Finite Group Databasebeta

← #10829314

Subgroups — #10829314

Order 768.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5565C211yesmaximal, characteristic, complemented
2#82417C211yesmaximal, characteristic, complemented
3C2×#4847C211yesmaximal, characteristic, complemented
4C2×#4711C211yesmaximal, characteristic, complemented
5C3×#1955C211yesmaximal, characteristic, complemented
6#70479C211yesmaximal, characteristic, complemented
7#69961C211yesmaximal, characteristic, complemented
8#69961C211yesmaximal, characteristic, complemented
9#69935C211yesmaximal, characteristic, complemented
10#69934C211yesmaximal, characteristic, complemented
11#69933C211yesmaximal, characteristic, complemented
12#69932C211yesmaximal, characteristic, complemented
13#69929C211yesmaximal, characteristic, complemented
14#69928C211yesmaximal, characteristic, complemented
15#69827C211yesmaximal, characteristic, complemented
16#24136—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×#939—21no—
19C2×#938—21no—
20C2×#930C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#926C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26C22×D24C2211yescharacteristic
27#5565—24no—
28#5565—24no—
29C2×#898—21no—
30C2×#883—21no—
31C2×#67⋊C4—21no—
32C2×C4×D12C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34C2×#870C2211yescharacteristic
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×#97C2211yescharacteristic
41#5212C2211yescharacteristic
42#5212C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×#818C2211yescharacteristic
50C2×#817C2211yescharacteristic
51C2×#817C2211yescharacteristic
52#4987—21no—
53#4961—21no—
54#4961—21no—
55#4935C2211yescharacteristic
56#4847—24no—
57#4711—24no—
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#553—31no—
65C2×#478—31no—
66C2×#442—31no—
67#2537—31no—
68#2034—31no—
69#2033—31no—
70#1999—31no—
71#1999—31no—
72#1992—31no—
73#1955D311yescharacteristic, complemented
74#1875—31no—
75#1874—31no—
76#1854—31no—
77#1853—31no—
78#1802—31no—
79C22×C3×D4D411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C23×Dic3—21no—
87C22×D12C2311yescharacteristic
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3—21no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C2×C3×C4⋊C4D411yescharacteristic
98C2×C3×C22⋊C4D411yescharacteristic
99C2×C3×C22⋊C4D411yescharacteristic
100C2×C3×C42C2311yescharacteristic
101C2×#217—21no—
102C2×#217—21no—
103C2×#217—21no—
104#939—28no—
105#938—44no—
106#930—22no—
107#930—22no—
108#930—22no—
109#930—22no—
110#930—22no—
111#930—22no—
112#930—41no—
113#930—41no—
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—
120#926—22no—
121#926—22no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—22no—
124C2×C4⋊Dic3—22no—
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C2×D24—22no—
137C2×D24—22no—
138C2×D24—22no—
139#898—28no—
140#883—28no—
141#67⋊C4—28no—
142C4×D12—22no—
143C4×D12—22no—
144C4×D12—22no—
145C4×D12D414yescomplemented
146#870—22no—
147#870D414yescomplemented
148C3×C4⋊C8—22no—
149C3×C22⋊C8—22no—
150C3×C22⋊C8—22no—
151C3×C22⋊C8—41no—
152C3×C22⋊C8—41no—
153C3×#97—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#821—22no—
157#821—22no—
158#821—22no—
159#821—22no—
160#821—41no—
161#821—41no—
162#818—22no—
163#817—22no—
164#817—22no—
165C22×D8—31no—
166#553—64no—
167#553—64no—
168C2×#126—61no—
169C2×#125—31no—
170C2×#123—61no—
171C2×#121—31no—
172C2×#121—31no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—61no—
176C2×#121—61no—
177C2×C4×D4—31no—
178C2×C4×D4—31no—
179C2×C4×D4—61no—
180C2×C4×D4C2×D311yescharacteristic
181C2×#117—31no—
182C22×C4⋊C4—31no—
183#478—64no—
184#442—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×#106—31no—
188C2×C4⋊C8C2×D311yescharacteristic
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8C2×D311yescharacteristic
196C2×C22⋊C8C2×D311yescharacteristic
197C2×C22⋊C8C2×D311yescharacteristic
198C2×C22⋊C8C2×D311yescharacteristic
199C2×#97C2×D311yescharacteristic
200#394—61no—
201#394—61no—
202#384—31no—
203#380—31no—
204#380—31no—
205#380—61no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212C24×C3C2×D411yescharacteristic
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C23×D3—21no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—41no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
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×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—24no—
237C2×#67—24no—
238C2×#67—42no—
239C2×#67—42no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—81no—
245C2×#67—81no—
246C2×#67—81no—
247C2×#67—81no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—24no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—81no—
256C22×Dic3—81no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12C2×D412yes—
268C2×D12#4112yes—
269C2×C4×D3—24no—
270C2×C4×D3—42no—
271C2×C4×D3—42no—
272C2×C4×D3—42no—
273C2×C4×D3—81no—
274C2×C4×D3—81no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8#4112yes—
287C3×C4⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C42C2×D412yes—
291C3×C42C2×D412yes—
292#217—24no—
293#217—42no—
294#217—42no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—24no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301C4⋊Dic3—24no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—42no—
312C4⋊Dic3—81no—
313C4⋊Dic3C2×D412yes—
314C4⋊Dic3C2×D412yes—
315C4⋊Dic3C2×D412yes—
316Dic3⋊C4—24no—
317Dic3⋊C4—24no—
318C4×Dic3—24no—
319D24—28no—
320C22×D4—31no—
321C22×D4—31no—
322C22×D4—61no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4D1211yescharacteristic
327C23×C4—61no—
328C23×C4—61no—
329C23×C4—61no—
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C2×D8—62no—
333C2×D8—62no—
334C2×D8—62no—
335C22×C8C22×D311yescharacteristic
336C22×C8C22×D311yescharacteristic
337C22×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
339#126—68no—
340#125—34no—
341#125—62no—
342#123—68no—
343#121—62no—
344#121—62no—
345#121—62no—
346#121—62no—
347#121—68no—
348#121—62no—
349#121—62no—
350#121—121no—
351#121—121no—
352#121—124no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—34no—
356C4×D4—68no—
357C4×D4—62no—
358C4×D4—62no—
359C4×D4—62no—
360#117—62no—
361#117—62no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4D1211yescharacteristic
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4D1211yescharacteristic
386C2×C22⋊C4D1211yescharacteristic
387C2×C42—61no—
388C2×C42C22×D311yescharacteristic
389#107—62no—
390#106—62no—
391#106—62no—
392C4⋊C8—22no—
393#102—62no—
394#102—62no—
395#102—62no—
396#102—62no—
397#102—121no—
398#102—121no—
399C22⋊C8—22no—
400C22⋊C8—22no—
401C22⋊C8—41no—
402C22⋊C8—41no—
403#97—22no—
404#95—61no—
405#95—61no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3AGL(1,ℤ/8)12yes—
420C23×C3C22×D411yescharacteristic
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—41no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C3×D4—44no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4#12012yes—
455C2×C3×C4#12012yes—
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4H(5,𝔽2)11yescharacteristic
461C2×C3×C42−1+411yescharacteristic
462#67—48no—
463#67—84no—
464#67—84no—
465#67—84no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—84no—
485D12—22no—
486D12—22no—
487D12—22no—
488D12—22no—
489D12—41no—
490D12—41no—
491D12—41no—
492D12—41no—
493C4×D3—84no—
494C4×D3—84no—
495C3×C8—22no—
496C3×C8—41no—
497C3×C8—41no—
498C3×C8—41no—
499C24—61no—
500C24—61no—
501C24C2×D1211yescharacteristic
502C24C2×D1211yescharacteristic
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—32no—
506C2×D4—32no—
507C2×D4—41no—
508C2×D4—64no—
509C2×D4—64no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—122no—
521C2×D4—122no—
522C2×D4—122no—
523C2×D4—122no—
524C2×D4—122no—
525C2×D4—122no—
526C2×D4—241no—
527C2×D4—241no—
528C2×D4—241no—
529C2×D4—241no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—122no—
551C22×C4—122no—
552C22×C4—122no—
553C22×C4—241no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4C2×D1211yescharacteristic
558C22×C4C2×D1211yescharacteristic
559C22×C4C2×D1211yescharacteristic
560C22×C4C2×D1211yescharacteristic
561C22×C4C23×D311yescharacteristic
562D8—68no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8#23712yes—
575C4⋊C4—22no—
576C4⋊C4—32no—
577C4⋊C4—32no—
578C4⋊C4—32no—
579C4⋊C4—64no—
580C4⋊C4—64no—
581C4⋊C4—64no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—122no—
592C4⋊C4—241no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—64no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C42—64no—
605C42D3×D412yes—
606C42D3×D412yes—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3C2×#12011yescharacteristic
622C22×C3#54611yescharacteristic
623C22×C3#54711yescharacteristic
624C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
625C22×C3#57511yescharacteristic
626C22×C3#57611yescharacteristic
627C22×C3#57711yescharacteristic
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—81no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4#52511yescharacteristic
647C3×C4#53711yescharacteristic
648C3×C4#54811yescharacteristic
649C3×C4#55011yescharacteristic
650Dic3—42no—
651Dic3—42no—
652Dic3—42no—
653Dic3—81no—
654Dic3—81no—
655Dic3—81no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—62no—
670C23—62no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23—121no—
676C23—121no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23#90812yes—
684C23C22×D1211yescharacteristic
685D4—44no—
686D4—62no—
687D4—62no—
688D4—62no—
689D4—62no—
690D4—128no—
691D4—121no—
692D4—121no—
693D4—121no—
694D4—121no—
695D4—244no—
696D4—244no—
697D4—244no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—121no—
720C2×C4—121no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—244no—
735C2×C4—244no—
736C2×C4—244no—
737C2×C4#88212yes—
738C2×C4#88212yes—
739C2×C4C2×D3×D411yescharacteristic
740C2×C4C2×D3×D411yescharacteristic
741C2×C4C2×#23711yescharacteristic
742C2×C4#100411yescharacteristic
743C2×C4D3×#4111yescharacteristic
744C2×C4#101011yescharacteristic
745C8—22no—
746C8—41no—
747C8—41no—
748C8—41no—
749C2×C3—42no—
750C2×C3—81no—
751C2×C3#240711yescharacteristic
752C2×C3#300611yescharacteristic
753C2×C3#301211yescharacteristic
754C2×C3#330711yescharacteristic
755C2×C3#331811yescharacteristic
756C2×C3#334511yescharacteristic
757C2×C3#334711yescharacteristic
758D3—82no—
759D3—82no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—122no—
775C22—122no—
776C22—122no—
777C22—122no—
778C22—122no—
779C22—122no—
780C22—241no—
781C22—241no—
782C22—241no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22—241no—
787C22—241no—
788C22C2×#88211yescharacteristic
789C22#555411yescharacteristic
790C22#555511yescharacteristic
791C22C2×#90811yescharacteristic
792C22#574811yescharacteristic
793C22#575111yescharacteristic
794C22#575211yescharacteristic
795C4—22no—
796C4—22no—
797C4—41no—
798C4—41no—
799C4—122no—
800C4—122no—
801C4—122no—
802C4—241no—
803C4—241no—
804C4—241no—
805C4#560611yescharacteristic
806C4#560811yescharacteristic
807C4#567711yescharacteristic
808C4#571811yescharacteristic
809C3#2413611yescharacteristic, complemented, Sylow
810C2—42no—
811C2—81no—
812C2—242no—
813C2—242no—
814C2#7643511yescharacteristic
815C2#7863911yescharacteristic
816C2#7867211yescharacteristic
817C2#7947111yescharacteristic
818C2#7947311yescharacteristic
819C2#7950011yescharacteristic
820C2#7950511yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1955C2
socleC23×C3C22×D4
hypercenter#1955D3
hypocenterC3#24136
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. C2×#5565C2semidirect
2. #82417C2semidirect
3. C2×#4847C2semidirect
4. C2×#4711C2semidirect
5. C3×#1955C2semidirect
6. #70479C2semidirect
7. #69961C2semidirect
8. #69961C2semidirect
9. #69935C2semidirect
10. #69934C2semidirect
11. #69933C2semidirect
12. #69932C2semidirect
13. #69929C2semidirect
14. #69928C2semidirect
15. #69827C2semidirect
73. #1955D3semidirect
145. C4×D12D4semidirect
147. #870D4semidirect
809. C3#24136semidirect

Maximal subgroups

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

subgroupindex
C2×#55652
#824172
C2×#48472
C2×#47112
C3×#19552
#704792
#699612
#699352
#699342
#699332
#699322
#699292
#699282
#698272
#241363