Finite Group Databasebeta

← #10829293

Subgroups — #10829293

Order 768.

1120 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×#5511C211yesmaximal, characteristic
2C2×#4854C211yesmaximal, characteristic, complemented
3C2×#4853C211yesmaximal, characteristic, complemented
4#73934C211yesmaximal, characteristic
5C3×#1853C211yesmaximal, characteristic, complemented
6#71559C211yesmaximal, characteristic, complemented
7#70582C211yesmaximal, characteristic, complemented
8#70579C211yesmaximal, characteristic, complemented
9#69964C211yesmaximal, characteristic, complemented
10#69917C211yesmaximal, characteristic
11#69526C211yesmaximal, characteristic, complemented
12#68905C211yesmaximal, characteristic, complemented
13#68888C211yesmaximal, characteristic, complemented
14#68878C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24134—31nomaximal, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C2×C4×#67—21no—
19C2×C4×#67C2211yescharacteristic
20C2×#924—21no—
21C2×#924C2211yescharacteristic
22C2×#924C2211yescharacteristic
23C22×Dic12C2211yescharacteristic
24#5511—24no—
25#5511—24no—
26C2×#897C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×#896—21no—
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#889—21no—
31C2×#888C2211yescharacteristic
32C2×#887C2211yescharacteristic
33C2×#887C2211yescharacteristic
34C2×C3×#106C2211yescharacteristic
35C2×C3×#106C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#380C2211yescharacteristic
38C2×#830C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#816C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×#815C2211yescharacteristic
44C2×Dic3⋊C8C2211yescharacteristic
45#4987C2211yescharacteristic
46#4977C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#808C2211yescharacteristic
52#4959—21no—
53#4951—21no—
54#4854—24no—
55#4853—24no—
56#4669—21no—
57#4657—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#554—31no—
65C2×#475—31no—
66C2×#441—31no—
67#2536—31no—
68#2035—31no—
69#2035—31no—
70#2001—31no—
71#2001—31no—
72#1993—31no—
73#1955—31no—
74#1872—31no—
75#1872—31no—
76#1853—31no—
77#1853D311yescharacteristic, complemented
78#1805—31no—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C22×#67D411yescharacteristic
82C22×C4×D3—21no—
83C22×C4×D3C2311yescharacteristic
84C22×Dic6—21no—
85C22×Dic6C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C22⋊C4—21no—
97C2×#217—21no—
98C2×#217—21no—
99C2×#217D411yescharacteristic
100C4×#67—28no—
101C4×#67—22no—
102C4×#67—22no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4D411yescharacteristic
107C2×C4⋊Dic3—21no—
108C2×C4⋊Dic3—21no—
109C2×C4⋊Dic3C2311yescharacteristic
110C2×C4⋊Dic3C2311yescharacteristic
111#924—28no—
112#924—22no—
113#924—22no—
114#924—22no—
115#924—41no—
116C2×Dic3⋊C4—21no—
117C2×Dic3⋊C4—21no—
118C2×Dic3⋊C4—21no—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4D411yescharacteristic
123C2×C4×Dic3—21no—
124C2×C4×Dic3—21no—
125C2×C4×Dic3C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128C2×Dic12—22no—
129C2×Dic12—22no—
130C2×Dic12—22no—
131#897—22no—
132#897—22no—
133#897—22no—
134#897—41no—
135#896—28no—
136D3×C4⋊C4—22no—
137D3×C4⋊C4—22no—
138#889—28no—
139#888—22no—
140#888D414yes—
141#887—22no—
142#887—22no—
143#887—22no—
144#887D414yes—
145C3×#106—22no—
146C3×#106—22no—
147C3×C22⋊C8—22no—
148C3×#95—21no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152#830—41no—
153(C2×D3)⋊C8—22no—
154(C2×D3)⋊C8—41no—
155#816—22no—
156#816—41no—
157#815—22no—
158Dic3⋊C8—22no—
159#810—22no—
160#810—22no—
161#810—22no—
162#810—41no—
163#808—22no—
164C22×Q16—31no—
165#554—64no—
166#554—64no—
167C2×C4⋊Q8—31no—
168C2×#125—61no—
169C2×C22⋊Q8—31no—
170C2×C22⋊Q8—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—61no—
174C2×C22⋊Q8—61no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4C2×D311yescharacteristic
181#475—64no—
182#441—64no—
183C2×#106—31no—
184C2×#106C2×D311yescharacteristic
185C2×#106C2×D311yescharacteristic
186C2×C4⋊C8—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×#97—31no—
198#398—61no—
199#394—61no—
200#388—61no—
201#388—61no—
202#382—31no—
203#380—31no—
204#380C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340C2×D311yescharacteristic
210#340C2×D311yescharacteristic
211C24×C3C2×D411yescharacteristic
212C23×D3C2×D411yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—24no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—81no—
225C22×C3×C4—81no—
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2411yescharacteristic
228C2×#67—22no—
229C2×#67—22no—
230C2×#67—22no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—24no—
245C2×C4×D3—81no—
246C2×C4×D3—81no—
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—24no—
258C2×Dic6—81no—
259C2×Dic6—81no—
260C2×Dic6C2×D412yes—
261C2×Dic6#4112yes—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8#4112yes—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4C2×D412yes—
276C3×C4⋊C4C2×D412yes—
277C3×C22⋊C4—42no—
278#217—24no—
279#217—22no—
280#217—42no—
281(C2×D3)⋊C4—24no—
282(C2×D3)⋊C4—22no—
283(C2×D3)⋊C4—42no—
284(C2×D3)⋊C4—42no—
285C4⋊Dic3—24no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—42no—
290C4⋊Dic3C2×D412yes—
291Dic3⋊C4—24no—
292Dic3⋊C4—24no—
293Dic3⋊C4—24no—
294Dic3⋊C4—24no—
295Dic3⋊C4—22no—
296Dic3⋊C4—42no—
297Dic3⋊C4—42no—
298C4×Dic3—24no—
299C4×Dic3—42no—
300C4×Dic3C2×D412yes—
301C4×Dic3C2×D412yes—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308Dic12—28no—
309C22×Q8—31no—
310C22×Q8—31no—
311C22×Q8—61no—
312C22×D4—31no—
313C23×C4—21no—
314C23×C4—31no—
315C23×C4—61no—
316C23×C4C22×D311yescharacteristic
317C2×Q16—62no—
318C2×Q16—62no—
319C2×Q16—62no—
320C22×C8—31no—
321C22×C8—31no—
322C22×C8C22×D311yescharacteristic
323C22×C8C22×D311yescharacteristic
324C4⋊Q8—34no—
325C4⋊Q8—62no—
326#125—68no—
327C22⋊Q8—62no—
328C22⋊Q8—68no—
329C22⋊Q8—62no—
330C22⋊Q8—62no—
331C22⋊Q8—68no—
332C22⋊Q8—62no—
333C22⋊Q8—62no—
334C22⋊Q8—62no—
335C22⋊Q8—121no—
336C22⋊Q8—121no—
337C4×Q8—34no—
338C4×Q8—62no—
339C4×Q8—62no—
340C4×Q8—62no—
341C4×D4—62no—
342C4×D4—62no—
343C4×D4—68no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—62no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—62no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4C22×D311yescharacteristic
361C2×C4⋊C4C22×D311yescharacteristic
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C42—31no—
373C2×C42—61no—
374C2×C42—61no—
375#106—22no—
376#106—22no—
377#106—62no—
378C4⋊C8—62no—
379#103—62no—
380#103—62no—
381#103—62no—
382#103—62no—
383#103—121no—
384#103—121no—
385C22⋊C8—22no—
386C22⋊C8—62no—
387C22⋊C8—121no—
388C22⋊C8—121no—
389#97—62no—
390#95—21no—
391#95—61no—
392#95—61no—
393#95—61no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3#13712yes—
401C23×C3C22×D411yescharacteristic
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3#13712yes—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
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—84no—
429C2×C3×C4C22×D411yescharacteristic
430C2×C3×C4C22×D411yescharacteristic
431C2×C3×C4C2×#4111yescharacteristic
432C2×C3×C4C2×#4111yescharacteristic
433C2×C3×C4H(5,𝔽2)11yescharacteristic
434C2×C3×C42−1+411yescharacteristic
435#67—28no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3#12012yes—
456C2×Dic3#12012yes—
457C4×D3—41no—
458C4×D3—41no—
459C4×D3—41no—
460C4×D3—41no—
461C4×D3—84no—
462Dic6—22no—
463Dic6—22no—
464Dic6—22no—
465Dic6—22no—
466Dic6—41no—
467Dic6—41no—
468Dic6—41no—
469Dic6—41no—
470Dic6—84no—
471C3×C8—22no—
472C3×C8—41no—
473C3⋊C8—41no—
474C3⋊C8—41no—
475C24—31no—
476C24D3×D411yescharacteristic
477C2×Q8—32no—
478C2×Q8—32no—
479C2×Q8—64no—
480C2×Q8—61no—
481C2×Q8—61no—
482C2×Q8—61no—
483C2×Q8—61no—
484C2×Q8—61no—
485C2×Q8—61no—
486C2×Q8—61no—
487C2×Q8—61no—
488C2×Q8—61no—
489C2×Q8—61no—
490C2×Q8—241no—
491C2×Q8—241no—
492C2×D4—62no—
493C2×D4—62no—
494C2×D4—62no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—64no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—241no—
523C22×C4—241no—
524C22×C4D3×D411yescharacteristic
525C22×C4C23×D311yescharacteristic
526Q16—68no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8#23512yes—
539C4⋊C4—24no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—32no—
547C4⋊C4—62no—
548C4⋊C4—64no—
549C4⋊C4—64no—
550C4⋊C4—64no—
551C4⋊C4—64no—
552C4⋊C4—64no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—122no—
557C4⋊C4—122no—
558C4⋊C4—122no—
559C4⋊C4D3×D412yes—
560C4⋊C4D3×D412yes—
561C22⋊C4—42no—
562C22⋊C4—62no—
563C22⋊C4—64no—
564C22⋊C4—62no—
565C22⋊C4—64no—
566C22⋊C4—122no—
567C22⋊C4—122no—
568C22⋊C4—122no—
569C42—32no—
570C42—32no—
571C42—64no—
572C42—122no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3C2×#12011yescharacteristic
581C22×C3#54611yescharacteristic
582C22×C3#54711yescharacteristic
583C22×C3C2×#13711yescharacteristic
584C22×C3C2×#13711yescharacteristic
585C22×C3#57711yescharacteristic
586C22×C3#57711yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—41no—
595C3×C4—42no—
596C3×C4—42no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4#52511yescharacteristic
600C3×C4#53711yescharacteristic
601C3×C4#54811yescharacteristic
602C3×C4#55011yescharacteristic
603Dic3—22no—
604Dic3—22no—
605Dic3—42no—
606Dic3—42no—
607Dic3—41no—
608Dic3—42no—
609Dic3—81no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—32no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23#91512yes—
624C23C2×D3×D411yescharacteristic
625Q8—62no—
626Q8—62no—
627Q8—62no—
628Q8—62no—
629Q8—121no—
630Q8—121no—
631Q8—121no—
632Q8—121no—
633Q8—244no—
634D4—68no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—41no—
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—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—62no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—84no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—244no—
681C2×C4C2×#23511yescharacteristic
682C2×C4C2×D3×D411yescharacteristic
683C2×C4C2×D3×D411yescharacteristic
684C2×C4#100711yescharacteristic
685C2×C4D3×#4111yescharacteristic
686C2×C4#100911yescharacteristic
687C8—22no—
688C8—41no—
689C8—121no—
690C8—121no—
691C2×C3—42no—
692C2×C3#240711yescharacteristic
693C2×C3#300411yescharacteristic
694C2×C3#300911yescharacteristic
695C2×C3#331611yescharacteristic
696C2×C3#331611yescharacteristic
697C2×C3#334411yescharacteristic
698C2×C3#334411yescharacteristic
699D3—42no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—62no—
708C22—62no—
709C22—62no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22#550711yescharacteristic
715C22D3×#12011yescharacteristic
716C22#565411yescharacteristic
717C22C2×#91511yescharacteristic
718C22#576211yescharacteristic
719C22#577511yescharacteristic
720C22D3×#13711yescharacteristic
721C4—42no—
722C4—42no—
723C4—41no—
724C4—62no—
725C4—62no—
726C4—81no—
727C4—81no—
728C4—122no—
729C4—121no—
730C4—122no—
731C4—122no—
732C4—241no—
733C4#554711yescharacteristic
734C4#555311yescharacteristic
735C4#562911yescharacteristic
736C4#563311yescharacteristic
737C3#2413411yescharacteristic, complemented, Sylow
738C2—42no—
739C2—122no—
740C2#7440411yescharacteristic
741C2#7912611yescharacteristic
742C2#7922411yescharacteristic
743C2#8003911yescharacteristic
744C2#8014811yescharacteristic
745C2#8134611yescharacteristic
746C2#8143311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1853C2
socleC23×C3C22×D4
prime radicalC22×#67D4
hypercenter#1853D3
hypocenterC3#24134
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×#4854C2semidirect
3. C2×#4853C2semidirect
5. C3×#1853C2semidirect
6. #71559C2semidirect
7. #70582C2semidirect
8. #70579C2semidirect
9. #69964C2semidirect
11. #69526C2semidirect
12. #68905C2semidirect
13. #68888C2semidirect
14. #68878C2semidirect
15. #68806C2semidirect
77. #1853D3semidirect
737. C3#24134semidirect

Maximal subgroups

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

subgroupindex
C2×#55112
C2×#48542
C2×#48532
#739342
C3×#18532
#715592
#705822
#705792
#699642
#699172
#695262
#689052
#688882
#688782
#688062
#241343