Finite Group Databasebeta

← C23×#16512 #19164138

Subgroups — C23×#16512 #19164138

Order 5888.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#394C211yesmaximal, characteristic, complemented
2C2×C23×#394C211yesmaximal, characteristic, complemented
3C2×C23×#392C211yesmaximal, characteristic
4C2×C23×#386C211yesmaximal, characteristic, complemented
5C2×C23×#386C211yesmaximal, characteristic, complemented
6C2×C23×#380C211yesmaximal, characteristic, complemented
7C23×#1443C211yesmaximal, characteristic, complemented
8C23×#1441C211yesmaximal, characteristic, complemented
9C23×#1440C211yesmaximal, characteristic, complemented
10C23×#1440C211yesmaximal, characteristic, complemented
11C23×#1439C211yesmaximal, characteristic, complemented
12C23×#1439C211yesmaximal, characteristic, complemented
13C23×#1439C211yesmaximal, characteristic, complemented
14C23×#1438C211yesmaximal, characteristic, complemented
15C23×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C23C2211yescharacteristic
17C23×D4×C23C2211yescharacteristic
18C23×D4×C23C2211yescharacteristic
19C24×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
37C23×#394—24no—
38C23×#394—24no—
39C23×#392—24no—
40C23×#386—24no—
41C23×#386—24no—
42C23×#380—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
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—22no—
69C22×D4×C23—22no—
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×C23—22no—
82C23×C4×C23—22no—
83C23×C4×C23—41no—
84C23×C4×C23—41no—
85C23×C4×C23—41no—
86C23×C4×C23—41no—
87C23×C4×C23D414yescomplemented
88C23×C4×C23C2311yescharacteristic
89C23×C4×C23C2311yescharacteristic
90C23×C4×C23C2311yescharacteristic
91C23×C4×C23C2311yescharacteristic
92C23×C4×C23C2311yescharacteristic
93C23×C4×C23C2311yescharacteristic
94C23×C4×C23C2311yescharacteristic
95C23×C4×C23C2311yescharacteristic
96C23×C4×C23C2311yescharacteristic
97C23×C4×C23C2311yescharacteristic
98C23×C4×C23C2311yescharacteristic
99C23×C4×C23C2311yescharacteristic
100C2×C4⋊C4×C23—22no—
101C2×C4⋊C4×C23—22no—
102C2×C4⋊C4×C23—41no—
103C2×C4⋊C4×C23—41no—
104C2×C4⋊C4×C23—41no—
105C2×C4⋊C4×C23—41no—
106C2×C4⋊C4×C23—41no—
107C2×C4⋊C4×C23—41no—
108C2×C4⋊C4×C23D414yescomplemented
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—22no—
132C2×C22⋊C4×C23—22no—
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×C23—41no—
150C2×C22⋊C4×C23—41no—
151C23×#95—22no—
152C23×#95—22no—
153C23×#95—22no—
154C23×#95—22no—
155C23×#95—22no—
156C23×#95—22no—
157C23×#95—22no—
158C23×#95—22no—
159C23×#95—22no—
160C23×#95—22no—
161C23×#95—41no—
162C23×#95—41no—
163C23×#95—41no—
164C23×#95—41no—
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×C23C2×D412yes—
206C24×C23C2×D412yes—
207C24×C23C2×D412yes—
208C24×C23#4112yes—
209C24×C23#4112yes—
210C24×C23C2411yescharacteristic
211C2×D4×C23—28no—
212C2×D4×C23—28no—
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—28no—
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×C23—21no—
307C22×C4×C23—21no—
308C22×C4×C23—21no—
309C22×C4×C23—44no—
310C22×C4×C23—44no—
311C22×C4×C23—44no—
312C22×C4×C23—44no—
313C22×C4×C23—44no—
314C22×C4×C23—44no—
315C22×C4×C23C2×D412yes—
316C22×C4×C23C2×D412yes—
317C22×C4×C23C2×D412yes—
318C22×C4×C23C2×D412yes—
319C22×C4×C23C2×D412yes—
320C22×C4×C23C2×D412yes—
321C22×C4×C23#4112yes—
322C22×C4×C23#4112yes—
323C4⋊C4×C23—44no—
324C4⋊C4×C23—44no—
325C4⋊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—
335C22⋊C4×C23—44no—
336C22⋊C4×C23—44no—
337C22⋊C4×C23—44no—
338C22⋊C4×C23—44no—
339C22⋊C4×C23—44no—
340#16512C2311yesmaximal, characteristic, direct product factor, Sylow
341C23×C23—22no—
342C23×C23—22no—
343C23×C23—22no—
344C23×C23—22no—
345C23×C23—22no—
346C23×C23—22no—
347C23×C23—22no—
348C23×C23—22no—
349C23×C23—22no—
350C23×C23—22no—
351C23×C23—22no—
352C23×C23—22no—
353C23×C23—22no—
354C23×C23—22no—
355C23×C23—22no—
356C23×C23—22no—
357C23×C23—22no—
358C23×C23—22no—
359C23×C23—22no—
360C23×C23—22no—
361C23×C23—22no—
362C23×C23—22no—
363C23×C23—22no—
364C23×C23—22no—
365C23×C23—22no—
366C23×C23—22no—
367C23×C23—22no—
368C23×C23—22no—
369C23×C23—22no—
370C23×C23—22no—
371C23×C23—22no—
372C23×C23—22no—
373C23×C23—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×C23—41no—
443C23×C23—41no—
444C23×C23—41no—
445C23×C23#12114yes—
446C23×C23C22×D411yescharacteristic
447C23×C23C22×D411yescharacteristic
448C23×C23C22×D411yescharacteristic
449C23×C23C2×#4111yescharacteristic
450C23×C23C2×#4111yescharacteristic
451C23×C23C2×#4111yescharacteristic
452C23×C23C2×#4111yescharacteristic
453C23×C23H(5,𝔽2)11yescharacteristic
454C23×C23H(5,𝔽2)11yescharacteristic
455C23×C23H(5,𝔽2)11yescharacteristic
456C23×C23H(5,𝔽2)11yescharacteristic
457C23×C23H(5,𝔽2)11yescharacteristic
458C23×C23H(5,𝔽2)11yescharacteristic
459C23×C23H(5,𝔽2)11yescharacteristic
460C23×C232−1+411yescharacteristic
461D4×C23—416no—
462D4×C23—416no—
463D4×C23—416no—
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—416no—
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—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—41no—
544C2×C4×C23—41no—
545C2×C4×C23—41no—
546C2×C4×C23—41no—
547C2×C4×C23—41no—
548C2×C4×C23#12114yes—
549C2×#394C2×C2311yescharacteristic, complemented
550C2×#394C2×C2311yescharacteristic, complemented
551C2×#392C2×C2311yescharacteristic
552C2×#386C2×C2311yescharacteristic, complemented
553C2×#386C2×C2311yescharacteristic, complemented
554C2×#380C2×C2311yescharacteristic, complemented
555#1443C2×C2311yescharacteristic, complemented
556#1441C2×C2311yescharacteristic, complemented
557#1440C2×C2311yescharacteristic, complemented
558#1440C2×C2311yescharacteristic, complemented
559#1439C2×C2311yescharacteristic, complemented
560#1439C2×C2311yescharacteristic, complemented
561#1439C2×C2311yescharacteristic, complemented
562#1438C2×C2311yescharacteristic, complemented
563#1438C2×C2311yescharacteristic, complemented
564C22×C23—24no—
565C22×C23—24no—
566C22×C23—24no—
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—42no—
581C22×C23—42no—
582C22×C23—42no—
583C22×C23—42no—
584C22×C23—42no—
585C22×C23—42no—
586C22×C23—42no—
587C22×C23—42no—
588C22×C23—42no—
589C22×C23—42no—
590C22×C23—42no—
591C22×C23—42no—
592C22×C23—42no—
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×C23—81no—
605C22×C23—81no—
606C22×C23—81no—
607C22×C23—81no—
608C22×C23—81no—
609C22×C23C2×#12111yescharacteristic
610C22×C23C2×#12111yescharacteristic
611C22×C23#52511yescharacteristic
612C22×C23#53411yescharacteristic
613C22×C23#53411yescharacteristic
614C22×C23#53411yescharacteristic
615C22×C23#53411yescharacteristic
616C22×C23#53411yescharacteristic
617C22×C23#53511yescharacteristic
618C22×C23#53511yescharacteristic
619C22×C23#53711yescharacteristic
620C22×C23#53811yescharacteristic
621C22×C23#53811yescharacteristic
622C22×C23#53811yescharacteristic
623C22×C23#53811yescharacteristic
624C22×C23#53811yescharacteristic
625C22×C23#53911yescharacteristic
626C22×C23#54011yescharacteristic
627C22×C23#54211yescharacteristic
628C22×C23D4211yescharacteristic
629C22×C23#54611yescharacteristic
630C22×C23#54611yescharacteristic
631C22×C23#54611yescharacteristic
632C22×C23#54711yescharacteristic
633C22×C23#54811yescharacteristic
634C22×C23#55011yescharacteristic
635C22×C23#55111yescharacteristic
636C22×C23#55111yescharacteristic
637C22×C23#55311yescharacteristic
638C22×C23#55311yescharacteristic
639C22×C23#55511yescharacteristic
640C22×C23#56011yescharacteristic
641C22×C23#56011yescharacteristic
642C22×C23#56211yescharacteristic
643C22×C23#56211yescharacteristic
644C4×C23—24no—
645C4×C23—42no—
646C4×C23—42no—
647C4×C23—42no—
648C4×C23—42no—
649C4×C23—42no—
650C4×C23—81no—
651C4×C23—81no—
652C4×C23—81no—
653C4×C23—81no—
654C4×C23—81no—
655C4×C23—81no—
656C23×D4C22×C2311yescharacteristic
657C23×D4C22×C2311yescharacteristic
658C23×D4C22×C2311yescharacteristic
659C24×C4C22×C2311yescharacteristic
660C22×C4⋊C4C22×C2311yescharacteristic
661C22×C4⋊C4C22×C2311yescharacteristic
662C22×C4⋊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×C22⋊C4C22×C2311yescharacteristic
674C22×C22⋊C4C22×C2311yescharacteristic
675C22×C22⋊C4C22×C2311yescharacteristic
676C22×C22⋊C4C22×C2311yescharacteristic
677#394—24no—
678#394—24no—
679#392—24no—
680#386—24no—
681#386—24no—
682#380—24no—
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×#95C22×C2311yescharacteristic
693C2×#95C22×C2311yescharacteristic
694C2×#95C22×C2311yescharacteristic
695C2×#95C22×C2311yescharacteristic
696C2×#95C22×C2311yescharacteristic
697C2×C23—44no—
698C2×C23—82no—
699C2×C23—82no—
700C2×C23#241411yescharacteristic
701C2×C23#241611yescharacteristic
702C2×C23#253411yescharacteristic
703C2×C23#261711yescharacteristic
704C2×C23#261711yescharacteristic
705C2×C23#263011yescharacteristic
706C2×C23#266811yescharacteristic
707C2×C23#267311yescharacteristic
708C2×C23#268611yescharacteristic
709C2×C23#269611yescharacteristic
710C2×C23#270811yescharacteristic
711C2×C23#273011yescharacteristic
712C2×C23#275611yescharacteristic
713C2×C23#277811yescharacteristic
714C2×C23#281311yescharacteristic
715C25C23×C2311yescharacteristic
716C25C23×C2311yescharacteristic
717C25C23×C2311yescharacteristic
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4D4×C2314yes—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4D4×C2314yescomplemented
746C23×C4C23×C2311yescharacteristic
747C23×C4C23×C2311yescharacteristic
748C23×C4C23×C2311yescharacteristic
749C23×C4C23×C2311yescharacteristic
750C23×C4C23×C2311yescharacteristic
751C23×C4C23×C2311yescharacteristic
752C23×C4C23×C2311yescharacteristic
753C23×C4C23×C2311yescharacteristic
754C23×C4C23×C2311yescharacteristic
755C23×C4C23×C2311yescharacteristic
756C23×C4C23×C2311yescharacteristic
757C23×C4C23×C2311yescharacteristic
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—41no—
761C2×C4⋊C4—41no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—41no—
766C2×C4⋊C4D4×C2314yescomplemented
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—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
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⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823C23#1651211yescharacteristic, direct product factor, Sylow
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—
861C24—21no—
862C24—21no—
863C24—21no—
864C24C2×D4×C2312yes—
865C24C2×D4×C2312yes—
866C24C2×D4×C2312yes—
867C24#41×C2312yes—
868C24#41×C2312yes—
869C24C24×C2311yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
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—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
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—28no—
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×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4C2×D4×C2312yes—
975C22×C4C2×D4×C2312yes—
976C22×C4C2×D4×C2312yes—
977C22×C4C2×D4×C2312yes—
978C22×C4C2×D4×C2312yes—
979C22×C4C2×D4×C2312yes—
980C22×C4#41×C2312yes—
981C22×C4#41×C2312yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
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—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
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—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23C23×#12114yes—
1104C23C22×D4×C2311yescharacteristic
1105C23C22×D4×C2311yescharacteristic
1106C23C22×D4×C2311yescharacteristic
1107C23C2×#41×C2311yescharacteristic
1108C23C2×#41×C2311yescharacteristic
1109C23C2×#41×C2311yescharacteristic
1110C23C2×#41×C2311yescharacteristic
1111C23C23×H(5,𝔽2)11yescharacteristic
1112C23C23×H(5,𝔽2)11yescharacteristic
1113C23C23×H(5,𝔽2)11yescharacteristic
1114C23C23×H(5,𝔽2)11yescharacteristic
1115C23C23×H(5,𝔽2)11yescharacteristic
1116C23C23×H(5,𝔽2)11yescharacteristic
1117C23C23×H(5,𝔽2)11yescharacteristic
1118C23C23×2−1+411yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
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—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—416no—
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×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4C23×#12114yes—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×C23×#12111yescharacteristic
1253C22C2×C23×#12111yescharacteristic
1254C22C23×#52511yescharacteristic
1255C22C23×#53411yescharacteristic
1256C22C23×#53411yescharacteristic
1257C22C23×#53411yescharacteristic
1258C22C23×#53411yescharacteristic
1259C22C23×#53411yescharacteristic
1260C22C23×#53511yescharacteristic
1261C22C23×#53511yescharacteristic
1262C22C23×#53711yescharacteristic
1263C22C23×#53811yescharacteristic
1264C22C23×#53811yescharacteristic
1265C22C23×#53811yescharacteristic
1266C22C23×#53811yescharacteristic
1267C22C23×#53811yescharacteristic
1268C22C23×#53911yescharacteristic
1269C22C23×#54011yescharacteristic
1270C22C23×#54211yescharacteristic
1271C22D42×C2311yescharacteristic
1272C22C23×#54611yescharacteristic
1273C22C23×#54611yescharacteristic
1274C22C23×#54611yescharacteristic
1275C22C23×#54711yescharacteristic
1276C22C23×#54811yescharacteristic
1277C22C23×#55011yescharacteristic
1278C22C23×#55111yescharacteristic
1279C22C23×#55111yescharacteristic
1280C22C23×#55311yescharacteristic
1281C22C23×#55311yescharacteristic
1282C22C23×#55511yescharacteristic
1283C22C23×#56011yescharacteristic
1284C22C23×#56011yescharacteristic
1285C22C23×#56211yescharacteristic
1286C22C23×#56211yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C23×#241411yescharacteristic
1303C2C23×#241611yescharacteristic
1304C2C23×#253411yescharacteristic
1305C2C23×#261711yescharacteristic
1306C2C23×#261711yescharacteristic
1307C2C23×#263011yescharacteristic
1308C2C23×#266811yescharacteristic
1309C2C23×#267311yescharacteristic
1310C2C23×#268611yescharacteristic
1311C2C23×#269611yescharacteristic
1312C2C23×#270811yescharacteristic
1313C2C23×#273011yescharacteristic
1314C2C23×#275611yescharacteristic
1315C2C23×#277811yescharacteristic
1316C2C23×#281311yescharacteristic
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×#394C2semidirect
2. C2×C23×#394C2semidirect
4. C2×C23×#386C2semidirect
5. C2×C23×#386C2semidirect
6. C2×C23×#380C2semidirect
7. C23×#1443C2semidirect
8. C23×#1441C2semidirect
9. C23×#1440C2semidirect
10. C23×#1440C2semidirect
11. C23×#1439C2semidirect
12. C23×#1439C2semidirect
13. C23×#1439C2semidirect
14. C23×#1438C2semidirect
15. C23×#1438C2semidirect
87. C23×C4×C23D4semidirect
108. C2×C4⋊C4×C23D4semidirect
340. #16512C23direct (N × H)
549. C2×#394C2×C23semidirect
550. C2×#394C2×C23semidirect
552. C2×#386C2×C23semidirect
553. C2×#386C2×C23semidirect
554. C2×#380C2×C23semidirect
555. #1443C2×C23semidirect
556. #1441C2×C23semidirect
557. #1440C2×C23semidirect
558. #1440C2×C23semidirect
559. #1439C2×C23semidirect
560. #1439C2×C23semidirect
561. #1439C2×C23semidirect
562. #1438C2×C23semidirect
563. #1438C2×C23semidirect
745. C23×C4D4×C23semidirect
766. C2×C4⋊C4D4×C23semidirect
823. C23#16512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C23×#3942
C2×C23×#3922
C2×C23×#3862
C2×C23×#3802
C23×#14432
C23×#14412
C23×#14402
C23×#14392
C23×#14382
#1651223