Finite Group Databasebeta

← #10801889

Subgroups — #10801889

Order 768.

1170 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×#4782C211yesmaximal, characteristic
2C2×#4785C211yesmaximal, characteristic, complemented
3C2×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4#76291C211yesmaximal, characteristic, complemented
5#75964C211yesmaximal, characteristic, complemented
6C3×#1934C211yesmaximal, characteristic, complemented
7#70203C211yesmaximal, characteristic, complemented
8#70152C211yesmaximal, characteristic, complemented
9#69768C211yesmaximal, characteristic, complemented
10#69647C211yesmaximal, characteristic, complemented
11#69618C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68870C211yesmaximal, characteristic, complemented
14#68786C211yesmaximal, characteristic, complemented
15#68782C211yesmaximal, characteristic, complemented
16#21538—31nomaximal, Sylow
17C2×#938C2211yescharacteristic
18C2×D4×Dic3C2211yescharacteristic
19C22×#213C2211yescharacteristic
20C22×ΓL(1,𝔽25)C2211yescharacteristic
21C22×ΓL(1,𝔽25)C2211yescharacteristic
22C2×#895C2211yescharacteristic
23C2×#893—21no—
24C2×#893C2211yescharacteristic
25C2×#67⋊C4—21no—
26C2×C42×D3C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×C4×C8C2211yescharacteristic
30C3×#390C2211yescharacteristic
31C3×#389C2211yescharacteristic
32C2×#832C2211yescharacteristic
33C2×#821C2211yescharacteristic
34C2×#821C2211yescharacteristic
35C2×#815C2211yescharacteristic
36C2×#815C2211yescharacteristic
37#4990—21no—
38#4987C2211yescharacteristic
39#4987C2211yescharacteristic
40Dic3×C4⋊C4C2211yescharacteristic
41Dic3×C4⋊C4C2211yescharacteristic
42C2×#809C2211yescharacteristic
43C2×#808C2211yescharacteristic
44C2×#808C2211yescharacteristic
45C2×#807C2211yescharacteristic
46#4956—21no—
47#4945—21no—
48Dic3×C22⋊C4—21no—
49#4939C2211yescharacteristic
50#4928C2211yescharacteristic
51C2×C4×C3⋊C8C2211yescharacteristic
52#4785—24no—
53#4782C418yescomplemented
54C4×ΓL(1,𝔽25)—24no—
55#4666—21no—
56#4665—21no—
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63C2×#469—31no—
64C2×#442—31no—
65C2×C4×M16—31no—
66C4×#121—31no—
67C4×#121—31no—
68#1970—31no—
69#1941—31no—
70#1934—31no—
71#1934D311yescharacteristic, complemented
72#1895—31no—
73#1895—31no—
74#1809—31no—
75#1776—31no—
76#1762—31no—
77#1762—31no—
78C22×C3×D4C2311yescharacteristic
79C22×#67—21no—
80C23×Dic3—21no—
81C22×D12—21no—
82C22×D12C2311yescharacteristic
83C22×C4×D3—21no—
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4C2311yescharacteristic
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C22⋊C4—21no—
94C2×C3×C22⋊C4—21no—
95C2×C3×C42C2311yescharacteristic
96C2×#217—21no—
97C2×#217—21no—
98#938—22no—
99#938C2×C414yescomplemented
100D4×Dic3—22no—
101D4×Dic3—22no—
102C2×#213—22no—
103C2×#213—22no—
104C2×#213C2×C414yescomplemented
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×C4⋊Dic3C2311yescharacteristic
112C2×C4⋊Dic3C2311yescharacteristic
113C2×C4⋊Dic3C2311yescharacteristic
114C2×Dic3⋊C4—21no—
115C2×C4×Dic3—21no—
116C2×C4×Dic3—21no—
117C2×C4×Dic3D411yescharacteristic
118C2×C4×Dic3D411yescharacteristic
119C2×C4×Dic3C2311yescharacteristic
120C22×C3⋊C8C2311yescharacteristic
121C22×C3⋊C8C2311yescharacteristic
122C2×ΓL(1,𝔽25)—22no—
123C2×ΓL(1,𝔽25)—22no—
124C2×ΓL(1,𝔽25)—22no—
125C2×ΓL(1,𝔽25)—22no—
126C2×ΓL(1,𝔽25)—22no—
127C2×ΓL(1,𝔽25)C2×C414yescomplemented
128#895—22no—
129#895C2×C414yescomplemented
130#893—22no—
131#893—22no—
132#893—44no—
133#67⋊C4—44no—
134C42×D3—22no—
135C42×D3—22no—
136C3×#102—22no—
137C3×#102C2×C414yescomplemented
138C3×C4×C8—22no—
139C3×#95—21no—
140#832—22no—
141C3⋊#95—21no—
142C3⋊#95—21no—
143C3⋊#95—21no—
144C3⋊#95—21no—
145C3⋊#95—21no—
146#821—22no—
147#821C2×C414yescomplemented
148#815—22no—
149#815D414yescomplemented
150#809—22no—
151#808—22no—
152#808C2×C414yescomplemented
153#807—22no—
154C4×C3⋊C8—22no—
155C22×D8—31no—
156C22×M16—31no—
157C22×M16—31no—
158C2×#121—31no—
159C2×#121—31no—
160C2×C4×D4—31no—
161C2×C4×D4—31no—
162C2×C4×D4—61no—
163C2×C4×D4—61no—
164C22×C42—31no—
165#469—38no—
166#442—64no—
167C2×#107—31no—
168C2×#106—31no—
169C2×#106—31no—
170C2×#102—31no—
171C2×#102—31no—
172C2×#102—31no—
173C2×#102—31no—
174C2×#102C2×D311yescharacteristic
175C2×#102C2×D311yescharacteristic
176C4×M16—64no—
177C2×#97—31no—
178C2×#97—31no—
179C2×C4×C8—31no—
180C2×C4×C8C2×D311yescharacteristic
181#390—31no—
182#390C2×D311yescharacteristic
183#389—31no—
184#389C2×D311yescharacteristic
185#388—61no—
186#388—61no—
187#386—61no—
188#386—61no—
189#380—31no—
190#380—31no—
191C4×C4⋊C4—31no—
192C4×C4⋊C4—31no—
193C4×C22⋊C4—61no—
194C4×C22⋊C4—61no—
195#340—31no—
196#340—31no—
197#340—31no—
198#340—31no—
199#340C2×D311yescharacteristic
200#340C2×D311yescharacteristic
201C24×C3—21no—
202C23×D3—21no—
203C23×D3C2×D411yescharacteristic
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4C22×C412yes—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4C2×D411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2411yescharacteristic
216C2×#67—24no—
217C2×#67—42no—
218C2×#67—42no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—42no—
223C22×Dic3—42no—
224C22×Dic3—42no—
225C22×Dic3C2×D411yescharacteristic
226C22×Dic3C2×D411yescharacteristic
227C22×Dic3C2×D411yescharacteristic
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—24no—
233C2×D12—21no—
234C2×D12—42no—
235C2×D12—42no—
236C2×D12C22×C412yes—
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—22no—
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3—22no—
245C2×C4×D3—41no—
246C2×C4×D3—41no—
247C2×C4×D3—42no—
248C2×C4×D3—42no—
249C2×C4×D3—42no—
250C2×C4×D3C22×C412yes—
251C2×C4×D3#4112yes—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8C22×C412yes—
257C2×C3×C8C2×D412yes—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—42no—
264C3×C4⋊C4C22×C412yes—
265C3×C22⋊C4—42no—
266C3×C22⋊C4—42no—
267C3×C42—21no—
268C3×C42—21no—
269#217—24no—
270#217—42no—
271#213—28no—
272(C2×D3)⋊C4—24no—
273(C2×D3)⋊C4—42no—
274(C2×D3)⋊C4—42no—
275(C2×D3)⋊C4—42no—
276(C2×D3)⋊C4—42no—
277(C2×D3)⋊C4—42no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—21no—
283C4⋊Dic3C22×C412yes—
284Dic3⋊C4—42no—
285C4×Dic3—22no—
286C4×Dic3—22no—
287C4×Dic3—42no—
288C4×Dic3—42no—
289C4×Dic3C2×D412yes—
290C4×Dic3#4112yes—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8C22×C412yes—
294C2×C3⋊C8C2×D412yes—
295C2×C3⋊C8#4112yes—
296C2×C3⋊C8#4112yes—
297ΓL(1,𝔽25)—28no—
298ΓL(1,𝔽25)—28no—
299C22×D4—31no—
300C22×D4—61no—
301C22×D4—61no—
302C22×D4C22×D311yescharacteristic
303C23×C4—31no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—61no—
307C23×C4—61no—
308C2×D8—34no—
309C2×D8—62no—
310C2×D8—62no—
311C2×M16—34no—
312C2×M16—62no—
313C2×M16—62no—
314C2×M16—62no—
315C2×M16—62no—
316C2×M16—62no—
317C22×C8—31no—
318C22×C8—31no—
319C22×C8C22×D311yescharacteristic
320C22×C8C22×D311yescharacteristic
321#121—34no—
322#121—34no—
323#121—62no—
324#121—62no—
325C4×D4—62no—
326C4×D4—62no—
327C4×D4—62no—
328C4×D4—62no—
329C4×D4—124no—
330C4×D4—124no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—31no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—61no—
336C2×C4⋊C4C22×D311yescharacteristic
337C2×C4⋊C4C22×D311yescharacteristic
338C2×C4⋊C4C22×D311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—61no—
342C2×C22⋊C4—61no—
343C2×C22⋊C4—61no—
344C2×C22⋊C4—61no—
345C2×C22⋊C4—61no—
346C2×C22⋊C4—61no—
347C2×C22⋊C4—61no—
348C2×C22⋊C4—61no—
349C2×C42—31no—
350C2×C42—31no—
351C2×C42—31no—
352C2×C42—62no—
353C2×C42—62no—
354C2×C42—61no—
355C2×C42—61no—
356C2×C42C22×D311yescharacteristic
357#107—62no—
358#106—34no—
359#106—62no—
360#102—22no—
361#102—34no—
362#102—62no—
363#102—62no—
364#102—62no—
365#102C4×D314yescomplemented
366#97—34no—
367#97—62no—
368C4×C8—22no—
369C4×C8—62no—
370#95—21no—
371#95—61no—
372#95—61no—
373#95—61no—
374#95—61no—
375#95—61no—
376C23×C3—22no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3C22×D411yescharacteristic
384C22×D3—21no—
385C22×D3—21no—
386C22×D3—21no—
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—22no—
391C22×D3—41no—
392C22×D3—41no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3C4×D412yes—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—41no—
401C3×D4—41no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—22no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4AGL(1,ℤ/8)12yes—
416C2×C3×C4AGL(1,ℤ/8)12yes—
417C2×C3×C4C23×C411yescharacteristic
418C2×C3×C4C22×D411yescharacteristic
419C2×C3×C4C2×#4111yescharacteristic
420C2×C3×C4C2×#4111yescharacteristic
421C2×C3×C4C2×#4111yescharacteristic
422C2×C3×C4C2×#4111yescharacteristic
423#67—48no—
424C2×Dic3—21no—
425C2×Dic3—21no—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—84no—
440C2×Dic3C4×D412yes—
441C2×Dic3#12112yes—
442C2×Dic3#12112yes—
443D12—22no—
444D12—22no—
445D12—48no—
446D12—41no—
447D12—41no—
448C4×D3—22no—
449C4×D3—22no—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—44no—
453C4×D3—44no—
454C4×D3—84no—
455C3×C8—22no—
456C3×C8—22no—
457C3⋊C8—22no—
458C3⋊C8C4×D414yescomplemented
459C24—21no—
460C24—31no—
461C24—61no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—32no—
468C2×D4—64no—
469C2×D4—64no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—61no—
473C2×D4—61no—
474C2×D4—61no—
475C2×D4—122no—
476C2×D4—122no—
477C2×D4—122no—
478C2×D4—122no—
479C2×D4C2×C4×D312yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—32no—
488C22×C4—62no—
489C22×C4—62no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—121no—
500C22×C4—121no—
501C22×C4—122no—
502C22×C4—122no—
503C22×C4—122no—
504C22×C4—122no—
505C22×C4—122no—
506C22×C4—122no—
507C22×C4D3×D411yescharacteristic
508C22×C4D3×D411yescharacteristic
509C22×C4C23×D311yescharacteristic
510D8—68no—
511M16—68no—
512M16—68no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—32no—
518C2×C8—32no—
519C2×C8—32no—
520C2×C8—32no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8C2×C4×D312yes—
524C2×C8D3×D412yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—32no—
531C4⋊C4—42no—
532C4⋊C4—61no—
533C4⋊C4—61no—
534C4⋊C4—61no—
535C4⋊C4—61no—
536C4⋊C4—61no—
537C4⋊C4—122no—
538C4⋊C4C2×C4×D312yes—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—64no—
542C22⋊C4—64no—
543C22⋊C4—122no—
544C22⋊C4—122no—
545C22⋊C4—122no—
546C22⋊C4—122no—
547C22⋊C4—122no—
548C22⋊C4—122no—
549C42—21no—
550C42—21no—
551C42—32no—
552C42—32no—
553C42—62no—
554C42—62no—
555C42—122no—
556C42—122no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3—81no—
563C22×C3—81no—
564C22×C3C2×C4×D411yescharacteristic
565C22×C3C2×#12111yescharacteristic
566C22×C3#53211yescharacteristic
567C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
568C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
569C22×C3#57511yescharacteristic
570C22×C3#57511yescharacteristic
571C2×D3—22no—
572C2×D3—22no—
573C2×D3—22no—
574C2×D3—41no—
575C2×D3—41no—
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—42no—
579C2×D3—42no—
580C2×D3—42no—
581C2×D3—81no—
582C2×D3—81no—
583C2×D3—81no—
584C2×D3—81no—
585C3×C4—22no—
586C3×C4—22no—
587C3×C4—42no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4C2×C4×D411yescharacteristic
591C3×C4C4×#4111yescharacteristic
592C3×C4#52511yescharacteristic
593C3×C4#52911yescharacteristic
594Dic3—22no—
595Dic3—22no—
596Dic3—22no—
597Dic3—42no—
598Dic3—81no—
599Dic3—81no—
600C23—22no—
601C23—32no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—61no—
609C23—61no—
610C23—61no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23—62no—
615C23—121no—
616C23—121no—
617C23—121no—
618C23—121no—
619C23—121no—
620C23—121no—
621C23C2×D3×D411yescharacteristic
622D4—22no—
623D4—22no—
624D4—41no—
625D4—41no—
626D4—62no—
627D4—62no—
628D4—128no—
629D4—128no—
630D4—121no—
631D4—121no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—32no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—124no—
660C2×C4—124no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—244no—
670C2×C4—244no—
671C2×C4#91112yes—
672C2×C4#91412yes—
673C2×C4C22×C4×D311yescharacteristic
674C2×C4C2×D3×D411yescharacteristic
675C2×C4D3×#4111yescharacteristic
676C2×C4D3×#4111yescharacteristic
677C2×C4D3×#4111yescharacteristic
678C2×C4D3×#4111yescharacteristic
679C8—22no—
680C8—22no—
681C8—34no—
682C8—62no—
683C2×C3—82no—
684C2×C3C4×#12111yescharacteristic
685C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
686C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
687C2×C3#305511yescharacteristic
688C2×C3#305511yescharacteristic
689C2×C3#318311yescharacteristic
690C2×C3#318411yescharacteristic
691D3—42no—
692D3—82no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—62no—
697C22—62no—
698C22—62no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—121no—
704C22—121no—
705C22—121no—
706C22—121no—
707C22—122no—
708C22—122no—
709C22—122no—
710C22—241no—
711C22—241no—
712C22—241no—
713C22—241no—
714C22C4×D3×D411yescharacteristic
715C22D3×#12111yescharacteristic
716C22#566811yescharacteristic
717C22C2×#91111yescharacteristic
718C22C2×#91411yescharacteristic
719C22#576811yescharacteristic
720C22#576811yescharacteristic
721C4—22no—
722C4—22no—
723C4—42no—
724C4—62no—
725C4—62no—
726C4—62no—
727C4—81no—
728C4—81no—
729C4—122no—
730C4—241no—
731C4—241no—
732C4#552211yescharacteristic
733C4C4×D3×D411yescharacteristic
734C4#565611yescharacteristic
735C4#570611yescharacteristic
736C3#2153811yescharacteristic, complemented, Sylow
737C2—82no—
738C2—122no—
739C2—242no—
740C2#7545211yescharacteristic
741C2C4×#91111yescharacteristic
742C2C4×#91411yescharacteristic
743C2#8065711yescharacteristic
744C2#8071511yescharacteristic
745C2#8156011yescharacteristic
746C2#8163111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1934C2
socleC23×C3C22×D4
prime radicalC2×#4782C2
cosocleC22×C3×C4C24
hypercenter#1934D3
hypocenterC3#21538
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. C2×#4785C2semidirect
3. C2×C4×ΓL(1,𝔽25)C2semidirect
4. #76291C2semidirect
5. #75964C2semidirect
6. C3×#1934C2semidirect
7. #70203C2semidirect
8. #70152C2semidirect
9. #69768C2semidirect
10. #69647C2semidirect
11. #69618C2semidirect
12. #68885C2semidirect
13. #68870C2semidirect
14. #68786C2semidirect
15. #68782C2semidirect
53. #4782C4semidirect
71. #1934D3semidirect
99. #938C2×C4semidirect
104. C2×#213C2×C4semidirect
127. C2×ΓL(1,𝔽25)C2×C4semidirect
129. #895C2×C4semidirect
137. C3×#102C2×C4semidirect
147. #821C2×C4semidirect
149. #815D4semidirect
152. #808C2×C4semidirect
365. #102C4×D3semidirect
458. C3⋊C8C4×D4semidirect
736. C3#21538semidirect

Maximal subgroups

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

subgroupindex
C2×#47822
C2×#47852
C2×C4×ΓL(1,𝔽25)2
#762912
#759642
C3×#19342
#702032
#701522
#697682
#696472
#696182
#688852
#688702
#687862
#687822
#215383