Finite Group Databasebeta

← #10846265

Subgroups — #10846265

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
1C2×#5114C211yesmaximal, characteristic, complemented
2C2×#5114C211yesmaximal, characteristic, complemented
3C2×C4×#204C211yesmaximal, characteristic, complemented
4C2×#4696C211yesmaximal, characteristic, complemented
5#73486C211yesmaximal, characteristic, complemented
6#73485C211yesmaximal, characteristic, complemented
7C3×C8×C22⋊C4C211yesmaximal, characteristic, complemented
8#69964C211yesmaximal, characteristic, complemented
9#69961C211yesmaximal, characteristic
10#69774C211yesmaximal, characteristic, complemented
11#69769C211yesmaximal, characteristic, complemented
12#68685C211yesmaximal, characteristic, complemented
13#68673C211yesmaximal, characteristic, complemented
14#68630C211yesmaximal, characteristic, complemented
15#68630C211yesmaximal, characteristic, complemented
16#25411—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×#930C2211yescharacteristic
19C2×#930C2211yescharacteristic
20C2×#924C2211yescharacteristic
21C2×#924C2211yescharacteristic
22C22×Dic12C2211yescharacteristic
23C22×D24C2211yescharacteristic
24C22×#204C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C2×#875C2211yescharacteristic
27C2×#875C2211yescharacteristic
28C2×C4×D12C2211yescharacteristic
29C2×C4×Dic6C2211yescharacteristic
30C2×C3×C22⋊C8C2211yescharacteristic
31C2×C3×C4×C8C2211yescharacteristic
32C2×C3×C4×C8C2211yescharacteristic
33C3×C4×C22⋊C4C2211yescharacteristic
34#5114—24no—
35#5114—24no—
36C2×#821C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#817C2211yescharacteristic
41C2×#817C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×#816C2211yescharacteristic
45C2×#816C2211yescharacteristic
46#4959—21no—
47#4959—21no—
48#4957—21no—
49#4956—21no—
50#4939C2211yescharacteristic
51#4929C2211yescharacteristic
52#4928C2211yescharacteristic
53#4928C2211yescharacteristic
54#4696—24no—
55C4×#204—24no—
56#4676—21no—
57#4675—21no—
58#4669—21no—
59#4667—21no—
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4551C2211yescharacteristic
64C2×#495—31no—
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16—31no—
68#2427—31no—
69#2426—31no—
70#2042—31no—
71#2042—31no—
72#2001—31no—
73#1999—31no—
74#1968—31no—
75#1941—31no—
76#1879—31no—
77#1878—31no—
78C8×C22⋊C4D311yescharacteristic, complemented
79C23×C3×C4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—21no—
82C22×D12C2311yescharacteristic
83C22×D12C2311yescharacteristic
84C22×C4×D3—21no—
85C22×Dic6C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×C3×C8—22no—
88C22×C3×C8—22no—
89C22×C3×C8—22no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C2×C3×C22⋊C4D411yescharacteristic
95C2×C3×C22⋊C4D411yescharacteristic
96C2×C3×C42C2311yescharacteristic
97C2×C3×C42C2311yescharacteristic
98C2×#217—21no—
99C2×#217—21no—
100#930—22no—
101#930—22no—
102#930—41no—
103#930—41no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×C4⋊Dic3C2311yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C2×C4⋊Dic3C2311yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117#924—22no—
118#924—22no—
119#924—41no—
120#924—41no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×C4×Dic3—21no—
127C2×Dic12—22no—
128C2×Dic12—22no—
129C2×Dic12—41no—
130C2×D24—22no—
131C2×D24—22no—
132C2×D24—41no—
133C2×#204—22no—
134C2×#204—22no—
135C2×#204—22no—
136C2×#204—22no—
137C2×#204—22no—
138C2×#204D414yescomplemented
139#875—22no—
140#875—22no—
141#875—41no—
142#875—41no—
143C4×D12—22no—
144C4×D12—41no—
145C4×Dic6—22no—
146C4×Dic6—41no—
147C3×C22⋊C8—22no—
148C3×C4×C8—22no—
149C3×C4×C8—22no—
150C3×#95D411yescharacteristic
151C3×#95D411yescharacteristic
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#821—22no—
157#821—22no—
158#821—22no—
159#821—41no—
160#817—22no—
161#817D414yescomplemented
162#816—22no—
163#816—22no—
164#816—22no—
165#816—41no—
166C22×Q16—31no—
167C22×SD16—31no—
168C22×SD16—31no—
169C22×D8—31no—
170C23×C8C2×D311yescharacteristic
171C2×#124—31no—
172C2×#124—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179#495—64no—
180#465—64no—
181#465—64no—
182C4×SD16—64no—
183C2×#106—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8C2×D311yescharacteristic
194C2×C4×C8C2×D311yescharacteristic
195C2×C4×C8C2×D311yescharacteristic
196#397—61no—
197#396—61no—
198#394—61no—
199#394—61no—
200#391—31no—
201#390—31no—
202#390—61no—
203#389—31no—
204#389—31no—
205#388—61no—
206#386—61no—
207#380—61no—
208C4×C22⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#336C2×D311yescharacteristic
212#336C2×D311yescharacteristic
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C23×D3—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2411yescharacteristic
228C2×#67—42no—
229C2×#67—42no—
230C2×#67—42no—
231C2×#67—42no—
232C2×#67—81no—
233C2×#67—81no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12C2×D412yes—
252C2×C4×D3—42no—
253C2×C4×D3—42no—
254C2×C4×D3—81no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—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×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—44no—
276C2×C3×C8C2×D412yes—
277C2×C3×C8C2×D412yes—
278C2×C3×C8#4112yes—
279C2×C3×C8#4112yes—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—21no—
286#217—42no—
287#217—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—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—81no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3C2×D412yes—
304C4⋊Dic3C2×D412yes—
305Dic3⋊C4—42no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308Dic3⋊C4—81no—
309Dic3⋊C4—81no—
310C4×Dic3—42no—
311Dic12—44no—
312D24—44no—
313#204—28no—
314#204—44no—
315C22×Q8—31no—
316C22×Q8—31no—
317C22×D4—31no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4—61no—
321C23×C4—61no—
322C23×C4C22×D311yescharacteristic
323C2×Q16—62no—
324C2×Q16—62no—
325C2×Q16—121no—
326C2×SD16—34no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×SD16—62no—
330C2×SD16—62no—
331C2×SD16—62no—
332C2×D8—62no—
333C2×D8—62no—
334C2×D8—121no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8C22×D311yescharacteristic
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341C22×C8C22×D311yescharacteristic
342#124—62no—
343#124—62no—
344#124—121no—
345#124—121no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350#121—62no—
351#121—62no—
352#121—121no—
353#121—121no—
354C4×Q8—62no—
355C4×Q8—121no—
356C4×D4—62no—
357C4×D4—121no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
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⋊C4D1211yescharacteristic
379C2×C22⋊C4D1211yescharacteristic
380C2×C42—61no—
381C2×C42C22×D311yescharacteristic
382C2×C42C22×D311yescharacteristic
383#106—34no—
384#106—62no—
385#103—62no—
386#103—62no—
387#103—62no—
388#103—121no—
389#102—62no—
390#102—62no—
391#102—62no—
392#102—121no—
393C22⋊C8—22no—
394C4×C8—22no—
395C4×C8—22no—
396#95—61no—
397#95—61no—
398#95—61no—
399#95—61no—
400#95D1211yescharacteristic
401#95D1211yescharacteristic
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3#13512yes—
409C23×C3C22×D411yescharacteristic
410C22×D3—22no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4#13512yes—
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4H(5,𝔽2)11yescharacteristic
448C2×C3×C4H(5,𝔽2)11yescharacteristic
449#67—84no—
450#67—84no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469D12—22no—
470D12—22no—
471D12—41no—
472D12—41no—
473D12—41no—
474D12—41no—
475D12—41no—
476D12—41no—
477C4×D3—84no—
478Dic6—22no—
479Dic6—22no—
480Dic6—41no—
481Dic6—41no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486C3×C8—22no—
487C3×C8—41no—
488C3×C8—41no—
489C3×C8#12114yes—
490C24—61no—
491C24—61no—
492C24C2×D1211yescharacteristic
493C2×Q8—32no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×D4—32no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4—122no—
521C2×D4—241no—
522C2×D4—241no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—122no—
536C22×C4—122no—
537C22×C4—241no—
538C22×C4C2×D1211yescharacteristic
539C22×C4C2×D1211yescharacteristic
540C22×C4C2×D1211yescharacteristic
541C22×C4C2×D1211yescharacteristic
542C22×C4C2×D1211yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—124no—
545SD16—68no—
546SD16—124no—
547D8—124no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—44no—
557C2×C8#23512yes—
558C2×C8#23512yes—
559C2×C8D3×D412yes—
560C2×C8D3×D412yes—
561C4⋊C4—32no—
562C4⋊C4—32no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—122no—
570C4⋊C4—122no—
571C4⋊C4—122no—
572C4⋊C4—241no—
573C4⋊C4—241no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—122no—
577C22⋊C4—122no—
578C22⋊C4—122no—
579C22⋊C4—122no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—241no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—122no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3#53211yescharacteristic
600C22×C3D4211yescharacteristic
601C22×C3D4211yescharacteristic
602C22×C3C2×#13511yescharacteristic
603C22×C3C2×#13511yescharacteristic
604C22×C3#57711yescharacteristic
605C22×C3#57711yescharacteristic
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—81no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C3×C4—22no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4C2×#12111yescharacteristic
626C3×C4#54011yescharacteristic
627C3×C4#54611yescharacteristic
628C3×C4#55011yescharacteristic
629Dic3—42no—
630Dic3—42no—
631Dic3—42no—
632Dic3—81no—
633Dic3—81no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—62no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23#90412yes—
656C23C22×D1211yescharacteristic
657Q8—62no—
658Q8—62no—
659Q8—121no—
660Q8—121no—
661Q8—121no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665D4—62no—
666D4—62no—
667D4—121no—
668D4—121no—
669D4—121no—
670D4—121no—
671D4—121no—
672D4—121no—
673D4—244no—
674D4—244no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
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—244no—
712C2×C4#90412yes—
713C2×C4C2×#23511yescharacteristic
714C2×C4C2×#23511yescharacteristic
715C2×C4C2×D3×D411yescharacteristic
716C2×C4C2×D3×D411yescharacteristic
717C2×C4#100911yescharacteristic
718C2×C4#100911yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8#88414yes—
723C2×C3—42no—
724C2×C3#242811yescharacteristic
725C2×C3#316811yescharacteristic
726C2×C3#317311yescharacteristic
727C2×C3#328211yescharacteristic
728C2×C3#328211yescharacteristic
729C2×C3#328211yescharacteristic
730C2×C3#328411yescharacteristic
731D3—82no—
732D3—161no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—122no—
741C22—122no—
742C22—122no—
743C22—241no—
744C22—241no—
745C22—241no—
746C22—241no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22#547711yescharacteristic
755C22D4×D1211yescharacteristic
756C22D4×D1211yescharacteristic
757C22C2×#90411yescharacteristic
758C22C2×#90411yescharacteristic
759C22#575111yescharacteristic
760C22#575111yescharacteristic
761C4—22no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—122no—
767C4—122no—
768C4—122no—
769C4—241no—
770C4—241no—
771C4—241no—
772C4C2×#88411yescharacteristic
773C4#553511yescharacteristic
774C4#555011yescharacteristic
775C4#555311yescharacteristic
776C3#2541111yescharacteristic, complemented, Sylow
777C2—42no—
778C2—242no—
779C2—481no—
780C2#7348711yescharacteristic
781C2#7846911yescharacteristic
782C2#7856611yescharacteristic
783C2#7943511yescharacteristic
784C2#7943511yescharacteristic
785C2#7943511yescharacteristic
786C2#7943711yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×C8×C22⋊C4C2
socleC23×C3C22×D4
prime radical#69961C2
hypercenterC8×C22⋊C4D3
hypocenterC3#25411
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#5114C2semidirect
2. C2×#5114C2semidirect
3. C2×C4×#204C2semidirect
4. C2×#4696C2semidirect
5. #73486C2semidirect
6. #73485C2semidirect
7. C3×C8×C22⋊C4C2semidirect
8. #69964C2semidirect
10. #69774C2semidirect
11. #69769C2semidirect
12. #68685C2semidirect
13. #68673C2semidirect
14. #68630C2semidirect
15. #68630C2semidirect
78. C8×C22⋊C4D3semidirect
138. C2×#204D4semidirect
161. #817D4semidirect
776. C3#25411semidirect

Maximal subgroups

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

subgroupindex
C2×#51142
C2×C4×#2042
C2×#46962
#734862
#734852
C3×C8×C22⋊C42
#699642
#699612
#697742
#697692
#686852
#686732
#686302
#254113