Finite Group Databasebeta

← #10827360

Subgroups — #10827360

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×#5614C211yesmaximal, characteristic, complemented
2C2×#5113C211yesmaximal, characteristic, complemented
3C2×#5037C211yesmaximal, characteristic, complemented
4#74015C211yesmaximal, characteristic, complemented
5C3×#1893C211yesmaximal, characteristic, complemented
6#71975C211yesmaximal, characteristic, complemented
7#70205C211yesmaximal, characteristic, complemented
8#70204C211yesmaximal, characteristic, complemented
9#70172C211yesmaximal, characteristic, complemented
10#70171C211yesmaximal, characteristic, complemented
11#69503C211yesmaximal, characteristic, complemented
12#68911C211yesmaximal, characteristic, complemented
13#68899C211yesmaximal, characteristic, complemented
14#68880C211yesmaximal, characteristic, complemented
15#68878C211yesmaximal, characteristic, complemented
16#23962—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#938—21no—
21C2×#938C2211yescharacteristic
22C2×#935—21no—
23C2×D4×Dic3C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C2×C4×#67C2211yescharacteristic
27C2×#926C2211yescharacteristic
28#5614—24no—
29#5614—24no—
30C2×#897C2211yescharacteristic
31C2×#895C2211yescharacteristic
32C2×D3×C4⋊C4C2211yescharacteristic
33C2×#890C2211yescharacteristic
34C2×#67⋊C4—21no—
35C2×#879—21no—
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#830C2211yescharacteristic
40#5113—24no—
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47#5037—24no—
48#4988C2211yescharacteristic
49#4973C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4961—21no—
53#4960—21no—
54#4668—21no—
55#4665—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
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#1893D311yescharacteristic, complemented
73#1879—31no—
74#1877—31no—
75#1874—31no—
76#1872—31no—
77#1869—31no—
78#1825—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67D411yescharacteristic
85C23×Dic3—21no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—41no—
91C2×#235—41no—
92C22×D12—21no—
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3C2311yescharacteristic
97C22×Dic6C2311yescharacteristic
98C22×C3×C8—22no—
99C22×C3×C8—41no—
100C22×C3×C8—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×#121—22no—
104C3×#121D414yescomplemented
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#217—21no—
113C2×#217D411yescharacteristic
114#938—28no—
115#938—22no—
116#938—22no—
117#935—28no—
118D4×Dic3—22no—
119D4×Dic3—22no—
120C2×#214—22no—
121C2×#214—22no—
122C2×#214—41no—
123C2×#213—22no—
124C2×#213—22no—
125C2×#213—41no—
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
133#926—22no—
134#926D414yescomplemented
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3—21no—
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4D411yescharacteristic
142C2×C4×Dic3—21no—
143C2×C4×Dic3C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146#897—22no—
147#897—41no—
148#895—22no—
149#895—41no—
150D3×C4⋊C4—22no—
151D3×C4⋊C4—22no—
152#890—22no—
153#890—22no—
154#67⋊C4—28no—
155#879—28no—
156C3×#102—41no—
157C3×#102—41no—
158C3×#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#830—22no—
162#821—22no—
163#821—22no—
164(C2×D3)⋊C8—41no—
165(C2×D3)⋊C8—41no—
166#816—22no—
167#816—22no—
168#810—22no—
169#809—22no—
170C22×#41—31no—
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—61no—
183C2×#121C2×D311yescharacteristic
184C2×C4×D4—31no—
185C2×C4×D4—31no—
186C2×C4×D4—61no—
187C2×#117—31no—
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×#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#380C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340C2×D311yescharacteristic
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C23×D3C2×D411yescharacteristic
221C2×C3×D4—24no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—81no—
228C2×C3×D4—81no—
229C2×C3×D4C2×D412yes—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4C2×D412yes—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—22no—
243C2×#67—22no—
244C2×#67—41no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3—24no—
254C22×Dic3—81no—
255C22×Dic3—81no—
256C22×Dic3C2×D411yescharacteristic
257C22×Dic3C2×D411yescharacteristic
258C22×Dic3C2×D411yescharacteristic
259#235—28no—
260#235—44no—
261#235—44no—
262#235—44no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—42no—
269C2×D12—42no—
270C2×D12—81no—
271C2×D12#4112yes—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—24no—
279C2×C4×D3—42no—
280C2×C4×D3—42no—
281C2×C4×D3—42no—
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—
296C2×C3×C8—44no—
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×C22⋊C4—24no—
304C3×C22⋊C4—81no—
305#217—24no—
306#217—24no—
307#217—24no—
308#217—22no—
309#214—44no—
310#213—44no—
311(C2×D3)⋊C4—22no—
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—21no—
319C4⋊Dic3—42no—
320C4⋊Dic3C2×D412yes—
321C4⋊Dic3C2×D412yes—
322Dic3⋊C4—24no—
323Dic3⋊C4—24no—
324Dic3⋊C4—22no—
325C4×Dic3—24no—
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—62no—
335C2×#41—62no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—121no—
339C2×#41—121no—
340C22×Q8—31no—
341C22×D4—21no—
342C22×D4—31no—
343C22×D4—31no—
344C22×D4—61no—
345C22×D4—61no—
346C22×D4—61no—
347C22×D4C22×D311yescharacteristic
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—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—22no—
373#121—62no—
374#121—68no—
375#121—62no—
376#121—62no—
377#121—121no—
378#121D1214yescomplemented
379C4×D4—68no—
380C4×D4—62no—
381C4×D4—62no—
382C4×D4—62no—
383C4×D4—62no—
384#117—34no—
385#117—62no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—62no—
390C2×C4⋊C4—61no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—62no—
394C2×C4⋊C4—61no—
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—31no—
410C2×C42—61no—
411#103—62no—
412#103—62no—
413#103—62no—
414#102—41no—
415#102—41no—
416#102—62no—
417#102—62no—
418#102—62no—
419C22⋊C8—62no—
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—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×D4—22no—
455C3×D4—22no—
456C3×D4—41no—
457C3×D4—41no—
458C3×D4—84no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
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—41no—
473C2×C3×C4—41no—
474C2×C3×C4#12012yes—
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480C2×C3×C4H(5,𝔽2)11yescharacteristic
481#67—44no—
482#67—48no—
483#67—48no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—22no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3—41no—
500C2×Dic3—41no—
501C2×Dic3—41no—
502C2×Dic3—84no—
503D12—22no—
504D12—22no—
505D12—41no—
506D12—41no—
507D12—84no—
508C4×D3—48no—
509C4×D3—41no—
510C4×D3—41no—
511C4×D3—41no—
512C4×D3—41no—
513C4×D3—84no—
514Dic6—22no—
515Dic6—22no—
516Dic6—41no—
517Dic6—41no—
518C3×C8—41no—
519C3×C8—41no—
520C3⋊C8—41no—
521C3⋊C8—41no—
522C24—21no—
523C24—31no—
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—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—32no—
543C2×D4—62no—
544C2×D4—64no—
545C2×D4—62no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4—121no—
556C2×D4—122no—
557C2×D4—122no—
558C2×D4—122no—
559C2×D4—122no—
560C2×D4—122no—
561C2×D4—241no—
562C2×D4C2×D1212yes—
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—64no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—64no—
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—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—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—32no—
616C4⋊C4—32no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—64no—
620C4⋊C4—62no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—122no—
624C4⋊C4C2×D1212yes—
625C22⋊C4—24no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—62no—
629C22⋊C4—64no—
630C22⋊C4—62no—
631C22⋊C4—81no—
632C22⋊C4—122no—
633C22⋊C4—122no—
634C22⋊C4—122no—
635C22⋊C4—241no—
636C42—64no—
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—81no—
677C3×C4—81no—
678C3×C4#52511yescharacteristic
679C3×C4#53511yescharacteristic
680C3×C4#54611yescharacteristic
681C3×C4#54611yescharacteristic
682Dic3—42no—
683Dic3—41no—
684Dic3—41no—
685Dic3—42no—
686Dic3—42no—
687Dic3—41no—
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#88212yes—
716C23C2×D3×D411yescharacteristic
717Q8—62no—
718Q8—62no—
719Q8—121no—
720Q8—121no—
721D4—22no—
722D4—22no—
723D4—41no—
724D4—41no—
725D4—62no—
726D4—62no—
727D4—84no—
728D4—124no—
729D4—128no—
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—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—62no—
750C2×C4—62no—
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—61no—
761C2×C4—128no—
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#88212yes—
775C2×C4C22×D1211yescharacteristic
776C2×C4C2×D3×D411yescharacteristic
777C2×C4#100411yescharacteristic
778C2×C4#100411yescharacteristic
779C2×C4D3×#4111yescharacteristic
780C2×C4D3×#4111yescharacteristic
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—
824C22C2×#88211yescharacteristic
825C22#561011yescharacteristic
826C22#561011yescharacteristic
827C22#575711yescharacteristic
828C22#576211yescharacteristic
829C22D3×#13511yescharacteristic
830C22#576811yescharacteristic
831C4—22no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—121no—
836C4—122no—
837C4—121no—
838C4—122no—
839C4—121no—
840C4—122no—
841C4#555411yescharacteristic
842C4#555411yescharacteristic
843C4#559211yescharacteristic
844C4#565611yescharacteristic
845C3#2396211yescharacteristic, complemented, Sylow
846C2—42no—
847C2—82no—
848C2—122no—
849C2—242no—
850C2#7488511yescharacteristic
851C2#7874711yescharacteristic
852C2#7883311yescharacteristic
853C2#8067211yescharacteristic
854C2#8068411yescharacteristic
855C2#8072511yescharacteristic
856C2#8073911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1893C2
socleC23×C3C22×D4
hypercenter#1893D3
hypocenterC3#23962
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
1. C2×#5614C2semidirect
2. C2×#5113C2semidirect
3. C2×#5037C2semidirect
4. #74015C2semidirect
5. C3×#1893C2semidirect
6. #71975C2semidirect
7. #70205C2semidirect
8. #70204C2semidirect
9. #70172C2semidirect
10. #70171C2semidirect
11. #69503C2semidirect
12. #68911C2semidirect
13. #68899C2semidirect
14. #68880C2semidirect
15. #68878C2semidirect
72. #1893D3semidirect
104. C3×#121D4semidirect
134. #926D4semidirect
378. #121D12semidirect
845. C3#23962semidirect

Maximal subgroups

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

subgroupindex
C2×#56142
C2×#51132
C2×#50372
#740152
C3×#18932
#719752
#702052
#702042
#701722
#701712
#695032
#689112
#688992
#688802
#688782
#239623