Finite Group Databasebeta

← #10846142

Subgroups — #10846142

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#460C211yesmaximal, characteristic, complemented
2C2×#5174C211yesmaximal, characteristic, complemented
3C2×#5171C211yesmaximal, characteristic, complemented
4#83188C211yesmaximal, characteristic
5#82499C211yesmaximal, characteristic, complemented
6C2×#4836C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71765C211yesmaximal, characteristic, complemented
10#71631C211yesmaximal, characteristic, complemented
11#70455C211yesmaximal, characteristic, complemented
12#70203C211yesmaximal, characteristic, complemented
13#70202C211yesmaximal, characteristic, complemented
14#70176C211yesmaximal, characteristic, complemented
15#70175C211yesmaximal, characteristic, complemented
16#25402—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×#127C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#940—21no—
24C2×#938C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C2×#938C2211yescharacteristic
28C22×ΓL(1,𝔽25)C2211yescharacteristic
29C22×D3×C8C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C3×#460—24no—
32C2×C3×C4⋊C8C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37#5223—21no—
38#5223—21no—
39#5221—21no—
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44#5174—24no—
45#5171—24no—
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×#818C2211yescharacteristic
49C2×#817C2211yescharacteristic
50#4991—21no—
51#4987C2211yescharacteristic
52#4987C2211yescharacteristic
53#4981—21no—
54#4940—21no—
55#4940—21no—
56#4936C2211yescharacteristic
57C4×C4⋊Dic3C2211yescharacteristic
58C2×#803C2211yescharacteristic
59#4836—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#465—31no—
66C2×#460D311yescharacteristic, complemented
67C2×#435—31no—
68#2541—31no—
69#2536—31no—
70#2034—31no—
71#2033—31no—
72#2000—31no—
73#2000—31no—
74#1961—31no—
75#1949—31no—
76#1895—31no—
77#1893—31no—
78#1763—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×D12D411yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—41no—
96C2×C3×SD16—41no—
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C3×#127—22no—
100C3×#127—22no—
101C3×C4×Q8—22no—
102C3×C4×Q8—22no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C42—21no—
106C2×C3×C42C2311yescharacteristic
107C2×#217—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111#946—22no—
112#946—22no—
113#946—41no—
114#946—41no—
115#940—44no—
116#938—22no—
117#938—22no—
118#938—22no—
119#938—22no—
120#938—41no—
121#938—41no—
122#938—41no—
123#938—41no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4D411yescharacteristic
129C2×(C2×D3)⋊C4D411yescharacteristic
130C2×C4⋊Dic3D411yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×C4⋊Dic3C2311yescharacteristic
134C2×C4⋊Dic3C2311yescharacteristic
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×C4×Dic3—21no—
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—41no—
143C2×D3×C8—22no—
144C2×D3×C8—22no—
145C2×D3×C8—41no—
146C4×D12—22no—
147C4×D12—22no—
148C3×C4⋊C8D414yescomplemented
149C3×#102—22no—
150C3×#102—22no—
151#835—22no—
152#835D414yescomplemented
153#832—22no—
154#832—22no—
155#832—41no—
156#832—41no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162(C2×D3)⋊C8—22no—
163(C2×D3)⋊C8—22no—
164#818—22no—
165#817—22no—
166#803—22no—
167C22×SD16C2×D311yescharacteristic
168C22×SD16C2×D311yescharacteristic
169C22×M16—31no—
170C23×C8—31no—
171C2×#127—61no—
172C2×#127C2×D311yescharacteristic
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×#121—31no—
178C2×#121—31no—
179C2×C4×Q8C2×D311yescharacteristic
180C2×C4×D4—31no—
181#468—64no—
182#465—64no—
183#460—24no—
184#435—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×C4⋊C8C2×D311yescharacteristic
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×#102C2×D311yescharacteristic
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×#97—31no—
199#398—61no—
200#394—61no—
201#392—61no—
202#392—61no—
203#390—61no—
204#388—61no—
205#388—61no—
206#382—31no—
207#380—31no—
208#380—31no—
209C4×C4⋊C4—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214C24×C3—21no—
215C24×C3—21no—
216C23×D3C2×D411yescharacteristic
217C23×D3C2×D411yescharacteristic
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
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—42no—
240C2×C3×D4—81no—
241C2×C3×D4—81no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C2×#67—42no—
248C2×#67—42no—
249C2×#67—42no—
250C2×#67—42no—
251C2×#67—42no—
252C2×#67—42no—
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—81no—
256C2×#67—81no—
257C2×#67—81no—
258C2×#67—81no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—21no—
263C22×Dic3C2×D411yescharacteristic
264C22×Dic3C2×D411yescharacteristic
265C2×D12—22no—
266C2×D12—22no—
267C2×D12—41no—
268C2×C4×D3—21no—
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—21no—
276C2×C4×D3—21no—
277C2×C4×D3—21no—
278C2×C4×D3—21no—
279C2×C4×D3—21no—
280C3×SD16—44no—
281C3×SD16—44no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8C2×D412yes—
287C2×C3×C8C2×D412yes—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—42no—
291C3×C42—42no—
292C3×C42C2×D412yes—
293C3×C42#4112yes—
294#217—42no—
295#217—42no—
296#217—42no—
297#217—42no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—22no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304C4⋊Dic3—22no—
305C4⋊Dic3—21no—
306C4⋊Dic3—21no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3C2×D412yes—
312C4⋊Dic3#4112yes—
313Dic3⋊C4—42no—
314Dic3⋊C4—42no—
315C4×Dic3—42no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8C2×D412yes—
322ΓL(1,𝔽25)—44no—
323D3×C8—44no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4—61no—
330C22×D4—61no—
331C22×D4—61no—
332C22×D4C22×D311yescharacteristic
333C22×D4C22×D311yescharacteristic
334C23×C4—31no—
335C23×C4—31no—
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—41no—
341C2×SD16—41no—
342C2×M16—62no—
343C2×M16—62no—
344C2×M16—121no—
345C22×C8—31no—
346C22×C8—31no—
347C22×C8—62no—
348C22×C8—62no—
349C22×C8—121no—
350C22×C8C22×D311yescharacteristic
351C22×C8C22×D311yescharacteristic
352#127—22no—
353#127—22no—
354#127—124no—
355C22⋊Q8—62no—
356C22⋊Q8—62no—
357C22⋊Q8—121no—
358C22⋊Q8—121no—
359#121—62no—
360#121—62no—
361#121—62no—
362#121—62no—
363#121—121no—
364#121—121no—
365#121—121no—
366#121—121no—
367C4×Q8—22no—
368C4×Q8—22no—
369C4×D4—62no—
370C4×D4—62no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C42—21no—
391C2×C42—61no—
392C2×C42C22×D311yescharacteristic
393#107—62no—
394#106—62no—
395C4⋊C8#6714yescomplemented
396#103—34no—
397#103—62no—
398#102—22no—
399#102—22no—
400#102—62no—
401#102—62no—
402#102—121no—
403#102—121no—
404C22⋊C8—62no—
405C22⋊C8—62no—
406#97—62no—
407#95—61no—
408#95—61no—
409#95—61no—
410#95—61no—
411#95—61no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3C22×D411yescharacteristic
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3—21no—
433C22×D3—21no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3AGL(1,ℤ/8)12yes—
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—41no—
446C3×D4—41no—
447C3×D4—41no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—84no—
454C3×D4—84no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4#12112yes—
466C2×C3×C4#12112yes—
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C2×#4111yescharacteristic
470C2×C3×C4C2×#4111yescharacteristic
471C2×C3×C4H(5,𝔽2)11yescharacteristic
472C2×C3×C4H(5,𝔽2)11yescharacteristic
473#67—84no—
474#67—84no—
475#67—84no—
476#67—84no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495D12—44no—
496C4×D3—41no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501C4×D3—41no—
502C4×D3—41no—
503C4×D3—41no—
504C3×C8—22no—
505C3×C8—22no—
506C3⋊C8—22no—
507C3⋊C8—41no—
508C24—21no—
509C24—21no—
510C24—31no—
511C24—31no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8D3×D412yes—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—62no—
535C2×D4—62no—
536C2×D4—81no—
537C2×D4—81no—
538C2×D4—121no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—122no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—241no—
548C2×D4—241no—
549C2×D4—241no—
550C2×D4—241no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4D3×D411yescharacteristic
572C22×C4D3×D411yescharacteristic
573C22×C4C23×D311yescharacteristic
574SD16—44no—
575SD16—44no—
576M16—124no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—32no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—124no—
588C2×C8C2×#6712yes—
589C2×C8C2×#6712yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—32no—
593C4⋊C4—32no—
594C4⋊C4—42no—
595C4⋊C4—62no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—122no—
603C4⋊C4—122no—
604C22⋊C4—62no—
605C22⋊C4—62no—
606C22⋊C4—122no—
607C22⋊C4—122no—
608C22⋊C4—122no—
609C22⋊C4—122no—
610C22⋊C4—122no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C42—42no—
615C42—122no—
616C42#23712yes—
617C42C2×#6712yes—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3C2×#12111yescharacteristic
633C22×C3D4211yescharacteristic
634C22×C3#54611yescharacteristic
635C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
636C22×C3#57511yescharacteristic
637C22×C3#57711yescharacteristic
638C22×C3#57711yescharacteristic
639C2×D3—22no—
640C2×D3—22no—
641C2×D3—22no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—42no—
656C3×C4—81no—
657C3×C4#53211yescharacteristic
658C3×C4#54011yescharacteristic
659C3×C4D4211yescharacteristic
660C3×C4#55011yescharacteristic
661Dic3—41no—
662Dic3—41no—
663Dic3—42no—
664Dic3—42no—
665Dic3—81no—
666Dic3—81no—
667C23—32no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—61no—
692C23—61no—
693C23—61no—
694C23—61no—
695C23C2×D3×D411yescharacteristic
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—84no—
709D4—84no—
710D4—124no—
711D4—244no—
712D4—244no—
713D4—244no—
714D4—244no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—62no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—62no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4#93812yes—
752C2×C4#93812yes—
753C2×C4C2×D3×D411yescharacteristic
754C2×C4C2×#23711yescharacteristic
755C2×C4#100411yescharacteristic
756C2×C4D3×#4111yescharacteristic
757C2×C4#100911yescharacteristic
758C2×C4C22×#6711yescharacteristic
759C8—22no—
760C8—22no—
761C8—62no—
762C8—121no—
763C2×C3—161no—
764C2×C3—161no—
765C2×C3#242811yescharacteristic
766C2×C3#305511yescharacteristic
767C2×C3#305711yescharacteristic
768C2×C3#326511yescharacteristic
769C2×C3#327111yescharacteristic
770C2×C3#331011yescharacteristic
771C2×C3#331711yescharacteristic
772D3—42no—
773D3—81no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22#560911yescharacteristic
803C22#561211yescharacteristic
804C22#576211yescharacteristic
805C22#576211yescharacteristic
806C22D3×AGL(1,ℤ/8)11yescharacteristic
807C22#577311yescharacteristic
808C22C2×#93811yescharacteristic
809C4—22no—
810C4—22no—
811C4—42no—
812C4—81no—
813C4—122no—
814C4—122no—
815C4—121no—
816C4—121no—
817C4—241no—
818C4—241no—
819C4#559611yescharacteristic
820C4#561911yescharacteristic
821C4D4×#6711yescharacteristic
822C4#583411yescharacteristic
823C3#2540211yescharacteristic, complemented, Sylow
824C2—122no—
825C2—161no—
826C2—161no—
827C2—241no—
828C2#8039711yescharacteristic
829C2#8039811yescharacteristic
830C2#8040411yescharacteristic
831C2#8040711yescharacteristic
832C2#8264811yescharacteristic
833C2#8386311yescharacteristic
834C2#8395011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#460C2
socleC23×C3C22×D4
prime radical#83188C2
hypercenterC2×#460D3
hypocenterC3#25402
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×C3×#460C2semidirect
2. C2×#5174C2semidirect
3. C2×#5171C2semidirect
5. #82499C2semidirect
6. C2×#4836C2semidirect
7. #72054C2semidirect
8. #72054C2semidirect
9. #71765C2semidirect
10. #71631C2semidirect
11. #70455C2semidirect
12. #70203C2semidirect
13. #70202C2semidirect
14. #70176C2semidirect
15. #70175C2semidirect
66. C2×#460D3semidirect
148. C3×C4⋊C8D4semidirect
152. #835D4semidirect
395. C4⋊C8#67semidirect
823. C3#25402semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4602
C2×#51742
C2×#51712
#831882
#824992
C2×#48362
#720542
#717652
#716312
#704552
#702032
#702022
#701762
#701752
#254023