Finite Group Databasebeta

← #13178343

Subgroups — #13178343

Order 1728.

1122 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64104C211yesmaximal, characteristic
2C3×#64097C211yesmaximal, characteristic, complemented
3C3×#64096C211yesmaximal, characteristic, complemented
4#11723691C211yesmaximal, characteristic, complemented
5#11723688C212yesmaximal, complemented
6#11723686C212yesmaximal, complemented
7#11723677C212yesmaximal, complemented
8#11723677C211yesmaximal, characteristic, complemented
9#11723676C212yesmaximal, complemented
10#11723674C211yesmaximal, characteristic, complemented
11#11723673C211yesmaximal, characteristic, complemented
12#10594498—31nomaximal
13#10594494—31nomaximal
14#10594352—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C3×#634C2211yescharacteristic
19C2×C3×#634C2212yes—
20C2×#6294C2212yes—
21C33×C4⋊C4C2211yescharacteristic
22C3×#3752C2212yes—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×#3750C2212yes—
25C3×#3750C2212yes—
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C3×C4×C3⋊Dic3C2212yes—
28C3×C4×C3⋊Dic3C2211yescharacteristic
29#88815C2211yescharacteristic
30#88815C2211yescharacteristic
31#88815C2212yes—
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88814C2212yes—
35#88814C2212yes—
36#88814C2212yes—
37#88814C2212yes—
38#64104D311yescharacteristic
39#64097D311yescharacteristic, complemented
40#64096D311yescharacteristic, complemented
41C3×#895—31no—
42C3×#895—31no—
43C3×#895—61no—
44C3×#888—31no—
45C3×#888—31no—
46C3×#888—61no—
47C3×#887—31no—
48C3×#887—31no—
49C3×#887—61no—
50#63898—31no—
51#63897—32no—
52#63896—32no—
53#63894—31no—
54Dic3×D12—31no—
55#63888—32no—
56#63887—32no—
57#63884—32no—
58#63884—32no—
59#63874—31no—
60#63871—31no—
61#63868—32no—
62#63864—31no—
63#63864—32no—
64#63863—32no—
65#63863—31no—
66#63862—32no—
67#63860—31no—
68#63860—32no—
69#63859—32no—
70#63857—31no—
71#63856—31no—
72#63855—31no—
73#63855—31no—
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⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4⋊(C3⋊D3)—22no—
86C3×C4⋊(C3⋊D3)—42no—
87C3×C4×C3⋊D3—22no—
88C3×#634—22no—
89C3×#634—42no—
90#6294—42no—
91#5733—91no—
92#5603—91no—
93#5582—91no—
94C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
95C2×C4⋊(C3⋊D3)C2×D312yes—
96C2×C4×C3⋊D3C2×D311yescharacteristic
97C2×#634C2×D311yescharacteristic
98C2×#634C2×D312yes—
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—32no—
111C2×C3×Dic6—32no—
112C2×C3×Dic6—61no—
113C2×C3×Dic6—62no—
114C2×#624—32no—
115C2×D3×Dic3—32no—
116C2×D3×Dic3—32no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4—21no—
119C32×C4⋊C4—21no—
120C32×C4⋊C4—41no—
121C32×C4⋊C4C2×D311yescharacteristic
122C32×C4⋊C4C2×D311yescharacteristic
123C32×C4⋊C4C2×D311yescharacteristic
124#3752C2×D312yes—
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic
126#3750C2×D312yes—
127#3750C2×D312yes—
128C4×C3⋊Dic3C2×D311yescharacteristic
129C4×C3⋊Dic3C2×D312yes—
130C4×C3⋊Dic3C2×D311yescharacteristic
131C3×(C2×D3)⋊C4—32no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—62no—
134C3×C4⋊Dic3—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—61no—
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—62no—
142C3×Dic3⋊C4—62no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—32no—
145C3×C4×Dic3—32no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—62no—
150C3×C4×Dic3—61no—
151C3×C4×Dic3—61no—
152#3724—32no—
153#3724—31no—
154#3724—31no—
155Dic3⋊Dic3—31no—
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—31no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161#3722—31no—
162#3722—32no—
163#3722—32no—
164#3722—32no—
165#3722—32no—
166#3722—31no—
167(C2×D3)⋊Dic3—31no—
168(C2×D3)⋊Dic3—31no—
169(C2×D3)⋊Dic3—31no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—32no—
179C22×C33C2411yescharacteristic
180C2×C3×C3⋊D3—21no—
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3—21no—
183C2×C3×C3⋊D3—22no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—22no—
186C33×C4—22no—
187C33×C4#4112yes—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—21no—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×C4⋊Q8—91no—
196C3×#121—91no—
197C3×C4×Q8—91no—
198#947—92no—
199#947—91no—
200#946—92no—
201#946—91no—
202#936—92no—
203#936—91no—
204#935—92no—
205D4×Dic3—91no—
206#926—91no—
207#924—91no—
208#898—92no—
209#897—91no—
210#896—92no—
211#895—31no—
212#895—31no—
213#895—61no—
214#894—92no—
215#894—92no—
216#893—91no—
217#888—31no—
218#888—31no—
219#888—61no—
220#887—31no—
221#887—31no—
222#887—61no—
223#879—92no—
224#878—92no—
225#876—92no—
226#875—91no—
227#875—92no—
228C4×D12—91no—
229#872—91no—
230#872—91no—
231C22×C3⋊D3C22×D311yescharacteristic
232C22×C3⋊D3C22×D312yes—
233C22×C3×D3—31no—
234C22×C3×D3—31no—
235C22×C3×D3—32no—
236C22×C3×D3—32no—
237C22×C3×D3—61no—
238C22×C3×D3—62no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—22no—
243C2×C32×C4—22no—
244C2×C32×C4—22no—
245C2×C32×C4—41no—
246C2×C32×C4—42no—
247C2×C32×C4C22×D312yes—
248C2×C32×C4C22×D312yes—
249C2×C32×C4C22×D312yes—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C3⋊Dic3C22×D311yescharacteristic
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D312yes—
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D311yescharacteristic
260C4⋊(C3⋊D3)—22no—
261C4⋊(C3⋊D3)—42no—
262C4×C3⋊D3—22no—
263#634—22no—
264#634—42no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—32no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C2×C3×Dic3—61no—
286C3×D12—62no—
287C3×D12—62no—
288C3×D12—122no—
289C3×D12—122no—
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—
298C3×Dic6—122no—
299C3×Dic6—122no—
300C3×Dic6—124no—
301#624—122no—
302D3×Dic3—122no—
303D3×Dic3—122no—
304#542—271noSylow
305C2×C33C2×#4111yescharacteristic
306C2×C33H(5,𝔽2)11yescharacteristic
307C2×C332−1+411yescharacteristic
308C3×C3⋊D3—41no—
309C3×C3⋊D3—42no—
310C2×C3×Q8—91no—
311C2×C3×Q8—92no—
312C2×C3×D4—91no—
313C2×C3×D4—92no—
314C22×C3×C4—91no—
315C22×Dic3—92no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—32no—
319C2×D12—32no—
320C2×D12—61no—
321C2×D12—62no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—61no—
325C2×C4×D3—92no—
326C2×C4×D3—92no—
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—32no—
330C2×Dic6—32no—
331C2×Dic6—61no—
332C2×Dic6—62no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—41no—
337C3×C4⋊C4—91no—
338C3×C4⋊C4—92no—
339C3×C4⋊C4—92no—
340C3×C4⋊C4D3211yescharacteristic
341C3×C4⋊C4D3211yescharacteristic
342C3×C4⋊C4D3211yescharacteristic
343C3×C22⋊C4—92no—
344C3×C42—91no—
345C3×C42—91no—
346C3×C42—92no—
347#217—92no—
348#217—92no—
349#217—92no—
350#217—92no—
351#217—91no—
352#217—91no—
353(C2×D3)⋊C4—32no—
354(C2×D3)⋊C4—32no—
355(C2×D3)⋊C4—62no—
356(C2×D3)⋊C4—91no—
357(C2×D3)⋊C4—91no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
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—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3—92no—
374Dic3⋊C4—32no—
375Dic3⋊C4—32no—
376Dic3⋊C4—32no—
377Dic3⋊C4—32no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—92no—
385Dic3⋊C4—92no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—32no—
389C4×Dic3—32no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—62no—
394C4×Dic3—61no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—41no—
399C22×C32C23×D311yescharacteristic
400C22×C32C23×D311yescharacteristic
401C22×C32C23×D311yescharacteristic
402C2×C3⋊D3—21no—
403C2×C3⋊D3—21no—
404C2×C3⋊D3—22no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—21no—
407C2×C3⋊D3—22no—
408C2×C3×D3—62no—
409C2×C3×D3—61no—
410C2×C3×D3—62no—
411C2×C3×D3—62no—
412C2×C3×D3—61no—
413C2×C3×D3—61no—
414C2×C3×D3—62no—
415C2×C3×D3—61no—
416C2×C3×D3—62no—
417C2×C3×D3—61no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—61no—
421C2×C3×D3—121no—
422C2×C3×D3—121no—
423C2×C3×D3—122no—
424C2×C3×D3—122no—
425C2×C3×D3—122no—
426C32×C4—22no—
427C32×C4—22no—
428C32×C4—22no—
429C32×C4—22no—
430C32×C4—22no—
431C32×C4—22no—
432C32×C4—42no—
433C32×C4—42no—
434C32×C4—42no—
435C32×C4—42no—
436C32×C4—82no—
437C32×C4#23512yes—
438C32×C4#23712yes—
439C32×C4#23912yes—
440C3⋊Dic3—22no—
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—21no—
445C3⋊Dic3—22no—
446C3⋊Dic3—21no—
447C3×Dic3—64no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3—62no—
451C3×Dic3—61no—
452C3×Dic3—62no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3—62no—
456C3×Dic3—61no—
457C3×Dic3—62no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—61no—
461C3×Dic3—62no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—122no—
466C3×Dic3—121no—
467C3×Dic3—121no—
468C4⋊Q8—91no—
469#126—272no—
470#124—271no—
471#124—272no—
472#123—272no—
473C22⋊Q8—272no—
474C22⋊Q8—271no—
475#121—91no—
476C4×Q8—91no—
477C4×D4—271no—
478#117—271no—
479C33#54211yescharacteristic, complemented, Sylow
480C23×C3—91no—
481C23×C3—92no—
482C22×D3—32no—
483C22×D3—32no—
484C22×D3—31no—
485C22×D3—31no—
486C22×D3—61no—
487C22×D3—62no—
488C3×Q8—182no—
489C3×Q8—362no—
490C3×D4—182no—
491C3×D4—362no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
503C2×C3×C4—92no—
504C2×C3×C4—91no—
505C2×C3×C4—91no—
506C2×C3×C4—92no—
507C2×C3×C4—182no—
508C2×C3×C4C2×D3212yes—
509C2×C3×C4C2×D3212yes—
510C2×C3×C4C2×D3212yes—
511C2×C3×C4C2×D3211yescharacteristic
512C2×C3×C4C2×D3211yescharacteristic
513C2×C3×C4C2×D3211yescharacteristic
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—32no—
521C2×Dic3—32no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—62no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—62no—
534C2×Dic3—61no—
535C2×Dic3—362no—
536D12—62no—
537D12—62no—
538D12—122no—
539D12—122no—
540D12—122no—
541D12—124no—
542C4×D3—62no—
543C4×D3—62no—
544C4×D3—122no—
545C4×D3—362no—
546C4×D3—362no—
547Dic6—64no—
548Dic6—62no—
549Dic6—62no—
550Dic6—122no—
551Dic6—122no—
552Dic6—124no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—21no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—41no—
563C2×C32—41no—
564C2×C32—41no—
565C2×C32C2×#23511yescharacteristic
566C2×C32C2×#23711yescharacteristic
567C2×C32#100411yescharacteristic
568C2×C32#100411yescharacteristic
569C2×C32C2×#23911yescharacteristic
570C2×C32#100711yescharacteristic
571C2×C32#100711yescharacteristic
572C2×C32#100911yescharacteristic
573C2×C32#101011yescharacteristic
574C3⋊D3—41no—
575C3⋊D3—42no—
576C3×D3—122no—
577C3×D3—121no—
578C3×D3—122no—
579C3×D3—121no—
580C3×D3—122no—
581C3×D3—242no—
582C2×Q8—91no—
583C2×Q8—92no—
584C2×D4—91no—
585C2×D4—92no—
586C22×C4—91no—
587C22×C4—272no—
588C4⋊C4—91no—
589C4⋊C4—92no—
590C4⋊C4—92no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C4⋊C4—272no—
594C4⋊C4#111311yescharacteristic
595C22⋊C4—92no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—272no—
599C22⋊C4—272no—
600C22⋊C4—272no—
601C22⋊C4—272no—
602C42—91no—
603C42—91no—
604C42—92no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—41no—
609C22×C3—181no—
610C22×C3—182no—
611C22×C3—182no—
612C22×C3—181no—
613C22×C3—181no—
614C22×C3—182no—
615C22×C3C22×D3211yescharacteristic
616C22×C3C22×D3211yescharacteristic
617C22×C3C22×D3211yescharacteristic
618C2×D3—62no—
619C2×D3—61no—
620C2×D3—62no—
621C2×D3—61no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—61no—
625C2×D3—62no—
626C2×D3—61no—
627C2×D3—62no—
628C2×D3—61no—
629C2×D3—62no—
630C2×D3—61no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—122no—
634C2×D3—122no—
635C2×D3—122no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—82no—
647C3×C4—182no—
648C3×C4—181no—
649C3×C4—181no—
650C3×C4—182no—
651C3×C4—181no—
652C3×C4—181no—
653C3×C4—181no—
654C3×C4#379512yes—
655C3×C4#379612yes—
656C3×C4#379912yes—
657Dic3—64no—
658Dic3—62no—
659Dic3—62no—
660Dic3—62no—
661Dic3—62no—
662Dic3—61no—
663Dic3—61no—
664Dic3—62no—
665Dic3—61no—
666Dic3—62no—
667Dic3—61no—
668Dic3—62no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—122no—
676Dic3—121no—
677Dic3—121no—
678C32—21no—
679C32—21no—
680C32—21no—
681C32—41no—
682C32#558211yescharacteristic, complemented
683C32#560311yescharacteristic, complemented
684C32#573311yescharacteristic, complemented
685C23—92no—
686C23—91no—
687Q8—182no—
688Q8—362no—
689D4—182no—
690D4—362no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—92no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—92no—
698C2×C4—182no—
699C2×C4—1082no—
700C2×C4C2×#111312yes—
701C2×C4C2×#111311yescharacteristic
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—41no—
712C2×C3—41no—
713C2×C3—41no—
714C2×C3—361no—
715C2×C3—362no—
716C2×C3C2×#379511yescharacteristic
717C2×C3C2×#379611yescharacteristic
718C2×C3C2×#379911yescharacteristic
719C2×C3#6431311yescharacteristic
720C2×C3#6431411yescharacteristic
721C2×C3#6431411yescharacteristic
722C2×C3#6431511yescharacteristic
723C2×C3#6431511yescharacteristic
724C2×C3#6431611yescharacteristic
725D3—122no—
726D3—121no—
727D3—122no—
728D3—121no—
729D3—122no—
730D3—242no—
731C22—181no—
732C22—182no—
733C22—182no—
734C22—181no—
735C22—181no—
736C22—182no—
737C22C22×#111311yescharacteristic
738C4—22no—
739C4—181no—
740C4—182no—
741C4—181no—
742C4—182no—
743C4—181no—
744C4—181no—
745C4—181no—
746C4#8904112yes—
747C3—21no—
748C3—21no—
749C3—21no—
750C3—41no—
751C3#1059435211yescharacteristic, complemented
752C3#1059449411yescharacteristic, complemented
753C3#1059449811yescharacteristic, complemented
754C2—361no—
755C2—362no—
756C2C2×#8904111yescharacteristic
757C2#1172462311yescharacteristic
758C2#1172462411yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC3×#64104C2
hypercenterC4⋊C4#1113
hypocenterC33#542
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64097C2semidirect
3. C3×#64096C2semidirect
4. #11723691C2semidirect
5. #11723688C2semidirect
6. #11723686C2semidirect
7. #11723677C2semidirect
8. #11723677C2semidirect
9. #11723676C2semidirect
10. #11723674C2semidirect
11. #11723673C2semidirect
39. #64097D3semidirect
40. #64096D3semidirect
479. C33#542semidirect
682. C32#5582semidirect
683. C32#5603semidirect
684. C32#5733semidirect
751. C3#10594352semidirect
752. C3#10594494semidirect
753. C3#10594498semidirect

Maximal subgroups

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

subgroupindex
C3×#641042
C3×#640972
C3×#640962
#117236912
#117236882
#117236862
#117236772
#117236762
#117236742
#117236732
#105944983
#105944943
#105943523