Finite Group Databasebeta

← #13178699

Subgroups — #13178699

Order 1728.

1182 conjugacy classes of subgroups.

The subgroup lattice has 784 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#11723721C212yesmaximal, complemented
5#11723720C212yesmaximal, complemented
6#11723718C212yesmaximal, complemented
7#11723716C212yesmaximal, complemented
8C4⋊#6296C211yesmaximal, characteristic, complemented
9#11723674C211yesmaximal, characteristic, complemented
10#11723673C211yesmaximal, characteristic, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10595126—31nomaximal
13#10595124—31nomaximal
14#10595121—31nomaximal
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C22×C3×C3⋊Dic3C2212yes—
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#634C2211yescharacteristic
20C2×#6296C2212yes—
21C3×#3757C2212yes—
22C3×#3757C2212yes—
23C3×#3757C2212yes—
24C3×#3757C2212yes—
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29#88815C2212yes—
30#88815C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2212yes—
33#88815C2212yes—
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88814C2212yes—
37#88813C2212yes—
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#63982—32no—
51#63966—32no—
52#63964—32no—
53#63964—32no—
54#63962—32no—
55#63961—32no—
56#63959—32no—
57#63959—32no—
58#63956—32no—
59#63956—32no—
60#63956—32no—
61#63953—32no—
62#63919—31no—
63#63918—31no—
64#63918—31no—
65#63874—31no—
66#63871—31no—
67#63857—31no—
68#63856—31no—
69#63855—31no—
70#63855—31no—
71#63844—31no—
72#63843—31no—
73Dic3×Dic6—31no—
74C23×C33C2312yes—
75C22×C3×C3⋊D3C2311yescharacteristic
76C33×D4—22no—
77C2×C33×C4C2311yescharacteristic
78C3×#638—42no—
79C2×C3×C3⋊Dic3—42no—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4×C3⋊D3—22no—
89C3×#634—22no—
90#6296—42no—
91#5682—91no—
92#5603—91no—
93#5561—91no—
94C2×C32×D4—21no—
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4—41no—
98C2×C32×D4C2×D311yescharacteristic
99C2×C32×D4C2×D311yescharacteristic
100C2×C32×D4C2×D311yescharacteristic
101C2×#638C2×D312yes—
102C22×C3⋊Dic3C2×D312yes—
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C2×#634C2×D311yescharacteristic
105C2×C3×#67—32no—
106C2×C3×#67—32no—
107C2×C3×#67—62no—
108C22×C3×Dic3—32no—
109C22×C3×Dic3—32no—
110C22×C3×Dic3—62no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—61no—
114C2×C3×Dic6—31no—
115C2×C3×Dic6—31no—
116C2×C3×Dic6—61no—
117C2×#627—32no—
118C2×#627—32no—
119C2×#627—32no—
120#3757C2×D312yes—
121#3757C2×D312yes—
122#3757C2×D312yes—
123#3757C2×D312yes—
124C4⋊(C3⋊Dic3)C2×D311yescharacteristic
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic
126C4×C3⋊Dic3C2×D311yescharacteristic
127C4×C3⋊Dic3C2×D311yescharacteristic
128C3×#217—32no—
129C3×#217—32no—
130C3×#217—32no—
131C3×#217—32no—
132C3×#217—32no—
133C3×#217—32no—
134C3×#217—32no—
135C3×#217—32no—
136C3×#217—62no—
137C3×#217—62no—
138C3×#217—62no—
139C3×#217—62no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—31no—
144C3×C4⋊Dic3—61no—
145C3×C4⋊Dic3—61no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—61no—
151C3×C4×Dic3—61no—
152#3724—32no—
153#3724—32no—
154#3724—31no—
155#3724—31no—
156#3724—32no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—31no—
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—32no—
164Dic3⋊Dic3—32no—
165Dic3⋊Dic3—32no—
166Dic3⋊Dic3—32no—
167#3722—32no—
168#3722—31no—
169#3722—31no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—31no—
172(C2×D3)⋊Dic3—31no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176Dic32—32no—
177Dic32—32no—
178Dic32—32no—
179C22×C33—22no—
180C22×C33—22no—
181C22×C33—22no—
182C22×C33C2411yescharacteristic
183C2×C3×C3⋊D3—21no—
184C2×C3×C3⋊D3—21no—
185C2×C3×C3⋊D3—21no—
186C33×C4#4112yes—
187C3×C3⋊Dic3—22no—
188C3×C3⋊Dic3—21no—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—22no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×#124—91no—
196C3×#121—91no—
197C3×C4×D4—91no—
198#946—91no—
199Q8×Dic3—91no—
200#938—31no—
201#938—31no—
202#938—61no—
203#936—31no—
204#936—31no—
205#936—61no—
206#936—92no—
207#935—92no—
208D4×Dic3—31no—
209D4×Dic3—31no—
210D4×Dic3—61no—
211#929—92no—
212#926—91no—
213#924—91no—
214#924—92no—
215#897—91no—
216#888—91no—
217#888—91no—
218#887—91no—
219#886—92no—
220#885—92no—
221#885—92no—
222#879—92no—
223#879—92no—
224#879—92no—
225#878—92no—
226#878—92no—
227#872—91no—
228#872—91no—
229#869—91no—
230C4×Dic6—91no—
231C23×C32—22no—
232C23×C32—22no—
233C23×C32—22no—
234C23×C32—42no—
235C23×C32C22×D312yes—
236C23×C32C22×D312yes—
237C23×C32C22×D312yes—
238C22×C3⋊D3C22×D311yescharacteristic
239C22×C3×D3—31no—
240C22×C3×D3—31no—
241C22×C3×D3—61no—
242C32×D4—22no—
243C32×D4—24no—
244C32×D4—22no—
245C32×D4—22no—
246C32×D4—42no—
247C32×D4—42no—
248C32×D4—44no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—41no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256#638—42no—
257C2×C3⋊Dic3—42no—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C2×C3⋊Dic3C22×D312yes—
260C2×C3⋊Dic3C22×D312yes—
261C2×C3⋊Dic3C22×D311yescharacteristic
262C2×C3⋊Dic3C22×D311yescharacteristic
263C2×C3⋊Dic3C22×D312yes—
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C4×C3⋊D3—22no—
267#634—22no—
268C3×#67—122no—
269C3×#67—122no—
270C3×#67—124no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—32no—
275C2×C3×Dic3—32no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—61no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3—61no—
295C2×C3×Dic3—122no—
296C2×C3×Dic3—122no—
297C2×C3×Dic3—124no—
298C3×C4×D3—62no—
299C3×C4×D3—62no—
300C3×C4×D3—122no—
301C3×Dic6—62no—
302C3×Dic6—62no—
303C3×Dic6—122no—
304#627—122no—
305#627—122no—
306#627—122no—
307#542—271noSylow
308C2×C33—42no—
309C2×C33C2×#4111yescharacteristic
310C2×C33H(5,𝔽2)11yescharacteristic
311C2×C332−1+411yescharacteristic
312C3×C3⋊D3—41no—
313C2×C3×Q8—91no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—41no—
318C2×C3×D4—92no—
319C2×C3×D4D3211yescharacteristic
320C2×C3×D4D3211yescharacteristic
321C2×C3×D4D3211yescharacteristic
322C22×C3×C4—92no—
323C22×C3×C4—91no—
324C2×#67—32no—
325C2×#67—32no—
326C2×#67—62no—
327C22×Dic3—32no—
328C22×Dic3—32no—
329C22×Dic3—62no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—61no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—92no—
337C2×Dic6—92no—
338C2×Dic6—92no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C22⋊C4—92no—
342C3×C22⋊C4—92no—
343C3×C22⋊C4—92no—
344C3×C22⋊C4—92no—
345C3×C42—91no—
346C3×C42—91no—
347#217—32no—
348#217—32no—
349#217—32no—
350#217—32no—
351#217—32no—
352#217—32no—
353#217—32no—
354#217—32no—
355#217—62no—
356#217—62no—
357#217—62no—
358#217—62no—
359#217—92no—
360#217—91no—
361#217—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—92no—
367(C2×D3)⋊C4—92no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—92no—
375C4⋊Dic3—91no—
376C4⋊Dic3—92no—
377C4⋊Dic3—91no—
378C4⋊Dic3—92no—
379Dic3⋊C4—92no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—92no—
385Dic3⋊C4—92no—
386Dic3⋊C4—92no—
387Dic3⋊C4—92no—
388Dic3⋊C4—92no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—92no—
396C4×Dic3—92no—
397C4×Dic3—92no—
398C22×C32—22no—
399C22×C32—24no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—22no—
404C22×C32—22no—
405C22×C32—22no—
406C22×C32—22no—
407C22×C32—22no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—41no—
412C22×C32—42no—
413C22×C32—42no—
414C22×C32—44no—
415C22×C32—42no—
416C22×C32—42no—
417C22×C32—42no—
418C22×C32—42no—
419C22×C32—42no—
420C22×C32—42no—
421C22×C32—82no—
422C22×C32—82no—
423C22×C32C23×D311yescharacteristic
424C22×C32C23×D311yescharacteristic
425C22×C32C23×D311yescharacteristic
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—21no—
429C2×C3×D3—62no—
430C2×C3×D3—61no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—121no—
437C2×C3×D3—121no—
438C32×C4—22no—
439C32×C4—22no—
440C32×C4—22no—
441C32×C4—42no—
442C32×C4#23512yes—
443C32×C4#23712yes—
444C32×C4#23712yes—
445C3⋊Dic3—21no—
446C3⋊Dic3—22no—
447C3⋊Dic3—21no—
448C3⋊Dic3—22no—
449C3⋊Dic3—22no—
450C3⋊Dic3—21no—
451C3⋊Dic3—21no—
452C3⋊Dic3—21no—
453C3×Dic3—62no—
454C3×Dic3—62no—
455C3×Dic3—61no—
456C3×Dic3—62no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—61no—
463C3×Dic3—62no—
464C3×Dic3—62no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—61no—
470C3×Dic3—122no—
471C3×Dic3—121no—
472C3×Dic3—121no—
473C3×Dic3—121no—
474C3×Dic3—121no—
475C3×Dic3—122no—
476C3×Dic3—122no—
477C4⋊Q8—271no—
478#126—272no—
479#124—91no—
480#124—272no—
481#123—272no—
482C22⋊Q8—272no—
483C22⋊Q8—271no—
484#121—91no—
485C4×Q8—271no—
486C4×D4—91no—
487#117—271no—
488C33#54211yescharacteristic, complemented, Sylow
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—42no—
493C23×C3—91no—
494C23×C3C2×D3212yes—
495C23×C3C2×D3212yes—
496C23×C3C2×D3212yes—
497C22×D3—31no—
498C22×D3—31no—
499C22×D3—61no—
500C3×Q8—182no—
501C3×D4—24no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—42no—
506C3×D4—42no—
507C3×D4—44no—
508C3×D4—362no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—41no—
513C2×C3×C4—91no—
514C2×C3×C4—92no—
515C2×C3×C4—92no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—92no—
520C2×C3×C4—91no—
521C2×C3×C4—182no—
522C2×C3×C4—362no—
523C2×C3×C4C2×D3211yescharacteristic
524C2×C3×C4C2×D3211yescharacteristic
525C2×C3×C4C2×D3211yescharacteristic
526#67—122no—
527#67—122no—
528#67—124no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—31no—
542C2×Dic3—32no—
543C2×Dic3—31no—
544C2×Dic3—32no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—62no—
552C2×Dic3—61no—
553C2×Dic3—122no—
554C2×Dic3—122no—
555C2×Dic3—124no—
556C4×D3—62no—
557C4×D3—62no—
558C4×D3—122no—
559Dic6—62no—
560Dic6—62no—
561Dic6—122no—
562Dic6—362no—
563Dic6—362no—
564Dic6—362no—
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—21no—
568C2×C32—21no—
569C2×C32—21no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—41no—
575C2×C32—41no—
576C2×C32—41no—
577C2×C32—42no—
578C2×C32—44no—
579C2×C32—42no—
580C2×C32—42no—
581C2×C32—82no—
582C2×C32—82no—
583C2×C32—84no—
584C2×C32C2×#23511yescharacteristic
585C2×C32C2×#23711yescharacteristic
586C2×C32C2×#23711yescharacteristic
587C2×C32#100411yescharacteristic
588C2×C32#100411yescharacteristic
589C2×C32#100911yescharacteristic
590C2×C32#101011yescharacteristic
591C2×C32#101011yescharacteristic
592C2×C32#101011yescharacteristic
593C3⋊D3—41no—
594C3×D3—122no—
595C3×D3—121no—
596C3×D3—121no—
597C2×Q8—91no—
598C2×Q8—272no—
599C2×D4—92no—
600C2×D4#111311yescharacteristic
601C22×C4—92no—
602C22×C4—91no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—272no—
608C4⋊C4—272no—
609C4⋊C4—272no—
610C22⋊C4—92no—
611C22⋊C4—92no—
612C22⋊C4—92no—
613C22⋊C4—92no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—272no—
617C42—91no—
618C42—91no—
619C42—272no—
620C22×C3—24no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—42no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—44no—
642C22×C3—41no—
643C22×C3—82no—
644C22×C3—82no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3C22×D3211yescharacteristic
649C22×C3C22×D3211yescharacteristic
650C22×C3C22×D3211yescharacteristic
651C2×D3—62no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—121no—
659C2×D3—121no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—42no—
664C3×C4—181no—
665C3×C4—181no—
666C3×C4—181no—
667C3×C4—182no—
668C3×C4—182no—
669C3×C4—181no—
670C3×C4—181no—
671C3×C4—182no—
672C3×C4#380412yes—
673C3×C4#380412yes—
674C3×C4#380512yes—
675Dic3—62no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—62no—
681Dic3—62no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—62no—
686Dic3—62no—
687Dic3—61no—
688Dic3—62no—
689Dic3—61no—
690Dic3—62no—
691Dic3—61no—
692Dic3—122no—
693Dic3—121no—
694Dic3—122no—
695Dic3—122no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699C32—21no—
700C32—21no—
701C32—21no—
702C32—41no—
703C32#556111yescharacteristic, complemented
704C32#560311yescharacteristic, complemented
705C32#568211yescharacteristic, complemented
706C23—91no—
707C23C2×#111312yes—
708Q8—182no—
709Q8—1082no—
710D4—22no—
711D4—362no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—92no—
717C2×C4—92no—
718C2×C4—91no—
719C2×C4—92no—
720C2×C4—182no—
721C2×C4—362no—
722C2×C4C2×#111311yescharacteristic
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—44no—
733C2×C3—42no—
734C2×C3—42no—
735C2×C3—42no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—41no—
739C2×C3—82no—
740C2×C3—82no—
741C2×C3—84no—
742C2×C3—361no—
743C2×C3#6430911yescharacteristic
744C2×C3#6430911yescharacteristic
745C2×C3#6430911yescharacteristic
746C2×C3#6431311yescharacteristic
747C2×C3#6431411yescharacteristic
748C2×C3#6431411yescharacteristic
749C2×C3C2×#380411yescharacteristic
750C2×C3C2×#380411yescharacteristic
751C2×C3C2×#380511yescharacteristic
752D3—122no—
753D3—121no—
754D3—121no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—181no—
759C22—181no—
760C22—181no—
761C22C22×#111311yescharacteristic
762C4—181no—
763C4—181no—
764C4—181no—
765C4—182no—
766C4—182no—
767C4—181no—
768C4—181no—
769C4—182no—
770C4#8904612yes—
771C3—21no—
772C3—21no—
773C3—21no—
774C3—41no—
775C3#1059512111yescharacteristic, complemented
776C3#1059512411yescharacteristic, complemented
777C3#1059512611yescharacteristic, complemented
778C2—42no—
779C2—361no—
780C2#1172462011yescharacteristic
781C2#1172462311yescharacteristic
782C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
prime radicalC3×#64147C2
hypercenterC2×D4#1113
hypocenterC33#542
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. #11723721C2semidirect
5. #11723720C2semidirect
6. #11723718C2semidirect
7. #11723716C2semidirect
8. C4⋊#6296C2semidirect
9. #11723674C2semidirect
10. #11723673C2semidirect
11. #11723668C2semidirect
39. #64145D3semidirect
40. D4×C3⋊Dic3D3semidirect
488. C33#542semidirect
703. C32#5561semidirect
704. C32#5603semidirect
705. C32#5682semidirect
775. C3#10595121semidirect
776. C3#10595124semidirect
777. C3#10595126semidirect

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
#117237212
#117237202
#117237182
#117237162
C4⋊#62962
#117236742
#117236732
#117236682
#105951263
#105951243
#105951213