Finite Group Databasebeta

← C23×#15507 #19163133

Subgroups — C23×#15507 #19163133

Order 5888.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#398C211yesmaximal, characteristic, complemented
2C2×C23×#396C211yesmaximal, characteristic, complemented
3C2×C23×#396C211yesmaximal, characteristic, complemented
4C2×C23×#390C211yesmaximal, characteristic
5C2×C23×#386C211yesmaximal, characteristic
6C2×C23×#385C211yesmaximal, characteristic, complemented
7C23×#1442C211yesmaximal, characteristic, complemented
8C23×#1439C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1438C211yesmaximal, characteristic
13C23×#1436C211yesmaximal, characteristic, complemented
14C23×C4⋊#95C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C24×C4×C23C2211yescharacteristic
18C22×C4⋊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×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
33C22×C22⋊C4×C23C2211yescharacteristic
34C22×C22⋊C4×C23C2211yescharacteristic
35C22×C22⋊C4×C23C2211yescharacteristic
36C22×C42×C23C2211yescharacteristic
37C23×#398—24no—
38C23×#396—24no—
39C23×#396—24no—
40C23×#390—24no—
41C23×#386—24no—
42C23×#385—24no—
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
57C25×C23C2311yescharacteristic
58C25×C23C2311yescharacteristic
59C22×D4×C23—22no—
60C22×D4×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23—22no—
63C22×D4×C23—41no—
64C22×D4×C23—41no—
65C22×D4×C23Q814yes—
66C23×C4×C23—22no—
67C23×C4×C23—22no—
68C23×C4×C23—22no—
69C23×C4×C23—41no—
70C23×C4×C23—41no—
71C23×C4×C23—41no—
72C23×C4×C23—41no—
73C23×C4×C23C2311yescharacteristic
74C23×C4×C23C2311yescharacteristic
75C23×C4×C23C2311yescharacteristic
76C23×C4×C23C2311yescharacteristic
77C23×C4×C23C2311yescharacteristic
78C23×C4×C23C2311yescharacteristic
79C23×C4×C23C2311yescharacteristic
80C23×C4×C23C2311yescharacteristic
81C23×C4×C23C2311yescharacteristic
82C23×C4×C23C2311yescharacteristic
83C23×C4×C23C2311yescharacteristic
84C23×C4×C23C2311yescharacteristic
85C23×C4×C23C2311yescharacteristic
86C2×C4⋊C4×C23—22no—
87C2×C4⋊C4×C23—22no—
88C2×C4⋊C4×C23—22no—
89C2×C4⋊C4×C23—22no—
90C2×C4⋊C4×C23—22no—
91C2×C4⋊C4×C23—22no—
92C2×C4⋊C4×C23—22no—
93C2×C4⋊C4×C23—22no—
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—41no—
100C2×C4⋊C4×C23—41no—
101C2×C4⋊C4×C23—41no—
102C2×C4⋊C4×C23—41no—
103C2×C4⋊C4×C23—41no—
104C2×C4⋊C4×C23—41no—
105C2×C4⋊C4×C23—41no—
106C2×C4⋊C4×C23D414yescomplemented
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—22no—
117C2×C22⋊C4×C23—22no—
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×C23—22no—
126C2×C22⋊C4×C23—22no—
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×C23—41no—
133C2×C22⋊C4×C23—41no—
134C2×C22⋊C4×C23—41no—
135C2×C22⋊C4×C23—41no—
136C2×C22⋊C4×C23—41no—
137C2×C22⋊C4×C23—41no—
138C2×C22⋊C4×C23—41no—
139C2×C22⋊C4×C23D414yes—
140C2×C42×C23—22no—
141C2×C42×C23—22no—
142C2×C42×C23—41no—
143C23×#95—22no—
144C23×#95—22no—
145C23×#95—22no—
146C23×#95—22no—
147C23×#95—22no—
148C23×#95—22no—
149C23×#95—22no—
150C23×#95—22no—
151C23×#95—22no—
152C23×#95—41no—
153C23×#95—41no—
154C23×#95—41no—
155C23×#95—41no—
156C23×#95D414yes—
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×C23—21no—
178C24×C23—21no—
179C24×C23—21no—
180C24×C23—21no—
181C24×C23—21no—
182C24×C23—21no—
183C24×C23C2×D412yes—
184C24×C23C2×Q812yes—
185C24×C23C2×Q812yes—
186C24×C23#4112yes—
187C24×C23C2411yescharacteristic
188C2×D4×C23—28no—
189C2×D4×C23—28no—
190C2×D4×C23—44no—
191C2×D4×C23—44no—
192C2×D4×C23—44no—
193C2×D4×C23—44no—
194C2×D4×C23—44no—
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—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—44no—
274C22×C4×C23—44no—
275C22×C4×C23—44no—
276C22×C4×C23—44no—
277C22×C4×C23—44no—
278C22×C4×C23—44no—
279C22×C4×C23—44no—
280C22×C4×C23C2×D412yes—
281C22×C4×C23C2×D412yes—
282C22×C4×C23C2×D412yes—
283C22×C4×C23C2×D412yes—
284C22×C4×C23C2×D412yes—
285C22×C4×C23C2×D412yes—
286C22×C4×C23C2×D412yes—
287C22×C4×C23C2×D412yes—
288C22×C4×C23C2×Q812yes—
289C22×C4×C23#4112yes—
290C22×C4×C23#4112yes—
291C22×C4×C23#4112yes—
292C22×C4×C23#4112yes—
293C4⋊C4×C23—44no—
294C4⋊C4×C23—44no—
295C4⋊C4×C23—44no—
296C4⋊C4×C23—44no—
297C4⋊C4×C23—44no—
298C4⋊C4×C23—44no—
299C4⋊C4×C23—44no—
300C22⋊C4×C23—28no—
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×C23—44no—
310C22⋊C4×C23—44no—
311C42×C23—44no—
312#15507C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
335C23×C23—22no—
336C23×C23—22no—
337C23×C23—22no—
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×C23—41no—
379C23×C23—41no—
380C23×C23—41no—
381C23×C23—41no—
382C23×C23C22⋊Q814yes—
383C23×C23C22×D411yescharacteristic
384C23×C23C22×D411yescharacteristic
385C23×C23C22×D411yescharacteristic
386C23×C23C22×Q811yescharacteristic
387C23×C23C2×#4111yescharacteristic
388C23×C23C2×#4111yescharacteristic
389C23×C23C2×#4111yescharacteristic
390C23×C23C2×#4111yescharacteristic
391C23×C23C2×#4111yescharacteristic
392C23×C23H(5,𝔽2)11yescharacteristic
393C23×C23H(5,𝔽2)11yescharacteristic
394C23×C23H(5,𝔽2)11yescharacteristic
395C23×C23H(5,𝔽2)11yescharacteristic
396C23×C23H(5,𝔽2)11yescharacteristic
397C23×C232−1+411yescharacteristic
398D4×C23—416no—
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—22no—
424C2×C4×C23—22no—
425C2×C4×C23—22no—
426C2×C4×C23—22no—
427C2×C4×C23—22no—
428C2×C4×C23—22no—
429C2×C4×C23—22no—
430C2×C4×C23—22no—
431C2×C4×C23—22no—
432C2×C4×C23—416no—
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×C4×C23—41no—
489C2×C4×C23#12114yes—
490C2×C4×C23C22⋊Q814yes—
491C2×#398C2×C2311yescharacteristic, complemented
492C2×#396C2×C2311yescharacteristic, complemented
493C2×#396C2×C2311yescharacteristic, complemented
494C2×#390C2×C2311yescharacteristic
495C2×#386C2×C2311yescharacteristic
496C2×#385C2×C2311yescharacteristic, complemented
497#1442C2×C2311yescharacteristic, complemented
498#1439C2×C2311yescharacteristic, complemented
499#1439C2×C2311yescharacteristic, complemented
500#1439C2×C2311yescharacteristic, complemented
501#1439C2×C2311yescharacteristic, complemented
502#1438C2×C2311yescharacteristic
503#1436C2×C2311yescharacteristic, complemented
504C4⋊#95C2×C2311yescharacteristic, complemented
505C22⋊#95C2×C2311yescharacteristic, complemented
506C22×C23—24no—
507C22×C23—24no—
508C22×C23—24no—
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—42no—
526C22×C23—42no—
527C22×C23—42no—
528C22×C23—81no—
529C22×C23—81no—
530C22×C23—81no—
531C22×C23—81no—
532C22×C23—81no—
533C22×C23—81no—
534C22×C23—81no—
535C22×C23—81no—
536C22×C23C2×#12111yescharacteristic
537C22×C23C2×C22⋊Q811yescharacteristic
538C22×C23C2×C22⋊Q811yescharacteristic
539C22×C23#52911yescharacteristic
540C22×C23#53211yescharacteristic
541C22×C23#53211yescharacteristic
542C22×C23#53411yescharacteristic
543C22×C23#53511yescharacteristic
544C22×C23#53711yescharacteristic
545C22×C23#53811yescharacteristic
546C22×C23#53811yescharacteristic
547C22×C23#53911yescharacteristic
548C22×C23#54011yescharacteristic
549C22×C23#54211yescharacteristic
550C22×C23#54311yescharacteristic
551C22×C23D4211yescharacteristic
552C22×C23D4211yescharacteristic
553C22×C23#54611yescharacteristic
554C22×C23#54611yescharacteristic
555C22×C23#54611yescharacteristic
556C22×C23#54611yescharacteristic
557C22×C23#54611yescharacteristic
558C22×C23#54811yescharacteristic
559C22×C23D4×Q811yescharacteristic
560C22×C23#55011yescharacteristic
561C22×C23#55111yescharacteristic
562C22×C23#55211yescharacteristic
563C22×C23#55311yescharacteristic
564C22×C23#55311yescharacteristic
565C22×C23#55311yescharacteristic
566C22×C23#55411yescharacteristic
567C22×C23#55411yescharacteristic
568C22×C23#55411yescharacteristic
569C22×C23#56011yescharacteristic
570C22×C23#56211yescharacteristic
571C4×C23—24no—
572C4×C23—24no—
573C4×C23—42no—
574C4×C23—42no—
575C4×C23—42no—
576C4×C23—42no—
577C4×C23—42no—
578C4×C23—42no—
579C4×C23—42no—
580C4×C23—81no—
581C4×C23—81no—
582C4×C23—81no—
583C4×C23—81no—
584C23×D4C22×C2311yescharacteristic
585C24×C4C22×C2311yescharacteristic
586C22×C4⋊C4C22×C2311yescharacteristic
587C22×C4⋊C4C22×C2311yescharacteristic
588C22×C4⋊C4C22×C2311yescharacteristic
589C22×C4⋊C4C22×C2311yescharacteristic
590C22×C4⋊C4C22×C2311yescharacteristic
591C22×C4⋊C4C22×C2311yescharacteristic
592C22×C4⋊C4C22×C2311yescharacteristic
593C22×C22⋊C4C22×C2311yescharacteristic
594C22×C22⋊C4C22×C2311yescharacteristic
595C22×C22⋊C4C22×C2311yescharacteristic
596C22×C22⋊C4C22×C2311yescharacteristic
597C22×C22⋊C4C22×C2311yescharacteristic
598C22×C22⋊C4C22×C2311yescharacteristic
599C22×C22⋊C4C22×C2311yescharacteristic
600C22×C22⋊C4C22×C2311yescharacteristic
601C22×C22⋊C4C22×C2311yescharacteristic
602C22×C22⋊C4C22×C2311yescharacteristic
603C22×C22⋊C4C22×C2311yescharacteristic
604C22×C42C22×C2311yescharacteristic
605#398—24no—
606#396—24no—
607#396—24no—
608#390—24no—
609#386—24no—
610#385—24no—
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×#95C22×C2311yescharacteristic
621C2×#95C22×C2311yescharacteristic
622C2×#95C22×C2311yescharacteristic
623C2×#95C22×C2311yescharacteristic
624C2×#95C22×C2311yescharacteristic
625C2×C23—44no—
626C2×C23—82no—
627C2×C23#241711yescharacteristic
628C2×C23#242811yescharacteristic
629C2×C23#243711yescharacteristic
630C2×C23#245011yescharacteristic
631C2×C23#245211yescharacteristic
632C2×C23#254311yescharacteristic
633C2×C23#255411yescharacteristic
634C2×C23#255811yescharacteristic
635C2×C23#256611yescharacteristic
636C2×C23#267611yescharacteristic
637C2×C23#267811yescharacteristic
638C2×C23#269111yescharacteristic
639C2×C23#273211yescharacteristic
640C2×C23#276111yescharacteristic
641C2×C23#278011yescharacteristic
642C25C23×C2311yescharacteristic
643C25C23×C2311yescharacteristic
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—41no—
649C22×D4—41no—
650C22×D4Q8×C2314yes—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—41no—
655C23×C4—41no—
656C23×C4—41no—
657C23×C4—41no—
658C23×C4C23×C2311yescharacteristic
659C23×C4C23×C2311yescharacteristic
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
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—41no—
686C2×C4⋊C4—41no—
687C2×C4⋊C4—41no—
688C2×C4⋊C4—41no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4D4×C2314yescomplemented
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—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4D4×C2314yes—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—41no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—41no—
738#95—41no—
739#95—41no—
740#95—41no—
741#95D4×C2314yes—
742C23#1550711yescharacteristic, direct product factor, Sylow
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—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24C2×D4×C2312yes—
770C24C2×Q8×C2312yes—
771C24C2×Q8×C2312yes—
772C24#41×C2312yes—
773C24C24×C2311yescharacteristic
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
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—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4C2×D4×C2312yes—
867C22×C4C2×D4×C2312yes—
868C22×C4C2×D4×C2312yes—
869C22×C4C2×D4×C2312yes—
870C22×C4C2×D4×C2312yes—
871C22×C4C2×D4×C2312yes—
872C22×C4C2×D4×C2312yes—
873C22×C4C2×D4×C2312yes—
874C22×C4C2×Q8×C2312yes—
875C22×C4#41×C2312yes—
876C22×C4#41×C2312yes—
877C22×C4#41×C2312yes—
878C22×C4#41×C2312yes—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C22⋊C4—28no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C42—44no—
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—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
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—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23C23×C22⋊Q814yes—
968C23C22×D4×C2311yescharacteristic
969C23C22×D4×C2311yescharacteristic
970C23C22×D4×C2311yescharacteristic
971C23C22×Q8×C2311yescharacteristic
972C23C2×#41×C2311yescharacteristic
973C23C2×#41×C2311yescharacteristic
974C23C2×#41×C2311yescharacteristic
975C23C2×#41×C2311yescharacteristic
976C23C2×#41×C2311yescharacteristic
977C23C23×H(5,𝔽2)11yescharacteristic
978C23C23×H(5,𝔽2)11yescharacteristic
979C23C23×H(5,𝔽2)11yescharacteristic
980C23C23×H(5,𝔽2)11yescharacteristic
981C23C23×H(5,𝔽2)11yescharacteristic
982C23C23×2−1+411yescharacteristic
983D4—416no—
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—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—416no—
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—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4C23×#12114yes—
1075C2×C4C23×C22⋊Q814yes—
1076C22—24no—
1077C22—24no—
1078C22—24no—
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—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—81no—
1099C22—81no—
1100C22—81no—
1101C22—81no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22C2×C23×#12111yescharacteristic
1107C22C2×C23×C22⋊Q811yescharacteristic
1108C22C2×C23×C22⋊Q811yescharacteristic
1109C22C23×#52911yescharacteristic
1110C22C23×#53211yescharacteristic
1111C22C23×#53211yescharacteristic
1112C22C23×#53411yescharacteristic
1113C22C23×#53511yescharacteristic
1114C22C23×#53711yescharacteristic
1115C22C23×#53811yescharacteristic
1116C22C23×#53811yescharacteristic
1117C22C23×#53911yescharacteristic
1118C22C23×#54011yescharacteristic
1119C22C23×#54211yescharacteristic
1120C22C23×#54311yescharacteristic
1121C22D42×C2311yescharacteristic
1122C22D42×C2311yescharacteristic
1123C22C23×#54611yescharacteristic
1124C22C23×#54611yescharacteristic
1125C22C23×#54611yescharacteristic
1126C22C23×#54611yescharacteristic
1127C22C23×#54611yescharacteristic
1128C22C23×#54811yescharacteristic
1129C22D4×Q8×C2311yescharacteristic
1130C22C23×#55011yescharacteristic
1131C22C23×#55111yescharacteristic
1132C22C23×#55211yescharacteristic
1133C22C23×#55311yescharacteristic
1134C22C23×#55311yescharacteristic
1135C22C23×#55311yescharacteristic
1136C22C23×#55411yescharacteristic
1137C22C23×#55411yescharacteristic
1138C22C23×#55411yescharacteristic
1139C22C23×#56011yescharacteristic
1140C22C23×#56211yescharacteristic
1141C4—24no—
1142C4—24no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C2—44no—
1155C2—82no—
1156C2C23×#241711yescharacteristic
1157C2C23×#242811yescharacteristic
1158C2C23×#243711yescharacteristic
1159C2C23×#245011yescharacteristic
1160C2C23×#245211yescharacteristic
1161C2C23×#254311yescharacteristic
1162C2C23×#255411yescharacteristic
1163C2C23×#255811yescharacteristic
1164C2C23×#256611yescharacteristic
1165C2C23×#267611yescharacteristic
1166C2C23×#267811yescharacteristic
1167C2C23×#269111yescharacteristic
1168C2C23×#273211yescharacteristic
1169C2C23×#276111yescharacteristic
1170C2C23×#278011yescharacteristic
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×#398C2semidirect
2. C2×C23×#396C2semidirect
3. C2×C23×#396C2semidirect
6. C2×C23×#385C2semidirect
7. C23×#1442C2semidirect
8. C23×#1439C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
11. C23×#1439C2semidirect
13. C23×#1436C2semidirect
14. C23×C4⋊#95C2semidirect
15. C23×C22⋊#95C2semidirect
106. C2×C4⋊C4×C23D4semidirect
312. #15507C23direct (N × H)
491. C2×#398C2×C23semidirect
492. C2×#396C2×C23semidirect
493. C2×#396C2×C23semidirect
496. C2×#385C2×C23semidirect
497. #1442C2×C23semidirect
498. #1439C2×C23semidirect
499. #1439C2×C23semidirect
500. #1439C2×C23semidirect
501. #1439C2×C23semidirect
503. #1436C2×C23semidirect
504. C4⋊#95C2×C23semidirect
505. C22⋊#95C2×C23semidirect
691. C2×C4⋊C4D4×C23semidirect
742. C23#15507direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3982
C2×C23×#3962
C2×C23×#3902
C2×C23×#3862
C2×C23×#3852
C23×#14422
C23×#14392
C23×#14382
C23×#14362
C23×C4⋊#952
C23×C22⋊#952
#1550723