Finite Group Databasebeta

← #10823401

Subgroups — #10823401

Order 768.

1188 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5580C211yesmaximal, characteristic
2C2×C3×C4×Q16C211yesmaximal, characteristic, complemented
3C4×#946C211yesmaximal, characteristic, complemented
4C2×C4×#215C211yesmaximal, characteristic, complemented
5#72072C211yesmaximal, characteristic, complemented
6#72071C211yesmaximal, characteristic, complemented
7C4×#835C211yesmaximal, characteristic, complemented
8#70634C211yesmaximal, characteristic
9#70618C211yesmaximal, characteristic, complemented
10#70279C211yesmaximal, characteristic, complemented
11#70274C211yesmaximal, characteristic, complemented
12#70272C211yesmaximal, characteristic
13#70232C211yesmaximal, characteristic, complemented
14C4×#821C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
16#23572—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C22×#215C2211yescharacteristic
24#5580—24no—
25#5580—24no—
26C2×#898—21no—
27C2×#895C2211yescharacteristic
28C2×#894—21no—
29C2×#890C2211yescharacteristic
30C2×C4×D12—21no—
31C2×C4×D12C2211yescharacteristic
32C2×#872—21no—
33C2×C42×D3C2211yescharacteristic
34C3×C4×Q16—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×C4×C8C2211yescharacteristic
39#5229C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C4×#215—24no—
48#4989—21no—
49#4987C2211yescharacteristic
50#4978—21no—
51#4972C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C4×(C2×D3)⋊C4—21no—
55C4×C4⋊Dic3C2211yescharacteristic
56C4×Dic3⋊C4—21no—
57C2×C4×C3⋊C8C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×C4×Q16D311yescharacteristic, complemented
66C2×C4×SD16—31no—
67C4×C22⋊Q8—31no—
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2026—31no—
73#2015—31no—
74#2001—31no—
75#2000—31no—
76C4×#103—31no—
77C4×#102—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×D12—21no—
82C22×D12C2311yescharacteristic
83C22×C4×D3—21no—
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—22no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C4×Q8—22no—
93C3×C4×Q8—22no—
94C3×C4×Q8—22no—
95C3×C4×Q8D414yes—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C42—21no—
101C2×C3×C42—21no—
102C2×C3×C42C2311yescharacteristic
103#947—22no—
104#947—22no—
105#946—22no—
106#946—22no—
107#946—22no—
108#946—22no—
109C2×#215—22no—
110C2×#215—22no—
111C2×#215—22no—
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)⋊C4—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×C4×Dic3—21no—
128C2×C4×Dic3D411yescharacteristic
129C2×C4×Dic3D411yescharacteristic
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#898—28no—
134#895—22no—
135#895—22no—
136#894—28no—
137#890—22no—
138#890—22no—
139C4×D12—28no—
140C4×D12—22no—
141C4×D12D414yes—
142#872—28no—
143C42×D3—22no—
144C42×D3—22no—
145C3×#107—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×C4×C8—22no—
149#835—22no—
150#835—22no—
151#835—22no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—22no—
158#821—22no—
159(C2×D3)⋊C8—22no—
160(C2×D3)⋊C8—22no—
161#809—22no—
162#808—22no—
163C4×C3⋊C8—22no—
164C22×Q16C2×D311yescharacteristic
165C22×SD16—31no—
166#529—64no—
167#529—64no—
168C2×#126—61no—
169C2×#125—31no—
170C2×#124—31no—
171C2×#123—61no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×C4×Q8C2×D311yescharacteristic
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C2×#117—61no—
180C22×C42—31no—
181C4×Q16—24no—
182C4×SD16—64no—
183C2×#107C2×D311yescharacteristic
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C4×C8—31no—
196C2×C4×C8C2×D311yescharacteristic
197#391—31no—
198#389—31no—
199#387—61no—
200#385—61no—
201#380—31no—
202C4×C4⋊C4—31no—
203C4×C4⋊C4—61no—
204C4×C22⋊C4—61no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C23×D3—21no—
212C23×D3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
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×Q8C2×D412yes—
224C2×C3×Q8#4112yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—24no—
243C2×D12—21no—
244C2×D12—42no—
245C2×D12—42no—
246C2×D12C2×D412yes—
247C2×C4×D3—22no—
248C2×C4×D3—22no—
249C2×C4×D3—22no—
250C2×C4×D3—24no—
251C2×C4×D3—22no—
252C2×C4×D3—22no—
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—41no—
260C2×C4×D3—42no—
261C2×C4×D3—42no—
262C3×Q16—28no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8#4112yes—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4C2×D412yes—
275C3×C42—24no—
276C3×C42—42no—
277C3×C42C2×D412yes—
278C3×C42C2×D412yes—
279#215—28no—
280(C2×D3)⋊C4—24no—
281(C2×D3)⋊C4—24no—
282(C2×D3)⋊C4—24no—
283(C2×D3)⋊C4—24no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—24no—
286(C2×D3)⋊C4—42no—
287C4⋊Dic3—24no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3C2×D412yes—
293C4⋊Dic3#4112yes—
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296Dic3⋊C4—24no—
297Dic3⋊C4—42no—
298C4×Dic3—22no—
299C4×Dic3—22no—
300C4×Dic3—21no—
301C4×Dic3—21no—
302C4×Dic3—42no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8#4112yes—
309C22×Q8C22×D311yescharacteristic
310C22×Q8C22×D311yescharacteristic
311C22×D4—31no—
312C22×D4—61no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—61no—
317C2×Q16—22no—
318C2×Q16—22no—
319C2×Q16—22no—
320C2×SD16—62no—
321C2×SD16—62no—
322C2×SD16—62no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8C22×D311yescharacteristic
326C22×C8C22×D311yescharacteristic
327#126—68no—
328#125—62no—
329#125—62no—
330#124—62no—
331#124—62no—
332#123—68no—
333C22⋊Q8—62no—
334C22⋊Q8—62no—
335C22⋊Q8—62no—
336C22⋊Q8—62no—
337#121—62no—
338#121—62no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8#6714yes—
343C4×D4—34no—
344C4×D4—68no—
345C4×D4—62no—
346#117—68no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C4⋊C4C22×D311yescharacteristic
359C2×C22⋊C4—61no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4—61no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—31no—
371C2×C42—62no—
372C2×C42—62no—
373C2×C42—61no—
374C2×C42C22×D311yescharacteristic
375#107—22no—
376#106—62no—
377#103—22no—
378#103—22no—
379#103—62no—
380#103—62no—
381#103—62no—
382#102—62no—
383#102—62no—
384#102—62no—
385C22⋊C8—62no—
386C22⋊C8—62no—
387C4×C8—22no—
388C4×C8—62no—
389#95—61no—
390#95—61no—
391#95—61no—
392#95—61no—
393#95—61no—
394C23×C3C22×D411yescharacteristic
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—22no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3#13512yes—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4#12012yes—
432C2×C3×C4#12012yes—
433C2×C3×C4#13512yes—
434C2×C3×C4#13712yes—
435C2×C3×C4C22×D411yescharacteristic
436C2×C3×C4C22×D411yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—22no—
445C2×Dic3—21no—
446C2×Dic3—22no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459D12—22no—
460D12—22no—
461D12—48no—
462D12—41no—
463D12—41no—
464C4×D3—44no—
465C4×D3—41no—
466C4×D3—41no—
467C4×D3—41no—
468C4×D3—41no—
469C4×D3—44no—
470C4×D3—48no—
471C3×C8—22no—
472C3×C8—41no—
473C3⋊C8—22no—
474C3⋊C8—41no—
475C24—31no—
476C24—61no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8#23512yes—
488C2×Q8C2×#6712yes—
489C2×D4—32no—
490C2×D4—64no—
491C2×D4—61no—
492C2×D4—61no—
493C2×D4—61no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—122no—
497C2×D4—122no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—31no—
503C22×C4—31no—
504C22×C4—31no—
505C22×C4—62no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—62no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—64no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—121no—
521C22×C4—122no—
522C22×C4—122no—
523C22×C4D3×D411yescharacteristic
524C22×C4D3×D411yescharacteristic
525C22×C4C23×D311yescharacteristic
526Q16—28no—
527SD16—68no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—32no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8#23512yes—
540C4⋊C4—24no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—32no—
545C4⋊C4—32no—
546C4⋊C4—42no—
547C4⋊C4—64no—
548C4⋊C4—64no—
549C4⋊C4—64no—
550C4⋊C4—64no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—122no—
556C4⋊C4C2×#6712yes—
557C22⋊C4—64no—
558C22⋊C4—64no—
559C22⋊C4—64no—
560C22⋊C4—64no—
561C22⋊C4—64no—
562C22⋊C4—64no—
563C22⋊C4—122no—
564C42—24no—
565C42—42no—
566C42—62no—
567C42—62no—
568C42—61no—
569C42—61no—
570C42—122no—
571C42D3×D412yes—
572C42C2×#6712yes—
573C22×C3C2×#12011yescharacteristic
574C22×C3#52511yescharacteristic
575C22×C3#53211yescharacteristic
576C22×C3C2×#13511yescharacteristic
577C22×C3C2×#13511yescharacteristic
578C22×C3C2×#13711yescharacteristic
579C22×C3#57511yescharacteristic
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—22no—
583C2×D3—41no—
584C2×D3—41no—
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—81no—
591C2×D3—81no—
592C2×D3—81no—
593C2×D3—81no—
594C3×C4—22no—
595C3×C4—42no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—81no—
599C3×C4#45214yes—
600C3×C4#52511yescharacteristic
601C3×C4#52511yescharacteristic
602C3×C4#53211yescharacteristic
603C3×C4#53211yescharacteristic
604Dic3—42no—
605Dic3—41no—
606Dic3—41no—
607Dic3—42no—
608Dic3—41no—
609Dic3—81no—
610C23—32no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23—61no—
615C23—61no—
616C23—61no—
617C23—62no—
618C23—121no—
619C23—121no—
620C23—121no—
621C23—121no—
622C23—121no—
623C23—121no—
624C23C2×D3×D411yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—62no—
634D4—62no—
635D4—128no—
636D4—121no—
637D4—121no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—124no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—124no—
669C2×C4—128no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4#91812yes—
678C2×C4#91912yes—
679C2×C4#93712yes—
680C2×C4#93712yes—
681C2×C4C2×#23511yescharacteristic
682C2×C4C2×#23511yescharacteristic
683C2×C4C2×D3×D411yescharacteristic
684C2×C4D3×#4111yescharacteristic
685C2×C4D3×#4111yescharacteristic
686C2×C4C22×#6711yescharacteristic
687C8—22no—
688C8—41no—
689C8—62no—
690C8—121no—
691C2×C3#238811yescharacteristic
692C2×C3C2×#45211yescharacteristic
693C2×C3#300211yescharacteristic
694C2×C3#310211yescharacteristic
695C2×C3#310811yescharacteristic
696C2×C3#316811yescharacteristic
697C2×C3#317211yescharacteristic
698D3—42no—
699D3—82no—
700C22—62no—
701C22—62no—
702C22—62no—
703C22—121no—
704C22—121no—
705C22—121no—
706C22—121no—
707C22—122no—
708C22—122no—
709C22—122no—
710C22—241no—
711C22—241no—
712C22—241no—
713C22—241no—
714C22#554711yescharacteristic
715C22#554811yescharacteristic
716C22C2×#91811yescharacteristic
717C22C2×#91911yescharacteristic
718C22D3×#13511yescharacteristic
719C22#576811yescharacteristic
720C22C2×#93711yescharacteristic
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—81no—
726C4—122no—
727C4—121no—
728C4—122no—
729C4—121no—
730C4—121no—
731C4—241no—
732C4#518714yes—
733C4#554711yescharacteristic
734C4#554811yescharacteristic
735C4#579111yescharacteristic
736C4#583211yescharacteristic
737C3#2357211yescharacteristic, complemented, Sylow
738C2—122no—
739C2—242no—
740C2#7971511yescharacteristic
741C2#7972311yescharacteristic
742C2#7972611yescharacteristic
743C2#7974611yescharacteristic
744C2#8240011yescharacteristic
745C2C2×#518711yescharacteristic
746C2#8391111yescharacteristic
subgroupG/H
centerC22×C4D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C4×Q16C2
socleC23×C3C22×D4
prime radicalC2×#895C22
hypercenterC2×C4×Q16D3
hypocenterC3#23572
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Q16C2semidirect
3. C4×#946C2semidirect
4. C2×C4×#215C2semidirect
5. #72072C2semidirect
6. #72071C2semidirect
7. C4×#835C2semidirect
9. #70618C2semidirect
10. #70279C2semidirect
11. #70274C2semidirect
13. #70232C2semidirect
14. C4×#821C2semidirect
15. C4×(C2×D3)⋊C8C2semidirect
65. C2×C4×Q16D3semidirect
737. C3#23572semidirect

Maximal subgroups

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

subgroupindex
C2×#55802
C2×C3×C4×Q162
C4×#9462
C2×C4×#2152
#720722
#720712
C4×#8352
#706342
#706182
#702792
#702742
#702722
#702322
C4×#8212
C4×(C2×D3)⋊C82
#235723