Finite Group Databasebeta

← #10944022

Subgroups — #10944022

Order 768.

1468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×#41C211yesmaximal, characteristic
2C2×C3×#452C211yesmaximal, characteristic
3C2×#5239C211yesmaximal, characteristic
4C2×#5182C211yesmaximal, characteristic, complemented
5C2×#5162C211yesmaximal, characteristic, complemented
6#82811C211yesmaximal, characteristic, complemented
7#72065C211yesmaximal, characteristic, complemented
8#72047C211yesmaximal, characteristic, complemented
9#71693C211yesmaximal, characteristic, complemented
10#70239C211yesmaximal, characteristic, complemented
11#70221C211yesmaximal, characteristic, complemented
12#70171C211yesmaximal, characteristic, complemented
13#70153C211yesmaximal, characteristic, complemented
14#69931C211yesmaximal, characteristic, complemented
15#69908C211yesmaximal, characteristic, complemented
16#32907—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21Dic3×#41—24no—
22Dic3×#41—24no—
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×#944C2211yescharacteristic
26C22×#216C2211yescharacteristic
27C2×D4×Dic3—21no—
28C2×D4×Dic3—21no—
29C2×D4×Dic3C2211yescharacteristic
30C2×D4×Dic3C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C2×#926—21no—
33C2×#926C2211yescharacteristic
34C2×#924C2211yescharacteristic
35C22×C4×Dic3—21no—
36C22×C4×Dic3C2211yescharacteristic
37C3×#452—24no—
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41#5239—24no—
42#5229C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×#835C2211yescharacteristic
46C2×#832C2211yescharacteristic
47C2×#830C2211yescharacteristic
48#5182—24no—
49#5162—24no—
50C2×#816C2211yescharacteristic
51C2×#816C2211yescharacteristic
52C2×Dic3⋊C8C2211yescharacteristic
53C2×Dic3⋊C8C2211yescharacteristic
54#4976—21no—
55#4976—21no—
56#4975C2211yescharacteristic
57#4973C2211yescharacteristic
58#4942—21no—
59#4942—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64#4529C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×C4×#41—31no—
67C2×#462—31no—
68C2×#461—31no—
69C2×#452—31no—
70C2×#452D311yescharacteristic
71#2857—31no—
72#1878—31no—
73#1878—31no—
74#1877—31no—
75#1877—31no—
76#1873—31no—
77#1873—31no—
78#1803—31no—
79#1802—31no—
80#1797—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41D414yes—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C23×Dic3—21no—
94C23×Dic3—21no—
95C23×Dic3D411yescharacteristic
96C23×Dic3D411yescharacteristic
97C22×Dic6C2311yescharacteristic
98C2×C3×Q16—22no—
99C2×C3×Q16—22no—
100C2×C3×Q16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217—21no—
114C2×#217—21no—
115Q8×Dic3—22no—
116Q8×Dic3—22no—
117Q8×Dic3—22no—
118Q8×Dic3D414yes—
119#944—22no—
120#944—22no—
121C2×#216—22no—
122C2×#216—22no—
123C2×#216—22no—
124D4×Dic3—28no—
125D4×Dic3—28no—
126D4×Dic3—22no—
127D4×Dic3—22no—
128D4×Dic3—22no—
129D4×Dic3D414yes—
130C2×#214—22no—
131C2×#214—22no—
132C2×#214—22no—
133#926—28no—
134#926—22no—
135#926—22no—
136C2×C4⋊Dic3—21no—
137C2×C4⋊Dic3—21no—
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141#924—22no—
142#924—22no—
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4—21no—
147C2×Dic3⋊C4—21no—
148C2×C4×Dic3—28no—
149C2×C4×Dic3—21no—
150C2×C4×Dic3—21no—
151C2×C4×Dic3—21no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3D411yescharacteristic
155C2×C4×Dic3D411yescharacteristic
156C2×C4×Dic3C2311yescharacteristic
157C2×C4×Dic3C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C3×#103—22no—
161C3×#102—22no—
162C3×C22⋊C8—22no—
163#835—22no—
164#835—22no—
165#835—22no—
166#832—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#830—22no—
172#816—22no—
173#816—22no—
174Dic3⋊C8—22no—
175Dic3⋊C8—22no—
176C22×#41C2×D311yescharacteristic
177C22×Q16—31no—
178C22×Q16C2×D311yescharacteristic
179C22×SD16—31no—
180C22×SD16C2×D311yescharacteristic
181C2×C4⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8C2×D311yescharacteristic
184C4×#41—64no—
185C4×#41—64no—
186C2×C4×Q8—31no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—31no—
190C2×C4×D4—61no—
191C2×C4×D4—61no—
192C2×#117—31no—
193C2×#117—61no—
194C22×C42—31no—
195C22×C42—61no—
196#462—64no—
197#461—64no—
198#452—24no—
199#452—64no—
200C2×C4⋊C8—31no—
201C2×C4⋊C8—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103—31no—
205C2×#103—31no—
206C2×#103—31no—
207C2×#103C2×D311yescharacteristic
208C2×#102—31no—
209C2×#102C2×D311yescharacteristic
210C2×C22⋊C8—31no—
211C2×C22⋊C8C2×D311yescharacteristic
212#391—31no—
213#391—31no—
214#389—61no—
215#389—61no—
216#384—31no—
217#380—61no—
218#380—61no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223#336—31no—
224#336—31no—
225C24×C3—21no—
226C24×C3C2×D411yescharacteristic
227C3×#41—28no—
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—28no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8C2×D412yes—
241C2×C3×Q8C2×D412yes—
242C2×C3×Q8#4112yes—
243C2×C3×D4—24no—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4C2×D412yes—
250C2×C3×D4C2×D412yes—
251C2×C3×D4#4112yes—
252C22×C3×C4—24no—
253C22×C3×C4—24no—
254C22×C3×C4—21no—
255C22×C3×C4—24no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D412yes—
264C22×C3×C4#4112yes—
265C22×C3×C4C2411yescharacteristic
266C22×Dic3—24no—
267C22×Dic3—21no—
268C22×Dic3—21no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—24no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—41no—
278C22×Dic3—42no—
279C22×Dic3—42no—
280C22×Dic3—42no—
281C22×Dic3—42no—
282C22×Dic3C2×D411yescharacteristic
283C22×Dic3C2×D411yescharacteristic
284C22×Dic3C2×D411yescharacteristic
285C22×Dic3C2×D411yescharacteristic
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C3×Q16—44no—
293C3×SD16—44no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—42no—
303C3×C22⋊C4—42no—
304#217—24no—
305#217—24no—
306#217—24no—
307#217—42no—
308#216—44no—
309#214—44no—
310C4⋊Dic3—24no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—24no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316C4⋊Dic3C2×D412yes—
317C4⋊Dic3C2×D412yes—
318Dic3⋊C4—42no—
319Dic3⋊C4—42no—
320Dic3⋊C4—42no—
321Dic3⋊C4—42no—
322Dic3⋊C4—42no—
323C4×Dic3—24no—
324C4×Dic3—24no—
325C4×Dic3—21no—
326C4×Dic3—21no—
327C4×Dic3—22no—
328C4×Dic3—24no—
329C4×Dic3—22no—
330C4×Dic3C2×D412yes—
331C4×Dic3C2×D412yes—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—21no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41#6714yes—
344C22×Q8—31no—
345C22×Q8C22×D311yescharacteristic
346C22×Q8C22×D311yescharacteristic
347C22×D4—21no—
348C22×D4C22×D311yescharacteristic
349C23×C4—21no—
350C23×C4—31no—
351C23×C4—31no—
352C23×C4—61no—
353C23×C4—61no—
354C23×C4C22×D311yescharacteristic
355C2×Q16—22no—
356C2×Q16—22no—
357C2×Q16—22no—
358C2×Q16—62no—
359C2×Q16—62no—
360C2×Q16—62no—
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—22no—
364C2×SD16—62no—
365C2×SD16—62no—
366C2×SD16—62no—
367C22×C8—31no—
368C22×C8—31no—
369C22×C8C22×D311yescharacteristic
370C22×C8C22×D311yescharacteristic
371C4⋊Q8—62no—
372C4⋊Q8—62no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—62no—
376C22⋊Q8—62no—
377C4×Q8—34no—
378C4×Q8—62no—
379C4×Q8—62no—
380C4×Q8—62no—
381C4×D4—34no—
382C4×D4—62no—
383C4×D4—62no—
384C4×D4—68no—
385C4×D4—68no—
386C4×D4—62no—
387#117—62no—
388#117—62no—
389#117—68no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4—61no—
399C2×C4⋊C4—61no—
400C2×C4⋊C4—61no—
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C42—31no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—62no—
412C2×C42—62no—
413C2×C42—61no—
414C2×C42—61no—
415C2×C42—68no—
416C2×C42—61no—
417C4⋊C8—62no—
418C4⋊C8—62no—
419#103—22no—
420#103—62no—
421#103—62no—
422#103—62no—
423#103—62no—
424#103—62no—
425#102—22no—
426#102—62no—
427C22⋊C8—22no—
428C22⋊C8—62no—
429#95—61no—
430#95—61no—
431#95—61no—
432#95—61no—
433C23×C3—21no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3#12112yes—
447C23×C3C22×D411yescharacteristic
448C3×Q8—22no—
449C3×Q8—22no—
450C3×Q8—22no—
451C3×Q8—41no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×Q8—41no—
455C3×Q8#12114yes—
456C3×D4—216no—
457C3×D4—22no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4#12114yes—
461C2×C3×C4—216no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4#12112yes—
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—44no—
494C2×Dic3—48no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—44no—
500C2×Dic3—48no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3#12012yes—
508C2×Dic3#12012yes—
509C2×Dic3#13512yes—
510C2×Dic3#13712yes—
511C2×Dic3#13712yes—
512Dic6—41no—
513Dic6—41no—
514Dic6—41no—
515Dic6—41no—
516C3×C8—41no—
517C3×C8—41no—
518C3⋊C8—41no—
519C3⋊C8—41no—
520C24—21no—
521C24D3×D411yescharacteristic
522#41—28no—
523#41—28no—
524#41—28no—
525#41—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8D3×D412yes—
542C2×Q8#23712yes—
543C2×Q8C2×#6712yes—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4D3×D412yes—
551C2×D4#23712yes—
552C2×D4C2×#6712yes—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—24no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—64no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—64no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—122no—
579C22×C4—122no—
580C22×C4—122no—
581C22×C4—121no—
582C22×C4—122no—
583C22×C4D3×D411yescharacteristic
584C22×C4#23712yes—
585C22×C4C2×#6712yes—
586C22×C4C23×D311yescharacteristic
587Q16—44no—
588Q16—124no—
589SD16—44no—
590SD16—124no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—61no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—32no—
606C4⋊C4—32no—
607C4⋊C4—42no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—122no—
615C4⋊C4—122no—
616C4⋊C4—122no—
617C4⋊C4—122no—
618C4⋊C4—122no—
619C22⋊C4—42no—
620C22⋊C4—64no—
621C22⋊C4—64no—
622C22⋊C4—64no—
623C22⋊C4—122no—
624C42—32no—
625C42—32no—
626C42—62no—
627C42—62no—
628C42—64no—
629C42—64no—
630C42—64no—
631C42—61no—
632C42—61no—
633C22×C3—22no—
634C22×C3—24no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—42no—
641C22×C3—41no—
642C22×C3—42no—
643C22×C3—41no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3C2×#12011yescharacteristic
648C22×C3C2×#12111yescharacteristic
649C22×C3#52511yescharacteristic
650C22×C3C2×#13511yescharacteristic
651C22×C3C2×#13711yescharacteristic
652C22×C3C2×#13711yescharacteristic
653C22×C3#57511yescharacteristic
654C3×C4—22no—
655C3×C4—24no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4C2×#12111yescharacteristic
659C3×C4C2×#12111yescharacteristic
660C3×C4#52511yescharacteristic
661C3×C4#52511yescharacteristic
662Dic3—22no—
663Dic3—22no—
664Dic3—41no—
665Dic3—42no—
666Dic3—42no—
667Dic3—81no—
668Dic3—81no—
669Dic3#45214yescomplemented
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—22no—
675C23—21no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23#93912yes—
684C23C2×D3×D411yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—121no—
693Q8—121no—
694Q8—121no—
695Q8—121no—
696Q8#93914yes—
697D4—216no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4#93914yes—
702C2×C4—216no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—32no—
716C2×C4—32no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—61no—
732C2×C4—124no—
733C2×C4—128no—
734C2×C4—124no—
735C2×C4—128no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4#93912yes—
747C2×C4C2×D3×D411yescharacteristic
748C2×C4C2×D3×D411yescharacteristic
749C2×C4C2×#23711yescharacteristic
750C2×C4C2×#23711yescharacteristic
751C2×C4C2×#23711yescharacteristic
752C2×C4C22×#6711yescharacteristic
753C8—41no—
754C8—41no—
755C8—121no—
756C8—121no—
757C2×C3—42no—
758C2×C3—44no—
759C2×C3#284711yescharacteristic
760C2×C3C2×#45211yescharacteristic
761C2×C3#300711yescharacteristic
762C2×C3#303511yescharacteristic
763C2×C3#303911yescharacteristic
764C2×C3#310711yescharacteristic
765C2×C3#311611yescharacteristic
766C22—22no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22#558611yescharacteristic
781C22D3×#12011yescharacteristic
782C22D3×#13511yescharacteristic
783C22#576811yescharacteristic
784C22D3×#13711yescharacteristic
785C22D3×#13711yescharacteristic
786C22C2×#93911yescharacteristic
787C4—22no—
788C4—24no—
789C4—34no—
790C4—62no—
791C4—62no—
792C4—81no—
793C4—81no—
794C4—121no—
795C4—122no—
796C4—122no—
797C4—241no—
798C4—241no—
799C4#558611yescharacteristic
800C4#558611yescharacteristic
801C4C2×#93911yescharacteristic
802C4C2×#93911yescharacteristic
803C3#3290711yescharacteristic, complemented, Sylow
804C2—42no—
805C2—44no—
806C2#8021311yescharacteristic
807C2#8021511yescharacteristic
808C2D3×#45211yescharacteristic
809C2#8022811yescharacteristic
810C2#8260111yescharacteristic
811C2#8390011yescharacteristic
812C2#8396711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
prime radicalC22×C3×#41C22
hypercenterC2×#452D3
hypocenterC3#32907
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
4. C2×#5182C2semidirect
5. C2×#5162C2semidirect
6. #82811C2semidirect
7. #72065C2semidirect
8. #72047C2semidirect
9. #71693C2semidirect
10. #70239C2semidirect
11. #70221C2semidirect
12. #70171C2semidirect
13. #70153C2semidirect
14. #69931C2semidirect
15. #69908C2semidirect
669. Dic3#452semidirect
803. C3#32907semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×#412
C2×C3×#4522
C2×#52392
C2×#51822
C2×#51622
#828112
#720652
#720472
#716932
#702392
#702212
#701712
#701532
#699312
#699082
#329073