Finite Group Databasebeta

← #10799097

Subgroups — #10799097

Order 768.

1678 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
1C22×#914C211yesmaximal, characteristic
2C2×#4881C211yesmaximal, characteristic, complemented
3C2×#4804C211yesmaximal, characteristic, complemented
4C2×D3×#102C211yesmaximal, characteristic, complemented
5C2×#4708C211yesmaximal, characteristic, complemented
6#76482C211yesmaximal, characteristic, complemented
7#76428C211yesmaximal, characteristic, complemented
8C3×#1973C211yesmaximal, characteristic, complemented
9#72049C211yesmaximal, characteristic, complemented
10#70628C211yesmaximal, characteristic, complemented
11#70260C211yesmaximal, characteristic, complemented
12#70191C211yesmaximal, characteristic, complemented
13#69825C211yesmaximal, characteristic, complemented
14#69676C211yesmaximal, characteristic, complemented
15#69647C211yesmaximal, characteristic, complemented
16#21235—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#914—24no—
23C2×#914—24no—
24C2×#914C418yescomplemented
25C22×D24C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#872C2211yescharacteristic
31C2×C3×#107C2211yescharacteristic, complemented
32C2×C3×#103C2211yescharacteristic, complemented
33C2×C3×#102C2211yescharacteristic
34C2×C3×#97C2211yescharacteristic, complemented
35C3×#391C2211yescharacteristic, complemented
36C3×#390C2211yescharacteristic
37#5229C2211yescharacteristic, complemented
38C2×#835C2211yescharacteristic, complemented
39#5221C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic, complemented
43C2×#817C2211yescharacteristic, complemented
44C2×#815C2211yescharacteristic, complemented
45C2×C8×Dic3C2211yescharacteristic, complemented
46#4988C2211yescharacteristic
47#4988C2211yescharacteristic, complemented
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic, complemented
50C2×#808C2211yescharacteristic, complemented
51C2×#807C2211yescharacteristic, complemented
52#4957—22no—
53#4955—22no—
54#4939C2211yescharacteristic
55#4939C2211yescharacteristic, complemented
56C2×C4×C3⋊C8C2211yescharacteristic, complemented
57#4881—24no—
58#4804—24no—
59D3×#102—24no—
60#4708—24no—
61#4667—22no—
62#4665—22no—
63C22×AGL(1,ℤ/8)—31no—
64C2×#428—31no—
65C2×#416—31no—
66C22×#102—31no—
67C2×#405—31no—
68#2311—31no—
69#2309—31no—
70#1973—31no—
71#1973D311yescharacteristic, complemented
72#1972—31no—
73#1972—31no—
74#1970—31no—
75#1970—31no—
76#1968—31no—
77#1968—31no—
78C24×D3—21no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239C2×C414yes—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4C2×C414yes—
94C22×D12—21no—
95C22×D12C2311yescharacteristic
96C22×D12C2311yescharacteristic
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C4×D3C2311yescharacteristic
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16C2×C414yescomplemented
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—22no—
108C2×C3×C42C2311yescharacteristic
109C2×#217—22no—
110C2×#215—22no—
111C2×#215—22no—
112C2×#215C2×C414yescomplemented
113C2×#213—22no—
114C2×#213—22no—
115C2×#213C2×C414yescomplemented
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4—22no—
119C2×(C2×D3)⋊C4—22no—
120C2×(C2×D3)⋊C4—22no—
121C2×(C2×D3)⋊C4D412yes—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4D412yes—
126C2×C4×Dic3—21no—
127C2×C4×Dic3C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130#914—232no—
131C2×D24—22no—
132C2×D24—22no—
133C2×D24C2×C414yescomplemented
134C2×ΓL(1,𝔽25)C2×C414yes—
135C2×ΓL(1,𝔽25)D414yes—
136C2×ΓL(1,𝔽25)D414yes—
137C2×D3×C8—22no—
138C2×D3×C8—22no—
139C2×D3×C8D414yes—
140#892—22no—
141#892—22no—
142D3×C4⋊C4—22no—
143D3×C4⋊C4—22no—
144#872—22no—
145#872—22no—
146C3×#107—22no—
147C3×#103—22no—
148C3×#102—22no—
149C3×#97—22no—
150C3×#95—22no—
151#835—22no—
152#832—22no—
153C3⋊#95—22no—
154#821—22no—
155#821—22no—
156#817—22no—
157#815—22no—
158C8×Dic3—22no—
159#809—22no—
160#809—22no—
161#808—22no—
162#807—22no—
163C4×C3⋊C8—22no—
164C22×#41—31no—
165C23×D4—31no—
166C2×AGL(1,ℤ/8)—38no—
167C2×AGL(1,ℤ/8)—64no—
168C2×AGL(1,ℤ/8)—64no—
169C22×SD16—31no—
170C22×SD16C2×D311yescharacteristic
171C22×D8—31no—
172C22×D8—31no—
173C22×M16—31no—
174C23×C8—31no—
175C2×#117—31no—
176C2×#117—31no—
177C22×C4⋊C4—31no—
178#428—64no—
179C2×#107—31no—
180C2×#107C2×D311yescharacteristic, complemented
181C2×#106—31no—
182C2×#106—31no—
183#416—64no—
184C2×#103—31no—
185C2×#103C2×D311yescharacteristic, complemented
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—64no—
192C2×#102C2×D311yescharacteristic
193#405—64no—
194C2×#97—31no—
195C2×#97C2×D311yescharacteristic, complemented
196C2×C4×C8—31no—
197C2×C4×C8—31no—
198#391—31no—
199#391C2×D311yescharacteristic, complemented
200#390—31no—
201#390—31no—
202#390—31no—
203#390—31no—
204#390—31no—
205#390—62no—
206#390C2×D311yescharacteristic
207#386—62no—
208#380—62no—
209#379—62no—
210C24×C3—21no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3—24no—
214C23×D3—42no—
215C23×D3—42no—
216C23×D3—82no—
217C23×D3—82no—
218C23×D3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C22×C412yes—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4C22×C412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4C2×D412yes—
235C22×C3×C4C2411yescharacteristic
236C2×#67—24no—
237C2×#67—42no—
238C2×#67—42no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×D412yes—
242C22×Dic3C2×D411yescharacteristic
243#239—28no—
244#239—28no—
245#239—44no—
246#239—44no—
247D3×D4—28no—
248D3×D4—28no—
249D3×D4—44no—
250D3×D4—44no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—24no—
260C2×D12—21no—
261C2×D12—21no—
262C2×D12—42no—
263C2×D12—42no—
264C2×D12C22×C412yes—
265C2×D12C22×C412yes—
266C2×C4×D3—24no—
267C2×C4×D3—42no—
268C2×C4×D3—42no—
269C2×C4×D3—42no—
270C2×C4×D3—82no—
271C2×C4×D3C22×C412yes—
272C2×C4×D3C2×D412yes—
273C2×C4×D3C2×D412yes—
274C2×C4×D3C2×D412yes—
275C2×C4×D3#4112yes—
276C2×C4×D3#4112yes—
277C3×SD16—28no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8C22×C412yes—
281C2×C3×C8C2×D412yes—
282C2×C3×C8C2×D412yes—
283C2×C3×C8C2×D412yes—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C22⋊C4—82no—
289C3×C42—21no—
290C3×C42—21no—
291#217—82no—
292#215—28no—
293#213—28no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—82no—
297(C2×D3)⋊C4—82no—
298(C2×D3)⋊C4—82no—
299(C2×D3)⋊C4—82no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304Dic3⋊C4—24no—
305Dic3⋊C4—42no—
306C4×Dic3—21no—
307C4×Dic3—21no—
308C4×Dic3—42no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8C22×C412yes—
312C2×C3⋊C8C2×D412yes—
313C2×C3⋊C8C2×D412yes—
314C2×C3⋊C8C2×D412yes—
315D24—28no—
316ΓL(1,𝔽25)C22⋊C4116yescomplemented
317D3×C8—28no—
318C25—61no—
319C2×#41—34no—
320C2×#41—62no—
321C2×#41—62no—
322C2×#41—62no—
323C2×#41—62no—
324C2×#41—62no—
325C22×Q8C22×D311yescharacteristic
326C22×D4—34no—
327C22×D4—31no—
328C22×D4—31no—
329C22×D4—61no—
330C22×D4—62no—
331C22×D4—62no—
332C22×D4—62no—
333C22×D4—62no—
334C22×D4—62no—
335C22×D4—61no—
336C22×D4C22×D311yescharacteristic
337C23×C4—31no—
338C23×C4—61no—
339C23×C4—61no—
340AGL(1,ℤ/8)—632no—
341C2×SD16—22no—
342C2×SD16—22no—
343C2×SD16—34no—
344C2×SD16—62no—
345C2×SD16—62no—
346C2×SD16C4×D314yescomplemented
347C2×D8—34no—
348C2×D8—34no—
349C2×D8—62no—
350C2×D8—62no—
351C2×D8—62no—
352C2×D8—62no—
353C2×M16—34no—
354C2×M16—34no—
355C2×M16—34no—
356C22×C8—31no—
357C22×C8—31no—
358C22×C8—34no—
359C22×C8—62no—
360C22×C8—62no—
361C22×C8C22×D311yescharacteristic
362C22×C8C22×D311yescharacteristic
363#117—62no—
364#117—62no—
365#117—62no—
366#117—62no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C22⋊C4—22no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—62no—
379C2×C22⋊C4—62no—
380C2×C22⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C42—31no—
384C2×C42—61no—
385C2×C42C22×D311yescharacteristic
386#107—22no—
387#107—62no—
388#106—62no—
389#106—62no—
390#103—22no—
391#103—62no—
392#102—22no—
393#102—62no—
394#102—62no—
395#102—62no—
396#102—62no—
397#102—62no—
398#97—22no—
399#97—62no—
400C4×C8—62no—
401C4×C8—62no—
402#95—22no—
403#95—62no—
404C23×C3—22no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3C22×D411yescharacteristic
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—42no—
419C22×D3—42no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3—48no—
423C22×D3—88no—
424C22×D3—84no—
425C22×D3—84no—
426C22×D3—88no—
427C22×D3C4×D412yes—
428C22×D3#12112yes—
429C22×D3#12712yes—
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—41no—
437C3×D4—41no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4C23×C411yescharacteristic
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C22×D411yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454#67—48no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—42no—
461C2×Dic3—42no—
462C2×Dic3C4×D412yes—
463C2×Dic3#12112yes—
464C2×Dic3#12712yes—
465D12—22no—
466D12—22no—
467D12—22no—
468D12—22no—
469D12—48no—
470D12—41no—
471D12—41no—
472D12—41no—
473D12—41no—
474C4×D3—48no—
475C4×D3—84no—
476C4×D3C2×C22⋊C414yes—
477C4×D3C4×D414yes—
478C4×D3#12114yes—
479C4×D3#12414yes—
480C3×C8—22no—
481C3×C8C2×C22⋊C414yes—
482C3⋊C8—22no—
483C3⋊C8C2×C22⋊C414yes—
484C24—21no—
485C24—31no—
486C24—64no—
487C24—61no—
488C24—61no—
489C24—122no—
490C24—122no—
491C24—242no—
492C24—242no—
493#41—68no—
494#41—68no—
495#41—124no—
496#41—124no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8C2×C4×D312yes—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—32no—
509C2×D4—32no—
510C2×D4—64no—
511C2×D4—68no—
512C2×D4—68no—
513C2×D4—64no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—124no—
525C2×D4—124no—
526C2×D4—122no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4C2×C4×D312yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—31no—
535C22×C4—32no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—32no—
542C22×C4—64no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—122no—
546C22×C4—122no—
547C22×C4—122no—
548C22×C4—242no—
549C22×C4D3×D412yes—
550C22×C4C23×D311yescharacteristic
551SD16—28no—
552SD16—68no—
553D8—68no—
554D8—68no—
555M16—316no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—32no—
559C2×C8—32no—
560C2×C8—32no—
561C2×C8—32no—
562C2×C8—68no—
563C2×C8—61no—
564C2×C8—61no—
565C2×C8C2×C4×D312yes—
566C2×C8D3×D412yes—
567C2×C8D3×D412yes—
568C2×C8D3×D412yes—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—64no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—122no—
579C22⋊C4—64no—
580C22⋊C4—82no—
581C22⋊C4—122no—
582C22⋊C4—242no—
583C22⋊C4—242no—
584C22⋊C4—242no—
585C22⋊C4—242no—
586C22⋊C4—242no—
587C42—21no—
588C42—21no—
589C42—61no—
590C42—61no—
591C42—122no—
592C22×C3—44no—
593C22×C3—42no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—82no—
597C22×C3C2×C4×D411yescharacteristic
598C22×C3C2×#12111yescharacteristic
599C22×C3C2×#12711yescharacteristic
600C22×C3#57612yes—
601C22×C3#57712yes—
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—24no—
605C2×D3—24no—
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—42no—
609C2×D3—42no—
610C2×D3—816no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—82no—
616C2×D3—82no—
617C2×D3#39014yes—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—81no—
621C3×C4—81no—
622C3×C4C22×C22⋊C411yescharacteristic
623C3×C4C2×C4×D411yescharacteristic
624C3×C4C2×#12111yescharacteristic
625C3×C4C2×#12411yescharacteristic
626Dic3—42no—
627Dic3—81no—
628Dic3—81no—
629Dic3#39014yes—
630C23—22no—
631C23—32no—
632C23—32no—
633C23—32no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—128no—
643C23—121no—
644C23—121no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23—122no—
649C23—121no—
650C23—121no—
651C23—248no—
652C23—248no—
653C23—244no—
654C23—244no—
655C23C2×D3×D411yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—41no—
659Q8—41no—
660D4—22no—
661D4—22no—
662D4—41no—
663D4—41no—
664D4—62no—
665D4—62no—
666D4—62no—
667D4—62no—
668D4—128no—
669D4—128no—
670D4—121no—
671D4—121no—
672D4—121no—
673D4—121no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—32no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—34no—
682C2×C4—34no—
683C2×C4—34no—
684C2×C4—34no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—128no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4—244no—
700C2×C4C22×C4×D311yescharacteristic
701C2×C4C2×D3×D411yescharacteristic
702C2×C4C2×D3×D411yescharacteristic
703C2×C4C2×D3×D411yescharacteristic
704C2×C4D3×#4111yescharacteristic
705C2×C4D3×#4111yescharacteristic
706C8—22no—
707C8—34no—
708C8—62no—
709C8D3×C22⋊C414yes—
710C2×C3—82no—
711C2×C3C2×#39011yescharacteristic
712C2×C3#294612yes—
713C2×C3#306212yes—
714C2×C3#315411yescharacteristic
715C2×C3#315511yescharacteristic
716D3—24no—
717D3—82no—
718D3—82no—
719C22—34no—
720C22—42no—
721C22—44no—
722C22—64no—
723C22—64no—
724C22—62no—
725C22—62no—
726C22—82no—
727C22—81no—
728C22—81no—
729C22—122no—
730C22—122no—
731C22—124no—
732C22—124no—
733C22—2416no—
734C22—242no—
735C22—242no—
736C22—241no—
737C22—241no—
738C22—241no—
739C22—241no—
740C22C4×D3×D411yescharacteristic
741C22D3×#12111yescharacteristic
742C22D3×#12711yescharacteristic
743C22#577412yes—
744C22#577812yes—
745C4—34no—
746C4—42no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4—122no—
751C4—241no—
752C4—241no—
753C4C2×D3×C22⋊C411yescharacteristic
754C4C4×D3×D411yescharacteristic
755C4D3×#12111yescharacteristic
756C4D3×#12411yescharacteristic
757C3#2123511yescharacteristic, complemented, Sylow
758C2—64no—
759C2—82no—
760C2—242no—
761C2—242no—
762C2D3×#39011yescharacteristic
763C2#7977512yes—
764C2#8080912yes—
765C2#8184811yescharacteristic
766C2#8187211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1973C2
socleC23×C3C22×D4
prime radicalC22×#914C2
cosocleC22×C3×C4C24
hypercenter#1973D3
hypocenterC3#21235
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1973

Complements

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

NH ≅ G/Ntype
2. C2×#4881C2semidirect
3. C2×#4804C2semidirect
4. C2×D3×#102C2semidirect
5. C2×#4708C2semidirect
6. #76482C2semidirect
7. #76428C2semidirect
8. C3×#1973C2semidirect
9. #72049C2semidirect
10. #70628C2semidirect
11. #70260C2semidirect
12. #70191C2semidirect
13. #69825C2semidirect
14. #69676C2semidirect
15. #69647C2semidirect
24. C2×#914C4semidirect
31. C2×C3×#107C22semidirect
32. C2×C3×#103C22semidirect
34. C2×C3×#97C22semidirect
35. C3×#391C22semidirect
37. #5229C22semidirect
38. C2×#835C22semidirect
42. C2×#821C22semidirect
43. C2×#817C22semidirect
44. C2×#815C22semidirect
45. C2×C8×Dic3C22semidirect
47. #4988C22semidirect
49. C2×#809C22semidirect
50. C2×#808C22semidirect
51. C2×#807C22semidirect
55. #4939C22semidirect
56. C2×C4×C3⋊C8C22semidirect
71. #1973D3semidirect
102. C2×C3×SD16C2×C4semidirect
112. C2×#215C2×C4semidirect
115. C2×#213C2×C4semidirect
133. C2×D24C2×C4semidirect
180. C2×#107C2×D3semidirect
185. C2×#103C2×D3semidirect
195. C2×#97C2×D3semidirect
199. #391C2×D3semidirect
316. ΓL(1,𝔽25)C22⋊C4semidirect
346. C2×SD16C4×D3semidirect
757. C3#21235semidirect

Maximal subgroups

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

subgroupindex
C22×#9142
C2×#48812
C2×#48042
C2×D3×#1022
C2×#47082
#764822
#764282
C3×#19732
#720492
#706282
#702602
#701912
#698252
#696762
#696472
#212353