Finite Group Databasebeta

← C23×#14004 #19161630

Subgroups — C23×#14004 #19161630

Order 5888.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#389C211yesmaximal, characteristic, complemented
2C2×C23×#385C211yesmaximal, characteristic
3C2×C23×#385C211yesmaximal, characteristic
4C2×C23×#385C211yesmaximal, characteristic
5C2×C23×#380C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C23C211yesmaximal, characteristic
7C22×C23×#95C211yesmaximal, characteristic
8C23×#1444C211yesmaximal, characteristic, complemented
9C23×#1442C211yesmaximal, characteristic, complemented
10C23×#1441C211yesmaximal, characteristic, complemented
11C23×#1441C211yesmaximal, characteristic, complemented
12C23×#1436C211yesmaximal, characteristic, complemented
13C23×#1436C211yesmaximal, characteristic, complemented
14C23×C4⋊#95C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C24×C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C4⋊C4×C23C2211yescharacteristic
22C22×C4⋊C4×C23C2211yescharacteristic
23C22×C4⋊C4×C23C2211yescharacteristic
24C22×C4⋊C4×C23C2211yescharacteristic
25C22×C4⋊C4×C23C2211yescharacteristic
26C22×C4⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C42×C23C2211yescharacteristic
32C22×C42×C23C2211yescharacteristic
33C23×#389—24no—
34C23×#385—24no—
35C23×#385—24no—
36C23×#385C418yescomplemented
37C23×#380—24no—
38C4×C22⋊C4×C23—24no—
39C2×C23×#95—24no—
40C2×C23×#95C2211yescharacteristic
41C2×C23×#95C2211yescharacteristic
42C2×C23×#95C2211yescharacteristic
43C2×C23×#95C2211yescharacteristic
44C2×C23×#95C2211yescharacteristic
45C2×C23×#95C2211yescharacteristic
46C2×C23×#95C2211yescharacteristic
47C2×C23×#95C2211yescharacteristic
48C2×C23×#95C2211yescharacteristic
49C2×C23×#95C2211yescharacteristic
50C2×C23×#95C2211yescharacteristic
51C2×C23×#95C2211yescharacteristic
52C2×C23×#95C2211yescharacteristic
53C2×C23×#95C2211yescharacteristic
54C2×C23×#95C2211yescharacteristic
55C2×C23×#95C2211yescharacteristic
56C2×C23×#95C2211yescharacteristic
57C2×C23×#95C2211yescharacteristic
58C25×C23C2311yescharacteristic
59C23×C4×C23—22no—
60C23×C4×C23—22no—
61C23×C4×C23—22no—
62C23×C4×C23—22no—
63C23×C4×C23—22no—
64C23×C4×C23—22no—
65C23×C4×C23—22no—
66C23×C4×C23—22no—
67C23×C4×C23—22no—
68C23×C4×C23—22no—
69C23×C4×C23—22no—
70C23×C4×C23—22no—
71C23×C4×C23—22no—
72C23×C4×C23—41no—
73C23×C4×C23—41no—
74C23×C4×C23—41no—
75C23×C4×C23—41no—
76C23×C4×C23—41no—
77C23×C4×C23—41no—
78C23×C4×C23C2×C414yes—
79C23×C4×C23Q814yes—
80C23×C4×C23C2311yescharacteristic
81C23×C4×C23C2311yescharacteristic
82C23×C4×C23C2311yescharacteristic
83C23×C4×C23C2311yescharacteristic
84C23×C4×C23C2311yescharacteristic
85C23×C4×C23C2311yescharacteristic
86C23×C4×C23C2311yescharacteristic
87C23×C4×C23C2311yescharacteristic
88C23×C4×C23C2311yescharacteristic
89C23×C4×C23C2311yescharacteristic
90C23×C4×C23C2311yescharacteristic
91C23×C4×C23C2311yescharacteristic
92C23×C4×C23C2311yescharacteristic
93C23×C4×C23C2311yescharacteristic
94C2×C4⋊C4×C23—22no—
95C2×C4⋊C4×C23—22no—
96C2×C4⋊C4×C23—22no—
97C2×C4⋊C4×C23—22no—
98C2×C4⋊C4×C23—22no—
99C2×C4⋊C4×C23—22no—
100C2×C4⋊C4×C23—22no—
101C2×C4⋊C4×C23—22no—
102C2×C4⋊C4×C23—22no—
103C2×C4⋊C4×C23—22no—
104C2×C4⋊C4×C23—22no—
105C2×C4⋊C4×C23—22no—
106C2×C4⋊C4×C23—22no—
107C2×C4⋊C4×C23—22no—
108C2×C4⋊C4×C23—41no—
109C2×C4⋊C4×C23—41no—
110C2×C4⋊C4×C23—41no—
111C2×C4⋊C4×C23—41no—
112C2×C4⋊C4×C23—41no—
113C2×C4⋊C4×C23—41no—
114C2×C4⋊C4×C23—41no—
115C2×C4⋊C4×C23—41no—
116C2×C4⋊C4×C23C2×C414yescomplemented
117C2×C4⋊C4×C23C2×C414yescomplemented
118C2×C22⋊C4×C23—22no—
119C2×C22⋊C4×C23—22no—
120C2×C22⋊C4×C23—22no—
121C2×C22⋊C4×C23—22no—
122C2×C22⋊C4×C23—22no—
123C2×C22⋊C4×C23—22no—
124C2×C22⋊C4×C23—22no—
125C2×C22⋊C4×C23C2×C414yes—
126C2×C22⋊C4×C23C2×C414yes—
127C2×C22⋊C4×C23D414yes—
128C2×C22⋊C4×C23D414yes—
129C2×C22⋊C4×C23Q814yes—
130C2×C42×C23—22no—
131C2×C42×C23—22no—
132C2×C42×C23—22no—
133C2×C42×C23—22no—
134C2×C42×C23—41no—
135C2×C42×C23—41no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—22no—
139C23×#95—22no—
140C23×#95—22no—
141C23×#95—22no—
142C23×#95—22no—
143C23×#95—22no—
144C23×#95—22no—
145C23×#95—22no—
146C23×#95—22no—
147C23×#95—22no—
148C23×#95—22no—
149C23×#95—41no—
150C23×#95—41no—
151C23×#95C2×C414yescomplemented
152C23×#95C2×C414yescomplemented
153C23×#95D414yes—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23—21no—
157C24×C23—21no—
158C24×C23—21no—
159C24×C23—21no—
160C24×C23—21no—
161C24×C23—21no—
162C24×C23C22×C412yes—
163C24×C23C2×D412yes—
164C24×C23C2×D412yes—
165C24×C23C2×Q812yes—
166C24×C23C2×Q812yes—
167C24×C23#4112yes—
168C24×C23#4112yes—
169C24×C23C2411yescharacteristic
170C22×C4×C23—21no—
171C22×C4×C23—21no—
172C22×C4×C23—21no—
173C22×C4×C23—21no—
174C22×C4×C23—21no—
175C22×C4×C23—21no—
176C22×C4×C23—21no—
177C22×C4×C23—21no—
178C22×C4×C23—21no—
179C22×C4×C23—21no—
180C22×C4×C23—21no—
181C22×C4×C23—21no—
182C22×C4×C23—21no—
183C22×C4×C23—21no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—28no—
187C22×C4×C23—28no—
188C22×C4×C23—28no—
189C22×C4×C23—21no—
190C22×C4×C23—21no—
191C22×C4×C23—21no—
192C22×C4×C23—21no—
193C22×C4×C23—21no—
194C22×C4×C23—21no—
195C22×C4×C23—21no—
196C22×C4×C23—21no—
197C22×C4×C23—21no—
198C22×C4×C23—21no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—21no—
204C22×C4×C23—21no—
205C22×C4×C23—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—21no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—28no—
238C22×C4×C23—28no—
239C22×C4×C23—21no—
240C22×C4×C23—21no—
241C22×C4×C23—21no—
242C22×C4×C23—21no—
243C22×C4×C23—21no—
244C22×C4×C23—21no—
245C22×C4×C23—21no—
246C22×C4×C23—21no—
247C22×C4×C23—21no—
248C22×C4×C23—21no—
249C22×C4×C23—21no—
250C22×C4×C23—21no—
251C22×C4×C23—21no—
252C22×C4×C23—21no—
253C22×C4×C23—44no—
254C22×C4×C23—44no—
255C22×C4×C23—44no—
256C22×C4×C23—44no—
257C22×C4×C23—44no—
258C22×C4×C23—44no—
259C22×C4×C23—44no—
260C22×C4×C23—44no—
261C22×C4×C23—44no—
262C22×C4×C23—44no—
263C22×C4×C23—44no—
264C22×C4×C23—44no—
265C22×C4×C23—44no—
266C22×C4×C23—44no—
267C22×C4×C23—44no—
268C22×C4×C23—44no—
269C22×C4×C23C22×C412yes—
270C22×C4×C23C22×C412yes—
271C22×C4×C23C22×C412yes—
272C22×C4×C23C22×C412yes—
273C22×C4×C23C22×C412yes—
274C22×C4×C23C22×C412yes—
275C22×C4×C23C2×D412yes—
276C22×C4×C23C2×D412yes—
277C22×C4×C23C2×D412yes—
278C22×C4×C23C2×D412yes—
279C22×C4×C23C2×D412yes—
280C22×C4×C23C2×D412yes—
281C22×C4×C23C2×D412yes—
282C22×C4×C23C2×Q812yes—
283C22×C4×C23C2×Q812yes—
284C22×C4×C23C2×Q812yes—
285C22×C4×C23C2×Q812yes—
286C22×C4×C23#4112yes—
287C22×C4×C23#4112yes—
288C22×C4×C23#4112yes—
289C4⋊C4×C23—28no—
290C4⋊C4×C23—44no—
291C4⋊C4×C23—44no—
292C4⋊C4×C23—44no—
293C4⋊C4×C23—44no—
294C4⋊C4×C23—44no—
295C4⋊C4×C23—44no—
296C4⋊C4×C23—44no—
297C22⋊C4×C23—28no—
298C22⋊C4×C23—28no—
299C22⋊C4×C23—44no—
300C22⋊C4×C23C4⋊C4116yescomplemented
301C42×C23—44no—
302C42×C23—44no—
303#14004C2311yesmaximal, characteristic, direct product factor, Sylow
304C23×C23—22no—
305C23×C23—22no—
306C23×C23—22no—
307C23×C23—22no—
308C23×C23—22no—
309C23×C23—22no—
310C23×C23—22no—
311C23×C23—22no—
312C23×C23—22no—
313C23×C23—22no—
314C23×C23—22no—
315C23×C23—22no—
316C23×C23—22no—
317C23×C23—22no—
318C23×C23—22no—
319C23×C23—22no—
320C23×C23—22no—
321C23×C23—22no—
322C23×C23—22no—
323C23×C23—22no—
324C23×C23—22no—
325C23×C23—22no—
326C23×C23—22no—
327C23×C23—22no—
328C23×C23—22no—
329C23×C23—22no—
330C23×C23—22no—
331C23×C23—22no—
332C23×C23C2×C4⋊C414yes—
333C23×C23C4×D414yes—
334C23×C23C4×Q814yes—
335C23×C23#12114yes—
336C23×C23C22⋊Q814yes—
337C23×C23#12514yes—
338C23×C23C4⋊Q814yes—
339C23×C23C23×C411yescharacteristic
340C23×C23C22×D411yescharacteristic
341C23×C23C22×D411yescharacteristic
342C23×C23C22×D411yescharacteristic
343C23×C23C22×Q811yescharacteristic
344C23×C23C22×Q811yescharacteristic
345C23×C23C2×#4111yescharacteristic
346C23×C23C2×#4111yescharacteristic
347C23×C23C2×#4111yescharacteristic
348C23×C23C2×#4111yescharacteristic
349C23×C23C2×#4111yescharacteristic
350C23×C23H(5,𝔽2)11yescharacteristic
351C23×C23H(5,𝔽2)11yescharacteristic
352C23×C23H(5,𝔽2)11yescharacteristic
353C23×C232−1+411yescharacteristic
354C2×C4×C23—22no—
355C2×C4×C23—22no—
356C2×C4×C23—22no—
357C2×C4×C23—22no—
358C2×C4×C23—22no—
359C2×C4×C23—22no—
360C2×C4×C23—22no—
361C2×C4×C23—22no—
362C2×C4×C23—22no—
363C2×C4×C23—22no—
364C2×C4×C23—22no—
365C2×C4×C23—22no—
366C2×C4×C23—22no—
367C2×C4×C23—22no—
368C2×C4×C23—22no—
369C2×C4×C23—22no—
370C2×C4×C23—22no—
371C2×C4×C23—22no—
372C2×C4×C23—22no—
373C2×C4×C23—22no—
374C2×C4×C23—22no—
375C2×C4×C23—22no—
376C2×C4×C23—22no—
377C2×C4×C23—22no—
378C2×C4×C23—22no—
379C2×C4×C23—22no—
380C2×C4×C23—22no—
381C2×C4×C23—22no—
382C2×C4×C23—22no—
383C2×C4×C23—22no—
384C2×C4×C23—22no—
385C2×C4×C23—22no—
386C2×C4×C23—22no—
387C2×C4×C23—22no—
388C2×C4×C23—22no—
389C2×C4×C23—22no—
390C2×C4×C23—22no—
391C2×C4×C23—22no—
392C2×C4×C23—22no—
393C2×C4×C23—22no—
394C2×C4×C23—22no—
395C2×C4×C23—22no—
396C2×C4×C23—22no—
397C2×C4×C23—22no—
398C2×C4×C23—22no—
399C2×C4×C23—22no—
400C2×C4×C23—22no—
401C2×C4×C23—22no—
402C2×C4×C23—416no—
403C2×C4×C23—416no—
404C2×C4×C23—416no—
405C2×C4×C23—41no—
406C2×C4×C23—41no—
407C2×C4×C23—41no—
408C2×C4×C23—41no—
409C2×C4×C23—41no—
410C2×C4×C23—41no—
411C2×C4×C23—41no—
412C2×C4×C23—41no—
413C2×C4×C23—41no—
414C2×C4×C23—41no—
415C2×C4×C23—41no—
416C2×C4×C23—41no—
417C2×C4×C23—41no—
418C2×C4×C23—41no—
419C2×C4×C23—41no—
420C2×C4×C23—41no—
421C2×C4×C23—41no—
422C2×C4×C23—41no—
423C2×C4×C23—41no—
424C2×C4×C23—41no—
425C2×C4×C23—41no—
426C2×C4×C23—41no—
427C2×C4×C23—41no—
428C2×C4×C23—41no—
429C2×C4×C23—41no—
430C2×C4×C23—41no—
431C2×C4×C23—41no—
432C2×C4×C23—41no—
433C2×C4×C23—41no—
434C2×C4×C23—41no—
435C2×C4×C23—41no—
436C2×C4×C23—41no—
437C2×C4×C23—41no—
438C2×C4×C23—41no—
439C2×C4×C23—41no—
440C2×C4×C23—41no—
441C2×C4×C23—41no—
442C2×C4×C23—41no—
443C2×C4×C23—41no—
444C2×C4×C23—41no—
445C2×C4×C23—41no—
446C2×C4×C23—41no—
447C2×C4×C23—41no—
448C2×C4×C23—41no—
449C2×C4×C23—41no—
450C2×C4×C23—41no—
451C2×C4×C23C2×C4⋊C414yes—
452C2×C4×C23C2×C4⋊C414yes—
453C2×C4×C23C4×D414yes—
454C2×C4×C23C22⋊Q814yes—
455C2×#389C2×C2311yescharacteristic, complemented
456C2×#385C2×C2311yescharacteristic
457C2×#385C2×C2311yescharacteristic
458C2×#385C2×C2311yescharacteristic
459C2×#380C2×C2311yescharacteristic
460C2×C4×C22⋊C4C2×C2311yescharacteristic
461C22×#95C2×C2311yescharacteristic
462#1444C2×C2311yescharacteristic, complemented
463#1442C2×C2311yescharacteristic, complemented
464#1441C2×C2311yescharacteristic, complemented
465#1441C2×C2311yescharacteristic, complemented
466#1436C2×C2311yescharacteristic, complemented
467#1436C2×C2311yescharacteristic, complemented
468C4⋊#95C2×C2311yescharacteristic, complemented
469C22⋊#95C2×C2311yescharacteristic
470C22×C23—24no—
471C22×C23—24no—
472C22×C23—24no—
473C22×C23—24no—
474C22×C23—24no—
475C22×C23—24no—
476C22×C23—24no—
477C22×C23—24no—
478C22×C23—24no—
479C22×C23—24no—
480C22×C23—24no—
481C22×C23—24no—
482C22×C23—24no—
483C22×C23—24no—
484C22×C23#38918yescomplemented
485C22×C23C22×C4⋊C411yescharacteristic
486C22×C23C2×C4×D411yescharacteristic
487C22×C23C2×C4×D411yescharacteristic
488C22×C23C2×C4×Q811yescharacteristic
489C22×C23C4×#4111yescharacteristic
490C22×C23#51811yescharacteristic
491C22×C23#52011yescharacteristic
492C22×C23C2×#12111yescharacteristic
493C22×C23C2×C22⋊Q811yescharacteristic
494C22×C23C2×C22⋊Q811yescharacteristic
495C22×C23#52511yescharacteristic
496C22×C23C2×#12511yescharacteristic
497C22×C23#52911yescharacteristic
498C22×C23C2×C4⋊Q811yescharacteristic
499C22×C23#53311yescharacteristic
500C22×C23#53811yescharacteristic
501C22×C23#53911yescharacteristic
502C22×C23#54311yescharacteristic
503C22×C23#54411yescharacteristic
504C22×C23D4211yescharacteristic
505C22×C23D4211yescharacteristic
506C22×C23#54611yescharacteristic
507C22×C23#54611yescharacteristic
508C22×C23#54611yescharacteristic
509C22×C23#54611yescharacteristic
510C22×C23#54611yescharacteristic
511C22×C23#54711yescharacteristic
512C22×C23#54711yescharacteristic
513C22×C23D4×Q811yescharacteristic
514C22×C23#55111yescharacteristic
515C22×C23#55111yescharacteristic
516C22×C23#55211yescharacteristic
517C22×C23#55411yescharacteristic
518C22×C23#55411yescharacteristic
519C22×C23#55411yescharacteristic
520C4×C23—24no—
521C4×C23—24no—
522C4×C23—24no—
523C4×C23—24no—
524C4×C23—42no—
525C4×C23—42no—
526C4×C23—42no—
527C4×C23—42no—
528C4×C23—42no—
529C4×C23—42no—
530C4×C23—42no—
531C4×C23—42no—
532C4×C23—81no—
533C4×C23—81no—
534C24×C4C22×C2311yescharacteristic
535C24×C4C22×C2311yescharacteristic
536C24×C4C22×C2311yescharacteristic
537C22×C4⋊C4C22×C2311yescharacteristic
538C22×C4⋊C4C22×C2311yescharacteristic
539C22×C4⋊C4C22×C2311yescharacteristic
540C22×C4⋊C4C22×C2311yescharacteristic
541C22×C4⋊C4C22×C2311yescharacteristic
542C22×C4⋊C4C22×C2311yescharacteristic
543C22×C4⋊C4C22×C2311yescharacteristic
544C22×C4⋊C4C22×C2311yescharacteristic
545C22×C22⋊C4C22×C2311yescharacteristic
546C22×C22⋊C4C22×C2311yescharacteristic
547C22×C22⋊C4C22×C2311yescharacteristic
548C22×C22⋊C4C22×C2311yescharacteristic
549C22×C42C22×C2311yescharacteristic
550C22×C42C22×C2311yescharacteristic
551#389—24no—
552#385—24no—
553#385—24no—
554#385C4×C2318yescomplemented
555#380—24no—
556C4×C22⋊C4—24no—
557C2×#95—24no—
558C2×#95C22×C2311yescharacteristic
559C2×#95C22×C2311yescharacteristic
560C2×#95C22×C2311yescharacteristic
561C2×#95C22×C2311yescharacteristic
562C2×#95C22×C2311yescharacteristic
563C2×#95C22×C2311yescharacteristic
564C2×#95C22×C2311yescharacteristic
565C2×#95C22×C2311yescharacteristic
566C2×#95C22×C2311yescharacteristic
567C2×#95C22×C2311yescharacteristic
568C2×#95C22×C2311yescharacteristic
569C2×#95C22×C2311yescharacteristic
570C2×#95C22×C2311yescharacteristic
571C2×#95C22×C2311yescharacteristic
572C2×#95C22×C2311yescharacteristic
573C2×#95C22×C2311yescharacteristic
574C2×#95C22×C2311yescharacteristic
575C2×#95C22×C2311yescharacteristic
576C2×C23—28no—
577C2×C23C2×#38911yescharacteristic
578C2×C23C4×C22⋊Q811yescharacteristic
579C2×C23#232911yescharacteristic
580C2×C23D4×C4⋊C411yescharacteristic
581C2×C23#234911yescharacteristic
582C2×C23#235811yescharacteristic
583C2×C23#235911yescharacteristic
584C2×C23#242411yescharacteristic
585C2×C23#242511yescharacteristic
586C2×C23#243711yescharacteristic
587C2×C23#243811yescharacteristic
588C2×C23#244011yescharacteristic
589C2×C23#247311yescharacteristic
590C2×C23#250511yescharacteristic
591C2×C23#254911yescharacteristic
592C25C23×C2311yescharacteristic
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—41no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4C2×C4×C2314yes—
613C23×C4Q8×C2314yes—
614C23×C4C23×C2311yescharacteristic
615C23×C4C23×C2311yescharacteristic
616C23×C4C23×C2311yescharacteristic
617C23×C4C23×C2311yescharacteristic
618C23×C4C23×C2311yescharacteristic
619C23×C4C23×C2311yescharacteristic
620C23×C4C23×C2311yescharacteristic
621C23×C4C23×C2311yescharacteristic
622C23×C4C23×C2311yescharacteristic
623C23×C4C23×C2311yescharacteristic
624C23×C4C23×C2311yescharacteristic
625C23×C4C23×C2311yescharacteristic
626C23×C4C23×C2311yescharacteristic
627C23×C4C23×C2311yescharacteristic
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4C2×C4×C2314yescomplemented
651C2×C4⋊C4C2×C4×C2314yescomplemented
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4C2×C4×C2314yes—
660C2×C22⋊C4C2×C4×C2314yes—
661C2×C22⋊C4D4×C2314yes—
662C2×C22⋊C4D4×C2314yes—
663C2×C22⋊C4Q8×C2314yes—
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—41no—
669C2×C42—41no—
670#95—22no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—41no—
684#95—41no—
685#95C2×C4×C2314yescomplemented
686#95C2×C4×C2314yescomplemented
687#95D4×C2314yes—
688C23#1400411yescharacteristic, direct product factor, Sylow
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C22×C4×C2312yes—
698C24C2×D4×C2312yes—
699C24C2×D4×C2312yes—
700C24C2×Q8×C2312yes—
701C24C2×Q8×C2312yes—
702C24#41×C2312yes—
703C24#41×C2312yes—
704C24C24×C2311yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4C22×C4×C2312yes—
805C22×C4C22×C4×C2312yes—
806C22×C4C22×C4×C2312yes—
807C22×C4C22×C4×C2312yes—
808C22×C4C22×C4×C2312yes—
809C22×C4C22×C4×C2312yes—
810C22×C4C2×D4×C2312yes—
811C22×C4C2×D4×C2312yes—
812C22×C4C2×D4×C2312yes—
813C22×C4C2×D4×C2312yes—
814C22×C4C2×D4×C2312yes—
815C22×C4C2×D4×C2312yes—
816C22×C4C2×D4×C2312yes—
817C22×C4C2×Q8×C2312yes—
818C22×C4C2×Q8×C2312yes—
819C22×C4C2×Q8×C2312yes—
820C22×C4C2×Q8×C2312yes—
821C22×C4#41×C2312yes—
822C22×C4#41×C2312yes—
823C22×C4#41×C2312yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—44no—
835C22⋊C4C4⋊C4×C23116yescomplemented
836C42—44no—
837C42—44no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4⋊C4×C2314yes—
867C23C4×D4×C2314yes—
868C23C4×Q8×C2314yes—
869C23C23×#12114yes—
870C23C23×C22⋊Q814yes—
871C23C23×#12514yes—
872C23C23×C4⋊Q814yes—
873C23C23×C4×C2311yescharacteristic
874C23C22×D4×C2311yescharacteristic
875C23C22×D4×C2311yescharacteristic
876C23C22×D4×C2311yescharacteristic
877C23C22×Q8×C2311yescharacteristic
878C23C22×Q8×C2311yescharacteristic
879C23C2×#41×C2311yescharacteristic
880C23C2×#41×C2311yescharacteristic
881C23C2×#41×C2311yescharacteristic
882C23C2×#41×C2311yescharacteristic
883C23C2×#41×C2311yescharacteristic
884C23C23×H(5,𝔽2)11yescharacteristic
885C23C23×H(5,𝔽2)11yescharacteristic
886C23C23×H(5,𝔽2)11yescharacteristic
887C23C23×2−1+411yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—416no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4C2×C4⋊C4×C2314yes—
986C2×C4C2×C4⋊C4×C2314yes—
987C2×C4C4×D4×C2314yes—
988C2×C4C23×C22⋊Q814yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C23×#38918yescomplemented
1004C22C22×C4⋊C4×C2311yescharacteristic
1005C22C2×C4×D4×C2311yescharacteristic
1006C22C2×C4×D4×C2311yescharacteristic
1007C22C2×C4×Q8×C2311yescharacteristic
1008C22C4×#41×C2311yescharacteristic
1009C22C23×#51811yescharacteristic
1010C22C23×#52011yescharacteristic
1011C22C2×C23×#12111yescharacteristic
1012C22C2×C23×C22⋊Q811yescharacteristic
1013C22C2×C23×C22⋊Q811yescharacteristic
1014C22C23×#52511yescharacteristic
1015C22C2×C23×#12511yescharacteristic
1016C22C23×#52911yescharacteristic
1017C22C2×C23×C4⋊Q811yescharacteristic
1018C22C23×#53311yescharacteristic
1019C22C23×#53811yescharacteristic
1020C22C23×#53911yescharacteristic
1021C22C23×#54311yescharacteristic
1022C22C23×#54411yescharacteristic
1023C22D42×C2311yescharacteristic
1024C22D42×C2311yescharacteristic
1025C22C23×#54611yescharacteristic
1026C22C23×#54611yescharacteristic
1027C22C23×#54611yescharacteristic
1028C22C23×#54611yescharacteristic
1029C22C23×#54611yescharacteristic
1030C22C23×#54711yescharacteristic
1031C22C23×#54711yescharacteristic
1032C22D4×Q8×C2311yescharacteristic
1033C22C23×#55111yescharacteristic
1034C22C23×#55111yescharacteristic
1035C22C23×#55211yescharacteristic
1036C22C23×#55411yescharacteristic
1037C22C23×#55411yescharacteristic
1038C22C23×#55411yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—24no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—81no—
1052C4—81no—
1053C2—28no—
1054C2C2×C23×#38911yescharacteristic
1055C2C4×C23×C22⋊Q811yescharacteristic
1056C2C23×#232911yescharacteristic
1057C2D4×C4⋊C4×C2311yescharacteristic
1058C2C23×#234911yescharacteristic
1059C2C23×#235811yescharacteristic
1060C2C23×#235911yescharacteristic
1061C2C23×#242411yescharacteristic
1062C2C23×#242511yescharacteristic
1063C2C23×#243711yescharacteristic
1064C2C23×#243811yescharacteristic
1065C2C23×#244011yescharacteristic
1066C2C23×#247311yescharacteristic
1067C2C23×#250511yescharacteristic
1068C2C23×#254911yescharacteristic
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
1. C2×C23×#389C2semidirect
8. C23×#1444C2semidirect
9. C23×#1442C2semidirect
10. C23×#1441C2semidirect
11. C23×#1441C2semidirect
12. C23×#1436C2semidirect
13. C23×#1436C2semidirect
14. C23×C4⋊#95C2semidirect
36. C23×#385C4semidirect
116. C2×C4⋊C4×C23C2×C4semidirect
117. C2×C4⋊C4×C23C2×C4semidirect
151. C23×#95C2×C4semidirect
152. C23×#95C2×C4semidirect
300. C22⋊C4×C23C4⋊C4semidirect
303. #14004C23direct (N × H)
455. C2×#389C2×C23semidirect
462. #1444C2×C23semidirect
463. #1442C2×C23semidirect
464. #1441C2×C23semidirect
465. #1441C2×C23semidirect
466. #1436C2×C23semidirect
467. #1436C2×C23semidirect
468. C4⋊#95C2×C23semidirect
484. C22×C23#389semidirect
554. #385C4×C23semidirect
650. C2×C4⋊C4C2×C4×C23semidirect
651. C2×C4⋊C4C2×C4×C23semidirect
685. #95C2×C4×C23semidirect
686. #95C2×C4×C23semidirect
688. C23#14004direct (N × H)
835. C22⋊C4C4⋊C4×C23semidirect
1003. C22C23×#389semidirect

Maximal subgroups

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

subgroupindex
C2×C23×#3892
C2×C23×#3852
C2×C23×#3802
C2×C4×C22⋊C4×C232
C22×C23×#952
C23×#14442
C23×#14422
C23×#14412
C23×#14362
C23×C4⋊#952
C23×C22⋊#952
#1400423