Finite Group Databasebeta

← #10827364

Subgroups — #10827364

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×#5002C211yesmaximal, characteristic, complemented
3C2×#4734C211yesmaximal, characteristic, complemented
4#74015C211yesmaximal, characteristic, complemented
5C3×#1825C211yesmaximal, characteristic, complemented
6#69952C211yesmaximal, characteristic, complemented
7#69515C211yesmaximal, characteristic, complemented
8#68911C211yesmaximal, characteristic, complemented
9#68899C211yesmaximal, characteristic, complemented
10#68897C211yesmaximal, characteristic, complemented
11#68896C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C23×C3⋊C8C2211yescharacteristic
22C22×D24C2211yescharacteristic
23C22×#204C2211yescharacteristic
24#5530—24no—
25#5530—24no—
26C2×#897C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#893C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×#890C2211yescharacteristic
32C2×#884—21no—
33C2×#883—21no—
34C2×#876—21no—
35C2×C4×D12—21no—
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#816C2211yescharacteristic
42#5002—24no—
43#4988C2211yescharacteristic
44#4973C2211yescharacteristic
45C2×#810C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4961—21no—
52#4960—21no—
53#4734—24no—
54#4668—21no—
55#4665—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
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#1825D311yescharacteristic, complemented
79C23×C3×C4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C2×#235—22no—
84C2×#235—22no—
85C2×#235—22no—
86C2×#235—22no—
87C2×#235—41no—
88C2×#235—41no—
89C22×D12—21no—
90C22×D12—21no—
91C22×D12C2311yescharacteristic
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3C2311yescharacteristic
97C22×Dic6C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×#117—22no—
101C3×#117D414yescomplemented
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C42—21no—
109C2×#217D411yescharacteristic
110#930—22no—
111#930D414yescomplemented
112C4×#67—22no—
113C4×#67—22no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4D411yescharacteristic
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4D411yescharacteristic
128C2×C4×Dic3C2311yescharacteristic
129C22×C3⋊C8—22no—
130C22×C3⋊C8—41no—
131C22×C3⋊C8—41no—
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C2×D24—22no—
135C2×D24—22no—
136C2×D24—41no—
137C2×#204—22no—
138C2×#204—22no—
139C2×#204—41no—
140#897—22no—
141#897—41no—
142#895—22no—
143#895—22no—
144#895—22no—
145#895—41no—
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×C22⋊C8—22no—
157C3×#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160#821—22no—
161(C2×D3)⋊C8—41no—
162(C2×D3)⋊C8—41no—
163#816—22no—
164#810—22no—
165#810—22no—
166#809—22no—
167#809—22no—
168#809—41no—
169#809—41no—
170C22×#41—31no—
171C22×SD16—31no—
172C22×D8—31no—
173C23×C8—31no—
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—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⋊C8C2×D311yescharacteristic
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C23×D3—21no—
219C23×D3—21no—
220C23×D3C2×D411yescharacteristic
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C2×D412yes—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2411yescharacteristic
233C2×#67—22no—
234C2×#67—22no—
235C2×#67—24no—
236C2×#67—41no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—81no—
241C2×#67—81no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247#235—28no—
248#235—44no—
249#235—44no—
250#235—44no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—24no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—42no—
263C2×D12—42no—
264C2×D12—42no—
265C2×D12—42no—
266C2×D12—81no—
267C2×D12C2×D412yes—
268C2×D12#4112yes—
269C2×C4×D3—21no—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—24no—
276C2×C4×D3—24no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3—42no—
280C2×C4×D3—81no—
281C2×C4×D3—81no—
282C2×C4×D3—81no—
283C2×C4×D3—81no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6#4112yes—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4C2×D412yes—
303C3×C4⋊C4C2×D412yes—
304C3×C22⋊C4—24no—
305C3×C22⋊C4—81no—
306C3×C42—24no—
307#217—22no—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—24no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—42no—
313(C2×D3)⋊C4—42no—
314(C2×D3)⋊C4—42no—
315(C2×D3)⋊C4—81no—
316C4⋊Dic3—24no—
317C4⋊Dic3—21no—
318C4⋊Dic3—42no—
319C4⋊Dic3C2×D412yes—
320Dic3⋊C4—24no—
321Dic3⋊C4—24no—
322Dic3⋊C4—22no—
323C4×Dic3—21no—
324C4×Dic3—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—44no—
332D24—44no—
333#204—44no—
334C2×#41—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8—31no—
341C22×D4—31no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4—61no—
348C23×C4—31no—
349C23×C4—61no—
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—31no—
360C22×C8—31no—
361C22×C8—62no—
362C22×C8—121no—
363C22×C8—121no—
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#117D1214yescomplemented
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—62no—
389C2×C4⋊C4—61no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—62no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4C22×D311yescharacteristic
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—31no—
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—62no—
412#103—62no—
413#103—62no—
414#102—62no—
415#102—62no—
416#102—62no—
417#102—121no—
418#102—121no—
419C22⋊C8—22no—
420C22⋊C8—121no—
421C22⋊C8—121no—
422#95—21no—
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#12012yes—
432C23×C3C22×D411yescharacteristic
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3—41no—
448C22×D3—41no—
449C22×D3—41no—
450C22×D3—41no—
451C22×D3—41no—
452C22×D3—41no—
453C22×D3#13512yes—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4#12012yes—
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4H(5,𝔽2)11yescharacteristic
478C2×C3×C4H(5,𝔽2)11yescharacteristic
479#67—44no—
480#67—48no—
481#67—84no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497D12—22no—
498D12—22no—
499D12—22no—
500D12—22no—
501D12—48no—
502D12—41no—
503D12—41no—
504D12—41no—
505D12—41no—
506D12—84no—
507C4×D3—48no—
508C4×D3—41no—
509C4×D3—41no—
510C4×D3—41no—
511C4×D3—41no—
512C4×D3—84no—
513C4×D3—84no—
514Dic6—22no—
515Dic6—22no—
516Dic6—41no—
517Dic6—41no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—31no—
523C24—61no—
524C24—61no—
525C24D3×D411yescharacteristic
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—32no—
537C2×D4—32no—
538C2×D4—64no—
539C2×D4—62no—
540C2×D4—62no—
541C2×D4—64no—
542C2×D4—61no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—122no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—122no—
556C2×D4—121no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—241no—
561C2×D4—241no—
562C2×D4—241no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—64no—
575C22×C4—64no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—122no—
585C22×C4—122no—
586C22×C4—122no—
587C22×C4—241no—
588C22×C4—241no—
589C22×C4—241no—
590C22×C4—241no—
591C22×C4C2×D1212yes—
592C22×C4D3×D411yescharacteristic
593C22×C4D3×D412yes—
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—61no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—61no—
607C2×C8—61no—
608C2×C8—61no—
609C2×C8—124no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—32no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—64no—
620C4⋊C4—62no—
621C4⋊C4—61no—
622C4⋊C4—122no—
623C4⋊C4C2×D1212yes—
624C4⋊C4C2×D1212yes—
625C22⋊C4—24no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—62no—
629C22⋊C4—62no—
630C22⋊C4—64no—
631C22⋊C4—81no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—122no—
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×C3C2×#12011yescharacteristic
647C22×C3#54611yescharacteristic
648C22×C3#54611yescharacteristic
649C22×C3C2×#13511yescharacteristic
650C22×C3#57511yescharacteristic
651C22×C3#57611yescharacteristic
652C22×C3#57711yescharacteristic
653C2×D3—22no—
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—42no—
661C2×D3—42no—
662C2×D3—42no—
663C2×D3—42no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—81no—
667C2×D3—81no—
668C2×D3—81no—
669C2×D3—81no—
670C2×D3—81no—
671C2×D3—81no—
672C2×D3—81no—
673C2×D3—81no—
674C3×C4—22no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4#52511yescharacteristic
680C3×C4#53511yescharacteristic
681C3×C4#54611yescharacteristic
682C3×C4#54611yescharacteristic
683Dic3—42no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—42no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—32no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—62no—
702C23—62no—
703C23—121no—
704C23—121no—
705C23—121no—
706C23—121no—
707C23—121no—
708C23—121no—
709C23—121no—
710C23—121no—
711C23—121no—
712C23—121no—
713C23—121no—
714C23—121no—
715C23#88212yes—
716C23C2×D3×D411yescharacteristic
717Q8—62no—
718Q8—62no—
719Q8—121no—
720Q8—121no—
721D4—62no—
722D4—62no—
723D4—62no—
724D4—62no—
725D4—128no—
726D4—124no—
727D4—128no—
728D4—121no—
729D4—121no—
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—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—61no—
753C2×C4—62no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—62no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—128no—
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#88212yes—
775C2×C4C22×D1211yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4D3×#4111yescharacteristic
778C2×C4D3×#4111yescharacteristic
779C2×C4#100911yescharacteristic
780C2×C4#100911yescharacteristic
781C8—41no—
782C8—41no—
783C8—121no—
784C8—121no—
785C2×C3—42no—
786C2×C3#240411yescharacteristic
787C2×C3#300211yescharacteristic
788C2×C3#301211yescharacteristic
789C2×C3#329711yescharacteristic
790C2×C3#330111yescharacteristic
791C2×C3#330711yescharacteristic
792C2×C3#330911yescharacteristic
793D3—42no—
794D3—82no—
795D3—82no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—62no—
804C22—62no—
805C22—62no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—122no—
811C22—122no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22—122no—
816C22—241no—
817C22—241no—
818C22—241no—
819C22—241no—
820C22—241no—
821C22—241no—
822C22—241no—
823C22—241no—
824C22C2×#88211yescharacteristic
825C22#565411yescharacteristic
826C22#565411yescharacteristic
827C22D3×#13511yescharacteristic
828C22#576811yescharacteristic
829C22#577411yescharacteristic
830C22#577811yescharacteristic
831C4—22no—
832C4—42no—
833C4—42no—
834C4—81no—
835C4—81no—
836C4—121no—
837C4—122no—
838C4—121no—
839C4—122no—
840C4—121no—
841C4#552411yescharacteristic
842C4#552511yescharacteristic
843C4#565411yescharacteristic
844C4#565411yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—122no—
848C2—242no—
849C2—242no—
850C2#7412511yescharacteristic
851C2#7883311yescharacteristic
852C2#7888611yescharacteristic
853C2#8138211yescharacteristic
854C2#8140811yescharacteristic
855C2#8152511yescharacteristic
856C2#8154611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1825C2
socleC23×C3C22×D4
hypercenter#1825D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
1. C2×#5530C2semidirect
2. C2×#5002C2semidirect
3. C2×#4734C2semidirect
4. #74015C2semidirect
5. C3×#1825C2semidirect
6. #69952C2semidirect
7. #69515C2semidirect
8. #68911C2semidirect
9. #68899C2semidirect
10. #68897C2semidirect
11. #68896C2semidirect
12. #68887C2semidirect
13. #68886C2semidirect
14. #68880C2semidirect
15. #68878C2semidirect
78. #1825D3semidirect
101. C3×#117D4semidirect
111. #930D4semidirect
385. #117D12semidirect
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×#50022
C2×#47342
#740152
C3×#18252
#699522
#695152
#689112
#688992
#688972
#688962
#688872
#688862
#688802
#688782
#239623