Finite Group Databasebeta

← C113×#25130 #43293150

Subgroups — C113×#25130 #43293150

Order 28928.

1166 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#448×C113C211yesmaximal, characteristic, complemented
3C2×#435×C113C211yesmaximal, characteristic, complemented
4C22×#103×C113C211yesmaximal, characteristic, complemented
5C113×#2416C211yesmaximal, characteristic
6C113×#2409C211yesmaximal, characteristic, complemented
7C113×#2068C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2036C211yesmaximal, characteristic, complemented
10C113×#2000C211yesmaximal, characteristic, complemented
11C113×#1973C211yesmaximal, characteristic, complemented
12C113×#1935C211yesmaximal, characteristic, complemented
13C113×#1894C211yesmaximal, characteristic, complemented
14C113×#1893C211yesmaximal, characteristic, complemented
15C113×#1852C211yesmaximal, characteristic, complemented
16C23×Q8×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×M16×C113C2211yescharacteristic
20C23×C8×C113C2211yescharacteristic
21C2×C22⋊Q8×C113C2211yescharacteristic
22C2×C22⋊Q8×C113C2211yescharacteristic
23C2×#121×C113—21no—
24C2×#121×C113C2211yescharacteristic
25C2×#121×C113C2211yescharacteristic
26C2×C4×D4×C113C2211yescharacteristic
27C22×C4⋊C4×C113C2211yescharacteristic
28#468×C113—24no—
29#448×C113—24no—
30#435×C113—24no—
31C2×#107×C113C2211yescharacteristic
32C2×#107×C113C2211yescharacteristic
33C2×C4⋊C8×C113C2211yescharacteristic
34C2×#103×C113—24no—
35C2×#103×C113C2211yescharacteristic
36C2×#103×C113C2211yescharacteristic
37C2×#103×C113C2211yescharacteristic
38C2×#103×C113C2211yescharacteristic
39C2×#103×C113C2211yescharacteristic
40C2×#103×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45C2×#97×C113C2211yescharacteristic
46#396×C113—21no—
47#395×C113—21no—
48#394×C113—21no—
49#393×C113—21no—
50#391×C113C2211yescharacteristic
51#391×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic
53#389×C113C2211yescharacteristic
54#386×C113—21no—
55#386×C113—21no—
56#385×C113—21no—
57#380×C113C2211yescharacteristic
58#380×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic
62#340×C113C2211yescharacteristic
63C22×Q8×C113—21no—
64C22×Q8×C113—22no—
65C22×Q8×C113—22no—
66C22×Q8×C113—22no—
67C22×Q8×C113—22no—
68C22×Q8×C113—41no—
69C22×Q8×C113—41no—
70C22×Q8×C113C2311yescharacteristic
71C22×Q8×C113C2311yescharacteristic
72C22×D4×C113—21no—
73C22×D4×C113—21no—
74C22×D4×C113D411yescharacteristic
75C22×D4×C113C2311yescharacteristic
76C23×C4×C113—21no—
77C23×C4×C113—21no—
78C23×C4×C113C2311yescharacteristic
79C23×C4×C113C2311yescharacteristic
80C2×SD16×C113—22no—
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—22no—
84C2×SD16×C113—41no—
85C2×SD16×C113—41no—
86C2×M16×C113—22no—
87C2×M16×C113—22no—
88C2×M16×C113—41no—
89C22×C8×C113—22no—
90C22×C8×C113—22no—
91C22×C8×C113—41no—
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113—41no—
99C22⋊Q8×C113—41no—
100#121×C113—22no—
101#121×C113—22no—
102#121×C113—22no—
103#121×C113—41no—
104#121×C113—44no—
105C4×D4×C113—22no—
106C4×D4×C113—22no—
107C2×C4⋊C4×C113—22no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113—21no—
112C2×C4⋊C4×C113—41no—
113C2×C4⋊C4×C113D411yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113D411yescharacteristic
128C2×C22⋊C4×C113D411yescharacteristic
129C2×C42×C113C2311yescharacteristic
130#107×C113—22no—
131#107×C113—41no—
132C4⋊C8×C113—22no—
133#103×C113—22no—
134#103×C113—22no—
135#103×C113—22no—
136#103×C113—22no—
137#103×C113—22no—
138#103×C113D414yescomplemented
139#102×C113—22no—
140#102×C113—41no—
141C22⋊C8×C113—22no—
142C22⋊C8×C113D414yescomplemented
143#97×C113—22no—
144#95×C113—21no—
145#95×C113—21no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113—21no—
149#95×C113—21no—
150#95×C113—21no—
151C24×C113—21no—
152C24×C113C2×D411yescharacteristic
153C24×C113C2×D411yescharacteristic
154C2×Q8×C113—21no—
155C2×Q8×C113—21no—
156C2×Q8×C113—28no—
157C2×Q8×C113—21no—
158C2×Q8×C113—21no—
159C2×Q8×C113—21no—
160C2×Q8×C113—21no—
161C2×Q8×C113—21no—
162C2×Q8×C113—21no—
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×Q8×C113—42no—
166C2×Q8×C113—42no—
167C2×Q8×C113—44no—
168C2×Q8×C113—44no—
169C2×Q8×C113—44no—
170C2×Q8×C113—42no—
171C2×Q8×C113C2×D412yes—
172C2×Q8×C113#4112yes—
173C2×D4×C113—22no—
174C2×D4×C113—22no—
175C2×D4×C113—22no—
176C2×D4×C113—21no—
177C2×D4×C113—21no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—21no—
181C2×D4×C113—21no—
182C2×D4×C113—42no—
183C2×D4×C113—42no—
184C2×D4×C113—42no—
185C2×D4×C113—42no—
186C2×D4×C113—42no—
187C2×D4×C113—81no—
188C22×C4×C113—21no—
189C22×C4×C113—21no—
190C22×C4×C113—21no—
191C22×C4×C113—21no—
192C22×C4×C113—21no—
193C22×C4×C113—21no—
194C22×C4×C113—21no—
195C22×C4×C113—21no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—42no—
206C22×C4×C113—42no—
207C22×C4×C113—42no—
208C22×C4×C113—42no—
209C22×C4×C113—42no—
210C22×C4×C113—81no—
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D412yes—
216C22×C4×C113#4112yes—
217C22×C4×C113C2411yescharacteristic
218SD16×C113—44no—
219SD16×C113—44no—
220M16×C113—44no—
221C2×C8×C113—21no—
222C2×C8×C113—21no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—44no—
231C2×C8×C113C2×D412yes—
232C2×C8×C113C2×D412yes—
233C2×C8×C113C2×D412yes—
234C4⋊C4×C113—22no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—21no—
243C4⋊C4×C113—21no—
244C4⋊C4×C113—42no—
245C4⋊C4×C113—42no—
246C4⋊C4×C113—42no—
247C4⋊C4×C113—42no—
248C4⋊C4×C113C2×D412yes—
249C22⋊C4×C113—22no—
250C22⋊C4×C113—22no—
251C22⋊C4×C113—42no—
252C22⋊C4×C113—42no—
253C22⋊C4×C113—42no—
254C22⋊C4×C113—42no—
255C22⋊C4×C113—42no—
256C22⋊C4×C113—42no—
257C22⋊C4×C113—42no—
258C22⋊C4×C113—81no—
259C42×C113—21no—
260C42×C113—21no—
261C23×C113—21no—
262C23×C113—21no—
263C23×C113—21no—
264C23×C113—21no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—21no—
272C23×C113—41no—
273C23×C113—41no—
274C23×C113—41no—
275C23×C113—41no—
276C23×C113—41no—
277C23×C113—41no—
278C23×C113—41no—
279C23×C113#12112yes—
280C23×C113AGL(1,ℤ/8)12yes—
281C23×C113#13712yes—
282C23×C113C22×D411yescharacteristic
283Q8×C113—22no—
284Q8×C113—22no—
285Q8×C113—22no—
286Q8×C113—22no—
287Q8×C113—48no—
288Q8×C113—41no—
289Q8×C113—41no—
290Q8×C113—41no—
291Q8×C113—41no—
292D4×C113—44no—
293D4×C113—41no—
294D4×C113—41no—
295D4×C113—41no—
296D4×C113—41no—
297D4×C113—84no—
298D4×C113—84no—
299C2×C4×C113—21no—
300C2×C4×C113—21no—
301C2×C4×C113—22no—
302C2×C4×C113—22no—
303C2×C4×C113—22no—
304C2×C4×C113—22no—
305C2×C4×C113—21no—
306C2×C4×C113—21no—
307C2×C4×C113—21no—
308C2×C4×C113—21no—
309C2×C4×C113—22no—
310C2×C4×C113—22no—
311C2×C4×C113—22no—
312C2×C4×C113—21no—
313C2×C4×C113—21no—
314C2×C4×C113—21no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—48no—
318C2×C4×C113—41no—
319C2×C4×C113—41no—
320C2×C4×C113—41no—
321C2×C4×C113—41no—
322C2×C4×C113—41no—
323C2×C4×C113—41no—
324C2×C4×C113—41no—
325C2×C4×C113—41no—
326C2×C4×C113—41no—
327C2×C4×C113—41no—
328C2×C4×C113—41no—
329C2×C4×C113—41no—
330C2×C4×C113—41no—
331C2×C4×C113—41no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113—41no—
339C2×C4×C113—41no—
340C2×C4×C113—84no—
341C2×C4×C113#12112yes—
342C2×C4×C113C22×D411yescharacteristic
343C2×C4×C113C22×D411yescharacteristic
344C2×C4×C113C2×#4111yescharacteristic
345C2×C4×C113C2×#4111yescharacteristic
346C2×C4×C113H(5,𝔽2)11yescharacteristic
347C2×C4×C113H(5,𝔽2)11yescharacteristic
348C8×C113—22no—
349C8×C113—22no—
350C8×C113—22no—
351C8×C113—41no—
352C22×C113—22no—
353C22×C113—22no—
354C22×C113—22no—
355C22×C113—22no—
356C22×C113—22no—
357C22×C113—22no—
358C22×C113—41no—
359C22×C113—41no—
360C22×C113—41no—
361C22×C113—41no—
362C22×C113—41no—
363C22×C113—41no—
364C22×C113—41no—
365C22×C113—81no—
366C22×C113—81no—
367C22×C113—81no—
368C22×C113—81no—
369C22×C113—81no—
370C22×C113—81no—
371C22×C113—81no—
372C22×C113#46814yescomplemented
373C22×C113C2×#12111yescharacteristic
374C22×C113D4211yescharacteristic
375C22×C113#54611yescharacteristic
376C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C113C2×#13711yescharacteristic
378C22×C113#57711yescharacteristic
379C22×C113#57811yescharacteristic
380C4×C113—22no—
381C4×C113—41no—
382C4×C113—42no—
383C4×C113—42no—
384C4×C113—42no—
385C4×C113—41no—
386C4×C113—41no—
387C4×C113—81no—
388C4×C113—81no—
389C4×C113—81no—
390C4×C113—81no—
391C4×C113#52511yescharacteristic
392C4×C113#53811yescharacteristic
393C4×C113D4211yescharacteristic
394C4×C113#54611yescharacteristic
395#25130C11311yesmaximal, characteristic, direct product factor, Sylow
396C2×C113—24no—
397C2×C113—81no—
398C2×C113—161no—
399C2×C113#242411yescharacteristic
400C2×C113C2×#46811yescharacteristic
401C2×C113#306311yescharacteristic
402C2×C113#326511yescharacteristic
403C2×C113#327011yescharacteristic
404C2×C113#330811yescharacteristic
405C2×C113#332011yescharacteristic
406C2×#468C2×C11311yescharacteristic, complemented
407C2×#448C2×C11311yescharacteristic, complemented
408C2×#435C2×C11311yescharacteristic, complemented
409C22×#103C2×C11311yescharacteristic, complemented
410#2416C2×C11311yescharacteristic
411#2409C2×C11311yescharacteristic, complemented
412#2068C2×C11311yescharacteristic, complemented
413#2055C2×C11311yescharacteristic, complemented
414#2036C2×C11311yescharacteristic, complemented
415#2000C2×C11311yescharacteristic, complemented
416#1973C2×C11311yescharacteristic, complemented
417#1935C2×C11311yescharacteristic, complemented
418#1894C2×C11311yescharacteristic, complemented
419#1893C2×C11311yescharacteristic, complemented
420#1852C2×C11311yescharacteristic, complemented
421C113#2513011yescharacteristic, direct product factor, Sylow
422C23×Q8C22×C11311yescharacteristic
423C22×SD16C22×C11311yescharacteristic
424C22×SD16C22×C11311yescharacteristic
425C22×M16C22×C11311yescharacteristic
426C23×C8C22×C11311yescharacteristic
427C2×C22⋊Q8C22×C11311yescharacteristic
428C2×C22⋊Q8C22×C11311yescharacteristic
429C2×#121—21no—
430C2×#121C22×C11311yescharacteristic
431C2×#121C22×C11311yescharacteristic
432C2×C4×D4C22×C11311yescharacteristic
433C22×C4⋊C4C22×C11311yescharacteristic
434#468—24no—
435#448—24no—
436#435—24no—
437C2×#107C22×C11311yescharacteristic
438C2×#107C22×C11311yescharacteristic
439C2×C4⋊C8C22×C11311yescharacteristic
440C2×#103—24no—
441C2×#103C22×C11311yescharacteristic
442C2×#103C22×C11311yescharacteristic
443C2×#103C22×C11311yescharacteristic
444C2×#103C22×C11311yescharacteristic
445C2×#103C22×C11311yescharacteristic
446C2×#103C22×C11311yescharacteristic
447C2×#102C22×C11311yescharacteristic
448C2×#102C22×C11311yescharacteristic
449C2×C22⋊C8C22×C11311yescharacteristic
450C2×C22⋊C8C22×C11311yescharacteristic
451C2×#97C22×C11311yescharacteristic
452#396—21no—
453#395—21no—
454#394—21no—
455#393—21no—
456#391C22×C11311yescharacteristic
457#391C22×C11311yescharacteristic
458#390C22×C11311yescharacteristic
459#389C22×C11311yescharacteristic
460#386—21no—
461#386—21no—
462#385—21no—
463#380C22×C11311yescharacteristic
464#380C22×C11311yescharacteristic
465#340C22×C11311yescharacteristic
466#340C22×C11311yescharacteristic
467#340C22×C11311yescharacteristic
468#340C22×C11311yescharacteristic
469C22×Q8—21no—
470C22×Q8—22no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—41no—
475C22×Q8—41no—
476C22×Q8C23×C11311yescharacteristic
477C22×Q8C23×C11311yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4D4×C11311yescharacteristic
481C22×D4C23×C11311yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C11311yescharacteristic
485C23×C4C23×C11311yescharacteristic
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—41no—
491C2×SD16—41no—
492C2×M16—22no—
493C2×M16—22no—
494C2×M16—41no—
495C22×C8—22no—
496C22×C8—22no—
497C22×C8—41no—
498C22×C8C23×C11311yescharacteristic
499C22×C8C23×C11311yescharacteristic
500C22×C8C23×C11311yescharacteristic
501C22×C8C23×C11311yescharacteristic
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506#121—22no—
507#121—22no—
508#121—22no—
509#121—41no—
510#121—44no—
511C4×D4—22no—
512C4×D4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4D4×C11311yescharacteristic
520C2×C4⋊C4C23×C11311yescharacteristic
521C2×C4⋊C4C23×C11311yescharacteristic
522C2×C4⋊C4C23×C11311yescharacteristic
523C2×C4⋊C4C23×C11311yescharacteristic
524C2×C4⋊C4C23×C11311yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C11311yescharacteristic
534C2×C22⋊C4D4×C11311yescharacteristic
535C2×C42C23×C11311yescharacteristic
536#107—22no—
537#107—41no—
538C4⋊C8—22no—
539#103—22no—
540#103—22no—
541#103—22no—
542#103—22no—
543#103—22no—
544#103D4×C11314yescomplemented
545#102—22no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8D4×C11314yescomplemented
549#97—22no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24C2×D4×C11311yescharacteristic
559C24C2×D4×C11311yescharacteristic
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—28no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—42no—
577C2×Q8C2×D4×C11312yes—
578C2×Q8#41×C11312yes—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—81no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C11311yescharacteristic
618C22×C4C2×D4×C11311yescharacteristic
619C22×C4C2×D4×C11311yescharacteristic
620C22×C4C2×D4×C11311yescharacteristic
621C22×C4C2×D4×C11312yes—
622C22×C4#41×C11312yes—
623C22×C4C24×C11311yescharacteristic
624SD16—44no—
625SD16—44no—
626M16—44no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—44no—
637C2×C8C2×D4×C11312yes—
638C2×C8C2×D4×C11312yes—
639C2×C8C2×D4×C11312yes—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4C2×D4×C11312yes—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23#121×C11312yes—
686C23AGL(1,ℤ/8)×C11312yes—
687C23#137×C11312yes—
688C23C22×D4×C11311yescharacteristic
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—48no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698D4—44no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—48no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—84no—
747C2×C4#121×C11312yes—
748C2×C4C22×D4×C11311yescharacteristic
749C2×C4C22×D4×C11311yescharacteristic
750C2×C4C2×#41×C11311yescharacteristic
751C2×C4C2×#41×C11311yescharacteristic
752C2×C4H(5,𝔽2)×C11311yescharacteristic
753C2×C4H(5,𝔽2)×C11311yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—41no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22#468×C11314yescomplemented
779C22C2×#121×C11311yescharacteristic
780C22D42×C11311yescharacteristic
781C22#546×C11311yescharacteristic
782C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
783C22C2×#137×C11311yescharacteristic
784C22#577×C11311yescharacteristic
785C22#578×C11311yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4#525×C11311yescharacteristic
798C4#538×C11311yescharacteristic
799C4D42×C11311yescharacteristic
800C4#546×C11311yescharacteristic
801C2—24no—
802C2—81no—
803C2—161no—
804C2C113×#242411yescharacteristic
805C2C2×#468×C11311yescharacteristic
806C2C113×#306311yescharacteristic
807C2C113×#326511yescharacteristic
808C2C113×#327011yescharacteristic
809C2C113×#330811yescharacteristic
810C2C113×#332011yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C113C2semidirect
2. C2×#448×C113C2semidirect
3. C2×#435×C113C2semidirect
4. C22×#103×C113C2semidirect
6. C113×#2409C2semidirect
7. C113×#2068C2semidirect
8. C113×#2055C2semidirect
9. C113×#2036C2semidirect
10. C113×#2000C2semidirect
11. C113×#1973C2semidirect
12. C113×#1935C2semidirect
13. C113×#1894C2semidirect
14. C113×#1893C2semidirect
15. C113×#1852C2semidirect
138. #103×C113D4semidirect
142. C22⋊C8×C113D4semidirect
372. C22×C113#468semidirect
395. #25130C113direct (N × H)
406. C2×#468C2×C113semidirect
407. C2×#448C2×C113semidirect
408. C2×#435C2×C113semidirect
409. C22×#103C2×C113semidirect
411. #2409C2×C113semidirect
412. #2068C2×C113semidirect
413. #2055C2×C113semidirect
414. #2036C2×C113semidirect
415. #2000C2×C113semidirect
416. #1973C2×C113semidirect
417. #1935C2×C113semidirect
418. #1894C2×C113semidirect
419. #1893C2×C113semidirect
420. #1852C2×C113semidirect
421. C113#25130direct (N × H)
544. #103D4×C113semidirect
548. C22⋊C8D4×C113semidirect
778. C22#468×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1132
C2×#448×C1132
C2×#435×C1132
C22×#103×C1132
C113×#24162
C113×#24092
C113×#20682
C113×#20552
C113×#20362
C113×#20002
C113×#19732
C113×#19352
C113×#18942
C113×#18932
C113×#18522
#25130113