—64no—
301C3×Dic6C4×D314yes—
302C3×Dic6C2×Dic314yes—
303#627C2×Dic318yes—
304D3×Dic3C2×Dic318yes—
305#519—271noSylow
306C2×C33C23×C411yescharacteristic
307C2×C332−1+411yescharacteristic
308C2×C332−1+411yescharacteristic
309C32×D3—22no—
310C2×C3×Q8—31no—
311C2×C3×Q8—31no—
312C2×C3×Q8—61no—
313C2×C3×Q8—92no—
314C2×C3×Q8—98no—
315C2×C3×Q8—91no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—92no—
320C22×Dic3—32no—
321D3×Q8—38no—
322C2×C4×D3—32no—
323C2×C4×D3D3211yescharacteristic
324C2×Dic6—31no—
325C2×Dic6—31no—
326C2×Dic6—32no—
327C2×Dic6—32no—
328C2×Dic6—38no—
329C2×Dic6—61no—
330C2×Dic6D3211yescharacteristic
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—92no—
335C3×C4⋊C4—91no—
336C3×C22⋊C4—92no—
337C3×C42—92no—
338C3×C42—92no—
339C3×C42—91no—
340#217—32no—
341#217—91no—
342#217—91no—
343#217—91no—
344#217—91no—
345#217—181no—
346#217—181no—
347(C2×D3)⋊C4—32no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—91no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—32no—
353C4⋊Dic3—61no—
354C4⋊Dic3—92no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—92no—
358C4⋊Dic3—91no—
359C4⋊Dic3—91no—
360C4⋊Dic3—92no—
361C4⋊Dic3—92no—
362C4⋊Dic3—181no—
363C4⋊Dic3—181no—
364C4⋊Dic3—182no—
365C4⋊Dic3D3211yescharacteristic
366Dic3⋊C4—32no—
367Dic3⋊C4—92no—
368Dic3⋊C4—92no—
369Dic3⋊C4—92no—
370Dic3⋊C4—92no—
371Dic3⋊C4—91no—
372Dic3⋊C4—92no—
373Dic3⋊C4—91no—
374Dic3⋊C4—182no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—32no—
378C4×Dic3—32no—
379C4×Dic3—32no—
380C4×Dic3—32no—
381C4×Dic3—61no—
382C4×Dic3—92no—
383C4×Dic3—92no—
384C4×Dic3—92no—
385C4×Dic3—92no—
386C4×Dic3—92no—
387C4×Dic3—92no—
388C4×Dic3—92no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—92no—
393C4×Dic3—92no—
394C4×Dic3—182no—
395C4×Dic3—182no—
396C4×Dic3—181no—
397C4×Dic3—181no—
398C4×Dic3—181no—
399C4×Dic3—361no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—32no—
404C22×C32—41no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32C23×D311yescharacteristic
408C22×C32C23×D311yescharacteristic
409C22×C32C23×D311yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3C2×C4×D312yes—
418C2×C3×D3C22×Dic312yes—
419C32×C4—22no—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—32no—
423C32×C4—34no—
424C32×C4—42no—
425C32×C4—62no—
426C32×C4C2×C4×D312yes—
427C32×C4C2×C4×D312yes—
428C32×C4C22×Dic312yes—
429C3⋊Dic3—21no—
430C3⋊Dic3—22no—
431C3⋊Dic3—21no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3⋊Dic3—62no—
435C3⋊Dic3—62no—
436C3⋊Dic3—61no—
437C3⋊Dic3—61no—
438C3⋊Dic3—61no—
439C3⋊Dic3—61no—
440C3⋊Dic3—121no—
441C3⋊Dic3—121no—
442C3⋊Dic3—121no—
443C3⋊Dic3—121no—
444C3⋊Dic3—122no—
445C3⋊Dic3—122no—
446C3⋊Dic3C22×Dic314yes—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—24no—
450C3×Dic3—22no—
451C3×Dic3—34no—
452C3×Dic3—34no—
453C3×Dic3—42no—
454C3×Dic3—64no—
455C3×Dic3—62no—
456C3×Dic3—61no—
457C3×Dic3—62no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—121no—
462C3×Dic3—121no—
463C3×Dic3—122no—
464C3×Dic3C2×C4×D312yes—
465C3×Dic3C2×C4×D314yes—
466C3×Dic3C22×Dic314yes—
467C3×Dic3C22×Dic312yes—
468C22×Q8—91no—
469C4×Q8—91no—
470C4×Q8—272no—
471C4×Q8—272no—
472C4×Q8—271no—
473C4×Q8—271no—
474C4×Q8—271no—
475#117—91no—
476#117—272no—
477#117—271no—
478#117—272no—
479C33#51911yescharacteristic, complemented, Sylow
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—61no—
483C22×D3C2×D3211yescharacteristic
484C3×Q8—34no—
485C3×Q8—34no—
486C3×Q8—64no—
487C3×Q8—98no—
488C3×Q8—94no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—32no—
494C2×C3×C4—32no—
495C2×C3×C4—31no—
496C2×C3×C4—34no—
497C2×C3×C4—34no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—41no—
501C2×C3×C4—64no—
502C2×C3×C4—62no—
503C2×C3×C4—61no—
504C2×C3×C4—62no—
505C2×C3×C4—98no—
506C2×C3×C4—92no—
507C2×C3×C4—92no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4C2×D3211yescharacteristic
511C2×C3×C4C2×D3211yescharacteristic
512C2×C3×C4C2×D3211yescharacteristic
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—38no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—32no—
520C2×Dic3—31no—
521C2×Dic3—32no—
522C2×Dic3—62no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—62no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—181no—
533C2×Dic3—181no—
534C2×Dic3—181no—
535C2×Dic3—181no—
536C2×Dic3—181no—
537C2×Dic3—181no—
538C2×Dic3—361no—
539C2×Dic3—361no—
540C2×Dic3C2×D3212yes—
541C2×Dic3C2×D3211yescharacteristic
542C2×Dic3C2×D3212yes—
543C4×D3—38no—
544C4×D3D3×Dic314yes—
545Dic6—34no—
546Dic6—34no—
547Dic6—38no—
548Dic6—38no—
549Dic6—64no—
550Dic6D3×Dic314yes—
551C2×C32—21no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—41no—
561C2×C32—41no—
562C2×C32—41no—
563C2×C32—62no—
564C2×C32C22×C4×D311yescharacteristic
565C2×C32C22×C4×D311yescharacteristic
566C2×C32#100711yescharacteristic
567C2×C32#100711yescharacteristic
568C2×C32#100711yescharacteristic
569C2×C32#101011yescharacteristic
570C2×C32#101011yescharacteristic
571C2×C32#101011yescharacteristic
572C2×C32C23×Dic311yescharacteristic
573C3×D3—22no—
574C3×D3—22no—
575C3×D3—42no—
576C2×Q8—31no—
577C2×Q8—92no—
578C2×Q8—98no—
579C2×Q8—91no—
580C22×C4—31no—
581C22×C4—92no—
582C4⋊C4—31no—
583C4⋊C4—92no—
584C4⋊C4—91no—
585C4⋊C4—272no—
586C4⋊C4—271no—
587C4⋊C4—271no—
588C4⋊C4—272no—
589C4⋊C4—272no—
590C22⋊C4—92no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C42—92no—
594C42—92no—
595C42—91no—
596C42—272no—
597C42—272no—
598C42—272no—
599C42—271no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—32no—
604C22×C3—32no—
605C22×C3—41no—
606C22×C3—62no—
607C22×C3—61no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3C22×D3211yescharacteristic
614C22×C3C22×D3211yescharacteristic
615C22×C3C22×D3211yescharacteristic
616C2×D3—21no—
617C2×D3—21no—
618C2×D3C2×D3×Dic312yes—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—32no—
623C3×C4—34no—
624C3×C4—32no—
625C3×C4—34no—
626C3×C4—42no—
627C3×C4—62no—
628C3×C4—64no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—94no—
632C3×C4—122no—
633C3×C4—181no—
634C3×C4—181no—
635C3×C4—182no—
636C3×C4C4×D3212yes—
637C3×C4C2×D3×Dic312yes—
638C3×C4C2×D3×Dic312yes—
639Dic3—22no—
640Dic3—34no—
641Dic3—34no—
642Dic3—64no—
643Dic3—62no—
644Dic3—61no—
645Dic3—61no—
646Dic3—61no—
647Dic3—62no—
648Dic3—61no—
649Dic3—121no—
650Dic3—122no—
651Dic3—121no—
652Dic3—182no—
653Dic3—182no—
654Dic3—181no—
655Dic3—181no—
656Dic3—181no—
657Dic3—181no—
658Dic3—181no—
659Dic3—181no—
660Dic3—361no—
661Dic3—361no—
662Dic3—361no—
663Dic3—361no—
664Dic3—362no—
665Dic3—362no—
666Dic3C2×D3×Dic312yes—
667Dic3C2×D3×Dic314yes—
668C32—21no—
669C32—21no—
670C32—21no—
671C32—41no—
672C32#551611yescharacteristic, complemented
673C32#557211yescharacteristic, complemented
674C32#581211yescharacteristic, complemented
675C23—31no—
676Q8—34no—
677Q8—98no—
678Q8—94no—
679C2×C4—31no—
680C2×C4—32no—
681C2×C4—34no—
682C2×C4—32no—
683C2×C4—98no—
684C2×C4—92no—
685C2×C4—91no—
686C2×C4—92no—
687C2×C4—91no—
688C2×C4—271no—
689C2×C4—271no—
690C2×C4D3311yescharacteristic
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—41no—
701C2×C3—41no—
702C2×C3—41no—
703C2×C3—62no—
704C2×C3—62no—
705C2×C3—122no—
706C2×C3#6429711yescharacteristic
707C2×C3#6429711yescharacteristic
708C2×C3C2×C4×D3211yescharacteristic
709C2×C3#6430911yescharacteristic
710C2×C3#6431511yescharacteristic
711C2×C3#6431511yescharacteristic
712C2×C3#6431611yescharacteristic
713C2×C3C22×D3×Dic311yescharacteristic
714C2×C3C22×D3×Dic311yescharacteristic
715D3—22no—
716C22—32no—
717C22—61no—
718C22—61no—
719C22C2×D3311yescharacteristic
720C4—32no—
721C4—34no—
722C4—62no—
723C4—94no—
724C4—181no—
725C4—181no—
726C4—182no—
727C4—541no—
728C4—541no—
729C4D32×Dic312yes—
730C3—21no—
731C3—21no—
732C3—21no—
733C3—41no—
734C3#1059435711yescharacteristic, complemented
735C3#1059481811yescharacteristic, complemented
736C3#1059534711yescharacteristic, complemented
737C2—62no—
738C2#1172439311yescharacteristic
739C2#1172439711yescharacteristic
740C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC22×C32×D3C23
hypercenterC2×C4D33
hypocenterC33#519
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723668C2semidirect
4. #11723410C2semidirect
5. #11723397C2semidirect
6. C3×#63843C2semidirect
8. #11722940C2semidirect
9. Dic3×#627C2semidirect
20. C3×D3×Dic6C4semidirect
67. #63843D3semidirect
114. D3×Dic6Dic3semidirect
479. C33#519semidirect
672. C32#5516semidirect
673. C32#5572semidirect
674. C32#5812semidirect
734. C3#10594357semidirect
735. C3#10594818semidirect
736. C3#10595347semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Dic62
#117236682
#117234232
#117234102
#117233972
C3×#638432
C3×#638412
#117229402
Dic3×#6272
#117229142
#117229132
#105953473
#105948183
#105943573