Finite Group Databasebeta

← C23×#16526 #19164152

Subgroups — C23×#16526 #19164152

Order 5888.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1308 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×#394C211yesmaximal, characteristic, complemented
4C2×C23×#394C211yesmaximal, characteristic, complemented
5C2×C23×#392C211yesmaximal, characteristic
6C2×C23×#390C211yesmaximal, characteristic, complemented
7C23×#1444C211yesmaximal, characteristic, complemented
8C23×#1440C211yesmaximal, characteristic, complemented
9C23×#1439C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, 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×C4⋊C4×C23C2211yescharacteristic
22C22×C4⋊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×C22⋊C4×C23C2211yescharacteristic
37C22×C22⋊C4×C23C2211yescharacteristic
38C22×C42×C23C2211yescharacteristic
39C23×#397—24no—
40C23×#394—24no—
41C23×#394—24no—
42C23×#394—24no—
43C23×#392—24no—
44C23×#390—24no—
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
59C25×C23C2311yescharacteristic
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—22no—
67C22×D4×C23—22no—
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×C23—41no—
79C22×D4×C23—41no—
80C22×D4×C23D414yes—
81C23×C4×C23C2311yescharacteristic
82C23×C4×C23C2311yescharacteristic
83C23×C4×C23C2311yescharacteristic
84C23×C4×C23C2311yescharacteristic
85C23×C4×C23C2311yescharacteristic
86C23×C4×C23C2311yescharacteristic
87C23×C4×C23C2311yescharacteristic
88C23×C4×C23C2311yescharacteristic
89C23×C4×C23C2311yescharacteristic
90C23×C4×C23C2311yescharacteristic
91C23×C4×C23C2311yescharacteristic
92C23×C4×C23C2311yescharacteristic
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×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—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—22no—
128C2×C22⋊C4×C23—22no—
129C2×C22⋊C4×C23—22no—
130C2×C22⋊C4×C23—22no—
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×C22⋊C4×C23—41no—
143C2×C22⋊C4×C23—41no—
144C2×C22⋊C4×C23—41no—
145C2×C22⋊C4×C23—41no—
146C2×C22⋊C4×C23—41no—
147C2×C22⋊C4×C23—41no—
148C2×C22⋊C4×C23—41no—
149C2×C22⋊C4×C23D414yescomplemented
150C2×C42×C23—22no—
151C2×C42×C23—41no—
152C2×C42×C23—41no—
153C23×#95—22no—
154C23×#95—22no—
155C23×#95—22no—
156C23×#95—22no—
157C23×#95—22no—
158C23×#95—22no—
159C23×#95—22no—
160C23×#95—41no—
161C23×#95—41no—
162C23×#95—41no—
163C23×#95—41no—
164C23×#95D414yescomplemented
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×C23—21no—
202C24×C23—21no—
203C24×C23—21no—
204C24×C23—21no—
205C24×C23—21no—
206C24×C23—21no—
207C24×C23C2×D412yes—
208C24×C23C2×D412yes—
209C24×C23C2×D412yes—
210C24×C23C2411yescharacteristic
211C2×D4×C23—28no—
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—
226C2×D4×C23—44no—
227C2×D4×C23—44no—
228C2×D4×C23—44no—
229C2×D4×C23—44no—
230C2×D4×C23—44no—
231C2×D4×C23—44no—
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×C23—21no—
303C22×C4×C23—21no—
304C22×C4×C23—21no—
305C22×C4×C23—21no—
306C22×C4×C23C2×D412yes—
307C22×C4×C23C2×D412yes—
308C22×C4×C23C2×D412yes—
309C22×C4×C23C2×D412yes—
310C22×C4×C23C2×D412yes—
311C22×C4×C23C2×D412yes—
312C22×C4×C23#4112yes—
313C22×C4×C23#4112yes—
314C22×C4×C23#4112yes—
315C22×C4×C23#4112yes—
316C4⋊C4×C23—44no—
317C4⋊C4×C23—44no—
318C4⋊C4×C23—44no—
319C4⋊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—
327C22⋊C4×C23—44no—
328C22⋊C4×C23—44no—
329C22⋊C4×C23—44no—
330C22⋊C4×C23—44no—
331C22⋊C4×C23—44no—
332C22⋊C4×C23—44no—
333C22⋊C4×C23—44no—
334C22⋊C4×C23—44no—
335C42×C23—44no—
336#16526C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
351C23×C23—22no—
352C23×C23—22no—
353C23×C23—22no—
354C23×C23—22no—
355C23×C23—22no—
356C23×C23—22no—
357C23×C23—22no—
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×C23—41no—
435C23×C23—41no—
436C23×C23—41no—
437C23×C23—41no—
438C23×C23—41no—
439C23×C23—41no—
440C23×C23—41no—
441C23×C23—41no—
442C23×C23C22×D411yescharacteristic
443C23×C23C22×D411yescharacteristic
444C23×C23C22×D411yescharacteristic
445C23×C23C2×#4111yescharacteristic
446C23×C23C2×#4111yescharacteristic
447C23×C23C2×#4111yescharacteristic
448C23×C23C2×#4111yescharacteristic
449C23×C23H(5,𝔽2)11yescharacteristic
450C23×C23H(5,𝔽2)11yescharacteristic
451C23×C23H(5,𝔽2)11yescharacteristic
452C23×C23H(5,𝔽2)11yescharacteristic
453C23×C23H(5,𝔽2)11yescharacteristic
454C23×C23H(5,𝔽2)11yescharacteristic
455C23×C23H(5,𝔽2)11yescharacteristic
456C23×C232−1+411yescharacteristic
457D4×C23—416no—
458D4×C23—416no—
459D4×C23—416no—
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—22no—
474C2×C4×C23—22no—
475C2×C4×C23—22no—
476C2×C4×C23—22no—
477C2×C4×C23—22no—
478C2×C4×C23—22no—
479C2×C4×C23—22no—
480C2×C4×C23—22no—
481C2×C4×C23—22no—
482C2×C4×C23—22no—
483C2×C4×C23—22no—
484C2×C4×C23—22no—
485C2×C4×C23—22no—
486C2×C4×C23—22no—
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—41no—
536C2×C4×C23—41no—
537C2×C4×C23—41no—
538C2×C4×C23—41no—
539C2×C4×C23—41no—
540C2×C4×C23—41no—
541C2×C4×C23—41no—
542C2×C4×C23—41no—
543C2×C4×C23#12314yes—
544C2×#397C2×C2311yescharacteristic, complemented
545C2×#394C2×C2311yescharacteristic, complemented
546C2×#394C2×C2311yescharacteristic, complemented
547C2×#394C2×C2311yescharacteristic, complemented
548C2×#392C2×C2311yescharacteristic
549C2×#390C2×C2311yescharacteristic, complemented
550#1444C2×C2311yescharacteristic, complemented
551#1440C2×C2311yescharacteristic, complemented
552#1439C2×C2311yescharacteristic, complemented
553#1439C2×C2311yescharacteristic, complemented
554#1439C2×C2311yescharacteristic, complemented
555#1438C2×C2311yescharacteristic, complemented
556#1438C2×C2311yescharacteristic, complemented
557#1437C2×C2311yescharacteristic, complemented
558#1436C2×C2311yescharacteristic, complemented
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—42no—
573C22×C23—42no—
574C22×C23—42no—
575C22×C23—42no—
576C22×C23—42no—
577C22×C23—42no—
578C22×C23—42no—
579C22×C23—42no—
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×C23—81no—
597C22×C23—81no—
598C22×C23—81no—
599C22×C23—81no—
600C22×C23—81no—
601C22×C23—81no—
602C22×C23—81no—
603C22×C23—81no—
604C22×C23C2×#12311yescharacteristic
605C22×C23#53211yescharacteristic
606C22×C23#53211yescharacteristic
607C22×C23#53411yescharacteristic
608C22×C23#53411yescharacteristic
609C22×C23#53411yescharacteristic
610C22×C23#53511yescharacteristic
611C22×C23#53511yescharacteristic
612C22×C23#53711yescharacteristic
613C22×C23#53811yescharacteristic
614C22×C23#53811yescharacteristic
615C22×C23#53811yescharacteristic
616C22×C23#53811yescharacteristic
617C22×C23#53811yescharacteristic
618C22×C23#53811yescharacteristic
619C22×C23#54011yescharacteristic
620C22×C23#54011yescharacteristic
621C22×C23#54211yescharacteristic
622C22×C23#54211yescharacteristic
623C22×C23D4211yescharacteristic
624C22×C23D4211yescharacteristic
625C22×C23D4211yescharacteristic
626C22×C23#54611yescharacteristic
627C22×C23#54611yescharacteristic
628C22×C23#54611yescharacteristic
629C22×C23#54711yescharacteristic
630C22×C23#54711yescharacteristic
631C22×C23#55011yescharacteristic
632C22×C23#55311yescharacteristic
633C22×C23#55511yescharacteristic
634C22×C23#55911yescharacteristic
635C22×C23#56011yescharacteristic
636C22×C23#56011yescharacteristic
637C22×C23#56211yescharacteristic
638C22×C23#56211yescharacteristic
639C4×C23—24no—
640C4×C23—42no—
641C4×C23—42no—
642C4×C23—42no—
643C4×C23—42no—
644C4×C23—42no—
645C4×C23—42no—
646C4×C23—42no—
647C4×C23—81no—
648C4×C23—81no—
649C4×C23—81no—
650C4×C23—81no—
651C23×D4C22×C2311yescharacteristic
652C23×D4C22×C2311yescharacteristic
653C23×D4C22×C2311yescharacteristic
654C22×C4⋊C4C22×C2311yescharacteristic
655C22×C4⋊C4C22×C2311yescharacteristic
656C22×C4⋊C4C22×C2311yescharacteristic
657C22×C4⋊C4C22×C2311yescharacteristic
658C22×C22⋊C4C22×C2311yescharacteristic
659C22×C22⋊C4C22×C2311yescharacteristic
660C22×C22⋊C4C22×C2311yescharacteristic
661C22×C22⋊C4C22×C2311yescharacteristic
662C22×C22⋊C4C22×C2311yescharacteristic
663C22×C22⋊C4C22×C2311yescharacteristic
664C22×C22⋊C4C22×C2311yescharacteristic
665C22×C22⋊C4C22×C2311yescharacteristic
666C22×C22⋊C4C22×C2311yescharacteristic
667C22×C22⋊C4C22×C2311yescharacteristic
668C22×C22⋊C4C22×C2311yescharacteristic
669C22×C22⋊C4C22×C2311yescharacteristic
670C22×C22⋊C4C22×C2311yescharacteristic
671C22×C22⋊C4C22×C2311yescharacteristic
672C22×C22⋊C4C22×C2311yescharacteristic
673C22×C42C22×C2311yescharacteristic
674#397—24no—
675#394—24no—
676#394—24no—
677#394—24no—
678#392—24no—
679#390—24no—
680C2×#95C22×C2311yescharacteristic
681C2×#95C22×C2311yescharacteristic
682C2×#95C22×C2311yescharacteristic
683C2×#95C22×C2311yescharacteristic
684C2×#95C22×C2311yescharacteristic
685C2×#95C22×C2311yescharacteristic
686C2×#95C22×C2311yescharacteristic
687C2×#95C22×C2311yescharacteristic
688C2×#95C22×C2311yescharacteristic
689C2×#95C22×C2311yescharacteristic
690C2×#95C22×C2311yescharacteristic
691C2×#95C22×C2311yescharacteristic
692C2×C23—82no—
693C2×C23—82no—
694C2×C23—82no—
695C2×C23#242211yescharacteristic
696C2×C23#244511yescharacteristic
697C2×C23#255511yescharacteristic
698C2×C23#262211yescharacteristic
699C2×C23#266111yescharacteristic
700C2×C23#266211yescharacteristic
701C2×C23#266811yescharacteristic
702C2×C23#266911yescharacteristic
703C2×C23#267111yescharacteristic
704C2×C23#268211yescharacteristic
705C2×C23#268611yescharacteristic
706C2×C23#271011yescharacteristic
707C2×C23#271411yescharacteristic
708C2×C23#280311yescharacteristic
709C2×C23#282911yescharacteristic
710C25C23×C2311yescharacteristic
711C25C23×C2311yescharacteristic
712C25C23×C2311yescharacteristic
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4D4×C2314yes—
734C23×C4C23×C2311yescharacteristic
735C23×C4C23×C2311yescharacteristic
736C23×C4C23×C2311yescharacteristic
737C23×C4C23×C2311yescharacteristic
738C23×C4C23×C2311yescharacteristic
739C23×C4C23×C2311yescharacteristic
740C23×C4C23×C2311yescharacteristic
741C23×C4C23×C2311yescharacteristic
742C23×C4C23×C2311yescharacteristic
743C23×C4C23×C2311yescharacteristic
744C23×C4C23×C2311yescharacteristic
745C23×C4C23×C2311yescharacteristic
746C2×C4⋊C4—22no—
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—41no—
753C2×C4⋊C4—41no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4D4×C2314yescomplemented
803C2×C42—22no—
804C2×C42—41no—
805C2×C42—41no—
806#95—22no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95D4×C2314yescomplemented
818C23#1652611yescharacteristic, direct product factor, Sylow
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—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24C2×D4×C2312yes—
862C24C2×D4×C2312yes—
863C24C2×D4×C2312yes—
864C24C24×C2311yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
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×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4C2×D4×C2312yes—
961C22×C4C2×D4×C2312yes—
962C22×C4C2×D4×C2312yes—
963C22×C4C2×D4×C2312yes—
964C22×C4C2×D4×C2312yes—
965C22×C4C2×D4×C2312yes—
966C22×C4#41×C2312yes—
967C22×C4#41×C2312yes—
968C22×C4#41×C2312yes—
969C22×C4#41×C2312yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
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—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
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—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C22×D4×C2311yescharacteristic
1096C23C22×D4×C2311yescharacteristic
1097C23C22×D4×C2311yescharacteristic
1098C23C2×#41×C2311yescharacteristic
1099C23C2×#41×C2311yescharacteristic
1100C23C2×#41×C2311yescharacteristic
1101C23C2×#41×C2311yescharacteristic
1102C23C23×H(5,𝔽2)11yescharacteristic
1103C23C23×H(5,𝔽2)11yescharacteristic
1104C23C23×H(5,𝔽2)11yescharacteristic
1105C23C23×H(5,𝔽2)11yescharacteristic
1106C23C23×H(5,𝔽2)11yescharacteristic
1107C23C23×H(5,𝔽2)11yescharacteristic
1108C23C23×H(5,𝔽2)11yescharacteristic
1109C23C23×2−1+411yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
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×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4C23×#12314yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×C23×#12311yescharacteristic
1243C22C23×#53211yescharacteristic
1244C22C23×#53211yescharacteristic
1245C22C23×#53411yescharacteristic
1246C22C23×#53411yescharacteristic
1247C22C23×#53411yescharacteristic
1248C22C23×#53511yescharacteristic
1249C22C23×#53511yescharacteristic
1250C22C23×#53711yescharacteristic
1251C22C23×#53811yescharacteristic
1252C22C23×#53811yescharacteristic
1253C22C23×#53811yescharacteristic
1254C22C23×#53811yescharacteristic
1255C22C23×#53811yescharacteristic
1256C22C23×#53811yescharacteristic
1257C22C23×#54011yescharacteristic
1258C22C23×#54011yescharacteristic
1259C22C23×#54211yescharacteristic
1260C22C23×#54211yescharacteristic
1261C22D42×C2311yescharacteristic
1262C22D42×C2311yescharacteristic
1263C22D42×C2311yescharacteristic
1264C22C23×#54611yescharacteristic
1265C22C23×#54611yescharacteristic
1266C22C23×#54611yescharacteristic
1267C22C23×#54711yescharacteristic
1268C22C23×#54711yescharacteristic
1269C22C23×#55011yescharacteristic
1270C22C23×#55311yescharacteristic
1271C22C23×#55511yescharacteristic
1272C22C23×#55911yescharacteristic
1273C22C23×#56011yescharacteristic
1274C22C23×#56011yescharacteristic
1275C22C23×#56211yescharacteristic
1276C22C23×#56211yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C23×#242211yescharacteristic
1293C2C23×#244511yescharacteristic
1294C2C23×#255511yescharacteristic
1295C2C23×#262211yescharacteristic
1296C2C23×#266111yescharacteristic
1297C2C23×#266211yescharacteristic
1298C2C23×#266811yescharacteristic
1299C2C23×#266911yescharacteristic
1300C2C23×#267111yescharacteristic
1301C2C23×#268211yescharacteristic
1302C2C23×#268611yescharacteristic
1303C2C23×#271011yescharacteristic
1304C2C23×#271411yescharacteristic
1305C2C23×#280311yescharacteristic
1306C2C23×#282911yescharacteristic
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
3. C2×C23×#394C2semidirect
4. C2×C23×#394C2semidirect
6. C2×C23×#390C2semidirect
7. C23×#1444C2semidirect
8. C23×#1440C2semidirect
9. C23×#1439C2semidirect
10. C23×#1439C2semidirect
11. C23×#1439C2semidirect
12. C23×#1438C2semidirect
13. C23×#1438C2semidirect
14. C23×#1437C2semidirect
15. C23×#1436C2semidirect
149. C2×C22⋊C4×C23D4semidirect
164. C23×#95D4semidirect
336. #16526C23direct (N × H)
544. C2×#397C2×C23semidirect
545. C2×#394C2×C23semidirect
546. C2×#394C2×C23semidirect
547. C2×#394C2×C23semidirect
549. C2×#390C2×C23semidirect
550. #1444C2×C23semidirect
551. #1440C2×C23semidirect
552. #1439C2×C23semidirect
553. #1439C2×C23semidirect
554. #1439C2×C23semidirect
555. #1438C2×C23semidirect
556. #1438C2×C23semidirect
557. #1437C2×C23semidirect
558. #1436C2×C23semidirect
802. C2×C22⋊C4D4×C23semidirect
817. #95D4×C23semidirect
818. C23#16526direct (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×#14442
C23×#14402
C23×#14392
C23×#14382
C23×#14372
C23×#14362
#1652623