Finite Group Databasebeta

← C23×#16530 #19164156

Subgroups — C23×#16530 #19164156

Order 5888.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#397C211yesmaximal, characteristic, complemented
2C2×C23×#394C211yesmaximal, characteristic, complemented
3C2×C23×#392C211yesmaximal, characteristic
4C2×C23×#390C211yesmaximal, characteristic, complemented
5C23×#1442C211yesmaximal, characteristic, complemented
6C23×#1440C211yesmaximal, characteristic, complemented
7C23×#1440C211yesmaximal, characteristic, complemented
8C23×#1440C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1438C211yesmaximal, characteristic, complemented
11C23×#1438C211yesmaximal, characteristic, complemented
12C23×#1438C211yesmaximal, characteristic, complemented
13C23×#1438C211yesmaximal, characteristic, complemented
14C23×#1437C211yesmaximal, characteristic, complemented
15C23×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C23×D4×C23C2211yescharacteristic
18C23×D4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C22⋊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
33C22×C22⋊C4×C23C2211yescharacteristic
34C22×C22⋊C4×C23C2211yescharacteristic
35C22×C22⋊C4×C23C2211yescharacteristic
36C22×C42×C23C2211yescharacteristic
37C23×#397—24no—
38C23×#394—24no—
39C23×#392—24no—
40C23×#390—24no—
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
57C25×C23C2311yescharacteristic
58C22×D4×C23—22no—
59C22×D4×C23—22no—
60C22×D4×C23—22no—
61C22×D4×C23—22no—
62C22×D4×C23—22no—
63C22×D4×C23—22no—
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×C23—41no—
71C22×D4×C23—41no—
72C22×D4×C23—41no—
73C22×D4×C23—41no—
74C22×D4×C23—41no—
75C22×D4×C23—41no—
76C22×D4×C23—41no—
77C22×D4×C23—41no—
78C22×D4×C23D414yes—
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—41no—
93C2×C4⋊C4×C23—41no—
94C2×C4⋊C4×C23—41no—
95C2×C4⋊C4×C23—41no—
96C2×C4⋊C4×C23D414yescomplemented
97C2×C22⋊C4×C23—22no—
98C2×C22⋊C4×C23—22no—
99C2×C22⋊C4×C23—22no—
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—22no—
117C2×C22⋊C4×C23—22no—
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×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×C23—41no—
140C2×C22⋊C4×C23—41no—
141C2×C22⋊C4×C23—41no—
142C2×C42×C23—22no—
143C2×C42×C23—41no—
144C2×C42×C23—41no—
145C23×#95—22no—
146C23×#95—22no—
147C23×#95—22no—
148C23×#95—22no—
149C23×#95—22no—
150C23×#95—22no—
151C23×#95—22no—
152C23×#95—22no—
153C23×#95—41no—
154C23×#95—41no—
155C23×#95—41no—
156C23×#95—41no—
157C23×#95—41no—
158C23×#95—41no—
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×C23—21no—
184C24×C23—21no—
185C24×C23—21no—
186C24×C23—21no—
187C24×C23—21no—
188C24×C23—21no—
189C24×C23—21no—
190C24×C23—21no—
191C24×C23—21no—
192C24×C23—21no—
193C24×C23—21no—
194C24×C23—21no—
195C24×C23—21no—
196C24×C23—21no—
197C24×C23—21no—
198C24×C23—21no—
199C24×C23—21no—
200C24×C23—21no—
201C24×C23C2×D412yes—
202C24×C23C2×D412yes—
203C24×C23#4112yes—
204C24×C23C2411yescharacteristic
205C2×D4×C23—28no—
206C2×D4×C23—44no—
207C2×D4×C23—44no—
208C2×D4×C23—44no—
209C2×D4×C23—44no—
210C2×D4×C23—44no—
211C2×D4×C23—44no—
212C2×D4×C23—44no—
213C2×D4×C23—44no—
214C2×D4×C23—44no—
215C2×D4×C23—44no—
216C2×D4×C23—44no—
217C2×D4×C23—44no—
218C2×D4×C23—44no—
219C2×D4×C23—44no—
220C2×D4×C23—44no—
221C2×D4×C23—44no—
222C2×D4×C23—44no—
223C2×D4×C23—44no—
224C2×D4×C23—44no—
225C2×D4×C23—44no—
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—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—21no—
288C22×C4×C23—21no—
289C22×C4×C23—21no—
290C22×C4×C23—21no—
291C22×C4×C23—21no—
292C22×C4×C23—21no—
293C22×C4×C23—21no—
294C22×C4×C23—21no—
295C22×C4×C23—21no—
296C22×C4×C23—21no—
297C22×C4×C23—21no—
298C22×C4×C23—21no—
299C22×C4×C23—21no—
300C22×C4×C23—21no—
301C22×C4×C23—21no—
302C22×C4×C23C2×D412yes—
303C22×C4×C23C2×D412yes—
304C22×C4×C23C2×D412yes—
305C22×C4×C23C2×D412yes—
306C22×C4×C23#4112yes—
307C22×C4×C23#4112yes—
308C22×C4×C23#4112yes—
309C22×C4×C23#4112yes—
310C4⋊C4×C23—44no—
311C4⋊C4×C23—44no—
312C22⋊C4×C23—44no—
313C22⋊C4×C23—44no—
314C22⋊C4×C23—44no—
315C22⋊C4×C23—44no—
316C22⋊C4×C23—44no—
317C22⋊C4×C23—44no—
318C22⋊C4×C23—44no—
319C22⋊C4×C23—44no—
320C22⋊C4×C23—44no—
321C22⋊C4×C23—44no—
322C22⋊C4×C23—44no—
323C22⋊C4×C23—44no—
324C22⋊C4×C23—44no—
325C22⋊C4×C23—44no—
326C22⋊C4×C23—44no—
327C42×C23—44no—
328#16530C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
339C23×C23—22no—
340C23×C23—22no—
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—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×C23—41no—
383C23×C23—41no—
384C23×C23—41no—
385C23×C23—41no—
386C23×C23—41no—
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×C23—41no—
404C23×C23—41no—
405C23×C23—41no—
406C23×C23—41no—
407C23×C23—41no—
408C23×C23—41no—
409C23×C23—41no—
410C23×C23—41no—
411C23×C23—41no—
412C23×C23—41no—
413C23×C23—41no—
414C23×C23—41no—
415C23×C23—41no—
416C23×C23—41no—
417C23×C23—41no—
418C23×C23—41no—
419C23×C23—41no—
420C23×C23—41no—
421C23×C23—41no—
422C23×C23—41no—
423C23×C23—41no—
424C23×C23—41no—
425C23×C23—41no—
426C23×C23—41no—
427C23×C23—41no—
428C23×C23—41no—
429C23×C23—41no—
430C23×C23—41no—
431C23×C23—41no—
432C23×C23—41no—
433C23×C23—41no—
434C23×C23C22×D411yescharacteristic
435C23×C23C22×D411yescharacteristic
436C23×C23C2×#4111yescharacteristic
437C23×C23C2×#4111yescharacteristic
438C23×C23C2×#4111yescharacteristic
439C23×C23C2×#4111yescharacteristic
440C23×C23C2×#4111yescharacteristic
441C23×C23H(5,𝔽2)11yescharacteristic
442C23×C23H(5,𝔽2)11yescharacteristic
443C23×C23H(5,𝔽2)11yescharacteristic
444C23×C23H(5,𝔽2)11yescharacteristic
445C23×C23H(5,𝔽2)11yescharacteristic
446C23×C23H(5,𝔽2)11yescharacteristic
447C23×C23H(5,𝔽2)11yescharacteristic
448C23×C23H(5,𝔽2)11yescharacteristic
449D4×C23—416no—
450D4×C23—416no—
451D4×C23—416no—
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—22no—
470C2×C4×C23—22no—
471C2×C4×C23—22no—
472C2×C4×C23—22no—
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×C23—41no—
520C2×C4×C23—41no—
521C2×C4×C23—41no—
522C2×C4×C23—41no—
523C2×C4×C23—41no—
524C2×C4×C23—41no—
525C2×C4×C23—41no—
526C2×C4×C23—41no—
527C2×C4×C23—41no—
528C2×C4×C23—41no—
529C2×C4×C23—41no—
530C2×C4×C23—41no—
531C2×C4×C23—41no—
532C2×C4×C23—41no—
533C2×C4×C23—41no—
534C2×C4×C23—41no—
535C2×C4×C23#12314yes—
536C2×#397C2×C2311yescharacteristic, complemented
537C2×#394C2×C2311yescharacteristic, complemented
538C2×#392C2×C2311yescharacteristic
539C2×#390C2×C2311yescharacteristic, complemented
540#1442C2×C2311yescharacteristic, complemented
541#1440C2×C2311yescharacteristic, complemented
542#1440C2×C2311yescharacteristic, complemented
543#1440C2×C2311yescharacteristic, complemented
544#1439C2×C2311yescharacteristic, complemented
545#1438C2×C2311yescharacteristic, complemented
546#1438C2×C2311yescharacteristic, complemented
547#1438C2×C2311yescharacteristic, complemented
548#1438C2×C2311yescharacteristic, complemented
549#1437C2×C2311yescharacteristic, complemented
550#1436C2×C2311yescharacteristic, complemented
551C22×C23—42no—
552C22×C23—42no—
553C22×C23—42no—
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—42no—
567C22×C23—42no—
568C22×C23—42no—
569C22×C23—42no—
570C22×C23—42no—
571C22×C23—42no—
572C22×C23—81no—
573C22×C23—81no—
574C22×C23—81no—
575C22×C23—81no—
576C22×C23—81no—
577C22×C23—81no—
578C22×C23—81no—
579C22×C23—81no—
580C22×C23—81no—
581C22×C23—81no—
582C22×C23—81no—
583C22×C23—81no—
584C22×C23—81no—
585C22×C23—81no—
586C22×C23—81no—
587C22×C23—81no—
588C22×C23—81no—
589C22×C23—81no—
590C22×C23—81no—
591C22×C23—81no—
592C22×C23—81no—
593C22×C23—81no—
594C22×C23—81no—
595C22×C23—81no—
596C22×C23C2×#12311yescharacteristic
597C22×C23#52911yescharacteristic
598C22×C23#53211yescharacteristic
599C22×C23#53411yescharacteristic
600C22×C23#53411yescharacteristic
601C22×C23#53411yescharacteristic
602C22×C23#53511yescharacteristic
603C22×C23#53811yescharacteristic
604C22×C23#53811yescharacteristic
605C22×C23#53811yescharacteristic
606C22×C23#53811yescharacteristic
607C22×C23#53811yescharacteristic
608C22×C23#53811yescharacteristic
609C22×C23#53811yescharacteristic
610C22×C23#53811yescharacteristic
611C22×C23#54011yescharacteristic
612C22×C23#54011yescharacteristic
613C22×C23#54011yescharacteristic
614C22×C23#54011yescharacteristic
615C22×C23D4211yescharacteristic
616C22×C23#54611yescharacteristic
617C22×C23#54611yescharacteristic
618C22×C23#54611yescharacteristic
619C22×C23#54611yescharacteristic
620C22×C23#55011yescharacteristic
621C22×C23#55011yescharacteristic
622C22×C23#55111yescharacteristic
623C22×C23#55311yescharacteristic
624C22×C23#55311yescharacteristic
625C22×C23#55511yescharacteristic
626C22×C23#55911yescharacteristic
627C22×C23#56011yescharacteristic
628C22×C23#56011yescharacteristic
629C22×C23#56011yescharacteristic
630C22×C23H(3,𝔽4)11yescharacteristic
631C4×C23—24no—
632C4×C23—42no—
633C4×C23—42no—
634C4×C23—42no—
635C4×C23—42no—
636C4×C23—42no—
637C4×C23—81no—
638C4×C23—81no—
639C4×C23—81no—
640C4×C23—81no—
641C4×C23—81no—
642C4×C23—81no—
643C23×D4C22×C2311yescharacteristic
644C23×D4C22×C2311yescharacteristic
645C23×D4C22×C2311yescharacteristic
646C22×C4⋊C4C22×C2311yescharacteristic
647C22×C4⋊C4C22×C2311yescharacteristic
648C22×C22⋊C4C22×C2311yescharacteristic
649C22×C22⋊C4C22×C2311yescharacteristic
650C22×C22⋊C4C22×C2311yescharacteristic
651C22×C22⋊C4C22×C2311yescharacteristic
652C22×C22⋊C4C22×C2311yescharacteristic
653C22×C22⋊C4C22×C2311yescharacteristic
654C22×C22⋊C4C22×C2311yescharacteristic
655C22×C22⋊C4C22×C2311yescharacteristic
656C22×C22⋊C4C22×C2311yescharacteristic
657C22×C22⋊C4C22×C2311yescharacteristic
658C22×C22⋊C4C22×C2311yescharacteristic
659C22×C22⋊C4C22×C2311yescharacteristic
660C22×C22⋊C4C22×C2311yescharacteristic
661C22×C22⋊C4C22×C2311yescharacteristic
662C22×C22⋊C4C22×C2311yescharacteristic
663C22×C42C22×C2311yescharacteristic
664#397—24no—
665#394—24no—
666#392—24no—
667#390—24no—
668C2×#95C22×C2311yescharacteristic
669C2×#95C22×C2311yescharacteristic
670C2×#95C22×C2311yescharacteristic
671C2×#95C22×C2311yescharacteristic
672C2×#95C22×C2311yescharacteristic
673C2×#95C22×C2311yescharacteristic
674C2×#95C22×C2311yescharacteristic
675C2×#95C22×C2311yescharacteristic
676C2×#95C22×C2311yescharacteristic
677C2×#95C22×C2311yescharacteristic
678C2×#95C22×C2311yescharacteristic
679C2×#95C22×C2311yescharacteristic
680C2×#95C22×C2311yescharacteristic
681C2×#95C22×C2311yescharacteristic
682C2×C23—82no—
683C2×C23—82no—
684C2×C23—82no—
685C2×C23#242011yescharacteristic
686C2×C23#244511yescharacteristic
687C2×C23#255411yescharacteristic
688C2×C23#262211yescharacteristic
689C2×C23#264811yescharacteristic
690C2×C23#266111yescharacteristic
691C2×C23#266811yescharacteristic
692C2×C23#267311yescharacteristic
693C2×C23#268411yescharacteristic
694C2×C23#268811yescharacteristic
695C2×C23#271411yescharacteristic
696C2×C23#273311yescharacteristic
697C2×C23#279711yescharacteristic
698C2×C23#280311yescharacteristic
699C2×C23#282811yescharacteristic
700C25C23×C2311yescharacteristic
701C25C23×C2311yescharacteristic
702C25C23×C2311yescharacteristic
703C22×D4—22no—
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—41no—
712C22×D4—41no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4D4×C2314yes—
724C23×C4C23×C2311yescharacteristic
725C23×C4C23×C2311yescharacteristic
726C23×C4C23×C2311yescharacteristic
727C23×C4C23×C2311yescharacteristic
728C23×C4C23×C2311yescharacteristic
729C23×C4C23×C2311yescharacteristic
730C23×C4C23×C2311yescharacteristic
731C23×C4C23×C2311yescharacteristic
732C23×C4C23×C2311yescharacteristic
733C23×C4C23×C2311yescharacteristic
734C23×C4C23×C2311yescharacteristic
735C23×C4C23×C2311yescharacteristic
736C2×C4⋊C4—22no—
737C2×C4⋊C4—41no—
738C2×C4⋊C4—41no—
739C2×C4⋊C4—41no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4D4×C2314yescomplemented
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—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C42—22no—
788C2×C42—41no—
789C2×C42—41no—
790#95—22no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—41no—
799#95—41no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804C23#1653011yescharacteristic, direct product factor, Sylow
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24C2×D4×C2312yes—
848C24C2×D4×C2312yes—
849C24#41×C2312yes—
850C24C24×C2311yescharacteristic
851C2×D4—28no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
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—21no—
889C22×C4—21no—
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—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4C2×D4×C2312yes—
949C22×C4C2×D4×C2312yes—
950C22×C4C2×D4×C2312yes—
951C22×C4C2×D4×C2312yes—
952C22×C4#41×C2312yes—
953C22×C4#41×C2312yes—
954C22×C4#41×C2312yes—
955C22×C4#41×C2312yes—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C42—44no—
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—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
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—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23C22×D4×C2311yescharacteristic
1080C23C22×D4×C2311yescharacteristic
1081C23C2×#41×C2311yescharacteristic
1082C23C2×#41×C2311yescharacteristic
1083C23C2×#41×C2311yescharacteristic
1084C23C2×#41×C2311yescharacteristic
1085C23C2×#41×C2311yescharacteristic
1086C23C23×H(5,𝔽2)11yescharacteristic
1087C23C23×H(5,𝔽2)11yescharacteristic
1088C23C23×H(5,𝔽2)11yescharacteristic
1089C23C23×H(5,𝔽2)11yescharacteristic
1090C23C23×H(5,𝔽2)11yescharacteristic
1091C23C23×H(5,𝔽2)11yescharacteristic
1092C23C23×H(5,𝔽2)11yescharacteristic
1093C23C23×H(5,𝔽2)11yescharacteristic
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
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×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4C23×#12314yes—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22C2×C23×#12311yescharacteristic
1227C22C23×#52911yescharacteristic
1228C22C23×#53211yescharacteristic
1229C22C23×#53411yescharacteristic
1230C22C23×#53411yescharacteristic
1231C22C23×#53411yescharacteristic
1232C22C23×#53511yescharacteristic
1233C22C23×#53811yescharacteristic
1234C22C23×#53811yescharacteristic
1235C22C23×#53811yescharacteristic
1236C22C23×#53811yescharacteristic
1237C22C23×#53811yescharacteristic
1238C22C23×#53811yescharacteristic
1239C22C23×#53811yescharacteristic
1240C22C23×#53811yescharacteristic
1241C22C23×#54011yescharacteristic
1242C22C23×#54011yescharacteristic
1243C22C23×#54011yescharacteristic
1244C22C23×#54011yescharacteristic
1245C22D42×C2311yescharacteristic
1246C22C23×#54611yescharacteristic
1247C22C23×#54611yescharacteristic
1248C22C23×#54611yescharacteristic
1249C22C23×#54611yescharacteristic
1250C22C23×#55011yescharacteristic
1251C22C23×#55011yescharacteristic
1252C22C23×#55111yescharacteristic
1253C22C23×#55311yescharacteristic
1254C22C23×#55311yescharacteristic
1255C22C23×#55511yescharacteristic
1256C22C23×#55911yescharacteristic
1257C22C23×#56011yescharacteristic
1258C22C23×#56011yescharacteristic
1259C22C23×#56011yescharacteristic
1260C22C23×H(3,𝔽4)11yescharacteristic
1261C4—24no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C23×#242011yescharacteristic
1277C2C23×#244511yescharacteristic
1278C2C23×#255411yescharacteristic
1279C2C23×#262211yescharacteristic
1280C2C23×#264811yescharacteristic
1281C2C23×#266111yescharacteristic
1282C2C23×#266811yescharacteristic
1283C2C23×#267311yescharacteristic
1284C2C23×#268411yescharacteristic
1285C2C23×#268811yescharacteristic
1286C2C23×#271411yescharacteristic
1287C2C23×#273311yescharacteristic
1288C2C23×#279711yescharacteristic
1289C2C23×#280311yescharacteristic
1290C2C23×#282811yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutator, Frattini, cosocleC24C24×C23
prime radicalC2×C23×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C23×#397C2semidirect
2. C2×C23×#394C2semidirect
4. C2×C23×#390C2semidirect
5. C23×#1442C2semidirect
6. C23×#1440C2semidirect
7. C23×#1440C2semidirect
8. C23×#1440C2semidirect
9. C23×#1439C2semidirect
10. C23×#1438C2semidirect
11. C23×#1438C2semidirect
12. C23×#1438C2semidirect
13. C23×#1438C2semidirect
14. C23×#1437C2semidirect
15. C23×#1436C2semidirect
96. C2×C4⋊C4×C23D4semidirect
328. #16530C23direct (N × H)
536. C2×#397C2×C23semidirect
537. C2×#394C2×C23semidirect
539. C2×#390C2×C23semidirect
540. #1442C2×C23semidirect
541. #1440C2×C23semidirect
542. #1440C2×C23semidirect
543. #1440C2×C23semidirect
544. #1439C2×C23semidirect
545. #1438C2×C23semidirect
546. #1438C2×C23semidirect
547. #1438C2×C23semidirect
548. #1438C2×C23semidirect
549. #1437C2×C23semidirect
550. #1436C2×C23semidirect
741. C2×C4⋊C4D4×C23semidirect
804. C23#16530direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3972
C2×C23×#3942
C2×C23×#3922
C2×C23×#3902
C23×#14422
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14362
#1653023