Finite Group Databasebeta

← #13178638

Subgroups — #13178638

Order 1728.

1254 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64147C211yesmaximal, characteristic
2C3×#64145C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723726C212yesmaximal, complemented
5#11723724C212yesmaximal, complemented
6#11723716C212yesmaximal, complemented
7#11723715C212yesmaximal, complemented
8C4×#6294C211yesmaximal, characteristic, complemented
9#11723680C211yesmaximal, characteristic, complemented
10#11723674C211yesmaximal, characteristic, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10595191—31nomaximal
13#10595173—31nomaximal
14#10595172—31nomaximal
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C22×C3×C3⋊Dic3C2212yes—
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#634C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C3×#3757C2212yes—
23C3×#3757C2212yes—
24C3×#3757C2212yes—
25C3×#3757C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30#88815C2212yes—
31#88815C2212yes—
32#88815C2212yes—
33#88815C2212yes—
34#88814C2212yes—
35#88813C2212yes—
36#88813C2211yescharacteristic
37#88813C2211yescharacteristic
38#64147D311yescharacteristic
39#64145D311yescharacteristic, complemented
40D4×C3⋊Dic3D311yescharacteristic, complemented
41C3×#938—31no—
42C3×#938—31no—
43C3×#938—61no—
44C3×#936—31no—
45C3×#936—31no—
46C3×#936—61no—
47C3×D4×Dic3—31no—
48C3×D4×Dic3—31no—
49C3×D4×Dic3—61no—
50#63975—32no—
51#67⋊Dic3—32no—
52Dic3×#67—32no—
53#63969—32no—
54#63969—32no—
55#63957—32no—
56#63956—32no—
57#63956—32no—
58#63956—32no—
59#63955—32no—
60#63955—32no—
61#63952—32no—
62C4×#624—31no—
63C4×D3×Dic3—31no—
64C4×D3×Dic3—31no—
65#63872—31no—
66#63871—31no—
67#63869—31no—
68#63869—31no—
69#63857—31no—
70#63856—31no—
71#63844—31no—
72#63843—31no—
73Dic3×Dic6—31no—
74C23×C33C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C33×D4—22no—
77C2×C33×C4C2311yescharacteristic
78C3×#638—24no—
79C2×C3×C3⋊Dic3—24no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4×C3⋊D3—22no—
89C3×#634—22no—
90#6294—22no—
91#6294—22no—
92#5680—91no—
93#5600—91no—
94#5557—91no—
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4—41no—
99C2×C32×D4C2×D311yescharacteristic
100C2×C32×D4C2×D311yescharacteristic
101C2×C32×D4C2×D311yescharacteristic
102C2×#638C2×D312yes—
103C22×C3⋊Dic3C2×D312yes—
104C2×C4×C3⋊D3C2×D311yescharacteristic
105C2×#634C2×D311yescharacteristic
106C2×C3×#67—32no—
107C2×C3×#67—32no—
108C2×C3×#67—62no—
109C22×C3×Dic3—32no—
110C22×C3×Dic3—32no—
111C22×C3×Dic3—62no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—61no—
115C2×C3×Dic6—31no—
116C2×C3×Dic6—31no—
117C2×C3×Dic6—61no—
118C2×#624—31no—
119C2×#624—31no—
120C2×D3×Dic3—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C2×D3×Dic3—31no—
124#3757C2×D312yes—
125#3757C2×D312yes—
126#3757C2×D312yes—
127#3757C2×D312yes—
128C4⋊(C3⋊Dic3)C2×D311yescharacteristic
129C4⋊(C3⋊Dic3)C2×D311yescharacteristic
130C4×C3⋊Dic3C2×D311yescharacteristic
131C4×C3⋊Dic3C2×D311yescharacteristic
132C3×#217—32no—
133C3×#217—32no—
134C3×#217—32no—
135C3×#217—32no—
136C3×#217—32no—
137C3×#217—32no—
138C3×#217—32no—
139C3×#217—32no—
140C3×#217—62no—
141C3×#217—62no—
142C3×#217—62no—
143C3×#217—62no—
144C3×C4⋊Dic3—31no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—61no—
149C3×C4⋊Dic3—61no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—61no—
155C3×C4×Dic3—61no—
156#3724—32no—
157#3724—32no—
158#3724—32no—
159#3724—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168#3722—32no—
169(C2×D3)⋊Dic3—32no—
170(C2×D3)⋊Dic3—32no—
171Dic32—32no—
172Dic32—32no—
173Dic32—32no—
174Dic32—31no—
175Dic32—31no—
176Dic32—31no—
177Dic32—31no—
178Dic32—31no—
179Dic32—31no—
180C22×C33—22no—
181C22×C33—22no—
182C22×C33—22no—
183C22×C33C2411yescharacteristic
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3#4112yes—
187C33×C4#4112yes—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—22no—
194C3×C3⋊Dic3—22no—
195C3×C3⋊Dic3#4112yes—
196C3×#124—91no—
197C3×#121—91no—
198C3×C4×D4—91no—
199#946—91no—
200Q8×Dic3—91no—
201#938—31no—
202#938—31no—
203#938—61no—
204#936—31no—
205#936—31no—
206#936—61no—
207#935—92no—
208D4×Dic3—31no—
209D4×Dic3—31no—
210D4×Dic3—61no—
211D4×Dic3—92no—
212C4×#67—92no—
213#926—92no—
214#924—91no—
215C2×C4×Dic3—91no—
216#897—91no—
217#890—91no—
218#890—91no—
219#887—91no—
220#883—92no—
221#883—92no—
222#67⋊C4—92no—
223#879—92no—
224#879—92no—
225#879—92no—
226#877—92no—
227#877—92no—
228C42×D3—91no—
229C42×D3—91no—
230#870—91no—
231C4×Dic6—91no—
232C23×C32—22no—
233C23×C32—22no—
234C23×C32—22no—
235C23×C32—42no—
236C23×C32C22×D312yes—
237C23×C32C22×D312yes—
238C23×C32C22×D312yes—
239C22×C3⋊D3C22×D311yescharacteristic
240C22×C3×D3—31no—
241C22×C3×D3—31no—
242C22×C3×D3—61no—
243C32×D4—22no—
244C32×D4—24no—
245C32×D4—22no—
246C32×D4—22no—
247C32×D4—42no—
248C32×D4—42no—
249C32×D4—44no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—41no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257#638—24no—
258C2×C3⋊Dic3—24no—
259C2×C3⋊Dic3C22×D311yescharacteristic
260C2×C3⋊Dic3C22×D312yes—
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D312yes—
266C2×C3⋊Dic3C22×D311yescharacteristic
267C4×C3⋊D3—22no—
268#634—22no—
269C3×#67—64no—
270C3×#67—64no—
271C3×#67—124no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—32no—
278C2×C3×Dic3—32no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—61no—
291C2×C3×Dic3—61no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—64no—
297C2×C3×Dic3—64no—
298C2×C3×Dic3—124no—
299C3×C4×D3—62no—
300C3×C4×D3—62no—
301C3×C4×D3—122no—
302C3×Dic6—62no—
303C3×Dic6—62no—
304C3×Dic6—122no—
305#624—62no—
306#624—62no—
307D3×Dic3—62no—
308D3×Dic3—62no—
309D3×Dic3—62no—
310D3×Dic3—62no—
311#529—271noSylow
312C2×C33—42no—
313C2×C33C2×#4111yescharacteristic
314C2×C33C2×#4111yescharacteristic
315C2×C33C2×#4111yescharacteristic
316C3×C3⋊D3—22no—
317C2×C3×Q8—91no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—41no—
322C2×C3×D4—92no—
323C2×C3×D4D3211yescharacteristic
324C2×C3×D4D3211yescharacteristic
325C2×C3×D4D3211yescharacteristic
326C22×C3×C4—92no—
327C22×C3×C4—91no—
328C2×#67—32no—
329C2×#67—32no—
330C2×#67—62no—
331C22×Dic3—32no—
332C22×Dic3—32no—
333C22×Dic3—62no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—61no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×Dic6—31no—
344C2×Dic6—31no—
345C2×Dic6—61no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C22⋊C4—92no—
349C3×C22⋊C4—92no—
350C3×C22⋊C4—92no—
351C3×C22⋊C4—92no—
352C3×C42—91no—
353C3×C42—91no—
354#217—32no—
355#217—32no—
356#217—32no—
357#217—32no—
358#217—32no—
359#217—32no—
360#217—32no—
361#217—32no—
362#217—62no—
363#217—62no—
364#217—62no—
365#217—62no—
366#217—92no—
367(C2×D3)⋊C4—92no—
368(C2×D3)⋊C4—92no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—92no—
376C4⋊Dic3—92no—
377C4⋊Dic3—92no—
378C4⋊Dic3—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—92no—
381Dic3⋊C4—92no—
382Dic3⋊C4—92no—
383Dic3⋊C4—92no—
384Dic3⋊C4—92no—
385Dic3⋊C4—92no—
386Dic3⋊C4—92no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—92no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C4×Dic3—91no—
399C4×Dic3—92no—
400C4×Dic3—92no—
401C4×Dic3—91no—
402C22×C32—22no—
403C22×C32—24no—
404C22×C32—22no—
405C22×C32—22no—
406C22×C32—22no—
407C22×C32—22no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—22no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—41no—
416C22×C32—42no—
417C22×C32—42no—
418C22×C32—44no—
419C22×C32—42no—
420C22×C32—42no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—42no—
424C22×C32—42no—
425C22×C32—82no—
426C22×C32—82no—
427C22×C32C23×D311yescharacteristic
428C22×C32C23×D311yescharacteristic
429C22×C32C23×D311yescharacteristic
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3#23712yes—
433C2×C3×D3—32no—
434C2×C3×D3—32no—
435C2×C3×D3—62no—
436C2×C3×D3—61no—
437C2×C3×D3—61no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—121no—
441C2×C3×D3—121no—
442C32×C4—22no—
443C32×C4—22no—
444C32×C4—22no—
445C32×C4—42no—
446C32×C4#23512yes—
447C32×C4#23712yes—
448C32×C4#23712yes—
449C3⋊Dic3—22no—
450C3⋊Dic3—21no—
451C3⋊Dic3—22no—
452C3⋊Dic3—22no—
453C3⋊Dic3—21no—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3#23712yes—
457C3×Dic3—32no—
458C3×Dic3—32no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—62no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—61no—
470C3×Dic3—62no—
471C3×Dic3—62no—
472C3×Dic3—62no—
473C3×Dic3—62no—
474C3×Dic3—122no—
475C3×Dic3—121no—
476C3×Dic3—121no—
477C3×Dic3—121no—
478C3×Dic3—121no—
479C3×Dic3—122no—
480C3×Dic3—122no—
481#126—272no—
482#125—271no—
483#124—91no—
484#123—272no—
485C22⋊Q8—271no—
486#121—91no—
487C4×Q8—271no—
488C4×D4—91no—
489C4×D4—272no—
490#117—272no—
491C2×C42—271no—
492C33#52911yescharacteristic, complemented, Sylow
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—42no—
497C23×C3—91no—
498C23×C3C2×D3212yes—
499C23×C3C2×D3212yes—
500C23×C3C2×D3212yes—
501C22×D3—31no—
502C22×D3—31no—
503C22×D3—61no—
504C3×Q8—182no—
505C3×D4—24no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—42no—
510C3×D4—42no—
511C3×D4—44no—
512C3×D4—184no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—41no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—92no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—92no—
524C2×C3×C4—92no—
525C2×C3×C4—184no—
526C2×C3×C4—182no—
527C2×C3×C4C2×D3211yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C2×D3211yescharacteristic
530#67—64no—
531#67—64no—
532#67—124no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—62no—
556C2×Dic3—61no—
557C2×Dic3—64no—
558C2×Dic3—64no—
559C2×Dic3—124no—
560C2×Dic3—182no—
561C2×Dic3—182no—
562C4×D3—62no—
563C4×D3—62no—
564C4×D3—122no—
565C4×D3—182no—
566C4×D3—182no—
567C4×D3—182no—
568C4×D3—182no—
569Dic6—62no—
570Dic6—62no—
571Dic6—122no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—41no—
582C2×C32—41no—
583C2×C32—41no—
584C2×C32—42no—
585C2×C32—44no—
586C2×C32—42no—
587C2×C32—42no—
588C2×C32—82no—
589C2×C32—82no—
590C2×C32—84no—
591C2×C32C2×#23511yescharacteristic
592C2×C32C2×#23711yescharacteristic
593C2×C32C2×#23711yescharacteristic
594C2×C32C2×#23711yescharacteristic
595C2×C32C2×#23711yescharacteristic
596C2×C32D3×#4111yescharacteristic
597C2×C32D3×#4111yescharacteristic
598C2×C32D3×#4111yescharacteristic
599C2×C32D3×#4111yescharacteristic
600C3⋊D3—22no—
601C3×D3—62no—
602C3×D3—62no—
603C3×D3—122no—
604C2×Q8—91no—
605C2×D4—92no—
606C2×D4#111311yescharacteristic
607C22×C4—92no—
608C22×C4—91no—
609C22×C4—271no—
610C22×C4—271no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—272no—
614C4⋊C4—272no—
615C4⋊C4—272no—
616C4⋊C4—272no—
617C22⋊C4—92no—
618C22⋊C4—92no—
619C22⋊C4—92no—
620C22⋊C4—92no—
621C22⋊C4—272no—
622C42—91no—
623C42—91no—
624C42—271no—
625C42—271no—
626C42—272no—
627C22×C3—24no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—44no—
649C22×C3—41no—
650C22×C3—82no—
651C22×C3—82no—
652C22×C3—92no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3C22×D3211yescharacteristic
656C22×C3C22×D3211yescharacteristic
657C22×C3C22×D3211yescharacteristic
658C2×D3—32no—
659C2×D3—32no—
660C2×D3—62no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—121no—
666C2×D3—121no—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—42no—
671C3×C4—92no—
672C3×C4—181no—
673C3×C4—181no—
674C3×C4—181no—
675C3×C4—182no—
676C3×C4—182no—
677C3×C4—181no—
678C3×C4—182no—
679C3×C4#380412yes—
680C3×C4#380412yes—
681C3×C4#380512yes—
682Dic3—32no—
683Dic3—32no—
684Dic3—62no—
685Dic3—61no—
686Dic3—61no—
687Dic3—62no—
688Dic3—62no—
689Dic3—61no—
690Dic3—62no—
691Dic3—62no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—62no—
696Dic3—61no—
697Dic3—62no—
698Dic3—61no—
699Dic3—122no—
700Dic3—121no—
701Dic3—122no—
702Dic3—122no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706C32—21no—
707C32—21no—
708C32—21no—
709C32—41no—
710C32#555711yescharacteristic, complemented
711C32#560011yescharacteristic, complemented
712C32#568011yescharacteristic, complemented
713C23—91no—
714C23C2×#111312yes—
715Q8—182no—
716D4—22no—
717D4—184no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—92no—
724C2×C4—92no—
725C2×C4—92no—
726C2×C4—184no—
727C2×C4—182no—
728C2×C4—542no—
729C2×C4—542no—
730C2×C4C2×#111311yescharacteristic
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—44no—
741C2×C3—42no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—41no—
747C2×C3—82no—
748C2×C3—82no—
749C2×C3—84no—
750C2×C3—182no—
751C2×C3D3×#23711yescharacteristic
752C2×C3D3×#23711yescharacteristic
753C2×C3D3×#23711yescharacteristic
754C2×C3D3×#23711yescharacteristic
755C2×C3#6431211yescharacteristic
756C2×C3#6431211yescharacteristic
757C2×C3C2×#380411yescharacteristic
758C2×C3C2×#380411yescharacteristic
759C2×C3C2×#380511yescharacteristic
760D3—62no—
761D3—62no—
762D3—122no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—92no—
767C22—181no—
768C22—181no—
769C22C22×#111311yescharacteristic
770C4—92no—
771C4—182no—
772C4—181no—
773C4—181no—
774C4—181no—
775C4—182no—
776C4—181no—
777C4—182no—
778C4#8904612yes—
779C3—21no—
780C3—21no—
781C3—21no—
782C3—41no—
783C3#1059517211yescharacteristic, complemented
784C3#1059517311yescharacteristic, complemented
785C3#1059519111yescharacteristic, complemented
786C2—42no—
787C2—182no—
788C2#1172462211yescharacteristic
789C2#1172462211yescharacteristic
790C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
prime radicalC3×#64147C2
hypercenterC2×D4#1113
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C3×#64145C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. #11723726C2semidirect
5. #11723724C2semidirect
6. #11723716C2semidirect
7. #11723715C2semidirect
8. C4×#6294C2semidirect
9. #11723680C2semidirect
10. #11723674C2semidirect
11. #11723668C2semidirect
39. #64145D3semidirect
40. D4×C3⋊Dic3D3semidirect
492. C33#529semidirect
710. C32#5557semidirect
711. C32#5600semidirect
712. C32#5680semidirect
783. C3#10595172semidirect
784. C3#10595173semidirect
785. C3#10595191semidirect

Maximal subgroups

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

subgroupindex
C3×#641472
C3×#641452
C3×D4×C3⋊Dic32
#117237262
#117237242
#117237162
#117237152
C4×#62942
#117236802
#117236742
#117236682
#105951913
#105951733
#105951723