Finite Group Databasebeta

← #10845969

Subgroups — #10845969

Order 768.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82998C211yesmaximal, characteristic
2C2×#5054C211yesmaximal, characteristic, complemented
3C2×#4813C211yesmaximal, characteristic, complemented
4C2×#4778C211yesmaximal, characteristic, complemented
5C2×C8×D12C211yesmaximal, characteristic, complemented
6#74240C211yesmaximal, characteristic, complemented
7C3×#1958C211yesmaximal, characteristic, complemented
8#70274C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic, complemented
10#70270C211yesmaximal, characteristic, complemented
11#70206C211yesmaximal, characteristic, complemented
12#70205C211yesmaximal, characteristic, complemented
13#70202C211yesmaximal, characteristic, complemented
14C4×#816C211yesmaximal, characteristic, complemented
15#69540C211yesmaximal, characteristic, complemented
16#25389—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C22×D3×C8C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26C2×#897C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×C4×D12C2211yescharacteristic
29C2×C4×Dic6C2211yescharacteristic
30C2×C3×#103C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×C4×C8C2211yescharacteristic
35C3×#382C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×#816C2211yescharacteristic
41C2×#816C2211yescharacteristic
42#5054—24no—
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45C2×#808C2211yescharacteristic
46C2×#807C2211yescharacteristic
47#4960—21no—
48#4957—21no—
49#4957—21no—
50#4949—21no—
51C4×C4⋊Dic3C2211yescharacteristic
52C2×C4⋊(C3⋊C8)C2211yescharacteristic
53#4813—24no—
54#4778—24no—
55C8×D12—24no—
56#4672—21no—
57#4670—21no—
58#4670—21no—
59#4661—21no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#467—31no—
65C2×#465—31no—
66C2×#464—31no—
67C2×C8×D4—31no—
68#2540—31no—
69#2536—31no—
70#2035—31no—
71#2033—31no—
72#2001—31no—
73#2000—31no—
74#1958D311yescharacteristic, complemented
75#1949—31no—
76#1893—31no—
77#1892—31no—
78C4×#103—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C22×#67—21no—
83C22×D12D411yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×#124—22no—
90C3×#124—22no—
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C22⋊C4—21no—
94C2×C3×C22⋊C4—21no—
95C2×C3×C42C2311yescharacteristic
96C2×#217—21no—
97C2×#217—21no—
98#946—22no—
99#946—22no—
100#946—41no—
101#946—41no—
102C2×#216—22no—
103C2×#216—22no—
104C2×#216—41no—
105#938—22no—
106#938—22no—
107#938—41no—
108#938—41no—
109C2×#214—22no—
110C2×#214—22no—
111C2×#214—41no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4D411yescharacteristic
119C2×(C2×D3)⋊C4D411yescharacteristic
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3D411yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3—21no—
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C2×D3×C8—22no—
134C2×D3×C8—22no—
135C2×D3×C8—22no—
136C2×D3×C8—22no—
137C2×D3×C8—41no—
138C2×D3×C8—41no—
139#897—22no—
140#897—22no—
141#897—41no—
142#897—41no—
143C4×D12—22no—
144C4×D12—22no—
145C4×Dic6—22no—
146C4×Dic6—22no—
147C3×#103—22no—
148C3×#103—41no—
149C3×#102—22no—
150C3×#102—41no—
151C3×C4×C8—22no—
152C3×#95—21no—
153C3×#95—21no—
154#835—22no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—22no—
161#816—22no—
162#816D414yescomplemented
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166C22×Q16—31no—
167C22×SD16—31no—
168C23×C8—31no—
169C23×C8—31no—
170C2×#124C2×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×Q8—31no—
178C2×C4×D4—31no—
179#467—64no—
180#465—64no—
181#464—64no—
182C8×D4—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102C2×D311yescharacteristic
193C2×#102C2×D311yescharacteristic
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8C2×D311yescharacteristic
197#399—61no—
198#398—61no—
199#394—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#388—61no—
204#388—61no—
205#382C2×D311yescharacteristic
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×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2411yescharacteristic
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C2×#67—81no—
239C2×#67—81no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C2×D12—22no—
247C2×D12—22no—
248C2×D12—22no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6C2×D412yes—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8C2×D412yes—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C42C2×D412yes—
280C3×C42#4112yes—
281#217—42no—
282#217—42no—
283#216—44no—
284#214—44no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293C4⋊Dic3—22no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—42no—
299C4⋊Dic3—42no—
300C4⋊Dic3C2×D412yes—
301C4⋊Dic3#4112yes—
302Dic3⋊C4—42no—
303Dic3⋊C4—42no—
304Dic3⋊C4—42no—
305C4×Dic3—42no—
306C4×Dic3—81no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8C2×D412yes—
312C2×C3⋊C8C2×D412yes—
313D3×C8—44no—
314D3×C8—44no—
315C22×Q8—31no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—61no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—31no—
323C2×Q16—62no—
324C2×Q16—62no—
325C2×Q16—121no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—121no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8—62no—
332C22×C8—62no—
333C22×C8—62no—
334C22×C8—62no—
335C22×C8—121no—
336C22×C8—121no—
337C22×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
339#124—22no—
340#124—22no—
341C22⋊Q8—62no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—121no—
346C22⋊Q8—121no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349#121—62no—
350#121—62no—
351#121—121no—
352#121—121no—
353C4×Q8—62no—
354C4×Q8—62no—
355C4×D4—62no—
356C4×D4—62no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C42—61no—
381C2×C42—61no—
382C2×C42C22×D311yescharacteristic
383#107—62no—
384#106—62no—
385C4⋊C8—34no—
386#103—22no—
387#103—34no—
388#103—41no—
389#103—62no—
390#103—62no—
391#102—22no—
392#102—41no—
393#102—62no—
394C22⋊C8—62no—
395C22⋊C8—62no—
396C4×C8—22no—
397#95—21no—
398#95—21no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3C22×D411yescharacteristic
410C22×D3—21no—
411C22×D3—21no—
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#13512yes—
423C22×D3#13512yes—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4#12112yes—
446C2×C3×C4#12112yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C4H(5,𝔽2)11yescharacteristic
453#67—84no—
454#67—84no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473D12—28no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—41no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—41no—
481C4×D3—41no—
482Dic6—22no—
483Dic6—22no—
484Dic6—41no—
485Dic6—41no—
486C3×C8—22no—
487C3×C8—41no—
488C3⋊C8—22no—
489C3⋊C8—22no—
490C24—21no—
491C24—31no—
492C24—31no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—32no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—62no—
512C2×D4—62no—
513C2×D4—62no—
514C2×D4—122no—
515C2×D4—122no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—241no—
519C2×D4—241no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
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×C4D3×D411yescharacteristic
542C22×C4D3×D411yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—124no—
545SD16—124no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—32no—
552C2×C8—32no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—124no—
558C2×C8—124no—
559C2×C8D3×D412yes—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—32no—
565C4⋊C4—32no—
566C4⋊C4—62no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4—122no—
574C4⋊C4—122no—
575C4⋊C4—122no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—62no—
579C22⋊C4—62no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C42—122no—
589C42—241no—
590C42#23512yes—
591C42D3×D412yes—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3C2×#12111yescharacteristic
600C22×C3D4211yescharacteristic
601C22×C3#54611yescharacteristic
602C22×C3C2×#13511yescharacteristic
603C22×C3C2×#13511yescharacteristic
604C22×C3#57711yescharacteristic
605C22×C3#57811yescharacteristic
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4—81no—
623C3×C4—81no—
624C3×C4—81no—
625C3×C4#53211yescharacteristic
626C3×C4#54011yescharacteristic
627C3×C4D4211yescharacteristic
628C3×C4#55011yescharacteristic
629Dic3—42no—
630Dic3—41no—
631Dic3—41no—
632Dic3—42no—
633Dic3—42no—
634Dic3—81no—
635C23—32no—
636C23—32no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23C2×D3×D411yescharacteristic
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—62no—
662Q8—62no—
663Q8—121no—
664Q8—121no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—68no—
670D4—244no—
671D4—244no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—62no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—61no—
690C2×C4—62no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
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#88412yes—
712C2×C4#88412yes—
713C2×C4C2×#23511yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4C2×D3×D411yescharacteristic
716C2×C4#100411yescharacteristic
717C2×C4D3×#4111yescharacteristic
718C2×C4#100911yescharacteristic
719C8—22no—
720C8—41no—
721C8—62no—
722C8—62no—
723C2×C3—161no—
724C2×C3#242811yescharacteristic
725C2×C3#305011yescharacteristic
726C2×C3#306311yescharacteristic
727C2×C3#328211yescharacteristic
728C2×C3#328511yescharacteristic
729C2×C3#329611yescharacteristic
730C2×C3#330011yescharacteristic
731D3—42no—
732D3—42no—
733C22—62no—
734C22—62no—
735C22—62no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22C2×#88411yescharacteristic
755C22#567611yescharacteristic
756C22#571711yescharacteristic
757C22D3×#13511yescharacteristic
758C22D3×#13511yescharacteristic
759C22#577011yescharacteristic
760C22#577111yescharacteristic
761C4—22no—
762C4—22no—
763C4—81no—
764C4—81no—
765C4—81no—
766C4—121no—
767C4—121no—
768C4—122no—
769C4—122no—
770C4—122no—
771C4—241no—
772C4#554811yescharacteristic
773C4#556211yescharacteristic
774C4#559911yescharacteristic
775C4#560911yescharacteristic
776C3#2538911yescharacteristic, complemented, Sylow
777C2—122no—
778C2—122no—
779C2—161no—
780C2#7644411yescharacteristic
781C2#7883811yescharacteristic
782C2#7884111yescharacteristic
783C2#8165211yescharacteristic
784C2#8165411yescharacteristic
785C2#8183211yescharacteristic
786C2#8183411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1958C2
socleC23×C3C22×D4
prime radical#82998C2
hypercenter#1958D3
hypocenterC3#25389
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. C2×#5054C2semidirect
3. C2×#4813C2semidirect
4. C2×#4778C2semidirect
5. C2×C8×D12C2semidirect
6. #74240C2semidirect
7. C3×#1958C2semidirect
8. #70274C2semidirect
9. #70273C2semidirect
10. #70270C2semidirect
11. #70206C2semidirect
12. #70205C2semidirect
13. #70202C2semidirect
14. C4×#816C2semidirect
15. #69540C2semidirect
74. #1958D3semidirect
162. #816D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
776. C3#25389semidirect

Maximal subgroups

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

subgroupindex
#829982
C2×#50542
C2×#48132
C2×#47782
C2×C8×D122
#742402
C3×#19582
#702742
#702732
#702702
#702062
#702052
#702022
C4×#8162
#695402
#253893