Finite Group Databasebeta

← #13168643

Subgroups — #13168643

Order 1728.

1398 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#634C211yesmaximal, characteristic
2#11723668C211yesmaximal, characteristic, complemented
3#11723406C211yesmaximal, characteristic, complemented
4#11723399C211yesmaximal, characteristic, complemented
5C3×#63855C211yesmaximal, characteristic
6C3×#63844C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic
8#11722943C212yesmaximal, complemented
9#11722942C212yesmaximal, complemented
10#11722917C212yesmaximal
11#11722916C212yesmaximal
12#10594828—31nomaximal
13#10594357—31nomaximal
14#10593885—31nomaximal
15C2×#6308C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6293C2212yes—
19C2×D3×C3⋊Dic3C2212yes—
20D3×#634C418yescomplemented
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4×C3⋊Dic3C2211yescharacteristic
23C32×C4⋊Dic3C2211yescharacteristic
24C32×C4×Dic3C2211yescharacteristic
25#88815C2212yes—
26#88813C2212yes—
27#88806C2212yes—
28#88806C2212yes—
29Dic3×C3⋊Dic3C2212yes—
30Dic3×C3⋊Dic3C2212yes—
31C3×#3724C2212yes—
32C3×Dic3⋊Dic3C2211yescharacteristic
33C3×Dic3⋊Dic3C2211yescharacteristic
34C3×(C2×D3)⋊Dic3C2212yes—
35C3×(C2×D3)⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×Dic32C2212yes—
38C3×Dic32C2212yes—
39C22×#634—31no—
40C2×D3×Dic6—31no—
41C2×D3×Dic6—31no—
42C2×D3×Dic6—61no—
43#64096—31no—
44C4×#634—31no—
45C3×#926—31no—
46C3×#926—31no—
47C3×#892—31no—
48C3×#887—31no—
49C3×#872—31no—
50C3×C4×Dic6—31no—
51#63957—32no—
52#63957—32no—
53C4×#627—32no—
54#63878—32no—
55#63878—32no—
56#63877—32no—
57#63877—32no—
58#63855D311yescharacteristic
59#63844—31no—
60#63844—31no—
61#63844—31no—
62#63844—31no—
63#63844—31no—
64#63844—32no—
65#63844—32no—
66#63844—61no—
67#63844—61no—
68#63844D311yescharacteristic, complemented
69#63843—31no—
70Dic3×Dic6—31no—
71#63841D311yescharacteristic
72#63838—32no—
73#63837—32no—
74#63837—32no—
75C22×C32×D3C2311yescharacteristic
76C2×C33×C4C2311yescharacteristic
77C2×C3⋊(C3⋊Dic3)C2312yes—
78#6308C2×C414yes—
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2312yes—
83C3×#634C2×C414yes—
84C2×C32×Dic3C2311yescharacteristic
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2311yescharacteristic
88C32×C4×D3C2×C414yes—
89#6293C2×C418yes—
90D3×C3⋊Dic3C2×C418yes—
91#5572—91no—
92#5516—91no—
93#5516—91no—
94C22×C32×C4—31no—
95C22×C3⋊Dic3—32no—
96C2×#634—31no—
97C2×#634—31no—
98C2×#634—31no—
99C2×#634—32no—
100C2×#634—38no—
101C2×#634—61no—
102C2×#634—61no—
103C2×#634—61no—
104C2×#634—121no—
105C2×#634C2×D311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2×D311yescharacteristic
108C2×C3×C4×D3C2×D311yescharacteristic
109C2×C3×Dic6—31no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—61no—
112C2×#627—32no—
113C2×#627—32no—
114C2×#627—62no—
115C2×D3×Dic3—32no—
116C2×D3×Dic3—32no—
117C2×D3×Dic3—62no—
118D3×Dic6—38no—
119D3×Dic6—38no—
120D3×Dic6—68no—
121C32×C4⋊C4—31no—
122C32×C42—31no—
123C4⋊(C3⋊Dic3)C2×D311yescharacteristic
124#3750—32no—
125#3750—32no—
126C4×C3⋊Dic3—32no—
127C4×C3⋊Dic3—32no—
128C4×C3⋊Dic3C2×D311yescharacteristic
129C3×#217—31no—
130C3×#217—32no—
131C3×#217—31no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—61no—
141C3×C4⋊Dic3C2×D311yescharacteristic
142C3×C4⋊Dic3C2×D311yescharacteristic
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—32no—
147C3×C4×Dic3—21no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—32no—
152C3×C4×Dic3—32no—
153C3×C4×Dic3—32no—
154C3×C4×Dic3—61no—
155C3×C4×Dic3C2×D311yescharacteristic
156C3×C4×Dic3C2×D311yescharacteristic
157#3724—32no—
158#3724—32no—
159#3724—32no—
160#3724—32no—
161#3724—32no—
162#3724—62no—
163#3724—62no—
164#3724C2×D312yes—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3C2×D311yescharacteristic
168Dic3⋊Dic3C2×D311yescharacteristic
169(C2×D3)⋊Dic3C2×D312yes—
170(C2×D3)⋊Dic3C2×D311yescharacteristic
171(C2×D3)⋊Dic3C2×D311yescharacteristic
172Dic32—32no—
173Dic32—32no—
174Dic32—32no—
175Dic32—32no—
176Dic32—32no—
177Dic32—32no—
178Dic32—32no—
179Dic32—62no—
180Dic32—62no—
181Dic32C2×D312yes—
182Dic32C2×D312yes—
183C22×C33C2411yescharacteristic
184C2×C32×D3—21no—
185C2×C32×D3—21no—
186C2×C32×D3C22×C412yes—
187C33×C4C22×C412yes—
188C3⋊(C3⋊Dic3)C22×C414yes—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3C22×C414yes—
193C32×Dic3—21no—
194C32×Dic3—21no—
195C32×Dic3—22no—
196C32×Dic3C22×C412yes—
197C2×D3×Q8—91no—
198C22×Dic6—91no—
199C22×Dic6—91no—
200C22×Dic6—181no—
201C3×C4×Q8—91no—
202C3×#117—91no—
203C3×#117—91no—
204Q8×Dic3—91no—
205#926—31no—
206#926—31no—
207#892—31no—
208#892—92no—
209#887—31no—
210#887—92no—
211#887—92no—
212#887—92no—
213#887—91no—
214#887—91no—
215#887—91no—
216#887—91no—
217#887—181no—
218#877—92no—
219#877—92no—
220#877—92no—
221#877—92no—
222#872—31no—
223#872—92no—
224C4×Dic6—31no—
225C4×Dic6—92no—
226C4×Dic6—92no—
227C4×Dic6—92no—
228C4×Dic6—91no—
229C4×Dic6—91no—
230C4×Dic6—91no—
231C4×Dic6—91no—
232C4×Dic6—181no—
233C23×C32—31no—
234C22×C3×D3—21no—
235C22×C3×D3C22×D311yescharacteristic
236C22×C3×D3C22×D311yescharacteristic
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—31no—
241C2×C32×C4—34no—
242C2×C32×C4—32no—
243C2×C32×C4—31no—
244C2×C32×C4—31no—
245C2×C32×C4—41no—
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C3⋊Dic3—32no—
250C2×C3⋊Dic3—32no—
251C2×C3⋊Dic3—32no—
252C2×C3⋊Dic3—38no—
253C2×C3⋊Dic3—62no—
254C2×C3⋊Dic3—62no—
255C2×C3⋊Dic3—62no—
256C2×C3⋊Dic3—122no—
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D312yes—
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D312yes—
261#634—34no—
262#634—34no—
263#634—34no—
264#634—38no—
265#634—64no—
266#634—64no—
267#634—64no—
268#634—124no—
269#634C4×D314yes—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—22no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3C22×D311yescharacteristic
287C2×C3×Dic3C22×D311yescharacteristic
288C2×C3×Dic3C22×D312yes—
289C2×C3×Dic3C22×D312yes—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D311yescharacteristic
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C3×C4×D3—24no—
295C3×C4×D3C4×D314yes—
296C3×C4×D3C4×D314yes—
297C3×Dic6—34no—
298C3×Dic6—34no—
299C3×Dic6—64no—
300#627—38no—
301#627—38no—
302#627—68no—
303D3×Dic3—38no—
304D3×Dic3—38no—
305D3×Dic3—68no—
306#519—271noSylow
307C2×C33C23×C411yescharacteristic
308C2×C332−1+411yescharacteristic
309C2×C332−1+411yescharacteristic
310C32×D3—22no—
311C2×C3×Q8—91no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×Dic3—92no—
316C22×Dic3—92no—
317C22×Dic3—182no—
318D3×Q8—98no—
319C2×C4×D3—92no—
320C2×C4×D3D3211yescharacteristic
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—61no—
324C2×Dic6—98no—
325C2×Dic6—98no—
326C2×Dic6—92no—
327C2×Dic6—92no—
328C2×Dic6—91no—
329C2×Dic6—91no—
330C2×Dic6—91no—
331C2×Dic6—92no—
332C2×Dic6—188no—
333C2×Dic6—182no—
334C2×Dic6—181no—
335C2×Dic6—181no—
336C2×Dic6—181no—
337C2×Dic6—361no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—92no—
344C3×C4⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—92no—
347C3×C22⋊C4—91no—
348C3×C42—31no—
349C3×C42—31no—
350C3×C42—61no—
351C3×C42—92no—
352C3×C42—92no—
353C3×C42—91no—
354#217—32no—
355#217—31no—
356#217—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—32no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—61no—
365C4⋊Dic3—92no—
366C4⋊Dic3D3211yescharacteristic
367Dic3⋊C4—32no—
368Dic3⋊C4—31no—
369Dic3⋊C4—32no—
370Dic3⋊C4—31no—
371Dic3⋊C4—92no—
372Dic3⋊C4—92no—
373Dic3⋊C4—92no—
374Dic3⋊C4—92no—
375Dic3⋊C4—92no—
376Dic3⋊C4—92no—
377Dic3⋊C4—92no—
378Dic3⋊C4—92no—
379Dic3⋊C4—182no—
380Dic3⋊C4—182no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—32no—
384C4×Dic3—32no—
385C4×Dic3—32no—
386C4×Dic3—32no—
387C4×Dic3—61no—
388C4×Dic3—92no—
389C4×Dic3—92no—
390C4×Dic3—92no—
391C4×Dic3—92no—
392C4×Dic3—92no—
393C4×Dic3—92no—
394C4×Dic3—92no—
395C4×Dic3—92no—
396C4×Dic3—92no—
397C4×Dic3—182no—
398C4×Dic3—182no—
399C4×Dic3D3211yescharacteristic
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—22no—
411C2×C3×D3—22no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3C2×C4×D312yes—
418C2×C3×D3C2×C4×D312yes—
419C32×C4—22no—
420C32×C4—22no—
421C32×C4—22no—
422C32×C4—32no—
423C32×C4—42no—
424C32×C4—61no—
425C32×C4—62no—
426C32×C4—61no—
427C32×C4C2×C4×D312yes—
428C32×C4C2×C4×D312yes—
429C32×C4C2×C4×D312yes—
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—22no—
433C3⋊Dic3—34no—
434C3⋊Dic3—34no—
435C3⋊Dic3—34no—
436C3⋊Dic3—64no—
437C3⋊Dic3—64no—
438C3⋊Dic3—64no—
439C3⋊Dic3—124no—
440C3⋊Dic3C2×C4×D314yes—
441C3×Dic3—22no—
442C3×Dic3—21no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—22no—
447C3×Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—34no—
450C3×Dic3—34no—
451C3×Dic3—41no—
452C3×Dic3—42no—
453C3×Dic3—64no—
454C3×Dic3—62no—
455C3×Dic3—61no—
456C3×Dic3—62no—
457C3×Dic3—62no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—122no—
462C3×Dic3—121no—
463C3×Dic3C2×C4×D312yes—
464C3×Dic3C2×C4×D312yes—
465C22×Q8—271no—
466C4×Q8—91no—
467C4×Q8—271no—
468C4×Q8—272no—
469C4×Q8—271no—
470C4×Q8—272no—
471C4×Q8—271no—
472#117—91no—
473#117—91no—
474#117—272no—
475#117—272no—
476C33#51911yescharacteristic, complemented, Sylow
477C23×C3—31no—
478C23×C3—31no—
479C23×C3—61no—
480C22×D3C2×D3211yescharacteristic
481C3×Q8—94no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—34no—
488C2×C3×C4—34no—
489C2×C3×C4—31no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—64no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—62no—
500C2×C3×C4—61no—
501C2×C3×C4—92no—
502C2×C3×C4—92no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507C2×C3×C4C2×D3211yescharacteristic
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—61no—
517C2×Dic3—62no—
518C2×Dic3—61no—
519C2×Dic3—62no—
520C2×Dic3—98no—
521C2×Dic3—98no—
522C2×Dic3—92no—
523C2×Dic3—92no—
524C2×Dic3—92no—
525C2×Dic3—188no—
526C2×Dic3—182no—
527C2×Dic3—182no—
528C2×Dic3—182no—
529C2×Dic3—362no—
530C2×Dic3C2×D3212yes—
531C2×Dic3C2×D3211yescharacteristic
532C2×Dic3C2×D3211yescharacteristic
533C2×Dic3C2×D3211yescharacteristic
534C4×D3—98no—
535C4×D3#62414yes—
536Dic6—34no—
537Dic6—34no—
538Dic6—64no—
539Dic6—98no—
540Dic6—98no—
541Dic6—94no—
542Dic6—94no—
543Dic6—94no—
544Dic6—98no—
545Dic6—188no—
546Dic6—184no—
547Dic6—184no—
548Dic6—184no—
549Dic6—364no—
550C2×C32—21no—
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—41no—
560C2×C32—41no—
561C2×C32—41no—
562C2×C32—62no—
563C2×C32C22×C4×D311yescharacteristic
564C2×C32C22×C4×D311yescharacteristic
565C2×C32C22×C4×D311yescharacteristic
566C2×C32#100711yescharacteristic
567C2×C32#101011yescharacteristic
568C2×C32#101011yescharacteristic
569C2×C32#101011yescharacteristic
570C2×C32#101011yescharacteristic
571C2×C32#101011yescharacteristic
572C3×D3—24no—
573C3×D3—22no—
574C3×D3—22no—
575C2×Q8—91no—
576C2×Q8—272no—
577C2×Q8—278no—
578C2×Q8—271no—
579C22×C4—31no—
580C22×C4—272no—
581C4⋊C4—31no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—92no—
585C4⋊C4—91no—
586C4⋊C4—272no—
587C4⋊C4—272no—
588C4⋊C4—272no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—92no—
592C42—31no—
593C42—92no—
594C42—92no—
595C42—91no—
596C42—272no—
597C42—272no—
598C42—272no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—32no—
603C22×C3—32no—
604C22×C3—41no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—62no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3C22×D3211yescharacteristic
613C22×C3C22×D3211yescharacteristic
614C22×C3C22×D3211yescharacteristic
615C2×D3—21no—
616C2×D3—21no—
617C2×D3C2×#62412yes—
618C3×C4—22no—
619C3×C4—22no—
620C3×C4—22no—
621C3×C4—32no—
622C3×C4—32no—
623C3×C4—42no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—61no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—61no—
632C3×C4—94no—
633C3×C4—122no—
634C3×C4—121no—
635C3×C4—182no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4C4×D3212yes—
639C3×C4C4×D3212yes—
640C3×C4C2×#62412yes—
641Dic3—21no—
642Dic3—21no—
643Dic3—22no—
644Dic3—34no—
645Dic3—34no—
646Dic3—64no—
647Dic3—62no—
648Dic3—61no—
649Dic3—61no—
650Dic3—61no—
651Dic3—61no—
652Dic3—62no—
653Dic3—62no—
654Dic3—94no—
655Dic3—94no—
656Dic3—94no—
657Dic3—121no—
658Dic3—122no—
659Dic3—184no—
660Dic3—184no—
661Dic3—184no—
662Dic3—364no—
663Dic3C2×#62412yes—
664C32—21no—
665C32—21no—
666C32—21no—
667C32—41no—
668C32#551611yescharacteristic, complemented
669C32#551611yescharacteristic, complemented
670C32#557211yescharacteristic, complemented
671C23—31no—
672Q8—94no—
673Q8—278no—
674Q8—274no—
675C2×C4—31no—
676C2×C4—34no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—32no—
680C2×C4—92no—
681C2×C4—91no—
682C2×C4—91no—
683C2×C4—92no—
684C2×C4—278no—
685C2×C4—272no—
686C2×C4D3311yescharacteristic
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—41no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—64no—
700C2×C3—62no—
701C2×C3—62no—
702C2×C3#6429711yescharacteristic
703C2×C3#6429811yescharacteristic
704C2×C3#6429811yescharacteristic
705C2×C3#6429811yescharacteristic
706C2×C3C2×C4×D3211yescharacteristic
707C2×C3C2×C4×D3211yescharacteristic
708C2×C3#6430911yescharacteristic
709C2×C3#6431511yescharacteristic
710C2×C3C22×#62411yescharacteristic
711D3—22no—
712C22—32no—
713C22—61no—
714C22—61no—
715C22C2×D3311yescharacteristic
716C4—32no—
717C4—61no—
718C4—62no—
719C4—61no—
720C4—94no—
721C4—181no—
722C4—181no—
723C4—182no—
724C4—274no—
725C4D3×#62412yes—
726C3—21no—
727C3—21no—
728C3—21no—
729C3—41no—
730C3#1059388511yescharacteristic, complemented
731C3#1059435711yescharacteristic, complemented
732C3#1059482811yescharacteristic, complemented
733C2—62no—
734C2#1172439211yescharacteristic
735C2#1172439611yescharacteristic
736C2C2×D3×#62411yescharacteristic
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
3. #11723406C2semidirect
4. #11723399C2semidirect
6. C3×#63844C2semidirect
8. #11722943C2semidirect
9. #11722942C2semidirect
20. D3×#634C4semidirect
68. #63844D3semidirect
476. C33#519semidirect
668. C32#5516semidirect
669. C32#5516semidirect
670. C32#5572semidirect
730. C3#10593885semidirect
731. C3#10594357semidirect
732. C3#10594828semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6342
#117236682
#117234062
#117233992
C3×#638552
C3×#638442
C3×#638412
#117229432
#117229422
#117229172
#117229162
#105948283
#105943573
#105938853