Finite Group Databasebeta

← #10842575

Subgroups — #10842575

Order 768.

1086 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#5228C211yesmaximal, characteristic, complemented
3C2×#5227C211yesmaximal, characteristic
4C2×#5028C211yesmaximal, characteristic, complemented
5C2×C4×#216C211yesmaximal, characteristic, complemented
6#73485C211yesmaximal, characteristic
7#71633C211yesmaximal, characteristic, complemented
8#71629C211yesmaximal, characteristic, complemented
9#69690C211yesmaximal, characteristic, complemented
10#69689C211yesmaximal, characteristic, complemented
11#69683C211yesmaximal, characteristic, complemented
12#69676C211yesmaximal, characteristic, complemented
13#69526C211yesmaximal, characteristic, complemented
14#69523C211yesmaximal, characteristic
15#69451C211yesmaximal, characteristic, complemented
16#25149—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C22×#215C2211yescharacteristic
23C22×#215C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#875C2211yescharacteristic
27C2×C4×Dic6C2211yescharacteristic
28C3×#391—21no—
29C3×#391—21no—
30C3×#391C2211yescharacteristic
31C3×#391C2211yescharacteristic
32C3×#380—21no—
33C3×#380C2211yescharacteristic
34C3×C4×C22⋊C4—21no—
35C3×C4×C22⋊C4C2211yescharacteristic
36#5228—24no—
37#5227—24no—
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C4×#216—24no—
45#5028—24no—
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4959—21no—
53#4957—21no—
54#4939C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×C4⋊(C3⋊C8)C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4676—21no—
59#4669—21no—
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#464—31no—
65C2×#451—31no—
66C2×#448—31no—
67C2×C4×Q16—31no—
68#2426—31no—
69Q8×C22⋊C4D311yescharacteristic, complemented
70#2068—31no—
71#2035—31no—
72#2033—31no—
73#2015—31no—
74#1968—31no—
75#1923—31no—
76#1880—31no—
77#1878—31no—
78#1865—31no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—21no—
82C22×C3×Q8—22no—
83C22×C3×Q8—22no—
84C22×C3×Q8—41no—
85C22×C3×Q8—41no—
86C22×C3×Q8C2311yescharacteristic
87C22×C3×Q8C2311yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4C2311yescharacteristic
90C22×#67—21no—
91C22×D12C2311yescharacteristic
92C22×Dic6C2311yescharacteristic
93C3×C4×Q8—22no—
94C3×C4×Q8—22no—
95C3×C4×Q8—41no—
96C3×C4×Q8—41no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4D411yescharacteristic
103C2×C3×C22⋊C4D411yescharacteristic
104C2×C3×C42—21no—
105C2×C3×C42—21no—
106C2×C3×C42C2311yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#216—22no—
110C2×#216—22no—
111C2×#216—22no—
112C2×#216—22no—
113C2×#216—41no—
114C2×#216D414yescomplemented
115C2×#215—22no—
116C2×#215—22no—
117C2×#215—22no—
118C2×#215—22no—
119C2×#215—22no—
120C2×#215—41no—
121#930—22no—
122#930—41no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130#924—22no—
131#924—41no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×C4×Dic3—21no—
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140#875—22no—
141#875—41no—
142C4×Dic6—22no—
143C4×Dic6—41no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95D411yescharacteristic
150C3×#95D411yescharacteristic
151#835—22no—
152#835—22no—
153#835—22no—
154#835D414yes—
155C3⋊#95—21no—
156#830—22no—
157#830—22no—
158#810—22no—
159#810—22no—
160#809—22no—
161#809—41no—
162#808—41no—
163#807—22no—
164C4⋊(C3⋊C8)—22no—
165C4×C3⋊C8—22no—
166C23×Q8C2×D311yescharacteristic
167C22×Q16—31no—
168C22×Q16—31no—
169C22×SD16—31no—
170C22×SD16—31no—
171C2×#124—31no—
172C2×C22⋊Q8—31no—
173C2×#121—31no—
174C2×C4×Q8—31no—
175C2×C4×Q8C2×D311yescharacteristic
176C2×C4×Q8C2×D311yescharacteristic
177#464—64no—
178#451—64no—
179#448—64no—
180C4×Q16—64no—
181C2×#107—31no—
182C2×#106—31no—
183C2×C4⋊C8—31no—
184C2×#103—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×C22⋊C8—31no—
193C2×C22⋊C8—31no—
194C2×C4×C8—31no—
195#396—61no—
196#394—61no—
197#391—21no—
198#391—21no—
199#391C2×D311yescharacteristic
200#391C2×D311yescharacteristic
201#390—31no—
202#390—61no—
203#389—31no—
204#388—61no—
205#380—21no—
206#380C2×D311yescharacteristic
207C4×C22⋊C4—21no—
208C4×C22⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#336—31no—
212#336—31no—
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C2×C3×Q8—24no—
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—42no—
225C2×C3×Q8—42no—
226C2×C3×Q8—44no—
227C2×C3×Q8—44no—
228C2×C3×Q8—44no—
229C2×C3×Q8—44no—
230C2×C3×Q8C2×D412yes—
231C2×C3×Q8C2×D412yes—
232C2×C3×Q8#4112yes—
233C2×C3×Q8#4112yes—
234C22×C3×C4—21no—
235C22×C3×C4—24no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—42no—
246C22×C3×C4—42no—
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2411yescharacteristic
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—81no—
256C22×Dic3—21no—
257C22×Dic3—21no—
258C22×Dic3—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6C2×D412yes—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—42no—
276C3×C4⋊C4—42no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—42no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—42no—
285C3×C42—42no—
286#217—42no—
287#216—28no—
288#216—44no—
289#215—44no—
290#215—44no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—81no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302Dic3⋊C4—81no—
303C4×Dic3—42no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8C2×D412yes—
315C2×C3⋊C8C2×D412yes—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—21no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—31no—
322C22×Q8—41no—
323C22×Q8—41no—
324C22×Q8C22×D311yescharacteristic
325C22×Q8C22×D311yescharacteristic
326C22×D4—31no—
327C22×D4—61no—
328C23×C4—21no—
329C23×C4C22×D311yescharacteristic
330C2×Q16—34no—
331C2×Q16—62no—
332C2×Q16—62no—
333C2×Q16—62no—
334C2×Q16—62no—
335C2×Q16—121no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—121no—
342C22×C8—31no—
343C22×C8—31no—
344C22×C8—31no—
345C22×C8—31no—
346#124—62no—
347#124—121no—
348C22⋊Q8—62no—
349C22⋊Q8—121no—
350#121—62no—
351#121—121no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—41no—
355C4×Q8—41no—
356C4×Q8—62no—
357C4×Q8—121no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
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#6711yescharacteristic
375C2×C22⋊C4#6711yescharacteristic
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—61no—
379C2×C42C22×D311yescharacteristic
380C2×C42C22×D311yescharacteristic
381#107—62no—
382#106—121no—
383C4⋊C8—62no—
384#103—34no—
385#103—62no—
386#103—62no—
387#103—62no—
388#103—62no—
389#103—62no—
390#102—62no—
391#102—121no—
392C22⋊C8—62no—
393C22⋊C8—62no—
394C4×C8—62no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—61no—
401#95#6711yescharacteristic
402#95#6711yescharacteristic
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3#13512yes—
410C23×C3C22×D411yescharacteristic
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—22no—
421C3×Q8—22no—
422C3×Q8—22no—
423C3×Q8—48no—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×Q8#12114yes—
427C2×C3×C4—22no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
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—48no—
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—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4#13712yes—
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4H(5,𝔽2)11yescharacteristic
464C2×C3×C4H(5,𝔽2)11yescharacteristic
465#67—84no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475D12—41no—
476D12—41no—
477D12—41no—
478D12—41no—
479Dic6—22no—
480Dic6—22no—
481Dic6—41no—
482Dic6—41no—
483C3⋊C8—22no—
484C3⋊C8—22no—
485C3⋊C8—41no—
486C3⋊C8—41no—
487C24—61no—
488C24C2×#6711yescharacteristic
489C2×Q8—24no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—32no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8#23512yes—
511C2×Q8#23512yes—
512C2×Q8D3×D412yes—
513C2×Q8D3×D412yes—
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—241no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4C2×#6711yescharacteristic
540C22×C4C2×#6711yescharacteristic
541C22×C4C2×#6711yescharacteristic
542C22×C4C2×#6711yescharacteristic
543C22×C4C2×#6711yescharacteristic
544C22×C4C23×D311yescharacteristic
545Q16—68no—
546Q16—124no—
547SD16—124no—
548SD16—124no—
549C2×C8—32no—
550C2×C8—32no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—32no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4—241no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—42no—
577C22⋊C4—122no—
578C22⋊C4—122no—
579C22⋊C4—122no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—241no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—42no—
588C42—42no—
589C42—122no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3#52511yescharacteristic
598C22×C3D4211yescharacteristic
599C22×C3D4211yescharacteristic
600C22×C3C2×#13511yescharacteristic
601C22×C3C2×#13711yescharacteristic
602C22×C3#57711yescharacteristic
603C22×C3#57811yescharacteristic
604C2×D3—81no—
605C2×D3—81no—
606C2×D3—81no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C2×D3—81no—
611C3×C4—24no—
612C3×C4—22no—
613C3×C4—41no—
614C3×C4—42no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—81no—
619C3×C4—81no—
620C3×C4C2×#12111yescharacteristic
621C3×C4#53811yescharacteristic
622C3×C4#54611yescharacteristic
623C3×C4#54611yescharacteristic
624Dic3—42no—
625Dic3—42no—
626Dic3—81no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—121no—
634C23—121no—
635C23—121no—
636C23—121no—
637C23—121no—
638C23—121no—
639C23—121no—
640C23#95012yes—
641C23C22×#6711yescharacteristic
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8—22no—
647Q8—48no—
648Q8—41no—
649Q8—41no—
650Q8—62no—
651Q8—62no—
652Q8—121no—
653Q8—121no—
654Q8#88414yes—
655D4—121no—
656D4—121no—
657D4—121no—
658D4—121no—
659D4—244no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—48no—
679C2×C4—41no—
680C2×C4—41no—
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—41no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4#94212yes—
701C2×C4C2×#23511yescharacteristic
702C2×C4C2×#23511yescharacteristic
703C2×C4C2×D3×D411yescharacteristic
704C2×C4C2×D3×D411yescharacteristic
705C2×C4#100411yescharacteristic
706C2×C4#100411yescharacteristic
707C8—62no—
708C8—62no—
709C8—121no—
710C8—121no—
711C2×C3—42no—
712C2×C3#242411yescharacteristic
713C2×C3#310811yescharacteristic
714C2×C3#312111yescharacteristic
715C2×C3#327011yescharacteristic
716C2×C3#327811yescharacteristic
717C2×C3#328211yescharacteristic
718C2×C3#328511yescharacteristic
719D3—161no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—241no—
728C22—241no—
729C22—241no—
730C22—241no—
731C22—241no—
732C22—241no—
733C22—241no—
734C22#579111yescharacteristic
735C22D4×#6711yescharacteristic
736C22D4×#6711yescharacteristic
737C22C2×#94211yescharacteristic
738C22C2×#95011yescharacteristic
739C22#583711yescharacteristic
740C22#583811yescharacteristic
741C4—22no—
742C4—24no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4—122no—
751C4—122no—
752C4—241no—
753C4C2×#88411yescharacteristic
754C4#549011yescharacteristic
755C4#549011yescharacteristic
756C4#549411yescharacteristic
757C3#2514911yescharacteristic, complemented, Sylow
758C2—42no—
759C2—481no—
760C2#8210911yescharacteristic
761C2#8244311yescharacteristic
762C2#8255211yescharacteristic
763C2#8354511yescharacteristic
764C2#8354911yescharacteristic
765C2#8356511yescharacteristic
766C2#8356611yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×Q8×C22⋊C4C2
socleC23×C3C22×D4
prime radicalC2×#930C22
hypercenterQ8×C22⋊C4D3
hypocenterC3#25149
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×Q8×C22⋊C4C2semidirect
2. C2×#5228C2semidirect
4. C2×#5028C2semidirect
5. C2×C4×#216C2semidirect
7. #71633C2semidirect
8. #71629C2semidirect
9. #69690C2semidirect
10. #69689C2semidirect
11. #69683C2semidirect
12. #69676C2semidirect
13. #69526C2semidirect
15. #69451C2semidirect
69. Q8×C22⋊C4D3semidirect
114. C2×#216D4semidirect
757. C3#25149semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×C22⋊C42
C2×#52282
C2×#52272
C2×#50282
C2×C4×#2162
#734852
#716332
#716292
#696902
#696892
#696832
#696762
#695262
#695232
#694512
#251493