Finite Group Databasebeta

← C23×#14403 #19162029

Subgroups — C23×#14403 #19162029

Order 5888.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#388C211yesmaximal, characteristic
2C2×C23×#388C211yesmaximal, characteristic
3C2×C23×#385C211yesmaximal, characteristic
4C2×C23×#385C211yesmaximal, characteristic
5C2×C23×#382C211yesmaximal, characteristic, complemented
6C23×#1444C211yesmaximal, characteristic, complemented
7C23×#1444C211yesmaximal, characteristic, complemented
8C23×#1442C211yesmaximal, characteristic, complemented
9C23×#1441C211yesmaximal, characteristic, complemented
10C23×#1439C211yesmaximal, characteristic
11C23×#1439C211yesmaximal, characteristic
12C23×#1436C211yesmaximal, characteristic, complemented
13C23×C4⋊#95C211yesmaximal, characteristic, complemented
14C23×C4⋊#95C211yesmaximal, characteristic, complemented
15C23×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C23C2211yescharacteristic
17C22×C4⋊C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C4⋊C4×C23C2211yescharacteristic
22C22×C4⋊C4×C23C2211yescharacteristic
23C22×C4⋊C4×C23C2211yescharacteristic
24C22×C4⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C22⋊C4×C23C2211yescharacteristic
28C22×C22⋊C4×C23C2211yescharacteristic
29C22×C22⋊C4×C23C2211yescharacteristic
30C22×C22⋊C4×C23C2211yescharacteristic
31C22×C42×C23C2211yescharacteristic
32C22×C42×C23C2211yescharacteristic
33C23×#388—24no—
34C23×#388C418yescomplemented
35C23×#385—24no—
36C23×#385—24no—
37C23×#382—24no—
38C2×C23×#95C2211yescharacteristic
39C2×C23×#95C2211yescharacteristic
40C2×C23×#95C2211yescharacteristic
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
55C2×C23×#95C2211yescharacteristic
56C25×C23C2311yescharacteristic
57C23×C4×C23—22no—
58C23×C4×C23—22no—
59C23×C4×C23—22no—
60C23×C4×C23—41no—
61C23×C4×C23—41no—
62C23×C4×C23—41no—
63C23×C4×C23—41no—
64C23×C4×C23C2311yescharacteristic
65C23×C4×C23C2311yescharacteristic
66C23×C4×C23C2311yescharacteristic
67C23×C4×C23C2311yescharacteristic
68C23×C4×C23C2311yescharacteristic
69C23×C4×C23C2311yescharacteristic
70C23×C4×C23C2311yescharacteristic
71C23×C4×C23C2311yescharacteristic
72C23×C4×C23C2311yescharacteristic
73C23×C4×C23C2311yescharacteristic
74C23×C4×C23C2311yescharacteristic
75C23×C4×C23C2311yescharacteristic
76C23×C4×C23C2311yescharacteristic
77C23×C4×C23C2311yescharacteristic
78C2×C4⋊C4×C23—22no—
79C2×C4⋊C4×C23—22no—
80C2×C4⋊C4×C23—22no—
81C2×C4⋊C4×C23—22no—
82C2×C4⋊C4×C23—22no—
83C2×C4⋊C4×C23—22no—
84C2×C4⋊C4×C23—22no—
85C2×C4⋊C4×C23—22no—
86C2×C4⋊C4×C23—22no—
87C2×C4⋊C4×C23—22no—
88C2×C4⋊C4×C23—22no—
89C2×C4⋊C4×C23—41no—
90C2×C4⋊C4×C23—41no—
91C2×C4⋊C4×C23—41no—
92C2×C4⋊C4×C23—41no—
93C2×C4⋊C4×C23—41no—
94C2×C4⋊C4×C23—41no—
95C2×C4⋊C4×C23—41no—
96C2×C4⋊C4×C23—41no—
97C2×C4⋊C4×C23—41no—
98C2×C4⋊C4×C23—41no—
99C2×C4⋊C4×C23—41no—
100C2×C4⋊C4×C23—41no—
101C2×C4⋊C4×C23C2×C414yescomplemented
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—41no—
110C2×C22⋊C4×C23—41no—
111C2×C22⋊C4×C23—41no—
112C2×C22⋊C4×C23—41no—
113C2×C22⋊C4×C23—41no—
114C2×C22⋊C4×C23—41no—
115C2×C22⋊C4×C23C2×C414yes—
116C2×C22⋊C4×C23C2×C414yes—
117C2×C22⋊C4×C23C2×C414yes—
118C2×C22⋊C4×C23D414yes—
119C2×C22⋊C4×C23Q814yes—
120C2×C42×C23—22no—
121C2×C42×C23—22no—
122C2×C42×C23—22no—
123C2×C42×C23—22no—
124C2×C42×C23—41no—
125C2×C42×C23C2×C414yescomplemented
126C23×#95—22no—
127C23×#95—22no—
128C23×#95—22no—
129C23×#95—22no—
130C23×#95—22no—
131C23×#95—22no—
132C23×#95—22no—
133C23×#95—22no—
134C23×#95—41no—
135C23×#95—41no—
136C23×#95—41no—
137C23×#95—41no—
138C23×#95—41no—
139C23×#95—41no—
140C23×#95—41no—
141C23×#95C2×C414yescomplemented
142C23×#95C2×C414yescomplemented
143C23×#95D414yes—
144C24×C23—21no—
145C24×C23—21no—
146C24×C23—21no—
147C24×C23—21no—
148C24×C23—21no—
149C24×C23—21no—
150C24×C23—21no—
151C24×C23—21no—
152C24×C23—21no—
153C24×C23—21no—
154C24×C23—21no—
155C24×C23—21no—
156C24×C23C22×C412yes—
157C24×C23C2×D412yes—
158C24×C23C2×Q812yes—
159C24×C23C2411yescharacteristic
160C22×C4×C23—21no—
161C22×C4×C23—21no—
162C22×C4×C23—21no—
163C22×C4×C23—21no—
164C22×C4×C23—21no—
165C22×C4×C23—21no—
166C22×C4×C23—21no—
167C22×C4×C23—21no—
168C22×C4×C23—21no—
169C22×C4×C23—21no—
170C22×C4×C23—21no—
171C22×C4×C23—21no—
172C22×C4×C23—21no—
173C22×C4×C23—21no—
174C22×C4×C23—21no—
175C22×C4×C23—21no—
176C22×C4×C23—21no—
177C22×C4×C23—21no—
178C22×C4×C23—21no—
179C22×C4×C23—21no—
180C22×C4×C23—21no—
181C22×C4×C23—21no—
182C22×C4×C23—21no—
183C22×C4×C23—21no—
184C22×C4×C23—21no—
185C22×C4×C23—21no—
186C22×C4×C23—21no—
187C22×C4×C23—21no—
188C22×C4×C23—21no—
189C22×C4×C23—21no—
190C22×C4×C23—21no—
191C22×C4×C23—21no—
192C22×C4×C23—21no—
193C22×C4×C23—21no—
194C22×C4×C23—21no—
195C22×C4×C23—21no—
196C22×C4×C23—21no—
197C22×C4×C23—21no—
198C22×C4×C23—21no—
199C22×C4×C23—21no—
200C22×C4×C23—21no—
201C22×C4×C23—21no—
202C22×C4×C23—21no—
203C22×C4×C23—21no—
204C22×C4×C23—21no—
205C22×C4×C23—21no—
206C22×C4×C23—21no—
207C22×C4×C23—21no—
208C22×C4×C23—21no—
209C22×C4×C23—21no—
210C22×C4×C23—21no—
211C22×C4×C23—21no—
212C22×C4×C23—21no—
213C22×C4×C23—21no—
214C22×C4×C23—21no—
215C22×C4×C23—21no—
216C22×C4×C23—21no—
217C22×C4×C23—21no—
218C22×C4×C23—21no—
219C22×C4×C23—21no—
220C22×C4×C23—21no—
221C22×C4×C23—21no—
222C22×C4×C23—21no—
223C22×C4×C23—21no—
224C22×C4×C23—21no—
225C22×C4×C23—21no—
226C22×C4×C23—21no—
227C22×C4×C23—21no—
228C22×C4×C23—21no—
229C22×C4×C23—21no—
230C22×C4×C23—21no—
231C22×C4×C23—21no—
232C22×C4×C23—21no—
233C22×C4×C23—21no—
234C22×C4×C23—21no—
235C22×C4×C23—21no—
236C22×C4×C23—21no—
237C22×C4×C23—21no—
238C22×C4×C23—21no—
239C22×C4×C23—21no—
240C22×C4×C23—21no—
241C22×C4×C23—21no—
242C22×C4×C23—44no—
243C22×C4×C23—44no—
244C22×C4×C23—44no—
245C22×C4×C23—44no—
246C22×C4×C23—44no—
247C22×C4×C23—44no—
248C22×C4×C23—44no—
249C22×C4×C23C22×C412yes—
250C22×C4×C23C22×C412yes—
251C22×C4×C23C22×C412yes—
252C22×C4×C23C22×C412yes—
253C22×C4×C23C22×C412yes—
254C22×C4×C23C22×C412yes—
255C22×C4×C23C2×D412yes—
256C22×C4×C23C2×D412yes—
257C22×C4×C23C2×D412yes—
258C22×C4×C23C2×D412yes—
259C22×C4×C23C2×D412yes—
260C22×C4×C23C2×Q812yes—
261C22×C4×C23C2×Q812yes—
262C22×C4×C23#4112yes—
263C22×C4×C23#4112yes—
264C22×C4×C23#4112yes—
265C4⋊C4×C23—44no—
266C4⋊C4×C23—44no—
267C4⋊C4×C23—44no—
268C4⋊C4×C23—44no—
269C4⋊C4×C23—44no—
270C4⋊C4×C23—44no—
271C4⋊C4×C23—44no—
272C4⋊C4×C23—44no—
273C22⋊C4×C23—28no—
274C22⋊C4×C23—44no—
275C22⋊C4×C23—44no—
276C22⋊C4×C23—44no—
277C22⋊C4×C23—44no—
278C22⋊C4×C23C4⋊C4116yescomplemented
279C42×C23—28no—
280C42×C23—44no—
281#14403C2311yesmaximal, characteristic, direct product factor, Sylow
282C23×C23—22no—
283C23×C23—22no—
284C23×C23—22no—
285C23×C23—22no—
286C23×C23—22no—
287C23×C23—22no—
288C23×C23—22no—
289C23×C23—22no—
290C23×C23—22no—
291C23×C23—22no—
292C23×C23—22no—
293C23×C23—22no—
294C23×C23—22no—
295C23×C23—22no—
296C23×C23—22no—
297C23×C23—22no—
298C23×C23—22no—
299C23×C23—22no—
300C23×C23—41no—
301C23×C23—41no—
302C23×C23—41no—
303C23×C23—41no—
304C23×C23—41no—
305C23×C23—41no—
306C23×C23—41no—
307C23×C23—41no—
308C23×C23—41no—
309C23×C23—41no—
310C23×C23—41no—
311C23×C23—41no—
312C23×C23—41no—
313C23×C23—41no—
314C23×C23—41no—
315C23×C23—41no—
316C23×C23C2×C4⋊C414yes—
317C23×C23C23×C411yescharacteristic
318C23×C23C22×D411yescharacteristic
319C23×C23C22×D411yescharacteristic
320C23×C23C22×Q811yescharacteristic
321C23×C23C2×#4111yescharacteristic
322C23×C23C2×#4111yescharacteristic
323C23×C23C2×#4111yescharacteristic
324C23×C23H(5,𝔽2)11yescharacteristic
325C23×C23H(5,𝔽2)11yescharacteristic
326C23×C23H(5,𝔽2)11yescharacteristic
327C23×C23H(5,𝔽2)11yescharacteristic
328C23×C23H(5,𝔽2)11yescharacteristic
329C23×C232−1+411yescharacteristic
330C23×C232−1+411yescharacteristic
331C23×C232−1+411yescharacteristic
332C2×C4×C23—22no—
333C2×C4×C23—22no—
334C2×C4×C23—22no—
335C2×C4×C23—22no—
336C2×C4×C23—22no—
337C2×C4×C23—22no—
338C2×C4×C23—22no—
339C2×C4×C23—22no—
340C2×C4×C23—22no—
341C2×C4×C23—22no—
342C2×C4×C23—22no—
343C2×C4×C23—22no—
344C2×C4×C23—22no—
345C2×C4×C23—22no—
346C2×C4×C23—22no—
347C2×C4×C23—22no—
348C2×C4×C23—22no—
349C2×C4×C23—22no—
350C2×C4×C23—22no—
351C2×C4×C23—22no—
352C2×C4×C23—22no—
353C2×C4×C23—22no—
354C2×C4×C23—22no—
355C2×C4×C23—22no—
356C2×C4×C23—22no—
357C2×C4×C23—22no—
358C2×C4×C23—22no—
359C2×C4×C23—22no—
360C2×C4×C23—22no—
361C2×C4×C23—22no—
362C2×C4×C23—22no—
363C2×C4×C23—22no—
364C2×C4×C23—22no—
365C2×C4×C23—22no—
366C2×C4×C23—22no—
367C2×C4×C23—22no—
368C2×C4×C23—22no—
369C2×C4×C23—22no—
370C2×C4×C23—22no—
371C2×C4×C23—416no—
372C2×C4×C23—41no—
373C2×C4×C23—41no—
374C2×C4×C23—41no—
375C2×C4×C23—41no—
376C2×C4×C23—41no—
377C2×C4×C23—41no—
378C2×C4×C23—41no—
379C2×C4×C23—41no—
380C2×C4×C23—41no—
381C2×C4×C23—41no—
382C2×C4×C23—41no—
383C2×C4×C23—41no—
384C2×C4×C23—41no—
385C2×C4×C23—41no—
386C2×C4×C23—41no—
387C2×C4×C23—41no—
388C2×C4×C23—41no—
389C2×C4×C23—41no—
390C2×C4×C23—41no—
391C2×C4×C23—41no—
392C2×C4×C23—41no—
393C2×C4×C23—41no—
394C2×C4×C23—41no—
395C2×C4×C23—41no—
396C2×C4×C23—41no—
397C2×C4×C23—41no—
398C2×C4×C23—41no—
399C2×C4×C23—41no—
400C2×C4×C23—41no—
401C2×C4×C23—41no—
402C2×C4×C23—41no—
403C2×C4×C23—41no—
404C2×C4×C23—41no—
405C2×C4×C23—41no—
406C2×C4×C23—41no—
407C2×C4×C23—41no—
408C2×C4×C23—41no—
409C2×C4×C23—41no—
410C2×C4×C23—41no—
411C2×C4×C23—41no—
412C2×C4×C23—41no—
413C2×C4×C23—41no—
414C2×C4×C23—41no—
415C2×C4×C23—41no—
416C2×C4×C23—41no—
417C2×C4×C23—41no—
418C2×C4×C23—41no—
419C2×C4×C23—41no—
420C2×C4×C23—41no—
421C2×C4×C23—41no—
422C2×C4×C23—41no—
423C2×C4×C23—41no—
424C2×C4×C23—41no—
425C2×C4×C23—41no—
426C2×C4×C23—41no—
427C2×C4×C23—41no—
428C2×C4×C23C2×C4⋊C414yes—
429C2×C4×C23C2×C4⋊C414yes—
430C2×C4×C23C4×D414yes—
431C2×#388C2×C2311yescharacteristic
432C2×#388C2×C2311yescharacteristic
433C2×#385C2×C2311yescharacteristic
434C2×#385C2×C2311yescharacteristic
435C2×#382C2×C2311yescharacteristic, complemented
436#1444C2×C2311yescharacteristic, complemented
437#1444C2×C2311yescharacteristic, complemented
438#1442C2×C2311yescharacteristic, complemented
439#1441C2×C2311yescharacteristic, complemented
440#1439C2×C2311yescharacteristic
441#1439C2×C2311yescharacteristic
442#1436C2×C2311yescharacteristic, complemented
443C4⋊#95C2×C2311yescharacteristic, complemented
444C4⋊#95C2×C2311yescharacteristic, complemented
445C22⋊#95C2×C2311yescharacteristic
446C22×C23—24no—
447C22×C23—24no—
448C22×C23—24no—
449C22×C23—42no—
450C22×C23—42no—
451C22×C23—42no—
452C22×C23—42no—
453C22×C23—42no—
454C22×C23—42no—
455C22×C23—42no—
456C22×C23—42no—
457C22×C23—42no—
458C22×C23—42no—
459C22×C23—42no—
460C22×C23—42no—
461C22×C23C22×C4⋊C411yescharacteristic
462C22×C23C2×C4×D411yescharacteristic
463C22×C23C4×#4111yescharacteristic
464C22×C23#51811yescharacteristic
465C22×C23#52011yescharacteristic
466C22×C23#52011yescharacteristic
467C22×C23#52011yescharacteristic
468C22×C23#53511yescharacteristic
469C22×C23#53511yescharacteristic
470C22×C23#53611yescharacteristic
471C22×C23#53711yescharacteristic
472C22×C23#53811yescharacteristic
473C22×C23#53911yescharacteristic
474C22×C23#54011yescharacteristic
475C22×C23#54111yescharacteristic
476C22×C23#54211yescharacteristic
477C22×C23#54211yescharacteristic
478C22×C23#54411yescharacteristic
479C22×C23#54411yescharacteristic
480C22×C23D4211yescharacteristic
481C22×C23#54611yescharacteristic
482C22×C23#54611yescharacteristic
483C22×C23#54611yescharacteristic
484C22×C23#54711yescharacteristic
485C22×C23#54711yescharacteristic
486C22×C23D4×Q811yescharacteristic
487C22×C23#55111yescharacteristic
488C22×C23#55211yescharacteristic
489C22×C23#55411yescharacteristic
490C22×C23#55411yescharacteristic
491C22×C23#55411yescharacteristic
492C22×C23H(3,𝔽4)11yescharacteristic
493C22×C23#56211yescharacteristic
494C22×C23#56211yescharacteristic
495C22×C23#56311yescharacteristic
496C4×C23—24no—
497C4×C23—24no—
498C4×C23—24no—
499C4×C23—42no—
500C4×C23—42no—
501C4×C23—42no—
502C4×C23—42no—
503C4×C23—42no—
504C4×C23—42no—
505C4×C23—42no—
506C4×C23—81no—
507C4×C23—81no—
508C4×C23—81no—
509C4×C23—81no—
510C24×C4C22×C2311yescharacteristic
511C22×C4⋊C4C22×C2311yescharacteristic
512C22×C4⋊C4C22×C2311yescharacteristic
513C22×C4⋊C4C22×C2311yescharacteristic
514C22×C4⋊C4C22×C2311yescharacteristic
515C22×C4⋊C4C22×C2311yescharacteristic
516C22×C4⋊C4C22×C2311yescharacteristic
517C22×C4⋊C4C22×C2311yescharacteristic
518C22×C4⋊C4C22×C2311yescharacteristic
519C22×C22⋊C4C22×C2311yescharacteristic
520C22×C22⋊C4C22×C2311yescharacteristic
521C22×C22⋊C4C22×C2311yescharacteristic
522C22×C22⋊C4C22×C2311yescharacteristic
523C22×C22⋊C4C22×C2311yescharacteristic
524C22×C22⋊C4C22×C2311yescharacteristic
525C22×C42C22×C2311yescharacteristic
526C22×C42C22×C2311yescharacteristic
527#388—24no—
528#388C4×C2318yescomplemented
529#385—24no—
530#385—24no—
531#382—24no—
532C2×#95C22×C2311yescharacteristic
533C2×#95C22×C2311yescharacteristic
534C2×#95C22×C2311yescharacteristic
535C2×#95C22×C2311yescharacteristic
536C2×#95C22×C2311yescharacteristic
537C2×#95C22×C2311yescharacteristic
538C2×#95C22×C2311yescharacteristic
539C2×#95C22×C2311yescharacteristic
540C2×#95C22×C2311yescharacteristic
541C2×#95C22×C2311yescharacteristic
542C2×#95C22×C2311yescharacteristic
543C2×#95C22×C2311yescharacteristic
544C2×#95C22×C2311yescharacteristic
545C2×#95C22×C2311yescharacteristic
546C2×#95C22×C2311yescharacteristic
547C2×#95C22×C2311yescharacteristic
548C2×#95C22×C2311yescharacteristic
549C2×#95C22×C2311yescharacteristic
550C2×C23—44no—
551C2×C23#231711yescharacteristic
552C2×C23#232411yescharacteristic
553C2×C23#233411yescharacteristic
554C2×C23D4×C4⋊C411yescharacteristic
555C2×C23#234911yescharacteristic
556C2×C23#235911yescharacteristic
557C2×C23#237911yescharacteristic
558C2×C23#267011yescharacteristic
559C2×C23#267211yescharacteristic
560C2×C23#269811yescharacteristic
561C2×C23#270411yescharacteristic
562C2×C23#270611yescharacteristic
563C2×C23#272011yescharacteristic
564C2×C23#276311yescharacteristic
565C2×C23#276811yescharacteristic
566C25C23×C2311yescharacteristic
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C23×C2311yescharacteristic
575C23×C4C23×C2311yescharacteristic
576C23×C4C23×C2311yescharacteristic
577C23×C4C23×C2311yescharacteristic
578C23×C4C23×C2311yescharacteristic
579C23×C4C23×C2311yescharacteristic
580C23×C4C23×C2311yescharacteristic
581C23×C4C23×C2311yescharacteristic
582C23×C4C23×C2311yescharacteristic
583C23×C4C23×C2311yescharacteristic
584C23×C4C23×C2311yescharacteristic
585C23×C4C23×C2311yescharacteristic
586C23×C4C23×C2311yescharacteristic
587C23×C4C23×C2311yescharacteristic
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×C4×C2314yescomplemented
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4—41no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4C2×C4×C2314yes—
626C2×C22⋊C4C2×C4×C2314yes—
627C2×C22⋊C4C2×C4×C2314yes—
628C2×C22⋊C4D4×C2314yes—
629C2×C22⋊C4Q8×C2314yes—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—41no—
635C2×C42C2×C4×C2314yescomplemented
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95C2×C4×C2314yescomplemented
652#95C2×C4×C2314yescomplemented
653#95D4×C2314yes—
654C23#1440311yescharacteristic, direct product factor, Sylow
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C2312yes—
668C24C2×D4×C2312yes—
669C24C2×Q8×C2312yes—
670C24C24×C2311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4C22×C4×C2312yes—
761C22×C4C22×C4×C2312yes—
762C22×C4C22×C4×C2312yes—
763C22×C4C22×C4×C2312yes—
764C22×C4C22×C4×C2312yes—
765C22×C4C22×C4×C2312yes—
766C22×C4C2×D4×C2312yes—
767C22×C4C2×D4×C2312yes—
768C22×C4C2×D4×C2312yes—
769C22×C4C2×D4×C2312yes—
770C22×C4C2×D4×C2312yes—
771C22×C4C2×Q8×C2312yes—
772C22×C4C2×Q8×C2312yes—
773C22×C4#41×C2312yes—
774C22×C4#41×C2312yes—
775C22×C4#41×C2312yes—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4C4⋊C4×C23116yescomplemented
790C42—28no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C2314yes—
827C23C23×C4×C2311yescharacteristic
828C23C22×D4×C2311yescharacteristic
829C23C22×D4×C2311yescharacteristic
830C23C22×Q8×C2311yescharacteristic
831C23C2×#41×C2311yescharacteristic
832C23C2×#41×C2311yescharacteristic
833C23C2×#41×C2311yescharacteristic
834C23C23×H(5,𝔽2)11yescharacteristic
835C23C23×H(5,𝔽2)11yescharacteristic
836C23C23×H(5,𝔽2)11yescharacteristic
837C23C23×H(5,𝔽2)11yescharacteristic
838C23C23×H(5,𝔽2)11yescharacteristic
839C23C23×2−1+411yescharacteristic
840C23C23×2−1+411yescharacteristic
841C23C23×2−1+411yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4C2×C4⋊C4×C2314yes—
939C2×C4C2×C4⋊C4×C2314yes—
940C2×C4C4×D4×C2314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C2311yescharacteristic
957C22C2×C4×D4×C2311yescharacteristic
958C22C4×#41×C2311yescharacteristic
959C22C23×#51811yescharacteristic
960C22C23×#52011yescharacteristic
961C22C23×#52011yescharacteristic
962C22C23×#52011yescharacteristic
963C22C23×#53511yescharacteristic
964C22C23×#53511yescharacteristic
965C22C23×#53611yescharacteristic
966C22C23×#53711yescharacteristic
967C22C23×#53811yescharacteristic
968C22C23×#53911yescharacteristic
969C22C23×#54011yescharacteristic
970C22C23×#54111yescharacteristic
971C22C23×#54211yescharacteristic
972C22C23×#54211yescharacteristic
973C22C23×#54411yescharacteristic
974C22C23×#54411yescharacteristic
975C22D42×C2311yescharacteristic
976C22C23×#54611yescharacteristic
977C22C23×#54611yescharacteristic
978C22C23×#54611yescharacteristic
979C22C23×#54711yescharacteristic
980C22C23×#54711yescharacteristic
981C22D4×Q8×C2311yescharacteristic
982C22C23×#55111yescharacteristic
983C22C23×#55211yescharacteristic
984C22C23×#55411yescharacteristic
985C22C23×#55411yescharacteristic
986C22C23×#55411yescharacteristic
987C22C23×H(3,𝔽4)11yescharacteristic
988C22C23×#56211yescharacteristic
989C22C23×#56211yescharacteristic
990C22C23×#56311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C23×#231711yescharacteristic
1007C2C23×#232411yescharacteristic
1008C2C23×#233411yescharacteristic
1009C2D4×C4⋊C4×C2311yescharacteristic
1010C2C23×#234911yescharacteristic
1011C2C23×#235911yescharacteristic
1012C2C23×#237911yescharacteristic
1013C2C23×#267011yescharacteristic
1014C2C23×#267211yescharacteristic
1015C2C23×#269811yescharacteristic
1016C2C23×#270411yescharacteristic
1017C2C23×#270611yescharacteristic
1018C2C23×#272011yescharacteristic
1019C2C23×#276311yescharacteristic
1020C2C23×#276811yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC23C23×C4×C23
Frattini, cosocleC24C24×C23
prime radicalC25×C23C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C23×#382C2semidirect
6. C23×#1444C2semidirect
7. C23×#1444C2semidirect
8. C23×#1442C2semidirect
9. C23×#1441C2semidirect
12. C23×#1436C2semidirect
13. C23×C4⋊#95C2semidirect
14. C23×C4⋊#95C2semidirect
34. C23×#388C4semidirect
101. C2×C4⋊C4×C23C2×C4semidirect
125. C2×C42×C23C2×C4semidirect
141. C23×#95C2×C4semidirect
142. C23×#95C2×C4semidirect
278. C22⋊C4×C23C4⋊C4semidirect
281. #14403C23direct (N × H)
435. C2×#382C2×C23semidirect
436. #1444C2×C23semidirect
437. #1444C2×C23semidirect
438. #1442C2×C23semidirect
439. #1441C2×C23semidirect
442. #1436C2×C23semidirect
443. C4⋊#95C2×C23semidirect
444. C4⋊#95C2×C23semidirect
528. #388C4×C23semidirect
611. C2×C4⋊C4C2×C4×C23semidirect
635. C2×C42C2×C4×C23semidirect
651. #95C2×C4×C23semidirect
652. #95C2×C4×C23semidirect
654. C23#14403direct (N × H)
789. C22⋊C4C4⋊C4×C23semidirect

Maximal subgroups

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

subgroupindex
C2×C23×#3882
C2×C23×#3852
C2×C23×#3822
C23×#14442
C23×#14422
C23×#14412
C23×#14392
C23×#14362
C23×C4⋊#952
C23×C22⋊#952
#1440323