Finite Group Databasebeta

← C23×#13876 #19161502

Subgroups — C23×#13876 #19161502

Order 5888.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#388C212yesmaximal
2C2×C23×#384C211yesmaximal, characteristic, complemented
3C2×C23×#380C211yesmaximal, characteristic
4C2×C23×#380C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C23C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C23C211yesmaximal, characteristic
7C23×#1442C212yesmaximal, complemented
8C23×#1439C212yesmaximal
9C23×#1436C212yesmaximal, complemented
10C23×C4⋊#95C211yesmaximal, characteristic, complemented
11C23×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C23C2211yescharacteristic
13C22×C4⋊C4×C23C2211yescharacteristic
14C22×C4⋊C4×C23C2211yescharacteristic
15C22×C4⋊C4×C23C2212yes—
16C22×C4⋊C4×C23C2212yes—
17C22×C4⋊C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C22⋊C4×C23C2212yes—
20C22×C22⋊C4×C23C2212yes—
21C22×C22⋊C4×C23C2211yescharacteristic
22C22×C22⋊C4×C23C2211yescharacteristic
23C22×C42×C23C2212yes—
24C22×C42×C23C2211yescharacteristic
25C22×C42×C23C2211yescharacteristic
26C23×#388—28no—
27C23×#384—24no—
28C23×#380—24no—
29C23×#380—24no—
30C4×C4⋊C4×C23—24no—
31C4×C22⋊C4×C23C418yescomplemented
32C2×C23×#95C2212yes—
33C2×C23×#95C2212yes—
34C2×C23×#95C2212yes—
35C2×C23×#95C2212yes—
36C2×C23×#95C2212yes—
37C2×C23×#95C2212yes—
38C2×C23×#95C2212yes—
39C2×C23×#95C2211yescharacteristic
40C2×C23×#95C2211yescharacteristic
41C25×C23C2311yescharacteristic
42C23×C4×C23—22no—
43C23×C4×C23—22no—
44C23×C4×C23—22no—
45C23×C4×C23—22no—
46C23×C4×C23—22no—
47C23×C4×C23—22no—
48C23×C4×C23C2×C414yes—
49C23×C4×C23C2312yes—
50C23×C4×C23C2312yes—
51C23×C4×C23C2311yescharacteristic
52C23×C4×C23C2311yescharacteristic
53C23×C4×C23C2312yes—
54C23×C4×C23C2312yes—
55C23×C4×C23C2311yescharacteristic
56C23×C4×C23C2311yescharacteristic
57C23×C4×C23C2311yescharacteristic
58C23×C4×C23C2311yescharacteristic
59C2×C4⋊C4×C23—22no—
60C2×C4⋊C4×C23—22no—
61C2×C4⋊C4×C23—22no—
62C2×C4⋊C4×C23—22no—
63C2×C4⋊C4×C23—22no—
64C2×C4⋊C4×C23—22no—
65C2×C4⋊C4×C23—24no—
66C2×C4⋊C4×C23—24no—
67C2×C4⋊C4×C23—22no—
68C2×C4⋊C4×C23—24no—
69C2×C4⋊C4×C23—24no—
70C2×C4⋊C4×C23—22no—
71C2×C4⋊C4×C23—22no—
72C2×C4⋊C4×C23—22no—
73C2×C4⋊C4×C23—42no—
74C2×C4⋊C4×C23—42no—
75C2×C4⋊C4×C23D414yes—
76C2×C4⋊C4×C23D414yes—
77C2×C22⋊C4×C23—22no—
78C2×C22⋊C4×C23—22no—
79C2×C22⋊C4×C23—24no—
80C2×C22⋊C4×C23—24no—
81C2×C22⋊C4×C23—24no—
82C2×C22⋊C4×C23—24no—
83C2×C22⋊C4×C23—42no—
84C2×C22⋊C4×C23—42no—
85C2×C22⋊C4×C23C2×C414yes—
86C2×C22⋊C4×C23C2×C414yes—
87C2×C22⋊C4×C23D414yes—
88C2×C22⋊C4×C23Q814yes—
89C2×C42×C23—22no—
90C2×C42×C23—22no—
91C2×C42×C23—22no—
92C2×C42×C23—22no—
93C2×C42×C23—24no—
94C2×C42×C23—24no—
95C2×C42×C23—42no—
96C2×C42×C23C2×C414yes—
97C2×C42×C23C2×C414yes—
98C23×#95—24no—
99C23×#95—24no—
100C23×#95—24no—
101C23×#95—24no—
102C23×#95—24no—
103C23×#95—24no—
104C23×#95—42no—
105C23×#95C2×C414yes—
106C23×#95C2×C414yes—
107C24×C23—21no—
108C24×C23—21no—
109C24×C23—21no—
110C24×C23—21no—
111C24×C23—21no—
112C24×C23—21no—
113C24×C23—21no—
114C24×C23—21no—
115C24×C23—21no—
116C24×C23—21no—
117C24×C23—21no—
118C24×C23—21no—
119C24×C23C22×C412yes—
120C24×C23C2×D412yes—
121C24×C23C2×Q812yes—
122C24×C23C2411yescharacteristic
123C22×C4×C23—21no—
124C22×C4×C23—21no—
125C22×C4×C23—21no—
126C22×C4×C23—21no—
127C22×C4×C23—21no—
128C22×C4×C23—21no—
129C22×C4×C23—21no—
130C22×C4×C23—21no—
131C22×C4×C23—21no—
132C22×C4×C23—21no—
133C22×C4×C23—21no—
134C22×C4×C23—21no—
135C22×C4×C23—22no—
136C22×C4×C23—22no—
137C22×C4×C23—22no—
138C22×C4×C23—21no—
139C22×C4×C23—21no—
140C22×C4×C23—21no—
141C22×C4×C23—21no—
142C22×C4×C23—21no—
143C22×C4×C23—21no—
144C22×C4×C23—22no—
145C22×C4×C23—22no—
146C22×C4×C23—22no—
147C22×C4×C23—22no—
148C22×C4×C23—21no—
149C22×C4×C23—21no—
150C22×C4×C23—21no—
151C22×C4×C23—21no—
152C22×C4×C23—22no—
153C22×C4×C23—22no—
154C22×C4×C23—22no—
155C22×C4×C23—22no—
156C22×C4×C23—21no—
157C22×C4×C23—21no—
158C22×C4×C23—22no—
159C22×C4×C23—28no—
160C22×C4×C23—28no—
161C22×C4×C23—28no—
162C22×C4×C23—22no—
163C22×C4×C23—22no—
164C22×C4×C23—22no—
165C22×C4×C23—22no—
166C22×C4×C23—22no—
167C22×C4×C23—22no—
168C22×C4×C23—22no—
169C22×C4×C23—22no—
170C22×C4×C23—22no—
171C22×C4×C23—22no—
172C22×C4×C23—22no—
173C22×C4×C23—22no—
174C22×C4×C23—22no—
175C22×C4×C23—22no—
176C22×C4×C23—44no—
177C22×C4×C23—44no—
178C22×C4×C23—44no—
179C22×C4×C23—44no—
180C22×C4×C23C22×C412yes—
181C22×C4×C23C22×C412yes—
182C22×C4×C23C22×C412yes—
183C22×C4×C23C22×C412yes—
184C22×C4×C23C22×C412yes—
185C22×C4×C23C22×C412yes—
186C22×C4×C23C2×D414yes—
187C22×C4×C23C2×D414yes—
188C22×C4×C23C2×D412yes—
189C22×C4×C23C2×D412yes—
190C22×C4×C23C2×D412yes—
191C22×C4×C23C2×D412yes—
192C22×C4×C23C2×Q812yes—
193C22×C4×C23C2×Q812yes—
194C22×C4×C23#4112yes—
195C22×C4×C23#4112yes—
196C22×C4×C23#4112yes—
197C22×C4×C23#4112yes—
198C22×C4×C23#4112yes—
199C22×C4×C23#4112yes—
200C4⋊C4×C23—28no—
201C4⋊C4×C23—28no—
202C4⋊C4×C23—48no—
203C4⋊C4×C23—48no—
204C4⋊C4×C23—44no—
205C4⋊C4×C23—44no—
206C22⋊C4×C23—28no—
207C22⋊C4×C23—48no—
208C22⋊C4×C23—48no—
209C22⋊C4×C23C4⋊C4116yescomplemented
210C42×C23—28no—
211C42×C23—28no—
212C42×C23—48no—
213#13876C2311yesmaximal, characteristic, direct product factor, Sylow
214C23×C23—22no—
215C23×C23—22no—
216C23×C23—22no—
217C23×C23—22no—
218C23×C23—22no—
219C23×C23—22no—
220C23×C23—22no—
221C23×C23—22no—
222C23×C23—22no—
223C23×C23—22no—
224C23×C23—22no—
225C23×C23—22no—
226C23×C23—22no—
227C23×C23—22no—
228C23×C23—22no—
229C23×C23—22no—
230C23×C23—22no—
231C23×C23—22no—
232C23×C23—41no—
233C23×C23—41no—
234C23×C23—41no—
235C23×C23—41no—
236C23×C23—41no—
237C23×C23—41no—
238C23×C23—41no—
239C23×C23—41no—
240C23×C23—41no—
241C23×C23—41no—
242C23×C23—41no—
243C23×C23—41no—
244C23×C23—41no—
245C23×C23—41no—
246C23×C23—41no—
247C23×C23—41no—
248C23×C23C2×C4⋊C414yes—
249C23×C23C23×C411yescharacteristic
250C23×C23C22×D411yescharacteristic
251C23×C23C22×D411yescharacteristic
252C23×C23C22×D411yescharacteristic
253C23×C23C22×Q811yescharacteristic
254C23×C23C2×#4111yescharacteristic
255C23×C23C2×#4111yescharacteristic
256C23×C23C2×#4111yescharacteristic
257C23×C23C2×#4111yescharacteristic
258C23×C23C2×#4111yescharacteristic
259C23×C23C2×#4111yescharacteristic
260C23×C23H(5,𝔽2)11yescharacteristic
261C23×C23H(5,𝔽2)11yescharacteristic
262C23×C232−1+411yescharacteristic
263C23×C232−1+411yescharacteristic
264C2×C4×C23—22no—
265C2×C4×C23—22no—
266C2×C4×C23—22no—
267C2×C4×C23—22no—
268C2×C4×C23—22no—
269C2×C4×C23—22no—
270C2×C4×C23—22no—
271C2×C4×C23—22no—
272C2×C4×C23—22no—
273C2×C4×C23—22no—
274C2×C4×C23—22no—
275C2×C4×C23—22no—
276C2×C4×C23—22no—
277C2×C4×C23—22no—
278C2×C4×C23—22no—
279C2×C4×C23—22no—
280C2×C4×C23—22no—
281C2×C4×C23—22no—
282C2×C4×C23—22no—
283C2×C4×C23—22no—
284C2×C4×C23—22no—
285C2×C4×C23—22no—
286C2×C4×C23—22no—
287C2×C4×C23—22no—
288C2×C4×C23—24no—
289C2×C4×C23—24no—
290C2×C4×C23—24no—
291C2×C4×C23—24no—
292C2×C4×C23—24no—
293C2×C4×C23—24no—
294C2×C4×C23—41no—
295C2×C4×C23—41no—
296C2×C4×C23—41no—
297C2×C4×C23—41no—
298C2×C4×C23—42no—
299C2×C4×C23—42no—
300C2×C4×C23—42no—
301C2×C4×C23—42no—
302C2×C4×C23—42no—
303C2×C4×C23—41no—
304C2×C4×C23—42no—
305C2×C4×C23—41no—
306C2×C4×C23—42no—
307C2×C4×C23—42no—
308C2×C4×C23—41no—
309C2×C4×C23—41no—
310C2×C4×C23—416no—
311C2×C4×C23—42no—
312C2×C4×C23—42no—
313C2×C4×C23—42no—
314C2×C4×C23—42no—
315C2×C4×C23—42no—
316C2×C4×C23—42no—
317C2×C4×C23—42no—
318C2×C4×C23—42no—
319C2×C4×C23—42no—
320C2×C4×C23—42no—
321C2×C4×C23—42no—
322C2×C4×C23—42no—
323C2×C4×C23—42no—
324C2×C4×C23—42no—
325C2×C4×C23C2×C4⋊C414yes—
326C2×C4×C23C2×C4⋊C414yes—
327C2×C4×C23#11714yes—
328C2×C4×C23#11714yes—
329C2×C4×C23C4×D414yes—
330C2×C4×C23C4×D414yes—
331C2×C4×C23#12114yes—
332C2×C4×C23#12314yes—
333C2×C4×C23#12414yes—
334C2×C4×C23#12614yes—
335C2×#388C2×C2312yes—
336C2×#384C2×C2311yescharacteristic, complemented
337C2×#380C2×C2311yescharacteristic
338C2×#380C2×C2311yescharacteristic
339C2×C4×C4⋊C4C2×C2311yescharacteristic, complemented
340C2×C4×C22⋊C4C2×C2311yescharacteristic
341#1442C2×C2312yescomplemented
342#1439C2×C2312yes—
343#1436C2×C2312yescomplemented
344C4⋊#95C2×C2311yescharacteristic, complemented
345C4⋊#95C2×C2311yescharacteristic, complemented
346C22×C23—24no—
347C22×C23—24no—
348C22×C23—24no—
349C22×C23—42no—
350C22×C23—42no—
351C22×C23—42no—
352C22×C23—42no—
353C22×C23—42no—
354C22×C23—42no—
355C22×C23—42no—
356C22×C23—42no—
357C22×C23—42no—
358C22×C23—42no—
359C22×C23—42no—
360C22×C23—42no—
361C22×C23C22×C4⋊C411yescharacteristic
362C22×C23C2×#11711yescharacteristic
363C22×C23C2×#11711yescharacteristic
364C22×C23C2×C4×D411yescharacteristic
365C22×C23C2×C4×D411yescharacteristic
366C22×C23#52011yescharacteristic
367C22×C23#52011yescharacteristic
368C22×C23C2×#12111yescharacteristic
369C22×C23C2×#12311yescharacteristic
370C22×C23C2×#12411yescharacteristic
371C22×C23C2×#12611yescharacteristic
372C22×C23#53211yescharacteristic
373C22×C23#53211yescharacteristic
374C22×C23#53311yescharacteristic
375C22×C23#53311yescharacteristic
376C22×C23#54011yescharacteristic
377C22×C23#54111yescharacteristic
378C22×C23#54211yescharacteristic
379C22×C23#54211yescharacteristic
380C22×C23D4211yescharacteristic
381C22×C23D4211yescharacteristic
382C22×C23#54611yescharacteristic
383C22×C23#54711yescharacteristic
384C22×C23#54711yescharacteristic
385C22×C23#54711yescharacteristic
386C22×C23#54811yescharacteristic
387C22×C23D4×Q811yescharacteristic
388C22×C23D4×Q811yescharacteristic
389C22×C23#55011yescharacteristic
390C22×C23#55211yescharacteristic
391C22×C23#55311yescharacteristic
392C22×C23#55411yescharacteristic
393C22×C23#55411yescharacteristic
394C22×C23#55511yescharacteristic
395C22×C23#55611yescharacteristic
396C4×C23—24no—
397C4×C23—24no—
398C4×C23—24no—
399C4×C23—42no—
400C4×C23—44no—
401C4×C23—44no—
402C4×C23—42no—
403C4×C23—82no—
404C4×C23—82no—
405C4×C23#38818yescomplemented
406C24×C4C22×C2311yescharacteristic
407C22×C4⋊C4C22×C2311yescharacteristic
408C22×C4⋊C4C22×C2311yescharacteristic
409C22×C4⋊C4C22×C2312yes—
410C22×C4⋊C4C22×C2312yes—
411C22×C4⋊C4C22×C2311yescharacteristic
412C22×C4⋊C4C22×C2311yescharacteristic
413C22×C22⋊C4C22×C2312yes—
414C22×C22⋊C4C22×C2312yes—
415C22×C22⋊C4C22×C2311yescharacteristic
416C22×C22⋊C4C22×C2311yescharacteristic
417C22×C42C22×C2312yes—
418C22×C42C22×C2311yescharacteristic
419C22×C42C22×C2311yescharacteristic
420#388—28no—
421#384—24no—
422#380—24no—
423#380—24no—
424C4×C4⋊C4—24no—
425C4×C22⋊C4C4×C2318yescomplemented
426C2×#95C22×C2312yes—
427C2×#95C22×C2312yes—
428C2×#95C22×C2312yes—
429C2×#95C22×C2312yes—
430C2×#95C22×C2312yes—
431C2×#95C22×C2312yes—
432C2×#95C22×C2312yes—
433C2×#95C22×C2311yescharacteristic
434C2×#95C22×C2311yescharacteristic
435C2×C23—44no—
436C2×C23#228511yescharacteristic
437C2×C23C2×#38811yescharacteristic
438C2×C23#231411yescharacteristic
439C2×C23D4×C4⋊C411yescharacteristic
440C2×C23D4×C4⋊C411yescharacteristic
441C2×C23#235211yescharacteristic
442C2×C23#235411yescharacteristic
443C2×C23#242211yescharacteristic
444C2×C23#242311yescharacteristic
445C2×C23#242811yescharacteristic
446C2×C23#242911yescharacteristic
447C2×C23#249111yescharacteristic
448C2×C23#249211yescharacteristic
449C2×C23#249611yescharacteristic
450C2×C23#249711yescharacteristic
451C25C23×C2311yescharacteristic
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4C2×C4×C2314yes—
459C23×C4C23×C2312yes—
460C23×C4C23×C2312yes—
461C23×C4C23×C2311yescharacteristic
462C23×C4C23×C2311yescharacteristic
463C23×C4C23×C2312yes—
464C23×C4C23×C2312yes—
465C23×C4C23×C2311yescharacteristic
466C23×C4C23×C2311yescharacteristic
467C23×C4C23×C2311yescharacteristic
468C23×C4C23×C2311yescharacteristic
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4D4×C2314yes—
486C2×C4⋊C4D4×C2314yes—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4C2×C4×C2314yes—
496C2×C22⋊C4C2×C4×C2314yes—
497C2×C22⋊C4D4×C2314yes—
498C2×C22⋊C4Q8×C2314yes—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—24no—
504C2×C42—24no—
505C2×C42—42no—
506C2×C42C2×C4×C2314yes—
507C2×C42C2×C4×C2314yes—
508#95—24no—
509#95—24no—
510#95—24no—
511#95—24no—
512#95—24no—
513#95—24no—
514#95—42no—
515#95C2×C4×C2314yes—
516#95C2×C4×C2314yes—
517C23#1387611yescharacteristic, direct product factor, Sylow
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C22×C4×C2312yes—
531C24C2×D4×C2312yes—
532C24C2×Q8×C2312yes—
533C24C24×C2311yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4C22×C4×C2312yes—
592C22×C4C22×C4×C2312yes—
593C22×C4C22×C4×C2312yes—
594C22×C4C22×C4×C2312yes—
595C22×C4C22×C4×C2312yes—
596C22×C4C22×C4×C2312yes—
597C22×C4C2×D4×C2314yes—
598C22×C4C2×D4×C2314yes—
599C22×C4C2×D4×C2312yes—
600C22×C4C2×D4×C2312yes—
601C22×C4C2×D4×C2312yes—
602C22×C4C2×D4×C2312yes—
603C22×C4C2×Q8×C2312yes—
604C22×C4C2×Q8×C2312yes—
605C22×C4#41×C2312yes—
606C22×C4#41×C2312yes—
607C22×C4#41×C2312yes—
608C22×C4#41×C2312yes—
609C22×C4#41×C2312yes—
610C22×C4#41×C2312yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4C4⋊C4×C23116yescomplemented
621C42—28no—
622C42—28no—
623C42—48no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊C4×C2314yes—
659C23C23×C4×C2311yescharacteristic
660C23C22×D4×C2311yescharacteristic
661C23C22×D4×C2311yescharacteristic
662C23C22×D4×C2311yescharacteristic
663C23C22×Q8×C2311yescharacteristic
664C23C2×#41×C2311yescharacteristic
665C23C2×#41×C2311yescharacteristic
666C23C2×#41×C2311yescharacteristic
667C23C2×#41×C2311yescharacteristic
668C23C2×#41×C2311yescharacteristic
669C23C2×#41×C2311yescharacteristic
670C23C23×H(5,𝔽2)11yescharacteristic
671C23C23×H(5,𝔽2)11yescharacteristic
672C23C23×2−1+411yescharacteristic
673C23C23×2−1+411yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4C2×C4⋊C4×C2314yes—
736C2×C4C2×C4⋊C4×C2314yes—
737C2×C4C23×#11714yes—
738C2×C4C23×#11714yes—
739C2×C4C4×D4×C2314yes—
740C2×C4C4×D4×C2314yes—
741C2×C4C23×#12114yes—
742C2×C4C23×#12314yes—
743C2×C4C23×#12414yes—
744C2×C4C23×#12614yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C4⋊C4×C2311yescharacteristic
761C22C2×C23×#11711yescharacteristic
762C22C2×C23×#11711yescharacteristic
763C22C2×C4×D4×C2311yescharacteristic
764C22C2×C4×D4×C2311yescharacteristic
765C22C23×#52011yescharacteristic
766C22C23×#52011yescharacteristic
767C22C2×C23×#12111yescharacteristic
768C22C2×C23×#12311yescharacteristic
769C22C2×C23×#12411yescharacteristic
770C22C2×C23×#12611yescharacteristic
771C22C23×#53211yescharacteristic
772C22C23×#53211yescharacteristic
773C22C23×#53311yescharacteristic
774C22C23×#53311yescharacteristic
775C22C23×#54011yescharacteristic
776C22C23×#54111yescharacteristic
777C22C23×#54211yescharacteristic
778C22C23×#54211yescharacteristic
779C22D42×C2311yescharacteristic
780C22D42×C2311yescharacteristic
781C22C23×#54611yescharacteristic
782C22C23×#54711yescharacteristic
783C22C23×#54711yescharacteristic
784C22C23×#54711yescharacteristic
785C22C23×#54811yescharacteristic
786C22D4×Q8×C2311yescharacteristic
787C22D4×Q8×C2311yescharacteristic
788C22C23×#55011yescharacteristic
789C22C23×#55211yescharacteristic
790C22C23×#55311yescharacteristic
791C22C23×#55411yescharacteristic
792C22C23×#55411yescharacteristic
793C22C23×#55511yescharacteristic
794C22C23×#55611yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—44no—
799C4—44no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—82no—
804C4C23×#38818yescomplemented
805C2—44no—
806C2C23×#228511yescharacteristic
807C2C2×C23×#38811yescharacteristic
808C2C23×#231411yescharacteristic
809C2D4×C4⋊C4×C2311yescharacteristic
810C2D4×C4⋊C4×C2311yescharacteristic
811C2C23×#235211yescharacteristic
812C2C23×#235411yescharacteristic
813C2C23×#242211yescharacteristic
814C2C23×#242311yescharacteristic
815C2C23×#242811yescharacteristic
816C2C23×#242911yescharacteristic
817C2C23×#249111yescharacteristic
818C2C23×#249211yescharacteristic
819C2C23×#249611yescharacteristic
820C2C23×#249711yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC25×C23C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C23×#384C2semidirect
5. C2×C4×C4⋊C4×C23C2semidirect
7. C23×#1442C2semidirect
9. C23×#1436C2semidirect
10. C23×C4⋊#95C2semidirect
11. C23×C4⋊#95C2semidirect
31. C4×C22⋊C4×C23C4semidirect
209. C22⋊C4×C23C4⋊C4semidirect
213. #13876C23direct (N × H)
336. C2×#384C2×C23semidirect
339. C2×C4×C4⋊C4C2×C23semidirect
341. #1442C2×C23semidirect
343. #1436C2×C23semidirect
344. C4⋊#95C2×C23semidirect
345. C4⋊#95C2×C23semidirect
405. C4×C23#388semidirect
425. C4×C22⋊C4C4×C23semidirect
517. C23#13876direct (N × H)
620. C22⋊C4C4⋊C4×C23semidirect
804. C4C23×#388semidirect

Maximal subgroups

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

subgroupindex
C2×C23×#3882
C2×C23×#3842
C2×C23×#3802
C2×C4×C4⋊C4×C232
C2×C4×C22⋊C4×C232
C23×#14422
C23×#14392
C23×#14362
C23×C4⋊#952
#1387623