Finite Group Databasebeta

← #10846112

Subgroups — #10846112

Order 768.

1048 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#461C211yesmaximal, characteristic, complemented
2C2×#5174C211yesmaximal, characteristic, complemented
3C2×#5171C211yesmaximal, characteristic, complemented
4#83259C211yesmaximal, characteristic, complemented
5#82416C211yesmaximal, characteristic
6C2×#4836C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#71786C211yesmaximal, characteristic, complemented
10#71609C211yesmaximal, characteristic, complemented
11#70455C211yesmaximal, characteristic, complemented
12#70271C211yesmaximal, characteristic, complemented
13#70270C211yesmaximal, characteristic, complemented
14#70244C211yesmaximal, characteristic, complemented
15#70243C211yesmaximal, characteristic, complemented
16#25400—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×#938C2211yescharacteristic
26C2×#938C2211yescharacteristic
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C3×#461—24no—
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5213—21no—
41#5213—21no—
42#5174—24no—
43#5171—24no—
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#818C2211yescharacteristic
47C2×#817C2211yescharacteristic
48#4993—21no—
49#4993—21no—
50#4988—21no—
51#4987C2211yescharacteristic
52#4987C2211yescharacteristic
53#4975—21no—
54#4960—21no—
55#4953—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×#461D311yescharacteristic, complemented
67C2×#435—31no—
68#2542—31no—
69#2535—31no—
70#2036—31no—
71#2035—31no—
72#2000—31no—
73#2000—31no—
74#1960—31no—
75#1949—31no—
76#1894—31no—
77#1892—31no—
78#1762—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×D12D411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C2×C3×SD16—41no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×C4⋊Q8—22no—
97C3×C4⋊Q8—22no—
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C42C2311yescharacteristic
105C2×#217—21no—
106C2×#217—21no—
107#946—22no—
108#946—22no—
109#946—22no—
110#946—22no—
111#946—41no—
112#946—41no—
113#946—41no—
114#946—41no—
115#938—22no—
116#938—22no—
117#938—41no—
118#938—41no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—41no—
142C2×D3×C8—22no—
143C2×D3×C8—22no—
144C2×D3×C8—41no—
145C4×D12—22no—
146C4×D12—22no—
147C3×C4⋊C8D414yescomplemented
148C3×#103—22no—
149C3×#103—22no—
150#835—22no—
151#835—22no—
152#835—41no—
153#835—41no—
154#832—22no—
155#832D414yescomplemented
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161(C2×D3)⋊C8—22no—
162(C2×D3)⋊C8—22no—
163#818—22no—
164#817—22no—
165#803—22no—
166C22×SD16C2×D311yescharacteristic
167C22×SD16C2×D311yescharacteristic
168C22×M16—31no—
169C23×C8—31no—
170C2×C4⋊Q8C2×D311yescharacteristic
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×D4—31no—
178C2×C4×D4C2×D311yescharacteristic
179#468—64no—
180#465—64no—
181#461—24no—
182#435—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103C2×D311yescharacteristic
191C2×#103C2×D311yescharacteristic
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×#97—31no—
197#399—61no—
198#399—61no—
199#397—61no—
200#392—61no—
201#390—61no—
202#386—61no—
203#386—61no—
204#384—61no—
205#382—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3—21no—
214C23×D3C2×D411yescharacteristic
215C23×D3C2×D411yescharacteristic
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4C2×D412yes—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—42no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—81no—
248C2×#67—81no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—21no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C2×D12—22no—
256C2×D12—22no—
257C2×D12—41no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C3×SD16—44no—
271C3×SD16—44no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8C2×D412yes—
277C2×C3×C8C2×D412yes—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—42no—
281C3×C4⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C42C2×D412yes—
284C3×C42#4112yes—
285#217—42no—
286#217—42no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—81no—
294(C2×D3)⋊C4—81no—
295C4⋊Dic3—22no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3C2×D412yes—
303C4⋊Dic3#4112yes—
304Dic3⋊C4—42no—
305Dic3⋊C4—42no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308C4×Dic3—42no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8C2×D412yes—
315ΓL(1,𝔽25)—44no—
316D3×C8—44no—
317C22×Q8C22×D311yescharacteristic
318C22×Q8C22×D311yescharacteristic
319C22×D4—31no—
320C22×D4—61no—
321C22×D4—61no—
322C22×D4C22×D311yescharacteristic
323C23×C4—21no—
324C23×C4—31no—
325C23×C4—31no—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—22no—
329C2×SD16—22no—
330C2×SD16—41no—
331C2×SD16—41no—
332C2×M16—62no—
333C2×M16—62no—
334C2×M16—121no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—62no—
338C22×C8—62no—
339C22×C8—121no—
340C22×C8C22×D311yescharacteristic
341C22×C8C22×D311yescharacteristic
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344C22⋊Q8—62no—
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350C22⋊Q8—121no—
351C22⋊Q8—121no—
352#121—62no—
353#121—62no—
354#121—121no—
355#121—121no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—62no—
359C4×D4—62no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—61no—
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×C42—61no—
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387C4⋊C8#6714yescomplemented
388#103—22no—
389#103—22no—
390#103—62no—
391#103—62no—
392#103—121no—
393#103—121no—
394#102—34no—
395#102—62no—
396C22⋊C8—62no—
397C22⋊C8—62no—
398#97—62no—
399#95—61no—
400#95—61no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—22no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3C22×D411yescharacteristic
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3#13712yes—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×Q8—41no—
429C3×Q8—41no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—41no—
437C3×D4—41no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—84no—
452C2×C3×C4#12112yes—
453C2×C3×C4#12112yes—
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4H(5,𝔽2)11yescharacteristic
459C2×C3×C4H(5,𝔽2)11yescharacteristic
460#67—84no—
461#67—84no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—21no—
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—
480D12—44no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—41no—
484C4×D3—41no—
485C4×D3—41no—
486C4×D3—41no—
487C4×D3—41no—
488C4×D3—41no—
489C3×C8—22no—
490C3×C8—22no—
491C3⋊C8—22no—
492C3⋊C8—41no—
493C24—21no—
494C24—31no—
495C24—31no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—62no—
514C2×D4—62no—
515C2×D4—121no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4—241no—
521C2×D4—241no—
522C2×D4D3×D412yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—42no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4D3×D411yescharacteristic
548C22×C4D3×D411yescharacteristic
549C22×C4C23×D311yescharacteristic
550SD16—44no—
551SD16—44no—
552M16—124no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—32no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—124no—
564C2×C8C2×#6712yes—
565C2×C8C2×#6712yes—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—32no—
569C4⋊C4—32no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—62no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—122no—
580C4⋊C4—122no—
581C4⋊C4—122no—
582C4⋊C4—122no—
583C22⋊C4—42no—
584C22⋊C4—62no—
585C22⋊C4—62no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C22⋊C4—122no—
589C22⋊C4—122no—
590C22⋊C4—122no—
591C22⋊C4—122no—
592C22⋊C4—241no—
593C22⋊C4—241no—
594C42—122no—
595C42#23712yes—
596C42C2×#6712yes—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3C2×#12111yescharacteristic
605C22×C3D4211yescharacteristic
606C22×C3#54611yescharacteristic
607C22×C3C2×#13711yescharacteristic
608C22×C3#57511yescharacteristic
609C22×C3#57711yescharacteristic
610C22×C3#57711yescharacteristic
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4#53211yescharacteristic
631C3×C4#54011yescharacteristic
632C3×C4D4211yescharacteristic
633C3×C4#55011yescharacteristic
634Dic3—41no—
635Dic3—41no—
636Dic3—42no—
637Dic3—42no—
638Dic3—81no—
639Dic3—81no—
640C23—22no—
641C23—32no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23C2×D3×D411yescharacteristic
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—41no—
668Q8—41no—
669Q8—41no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—124no—
675D4—244no—
676D4—244no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—84no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4#93812yes—
718C2×C4#93812yes—
719C2×C4C2×D3×D411yescharacteristic
720C2×C4C2×#23711yescharacteristic
721C2×C4#100411yescharacteristic
722C2×C4D3×#4111yescharacteristic
723C2×C4#100911yescharacteristic
724C2×C4C22×#6711yescharacteristic
725C8—22no—
726C8—22no—
727C8—62no—
728C8—121no—
729C2×C3—82no—
730C2×C3#242811yescharacteristic
731C2×C3#305611yescharacteristic
732C2×C3#305711yescharacteristic
733C2×C3#326611yescharacteristic
734C2×C3#326711yescharacteristic
735C2×C3#330711yescharacteristic
736C2×C3#332011yescharacteristic
737D3—42no—
738D3—81no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—62no—
743C22—62no—
744C22—62no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22#560911yescharacteristic
761C22#561211yescharacteristic
762C22#576211yescharacteristic
763C22#576211yescharacteristic
764C22D3×#13711yescharacteristic
765C22#577711yescharacteristic
766C22C2×#93811yescharacteristic
767C4—22no—
768C4—22no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4—122no—
773C4—122no—
774C4—121no—
775C4—121no—
776C4—241no—
777C4—241no—
778C4#559611yescharacteristic
779C4#561911yescharacteristic
780C4D4×#6711yescharacteristic
781C4#583411yescharacteristic
782C3#2540011yescharacteristic, complemented, Sylow
783C2—82no—
784C2—122no—
785C2—241no—
786C2#8044411yescharacteristic
787C2#8044511yescharacteristic
788C2#8045211yescharacteristic
789C2#8045311yescharacteristic
790C2#8264811yescharacteristic
791C2#8386311yescharacteristic
792C2#8398511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#461C2
socleC23×C3C22×D4
prime radical#82416C2
hypercenterC2×#461D3
hypocenterC3#25400
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×C3×#461C2semidirect
2. C2×#5174C2semidirect
3. C2×#5171C2semidirect
4. #83259C2semidirect
6. C2×#4836C2semidirect
7. #72054C2semidirect
8. #72054C2semidirect
9. #71786C2semidirect
10. #71609C2semidirect
11. #70455C2semidirect
12. #70271C2semidirect
13. #70270C2semidirect
14. #70244C2semidirect
15. #70243C2semidirect
66. C2×#461D3semidirect
147. C3×C4⋊C8D4semidirect
155. #832D4semidirect
387. C4⋊C8#67semidirect
782. C3#25400semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4612
C2×#51742
C2×#51712
#832592
#824162
C2×#48362
#720542
#717862
#716092
#704552
#702712
#702702
#702442
#702432
#254003