Finite Group Databasebeta

← C23×#13789 #19161415

Subgroups — C23×#13789 #19161415

Order 5888.

1826 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×C4×C4⋊C4×C23C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C23C211yesmaximal, characteristic
6C23×#1437C211yesmaximal, characteristic
7C23×#1437C211yesmaximal, characteristic
8C23×#1436C211yesmaximal, characteristic, complemented
9C23×#1436C211yesmaximal, characteristic, complemented
10C23×#1436C211yesmaximal, characteristic, complemented
11C23×#1436C211yesmaximal, characteristic, complemented
12C23×C4⋊#95C211yesmaximal, characteristic, complemented
13C23×#1434C211yesmaximal, characteristic, complemented
14C23×C22⋊#95C211yesmaximal, characteristic
15C4×C23×#95C211yesmaximal, characteristic, complemented
16C24×C4×C23C2211yescharacteristic
17C22×C4⋊C4×C23C2211yescharacteristic
18C22×C4⋊C4×C23C2211yescharacteristic
19C22×C4⋊C4×C23C2211yescharacteristic
20C22×C4⋊C4×C23C2211yescharacteristic
21C22×C22⋊C4×C23C2211yescharacteristic
22C22×C22⋊C4×C23C2211yescharacteristic
23C22×C22⋊C4×C23C2211yescharacteristic
24C22×C22⋊C4×C23C2211yescharacteristic
25C22×C22⋊C4×C23C2211yescharacteristic
26C22×C22⋊C4×C23C2211yescharacteristic
27C22×C42×C23C2211yescharacteristic
28C22×C42×C23C2211yescharacteristic
29C22×C42×C23C2211yescharacteristic
30C22×C42×C23C2211yescharacteristic
31C22×C42×C23C2211yescharacteristic
32C22×C42×C23C2211yescharacteristic
33C23×#388C418yescomplemented
34C23×#388C418yescomplemented
35C23×#385C418yescomplemented
36C4×C4⋊C4×C23—24no—
37C4×C22⋊C4×C23—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—41no—
60C23×C4×C23—41no—
61C23×C4×C23—41no—
62C23×C4×C23—41no—
63C23×C4×C23C2×C414yes—
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—41no—
83C2×C4⋊C4×C23—41no—
84C2×C4⋊C4×C23—41no—
85C2×C4⋊C4×C23—41no—
86C2×C4⋊C4×C23C2×C414yes—
87C2×C4⋊C4×C23C2×C414yes—
88C2×C4⋊C4×C23C2×C414yescomplemented
89C2×C4⋊C4×C23C2×C414yescomplemented
90C2×C22⋊C4×C23—22no—
91C2×C22⋊C4×C23—22no—
92C2×C22⋊C4×C23—22no—
93C2×C22⋊C4×C23—22no—
94C2×C22⋊C4×C23—41no—
95C2×C22⋊C4×C23—41no—
96C2×C22⋊C4×C23—41no—
97C2×C22⋊C4×C23—41no—
98C2×C22⋊C4×C23—41no—
99C2×C22⋊C4×C23—41no—
100C2×C22⋊C4×C23C2×C414yes—
101C2×C22⋊C4×C23C2×C414yes—
102C2×C22⋊C4×C23C2×C414yes—
103C2×C22⋊C4×C23C2×C414yes—
104C2×C22⋊C4×C23C2×C414yes—
105C2×C22⋊C4×C23C2×C414yes—
106C2×C22⋊C4×C23C2×C414yes—
107C2×C22⋊C4×C23C2×C414yes—
108C2×C42×C23—22no—
109C2×C42×C23—22no—
110C2×C42×C23—22no—
111C2×C42×C23—22no—
112C2×C42×C23—22no—
113C2×C42×C23—41no—
114C2×C42×C23—41no—
115C2×C42×C23—41no—
116C2×C42×C23—41no—
117C2×C42×C23—41no—
118C2×C42×C23—41no—
119C2×C42×C23—41no—
120C2×C42×C23—41no—
121C2×C42×C23—41no—
122C2×C42×C23—41no—
123C2×C42×C23C2×C414yescomplemented
124C2×C42×C23C2×C414yescomplemented
125C2×C42×C23D414yes—
126C23×#95—22no—
127C23×#95—22no—
128C23×#95—22no—
129C23×#95—22no—
130C23×#95—22no—
131C23×#95—22no—
132C23×#95—41no—
133C23×#95—41no—
134C23×#95—41no—
135C23×#95—41no—
136C23×#95—41no—
137C23×#95—41no—
138C23×#95C2×C414yes—
139C23×#95C2×C414yes—
140C23×#95C2×C414yescomplemented
141C23×#95C2×C414yescomplemented
142C23×#95C2×C414yescomplemented
143C23×#95C2×C414yescomplemented
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×C23C22×C412yes—
158C24×C23C22×C412yes—
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—28no—
235C22×C4×C23—44no—
236C22×C4×C23—44no—
237C22×C4×C23—44no—
238C22×C4×C23—44no—
239C22×C4×C23—44no—
240C22×C4×C23—44no—
241C22×C4×C23C22×C412yes—
242C22×C4×C23C22×C412yes—
243C22×C4×C23C22×C412yes—
244C22×C4×C23C22×C412yes—
245C22×C4×C23C22×C412yes—
246C22×C4×C23C22×C412yes—
247C22×C4×C23C22×C412yes—
248C22×C4×C23C22×C412yes—
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×C23C22×C412yes—
256C22×C4×C23C22×C412yes—
257C22×C4×C23C22×C412yes—
258C22×C4×C23C22×C412yes—
259C22×C4×C23C2×D412yes—
260C22×C4×C23C2×D412yes—
261C22×C4×C23C2×D412yes—
262C22×C4×C23#4112yes—
263C22×C4×C23#4112yes—
264C22×C4×C23#4112yes—
265C4⋊C4×C23—28no—
266C4⋊C4×C23—28no—
267C4⋊C4×C23—44no—
268C4⋊C4×C23—44no—
269C22⋊C4×C23—28no—
270C22⋊C4×C23—28no—
271C22⋊C4×C23—44no—
272C22⋊C4×C23—44no—
273C22⋊C4×C23—44no—
274C22⋊C4×C23C42116yescomplemented
275C42×C23—28no—
276C42×C23—44no—
277C42×C23—44no—
278C42×C23—44no—
279C42×C23—44no—
280C42×C23—44no—
281#13789C2311yesmaximal, 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×C4214yes—
317C23×C23C23×C411yescharacteristic
318C23×C23C23×C411yescharacteristic
319C23×C23C23×C411yescharacteristic
320C23×C23C22×D411yescharacteristic
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—22no—
372C2×C4×C23—22no—
373C2×C4×C23—22no—
374C2×C4×C23—22no—
375C2×C4×C23—22no—
376C2×C4×C23—22no—
377C2×C4×C23—22no—
378C2×C4×C23—22no—
379C2×C4×C23—22no—
380C2×C4×C23—22no—
381C2×C4×C23—22no—
382C2×C4×C23—22no—
383C2×C4×C23—22no—
384C2×C4×C23—22no—
385C2×C4×C23—22no—
386C2×C4×C23—22no—
387C2×C4×C23—22no—
388C2×C4×C23—22no—
389C2×C4×C23—416no—
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×C23C2×C4214yes—
427C2×C4×C23C2×C4214yes—
428C2×C4×C23C4×D414yes—
429C2×C4×C23C4×D414yes—
430C2×C4×C23C4×D414yes—
431C2×#388C2×C2311yescharacteristic
432C2×#388C2×C2311yescharacteristic
433C2×#385C2×C2311yescharacteristic
434C2×C4×C4⋊C4C2×C2311yescharacteristic, complemented
435C2×C4×C22⋊C4C2×C2311yescharacteristic
436#1437C2×C2311yescharacteristic
437#1437C2×C2311yescharacteristic
438#1436C2×C2311yescharacteristic, complemented
439#1436C2×C2311yescharacteristic, complemented
440#1436C2×C2311yescharacteristic, complemented
441#1436C2×C2311yescharacteristic, complemented
442C4⋊#95C2×C2311yescharacteristic, complemented
443#1434C2×C2311yescharacteristic, complemented
444C22⋊#95C2×C2311yescharacteristic
445C4×#95C2×C2311yescharacteristic, complemented
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×C4211yescharacteristic
462C22×C23C2×C4×D411yescharacteristic
463C22×C23C2×C4×D411yescharacteristic
464C22×C23C2×C4×D411yescharacteristic
465C22×C23C4×#4111yescharacteristic
466C22×C23C4×#4111yescharacteristic
467C22×C23C4×#4111yescharacteristic
468C22×C23#51811yescharacteristic
469C22×C23#51811yescharacteristic
470C22×C23#51811yescharacteristic
471C22×C23#51811yescharacteristic
472C22×C23#51911yescharacteristic
473C22×C23#52011yescharacteristic
474C22×C23#52011yescharacteristic
475C22×C23#52011yescharacteristic
476C22×C23#52011yescharacteristic
477C22×C23#52011yescharacteristic
478C22×C23#52011yescharacteristic
479C22×C23#52011yescharacteristic
480C22×C23#53411yescharacteristic
481C22×C23#53511yescharacteristic
482C22×C23#53611yescharacteristic
483C22×C23#53711yescharacteristic
484C22×C23#53811yescharacteristic
485C22×C23#53811yescharacteristic
486C22×C23#53811yescharacteristic
487C22×C23#53911yescharacteristic
488C22×C23#53911yescharacteristic
489C22×C23#53911yescharacteristic
490C22×C23#54011yescharacteristic
491C22×C23#54111yescharacteristic
492C22×C23#54211yescharacteristic
493C22×C23#54211yescharacteristic
494C22×C23#54211yescharacteristic
495C22×C23#54211yescharacteristic
496C4×C23—24no—
497C4×C23—24no—
498C4×C23—24no—
499C4×C23—24no—
500C4×C23—24no—
501C4×C23—42no—
502C4×C23—42no—
503C4×C23—42no—
504C4×C23—42no—
505C4×C23—42no—
506C4×C23—42no—
507C4×C23—42no—
508C4×C23—42no—
509C4×C23—42no—
510C24×C4C22×C2311yescharacteristic
511C22×C4⋊C4C22×C2311yescharacteristic
512C22×C4⋊C4C22×C2311yescharacteristic
513C22×C4⋊C4C22×C2311yescharacteristic
514C22×C4⋊C4C22×C2311yescharacteristic
515C22×C22⋊C4C22×C2311yescharacteristic
516C22×C22⋊C4C22×C2311yescharacteristic
517C22×C22⋊C4C22×C2311yescharacteristic
518C22×C22⋊C4C22×C2311yescharacteristic
519C22×C22⋊C4C22×C2311yescharacteristic
520C22×C22⋊C4C22×C2311yescharacteristic
521C22×C42C22×C2311yescharacteristic
522C22×C42C22×C2311yescharacteristic
523C22×C42C22×C2311yescharacteristic
524C22×C42C22×C2311yescharacteristic
525C22×C42C22×C2311yescharacteristic
526C22×C42C22×C2311yescharacteristic
527#388C4×C2318yescomplemented
528#388C4×C2318yescomplemented
529#385C4×C2318yescomplemented
530C4×C4⋊C4—24no—
531C4×C22⋊C4—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×C23C42×D411yescharacteristic
552C2×C23#227411yescharacteristic
553C2×C23#227511yescharacteristic
554C2×C23#232111yescharacteristic
555C2×C23#232211yescharacteristic
556C2×C23#232311yescharacteristic
557C2×C23#232411yescharacteristic
558C2×C23#232511yescharacteristic
559C2×C23#232611yescharacteristic
560C2×C23#233211yescharacteristic
561C2×C23#233411yescharacteristic
562C2×C23#233411yescharacteristic
563C2×C23#233511yescharacteristic
564C2×C23#233511yescharacteristic
565C2×C23#233711yescharacteristic
566C25C23×C2311yescharacteristic
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—41no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4C2×C4×C2314yes—
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—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4C2×C4×C2314yes—
597C2×C4⋊C4C2×C4×C2314yes—
598C2×C4⋊C4C2×C4×C2314yescomplemented
599C2×C4⋊C4C2×C4×C2314yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4C2×C4×C2314yes—
611C2×C22⋊C4C2×C4×C2314yes—
612C2×C22⋊C4C2×C4×C2314yes—
613C2×C22⋊C4C2×C4×C2314yes—
614C2×C22⋊C4C2×C4×C2314yes—
615C2×C22⋊C4C2×C4×C2314yes—
616C2×C22⋊C4C2×C4×C2314yes—
617C2×C22⋊C4C2×C4×C2314yes—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—41no—
624C2×C42—41no—
625C2×C42—41no—
626C2×C42—41no—
627C2×C42—41no—
628C2×C42—41no—
629C2×C42—41no—
630C2×C42—41no—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42C2×C4×C2314yescomplemented
634C2×C42C2×C4×C2314yescomplemented
635C2×C42D4×C2314yes—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—41no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95C2×C4×C2314yes—
649#95C2×C4×C2314yes—
650#95C2×C4×C2314yescomplemented
651#95C2×C4×C2314yescomplemented
652#95C2×C4×C2314yescomplemented
653#95C2×C4×C2314yescomplemented
654C23#1378911yescharacteristic, 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—
668C24C22×C4×C2312yes—
669C24C22×C4×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—28no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4C22×C4×C2312yes—
753C22×C4C22×C4×C2312yes—
754C22×C4C22×C4×C2312yes—
755C22×C4C22×C4×C2312yes—
756C22×C4C22×C4×C2312yes—
757C22×C4C22×C4×C2312yes—
758C22×C4C22×C4×C2312yes—
759C22×C4C22×C4×C2312yes—
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×C4C22×C4×C2312yes—
767C22×C4C22×C4×C2312yes—
768C22×C4C22×C4×C2312yes—
769C22×C4C22×C4×C2312yes—
770C22×C4C2×D4×C2312yes—
771C22×C4C2×D4×C2312yes—
772C22×C4C2×D4×C2312yes—
773C22×C4#41×C2312yes—
774C22×C4#41×C2312yes—
775C22×C4#41×C2312yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4C42×C23116yescomplemented
786C42—28no—
787C42—44no—
788C42—44no—
789C42—44no—
790C42—44no—
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×C42×C2314yes—
827C23C23×C4×C2311yescharacteristic
828C23C23×C4×C2311yescharacteristic
829C23C23×C4×C2311yescharacteristic
830C23C22×D4×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—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—416no—
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×C4C2×C42×C2314yes—
937C2×C4C2×C42×C2314yes—
938C2×C4C4×D4×C2314yes—
939C2×C4C4×D4×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×C42×C2311yescharacteristic
957C22C2×C4×D4×C2311yescharacteristic
958C22C2×C4×D4×C2311yescharacteristic
959C22C2×C4×D4×C2311yescharacteristic
960C22C4×#41×C2311yescharacteristic
961C22C4×#41×C2311yescharacteristic
962C22C4×#41×C2311yescharacteristic
963C22C23×#51811yescharacteristic
964C22C23×#51811yescharacteristic
965C22C23×#51811yescharacteristic
966C22C23×#51811yescharacteristic
967C22C23×#51911yescharacteristic
968C22C23×#52011yescharacteristic
969C22C23×#52011yescharacteristic
970C22C23×#52011yescharacteristic
971C22C23×#52011yescharacteristic
972C22C23×#52011yescharacteristic
973C22C23×#52011yescharacteristic
974C22C23×#52011yescharacteristic
975C22C23×#53411yescharacteristic
976C22C23×#53511yescharacteristic
977C22C23×#53611yescharacteristic
978C22C23×#53711yescharacteristic
979C22C23×#53811yescharacteristic
980C22C23×#53811yescharacteristic
981C22C23×#53811yescharacteristic
982C22C23×#53911yescharacteristic
983C22C23×#53911yescharacteristic
984C22C23×#53911yescharacteristic
985C22C23×#54011yescharacteristic
986C22C23×#54111yescharacteristic
987C22C23×#54211yescharacteristic
988C22C23×#54211yescharacteristic
989C22C23×#54211yescharacteristic
990C22C23×#54211yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C2—44no—
1006C2C42×D4×C2311yescharacteristic
1007C2C23×#227411yescharacteristic
1008C2C23×#227511yescharacteristic
1009C2C23×#232111yescharacteristic
1010C2C23×#232211yescharacteristic
1011C2C23×#232311yescharacteristic
1012C2C23×#232411yescharacteristic
1013C2C23×#232511yescharacteristic
1014C2C23×#232611yescharacteristic
1015C2C23×#233211yescharacteristic
1016C2C23×#233411yescharacteristic
1017C2C23×#233411yescharacteristic
1018C2C23×#233511yescharacteristic
1019C2C23×#233511yescharacteristic
1020C2C23×#233711yescharacteristic
subgroupG/H
center, socleC24×C23C24
commutatorC22C22×C42×C23
Frattini, cosocleC24C24×C23
prime radicalC25×C23C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C23 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊C4×C23C2semidirect
8. C23×#1436C2semidirect
9. C23×#1436C2semidirect
10. C23×#1436C2semidirect
11. C23×#1436C2semidirect
12. C23×C4⋊#95C2semidirect
13. C23×#1434C2semidirect
15. C4×C23×#95C2semidirect
33. C23×#388C4semidirect
34. C23×#388C4semidirect
35. C23×#385C4semidirect
88. C2×C4⋊C4×C23C2×C4semidirect
89. C2×C4⋊C4×C23C2×C4semidirect
123. C2×C42×C23C2×C4semidirect
124. C2×C42×C23C2×C4semidirect
140. C23×#95C2×C4semidirect
141. C23×#95C2×C4semidirect
142. C23×#95C2×C4semidirect
143. C23×#95C2×C4semidirect
274. C22⋊C4×C23C42semidirect
281. #13789C23direct (N × H)
434. C2×C4×C4⋊C4C2×C23semidirect
438. #1436C2×C23semidirect
439. #1436C2×C23semidirect
440. #1436C2×C23semidirect
441. #1436C2×C23semidirect
442. C4⋊#95C2×C23semidirect
443. #1434C2×C23semidirect
445. C4×#95C2×C23semidirect
527. #388C4×C23semidirect
528. #388C4×C23semidirect
529. #385C4×C23semidirect
598. C2×C4⋊C4C2×C4×C23semidirect
599. C2×C4⋊C4C2×C4×C23semidirect
633. C2×C42C2×C4×C23semidirect
634. C2×C42C2×C4×C23semidirect
650. #95C2×C4×C23semidirect
651. #95C2×C4×C23semidirect
652. #95C2×C4×C23semidirect
653. #95C2×C4×C23semidirect
654. C23#13789direct (N × H)
785. C22⋊C4C42×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×C4×C4⋊C4×C232
C2×C4×C22⋊C4×C232
C23×#14372
C23×#14362
C23×C4⋊#952
C23×#14342
C23×C22⋊#952
C4×C23×#952
#1378923