Finite Group Databasebeta

← C23×#15498 #19163124

Subgroups — C23×#15498 #19163124

Order 5888.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1334 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×#394C211yesmaximal, characteristic, complemented
4C2×C23×#392C211yesmaximal, characteristic
5C2×C23×#390C211yesmaximal, characteristic, complemented
6C2×C23×#386C211yesmaximal, characteristic, complemented
7C2×C23×#386C211yesmaximal, characteristic, complemented
8C2×C23×#385C211yesmaximal, characteristic, complemented
9C23×#1441C211yesmaximal, characteristic, complemented
10C23×#1440C211yesmaximal, characteristic, complemented
11C23×#1440C211yesmaximal, characteristic, complemented
12C23×#1439C211yesmaximal, characteristic, complemented
13C23×#1439C211yesmaximal, characteristic, complemented
14C23×#1437C211yesmaximal, characteristic, complemented
15C23×C4⋊#95C211yesmaximal, 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×C4⋊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×#394—24no—
40C23×#394—24no—
41C23×#394—24no—
42C23×#392—24no—
43C23×#390—24no—
44C23×#386—24no—
45C23×#386—24no—
46C23×#385—24no—
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
57C2×C23×#95C2211yescharacteristic
58C2×C23×#95C2211yescharacteristic
59C25×C23C2311yescharacteristic
60C25×C23C2311yescharacteristic
61C25×C23C2311yescharacteristic
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—22no—
71C22×D4×C23—22no—
72C22×D4×C23—22no—
73C22×D4×C23—22no—
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×C23—41no—
81C22×D4×C23—41no—
82C22×D4×C23D414yes—
83C23×C4×C23—22no—
84C23×C4×C23—22no—
85C23×C4×C23—22no—
86C23×C4×C23—41no—
87C23×C4×C23—41no—
88C23×C4×C23—41no—
89C23×C4×C23—41no—
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
100C23×C4×C23C2311yescharacteristic
101C23×C4×C23C2311yescharacteristic
102C2×C4⋊C4×C23—22no—
103C2×C4⋊C4×C23—22no—
104C2×C4⋊C4×C23—22no—
105C2×C4⋊C4×C23—22no—
106C2×C4⋊C4×C23—22no—
107C2×C4⋊C4×C23—22no—
108C2×C4⋊C4×C23—41no—
109C2×C4⋊C4×C23—41no—
110C2×C4⋊C4×C23—41no—
111C2×C4⋊C4×C23—41no—
112C2×C4⋊C4×C23—41no—
113C2×C4⋊C4×C23D414yescomplemented
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—22no—
134C2×C22⋊C4×C23—22no—
135C2×C22⋊C4×C23—22no—
136C2×C22⋊C4×C23—22no—
137C2×C22⋊C4×C23—22no—
138C2×C22⋊C4×C23—22no—
139C2×C22⋊C4×C23—22no—
140C2×C22⋊C4×C23—22no—
141C2×C22⋊C4×C23—22no—
142C2×C22⋊C4×C23—22no—
143C2×C22⋊C4×C23—22no—
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—
151C2×C22⋊C4×C23—41no—
152C2×C22⋊C4×C23—41no—
153C2×C22⋊C4×C23—41no—
154C2×C22⋊C4×C23D414yescomplemented
155C2×C22⋊C4×C23D414yescomplemented
156C2×C42×C23—22no—
157C2×C42×C23—22no—
158C2×C42×C23—41no—
159C23×#95—22no—
160C23×#95—22no—
161C23×#95—22no—
162C23×#95—22no—
163C23×#95—22no—
164C23×#95—22no—
165C23×#95—22no—
166C23×#95—22no—
167C23×#95—22no—
168C23×#95—22no—
169C23×#95—41no—
170C23×#95—41no—
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×C23—21no—
208C24×C23—21no—
209C24×C23—21no—
210C24×C23—21no—
211C24×C23C2×D412yes—
212C24×C23C2×D412yes—
213C24×C23C2×D412yes—
214C24×C23C2×D412yes—
215C24×C23#4112yes—
216C24×C23C2411yescharacteristic
217C2×D4×C23—28no—
218C2×D4×C23—28no—
219C2×D4×C23—28no—
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—
232C2×D4×C23—44no—
233C2×D4×C23—44no—
234C2×D4×C23—44no—
235C2×D4×C23—44no—
236C2×D4×C23—44no—
237C2×D4×C23—44no—
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×C23—21no—
307C22×C4×C23—21no—
308C22×C4×C23—21no—
309C22×C4×C23—21no—
310C22×C4×C23—44no—
311C22×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×C23C2×D412yes—
318C22×C4×C23C2×D412yes—
319C22×C4×C23C2×D412yes—
320C22×C4×C23C2×D412yes—
321C22×C4×C23C2×D412yes—
322C22×C4×C23C2×D412yes—
323C22×C4×C23C2×D412yes—
324C22×C4×C23C2×D412yes—
325C22×C4×C23#4112yes—
326C22×C4×C23#4112yes—
327C22×C4×C23#4112yes—
328C22×C4×C23#4112yes—
329C4⋊C4×C23—44no—
330C4⋊C4×C23—44no—
331C4⋊C4×C23—44no—
332C4⋊C4×C23—44no—
333C22⋊C4×C23—28no—
334C22⋊C4×C23—44no—
335C22⋊C4×C23—44no—
336C22⋊C4×C23—44no—
337C22⋊C4×C23—44no—
338C22⋊C4×C23—44no—
339C22⋊C4×C23—44no—
340C22⋊C4×C23—44no—
341C22⋊C4×C23—44no—
342C22⋊C4×C23—44no—
343C22⋊C4×C23—44no—
344C22⋊C4×C23—44no—
345C22⋊C4×C23—44no—
346C22⋊C4×C23—44no—
347C42×C23—44no—
348#15498C2311yesmaximal, characteristic, direct product factor, Sylow
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—22no—
374C23×C23—22no—
375C23×C23—22no—
376C23×C23—22no—
377C23×C23—22no—
378C23×C23—22no—
379C23×C23—22no—
380C23×C23—22no—
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—41no—
446C23×C23—41no—
447C23×C23—41no—
448C23×C23—41no—
449C23×C23—41no—
450C23×C23—41no—
451C23×C23—41no—
452C23×C23—41no—
453C23×C23#12114yes—
454C23×C23C22×D411yescharacteristic
455C23×C23C22×D411yescharacteristic
456C23×C23C22×D411yescharacteristic
457C23×C23C22×D411yescharacteristic
458C23×C23C2×#4111yescharacteristic
459C23×C23C2×#4111yescharacteristic
460C23×C23C2×#4111yescharacteristic
461C23×C23C2×#4111yescharacteristic
462C23×C23C2×#4111yescharacteristic
463C23×C23H(5,𝔽2)11yescharacteristic
464C23×C23H(5,𝔽2)11yescharacteristic
465C23×C23H(5,𝔽2)11yescharacteristic
466C23×C23H(5,𝔽2)11yescharacteristic
467C23×C23H(5,𝔽2)11yescharacteristic
468C23×C232−1+411yescharacteristic
469D4×C23—416no—
470D4×C23—416no—
471D4×C23—416no—
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—22no—
488C2×C4×C23—22no—
489C2×C4×C23—22no—
490C2×C4×C23—22no—
491C2×C4×C23—22no—
492C2×C4×C23—22no—
493C2×C4×C23—22no—
494C2×C4×C23—22no—
495C2×C4×C23—22no—
496C2×C4×C23—22no—
497C2×C4×C23—22no—
498C2×C4×C23—22no—
499C2×C4×C23—22no—
500C2×C4×C23—22no—
501C2×C4×C23—22no—
502C2×C4×C23—416no—
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—41no—
549C2×C4×C23—41no—
550C2×C4×C23—41no—
551C2×C4×C23—41no—
552C2×C4×C23—41no—
553C2×C4×C23—41no—
554C2×C4×C23—41no—
555C2×C4×C23#12114yes—
556C2×C4×C23#12314yes—
557C2×#394C2×C2311yescharacteristic, complemented
558C2×#394C2×C2311yescharacteristic, complemented
559C2×#394C2×C2311yescharacteristic, complemented
560C2×#392C2×C2311yescharacteristic
561C2×#390C2×C2311yescharacteristic, complemented
562C2×#386C2×C2311yescharacteristic, complemented
563C2×#386C2×C2311yescharacteristic, complemented
564C2×#385C2×C2311yescharacteristic, complemented
565#1441C2×C2311yescharacteristic, complemented
566#1440C2×C2311yescharacteristic, complemented
567#1440C2×C2311yescharacteristic, complemented
568#1439C2×C2311yescharacteristic, complemented
569#1439C2×C2311yescharacteristic, complemented
570#1437C2×C2311yescharacteristic, complemented
571C4⋊#95C2×C2311yescharacteristic, complemented
572C22×C23—24no—
573C22×C23—24no—
574C22×C23—24no—
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—42no—
594C22×C23—42no—
595C22×C23—42no—
596C22×C23—42no—
597C22×C23—42no—
598C22×C23—42no—
599C22×C23—42no—
600C22×C23—42no—
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×C23—81no—
610C22×C23—81no—
611C22×C23—81no—
612C22×C23—81no—
613C22×C23—81no—
614C22×C23—81no—
615C22×C23—81no—
616C22×C23—81no—
617C22×C23C2×#12111yescharacteristic
618C22×C23C2×#12111yescharacteristic
619C22×C23C2×#12311yescharacteristic
620C22×C23#52511yescharacteristic
621C22×C23#53211yescharacteristic
622C22×C23#53211yescharacteristic
623C22×C23#53411yescharacteristic
624C22×C23#53411yescharacteristic
625C22×C23#53411yescharacteristic
626C22×C23#53711yescharacteristic
627C22×C23#53811yescharacteristic
628C22×C23#54011yescharacteristic
629C22×C23#54011yescharacteristic
630C22×C23#54211yescharacteristic
631C22×C23#54211yescharacteristic
632C22×C23D4211yescharacteristic
633C22×C23D4211yescharacteristic
634C22×C23D4211yescharacteristic
635C22×C23D4211yescharacteristic
636C22×C23#54611yescharacteristic
637C22×C23#54611yescharacteristic
638C22×C23#54611yescharacteristic
639C22×C23#54611yescharacteristic
640C22×C23#54711yescharacteristic
641C22×C23#54711yescharacteristic
642C22×C23#54811yescharacteristic
643C22×C23#55011yescharacteristic
644C22×C23#55111yescharacteristic
645C22×C23#55111yescharacteristic
646C22×C23#55311yescharacteristic
647C22×C23#55311yescharacteristic
648C22×C23#55311yescharacteristic
649C22×C23#55911yescharacteristic
650C22×C23H(3,𝔽4)11yescharacteristic
651C22×C23#56211yescharacteristic
652C4×C23—24no—
653C4×C23—24no—
654C4×C23—42no—
655C4×C23—42no—
656C4×C23—42no—
657C4×C23—42no—
658C4×C23—42no—
659C4×C23—42no—
660C4×C23—81no—
661C4×C23—81no—
662C4×C23—81no—
663C4×C23—81no—
664C23×D4C22×C2311yescharacteristic
665C23×D4C22×C2311yescharacteristic
666C23×D4C22×C2311yescharacteristic
667C24×C4C22×C2311yescharacteristic
668C22×C4⋊C4C22×C2311yescharacteristic
669C22×C4⋊C4C22×C2311yescharacteristic
670C22×C4⋊C4C22×C2311yescharacteristic
671C22×C4⋊C4C22×C2311yescharacteristic
672C22×C22⋊C4C22×C2311yescharacteristic
673C22×C22⋊C4C22×C2311yescharacteristic
674C22×C22⋊C4C22×C2311yescharacteristic
675C22×C22⋊C4C22×C2311yescharacteristic
676C22×C22⋊C4C22×C2311yescharacteristic
677C22×C22⋊C4C22×C2311yescharacteristic
678C22×C22⋊C4C22×C2311yescharacteristic
679C22×C22⋊C4C22×C2311yescharacteristic
680C22×C22⋊C4C22×C2311yescharacteristic
681C22×C22⋊C4C22×C2311yescharacteristic
682C22×C22⋊C4C22×C2311yescharacteristic
683C22×C22⋊C4C22×C2311yescharacteristic
684C22×C22⋊C4C22×C2311yescharacteristic
685C22×C22⋊C4C22×C2311yescharacteristic
686C22×C42C22×C2311yescharacteristic
687#394—24no—
688#394—24no—
689#394—24no—
690#392—24no—
691#390—24no—
692#386—24no—
693#386—24no—
694#385—24no—
695C2×#95C22×C2311yescharacteristic
696C2×#95C22×C2311yescharacteristic
697C2×#95C22×C2311yescharacteristic
698C2×#95C22×C2311yescharacteristic
699C2×#95C22×C2311yescharacteristic
700C2×#95C22×C2311yescharacteristic
701C2×#95C22×C2311yescharacteristic
702C2×#95C22×C2311yescharacteristic
703C2×#95C22×C2311yescharacteristic
704C2×#95C22×C2311yescharacteristic
705C2×#95C22×C2311yescharacteristic
706C2×#95C22×C2311yescharacteristic
707C2×C23—44no—
708C2×C23—82no—
709C2×C23—82no—
710C2×C23#241211yescharacteristic
711C2×C23#241611yescharacteristic
712C2×C23#242211yescharacteristic
713C2×C23#242411yescharacteristic
714C2×C23#242811yescharacteristic
715C2×C23#244511yescharacteristic
716C2×C23#246111yescharacteristic
717C2×C23#254311yescharacteristic
718C2×C23#260211yescharacteristic
719C2×C23#267111yescharacteristic
720C2×C23#267911yescharacteristic
721C2×C23#270111yescharacteristic
722C2×C23#271211yescharacteristic
723C2×C23#273011yescharacteristic
724C2×C23#275311yescharacteristic
725C25C23×C2311yescharacteristic
726C25C23×C2311yescharacteristic
727C25C23×C2311yescharacteristic
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4D4×C2314yes—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4C23×C2311yescharacteristic
757C23×C4C23×C2311yescharacteristic
758C23×C4C23×C2311yescharacteristic
759C23×C4C23×C2311yescharacteristic
760C23×C4C23×C2311yescharacteristic
761C23×C4C23×C2311yescharacteristic
762C23×C4C23×C2311yescharacteristic
763C23×C4C23×C2311yescharacteristic
764C23×C4C23×C2311yescharacteristic
765C23×C4C23×C2311yescharacteristic
766C23×C4C23×C2311yescharacteristic
767C23×C4C23×C2311yescharacteristic
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C4⋊C4—41no—
779C2×C4⋊C4D4×C2314yescomplemented
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—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4D4×C2314yescomplemented
821C2×C22⋊C4D4×C2314yescomplemented
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—41no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837C23#1549811yescharacteristic, direct product factor, Sylow
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—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24C2×D4×C2312yes—
879C24C2×D4×C2312yes—
880C24C2×D4×C2312yes—
881C24C2×D4×C2312yes—
882C24#41×C2312yes—
883C24C24×C2311yescharacteristic
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
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×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—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4C2×D4×C2312yes—
985C22×C4C2×D4×C2312yes—
986C22×C4C2×D4×C2312yes—
987C22×C4C2×D4×C2312yes—
988C22×C4C2×D4×C2312yes—
989C22×C4C2×D4×C2312yes—
990C22×C4C2×D4×C2312yes—
991C22×C4C2×D4×C2312yes—
992C22×C4#41×C2312yes—
993C22×C4#41×C2312yes—
994C22×C4#41×C2312yes—
995C22×C4#41×C2312yes—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C22⋊C4—28no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C42—44no—
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—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
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—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23C23×#12114yes—
1120C23C22×D4×C2311yescharacteristic
1121C23C22×D4×C2311yescharacteristic
1122C23C22×D4×C2311yescharacteristic
1123C23C22×D4×C2311yescharacteristic
1124C23C2×#41×C2311yescharacteristic
1125C23C2×#41×C2311yescharacteristic
1126C23C2×#41×C2311yescharacteristic
1127C23C2×#41×C2311yescharacteristic
1128C23C2×#41×C2311yescharacteristic
1129C23C23×H(5,𝔽2)11yescharacteristic
1130C23C23×H(5,𝔽2)11yescharacteristic
1131C23C23×H(5,𝔽2)11yescharacteristic
1132C23C23×H(5,𝔽2)11yescharacteristic
1133C23C23×H(5,𝔽2)11yescharacteristic
1134C23C23×2−1+411yescharacteristic
1135D4—416no—
1136D4—416no—
1137D4—416no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—416no—
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×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4C23×#12114yes—
1222C2×C4C23×#12314yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22C2×C23×#12111yescharacteristic
1269C22C2×C23×#12111yescharacteristic
1270C22C2×C23×#12311yescharacteristic
1271C22C23×#52511yescharacteristic
1272C22C23×#53211yescharacteristic
1273C22C23×#53211yescharacteristic
1274C22C23×#53411yescharacteristic
1275C22C23×#53411yescharacteristic
1276C22C23×#53411yescharacteristic
1277C22C23×#53711yescharacteristic
1278C22C23×#53811yescharacteristic
1279C22C23×#54011yescharacteristic
1280C22C23×#54011yescharacteristic
1281C22C23×#54211yescharacteristic
1282C22C23×#54211yescharacteristic
1283C22D42×C2311yescharacteristic
1284C22D42×C2311yescharacteristic
1285C22D42×C2311yescharacteristic
1286C22D42×C2311yescharacteristic
1287C22C23×#54611yescharacteristic
1288C22C23×#54611yescharacteristic
1289C22C23×#54611yescharacteristic
1290C22C23×#54611yescharacteristic
1291C22C23×#54711yescharacteristic
1292C22C23×#54711yescharacteristic
1293C22C23×#54811yescharacteristic
1294C22C23×#55011yescharacteristic
1295C22C23×#55111yescharacteristic
1296C22C23×#55111yescharacteristic
1297C22C23×#55311yescharacteristic
1298C22C23×#55311yescharacteristic
1299C22C23×#55311yescharacteristic
1300C22C23×#55911yescharacteristic
1301C22C23×H(3,𝔽4)11yescharacteristic
1302C22C23×#56211yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2C23×#241211yescharacteristic
1319C2C23×#241611yescharacteristic
1320C2C23×#242211yescharacteristic
1321C2C23×#242411yescharacteristic
1322C2C23×#242811yescharacteristic
1323C2C23×#244511yescharacteristic
1324C2C23×#246111yescharacteristic
1325C2C23×#254311yescharacteristic
1326C2C23×#260211yescharacteristic
1327C2C23×#267111yescharacteristic
1328C2C23×#267911yescharacteristic
1329C2C23×#270111yescharacteristic
1330C2C23×#271211yescharacteristic
1331C2C23×#273011yescharacteristic
1332C2C23×#275311yescharacteristic
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
3. C2×C23×#394C2semidirect
5. C2×C23×#390C2semidirect
6. C2×C23×#386C2semidirect
7. C2×C23×#386C2semidirect
8. C2×C23×#385C2semidirect
9. C23×#1441C2semidirect
10. C23×#1440C2semidirect
11. C23×#1440C2semidirect
12. C23×#1439C2semidirect
13. C23×#1439C2semidirect
14. C23×#1437C2semidirect
15. C23×C4⋊#95C2semidirect
113. C2×C4⋊C4×C23D4semidirect
154. C2×C22⋊C4×C23D4semidirect
155. C2×C22⋊C4×C23D4semidirect
348. #15498C23direct (N × H)
557. C2×#394C2×C23semidirect
558. C2×#394C2×C23semidirect
559. C2×#394C2×C23semidirect
561. C2×#390C2×C23semidirect
562. C2×#386C2×C23semidirect
563. C2×#386C2×C23semidirect
564. C2×#385C2×C23semidirect
565. #1441C2×C23semidirect
566. #1440C2×C23semidirect
567. #1440C2×C23semidirect
568. #1439C2×C23semidirect
569. #1439C2×C23semidirect
570. #1437C2×C23semidirect
571. C4⋊#95C2×C23semidirect
779. C2×C4⋊C4D4×C23semidirect
820. C2×C22⋊C4D4×C23semidirect
821. C2×C22⋊C4D4×C23semidirect
837. C23#15498direct (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×#3902
C2×C23×#3862
C2×C23×#3852
C23×#14412
C23×#14402
C23×#14392
C23×#14372
C23×C4⋊#952
#1549823