Finite Group Databasebeta

← #10827356

Subgroups — #10827356

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×C3×#553C211yesmaximal, characteristic, complemented
2C2×#5037C211yesmaximal, characteristic, complemented
3#82402C211yesmaximal, characteristic, complemented
4C2×#5002C211yesmaximal, characteristic, complemented
5#71744C211yesmaximal, characteristic, complemented
6#71743C211yesmaximal, characteristic, complemented
7#71685C211yesmaximal, characteristic, complemented
8#71684C211yesmaximal, characteristic, complemented
9#71681C211yesmaximal, characteristic, complemented
10#71613C211yesmaximal, characteristic, complemented
11#71612C211yesmaximal, characteristic, complemented
12#71610C211yesmaximal, characteristic, complemented
13#71575C211yesmaximal, characteristic, complemented
14#71560C211yesmaximal, characteristic, complemented
15#71559C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C3×#553—24no—
19C3×#553—24no—
20C2×C3×#126—21no—
21C2×C3×#125C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×#121—21no—
24C2×C3×#121C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×C4×D4—21no—
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C22×#213C2211yescharacteristic
33C2×#930C2211yescharacteristic
34C2×#924C2211yescharacteristic
35C23×C3⋊C8C2211yescharacteristic
36#5223—21no—
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39#5212C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5037—24no—
44#5002—24no—
45#4989—21no—
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4959—21no—
53#4956—21no—
54#4939C2211yescharacteristic
55#4929C2211yescharacteristic
56#4529C2211yescharacteristic
57#4529C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#553D311yescharacteristic, complemented
65C2×#449—31no—
66C2×#416—31no—
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—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4D411yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C22×#67—21no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—41no—
94C2×#235—41no—
95C22×D12C2311yescharacteristic
96C22×C4×D3—21no—
97C22×Dic6C2311yescharacteristic
98C3×#126—28no—
99C3×#125—22no—
100C3×#125—22no—
101C3×#123—28no—
102C3×#121—28no—
103C3×#121—22no—
104C3×#121—22no—
105C3×#121—22no—
106C3×#121D414yescomplemented
107C3×C4×D4—28no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C3×#117—22no—
113C3×#117D414yescomplemented
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4D411yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4D411yescharacteristic
128C2×C3×C22⋊C4D411yescharacteristic
129C2×C3×C42—21no—
130C2×C3×C42C2311yescharacteristic
131C2×#217—21no—
132C2×#217—21no—
133C2×#214—22no—
134C2×#214—22no—
135C2×#214—41no—
136C2×#213—22no—
137C2×#213—22no—
138C2×#213—41no—
139#930—22no—
140#930—41no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146#924—22no—
147#924—41no—
148C2×Dic3⋊C4—21no—
149C22×C3⋊C8—22no—
150C22×C3⋊C8—41no—
151C22×C3⋊C8—41no—
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156#832—41no—
157#832—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#830—22no—
162#830—41no—
163#830—41no—
164#810—22no—
165#810—22no—
166#810—22no—
167#809—22no—
168#809—22no—
169#809—22no—
170C22×#41—31no—
171C22×SD16—31no—
172C22×D8—31no—
173C23×C8—31no—
174#553—24no—
175#553—24no—
176C2×#126—21no—
177C2×#125C2×D311yescharacteristic
178C2×#123—21no—
179C2×C22⋊Q8—31no—
180C2×#121—21no—
181C2×#121—31no—
182C2×#121C2×D311yescharacteristic
183C2×#121C2×D311yescharacteristic
184C2×C4×D4—21no—
185C2×C4×D4C2×D311yescharacteristic
186C2×C4×D4C2×D311yescharacteristic
187C2×#117C2×D311yescharacteristic
188C22×C4⋊C4C2×D311yescharacteristic
189#449—64no—
190#416—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
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
219C24×C3C2×D411yescharacteristic
220C23×D3—21no—
221C2×C3×D4—24no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—24no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—41no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—81no—
234C2×C3×D4—81no—
235C2×C3×D4C2×D412yes—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—24no—
244C22×C3×C4—24no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—81no—
252C22×C3×C4—81no—
253C22×C3×C4—81no—
254C22×C3×C4—81no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2411yescharacteristic
262C2×#67—42no—
263C2×#67—42no—
264C2×#67—42no—
265C2×#67—42no—
266C2×#67—42no—
267C2×#67—81no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271#235—28no—
272#235—44no—
273#235—44no—
274#235—44no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12#4112yes—
281C2×C4×D3—42no—
282C2×C4×D3—42no—
283C2×C4×D3—42no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6#4112yes—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—24no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4C2×D412yes—
298C3×C4⋊C4C2×D412yes—
299C3×C4⋊C4C2×D412yes—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—24no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—24no—
305C3×C22⋊C4—22no—
306C3×C42—24no—
307C3×C42—21no—
308C3×C42—21no—
309#217—42no—
310#217—81no—
311#214—44no—
312#213—44no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—81no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320Dic3⋊C4—42no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8—21no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—44no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8—31no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4#6711yescharacteristic
347C22×D4C22×D311yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—61no—
351C23×C4C22×D311yescharacteristic
352C23×C4C22×D311yescharacteristic
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—121no—
356C2×D8—62no—
357C2×D8—62no—
358C2×D8—121no—
359C22×C8—31no—
360C22×C8—31no—
361C22×C8—31no—
362C22×C8—31no—
363C22×C8—62no—
364C22×C8—121no—
365C22×C8—121no—
366#126—28no—
367#125—22no—
368#125—22no—
369#123—28no—
370C22⋊Q8—62no—
371C22⋊Q8—121no—
372#121—28no—
373#121—22no—
374#121—22no—
375#121—22no—
376#121—62no—
377#121—121no—
378#121#6714yescomplemented
379C4×D4—28no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384#117—22no—
385#117#6714yescomplemented
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4#6711yescharacteristic
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—61no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4#6711yescharacteristic
408C2×C22⋊C4#6711yescharacteristic
409C2×C42—21no—
410C2×C42C22×D311yescharacteristic
411#103—62no—
412#103—62no—
413#103—62no—
414#102—62no—
415#102—62no—
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—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3#12012yes—
445C23×C3#13512yes—
446C23×C3C22×D411yescharacteristic
447C22×D3—22no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3—41no—
454C3×D4—22no—
455C3×D4—22no—
456C3×D4—44no—
457C3×D4—48no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—84no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—21no—
468C2×C3×C4—22no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—84no—
490C2×C3×C4—84no—
491C2×C3×C4#12012yes—
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C2×#4111yescharacteristic
495C2×C3×C4C2×#4111yescharacteristic
496C2×C3×C4H(5,𝔽2)11yescharacteristic
497C2×C3×C4H(5,𝔽2)11yescharacteristic
498#67—48no—
499#67—84no—
500C2×Dic3—22no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—41no—
506C2×Dic3—41no—
507C2×Dic3—41no—
508C2×Dic3—41no—
509D12—22no—
510D12—22no—
511D12—41no—
512D12—41no—
513C4×D3—48no—
514Dic6—22no—
515Dic6—22no—
516Dic6—41no—
517Dic6—41no—
518C3⋊C8—41no—
519C3⋊C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—21no—
523C24—61no—
524C24C2×#6711yescharacteristic
525C24C2×#6711yescharacteristic
526#41—68no—
527#41—124no—
528#41—124no—
529#41—124no—
530C2×Q8—32no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8—61no—
536C2×D4—24no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—32no—
546C2×D4—41no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—122no—
561C2×D4—241no—
562C2×D4C2×#6712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—122no—
586C22×C4—122no—
587C22×C4—122no—
588C22×C4C2×#6711yescharacteristic
589C22×C4C2×#6711yescharacteristic
590C22×C4C2×#6711yescharacteristic
591C22×C4C2×#6711yescharacteristic
592C22×C4C2×#6712yes—
593C22×C4C2×#6712yes—
594C22×C4C23×D311yescharacteristic
595SD16—124no—
596D8—124no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—61no—
603C2×C8—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—124no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—122no—
622C4⋊C4C2×#6712yes—
623C4⋊C4C2×#6712yes—
624C4⋊C4C2×#6712yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—122no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—241no—
635C22⋊C4—241no—
636C42—24no—
637C42—21no—
638C42—21no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3C2×#12011yescharacteristic
661C22×C3#54611yescharacteristic
662C22×C3#54611yescharacteristic
663C22×C3C2×#13511yescharacteristic
664C22×C3#57511yescharacteristic
665C22×C3#57611yescharacteristic
666C22×C3#57711yescharacteristic
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—41no—
676C3×C4—41no—
677C3×C4—42no—
678C3×C4—41no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4#52511yescharacteristic
682C3×C4#53511yescharacteristic
683C3×C4#54611yescharacteristic
684C3×C4#54611yescharacteristic
685Dic3—42no—
686Dic3—81no—
687Dic3—81no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—62no—
708C23—121no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23#95012yes—
715C23#95312yes—
716C23C22×#6711yescharacteristic
717Q8—62no—
718Q8—62no—
719Q8—121no—
720Q8—121no—
721D4—22no—
722D4—22no—
723D4—44no—
724D4—48no—
725D4—41no—
726D4—41no—
727D4—62no—
728D4—62no—
729D4—84no—
730D4—128no—
731D4—121no—
732D4—121no—
733D4—244no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—62no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—128no—
766C2×C4—121no—
767C2×C4—121no—
768C2×C4—121no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4#95312yes—
775C2×C4D3×#4111yescharacteristic
776C2×C4D3×#4111yescharacteristic
777C2×C4#100911yescharacteristic
778C2×C4#100911yescharacteristic
779C2×C4C22×#6711yescharacteristic
780C2×C4C22×#6711yescharacteristic
781C8—121no—
782C8—121no—
783C8—121no—
784C8—121no—
785C2×C3—42no—
786C2×C3—42no—
787C2×C3—82no—
788C2×C3#240411yescharacteristic
789C2×C3#300211yescharacteristic
790C2×C3#301211yescharacteristic
791C2×C3#329711yescharacteristic
792C2×C3#330111yescharacteristic
793C2×C3#330711yescharacteristic
794C2×C3#330911yescharacteristic
795D3—82no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—122no—
818C22—122no—
819C22—122no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22C2×#95011yescharacteristic
825C22#582211yescharacteristic
826C22#582911yescharacteristic
827C22#582911yescharacteristic
828C22#583511yescharacteristic
829C22#583611yescharacteristic
830C22C2×#95311yescharacteristic
831C4—22no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—42no—
838C4—122no—
839C4—241no—
840C4—241no—
841C4#582811yescharacteristic
842C4#582911yescharacteristic
843C4#582911yescharacteristic
844C4#583011yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—42no—
848C2—82no—
849C2—242no—
850C2#8361411yescharacteristic
851C2#8361511yescharacteristic
852C2#8361811yescharacteristic
853C2#8361911yescharacteristic
854C2#8408011yescharacteristic
855C2#8409611yescharacteristic
856C2#8410211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#553C2
socleC23×C3C22×D4
hypercenterC2×#553D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×C3×#553C2semidirect
2. C2×#5037C2semidirect
3. #82402C2semidirect
4. C2×#5002C2semidirect
5. #71744C2semidirect
6. #71743C2semidirect
7. #71685C2semidirect
8. #71684C2semidirect
9. #71681C2semidirect
10. #71613C2semidirect
11. #71612C2semidirect
12. #71610C2semidirect
13. #71575C2semidirect
14. #71560C2semidirect
15. #71559C2semidirect
64. C2×#553D3semidirect
106. C3×#121D4semidirect
113. C3×#117D4semidirect
378. #121#67semidirect
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×C3×#5532
C2×#50372
#824022
C2×#50022
#717442
#717432
#716852
#716842
#716812
#716132
#716122
#716102
#715752
#715602
#715592
#239623