Finite Group Databasebeta

← #10830643

Subgroups — #10830643

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5831C211yesmaximal, characteristic
2C2×C3×#452C211yesmaximal, characteristic, complemented
3C2×#5186C211yesmaximal, characteristic, complemented
4C2×Dic3×Q16C211yesmaximal, characteristic, complemented
5C2×#5166C211yesmaximal, characteristic, complemented
6#82777C211yesmaximal, characteristic, complemented
7#72135C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71700C211yesmaximal, characteristic, complemented
10#70266C211yesmaximal, characteristic, complemented
11#70222C211yesmaximal, characteristic, complemented
12#70175C211yesmaximal, characteristic, complemented
13#70158C211yesmaximal, characteristic, complemented
14#69937C211yesmaximal, characteristic, complemented
15#69916C211yesmaximal, characteristic, complemented
16#24246—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22#5831—24no—
23#5831—24no—
24C2×#946C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C2×Q8×Dic3C2211yescharacteristic
27C22×#216C2211yescharacteristic
28C2×#938—21no—
29C2×#938C2211yescharacteristic
30C2×#936—21no—
31C2×#936C2211yescharacteristic
32C2×C4×#67—21no—
33C2×C4×#67C2211yescharacteristic
34C2×#924—21no—
35C2×#924C2211yescharacteristic
36C3×#452—24no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47#5186—24no—
48Dic3×Q16—24no—
49#5166—24no—
50C2×(C2×D3)⋊C8C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×#818C2211yescharacteristic
53C2×#816C2211yescharacteristic
54C2×#816C2211yescharacteristic
55C2×Dic3⋊C8C2211yescharacteristic
56C2×C8×Dic3C2211yescharacteristic
57#4990—21no—
58#4987C2211yescharacteristic
59#4982—21no—
60#4977C2211yescharacteristic
61C2×#810C2211yescharacteristic
62#4961—21no—
63#4945—21no—
64#4551C2211yescharacteristic
65#4529C2211yescharacteristic
66C2×#548—31no—
67C2×#464—31no—
68C2×#452D311yescharacteristic, complemented
69C2×#451—31no—
70C2×C4×Q16—31no—
71#2536—31no—
72#2036—31no—
73#2033—31no—
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1805—31no—
79#1788—31no—
80#1787—31no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—41no—
86C2×C3×#41—41no—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C22×#67—21no—
94C22×#67D411yescharacteristic
95C2×D3×Q8—22no—
96C2×D3×Q8—22no—
97C2×D3×Q8—22no—
98C2×D3×Q8—22no—
99C2×D3×Q8—41no—
100C2×D3×Q8—41no—
101C22×C4×D3—21no—
102C22×C4×D3C2311yescharacteristic
103C22×Dic6—21no—
104C22×Dic6C2311yescharacteristic
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16D414yescomplemented
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—41no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C3×C22⋊Q8—22no—
114C3×C22⋊Q8—41no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C22⋊C4—21no—
118C2×#217—21no—
119C2×#217—21no—
120C2×#217—21no—
121C2×#217—21no—
122C2×#217—21no—
123C2×#217D411yescharacteristic
124#946—22no—
125#946—41no—
126Q8×Dic3—22no—
127Q8×Dic3—22no—
128Q8×Dic3—22no—
129Q8×Dic3D414yes—
130C2×#216—22no—
131C2×#216—22no—
132C2×#216—41no—
133#938—28no—
134#938—22no—
135#938—22no—
136#936—28no—
137#936—22no—
138#936D414yes—
139C4×#67—28no—
140C4×#67—22no—
141C4×#67—22no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4D411yescharacteristic
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150#924—28no—
151#924—22no—
152#924—22no—
153C2×Dic3⋊C4—21no—
154C2×Dic3⋊C4—21no—
155C2×Dic3⋊C4D411yescharacteristic
156C2×C4×Dic3—21no—
157C2×C4×Dic3—21no—
158C2×C4×Dic3C2311yescharacteristic
159C22×C3⋊C8C2311yescharacteristic
160C22×C3⋊C8C2311yescharacteristic
161C3×#103—22no—
162C3×#102—22no—
163C3×C22⋊C8—22no—
164#835—22no—
165#835—22no—
166#835—22no—
167#832—22no—
168#832—41no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172C3⋊#95—21no—
173#830—41no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—41no—
176#818—22no—
177#816—22no—
178#816—22no—
179Dic3⋊C8—22no—
180C8×Dic3—22no—
181#810—41no—
182C22×#41C2×D311yescharacteristic
183C23×Q8—31no—
184C22×Q16—31no—
185C22×Q16C2×D311yescharacteristic
186C22×SD16C2×D311yescharacteristic
187#548—64no—
188#548—64no—
189C2×#124—31no—
190C2×#124—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—61no—
194C2×C22⋊Q8C2×D311yescharacteristic
195C2×#121—31no—
196C2×#121—61no—
197C2×C4×Q8—31no—
198C2×C4×Q8—31no—
199C2×C4×D4—31no—
200C2×C4×D4—61no—
201#464—64no—
202#452—24no—
203#451—64no—
204C4×Q16—64no—
205C2×#107—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103—31no—
211C2×#103—31no—
212C2×#103—31no—
213C2×#103C2×D311yescharacteristic
214C2×#102—31no—
215C2×#102—31no—
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic
221C2×C4×C8—31no—
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C23×D3C2×D411yescharacteristic
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8C2×D412yes—
247C2×C3×Q8C2×D412yes—
248C2×C3×Q8C2×D412yes—
249C2×C3×Q8#4112yes—
250C2×C3×D4—24no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—42no—
257C2×C3×D4—42no—
258C2×C3×D4C2×D412yes—
259C22×C3×C4—21no—
260C22×C3×C4—24no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—42no—
270C22×C3×C4—42no—
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C2×#67—24no—
274C2×#67—22no—
275C2×#67—22no—
276C2×#67—41no—
277C2×#67—42no—
278C2×#67—42no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—21no—
283C22×Dic3C2×D411yescharacteristic
284C22×Dic3C2×D411yescharacteristic
285C22×Dic3C2×D411yescharacteristic
286D3×Q8—44no—
287D3×Q8—44no—
288D3×Q8—44no—
289D3×Q8—44no—
290C2×C4×D3—24no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—42no—
298C2×C4×D3—42no—
299C2×Dic6—21no—
300C2×Dic6—21no—
301C2×Dic6—21no—
302C2×Dic6—21no—
303C2×Dic6—24no—
304C2×Dic6—21no—
305C2×Dic6—42no—
306C2×Dic6—42no—
307C2×Dic6C2×D412yes—
308C3×Q16—28no—
309C3×SD16—44no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8C2×D412yes—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—42no—
319C3×C22⋊C4—42no—
320#217—24no—
321#217—24no—
322#217—24no—
323#217—22no—
324#217—24no—
325#217—42no—
326#216—44no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—42no—
329(C2×D3)⋊C4—42no—
330C4⋊Dic3—21no—
331C4⋊Dic3—24no—
332C4⋊Dic3—21no—
333C4⋊Dic3—21no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3—42no—
337C4⋊Dic3C2×D412yes—
338Dic3⋊C4—24no—
339Dic3⋊C4—22no—
340Dic3⋊C4—42no—
341C4×Dic3—24no—
342C4×Dic3—42no—
343C4×Dic3C2×D412yes—
344C4×Dic3C2×D412yes—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—41no—
356C2×#41—41no—
357C22×Q8—31no—
358C22×Q8—61no—
359C22×Q8—62no—
360C22×Q8—62no—
361C22×Q8—62no—
362C22×Q8—62no—
363C22×Q8—121no—
364C22×Q8—121no—
365C22×Q8C22×D311yescharacteristic
366C22×Q8C22×D311yescharacteristic
367C22×D4—21no—
368C22×D4—31no—
369C22×D4—61no—
370C22×D4C22×D311yescharacteristic
371C23×C4—21no—
372C23×C4—31no—
373C23×C4—61no—
374C23×C4C22×D311yescharacteristic
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16—62no—
378C2×Q16—62no—
379C2×Q16—121no—
380C2×Q16#6714yescomplemented
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—41no—
384C22×C8—31no—
385C22×C8—31no—
386C22×C8C22×D311yescharacteristic
387C22×C8C22×D311yescharacteristic
388#124—34no—
389#124—62no—
390#124—68no—
391C22⋊Q8—22no—
392C22⋊Q8—41no—
393C22⋊Q8—62no—
394C22⋊Q8—62no—
395C22⋊Q8—68no—
396C22⋊Q8—62no—
397C22⋊Q8—121no—
398#121—62no—
399#121—68no—
400#121—62no—
401C4×Q8—34no—
402C4×Q8—62no—
403C4×Q8—62no—
404C4×Q8—62no—
405C4×D4—62no—
406C4×D4—62no—
407C4×D4—68no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—31no—
420C2×C22⋊C4—31no—
421C2×C22⋊C4—61no—
422C2×C22⋊C4—61no—
423C2×C22⋊C4—61no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C42—31no—
429C2×C42—61no—
430C2×C42—61no—
431#107—62no—
432C4⋊C8—62no—
433#103—22no—
434#103—62no—
435#103—62no—
436#103—62no—
437#103—62no—
438#103—62no—
439#103—121no—
440#102—22no—
441#102—62no—
442#102—121no—
443C22⋊C8—22no—
444C22⋊C8—62no—
445C22⋊C8—121no—
446C22⋊C8—121no—
447C4×C8—62no—
448#95—61no—
449#95—61no—
450#95—61no—
451#95—61no—
452C23×C3—21no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3C22×D411yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3#13512yes—
474C3×Q8—22no—
475C3×Q8—22no—
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—22no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8#12114yes—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—48no—
485C3×D4—41no—
486C3×D4—41no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—48no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4C22×D411yescharacteristic
505C2×C3×C4C22×D411yescharacteristic
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C2×#4111yescharacteristic
508C2×C3×C4H(5,𝔽2)11yescharacteristic
509C2×C3×C4H(5,𝔽2)11yescharacteristic
510#67—44no—
511#67—48no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—22no—
517C2×Dic3—21no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—41no—
522C2×Dic3—41no—
523C2×Dic3—41no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3#12012yes—
532C2×Dic3#12012yes—
533C4×D3—48no—
534C4×D3—41no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3—41no—
538Dic6—22no—
539Dic6—22no—
540Dic6—48no—
541Dic6—41no—
542Dic6—41no—
543C3×C8—22no—
544C3×C8—41no—
545C3⋊C8—41no—
546C3⋊C8—41no—
547C24—21no—
548C24—31no—
549C24D3×D411yescharacteristic
550#41—44no—
551#41—44no—
552#41—44no—
553#41—44no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—32no—
563C2×Q8—64no—
564C2×Q8—61no—
565C2×Q8—61no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—61no—
569C2×Q8—122no—
570C2×Q8—122no—
571C2×Q8—124no—
572C2×Q8—124no—
573C2×Q8—124no—
574C2×Q8—124no—
575C2×Q8D3×D412yes—
576C2×Q8#23712yes—
577C2×Q8C2×#6712yes—
578C2×Q8C2×#6712yes—
579C2×D4—24no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—62no—
588C2×D4—62no—
589C2×D4—64no—
590C2×D4—121no—
591C2×D4—122no—
592C2×D4—122no—
593C2×D4D3×D412yes—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—64no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—122no—
621C22×C4—122no—
622C22×C4D3×D411yescharacteristic
623C22×C4C23×D311yescharacteristic
624Q16—28no—
625Q16—124no—
626SD16—44no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—61no—
633C2×C8—61no—
634C2×C8—61no—
635C2×C8—61no—
636C2×C8—61no—
637C2×C8—61no—
638C2×C8C2×#6712yes—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—32no—
642C4⋊C4—42no—
643C4⋊C4—62no—
644C4⋊C4—64no—
645C4⋊C4—64no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—122no—
652C4⋊C4—122no—
653C22⋊C4—42no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—64no—
660C22⋊C4—122no—
661C22⋊C4—122no—
662C22⋊C4—122no—
663C42—32no—
664C42—32no—
665C42—64no—
666C42—122no—
667C22×C3—42no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—42no—
671C22×C3—41no—
672C22×C3—42no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3C2×#12011yescharacteristic
682C22×C3D4211yescharacteristic
683C22×C3#54611yescharacteristic
684C22×C3C2×#13511yescharacteristic
685C22×C3#57511yescharacteristic
686C22×C3#57811yescharacteristic
687C22×C3#57811yescharacteristic
688C2×D3—22no—
689C2×D3—22no—
690C2×D3—22no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C3×C4—24no—
696C3×C4—41no—
697C3×C4—42no—
698C3×C4—81no—
699C3×C4C2×#12111yescharacteristic
700C3×C4#53511yescharacteristic
701C3×C4D4211yescharacteristic
702C3×C4#54611yescharacteristic
703Dic3—22no—
704Dic3—22no—
705Dic3—42no—
706Dic3—41no—
707Dic3—42no—
708Dic3—81no—
709Dic3—81no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—21no—
718C23—32no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—61no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—61no—
730C23—61no—
731C23C2×D3×D411yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—41no—
738Q8—41no—
739Q8—62no—
740Q8—62no—
741Q8—128no—
742Q8—121no—
743Q8—121no—
744Q8#93914yes—
745D4—22no—
746D4—22no—
747D4—48no—
748D4—41no—
749D4—41no—
750D4—124no—
751D4—128no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—48no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—62no—
777C2×C4—61no—
778C2×C4—62no—
779C2×C4—61no—
780C2×C4—128no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4C2×D3×D411yescharacteristic
796C2×C4C2×D3×D411yescharacteristic
797C2×C4C2×#23711yescharacteristic
798C2×C4#100411yescharacteristic
799C2×C4#100411yescharacteristic
800C2×C4C22×#6711yescharacteristic
801C8—22no—
802C8—41no—
803C8—121no—
804C8—121no—
805C2×C3—81no—
806C2×C3—82no—
807C2×C3#240811yescharacteristic
808C2×C3#300211yescharacteristic
809C2×C3#301111yescharacteristic
810C2×C3#327711yescharacteristic
811C2×C3#328511yescharacteristic
812C2×C3#330011yescharacteristic
813C2×C3#332711yescharacteristic
814D3—42no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—62no—
826C22—62no—
827C22—62no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22D3×#12011yescharacteristic
837C22#559111yescharacteristic
838C22D3×#13511yescharacteristic
839C22#577111yescharacteristic
840C22#577711yescharacteristic
841C22#577911yescharacteristic
842C22D4×#6711yescharacteristic
843C4—24no—
844C4—41no—
845C4—42no—
846C4—62no—
847C4—62no—
848C4—81no—
849C4—122no—
850C4—121no—
851C4—122no—
852C4—241no—
853C4—241no—
854C4#559111yescharacteristic
855C4#559211yescharacteristic
856C4D4×#6711yescharacteristic
857C4C2×#93911yescharacteristic
858C3#2424611yescharacteristic, complemented, Sylow
859C2—81no—
860C2—82no—
861C2—122no—
862C2#8022611yescharacteristic
863C2#8023011yescharacteristic
864C2#8024711yescharacteristic
865C2#8025911yescharacteristic
866C2#8258211yescharacteristic
867C2#8392011yescharacteristic
868C2#8399411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
prime radicalC2×#5831C2
hypercenterC2×#452D3
hypocenterC3#24246
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
2. C2×C3×#452C2semidirect
3. C2×#5186C2semidirect
4. C2×Dic3×Q16C2semidirect
5. C2×#5166C2semidirect
6. #82777C2semidirect
7. #72135C2semidirect
8. #72054C2semidirect
9. #71700C2semidirect
10. #70266C2semidirect
11. #70222C2semidirect
12. #70175C2semidirect
13. #70158C2semidirect
14. #69937C2semidirect
15. #69916C2semidirect
68. C2×#452D3semidirect
107. C2×C3×Q16D4semidirect
380. C2×Q16#67semidirect
858. C3#24246semidirect

Maximal subgroups

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

subgroupindex
C2×#58312
C2×C3×#4522
C2×#51862
C2×Dic3×Q162
C2×#51662
#827772
#721352
#720542
#717002
#702662
#702222
#701752
#701582
#699372
#699162
#242463