Finite Group Databasebeta

← #10826272

Subgroups — #10826272

Order 768.

1930 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×SD16C211yesmaximal, characteristic, complemented
2C2×Q8×D12C211yesmaximal, characteristic, complemented
3C2×#5170C211yesmaximal, characteristic, complemented
4C2×#4806C211yesmaximal, characteristic, complemented
5C2×#4776C211yesmaximal, characteristic, complemented
6#76436C211yesmaximal, characteristic
7C3×#1880C211yesmaximal, characteristic, complemented
8#71633C211yesmaximal, characteristic, complemented
9#70266C211yesmaximal, characteristic, complemented
10#70205C211yesmaximal, characteristic, complemented
11#69661C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68687C211yesmaximal, characteristic, complemented
15#68668C211yesmaximal, characteristic, complemented
16#23855—31nomaximal, Sylow
17C22×D3×Q8C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic, complemented
19C22×D3×D4C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic, complemented
22C22×#215C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C22×#214C2211yescharacteristic
26C2×D3×SD16—24no—
27C2×D3×SD16—24no—
28C2×D3×SD16—24no—
29C22×#204C2211yescharacteristic
30C22×#204C2211yescharacteristic
31C22×D3×C8C2211yescharacteristic
32Q8×D12—24no—
33Q8×D12—24no—
34C2×#897—21no—
35C2×#897—21no—
36C2×#897C2211yescharacteristic
37C2×#897C2211yescharacteristic, complemented
38C2×#895C2211yescharacteristic
39C2×#882—21no—
40C2×C4×D12—21no—
41C2×C4×D12C2211yescharacteristic
42C2×#869—21no—
43C2×#869C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C2×#835C2211yescharacteristic, complemented
48#5170—24no—
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C2×#816C2211yescharacteristic, complemented
53C2×#816C2211yescharacteristic, complemented
54#4987C2211yescharacteristic
55C2×#810C2211yescharacteristic, complemented
56C2×#810C2211yescharacteristic, complemented
57C2×#809C2211yescharacteristic
58#4961—21no—
59#4960—21no—
60#4955—21no—
61#4939C2211yescharacteristic
62#4806—24no—
63#4776—24no—
64C3×#340C2211yescharacteristic, complemented
65C3×#336C2211yescharacteristic, complemented
66#4529C2211yescharacteristic, complemented
67#4524C2211yescharacteristic, complemented
68C23×SD16—31no—
69C2×D4×Q8—31no—
70C2×#448—31no—
71C2×#448—31no—
72C2×#450—31no—
73#2408—31no—
74#2013—31no—
75#2013—31no—
76#2000—31no—
77#2000—31no—
78#1892—31no—
79#1880—31no—
80#1880D311yescharacteristic, complemented
81#1869—31no—
82#1787—31no—
83C24×D3—21no—
84C22×C3×Q8C2311yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8—22no—
91C2×D3×Q8—22no—
92C2×D3×Q8—22no—
93C2×D3×Q8—22no—
94C2×D3×Q8—22no—
95C2×D3×Q8—41no—
96C2×D3×Q8—41no—
97C2×D3×Q8—41no—
98C2×D3×Q8—41no—
99C2×D3×Q8D414yescomplemented
100C2×D3×D4—22no—
101C2×D3×D4—22no—
102C2×D3×D4—22no—
103C2×D3×D4—22no—
104C2×D3×D4—41no—
105C2×D3×D4—41no—
106C22×D12—21no—
107C22×D12D411yescharacteristic
108C22×D12C2311yescharacteristic
109C22×C4×D3—21no—
110C22×C4×D3—21no—
111C22×C4×D3C2311yescharacteristic
112C22×C4×D3C2311yescharacteristic
113C22×Dic6—21no—
114C22×Dic6—21no—
115C22×Dic6C2311yescharacteristic
116C22×Dic6C2311yescharacteristic
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16D414yescomplemented
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C3×C4×Q8—22no—
123C3×C4×Q8—22no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C42—21no—
130C2×C3×C42C2311yescharacteristic
131C2×#217—21no—
132C2×#215—22no—
133C2×#215—22no—
134C2×#215D414yescomplemented
135#938—22no—
136#938—41no—
137C2×#214—22no—
138C2×#214—22no—
139C2×#214—22no—
140C2×#214—22no—
141C2×#214—22no—
142C2×#214—41no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4—21no—
147C2×(C2×D3)⋊C4—21no—
148C2×(C2×D3)⋊C4—21no—
149C2×(C2×D3)⋊C4D411yescharacteristic
150C2×(C2×D3)⋊C4D411yescharacteristic
151C2×C4⋊Dic3—21no—
152C2×C4⋊Dic3—21no—
153C2×C4⋊Dic3—21no—
154C2×C4⋊Dic3—21no—
155C2×C4⋊Dic3D411yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159D3×SD16—232no—
160C2×#204—22no—
161C2×#204—22no—
162C2×#204—22no—
163C2×#204—22no—
164C2×#204—22no—
165C2×#204—41no—
166C2×D3×C8—22no—
167C2×D3×C8—22no—
168C2×D3×C8—22no—
169#897—28no—
170#897—28no—
171#897—22no—
172#897—22no—
173#897—22no—
174#897D414yescomplemented
175#895—22no—
176#895—41no—
177#882—44no—
178C4×D12—28no—
179C4×D12—22no—
180C4×D12—22no—
181#869—28no—
182#869—22no—
183#869—22no—
184C3×#103—22no—
185C3×#102—22no—
186#835—22no—
187C3⋊#95—21no—
188(C2×D3)⋊C8—22no—
189(C2×D3)⋊C8—22no—
190(C2×D3)⋊C8—22no—
191#816—22no—
192#816—41no—
193#810—22no—
194#810—41no—
195#809—22no—
196C23×Q8—31no—
197C23×Q8—31no—
198C23×D4—31no—
199C22×SD16—31no—
200C22×SD16—31no—
201C22×SD16—31no—
202C22×SD16—31no—
203C22×SD16—31no—
204C22×SD16—64no—
205C22×SD16—64no—
206C22×SD16—64no—
207C22×SD16C2×D311yescharacteristic
208C23×C8—31no—
209D4×Q8—64no—
210D4×Q8—64no—
211C2×C4⋊Q8—31no—
212C2×C4⋊Q8—61no—
213C2×C22⋊Q8—31no—
214C2×C22⋊Q8—31no—
215C2×C22⋊Q8—61no—
216C2×C22⋊Q8—61no—
217C2×#121—31no—
218C2×#121—31no—
219C2×#120—61no—
220C2×C4×Q8C2×D311yescharacteristic, complemented
221C2×C4×D4—31no—
222C2×C4×D4—61no—
223#450—64no—
224#448—64no—
225#448—64no—
226C2×#103—31no—
227C2×#103—31no—
228C2×#103—31no—
229C2×#103—31no—
230C2×#103—31no—
231C2×#103C2×D311yescharacteristic, complemented
232C2×#102—31no—
233C2×#102C2×D311yescharacteristic
234C2×C22⋊C8—31no—
235C2×C22⋊C8—31no—
236C2×C22⋊C8—31no—
237#394—61no—
238#392—61no—
239#390—31no—
240#390C2×D311yescharacteristic
241#380—31no—
242#379—61no—
243#340—31no—
244#340C2×D311yescharacteristic, complemented
245#336—31no—
246#336C2×D311yescharacteristic, complemented
247C24×C3—21no—
248C23×D3—21no—
249C23×D3—42no—
250C23×D3—42no—
251C23×D3—42no—
252C23×D3—42no—
253C23×D3—42no—
254C23×D3—81no—
255C23×D3—81no—
256C23×D3C2×D411yescharacteristic
257C23×D3C2×D411yescharacteristic
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8C2×D412yes—
262C2×C3×Q8C2×D412yes—
263C2×C3×Q8C2×D412yes—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4C2×D412yes—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C2×#67—42no—
277C2×#67—42no—
278C2×#67—42no—
279C2×#67—42no—
280C2×#67—42no—
281C2×#67—81no—
282C22×Dic3—21no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3C2×D411yescharacteristic
286C22×Dic3C2×D411yescharacteristic
287D3×Q8—28no—
288D3×Q8—44no—
289D3×Q8—44no—
290D3×Q8—44no—
291D3×Q8—44no—
292D3×Q8—44no—
293D3×Q8—44no—
294D3×Q8—44no—
295D3×D4—28no—
296D3×D4—44no—
297D3×D4—44no—
298D3×D4—44no—
299C2×D12—22no—
300C2×D12—22no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C2×D12—42no—
307C2×D12—42no—
308C2×D12—81no—
309C2×D12SD1614yescomplemented
310C2×D12C2×D412yes—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—24no—
316C2×C4×D3—24no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—42no—
324C2×C4×D3—42no—
325C2×C4×D3—42no—
326C2×C4×D3—42no—
327C2×C4×D3C2×D412yes—
328C2×C4×D3C2×D412yes—
329C2×Dic6—21no—
330C2×Dic6—21no—
331C2×Dic6—21no—
332C2×Dic6—21no—
333C2×Dic6—21no—
334C2×Dic6—21no—
335C2×Dic6—21no—
336C2×Dic6—21no—
337C2×Dic6—24no—
338C2×Dic6—21no—
339C2×Dic6—21no—
340C2×Dic6—24no—
341C2×Dic6—42no—
342C2×Dic6—42no—
343C2×Dic6—42no—
344C2×Dic6—42no—
345C2×Dic6C2×D412yes—
346C2×Dic6C2×D412yes—
347C3×SD16—28no—
348C2×C3×C8—21no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—21no—
352C2×C3×C8—21no—
353C2×C3×C8C2×D412yes—
354C3×C4⋊C4—24no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4C2×D412yes—
359C3×C22⋊C4—42no—
360C3×C22⋊C4—81no—
361C3×C42—24no—
362C3×C42—21no—
363C3×C42—21no—
364#217—42no—
365#215—28no—
366#214—28no—
367#214—44no—
368(C2×D3)⋊C4—24no—
369(C2×D3)⋊C4—22no—
370(C2×D3)⋊C4—24no—
371(C2×D3)⋊C4—22no—
372(C2×D3)⋊C4—42no—
373(C2×D3)⋊C4—42no—
374(C2×D3)⋊C4—42no—
375(C2×D3)⋊C4—81no—
376C4⋊Dic3—24no—
377C4⋊Dic3—24no—
378C4⋊Dic3—24no—
379C4⋊Dic3—22no—
380C4⋊Dic3—24no—
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C2×C3⋊C8—21no—
384C2×C3⋊C8—21no—
385C2×C3⋊C8—21no—
386C2×C3⋊C8—21no—
387C2×C3⋊C8—21no—
388C2×C3⋊C8C2×D412yes—
389#204—28no—
390#204—44no—
391D3×C8—28no—
392C25—61no—
393C22×Q8—34no—
394C22×Q8—31no—
395C22×Q8—31no—
396C22×Q8—61no—
397C22×Q8—61no—
398C22×Q8—62no—
399C22×Q8—62no—
400C22×Q8—62no—
401C22×Q8—62no—
402C22×Q8—62no—
403C22×Q8—62no—
404C22×Q8—62no—
405C22×Q8—121no—
406C22×Q8—121no—
407C22×Q8—121no—
408C22×Q8—121no—
409C22×Q8C22×D311yescharacteristic
410C22×D4—31no—
411C22×D4—31no—
412C22×D4—61no—
413C22×D4—62no—
414C22×D4—62no—
415C22×D4—61no—
416C22×D4—62no—
417C22×D4—62no—
418C22×D4—61no—
419C22×D4—121no—
420C22×D4—121no—
421C22×D4C22×D311yescharacteristic
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—61no—
425C23×C4—61no—
426C2×SD16—22no—
427C2×SD16—22no—
428C2×SD16—34no—
429C2×SD16—62no—
430C2×SD16—62no—
431C2×SD16—62no—
432C2×SD16—62no—
433C2×SD16—62no—
434C2×SD16—632no—
435C2×SD16—62no—
436C2×SD16—62no—
437C2×SD16—62no—
438C2×SD16—62no—
439C2×SD16—62no—
440C2×SD16—62no—
441C2×SD16—62no—
442C2×SD16—121no—
443C2×SD16—121no—
444C2×SD16D1214yescomplemented
445C22×C8—31no—
446C22×C8—31no—
447C22×C8—62no—
448C22×C8—62no—
449C22×C8—62no—
450C22×C8C22×D311yescharacteristic
451C22×C8C22×D311yescharacteristic
452C4⋊Q8—62no—
453C4⋊Q8—62no—
454C4⋊Q8—68no—
455C22⋊Q8—34no—
456C22⋊Q8—62no—
457C22⋊Q8—62no—
458C22⋊Q8—68no—
459C22⋊Q8—68no—
460C22⋊Q8—62no—
461#121—62no—
462#121—62no—
463#121—121no—
464#121—121no—
465#120—124no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×D4—62no—
469C4×D4—62no—
470C4×D4—68no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—61no—
475C2×C4⋊C4—61no—
476C2×C4⋊C4—61no—
477C2×C4⋊C4—61no—
478C2×C4⋊C4C22×D311yescharacteristic
479C2×C4⋊C4C22×D311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—31no—
484C2×C22⋊C4—61no—
485C2×C22⋊C4—61no—
486C2×C22⋊C4—61no—
487C2×C22⋊C4—61no—
488C2×C22⋊C4—61no—
489C2×C22⋊C4—61no—
490C2×C22⋊C4—61no—
491C2×C42—21no—
492C2×C42C22×D311yescharacteristic
493#103—22no—
494#103—62no—
495#103—62no—
496#103—62no—
497#103—121no—
498#103—121no—
499#102—22no—
500#102—62no—
501C22⋊C8—62no—
502C22⋊C8—62no—
503C22⋊C8—62no—
504#95—61no—
505C23×C3—22no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—41no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3C22×D411yescharacteristic
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—22no—
524C22×D3—48no—
525C22×D3—41no—
526C22×D3—41no—
527C22×D3—41no—
528C22×D3—41no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—84no—
532C22×D3—84no—
533C22×D3—84no—
534C22×D3—84no—
535C22×D3—84no—
536C22×D3—84no—
537C22×D3#12012yes—
538C22×D3C2×SD1612yes—
539C22×D3C2×SD1612yescomplemented
540C22×D3#13712yes—
541C3×Q8—22no—
542C3×Q8—22no—
543C3×Q8—22no—
544C3×Q8#12014yescomplemented
545C3×D4—22no—
546C3×D4—22no—
547C3×D4—41no—
548C3×D4—41no—
549C2×C3×C4—21no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4C2×SD1612yescomplemented
564C2×C3×C4C22×D411yescharacteristic
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4C22×D411yescharacteristic
567C2×C3×C4C22×D411yescharacteristic
568C2×C3×C4H(5,𝔽2)11yescharacteristic
569C2×C3×C4H(5,𝔽2)11yescharacteristic
570#67—48no—
571#67—84no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—41no—
580C2×Dic3—41no—
581C2×Dic3—41no—
582C2×Dic3—41no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3#12012yes—
587D12—28no—
588D12—22no—
589D12—22no—
590D12—41no—
591D12—41no—
592D12—84no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—22no—
596C4×D3—22no—
597C4×D3—48no—
598C4×D3—48no—
599C4×D3—41no—
600C4×D3—41no—
601C4×D3—41no—
602C4×D3—41no—
603Dic6—22no—
604Dic6—22no—
605Dic6—22no—
606Dic6—22no—
607Dic6—48no—
608Dic6—48no—
609Dic6—41no—
610Dic6—41no—
611Dic6—41no—
612Dic6—41no—
613C3×C8—22no—
614C3×C8—41no—
615C3⋊C8—22no—
616C3⋊C8—41no—
617C24—21no—
618C24—31no—
619C24—31no—
620C24—61no—
621C24—122no—
622C24—122no—
623C24—122no—
624C24—122no—
625C24—122no—
626C24—241no—
627C24—241no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—32no—
632C2×Q8—32no—
633C2×Q8—64no—
634C2×Q8—64no—
635C2×Q8—61no—
636C2×Q8—61no—
637C2×Q8—68no—
638C2×Q8—61no—
639C2×Q8—61no—
640C2×Q8—61no—
641C2×Q8—61no—
642C2×Q8—61no—
643C2×Q8—61no—
644C2×Q8—61no—
645C2×Q8—61no—
646C2×Q8—122no—
647C2×Q8—122no—
648C2×Q8—122no—
649C2×Q8—122no—
650C2×Q8—124no—
651C2×Q8—124no—
652C2×Q8—124no—
653C2×Q8—124no—
654C2×Q8—124no—
655C2×Q8—124no—
656C2×Q8—124no—
657C2×Q8C2×D1212yes—
658C2×Q8D3×D412yes—
659C2×Q8D3×D412yes—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—34no—
666C2×D4—32no—
667C2×D4—62no—
668C2×D4—62no—
669C2×D4—68no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—122no—
676C2×D4—122no—
677C2×D4—122no—
678C2×D4—124no—
679C2×D4—124no—
680C2×D4—124no—
681C2×D4—122no—
682C2×D4—122no—
683C2×D4—122no—
684C2×D4—122no—
685C2×D4—241no—
686C2×D4—241no—
687C2×D4C2×D1212yes—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—31no—
692C22×C4—32no—
693C22×C4—32no—
694C22×C4—31no—
695C22×C4—64no—
696C22×C4—64no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—61no—
708C22×C4—61no—
709C22×C4—61no—
710C22×C4—122no—
711C22×C4—122no—
712C22×C4—122no—
713C22×C4—122no—
714C22×C4D3×D411yescharacteristic
715C22×C4D3×D411yescharacteristic
716C22×C4C23×D311yescharacteristic
717SD16—28no—
718SD16—68no—
719SD16—68no—
720SD16—68no—
721SD16—124no—
722SD16—124no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—32no—
729C2×C8—68no—
730C2×C8—61no—
731C2×C8—61no—
732C2×C8—61no—
733C2×C8—61no—
734C2×C8—61no—
735C2×C8C2×D1212yes—
736C4⋊C4—24no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—62no—
741C4⋊C4—64no—
742C4⋊C4—64no—
743C4⋊C4—64no—
744C4⋊C4—64no—
745C4⋊C4—61no—
746C4⋊C4—61no—
747C4⋊C4D3×D412yes—
748C22⋊C4—42no—
749C22⋊C4—62no—
750C22⋊C4—62no—
751C22⋊C4—64no—
752C22⋊C4—64no—
753C22⋊C4—81no—
754C22⋊C4—122no—
755C22⋊C4—122no—
756C22⋊C4—122no—
757C22⋊C4—122no—
758C22⋊C4—241no—
759C42—24no—
760C42—21no—
761C42—21no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—42no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3C2×#12011yescharacteristic
770C22×C3D4211yescharacteristic
771C22×C3D4211yescharacteristic
772C22×C3C22×SD1611yescharacteristic
773C22×C3C2×#13711yescharacteristic
774C22×C3#57711yescharacteristic
775C22×C3#57711yescharacteristic
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—42no—
790C2×D3—42no—
791C2×D3—42no—
792C2×D3—816no—
793C2×D3—81no—
794C2×D3—81no—
795C2×D3—81no—
796C2×D3—81no—
797C2×D3#44814yescomplemented
798C3×C4—24no—
799C3×C4—22no—
800C3×C4—41no—
801C3×C4—42no—
802C3×C4—81no—
803C3×C4C2×#12011yescharacteristic
804C3×C4#53411yescharacteristic
805C3×C4D4211yescharacteristic
806C3×C4D4211yescharacteristic
807Dic3—22no—
808Dic3—42no—
809Dic3—42no—
810Dic3—41no—
811Dic3—81no—
812C23—22no—
813C23—32no—
814C23—32no—
815C23—32no—
816C23—32no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—62no—
834C23—128no—
835C23—121no—
836C23—121no—
837C23—121no—
838C23—121no—
839C23—121no—
840C23—121no—
841C23—244no—
842C23—244no—
843C23—244no—
844C23—244no—
845C23—244no—
846C23—244no—
847C23C2×D3×D411yescharacteristic
848Q8—22no—
849Q8—22no—
850Q8—22no—
851Q8—62no—
852Q8—62no—
853Q8—62no—
854Q8—62no—
855Q8—128no—
856Q8—128no—
857Q8—121no—
858Q8—121no—
859Q8—121no—
860Q8—121no—
861Q8#88214yescomplemented
862D4—22no—
863D4—22no—
864D4—41no—
865D4—41no—
866D4—68no—
867D4—62no—
868D4—62no—
869D4—128no—
870D4—121no—
871D4—121no—
872D4—244no—
873D4—244no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—32no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—62no—
898C2×C4—62no—
899C2×C4—61no—
900C2×C4—128no—
901C2×C4—128no—
902C2×C4—121no—
903C2×C4—121no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—121no—
911C2×C4—121no—
912C2×C4—121no—
913C2×C4D3×SD1612yescomplemented
914C2×C4C22×D1211yescharacteristic
915C2×C4C2×D3×D411yescharacteristic
916C2×C4C2×D3×D411yescharacteristic
917C2×C4C2×D3×D411yescharacteristic
918C2×C4#100911yescharacteristic
919C2×C4#100911yescharacteristic
920C8—22no—
921C8—41no—
922C8—62no—
923C8—121no—
924C2×C3—82no—
925C2×C3#240311yescharacteristic
926C2×C3C2×#44811yescharacteristic
927C2×C3#301011yescharacteristic
928C2×C3#326611yescharacteristic
929C2×C3#326611yescharacteristic
930C2×C3D4×SD1611yescharacteristic
931C2×C3D4×SD1611yescharacteristic
932D3—24no—
933D3—42no—
934D3—82no—
935C22—34no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—81no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—121no—
953C22—121no—
954C22—121no—
955C22—121no—
956C22—122no—
957C22—122no—
958C22—122no—
959C22—2416no—
960C22—241no—
961C22—241no—
962C22—241no—
963C22—241no—
964C22D4×D1211yescharacteristic
965C22D3×#12011yescharacteristic
966C22#560911yescharacteristic
967C22C2×D3×SD1611yescharacteristic
968C22#577011yescharacteristic
969C22#577511yescharacteristic
970C22D3×#13711yescharacteristic
971C4—24no—
972C4—22no—
973C4—41no—
974C4—42no—
975C4—62no—
976C4—81no—
977C4—121no—
978C4—122no—
979C4—122no—
980C4—241no—
981C4C2×#88211yescharacteristic
982C4D4×D1211yescharacteristic
983C4#560911yescharacteristic
984C4#565311yescharacteristic
985C3#2385511yescharacteristic, complemented, Sylow
986C2—64no—
987C2—82no—
988C2—122no—
989C2—242no—
990C2#7488411yescharacteristic
991C2SD16×D1211yescharacteristic
992C2#7979511yescharacteristic
993C2D3×#44811yescharacteristic
994C2#8008611yescharacteristic
995C2#8040611yescharacteristic
996C2#8062711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
prime radical#76436C2
hypercenter#1880D3
hypocenterC3#23855
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C22×D3×SD16C2semidirect
2. C2×Q8×D12C2semidirect
3. C2×#5170C2semidirect
4. C2×#4806C2semidirect
5. C2×#4776C2semidirect
7. C3×#1880C2semidirect
8. #71633C2semidirect
9. #70266C2semidirect
10. #70205C2semidirect
11. #69661C2semidirect
12. #68887C2semidirect
13. #68882C2semidirect
14. #68687C2semidirect
15. #68668C2semidirect
18. C22×D3×Q8C22semidirect
21. C2×C3×C4×Q8C22semidirect
37. C2×#897C22semidirect
43. C2×#869C22semidirect
44. C2×C3×#103C22semidirect
47. C2×#835C22semidirect
50. C2×(C2×D3)⋊C8C22semidirect
51. C2×(C2×D3)⋊C8C22semidirect
52. C2×#816C22semidirect
53. C2×#816C22semidirect
55. C2×#810C22semidirect
56. C2×#810C22semidirect
64. C3×#340C22semidirect
65. C3×#336C22semidirect
66. #4529C22semidirect
67. #4524C22semidirect
80. #1880D3semidirect
99. C2×D3×Q8D4semidirect
119. C2×C3×SD16D4semidirect
134. C2×#215D4semidirect
174. #897D4semidirect
220. C2×C4×Q8C2×D3semidirect
231. C2×#103C2×D3semidirect
244. #340C2×D3semidirect
246. #336C2×D3semidirect
309. C2×D12SD16semidirect
444. C2×SD16D12semidirect
539. C22×D3C2×SD16semidirect
544. C3×Q8#120semidirect
563. C2×C3×C4C2×SD16semidirect
797. C2×D3#448semidirect
861. Q8#882semidirect
913. C2×C4D3×SD16semidirect
985. C3#23855semidirect

Maximal subgroups

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

subgroupindex
C22×D3×SD162
C2×Q8×D122
C2×#51702
C2×#48062
C2×#47762
#764362
C3×#18802
#716332
#702662
#702052
#696612
#688872
#688822
#686872
#686682
#238553