Finite Group Databasebeta

← #13178331

Subgroups — #13178331

Order 1728.

1182 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64104C211yesmaximal, characteristic
2C3×#64099C211yesmaximal, characteristic, complemented
3C3×#64096C211yesmaximal, characteristic, complemented
4#11723691C211yesmaximal, characteristic, complemented
5#11723691C212yesmaximal, complemented
6#11723686C212yesmaximal, complemented
7#11723683C212yesmaximal, complemented
8C4×#6294C211yesmaximal, characteristic, complemented
9#11723677C211yesmaximal, characteristic, complemented
10#11723675C212yesmaximal, complemented
11#11723674C211yesmaximal, characteristic, complemented
12#10594464—31nomaximal
13#10594427—31nomaximal
14#10594426—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×#634C2211yescharacteristic
19C2×#6294C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×#6294C2212yes—
22C33×C4⋊C4C2211yescharacteristic
23C3×#3752C2212yes—
24C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C3×C4⋊(C3⋊Dic3)C2212yes—
26C3×#3750C2212yes—
27C3×#3750C2212yes—
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2212yes—
30C3×C4×C3⋊Dic3C2211yescharacteristic
31#88815C2212yes—
32#88814C2212yes—
33#88814C2212yes—
34#88814C2212yes—
35#88814C2212yes—
36#88813C2211yescharacteristic
37#88813C2211yescharacteristic
38#64104D311yescharacteristic
39#64099D311yescharacteristic, complemented
40#64096D311yescharacteristic, complemented
41C3×#895—31no—
42C3×#895—31no—
43C3×#895—61no—
44C3×#890—31no—
45C3×#890—31no—
46C3×#890—61no—
47C3×#887—31no—
48C3×#887—31no—
49C3×#887—61no—
50#63898—32no—
51#63898—31no—
52#63897—32no—
53#63894—32no—
54#63894—31no—
55Dic3×D12—32no—
56Dic3×D12—31no—
57#63884—32no—
58#63884—32no—
59C4×#624—31no—
60#63878—32no—
61#63877—32no—
62C4×D3×Dic3—31no—
63C4×D3×Dic3—31no—
64#63871—31no—
65#63864—31no—
66#63863—31no—
67#63861—32no—
68#63860—31no—
69#63858—32no—
70#63857—31no—
71#63856—31no—
72#63848—32no—
73#63836—32no—
74C22×C3×C3⋊D3C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C2×C33×C4C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2312yes—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4⋊(C3⋊D3)—24no—
86C3×C4⋊(C3⋊D3)—22no—
87C3×C4×C3⋊D3—22no—
88C3×#634—22no—
89#6294—22no—
90#6294—22no—
91#6294—24no—
92#5691—91no—
93#5600—91no—
94#5580—91no—
95C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
96C2×C4⋊(C3⋊D3)C2×D312yes—
97C2×C4×C3⋊D3C2×D311yescharacteristic
98C2×#634C2×D311yescharacteristic
99C2×C3×D12—31no—
100C2×C3×D12—31no—
101C2×C3×D12—32no—
102C2×C3×D12—32no—
103C2×C3×D12—61no—
104C2×C3×D12—62no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—61no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—61no—
111C2×#624—32no—
112C2×#624—31no—
113C2×#624—31no—
114C2×D3×Dic3—31no—
115C2×D3×Dic3—31no—
116C2×D3×Dic3—31no—
117C2×D3×Dic3—31no—
118C2×D3×Dic3—32no—
119C2×D3×Dic3—32no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—41no—
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C2×D311yescharacteristic
126C32×C4⋊C4C2×D311yescharacteristic
127#3752C2×D312yes—
128C4⋊(C3⋊Dic3)C2×D311yescharacteristic
129C4⋊(C3⋊Dic3)C2×D312yes—
130#3750C2×D312yes—
131#3750C2×D312yes—
132C4×C3⋊Dic3C2×D311yescharacteristic
133C4×C3⋊Dic3C2×D312yes—
134C4×C3⋊Dic3C2×D311yescharacteristic
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—62no—
138C3×C4⋊Dic3—32no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—32no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—62no—
143C3×C4⋊Dic3—61no—
144C3×Dic3⋊C4—32no—
145C3×Dic3⋊C4—32no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—62no—
149C3×Dic3⋊C4—62no—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—32no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—31no—
156C3×C4×Dic3—62no—
157C3×C4×Dic3—61no—
158C3×C4×Dic3—61no—
159#3724—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162#3722—32no—
163#3722—32no—
164#3722—32no—
165#3722—32no—
166(C2×D3)⋊Dic3—32no—
167(C2×D3)⋊Dic3—32no—
168(C2×D3)⋊Dic3—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179Dic32—31no—
180C22×C33C2411yescharacteristic
181C2×C3×C3⋊D3—21no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3—22no—
185C2×C3×C3⋊D3—22no—
186C2×C3×C3⋊D3#4112yes—
187C33×C4—22no—
188C33×C4#4112yes—
189C3×C3⋊Dic3—22no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—22no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3#4112yes—
196C3×#125—91no—
197C3×#121—91no—
198C3×C4×Q8—91no—
199#947—91no—
200#946—91no—
201#936—91no—
202#935—92no—
203D4×Dic3—92no—
204D4×Dic3—91no—
205#924—91no—
206C2×C4×Dic3—91no—
207#898—92no—
208#898—92no—
209#897—91no—
210#895—31no—
211#895—31no—
212#895—61no—
213#894—92no—
214#894—92no—
215#893—91no—
216#893—92no—
217#892—92no—
218#890—31no—
219#890—31no—
220#890—61no—
221#887—31no—
222#887—31no—
223#887—61no—
224#879—92no—
225#877—92no—
226#875—91no—
227C4×D12—92no—
228C4×D12—91no—
229#872—92no—
230C42×D3—91no—
231C42×D3—91no—
232C22×C3⋊D3C22×D312yes—
233C22×C3⋊D3C22×D311yescharacteristic
234C22×C3×D3—31no—
235C22×C3×D3—31no—
236C22×C3×D3—32no—
237C22×C3×D3—32no—
238C22×C3×D3—61no—
239C22×C3×D3—62no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—22no—
244C2×C32×C4—22no—
245C2×C32×C4—22no—
246C2×C32×C4—41no—
247C2×C32×C4—42no—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C22×D312yes—
250C2×C32×C4C22×D312yes—
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D311yescharacteristic
258C2×C3⋊Dic3C22×D312yes—
259C2×C3⋊Dic3C22×D312yes—
260C2×C3⋊Dic3C22×D311yescharacteristic
261C4⋊(C3⋊D3)—24no—
262C4⋊(C3⋊D3)—22no—
263C4×C3⋊D3—22no—
264#634—22no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—61no—
286C3×D12—64no—
287C3×D12—64no—
288C3×D12—62no—
289C3×D12—62no—
290C3×D12—122no—
291C3×D12—124no—
292C3×C4×D3—62no—
293C3×C4×D3—62no—
294C3×C4×D3—122no—
295C3×Dic6—64no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298#624—62no—
299#624—64no—
300#624—62no—
301D3×Dic3—62no—
302D3×Dic3—64no—
303D3×Dic3—62no—
304D3×Dic3—62no—
305D3×Dic3—62no—
306D3×Dic3—64no—
307#529—271noSylow
308C2×C33C2×#4111yescharacteristic
309C2×C33C2×#4111yescharacteristic
310C2×C33C2×#4111yescharacteristic
311C3×C3⋊D3—22no—
312C3×C3⋊D3—42no—
313C2×C3×Q8—91no—
314C2×C3×D4—92no—
315C2×C3×D4—91no—
316C22×C3×C4—91no—
317C22×Dic3—92no—
318C22×Dic3—91no—
319C22×Dic3—91no—
320C2×D12—32no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—32no—
324C2×D12—62no—
325C2×D12—61no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—91no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—92no—
334C2×C4×D3—92no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—92no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—92no—
345C3×C4⋊C4—92no—
346C3×C4⋊C4D3211yescharacteristic
347C3×C4⋊C4D3211yescharacteristic
348C3×C4⋊C4D3211yescharacteristic
349C3×C22⋊C4—92no—
350C3×C42—91no—
351C3×C42—91no—
352C3×C42—92no—
353#217—92no—
354#217—92no—
355#217—92no—
356#217—92no—
357(C2×D3)⋊C4—32no—
358(C2×D3)⋊C4—32no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—92no—
361(C2×D3)⋊C4—92no—
362(C2×D3)⋊C4—92no—
363(C2×D3)⋊C4—92no—
364(C2×D3)⋊C4—92no—
365(C2×D3)⋊C4—92no—
366(C2×D3)⋊C4—92no—
367(C2×D3)⋊C4—92no—
368C4⋊Dic3—32no—
369C4⋊Dic3—31no—
370C4⋊Dic3—32no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—62no—
374C4⋊Dic3—92no—
375Dic3⋊C4—32no—
376Dic3⋊C4—32no—
377Dic3⋊C4—32no—
378Dic3⋊C4—32no—
379Dic3⋊C4—62no—
380Dic3⋊C4—62no—
381Dic3⋊C4—92no—
382Dic3⋊C4—92no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—32no—
386C4×Dic3—32no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
390C4×Dic3—62no—
391C4×Dic3—61no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—41no—
402C22×C32C23×D311yescharacteristic
403C22×C32C23×D311yescharacteristic
404C22×C32C23×D311yescharacteristic
405C2×C3⋊D3—21no—
406C2×C3⋊D3—21no—
407C2×C3⋊D3—22no—
408C2×C3⋊D3—22no—
409C2×C3⋊D3—22no—
410C2×C3⋊D3#23712yes—
411C2×C3×D3—32no—
412C2×C3×D3—32no—
413C2×C3×D3—62no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—62no—
421C2×C3×D3—62no—
422C2×C3×D3—62no—
423C2×C3×D3—62no—
424C2×C3×D3—121no—
425C2×C3×D3—121no—
426C2×C3×D3—122no—
427C2×C3×D3—122no—
428C2×C3×D3—122no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—22no—
433C32×C4—22no—
434C32×C4—22no—
435C32×C4—42no—
436C32×C4—42no—
437C32×C4—42no—
438C32×C4—42no—
439C32×C4—82no—
440C32×C4#23512yes—
441C32×C4#23712yes—
442C32×C4#23912yes—
443C3⋊Dic3—22no—
444C3⋊Dic3—21no—
445C3⋊Dic3—21no—
446C3⋊Dic3—21no—
447C3⋊Dic3—21no—
448C3⋊Dic3—22no—
449C3⋊Dic3#23912yes—
450C3×Dic3—32no—
451C3×Dic3—32no—
452C3×Dic3—62no—
453C3×Dic3—64no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—62no—
458C3×Dic3—61no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—62no—
466C3×Dic3—121no—
467C3×Dic3—121no—
468C3×Dic3—121no—
469C3×Dic3—121no—
470C3×Dic3—122no—
471#126—272no—
472#125—91no—
473#124—271no—
474#123—272no—
475C22⋊Q8—271no—
476#121—91no—
477C4×Q8—91no—
478C4×D4—271no—
479C4×D4—272no—
480#117—272no—
481C2×C42—271no—
482C33#52911yescharacteristic, complemented, Sylow
483C23×C3—91no—
484C23×C3—92no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—32no—
488C22×D3—32no—
489C22×D3—61no—
490C22×D3—62no—
491C3×Q8—182no—
492C3×D4—184no—
493C3×D4—182no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—41no—
501C2×C3×C4—42no—
502C2×C3×C4—91no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—92no—
508C2×C3×C4—92no—
509C2×C3×C4—182no—
510C2×C3×C4C2×D3212yes—
511C2×C3×C4C2×D3212yes—
512C2×C3×C4C2×D3212yes—
513C2×C3×C4C2×D3211yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—61no—
531C2×Dic3—62no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—62no—
536C2×Dic3—61no—
537C2×Dic3—182no—
538C2×Dic3—184no—
539C2×Dic3—182no—
540D12—64no—
541D12—64no—
542D12—62no—
543D12—62no—
544D12—122no—
545D12—124no—
546C4×D3—62no—
547C4×D3—62no—
548C4×D3—122no—
549C4×D3—182no—
550C4×D3—184no—
551C4×D3—182no—
552C4×D3—184no—
553C4×D3—182no—
554C4×D3—182no—
555Dic6—64no—
556Dic6—62no—
557Dic6—62no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—41no—
568C2×C32—41no—
569C2×C32—41no—
570C2×C32C2×#23511yescharacteristic
571C2×C32C2×#23711yescharacteristic
572C2×C32C2×#23711yescharacteristic
573C2×C32C2×#23911yescharacteristic
574C2×C32C2×#23911yescharacteristic
575C2×C32D3×#4111yescharacteristic
576C2×C32D3×#4111yescharacteristic
577C2×C32D3×#4111yescharacteristic
578C2×C32D3×#4111yescharacteristic
579C3⋊D3—22no—
580C3⋊D3—42no—
581C3×D3—62no—
582C3×D3—62no—
583C3×D3—122no—
584C3×D3—122no—
585C3×D3—122no—
586C3×D3—242no—
587C2×Q8—91no—
588C2×D4—92no—
589C2×D4—91no—
590C22×C4—91no—
591C22×C4—271no—
592C22×C4—271no—
593C22×C4—272no—
594C4⋊C4—92no—
595C4⋊C4—91no—
596C4⋊C4—92no—
597C4⋊C4—92no—
598C4⋊C4—272no—
599C4⋊C4#111311yescharacteristic
600C22⋊C4—92no—
601C22⋊C4—272no—
602C22⋊C4—272no—
603C22⋊C4—272no—
604C22⋊C4—272no—
605C42—91no—
606C42—91no—
607C42—92no—
608C42—271no—
609C42—271no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—41no—
614C22×C3—92no—
615C22×C3—181no—
616C22×C3—181no—
617C22×C3—182no—
618C22×C3—182no—
619C22×C3—182no—
620C22×C3C22×D3211yescharacteristic
621C22×C3C22×D3211yescharacteristic
622C22×C3C22×D3211yescharacteristic
623C2×D3—32no—
624C2×D3—32no—
625C2×D3—62no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—62no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—122no—
639C2×D3—122no—
640C2×D3—122no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—42no—
651C3×C4—82no—
652C3×C4—92no—
653C3×C4—182no—
654C3×C4—181no—
655C3×C4—181no—
656C3×C4—181no—
657C3×C4—181no—
658C3×C4—182no—
659C3×C4#379512yes—
660C3×C4#379612yes—
661C3×C4#379912yes—
662Dic3—32no—
663Dic3—32no—
664Dic3—62no—
665Dic3—64no—
666Dic3—62no—
667Dic3—61no—
668Dic3—61no—
669Dic3—62no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—62no—
676Dic3—61no—
677Dic3—62no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—122no—
683C32—21no—
684C32—21no—
685C32—21no—
686C32—41no—
687C32#558011yescharacteristic, complemented
688C32#560011yescharacteristic, complemented
689C32#569111yescharacteristic, complemented
690C23—91no—
691C23—92no—
692Q8—182no—
693D4—184no—
694D4—182no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—92no—
700C2×C4—91no—
701C2×C4—92no—
702C2×C4—182no—
703C2×C4—542no—
704C2×C4—544no—
705C2×C4—542no—
706C2×C4C2×#111312yes—
707C2×C4C2×#111311yescharacteristic
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—182no—
721C2×C3—362no—
722C2×C3C2×#379511yescharacteristic
723C2×C3C2×#379611yescharacteristic
724C2×C3C2×#379911yescharacteristic
725C2×C3D3×#23711yescharacteristic
726C2×C3D3×#23711yescharacteristic
727C2×C3#6431211yescharacteristic
728C2×C3D3×#23911yescharacteristic
729C2×C3D3×#23911yescharacteristic
730C2×C3#6431911yescharacteristic
731D3—62no—
732D3—62no—
733D3—122no—
734D3—122no—
735D3—122no—
736D3—242no—
737C22—92no—
738C22—181no—
739C22—181no—
740C22—182no—
741C22—182no—
742C22—182no—
743C22C22×#111311yescharacteristic
744C4—22no—
745C4—92no—
746C4—181no—
747C4—182no—
748C4—181no—
749C4—181no—
750C4—181no—
751C4—182no—
752C4#8904112yes—
753C3—21no—
754C3—21no—
755C3—21no—
756C3—41no—
757C3#1059442611yescharacteristic, complemented
758C3#1059442711yescharacteristic, complemented
759C3#1059446411yescharacteristic, complemented
760C2—182no—
761C2—362no—
762C2C2×#8904111yescharacteristic
763C2#1172462211yescharacteristic
764C2#1172462611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC3×#64104C2
hypercenterC4⋊C4#1113
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64099C2semidirect
3. C3×#64096C2semidirect
4. #11723691C2semidirect
5. #11723691C2semidirect
6. #11723686C2semidirect
7. #11723683C2semidirect
8. C4×#6294C2semidirect
9. #11723677C2semidirect
10. #11723675C2semidirect
11. #11723674C2semidirect
39. #64099D3semidirect
40. #64096D3semidirect
482. C33#529semidirect
687. C32#5580semidirect
688. C32#5600semidirect
689. C32#5691semidirect
757. C3#10594426semidirect
758. C3#10594427semidirect
759. C3#10594464semidirect

Maximal subgroups

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

subgroupindex
C3×#641042
C3×#640992
C3×#640962
#117236912
#117236862
#117236832
C4×#62942
#117236772
#117236752
#117236742
#105944643
#105944273
#105944263