Finite Group Databasebeta

← #10827362

Subgroups — #10827362

Order 768.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5530C211yesmaximal, characteristic, complemented
2C2×C3×#416C211yesmaximal, characteristic, complemented
3#84097C211yesmaximal, characteristic, complemented
4C2×#5238C211yesmaximal, characteristic, complemented
5#71975C211yesmaximal, characteristic, complemented
6#71973C211yesmaximal, characteristic, complemented
7#71575C211yesmaximal, characteristic, complemented
8#70276C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70268C211yesmaximal, characteristic, complemented
11#70232C211yesmaximal, characteristic, complemented
12#70208C211yesmaximal, characteristic, complemented
13#70204C211yesmaximal, characteristic, complemented
14#70200C211yesmaximal, characteristic, complemented
15#70164C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×C4×#67C2211yescharacteristic
26#5530—24no—
27#5530—24no—
28C2×#895C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×#890C2211yescharacteristic
32C2×#884—21no—
33C2×#883—21no—
34C2×#876—21no—
35C2×C4×D12—21no—
36C3×#416—24no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41#5238—24no—
42#5229C2211yescharacteristic
43C2×#835C2211yescharacteristic
44#5223—21no—
45#5222—21no—
46#5221C2211yescharacteristic
47C2×#832C2211yescharacteristic
48#5213—21no—
49#5212C2211yescharacteristic
50#5210—21no—
51C2×#830C2211yescharacteristic
52C2×#821C2211yescharacteristic
53C2×#821C2211yescharacteristic
54C2×(C2×D3)⋊C8C2211yescharacteristic
55C2×(C2×D3)⋊C8C2211yescharacteristic
56#4551C2211yescharacteristic
57#4551C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#449—31no—
66C2×#416D311yescharacteristic, complemented
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2000—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1877—31no—
75#1874—31no—
76#1872—31no—
77#1869—31no—
78#1825—31no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4C2311yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C22×#67—21no—
91C22×#67—21no—
92C22×#67D411yescharacteristic
93C22×D12—21no—
94C22×D12C2311yescharacteristic
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3C2311yescharacteristic
98C22×C3×C8—22no—
99C22×C3×C8—41no—
100C22×C3×C8—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×#117—22no—
104C3×#117D414yescomplemented
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C42—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114#946—22no—
115#946—41no—
116C2×#215—22no—
117C2×#215—22no—
118C2×#215—41no—
119#938—22no—
120#938—41no—
121C2×#213—22no—
122C2×#213—22no—
123C2×#213—41no—
124#930—22no—
125#930D414yescomplemented
126C4×#67—22no—
127C4×#67—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4D411yescharacteristic
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144#895—22no—
145#895—22no—
146#893—22no—
147#893—22no—
148D3×C4⋊C4—22no—
149D3×C4⋊C4—22no—
150#890—22no—
151#890—22no—
152#884—28no—
153#883—28no—
154#876—28no—
155C4×D12—28no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#102—22no—
159C3×#102—22no—
160#835—22no—
161#832—22no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164C3⋊#95—21no—
165#830—22no—
166#821—41no—
167#821—41no—
168(C2×D3)⋊C8—41no—
169(C2×D3)⋊C8—41no—
170C22×#41C2×D311yescharacteristic
171C22×SD16—31no—
172C22×D8—31no—
173C23×C8C2×D311yescharacteristic
174#553—64no—
175#553—64no—
176C2×#126—61no—
177C2×#125—31no—
178C2×#123—61no—
179C2×C22⋊Q8—31no—
180C2×#121—31no—
181C2×#121—31no—
182C2×#121—31no—
183C2×#121—61no—
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C2×#117C2×D311yescharacteristic
188C22×C4⋊C4—31no—
189#449—64no—
190#416—24no—
191C2×#103—31no—
192C2×#103C2×D311yescharacteristic
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102C2×D311yescharacteristic
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C23×D3C2×D411yescharacteristic
221C3×#41—28no—
222C3×#41—44no—
223C3×#41—44no—
224C3×#41—44no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8#4112yes—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4#4112yes—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—42no—
248C22×C3×C4—42no—
249C22×C3×C4—42no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D412yes—
253C22×C3×C4C2411yescharacteristic
254C2×#67—22no—
255C2×#67—22no—
256C2×#67—24no—
257C2×#67—41no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—81no—
261C2×#67—81no—
262C2×#67—81no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12—24no—
274C2×D12—21no—
275C2×D12—42no—
276C2×D12—42no—
277C2×D12C2×D412yes—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C2×C4×D3—21no—
281C2×C4×D3—21no—
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—24no—
285C2×C4×D3—24no—
286C2×C4×D3—81no—
287C2×C4×D3—81no—
288C2×C4×D3—81no—
289C2×C4×D3—81no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—44no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4C2×D412yes—
300C3×C4⋊C4C2×D412yes—
301C3×C22⋊C4—24no—
302C3×C42—24no—
303#217—22no—
304#217—42no—
305#217—42no—
306#217—81no—
307#217—81no—
308#215—44no—
309#213—44no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—24no—
314(C2×D3)⋊C4—42no—
315C4⋊Dic3—24no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3C2×D412yes—
322Dic3⋊C4—24no—
323Dic3⋊C4—24no—
324Dic3⋊C4—22no—
325Dic3⋊C4—42no—
326C4×Dic3—21no—
327C4×Dic3—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—41no—
339C2×#41—41no—
340C22×Q8C22×D311yescharacteristic
341C22×D4—21no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4C22×D311yescharacteristic
348C23×C4—21no—
349C23×C4—31no—
350C23×C4—61no—
351C23×C4—61no—
352C23×C4C22×D311yescharacteristic
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C22×C8—22no—
360C22×C8—31no—
361C22×C8—31no—
362C22×C8—41no—
363C22×C8—41no—
364C22×C8C22×D311yescharacteristic
365C22×C8C22×D311yescharacteristic
366#126—68no—
367#125—62no—
368#125—62no—
369#123—68no—
370C22⋊Q8—62no—
371C22⋊Q8—121no—
372#121—34no—
373#121—68no—
374#121—62no—
375#121—62no—
376#121—62no—
377#121—62no—
378#121—121no—
379C4×D4—68no—
380C4×D4—62no—
381C4×D4—62no—
382C4×D4—62no—
383C4×D4—62no—
384#117—22no—
385#117#6714yescomplemented
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—62no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—62no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C22⋊C4—61no—
409C2×C42—21no—
410C2×C42—31no—
411#103—22no—
412#103—22no—
413#103—62no—
414#102—22no—
415#102—22no—
416#102—62no—
417#102—121no—
418#102—121no—
419C22⋊C8—62no—
420C22⋊C8—121no—
421C22⋊C8—121no—
422#95—61no—
423#95—61no—
424#95—61no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—22no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3#12012yes—
439C23×C3C22×D411yescharacteristic
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3—22no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3#13512yes—
454C3×Q8—22no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×D4—22no—
459C3×D4—22no—
460C3×D4—48no—
461C3×D4—41no—
462C3×D4—41no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—48no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4#12012yes—
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4C2×#4111yescharacteristic
484C2×C3×C4H(5,𝔽2)11yescharacteristic
485C2×C3×C4H(5,𝔽2)11yescharacteristic
486#67—44no—
487#67—84no—
488#67—84no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507D12—22no—
508D12—22no—
509D12—48no—
510D12—41no—
511D12—41no—
512C4×D3—41no—
513C4×D3—41no—
514C4×D3—41no—
515C4×D3—41no—
516C4×D3—84no—
517C4×D3—84no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—21no—
523C24—31no—
524C24—61no—
525C24D3×D411yescharacteristic
526#41—28no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8#23512yes—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—32no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—64no—
546C2×D4—62no—
547C2×D4—62no—
548C2×D4—64no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—121no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—241no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4#23512yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—64no—
577C22×C4—64no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—241no—
588C22×C4—241no—
589C22×C4—241no—
590C22×C4—241no—
591C22×C4D3×D411yescharacteristic
592C22×C4D3×D412yes—
593C22×C4C2×#6712yes—
594C22×C4C23×D311yescharacteristic
595SD16—124no—
596D8—124no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—44no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—61no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—32no—
613C4⋊C4—64no—
614C4⋊C4—64no—
615C4⋊C4—64no—
616C4⋊C4—62no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—122no—
623C4⋊C4C2×#6712yes—
624C4⋊C4C2×#6712yes—
625C22⋊C4—24no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—62no—
629C22⋊C4—62no—
630C22⋊C4—64no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—24no—
637C42—61no—
638C42—61no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3C2×#12011yescharacteristic
654C22×C3#54611yescharacteristic
655C22×C3#54611yescharacteristic
656C22×C3C2×#13511yescharacteristic
657C22×C3#57511yescharacteristic
658C22×C3#57611yescharacteristic
659C22×C3#57711yescharacteristic
660C2×D3—22no—
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—42no—
668C2×D3—42no—
669C2×D3—42no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—22no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4#52511yescharacteristic
679C3×C4#53511yescharacteristic
680C3×C4#54611yescharacteristic
681C3×C4#54611yescharacteristic
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—42no—
686Dic3—81no—
687Dic3—81no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—32no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23—61no—
708C23—62no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23#93712yes—
716C23C2×D3×D411yescharacteristic
717Q8—22no—
718Q8—22no—
719Q8—41no—
720Q8—41no—
721D4—22no—
722D4—22no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—62no—
727D4—62no—
728D4—128no—
729D4—124no—
730D4—121no—
731D4—121no—
732D4—244no—
733D4—244no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—62no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—121no—
763C2×C4—121no—
764C2×C4—121no—
765C2×C4—121no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—244no—
773C2×C4—244no—
774C2×C4#93712yes—
775C2×C4C2×#23511yescharacteristic
776C2×C4C2×#23511yescharacteristic
777C2×C4C2×D3×D411yescharacteristic
778C2×C4#100411yescharacteristic
779C2×C4#100411yescharacteristic
780C2×C4C22×#6711yescharacteristic
781C8—41no—
782C8—41no—
783C8—121no—
784C8—121no—
785C2×C3—42no—
786C2×C3—82no—
787C2×C3#240411yescharacteristic
788C2×C3#300211yescharacteristic
789C2×C3#301211yescharacteristic
790C2×C3#329711yescharacteristic
791C2×C3#330111yescharacteristic
792C2×C3#330711yescharacteristic
793C2×C3#330911yescharacteristic
794D3—42no—
795D3—82no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—62no—
807C22—62no—
808C22—62no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22#549011yescharacteristic
825C22#549011yescharacteristic
826C22D3×#13511yescharacteristic
827C22#576811yescharacteristic
828C22#576911yescharacteristic
829C22#577011yescharacteristic
830C22C2×#93711yescharacteristic
831C4—22no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—121no—
836C4—121no—
837C4—122no—
838C4—121no—
839C4—241no—
840C4—241no—
841C4#549011yescharacteristic
842C4#549011yescharacteristic
843C4#579111yescharacteristic
844C4#580511yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—82no—
848C2—122no—
849C2—242no—
850C2#7884611yescharacteristic
851C2#7884811yescharacteristic
852C2#7885311yescharacteristic
853C2#7885411yescharacteristic
854C2#8212511yescharacteristic
855C2#8391111yescharacteristic
856C2#8391211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#416C2
socleC23×C3C22×D4
hypercenterC2×#416D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#5530C2semidirect
2. C2×C3×#416C2semidirect
3. #84097C2semidirect
4. C2×#5238C2semidirect
5. #71975C2semidirect
6. #71973C2semidirect
7. #71575C2semidirect
8. #70276C2semidirect
9. #70272C2semidirect
10. #70268C2semidirect
11. #70232C2semidirect
12. #70208C2semidirect
13. #70204C2semidirect
14. #70200C2semidirect
15. #70164C2semidirect
66. C2×#416D3semidirect
104. C3×#117D4semidirect
125. #930D4semidirect
385. #117#67semidirect
845. C3#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#55302
C2×C3×#4162
#840972
C2×#52382
#719752
#719732
#715752
#702762
#702722
#702682
#702322
#702082
#702042
#702002
#701642
#239623