Finite Group Databasebeta

← C23×#16320 #19163946

Subgroups — C23×#16320 #19163946

Order 5888.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#393C211yesmaximal, characteristic, complemented
2C2×C23×#393C211yesmaximal, characteristic, complemented
3C2×C23×#386C211yesmaximal, characteristic
4C2×C23×#385C211yesmaximal, characteristic, complemented
5C23×#1446C211yesmaximal, characteristic, complemented
6C23×#1445C211yesmaximal, characteristic, complemented
7C23×#1443C211yesmaximal, characteristic, complemented
8C23×#1441C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1439C211yesmaximal, characteristic, complemented
13C23×#1438C211yesmaximal, characteristic
14C23×#1438C211yesmaximal, characteristic
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C23C2211yescharacteristic
17C23×D4×C23C2211yescharacteristic
18C24×C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C4⋊C4×C23C2211yescharacteristic
22C22×C22⋊C4×C23C2211yescharacteristic
23C22×C22⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C22⋊C4×C23C2211yescharacteristic
32C22×C22⋊C4×C23C2211yescharacteristic
33C23×#393—24no—
34C23×#393—24no—
35C23×#386—24no—
36C23×#385—24no—
37C2×C23×#95C2211yescharacteristic
38C2×C23×#95C2211yescharacteristic
39C2×C23×#95C2211yescharacteristic
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
55C25×C23C2311yescharacteristic
56C25×C23C2311yescharacteristic
57C22×Q8×C23—22no—
58C22×Q8×C23—22no—
59C22×Q8×C23—22no—
60C22×Q8×C23—41no—
61C22×Q8×C23—41no—
62C22×Q8×C23—41no—
63C22×Q8×C23—41no—
64C22×D4×C23—22no—
65C22×D4×C23—22no—
66C22×D4×C23—41no—
67C22×D4×C23—41no—
68C22×D4×C23—41no—
69C22×D4×C23—41no—
70C22×D4×C23Q814yescomplemented
71C23×C4×C23—22no—
72C23×C4×C23—22no—
73C23×C4×C23—22no—
74C23×C4×C23—41no—
75C23×C4×C23—41no—
76C23×C4×C23—41no—
77C23×C4×C23—41no—
78C23×C4×C23C2311yescharacteristic
79C23×C4×C23C2311yescharacteristic
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
91C2×C4⋊C4×C23—22no—
92C2×C4⋊C4×C23—22no—
93C2×C4⋊C4×C23—22no—
94C2×C4⋊C4×C23—22no—
95C2×C4⋊C4×C23—41no—
96C2×C4⋊C4×C23—41no—
97C2×C4⋊C4×C23—41no—
98C2×C4⋊C4×C23—41no—
99C2×C4⋊C4×C23—41no—
100C2×C22⋊C4×C23—22no—
101C2×C22⋊C4×C23—22no—
102C2×C22⋊C4×C23—22no—
103C2×C22⋊C4×C23—22no—
104C2×C22⋊C4×C23—22no—
105C2×C22⋊C4×C23—22no—
106C2×C22⋊C4×C23—22no—
107C2×C22⋊C4×C23—22no—
108C2×C22⋊C4×C23—22no—
109C2×C22⋊C4×C23—22no—
110C2×C22⋊C4×C23—22no—
111C2×C22⋊C4×C23—22no—
112C2×C22⋊C4×C23—22no—
113C2×C22⋊C4×C23—22no—
114C2×C22⋊C4×C23—22no—
115C2×C22⋊C4×C23—22no—
116C2×C22⋊C4×C23—41no—
117C2×C22⋊C4×C23—41no—
118C2×C22⋊C4×C23—41no—
119C2×C22⋊C4×C23—41no—
120C2×C22⋊C4×C23—41no—
121C2×C22⋊C4×C23—41no—
122C2×C22⋊C4×C23—41no—
123C2×C22⋊C4×C23—41no—
124C2×C22⋊C4×C23—41no—
125C2×C22⋊C4×C23—41no—
126C2×C22⋊C4×C23—41no—
127C2×C22⋊C4×C23—41no—
128C2×C22⋊C4×C23—41no—
129C2×C22⋊C4×C23—41no—
130C2×C22⋊C4×C23—41no—
131C2×C22⋊C4×C23—41no—
132C2×C22⋊C4×C23D414yes—
133C23×#95—22no—
134C23×#95—22no—
135C23×#95—22no—
136C23×#95—22no—
137C23×#95—22no—
138C23×#95—22no—
139C23×#95—22no—
140C23×#95—22no—
141C23×#95—41no—
142C23×#95—41no—
143C23×#95—41no—
144C23×#95—41no—
145C23×#95—41no—
146C23×#95—41no—
147C23×#95—41no—
148C23×#95—41no—
149C23×#95—41no—
150C23×#95D414yescomplemented
151C24×C23—21no—
152C24×C23—21no—
153C24×C23—21no—
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×C23—21no—
163C24×C23—21no—
164C24×C23—21no—
165C24×C23—21no—
166C24×C23—21no—
167C24×C23—21no—
168C24×C23—21no—
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×C23C2×D412yes—
178C24×C23C2×Q812yes—
179C24×C23C2×Q812yes—
180C24×C23#4112yes—
181C24×C23C2411yescharacteristic
182C2×Q8×C23—44no—
183C2×Q8×C23—44no—
184C2×Q8×C23—44no—
185C2×Q8×C23—44no—
186C2×Q8×C23—44no—
187C2×Q8×C23—44no—
188C2×Q8×C23—44no—
189C2×D4×C23—28no—
190C2×D4×C23—44no—
191C2×D4×C23—44no—
192C2×D4×C23—44no—
193C2×D4×C23—44no—
194C2×D4×C23—44no—
195C2×D4×C23—44no—
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—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—21no—
272C22×C4×C23—21no—
273C22×C4×C23—21no—
274C22×C4×C23—21no—
275C22×C4×C23—21no—
276C22×C4×C23—21no—
277C22×C4×C23—21no—
278C22×C4×C23—44no—
279C22×C4×C23—44no—
280C22×C4×C23—44no—
281C22×C4×C23—44no—
282C22×C4×C23—44no—
283C22×C4×C23—44no—
284C22×C4×C23—44no—
285C22×C4×C23C2×D412yes—
286C22×C4×C23C2×D412yes—
287C22×C4×C23C2×D412yes—
288C22×C4×C23C2×D412yes—
289C22×C4×C23C2×D412yes—
290C22×C4×C23C2×Q812yes—
291C22×C4×C23#4112yes—
292C22×C4×C23#4112yes—
293C22×C4×C23#4112yes—
294C4⋊C4×C23—44no—
295C4⋊C4×C23—44no—
296C4⋊C4×C23—44no—
297C22⋊C4×C23—28no—
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—
308#16320C2311yesmaximal, characteristic, direct product factor, Sylow
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×C23—22no—
333C23×C23—22no—
334C23×C23—41no—
335C23×C23—41no—
336C23×C23—41no—
337C23×C23—41no—
338C23×C23—41no—
339C23×C23—41no—
340C23×C23—41no—
341C23×C23—41no—
342C23×C23—41no—
343C23×C23—41no—
344C23×C23—41no—
345C23×C23—41no—
346C23×C23—41no—
347C23×C23—41no—
348C23×C23—41no—
349C23×C23—41no—
350C23×C23—41no—
351C23×C23—41no—
352C23×C23—41no—
353C23×C23—41no—
354C23×C23—41no—
355C23×C23—41no—
356C23×C23—41no—
357C23×C23—41no—
358C23×C23—41no—
359C23×C23—41no—
360C23×C23—41no—
361C23×C23—41no—
362C23×C23—41no—
363C23×C23—41no—
364C23×C23—41no—
365C23×C23—41no—
366C23×C23—41no—
367C23×C23—41no—
368C23×C23—41no—
369C23×C23—41no—
370C23×C23—41no—
371C23×C23—41no—
372C23×C23—41no—
373C23×C23—41no—
374C23×C23—41no—
375C23×C23—41no—
376C23×C23—41no—
377C23×C23—41no—
378C23×C23C22⋊Q814yes—
379C23×C23C22×D411yescharacteristic
380C23×C23C22×D411yescharacteristic
381C23×C23C22×Q811yescharacteristic
382C23×C23C2×#4111yescharacteristic
383C23×C23C2×#4111yescharacteristic
384C23×C23C2×#4111yescharacteristic
385C23×C23C2×#4111yescharacteristic
386C23×C23H(5,𝔽2)11yescharacteristic
387C23×C23H(5,𝔽2)11yescharacteristic
388C23×C23H(5,𝔽2)11yescharacteristic
389C23×C23H(5,𝔽2)11yescharacteristic
390C23×C23H(5,𝔽2)11yescharacteristic
391C23×C23H(5,𝔽2)11yescharacteristic
392C23×C23H(5,𝔽2)11yescharacteristic
393C23×C232−1+411yescharacteristic
394Q8×C23—416no—
395D4×C23—416no—
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—22no—
403C2×C4×C23—22no—
404C2×C4×C23—22no—
405C2×C4×C23—22no—
406C2×C4×C23—22no—
407C2×C4×C23—22no—
408C2×C4×C23—22no—
409C2×C4×C23—22no—
410C2×C4×C23—22no—
411C2×C4×C23—22no—
412C2×C4×C23—22no—
413C2×C4×C23—22no—
414C2×C4×C23—22no—
415C2×C4×C23—22no—
416C2×C4×C23—22no—
417C2×C4×C23—22no—
418C2×C4×C23—22no—
419C2×C4×C23—22no—
420C2×C4×C23—22no—
421C2×C4×C23—22no—
422C2×C4×C23—22no—
423C2×C4×C23—416no—
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×C23—41no—
452C2×C4×C23—41no—
453C2×C4×C23—41no—
454C2×C4×C23—41no—
455C2×C4×C23—41no—
456C2×C4×C23—41no—
457C2×C4×C23—41no—
458C2×C4×C23—41no—
459C2×C4×C23—41no—
460C2×C4×C23—41no—
461C2×C4×C23—41no—
462C2×C4×C23—41no—
463C2×C4×C23—41no—
464C2×C4×C23—41no—
465C2×C4×C23—41no—
466C2×C4×C23—41no—
467C2×C4×C23—41no—
468C2×C4×C23—41no—
469C2×C4×C23—41no—
470C2×C4×C23—41no—
471C2×C4×C23—41no—
472C2×C4×C23—41no—
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×#393C2×C2311yescharacteristic, complemented
489C2×#393C2×C2311yescharacteristic, complemented
490C2×#386C2×C2311yescharacteristic
491C2×#385C2×C2311yescharacteristic, complemented
492#1446C2×C2311yescharacteristic, complemented
493#1445C2×C2311yescharacteristic, complemented
494#1443C2×C2311yescharacteristic, complemented
495#1441C2×C2311yescharacteristic, complemented
496#1439C2×C2311yescharacteristic, complemented
497#1439C2×C2311yescharacteristic, complemented
498#1439C2×C2311yescharacteristic, complemented
499#1439C2×C2311yescharacteristic, complemented
500#1438C2×C2311yescharacteristic
501#1438C2×C2311yescharacteristic
502C22⋊#95C2×C2311yescharacteristic, complemented
503C22×C23—24no—
504C22×C23—24no—
505C22×C23—24no—
506C22×C23—42no—
507C22×C23—42no—
508C22×C23—42no—
509C22×C23—42no—
510C22×C23—42no—
511C22×C23—42no—
512C22×C23—42no—
513C22×C23—42no—
514C22×C23—42no—
515C22×C23—42no—
516C22×C23—42no—
517C22×C23—42no—
518C22×C23—42no—
519C22×C23—42no—
520C22×C23—42no—
521C22×C23—42no—
522C22×C23—42no—
523C22×C23—42no—
524C22×C23—42no—
525C22×C23—81no—
526C22×C23—81no—
527C22×C23—81no—
528C22×C23—81no—
529C22×C23—81no—
530C22×C23—81no—
531C22×C23—81no—
532C22×C23—81no—
533C22×C23C2×C22⋊Q811yescharacteristic
534C22×C23#52511yescharacteristic
535C22×C23#52911yescharacteristic
536C22×C23#53411yescharacteristic
537C22×C23#53511yescharacteristic
538C22×C23#53511yescharacteristic
539C22×C23#53511yescharacteristic
540C22×C23#53811yescharacteristic
541C22×C23#53811yescharacteristic
542C22×C23#53811yescharacteristic
543C22×C23#53811yescharacteristic
544C22×C23#53811yescharacteristic
545C22×C23#53811yescharacteristic
546C22×C23#53811yescharacteristic
547C22×C23#53911yescharacteristic
548C22×C23#54211yescharacteristic
549C22×C23#54211yescharacteristic
550C22×C23#54311yescharacteristic
551C22×C23#54311yescharacteristic
552C22×C23D4211yescharacteristic
553C22×C23#54611yescharacteristic
554C22×C23#54611yescharacteristic
555C22×C23#54611yescharacteristic
556C22×C23#54611yescharacteristic
557C22×C23#54711yescharacteristic
558C22×C23D4×Q811yescharacteristic
559C22×C23#55411yescharacteristic
560C22×C23#55411yescharacteristic
561C22×C23#55411yescharacteristic
562C22×C23#55511yescharacteristic
563C22×C23#55911yescharacteristic
564C22×C23#56011yescharacteristic
565C22×C23H(3,𝔽4)11yescharacteristic
566C22×C23#56211yescharacteristic
567C22×C23#56211yescharacteristic
568C4×C23—42no—
569C4×C23—42no—
570C4×C23—42no—
571C4×C23—42no—
572C4×C23—42no—
573C4×C23—42no—
574C4×C23—42no—
575C4×C23—42no—
576C4×C23—42no—
577C4×C23—81no—
578C4×C23—81no—
579C4×C23—81no—
580C4×C23—81no—
581C23×Q8C22×C2311yescharacteristic
582C23×D4C22×C2311yescharacteristic
583C24×C4C22×C2311yescharacteristic
584C22×C4⋊C4C22×C2311yescharacteristic
585C22×C4⋊C4C22×C2311yescharacteristic
586C22×C4⋊C4C22×C2311yescharacteristic
587C22×C22⋊C4C22×C2311yescharacteristic
588C22×C22⋊C4C22×C2311yescharacteristic
589C22×C22⋊C4C22×C2311yescharacteristic
590C22×C22⋊C4C22×C2311yescharacteristic
591C22×C22⋊C4C22×C2311yescharacteristic
592C22×C22⋊C4C22×C2311yescharacteristic
593C22×C22⋊C4C22×C2311yescharacteristic
594C22×C22⋊C4C22×C2311yescharacteristic
595C22×C22⋊C4C22×C2311yescharacteristic
596C22×C22⋊C4C22×C2311yescharacteristic
597C22×C22⋊C4C22×C2311yescharacteristic
598#393—24no—
599#393—24no—
600#386—24no—
601#385—24no—
602C2×#95C22×C2311yescharacteristic
603C2×#95C22×C2311yescharacteristic
604C2×#95C22×C2311yescharacteristic
605C2×#95C22×C2311yescharacteristic
606C2×#95C22×C2311yescharacteristic
607C2×#95C22×C2311yescharacteristic
608C2×#95C22×C2311yescharacteristic
609C2×#95C22×C2311yescharacteristic
610C2×#95C22×C2311yescharacteristic
611C2×#95C22×C2311yescharacteristic
612C2×#95C22×C2311yescharacteristic
613C2×#95C22×C2311yescharacteristic
614C2×#95C22×C2311yescharacteristic
615C2×#95C22×C2311yescharacteristic
616C2×#95C22×C2311yescharacteristic
617C2×#95C22×C2311yescharacteristic
618C2×#95C22×C2311yescharacteristic
619C2×#95C22×C2311yescharacteristic
620C2×C23—44no—
621C2×C23—82no—
622C2×C23#244911yescharacteristic
623C2×C23#245011yescharacteristic
624C2×C23#245911yescharacteristic
625C2×C23#262611yescharacteristic
626C2×C23#263111yescharacteristic
627C2×C23#265311yescharacteristic
628C2×C23#267011yescharacteristic
629C2×C23#267811yescharacteristic
630C2×C23#268611yescharacteristic
631C2×C23#269211yescharacteristic
632C2×C23#269211yescharacteristic
633C2×C23#271011yescharacteristic
634C2×C23#278411yescharacteristic
635C2×C23#280411yescharacteristic
636C2×C23#282411yescharacteristic
637C25C23×C2311yescharacteristic
638C25C23×C2311yescharacteristic
639C22×Q8—22no—
640C22×Q8—22no—
641C22×Q8—22no—
642C22×Q8—41no—
643C22×Q8—41no—
644C22×Q8—41no—
645C22×Q8—41no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—41no—
649C22×D4—41no—
650C22×D4—41no—
651C22×D4—41no—
652C22×D4Q8×C2314yescomplemented
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—41no—
657C23×C4—41no—
658C23×C4—41no—
659C23×C4—41no—
660C23×C4C23×C2311yescharacteristic
661C23×C4C23×C2311yescharacteristic
662C23×C4C23×C2311yescharacteristic
663C23×C4C23×C2311yescharacteristic
664C23×C4C23×C2311yescharacteristic
665C23×C4C23×C2311yescharacteristic
666C23×C4C23×C2311yescharacteristic
667C23×C4C23×C2311yescharacteristic
668C23×C4C23×C2311yescharacteristic
669C23×C4C23×C2311yescharacteristic
670C23×C4C23×C2311yescharacteristic
671C23×C4C23×C2311yescharacteristic
672C23×C4C23×C2311yescharacteristic
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—41no—
680C2×C4⋊C4—41no—
681C2×C4⋊C4—41no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4D4×C2314yes—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—41no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95—41no—
732#95D4×C2314yescomplemented
733C23#1632011yescharacteristic, direct product factor, Sylow
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24C2×D4×C2312yes—
761C24C2×Q8×C2312yes—
762C24C2×Q8×C2312yes—
763C24#41×C2312yes—
764C24C24×C2311yescharacteristic
765C2×Q8—44no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×D4—28no—
773C2×D4—44no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
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—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
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—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
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—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4C2×D4×C2312yes—
869C22×C4C2×D4×C2312yes—
870C22×C4C2×D4×C2312yes—
871C22×C4C2×D4×C2312yes—
872C22×C4C2×D4×C2312yes—
873C22×C4C2×Q8×C2312yes—
874C22×C4#41×C2312yes—
875C22×C4#41×C2312yes—
876C22×C4#41×C2312yes—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C22⋊C4—28no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23C23×C22⋊Q814yes—
961C23C22×D4×C2311yescharacteristic
962C23C22×D4×C2311yescharacteristic
963C23C22×Q8×C2311yescharacteristic
964C23C2×#41×C2311yescharacteristic
965C23C2×#41×C2311yescharacteristic
966C23C2×#41×C2311yescharacteristic
967C23C2×#41×C2311yescharacteristic
968C23C23×H(5,𝔽2)11yescharacteristic
969C23C23×H(5,𝔽2)11yescharacteristic
970C23C23×H(5,𝔽2)11yescharacteristic
971C23C23×H(5,𝔽2)11yescharacteristic
972C23C23×H(5,𝔽2)11yescharacteristic
973C23C23×H(5,𝔽2)11yescharacteristic
974C23C23×H(5,𝔽2)11yescharacteristic
975C23C23×2−1+411yescharacteristic
976Q8—416no—
977D4—416no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—416no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C22—24no—
1071C22—24no—
1072C22—24no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—81no—
1100C22C2×C23×C22⋊Q811yescharacteristic
1101C22C23×#52511yescharacteristic
1102C22C23×#52911yescharacteristic
1103C22C23×#53411yescharacteristic
1104C22C23×#53511yescharacteristic
1105C22C23×#53511yescharacteristic
1106C22C23×#53511yescharacteristic
1107C22C23×#53811yescharacteristic
1108C22C23×#53811yescharacteristic
1109C22C23×#53811yescharacteristic
1110C22C23×#53811yescharacteristic
1111C22C23×#53811yescharacteristic
1112C22C23×#53811yescharacteristic
1113C22C23×#53811yescharacteristic
1114C22C23×#53911yescharacteristic
1115C22C23×#54211yescharacteristic
1116C22C23×#54211yescharacteristic
1117C22C23×#54311yescharacteristic
1118C22C23×#54311yescharacteristic
1119C22D42×C2311yescharacteristic
1120C22C23×#54611yescharacteristic
1121C22C23×#54611yescharacteristic
1122C22C23×#54611yescharacteristic
1123C22C23×#54611yescharacteristic
1124C22C23×#54711yescharacteristic
1125C22D4×Q8×C2311yescharacteristic
1126C22C23×#55411yescharacteristic
1127C22C23×#55411yescharacteristic
1128C22C23×#55411yescharacteristic
1129C22C23×#55511yescharacteristic
1130C22C23×#55911yescharacteristic
1131C22C23×#56011yescharacteristic
1132C22C23×H(3,𝔽4)11yescharacteristic
1133C22C23×#56211yescharacteristic
1134C22C23×#56211yescharacteristic
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C2—44no—
1149C2—82no—
1150C2C23×#244911yescharacteristic
1151C2C23×#245011yescharacteristic
1152C2C23×#245911yescharacteristic
1153C2C23×#262611yescharacteristic
1154C2C23×#263111yescharacteristic
1155C2C23×#265311yescharacteristic
1156C2C23×#267011yescharacteristic
1157C2C23×#267811yescharacteristic
1158C2C23×#268611yescharacteristic
1159C2C23×#269211yescharacteristic
1160C2C23×#269211yescharacteristic
1161C2C23×#271011yescharacteristic
1162C2C23×#278411yescharacteristic
1163C2C23×#280411yescharacteristic
1164C2C23×#282411yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutator, Frattini, cosocleC24C24×C23
prime radicalC23×D4×C23C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C23×#393C2semidirect
2. C2×C23×#393C2semidirect
4. C2×C23×#385C2semidirect
5. C23×#1446C2semidirect
6. C23×#1445C2semidirect
7. C23×#1443C2semidirect
8. C23×#1441C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
11. C23×#1439C2semidirect
12. C23×#1439C2semidirect
15. C23×C22⋊#95C2semidirect
70. C22×D4×C23Q8semidirect
150. C23×#95D4semidirect
308. #16320C23direct (N × H)
488. C2×#393C2×C23semidirect
489. C2×#393C2×C23semidirect
491. C2×#385C2×C23semidirect
492. #1446C2×C23semidirect
493. #1445C2×C23semidirect
494. #1443C2×C23semidirect
495. #1441C2×C23semidirect
496. #1439C2×C23semidirect
497. #1439C2×C23semidirect
498. #1439C2×C23semidirect
499. #1439C2×C23semidirect
502. C22⋊#95C2×C23semidirect
652. C22×D4Q8×C23semidirect
732. #95D4×C23semidirect
733. C23#16320direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3932
C2×C23×#3862
C2×C23×#3852
C23×#14462
C23×#14452
C23×#14432
C23×#14412
C23×#14392
C23×#14382
C23×C22⋊#952
#1632023