Finite Group Databasebeta

← C23×#13975 #19161601

Subgroups — C23×#13975 #19161601

Order 5888.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C23C211yesmaximal, characteristic
2C2×C23×#386C211yesmaximal, characteristic
3C2×C23×#386C211yesmaximal, characteristic
4C2×C23×#385C211yesmaximal, characteristic, complemented
5C2×C23×#385C211yesmaximal, characteristic, complemented
6C2×C23×#380C211yesmaximal, characteristic, complemented
7C22×C23×#95C211yesmaximal, characteristic, complemented
8C23×#1444C211yesmaximal, characteristic, complemented
9C23×#1442C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1436C211yesmaximal, characteristic, complemented
13C23×#1436C211yesmaximal, characteristic, complemented
14C23×C22⋊#95C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C24×C4×C23C2211yescharacteristic
19C24×C4×C23C2211yescharacteristic
20C24×C4×C23C2211yescharacteristic
21C2×C4×D4×C23—24no—
22C2×C4×D4×C23—24no—
23C2×C4×D4×C23—24no—
24C22×C4⋊C4×C23C2211yescharacteristic
25C22×C4⋊C4×C23C2211yescharacteristic
26C22×C4⋊C4×C23C2211yescharacteristic
27C22×C4⋊C4×C23C2211yescharacteristic
28C22×C4⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C22⋊C4×C23C2211yescharacteristic
32C22×C22⋊C4×C23C2211yescharacteristic
33C22×C22⋊C4×C23C2211yescharacteristic
34C22×C22⋊C4×C23C2211yescharacteristic
35C22×C22⋊C4×C23C2211yescharacteristic
36C22×C22⋊C4×C23C2211yescharacteristic
37C22×C42×C23C2211yescharacteristic
38C23×#386—24no—
39C23×#386C418yescomplemented
40C23×#385—24no—
41C23×#385—24no—
42C23×#380—24no—
43C2×C23×#95—24no—
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
58C2×C23×#95C2211yescharacteristic
59C2×C23×#95C2211yescharacteristic
60C25×C23C2311yescharacteristic
61C25×C23C2311yescharacteristic
62C22×D4×C23—22no—
63C22×D4×C23—22no—
64C22×D4×C23—22no—
65C22×D4×C23—22no—
66C22×D4×C23C2×C414yes—
67C22×D4×C23D414yes—
68C22×D4×C23Q814yes—
69C23×C4×C23—22no—
70C23×C4×C23—22no—
71C23×C4×C23—22no—
72C23×C4×C23—22no—
73C23×C4×C23—22no—
74C23×C4×C23—22no—
75C23×C4×C23—22no—
76C23×C4×C23—22no—
77C23×C4×C23—22no—
78C23×C4×C23—22no—
79C23×C4×C23—22no—
80C23×C4×C23—22no—
81C23×C4×C23—22no—
82C23×C4×C23—22no—
83C23×C4×C23—22no—
84C23×C4×C23—22no—
85C23×C4×C23—22no—
86C23×C4×C23—22no—
87C23×C4×C23—41no—
88C23×C4×C23—41no—
89C23×C4×C23—41no—
90C23×C4×C23—41no—
91C23×C4×C23—41no—
92C23×C4×C23—41no—
93C23×C4×C23—41no—
94C23×C4×C23—41no—
95C23×C4×C23C2×C414yescomplemented
96C23×C4×C23D414yes—
97C23×C4×C23C2311yescharacteristic
98C23×C4×C23C2311yescharacteristic
99C23×C4×C23C2311yescharacteristic
100C23×C4×C23C2311yescharacteristic
101C23×C4×C23C2311yescharacteristic
102C23×C4×C23C2311yescharacteristic
103C23×C4×C23C2311yescharacteristic
104C23×C4×C23C2311yescharacteristic
105C23×C4×C23C2311yescharacteristic
106C23×C4×C23C2311yescharacteristic
107C23×C4×C23C2311yescharacteristic
108C23×C4×C23C2311yescharacteristic
109C23×C4×C23C2311yescharacteristic
110C4×D4×C23—232no—
111C2×C4⋊C4×C23—22no—
112C2×C4⋊C4×C23—22no—
113C2×C4⋊C4×C23—22no—
114C2×C4⋊C4×C23—22no—
115C2×C4⋊C4×C23—22no—
116C2×C4⋊C4×C23—22no—
117C2×C4⋊C4×C23—22no—
118C2×C4⋊C4×C23—22no—
119C2×C4⋊C4×C23—22no—
120C2×C4⋊C4×C23—22no—
121C2×C4⋊C4×C23—22no—
122C2×C4⋊C4×C23—41no—
123C2×C4⋊C4×C23—41no—
124C2×C4⋊C4×C23—41no—
125C2×C4⋊C4×C23—41no—
126C2×C22⋊C4×C23—22no—
127C2×C22⋊C4×C23—22no—
128C2×C22⋊C4×C23—22no—
129C2×C22⋊C4×C23—22no—
130C2×C22⋊C4×C23—22no—
131C2×C22⋊C4×C23—22no—
132C2×C22⋊C4×C23—22no—
133C2×C22⋊C4×C23—22no—
134C2×C22⋊C4×C23—22no—
135C2×C22⋊C4×C23—22no—
136C2×C22⋊C4×C23—22no—
137C2×C22⋊C4×C23—22no—
138C2×C22⋊C4×C23—22no—
139C2×C22⋊C4×C23—22no—
140C2×C22⋊C4×C23—22no—
141C2×C22⋊C4×C23—22no—
142C2×C22⋊C4×C23—41no—
143C2×C22⋊C4×C23—41no—
144C2×C22⋊C4×C23—41no—
145C2×C22⋊C4×C23—41no—
146C2×C22⋊C4×C23C2×C414yescomplemented
147C2×C22⋊C4×C23C2×C414yescomplemented
148C2×C22⋊C4×C23C2×C414yescomplemented
149C2×C22⋊C4×C23D414yes—
150C2×C42×C23—22no—
151C2×C42×C23—22no—
152C2×C42×C23—22no—
153C23×#95—22no—
154C23×#95—22no—
155C23×#95—22no—
156C23×#95—22no—
157C23×#95—22no—
158C23×#95—22no—
159C23×#95—22no—
160C23×#95—22no—
161C23×#95—22no—
162C23×#95—22no—
163C23×#95—22no—
164C23×#95—41no—
165C23×#95—41no—
166C23×#95C2×C414yescomplemented
167C23×#95C2×C414yescomplemented
168C23×#95D414yescomplemented
169C24×C23—21no—
170C24×C23—21no—
171C24×C23—21no—
172C24×C23—21no—
173C24×C23—21no—
174C24×C23—21no—
175C24×C23—21no—
176C24×C23—21no—
177C24×C23—21no—
178C24×C23—21no—
179C24×C23—21no—
180C24×C23—21no—
181C24×C23—21no—
182C24×C23—21no—
183C24×C23—21no—
184C24×C23—21no—
185C24×C23—21no—
186C24×C23—21no—
187C24×C23—21no—
188C24×C23—21no—
189C24×C23C22×C412yes—
190C24×C23C22×C412yes—
191C24×C23C2×D412yes—
192C24×C23C2×D412yes—
193C24×C23C2×D412yes—
194C24×C23C2×D412yes—
195C24×C23C2×Q812yes—
196C24×C23C2×Q812yes—
197C24×C23#4112yes—
198C24×C23#4112yes—
199C24×C23C2411yescharacteristic
200C2×D4×C23—28no—
201C2×D4×C23—28no—
202C2×D4×C23—28no—
203C2×D4×C23—28no—
204C2×D4×C23—28no—
205C2×D4×C23—28no—
206C2×D4×C23C4⋊C4116yescomplemented
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—28no—
220C22×C4×C23—28no—
221C22×C4×C23—28no—
222C22×C4×C23—28no—
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—21no—
238C22×C4×C23—21no—
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—21no—
254C22×C4×C23—21no—
255C22×C4×C23—21no—
256C22×C4×C23—21no—
257C22×C4×C23—21no—
258C22×C4×C23—21no—
259C22×C4×C23—21no—
260C22×C4×C23—21no—
261C22×C4×C23—21no—
262C22×C4×C23—21no—
263C22×C4×C23—21no—
264C22×C4×C23—21no—
265C22×C4×C23—21no—
266C22×C4×C23—21no—
267C22×C4×C23—21no—
268C22×C4×C23—21no—
269C22×C4×C23—21no—
270C22×C4×C23—21no—
271C22×C4×C23—28no—
272C22×C4×C23—28no—
273C22×C4×C23—21no—
274C22×C4×C23—21no—
275C22×C4×C23—21no—
276C22×C4×C23—21no—
277C22×C4×C23—21no—
278C22×C4×C23—21no—
279C22×C4×C23—21no—
280C22×C4×C23—21no—
281C22×C4×C23—21no—
282C22×C4×C23—21no—
283C22×C4×C23—21no—
284C22×C4×C23—21no—
285C22×C4×C23—21no—
286C22×C4×C23—21no—
287C22×C4×C23—44no—
288C22×C4×C23—44no—
289C22×C4×C23—44no—
290C22×C4×C23—44no—
291C22×C4×C23—44no—
292C22×C4×C23—44no—
293C22×C4×C23—44no—
294C22×C4×C23—44no—
295C22×C4×C23—44no—
296C22×C4×C23—44no—
297C22×C4×C23—44no—
298C22×C4×C23—44no—
299C22×C4×C23—44no—
300C22×C4×C23—44no—
301C22×C4×C23—44no—
302C22×C4×C23—44no—
303C22×C4×C23—44no—
304C22×C4×C23—44no—
305C22×C4×C23—44no—
306C22×C4×C23—44no—
307C22×C4×C23—44no—
308C22×C4×C23—44no—
309C22×C4×C23C22×C412yes—
310C22×C4×C23C22×C412yes—
311C22×C4×C23C22×C412yes—
312C22×C4×C23C22×C412yes—
313C22×C4×C23C22×C412yes—
314C22×C4×C23C2×D412yes—
315C22×C4×C23C2×D412yes—
316C22×C4×C23C2×D412yes—
317C22×C4×C23C2×D412yes—
318C22×C4×C23C2×D412yes—
319C22×C4×C23C2×D412yes—
320C22×C4×C23C2×D412yes—
321C22×C4×C23C2×D412yes—
322C22×C4×C23C2×Q812yes—
323C22×C4×C23#4112yes—
324C22×C4×C23#4112yes—
325C22×C4×C23#4112yes—
326C4⋊C4×C23—28no—
327C4⋊C4×C23—44no—
328C4⋊C4×C23—44no—
329C4⋊C4×C23—44no—
330C4⋊C4×C23—44no—
331C22⋊C4×C23—28no—
332C22⋊C4×C23—28no—
333C22⋊C4×C23—28no—
334C22⋊C4×C23—28no—
335C22⋊C4×C23—44no—
336C22⋊C4×C23—44no—
337C22⋊C4×C23—44no—
338C22⋊C4×C23—44no—
339C42×C23—28no—
340#13975C2311yesmaximal, characteristic, direct product factor, Sylow
341C23×C23—22no—
342C23×C23—22no—
343C23×C23—22no—
344C23×C23—22no—
345C23×C23—22no—
346C23×C23—22no—
347C23×C23—22no—
348C23×C23—22no—
349C23×C23—22no—
350C23×C23—22no—
351C23×C23—22no—
352C23×C23—22no—
353C23×C23—22no—
354C23×C23—22no—
355C23×C23—22no—
356C23×C23—22no—
357C23×C23—22no—
358C23×C23—22no—
359C23×C23—22no—
360C23×C23—22no—
361C23×C23—22no—
362C23×C23—22no—
363C23×C23—22no—
364C23×C23—22no—
365C23×C23—22no—
366C23×C23—22no—
367C23×C23—22no—
368C23×C23—22no—
369C23×C23—22no—
370C23×C23—22no—
371C23×C23—22no—
372C23×C23—22no—
373C23×C23—22no—
374C23×C23—22no—
375C23×C23—22no—
376C23×C23—22no—
377C23×C23—22no—
378C23×C23—22no—
379C23×C23—22no—
380C23×C23—22no—
381C23×C23—22no—
382C23×C23—22no—
383C23×C23—22no—
384C23×C23—22no—
385C23×C23—22no—
386C23×C23—22no—
387C23×C23—41no—
388C23×C23—41no—
389C23×C23—41no—
390C23×C23—41no—
391C23×C23—41no—
392C23×C23—41no—
393C23×C23—41no—
394C23×C23—41no—
395C23×C23—41no—
396C23×C23—41no—
397C23×C23—41no—
398C23×C23—41no—
399C23×C23—41no—
400C23×C23—41no—
401C23×C23—41no—
402C23×C23—41no—
403C23×C23C2×C4⋊C414yes—
404C23×C23C2×C4⋊C414yes—
405C23×C23C4×D414yes—
406C23×C23C4×D414yes—
407C23×C23#12014yes—
408C23×C23C22⋊Q814yes—
409C23×C23C22⋊Q814yes—
410C23×C23#12314yes—
411C23×C23C23×C411yescharacteristic
412C23×C23C22×D411yescharacteristic
413C23×C23C22×D411yescharacteristic
414C23×C23C22×D411yescharacteristic
415C23×C23C22×D411yescharacteristic
416C23×C23C22×Q811yescharacteristic
417C23×C23C2×#4111yescharacteristic
418C23×C23C2×#4111yescharacteristic
419C23×C23C2×#4111yescharacteristic
420C23×C23C2×#4111yescharacteristic
421C23×C23C2×#4111yescharacteristic
422C23×C23H(5,𝔽2)11yescharacteristic
423C23×C23H(5,𝔽2)11yescharacteristic
424C23×C23H(5,𝔽2)11yescharacteristic
425C23×C232−1+411yescharacteristic
426D4×C23—232no—
427C2×C4×C23—22no—
428C2×C4×C23—22no—
429C2×C4×C23—22no—
430C2×C4×C23—22no—
431C2×C4×C23—22no—
432C2×C4×C23—22no—
433C2×C4×C23—22no—
434C2×C4×C23—22no—
435C2×C4×C23—22no—
436C2×C4×C23—22no—
437C2×C4×C23—22no—
438C2×C4×C23—22no—
439C2×C4×C23—22no—
440C2×C4×C23—22no—
441C2×C4×C23—22no—
442C2×C4×C23—22no—
443C2×C4×C23—22no—
444C2×C4×C23—22no—
445C2×C4×C23—22no—
446C2×C4×C23—22no—
447C2×C4×C23—22no—
448C2×C4×C23—22no—
449C2×C4×C23—22no—
450C2×C4×C23—22no—
451C2×C4×C23—22no—
452C2×C4×C23—22no—
453C2×C4×C23—22no—
454C2×C4×C23—22no—
455C2×C4×C23—22no—
456C2×C4×C23—22no—
457C2×C4×C23—22no—
458C2×C4×C23—22no—
459C2×C4×C23—22no—
460C2×C4×C23—22no—
461C2×C4×C23—22no—
462C2×C4×C23—22no—
463C2×C4×C23—22no—
464C2×C4×C23—22no—
465C2×C4×C23—22no—
466C2×C4×C23—22no—
467C2×C4×C23—22no—
468C2×C4×C23—22no—
469C2×C4×C23—416no—
470C2×C4×C23—416no—
471C2×C4×C23—416no—
472C2×C4×C23—416no—
473C2×C4×C23—41no—
474C2×C4×C23—41no—
475C2×C4×C23—41no—
476C2×C4×C23—41no—
477C2×C4×C23—41no—
478C2×C4×C23—41no—
479C2×C4×C23—41no—
480C2×C4×C23—41no—
481C2×C4×C23—41no—
482C2×C4×C23—41no—
483C2×C4×C23—41no—
484C2×C4×C23—41no—
485C2×C4×C23—41no—
486C2×C4×C23—41no—
487C2×C4×C23—41no—
488C2×C4×C23—41no—
489C2×C4×C23—41no—
490C2×C4×C23—41no—
491C2×C4×C23—41no—
492C2×C4×C23—41no—
493C2×C4×C23—41no—
494C2×C4×C23—41no—
495C2×C4×C23—41no—
496C2×C4×C23—41no—
497C2×C4×C23—41no—
498C2×C4×C23—41no—
499C2×C4×C23—41no—
500C2×C4×C23—41no—
501C2×C4×C23—41no—
502C2×C4×C23—41no—
503C2×C4×C23—41no—
504C2×C4×C23—41no—
505C2×C4×C23—41no—
506C2×C4×C23—41no—
507C2×C4×C23—41no—
508C2×C4×C23—41no—
509C2×C4×C23—41no—
510C2×C4×C23—41no—
511C2×C4×C23—41no—
512C2×C4×C23—41no—
513C2×C4×C23—41no—
514C2×C4×C23—41no—
515C2×C4×C23—41no—
516C2×C4×C23—41no—
517C2×C4×C23—41no—
518C2×C4×C23—41no—
519C2×C4×C23C2×C4⋊C414yes—
520C2×C4×C23C4×D414yescomplemented
521C2×C4×C23#12114yes—
522C22×C4×D4C2×C2311yescharacteristic
523C2×#386C2×C2311yescharacteristic
524C2×#386C2×C2311yescharacteristic
525C2×#385C2×C2311yescharacteristic, complemented
526C2×#385C2×C2311yescharacteristic, complemented
527C2×#380C2×C2311yescharacteristic, complemented
528C22×#95C2×C2311yescharacteristic, complemented
529#1444C2×C2311yescharacteristic, complemented
530#1442C2×C2311yescharacteristic, complemented
531#1439C2×C2311yescharacteristic, complemented
532#1439C2×C2311yescharacteristic, complemented
533#1436C2×C2311yescharacteristic, complemented
534#1436C2×C2311yescharacteristic, complemented
535C22⋊#95C2×C2311yescharacteristic, complemented
536C22⋊#95C2×C2311yescharacteristic, complemented
537C22×C23—24no—
538C22×C23—24no—
539C22×C23—24no—
540C22×C23—24no—
541C22×C23—24no—
542C22×C23—24no—
543C22×C23—24no—
544C22×C23—24no—
545C22×C23—24no—
546C22×C23—24no—
547C22×C23—24no—
548C22×C23—24no—
549C22×C23—24no—
550C22×C23—24no—
551C22×C23—24no—
552C22×C23—24no—
553C22×C23—24no—
554C22×C23—42no—
555C22×C23—42no—
556C22×C23—42no—
557C22×C23—42no—
558C22×C23—42no—
559C22×C23—42no—
560C22×C23—42no—
561C22×C23—42no—
562C22×C23—42no—
563C22×C23—42no—
564C22×C23—42no—
565C22×C23—42no—
566C22×C23#38518yescomplemented
567C22×C23C22×C4⋊C411yescharacteristic
568C22×C23C2×C4×D411yescharacteristic
569C22×C23C2×C4×D411yescharacteristic
570C22×C23C2×C4×D411yescharacteristic
571C22×C23C4×#4111yescharacteristic
572C22×C23#51811yescharacteristic
573C22×C23#52011yescharacteristic
574C22×C23C2×#12011yescharacteristic
575C22×C23C2×#12111yescharacteristic
576C22×C23C2×C22⋊Q811yescharacteristic
577C22×C23C2×C22⋊Q811yescharacteristic
578C22×C23C2×#12311yescharacteristic
579C22×C23#52511yescharacteristic
580C22×C23#52911yescharacteristic
581C22×C23#53211yescharacteristic
582C22×C23#53411yescharacteristic
583C22×C23#53711yescharacteristic
584C22×C23#53811yescharacteristic
585C22×C23#53911yescharacteristic
586C22×C23D4211yescharacteristic
587C22×C23D4211yescharacteristic
588C22×C23#54611yescharacteristic
589C22×C23#54611yescharacteristic
590C22×C23#54611yescharacteristic
591C22×C23#54611yescharacteristic
592C22×C23#54611yescharacteristic
593C22×C23#54711yescharacteristic
594C22×C23#54711yescharacteristic
595C22×C23D4×Q811yescharacteristic
596C22×C23#55111yescharacteristic
597C22×C23#55111yescharacteristic
598C22×C23#55211yescharacteristic
599C22×C23#55411yescharacteristic
600C22×C23#55411yescharacteristic
601C22×C23#55411yescharacteristic
602C4×C23—24no—
603C4×C23—24no—
604C4×C23—24no—
605C4×C23—42no—
606C4×C23—42no—
607C4×C23—42no—
608C4×C23—42no—
609C4×C23—42no—
610C4×C23—42no—
611C4×C23—42no—
612C4×C23—42no—
613C4×C23—81no—
614C4×C23—81no—
615C23×D4C22×C2311yescharacteristic
616C24×C4C22×C2311yescharacteristic
617C24×C4C22×C2311yescharacteristic
618C24×C4C22×C2311yescharacteristic
619C24×C4C22×C2311yescharacteristic
620C2×C4×D4—24no—
621C2×C4×D4—24no—
622C2×C4×D4—24no—
623C22×C4⋊C4C22×C2311yescharacteristic
624C22×C4⋊C4C22×C2311yescharacteristic
625C22×C4⋊C4C22×C2311yescharacteristic
626C22×C4⋊C4C22×C2311yescharacteristic
627C22×C4⋊C4C22×C2311yescharacteristic
628C22×C22⋊C4C22×C2311yescharacteristic
629C22×C22⋊C4C22×C2311yescharacteristic
630C22×C22⋊C4C22×C2311yescharacteristic
631C22×C22⋊C4C22×C2311yescharacteristic
632C22×C22⋊C4C22×C2311yescharacteristic
633C22×C22⋊C4C22×C2311yescharacteristic
634C22×C22⋊C4C22×C2311yescharacteristic
635C22×C22⋊C4C22×C2311yescharacteristic
636C22×C42C22×C2311yescharacteristic
637#386—24no—
638#386C4×C2318yescomplemented
639#385—24no—
640#385—24no—
641#380—24no—
642C2×#95—24no—
643C2×#95C22×C2311yescharacteristic
644C2×#95C22×C2311yescharacteristic
645C2×#95C22×C2311yescharacteristic
646C2×#95C22×C2311yescharacteristic
647C2×#95C22×C2311yescharacteristic
648C2×#95C22×C2311yescharacteristic
649C2×#95C22×C2311yescharacteristic
650C2×#95C22×C2311yescharacteristic
651C2×#95C22×C2311yescharacteristic
652C2×#95C22×C2311yescharacteristic
653C2×#95C22×C2311yescharacteristic
654C2×#95C22×C2311yescharacteristic
655C2×#95C22×C2311yescharacteristic
656C2×#95C22×C2311yescharacteristic
657C2×#95C22×C2311yescharacteristic
658C2×#95C22×C2311yescharacteristic
659C2×C23—28no—
660C2×C23—44no—
661C2×C23C2×#38511yescharacteristic
662C2×C23C4×#12111yescharacteristic
663C2×C23#232511yescharacteristic
664C2×C23D4×C4⋊C411yescharacteristic
665C2×C23#234911yescharacteristic
666C2×C23#235811yescharacteristic
667C2×C23#235911yescharacteristic
668C2×C23#241011yescharacteristic
669C2×C23#241711yescharacteristic
670C2×C23#241811yescharacteristic
671C2×C23#241911yescharacteristic
672C2×C23#243011yescharacteristic
673C2×C23#244911yescharacteristic
674C2×C23#245011yescharacteristic
675C2×C23#256411yescharacteristic
676C25C23×C2311yescharacteristic
677C25C23×C2311yescharacteristic
678C22×D4—22no—
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4C2×C4×C2314yes—
683C22×D4D4×C2314yes—
684C22×D4Q8×C2314yes—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—22no—
691C23×C4—22no—
692C23×C4—22no—
693C23×C4—22no—
694C23×C4—22no—
695C23×C4—22no—
696C23×C4—22no—
697C23×C4—22no—
698C23×C4—22no—
699C23×C4—22no—
700C23×C4—22no—
701C23×C4—22no—
702C23×C4—22no—
703C23×C4—41no—
704C23×C4—41no—
705C23×C4—41no—
706C23×C4—41no—
707C23×C4—41no—
708C23×C4—41no—
709C23×C4—41no—
710C23×C4—41no—
711C23×C4C2×C4×C2314yescomplemented
712C23×C4D4×C2314yes—
713C23×C4C23×C2311yescharacteristic
714C23×C4C23×C2311yescharacteristic
715C23×C4C23×C2311yescharacteristic
716C23×C4C23×C2311yescharacteristic
717C23×C4C23×C2311yescharacteristic
718C23×C4C23×C2311yescharacteristic
719C23×C4C23×C2311yescharacteristic
720C23×C4C23×C2311yescharacteristic
721C23×C4C23×C2311yescharacteristic
722C23×C4C23×C2311yescharacteristic
723C23×C4C23×C2311yescharacteristic
724C23×C4C23×C2311yescharacteristic
725C23×C4C23×C2311yescharacteristic
726C4×D4—232no—
727C2×C4⋊C4—22no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—22no—
733C2×C4⋊C4—22no—
734C2×C4⋊C4—22no—
735C2×C4⋊C4—22no—
736C2×C4⋊C4—22no—
737C2×C4⋊C4—22no—
738C2×C4⋊C4—41no—
739C2×C4⋊C4—41no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4—41no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—41no—
759C2×C22⋊C4—41no—
760C2×C22⋊C4—41no—
761C2×C22⋊C4—41no—
762C2×C22⋊C4C2×C4×C2314yescomplemented
763C2×C22⋊C4C2×C4×C2314yescomplemented
764C2×C22⋊C4C2×C4×C2314yescomplemented
765C2×C22⋊C4D4×C2314yes—
766C2×C42—22no—
767C2×C42—22no—
768C2×C42—22no—
769#95—22no—
770#95—22no—
771#95—22no—
772#95—22no—
773#95—22no—
774#95—22no—
775#95—22no—
776#95—22no—
777#95—22no—
778#95—22no—
779#95—22no—
780#95—41no—
781#95—41no—
782#95C2×C4×C2314yescomplemented
783#95C2×C4×C2314yescomplemented
784#95D4×C2314yescomplemented
785C23#1397511yescharacteristic, direct product factor, Sylow
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24C22×C4×C2312yes—
807C24C22×C4×C2312yes—
808C24C2×D4×C2312yes—
809C24C2×D4×C2312yes—
810C24C2×D4×C2312yes—
811C24C2×D4×C2312yes—
812C24C2×Q8×C2312yes—
813C24C2×Q8×C2312yes—
814C24#41×C2312yes—
815C24#41×C2312yes—
816C24C24×C2311yescharacteristic
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4C4⋊C4×C23116yescomplemented
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—28no—
837C22×C4—28no—
838C22×C4—28no—
839C22×C4—28no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—28no—
889C22×C4—28no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4C22×C4×C2312yes—
927C22×C4C22×C4×C2312yes—
928C22×C4C22×C4×C2312yes—
929C22×C4C22×C4×C2312yes—
930C22×C4C22×C4×C2312yes—
931C22×C4C2×D4×C2312yes—
932C22×C4C2×D4×C2312yes—
933C22×C4C2×D4×C2312yes—
934C22×C4C2×D4×C2312yes—
935C22×C4C2×D4×C2312yes—
936C22×C4C2×D4×C2312yes—
937C22×C4C2×D4×C2312yes—
938C22×C4C2×D4×C2312yes—
939C22×C4C2×Q8×C2312yes—
940C22×C4#41×C2312yes—
941C22×C4#41×C2312yes—
942C22×C4#41×C2312yes—
943C4⋊C4—28no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C42—28no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23C2×C4⋊C4×C2314yes—
1020C23C2×C4⋊C4×C2314yes—
1021C23C4×D4×C2314yes—
1022C23C4×D4×C2314yes—
1023C23C23×#12014yes—
1024C23C23×C22⋊Q814yes—
1025C23C23×C22⋊Q814yes—
1026C23C23×#12314yes—
1027C23C23×C4×C2311yescharacteristic
1028C23C22×D4×C2311yescharacteristic
1029C23C22×D4×C2311yescharacteristic
1030C23C22×D4×C2311yescharacteristic
1031C23C22×D4×C2311yescharacteristic
1032C23C22×Q8×C2311yescharacteristic
1033C23C2×#41×C2311yescharacteristic
1034C23C2×#41×C2311yescharacteristic
1035C23C2×#41×C2311yescharacteristic
1036C23C2×#41×C2311yescharacteristic
1037C23C2×#41×C2311yescharacteristic
1038C23C23×H(5,𝔽2)11yescharacteristic
1039C23C23×H(5,𝔽2)11yescharacteristic
1040C23C23×H(5,𝔽2)11yescharacteristic
1041C23C23×2−1+411yescharacteristic
1042D4—232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—416no—
1086C2×C4—416no—
1087C2×C4—416no—
1088C2×C4—416no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4C2×C4⋊C4×C2314yes—
1136C2×C4C4×D4×C2314yescomplemented
1137C2×C4C23×#12114yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22C23×#38518yescomplemented
1168C22C22×C4⋊C4×C2311yescharacteristic
1169C22C2×C4×D4×C2311yescharacteristic
1170C22C2×C4×D4×C2311yescharacteristic
1171C22C2×C4×D4×C2311yescharacteristic
1172C22C4×#41×C2311yescharacteristic
1173C22C23×#51811yescharacteristic
1174C22C23×#52011yescharacteristic
1175C22C2×C23×#12011yescharacteristic
1176C22C2×C23×#12111yescharacteristic
1177C22C2×C23×C22⋊Q811yescharacteristic
1178C22C2×C23×C22⋊Q811yescharacteristic
1179C22C2×C23×#12311yescharacteristic
1180C22C23×#52511yescharacteristic
1181C22C23×#52911yescharacteristic
1182C22C23×#53211yescharacteristic
1183C22C23×#53411yescharacteristic
1184C22C23×#53711yescharacteristic
1185C22C23×#53811yescharacteristic
1186C22C23×#53911yescharacteristic
1187C22D42×C2311yescharacteristic
1188C22D42×C2311yescharacteristic
1189C22C23×#54611yescharacteristic
1190C22C23×#54611yescharacteristic
1191C22C23×#54611yescharacteristic
1192C22C23×#54611yescharacteristic
1193C22C23×#54611yescharacteristic
1194C22C23×#54711yescharacteristic
1195C22C23×#54711yescharacteristic
1196C22D4×Q8×C2311yescharacteristic
1197C22C23×#55111yescharacteristic
1198C22C23×#55111yescharacteristic
1199C22C23×#55211yescharacteristic
1200C22C23×#55411yescharacteristic
1201C22C23×#55411yescharacteristic
1202C22C23×#55411yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—42no—
1210C4—42no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—81no—
1215C4—81no—
1216C2—28no—
1217C2—44no—
1218C2C2×C23×#38511yescharacteristic
1219C2C4×C23×#12111yescharacteristic
1220C2C23×#232511yescharacteristic
1221C2D4×C4⋊C4×C2311yescharacteristic
1222C2C23×#234911yescharacteristic
1223C2C23×#235811yescharacteristic
1224C2C23×#235911yescharacteristic
1225C2C23×#241011yescharacteristic
1226C2C23×#241711yescharacteristic
1227C2C23×#241811yescharacteristic
1228C2C23×#241911yescharacteristic
1229C2C23×#243011yescharacteristic
1230C2C23×#244911yescharacteristic
1231C2C23×#245011yescharacteristic
1232C2C23×#256411yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC23×D4×C23C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C23×#385C2semidirect
5. C2×C23×#385C2semidirect
6. C2×C23×#380C2semidirect
7. C22×C23×#95C2semidirect
8. C23×#1444C2semidirect
9. C23×#1442C2semidirect
10. C23×#1439C2semidirect
11. C23×#1439C2semidirect
12. C23×#1436C2semidirect
13. C23×#1436C2semidirect
14. C23×C22⋊#95C2semidirect
15. C23×C22⋊#95C2semidirect
39. C23×#386C4semidirect
95. C23×C4×C23C2×C4semidirect
146. C2×C22⋊C4×C23C2×C4semidirect
147. C2×C22⋊C4×C23C2×C4semidirect
148. C2×C22⋊C4×C23C2×C4semidirect
166. C23×#95C2×C4semidirect
167. C23×#95C2×C4semidirect
168. C23×#95D4semidirect
206. C2×D4×C23C4⋊C4semidirect
340. #13975C23direct (N × H)
520. C2×C4×C23C4×D4semidirect
525. C2×#385C2×C23semidirect
526. C2×#385C2×C23semidirect
527. C2×#380C2×C23semidirect
528. C22×#95C2×C23semidirect
529. #1444C2×C23semidirect
530. #1442C2×C23semidirect
531. #1439C2×C23semidirect
532. #1439C2×C23semidirect
533. #1436C2×C23semidirect
534. #1436C2×C23semidirect
535. C22⋊#95C2×C23semidirect
536. C22⋊#95C2×C23semidirect
566. C22×C23#385semidirect
638. #386C4×C23semidirect
711. C23×C4C2×C4×C23semidirect
762. C2×C22⋊C4C2×C4×C23semidirect
763. C2×C22⋊C4C2×C4×C23semidirect
764. C2×C22⋊C4C2×C4×C23semidirect
782. #95C2×C4×C23semidirect
783. #95C2×C4×C23semidirect
784. #95D4×C23semidirect
785. C23#13975direct (N × H)
823. C2×D4C4⋊C4×C23semidirect
1136. C2×C4C4×D4×C23semidirect
1167. C22C23×#385semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C232
C2×C23×#3862
C2×C23×#3852
C2×C23×#3802
C22×C23×#952
C23×#14442
C23×#14422
C23×#14392
C23×#14362
C23×C22⋊#952
#1397523