Finite Group Databasebeta

← C23×#17597 #19165223

Subgroups — C23×#17597 #19165223

Order 5888.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3519C211yesmaximal, characteristic
2C23×#2974C211yesmaximal, characteristic, complemented
3C23×#2318C211yesmaximal, characteristic, complemented
4C23×#1521C211yesmaximal, characteristic, complemented
5C23×#1519C211yesmaximal, characteristic, complemented
6C23×#1517C211yesmaximal, characteristic, complemented
7C23×#1516C211yesmaximal, characteristic, complemented
8C23×#1514C211yesmaximal, characteristic, complemented
9C23×#1513C211yesmaximal, characteristic, complemented
10C23×#1512C211yesmaximal, characteristic, complemented
11C23×#1510C211yesmaximal, characteristic, complemented
12C23×#1507C211yesmaximal, characteristic, complemented
13C23×#1504C211yesmaximal, characteristic, complemented
14C23×#1501C211yesmaximal, characteristic, complemented
15C2×C23×#327C211yesmaximal, characteristic, complemented
16C23×#555C411yescharacteristic, complemented
17C23×#554C411yescharacteristic, complemented
18C23×#553—21no—
19C23×#553C411yescharacteristic, complemented
20C23×#553C411yescharacteristic, complemented
21C23×#550C411yescharacteristic, complemented
22C23×#546—21no—
23C23×#546—21no—
24C23×#546C411yescharacteristic, complemented
25C23×#546C411yescharacteristic, complemented
26D42×C23—21no—
27D42×C23C411yescharacteristic, complemented
28C23×#540—21no—
29C23×#538—21no—
30C23×#538—21no—
31C23×#532C2211yescharacteristic
32C23×#529C2211yescharacteristic
33C23×#525C2211yescharacteristic
34C23×#525C2211yescharacteristic
35C2×C23×#121C2211yescharacteristic
36C2×C23×#121C2211yescharacteristic
37C23×#518—21no—
38C2×C4×D4×C23C2211yescharacteristic
39C23×#436—21no—
40C23×#435—21no—
41C23×#435—21no—
42C8×D4×C23—21no—
43C23×#432C2211yescharacteristic, complemented
44C23×#431C2211yescharacteristic, complemented
45C23×#407C2211yescharacteristic, complemented
46C23×#407C2211yescharacteristic, complemented
47C2×C23×C22⋊C8C2211yescharacteristic, complemented
48C2×C23×C22⋊C8C2211yescharacteristic, complemented
49C23×#388—21no—
50C23×#387—21no—
51C23×#386—21no—
52C23×#385—21no—
53C23×#383C2211yescharacteristic, complemented
54C23×#382C2211yescharacteristic, complemented
55C23×#381C2211yescharacteristic, complemented
56C23×#380C2211yescharacteristic, complemented
57C4×C22⋊C4×C23C2211yescharacteristic, complemented
58C2×C23×#95C2211yescharacteristic, complemented
59C23×#328C2211yescharacteristic, complemented
60C23×#328C2211yescharacteristic, complemented
61C23×#328C2211yescharacteristic, complemented
62C23×#328C2211yescharacteristic, complemented
63C23×#327C2211yescharacteristic
64C23×#327C2211yescharacteristic
65C23×#327C2211yescharacteristic
66C23×#327C2211yescharacteristic
67C23×#327C2211yescharacteristic, complemented
68C23×#327C2211yescharacteristic, complemented
69C23×#327C2211yescharacteristic, complemented
70C23×#327C2211yescharacteristic, complemented
71C23×#327C2211yescharacteristic, complemented
72C23×#327C2211yescharacteristic, complemented
73C23×#327C2211yescharacteristic, complemented
74C23×#327C2211yescharacteristic, complemented
75C2×#41×C23—21no—
76C2×#41×C23C2×C411yescharacteristic
77C2×#41×C23C2×C411yescharacteristic, complemented
78C22×D4×C23—21no—
79C22×D4×C23—21no—
80C22×D4×C23—21no—
81C22×D4×C23C2×C411yescharacteristic
82C22×D4×C23C2×C411yescharacteristic, complemented
83C22×D4×C23D411yescharacteristic
84C23×C4×C23—21no—
85C23×C4×C23C2311yescharacteristic
86C23×C4×C23C2311yescharacteristic
87C2×M16×C23—21no—
88C2×M16×C23—21no—
89C22×C8×C23—21no—
90C22×C8×C23—21no—
91C23×C4⋊Q8C2×C411yescharacteristic, complemented
92C23×#127—21no—
93C23×#127C2×C411yescharacteristic, complemented
94C23×#126—21no—
95C23×#126—21no—
96C23×#126—21no—
97C23×#125—21no—
98C23×#125C2×C411yescharacteristic, complemented
99C23×#124—21no—
100C23×#124—21no—
101C23×#124—21no—
102C23×#124C2×C411yescharacteristic, complemented
103C23×#123—21no—
104C23×#123—21no—
105C23×#123—21no—
106C23×#123—21no—
107C23×#123—21no—
108C23×#123—21no—
109C23×#123—21no—
110C23×C22⋊Q8—21no—
111C23×C22⋊Q8—21no—
112C23×C22⋊Q8C2×C411yescharacteristic
113C23×C22⋊Q8C2×C411yescharacteristic, complemented
114C23×C22⋊Q8C2311yescharacteristic
115C23×#121—21no—
116C23×#121—21no—
117C23×#121—21no—
118C23×#121—21no—
119C23×#121—21no—
120C23×#121—21no—
121C23×#121—21no—
122C23×#121—21no—
123C23×#121—21no—
124C23×#121—21no—
125C23×#121—21no—
126C23×#121—21no—
127C23×#121—21no—
128C23×#121C2×C411yescharacteristic
129C23×#121C2×C411yescharacteristic
130C23×#121C2×C411yescharacteristic
131C23×#121C2×C411yescharacteristic, complemented
132C23×#121C2×C411yescharacteristic, complemented
133C23×#121C2×C411yescharacteristic, complemented
134C23×#121C2311yescharacteristic
135C23×#121C2311yescharacteristic
136C23×#121C2311yescharacteristic
137C23×#120—21no—
138C23×#120—21no—
139C23×#120—21no—
140C23×#120—21no—
141C23×#120—21no—
142C23×#120—21no—
143C4×Q8×C23C2×C411yescharacteristic, complemented
144C4×D4×C23—21no—
145C4×D4×C23—21no—
146C4×D4×C23—21no—
147C4×D4×C23—21no—
148C4×D4×C23—21no—
149C4×D4×C23—21no—
150C4×D4×C23—21no—
151C4×D4×C23—21no—
152C4×D4×C23—21no—
153C4×D4×C23—21no—
154C4×D4×C23C2×C411yescharacteristic
155C4×D4×C23C2×C411yescharacteristic
156C4×D4×C23C2×C411yescharacteristic
157C4×D4×C23C2×C411yescharacteristic
158C4×D4×C23C2×C411yescharacteristic, complemented
159C4×D4×C23C2×C411yescharacteristic, complemented
160C4×D4×C23C2×C411yescharacteristic, complemented
161C4×D4×C23D411yescharacteristic
162C4×D4×C23D411yescharacteristic
163C4×D4×C23D411yescharacteristic
164C4×D4×C23D411yescharacteristic
165C23×#117—21no—
166C23×#117—21no—
167C23×#117C2×C411yescharacteristic
168C23×#117C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C23—21no—
170C2×C4⋊C4×C23—21no—
171C2×C4⋊C4×C23C2×C411yescharacteristic
172C2×C4⋊C4×C23C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C23D411yescharacteristic
174C2×C22⋊C4×C23—21no—
175C2×C22⋊C4×C23—21no—
176C2×C22⋊C4×C23—21no—
177C2×C22⋊C4×C23—21no—
178C2×C22⋊C4×C23—21no—
179C2×C22⋊C4×C23—21no—
180C2×C22⋊C4×C23—21no—
181C2×C22⋊C4×C23D411yescharacteristic
182C2×C22⋊C4×C23D411yescharacteristic
183C2×C42×C23—21no—
184C2×C42×C23C2311yescharacteristic
185C23×C4⋊C8—21no—
186C23×C4⋊C8—21no—
187C23×C22⋊C8—21no—
188C23×C22⋊C8—21no—
189C23×C22⋊C8—21no—
190C23×C22⋊C8—21no—
191C23×C22⋊C8C2311yescharacteristic
192C23×C22⋊C8C2311yescharacteristic
193C23×C22⋊C8C2311yescharacteristic
194C23×C22⋊C8C2311yescharacteristic
195C23×#97—21no—
196C4×C8×C23—21no—
197C23×#95—21no—
198C23×#95—21no—
199C23×#95—21no—
200C23×#95—21no—
201C23×#95—21no—
202C23×#95C2311yescharacteristic
203C23×#95C2311yescharacteristic
204C23×#95C2311yescharacteristic
205C23×#95C2311yescharacteristic
206C24×C23—21no—
207C24×C23—21no—
208C24×C23C2×D411yescharacteristic
209C24×C23C2×D411yescharacteristic
210#41×C23—81no—
211#41×C23—81no—
212#41×C23—81no—
213#41×C23—81no—
214C2×Q8×C23—21no—
215C2×Q8×C23C22×C411yescharacteristic
216C2×D4×C23—21no—
217C2×D4×C23—21no—
218C2×D4×C23—21no—
219C2×D4×C23—21no—
220C2×D4×C23—21no—
221C2×D4×C23—21no—
222C2×D4×C23—21no—
223C2×D4×C23—21no—
224C2×D4×C23—21no—
225C2×D4×C23—21no—
226C2×D4×C23—21no—
227C2×D4×C23—21no—
228C2×D4×C23—21no—
229C2×D4×C23—21no—
230C2×D4×C23—21no—
231C2×D4×C23—42no—
232C2×D4×C23—44no—
233C2×D4×C23—81no—
234C2×D4×C23—81no—
235C2×D4×C23—81no—
236C2×D4×C23—81no—
237C2×D4×C23—81no—
238C2×D4×C23—81no—
239C2×D4×C23C22⋊C411yescharacteristic
240C2×D4×C23C22⋊C411yescharacteristic
241C2×D4×C23C22⋊C411yescharacteristic
242C2×D4×C23C22⋊C411yescharacteristic
243C2×D4×C23C22×C411yescharacteristic
244C2×D4×C23C22×C411yescharacteristic
245C2×D4×C23C22×C411yescharacteristic
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—42no—
258C22×C4×C23—81no—
259C22×C4×C23—81no—
260C22×C4×C23—81no—
261C22×C4×C23—81no—
262C22×C4×C23C22×C411yescharacteristic
263C22×C4×C23C22×C411yescharacteristic
264C22×C4×C23C22×C411yescharacteristic
265C22×C4×C23C22×C411yescharacteristic
266C22×C4×C23C2×D411yescharacteristic
267C22×C4×C23C2×D411yescharacteristic
268C22×C4×C23C2×D411yescharacteristic
269C22×C4×C23C2×D411yescharacteristic
270C22×C4×C23C2×D411yescharacteristic
271C22×C4×C23C2×D411yescharacteristic
272C22×C4×C23C2×D411yescharacteristic
273C22×C4×C23C2×D411yescharacteristic
274C22×C4×C23C2411yescharacteristic
275M16×C23—81no—
276M16×C23—81no—
277C2×C8×C23—21no—
278C2×C8×C23—21no—
279C2×C8×C23—21no—
280C2×C8×C23—21no—
281C2×C8×C23—81no—
282C2×C8×C23—81no—
283C4⋊C4×C23—21no—
284C4⋊C4×C23—21no—
285C4⋊C4×C23—21no—
286C4⋊C4×C23—21no—
287C4⋊C4×C23—21no—
288C4⋊C4×C23—21no—
289C4⋊C4×C23—21no—
290C4⋊C4×C23—21no—
291C4⋊C4×C23—21no—
292C4⋊C4×C23—81no—
293C4⋊C4×C23—81no—
294C4⋊C4×C23C22⋊C411yescharacteristic
295C4⋊C4×C23C22⋊C411yescharacteristic
296C4⋊C4×C23C22⋊C411yescharacteristic
297C4⋊C4×C23C22⋊C411yescharacteristic
298C4⋊C4×C23C22×C411yescharacteristic
299C4⋊C4×C23C22×C411yescharacteristic
300C4⋊C4×C23C22×C411yescharacteristic
301C4⋊C4×C23C22×C411yescharacteristic
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—21no—
311C22⋊C4×C23—21no—
312C22⋊C4×C23—21no—
313C22⋊C4×C23—21no—
314C22⋊C4×C23—21no—
315C22⋊C4×C23—21no—
316C22⋊C4×C23—21no—
317C22⋊C4×C23—21no—
318C22⋊C4×C23—21no—
319C22⋊C4×C23—21no—
320C22⋊C4×C23—21no—
321C22⋊C4×C23—42no—
322C22⋊C4×C23—81no—
323C22⋊C4×C23—81no—
324C22⋊C4×C23C22⋊C411yescharacteristic
325C22⋊C4×C23C22⋊C411yescharacteristic
326C22⋊C4×C23C22⋊C411yescharacteristic
327C22⋊C4×C23C22⋊C411yescharacteristic
328C22⋊C4×C23C22⋊C411yescharacteristic
329C22⋊C4×C23C22⋊C411yescharacteristic
330C22⋊C4×C23C22⋊C411yescharacteristic
331C22⋊C4×C23C22⋊C411yescharacteristic
332C42×C23—21no—
333C42×C23—21no—
334C42×C23—21no—
335C42×C23—81no—
336C42×C23C22×C411yescharacteristic
337C42×C23C22×C411yescharacteristic
338C42×C23C2×D411yescharacteristic
339C42×C23C2×D411yescharacteristic
340#17597C2311yesmaximal, characteristic, direct product factor, Sylow
341C23×C23—21no—
342C23×C23—21no—
343C23×C23—22no—
344C23×C23—21no—
345C23×C23—21no—
346C23×C23—21no—
347C23×C23—21no—
348C23×C23—21no—
349C23×C23—41no—
350C23×C23—41no—
351C23×C23—41no—
352C23×C23—42no—
353C23×C23—42no—
354C23×C23—81no—
355C23×C23—81no—
356C23×C23—81no—
357C23×C23—81no—
358C23×C23C2×C22⋊C411yescharacteristic
359C23×C23C2×C22⋊C411yescharacteristic
360C23×C23C2×C22⋊C411yescharacteristic
361C23×C23C2×C22⋊C411yescharacteristic
362C23×C23C22×D411yescharacteristic
363Q8×C23—41no—
364Q8×C23—81no—
365D4×C23—22no—
366D4×C23—22no—
367D4×C23—41no—
368D4×C23—41no—
369D4×C23—41no—
370D4×C23—41no—
371D4×C23—41no—
372D4×C23—42no—
373D4×C23—42no—
374D4×C23—41no—
375D4×C23—41no—
376D4×C23—41no—
377D4×C23—41no—
378D4×C23—41no—
379D4×C23—41no—
380D4×C23—42no—
381D4×C23—81no—
382D4×C23—81no—
383D4×C23—81no—
384D4×C23—81no—
385D4×C23—81no—
386D4×C23—81no—
387D4×C23—81no—
388D4×C23—81no—
389D4×C23—81no—
390C2×C4×C23—21no—
391C2×C4×C23—21no—
392C2×C4×C23—21no—
393C2×C4×C23—21no—
394C2×C4×C23—21no—
395C2×C4×C23—21no—
396C2×C4×C23—21no—
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—42no—
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—81no—
423C2×C4×C23—81no—
424C2×C4×C23—81no—
425C2×C4×C23—81no—
426C2×C4×C23—81no—
427C2×C4×C23—81no—
428C2×C4×C23—84no—
429C2×C4×C23C2×C22⋊C411yescharacteristic
430C2×C4×C23C2×C22⋊C411yescharacteristic
431C2×C4×C23C2×C22⋊C411yescharacteristic
432C2×C4×C23C2×C22⋊C411yescharacteristic
433C2×C4×C23C2×C22⋊C411yescharacteristic
434C2×C4×C23C2×C22⋊C411yescharacteristic
435C2×C4×C23C2×C22⋊C411yescharacteristic
436C2×C4×C23C2×C22⋊C411yescharacteristic
437C2×C4×C23C23×C411yescharacteristic
438C2×C4×C23C22×D411yescharacteristic
439C8×C23—41no—
440C8×C23—41no—
441C8×C23—41no—
442C8×C23—41no—
443#3519C2×C2311yescharacteristic
444#2974C2×C2311yescharacteristic, complemented
445#2318C2×C2311yescharacteristic, complemented
446#1521C2×C2311yescharacteristic, complemented
447#1519C2×C2311yescharacteristic, complemented
448#1517C2×C2311yescharacteristic, complemented
449#1516C2×C2311yescharacteristic, complemented
450#1514C2×C2311yescharacteristic, complemented
451#1513C2×C2311yescharacteristic, complemented
452#1512C2×C2311yescharacteristic, complemented
453#1510C2×C2311yescharacteristic, complemented
454#1507C2×C2311yescharacteristic, complemented
455#1504C2×C2311yescharacteristic, complemented
456#1501C2×C2311yescharacteristic, complemented
457C2×#327C2×C2311yescharacteristic, complemented
458C22×C23—21no—
459C22×C23—21no—
460C22×C23—21no—
461C22×C23—21no—
462C22×C23—21no—
463C22×C23—21no—
464C22×C23—21no—
465C22×C23—21no—
466C22×C23—21no—
467C22×C23—21no—
468C22×C23—21no—
469C22×C23—21no—
470C22×C23—21no—
471C22×C23—42no—
472C22×C23—42no—
473C22×C23—41no—
474C22×C23—41no—
475C22×C23—41no—
476C22×C23—41no—
477C22×C23—41no—
478C22×C23—41no—
479C22×C23—41no—
480C22×C23—41no—
481C22×C23—41no—
482C22×C23—81no—
483C22×C23—81no—
484C22×C23—162no—
485C22×C23—162no—
486C22×C23#42112yes—
487C22×C23C22×C22⋊C411yescharacteristic
488C22×C23#57611yescharacteristic
489C22×C23#57711yescharacteristic
490C4×C23—21no—
491C4×C23—21no—
492C4×C23—21no—
493C4×C23—21no—
494C4×C23—21no—
495C4×C23—21no—
496C4×C23—21no—
497C4×C23—21no—
498C4×C23—21no—
499C4×C23—21no—
500C4×C23—41no—
501C4×C23—41no—
502C4×C23—41no—
503C4×C23—41no—
504C4×C23—41no—
505C4×C23—81no—
506C4×C23—81no—
507C4×C23—81no—
508C4×C23—81no—
509#555C4×C2311yescharacteristic, complemented
510#554C4×C2311yescharacteristic, complemented
511#553—21no—
512#553C4×C2311yescharacteristic, complemented
513#553C4×C2311yescharacteristic, complemented
514#550C4×C2311yescharacteristic, complemented
515#546—21no—
516#546—21no—
517#546C4×C2311yescharacteristic, complemented
518#546C4×C2311yescharacteristic, complemented
519D42—21no—
520D42C4×C2311yescharacteristic, complemented
521#540—21no—
522#538—21no—
523#538—21no—
524#532C22×C2311yescharacteristic
525#529C22×C2311yescharacteristic
526#525C22×C2311yescharacteristic
527#525C22×C2311yescharacteristic
528C2×#121C22×C2311yescharacteristic
529C2×#121C22×C2311yescharacteristic
530#518—21no—
531C2×C4×D4C22×C2311yescharacteristic
532#436—21no—
533#435—21no—
534#435—21no—
535C8×D4—21no—
536#432C22×C2311yescharacteristic, complemented
537#431C22×C2311yescharacteristic, complemented
538#407C22×C2311yescharacteristic, complemented
539#407C22×C2311yescharacteristic, complemented
540C2×C22⋊C8C22×C2311yescharacteristic, complemented
541C2×C22⋊C8C22×C2311yescharacteristic, complemented
542#388—21no—
543#387—21no—
544#386—21no—
545#385—21no—
546#383C22×C2311yescharacteristic, complemented
547#382C22×C2311yescharacteristic, complemented
548#381C22×C2311yescharacteristic, complemented
549#380C22×C2311yescharacteristic, complemented
550C4×C22⋊C4C22×C2311yescharacteristic, complemented
551C2×#95C22×C2311yescharacteristic, complemented
552#328C22×C2311yescharacteristic, complemented
553#328C22×C2311yescharacteristic, complemented
554#328C22×C2311yescharacteristic, complemented
555#328C22×C2311yescharacteristic, complemented
556#327C22×C2311yescharacteristic
557#327C22×C2311yescharacteristic
558#327C22×C2311yescharacteristic
559#327C22×C2311yescharacteristic
560#327C22×C2311yescharacteristic, complemented
561#327C22×C2311yescharacteristic, complemented
562#327C22×C2311yescharacteristic, complemented
563#327C22×C2311yescharacteristic, complemented
564#327C22×C2311yescharacteristic, complemented
565#327C22×C2311yescharacteristic, complemented
566#327C22×C2311yescharacteristic, complemented
567#327C22×C2311yescharacteristic, complemented
568C2×C23—21no—
569C2×C23—21no—
570C2×C23—22no—
571C2×C23—41no—
572C2×C23—41no—
573C2×C23—41no—
574C2×C23—81no—
575C2×C23—81no—
576C2×C23—81no—
577C2×C23#288311yescharacteristic
578C2×C23#289711yescharacteristic
579C2×C23C2×#42111yescharacteristic
580C2×#41—21no—
581C2×#41C2×C4×C2311yescharacteristic
582C2×#41C2×C4×C2311yescharacteristic, complemented
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4C2×C4×C2311yescharacteristic
587C22×D4C2×C4×C2311yescharacteristic, complemented
588C22×D4D4×C2311yescharacteristic
589C23×C4—21no—
590C23×C4C23×C2311yescharacteristic
591C23×C4C23×C2311yescharacteristic
592C2×M16—21no—
593C2×M16—21no—
594C22×C8—21no—
595C22×C8—21no—
596C4⋊Q8C2×C4×C2311yescharacteristic, complemented
597#127—21no—
598#127C2×C4×C2311yescharacteristic, complemented
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125C2×C4×C2311yescharacteristic, complemented
604#124—21no—
605#124—21no—
606#124—21no—
607#124C2×C4×C2311yescharacteristic, complemented
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8C2×C4×C2311yescharacteristic
618C22⋊Q8C2×C4×C2311yescharacteristic, complemented
619C22⋊Q8C23×C2311yescharacteristic
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121C2×C4×C2311yescharacteristic
634#121C2×C4×C2311yescharacteristic
635#121C2×C4×C2311yescharacteristic
636#121C2×C4×C2311yescharacteristic, complemented
637#121C2×C4×C2311yescharacteristic, complemented
638#121C2×C4×C2311yescharacteristic, complemented
639#121C23×C2311yescharacteristic
640#121C23×C2311yescharacteristic
641#121C23×C2311yescharacteristic
642#120—21no—
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648C4×Q8C2×C4×C2311yescharacteristic, complemented
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4C2×C4×C2311yescharacteristic
660C4×D4C2×C4×C2311yescharacteristic
661C4×D4C2×C4×C2311yescharacteristic
662C4×D4C2×C4×C2311yescharacteristic
663C4×D4C2×C4×C2311yescharacteristic, complemented
664C4×D4C2×C4×C2311yescharacteristic, complemented
665C4×D4C2×C4×C2311yescharacteristic, complemented
666C4×D4D4×C2311yescharacteristic
667C4×D4D4×C2311yescharacteristic
668C4×D4D4×C2311yescharacteristic
669C4×D4D4×C2311yescharacteristic
670#117—21no—
671#117—21no—
672#117C2×C4×C2311yescharacteristic
673#117C2×C4×C2311yescharacteristic, complemented
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4C2×C4×C2311yescharacteristic
677C2×C4⋊C4C2×C4×C2311yescharacteristic, complemented
678C2×C4⋊C4D4×C2311yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C2311yescharacteristic
687C2×C22⋊C4D4×C2311yescharacteristic
688C2×C42—21no—
689C2×C42C23×C2311yescharacteristic
690C4⋊C8—21no—
691C4⋊C8—21no—
692C22⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8C23×C2311yescharacteristic
697C22⋊C8C23×C2311yescharacteristic
698C22⋊C8C23×C2311yescharacteristic
699C22⋊C8C23×C2311yescharacteristic
700#97—21no—
701C4×C8—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95C23×C2311yescharacteristic
708#95C23×C2311yescharacteristic
709#95C23×C2311yescharacteristic
710#95C23×C2311yescharacteristic
711C23#1759711yescharacteristic, direct product factor, Sylow
712C24—21no—
713C24—21no—
714C24C2×D4×C2311yescharacteristic
715C24C2×D4×C2311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C2311yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊C4×C2311yescharacteristic
746C2×D4C22⋊C4×C2311yescharacteristic
747C2×D4C22⋊C4×C2311yescharacteristic
748C2×D4C22⋊C4×C2311yescharacteristic
749C2×D4C22×C4×C2311yescharacteristic
750C2×D4C22×C4×C2311yescharacteristic
751C2×D4C22×C4×C2311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×C4×C2311yescharacteristic
769C22×C4C22×C4×C2311yescharacteristic
770C22×C4C22×C4×C2311yescharacteristic
771C22×C4C22×C4×C2311yescharacteristic
772C22×C4C2×D4×C2311yescharacteristic
773C22×C4C2×D4×C2311yescharacteristic
774C22×C4C2×D4×C2311yescharacteristic
775C22×C4C2×D4×C2311yescharacteristic
776C22×C4C2×D4×C2311yescharacteristic
777C22×C4C2×D4×C2311yescharacteristic
778C22×C4C2×D4×C2311yescharacteristic
779C22×C4C2×D4×C2311yescharacteristic
780C22×C4C24×C2311yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—81no—
799C4⋊C4—81no—
800C4⋊C4C22⋊C4×C2311yescharacteristic
801C4⋊C4C22⋊C4×C2311yescharacteristic
802C4⋊C4C22⋊C4×C2311yescharacteristic
803C4⋊C4C22⋊C4×C2311yescharacteristic
804C4⋊C4C22×C4×C2311yescharacteristic
805C4⋊C4C22×C4×C2311yescharacteristic
806C4⋊C4C22×C4×C2311yescharacteristic
807C4⋊C4C22×C4×C2311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—42no—
828C22⋊C4—81no—
829C22⋊C4—81no—
830C22⋊C4C22⋊C4×C2311yescharacteristic
831C22⋊C4C22⋊C4×C2311yescharacteristic
832C22⋊C4C22⋊C4×C2311yescharacteristic
833C22⋊C4C22⋊C4×C2311yescharacteristic
834C22⋊C4C22⋊C4×C2311yescharacteristic
835C22⋊C4C22⋊C4×C2311yescharacteristic
836C22⋊C4C22⋊C4×C2311yescharacteristic
837C22⋊C4C22⋊C4×C2311yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C2311yescharacteristic
843C42C22×C4×C2311yescharacteristic
844C42C2×D4×C2311yescharacteristic
845C42C2×D4×C2311yescharacteristic
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊C4×C2311yescharacteristic
864C23C2×C22⋊C4×C2311yescharacteristic
865C23C2×C22⋊C4×C2311yescharacteristic
866C23C2×C22⋊C4×C2311yescharacteristic
867C23C22×D4×C2311yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—42no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
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—42no—
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—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C22⋊C4×C2311yescharacteristic
935C2×C4C2×C22⋊C4×C2311yescharacteristic
936C2×C4C2×C22⋊C4×C2311yescharacteristic
937C2×C4C2×C22⋊C4×C2311yescharacteristic
938C2×C4C2×C22⋊C4×C2311yescharacteristic
939C2×C4C2×C22⋊C4×C2311yescharacteristic
940C2×C4C2×C22⋊C4×C2311yescharacteristic
941C2×C4C2×C22⋊C4×C2311yescharacteristic
942C2×C4C23×C4×C2311yescharacteristic
943C2×C4C22×D4×C2311yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22C23×#42112yes—
977C22C22×C22⋊C4×C2311yescharacteristic
978C22C23×#57611yescharacteristic
979C22C23×#57711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C23×#288311yescharacteristic
1009C2C23×#289711yescharacteristic
1010C2C2×C23×#42111yescharacteristic
subgroupG/H
center, socleC22×C23C22×C22⋊C4
commutatorC2×C4C23×C4×C23
Frattini, cosocleC22×C4C24×C23
prime radicalC23×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C4×D4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#2974C2semidirect
3. C23×#2318C2semidirect
4. C23×#1521C2semidirect
5. C23×#1519C2semidirect
6. C23×#1517C2semidirect
7. C23×#1516C2semidirect
8. C23×#1514C2semidirect
9. C23×#1513C2semidirect
10. C23×#1512C2semidirect
11. C23×#1510C2semidirect
12. C23×#1507C2semidirect
13. C23×#1504C2semidirect
14. C23×#1501C2semidirect
15. C2×C23×#327C2semidirect
16. C23×#555C4semidirect
17. C23×#554C4semidirect
19. C23×#553C4semidirect
20. C23×#553C4semidirect
21. C23×#550C4semidirect
24. C23×#546C4semidirect
25. C23×#546C4semidirect
27. D42×C23C4semidirect
43. C23×#432C22semidirect
44. C23×#431C22semidirect
45. C23×#407C22semidirect
46. C23×#407C22semidirect
47. C2×C23×C22⋊C8C22semidirect
48. C2×C23×C22⋊C8C22semidirect
53. C23×#383C22semidirect
54. C23×#382C22semidirect
55. C23×#381C22semidirect
56. C23×#380C22semidirect
57. C4×C22⋊C4×C23C22semidirect
58. C2×C23×#95C22semidirect
59. C23×#328C22semidirect
60. C23×#328C22semidirect
61. C23×#328C22semidirect
62. C23×#328C22semidirect
67. C23×#327C22semidirect
68. C23×#327C22semidirect
69. C23×#327C22semidirect
70. C23×#327C22semidirect
71. C23×#327C22semidirect
72. C23×#327C22semidirect
73. C23×#327C22semidirect
74. C23×#327C22semidirect
77. C2×#41×C23C2×C4semidirect
82. C22×D4×C23C2×C4semidirect
91. C23×C4⋊Q8C2×C4semidirect
93. C23×#127C2×C4semidirect
98. C23×#125C2×C4semidirect
102. C23×#124C2×C4semidirect
113. C23×C22⋊Q8C2×C4semidirect
131. C23×#121C2×C4semidirect
132. C23×#121C2×C4semidirect
133. C23×#121C2×C4semidirect
143. C4×Q8×C23C2×C4semidirect
158. C4×D4×C23C2×C4semidirect
159. C4×D4×C23C2×C4semidirect
160. C4×D4×C23C2×C4semidirect
168. C23×#117C2×C4semidirect
172. C2×C4⋊C4×C23C2×C4semidirect
340. #17597C23direct (N × H)
444. #2974C2×C23semidirect
445. #2318C2×C23semidirect
446. #1521C2×C23semidirect
447. #1519C2×C23semidirect
448. #1517C2×C23semidirect
449. #1516C2×C23semidirect
450. #1514C2×C23semidirect
451. #1513C2×C23semidirect
452. #1512C2×C23semidirect
453. #1510C2×C23semidirect
454. #1507C2×C23semidirect
455. #1504C2×C23semidirect
456. #1501C2×C23semidirect
457. C2×#327C2×C23semidirect
509. #555C4×C23semidirect
510. #554C4×C23semidirect
512. #553C4×C23semidirect
513. #553C4×C23semidirect
514. #550C4×C23semidirect
517. #546C4×C23semidirect
518. #546C4×C23semidirect
520. D42C4×C23semidirect
536. #432C22×C23semidirect
537. #431C22×C23semidirect
538. #407C22×C23semidirect
539. #407C22×C23semidirect
540. C2×C22⋊C8C22×C23semidirect
541. C2×C22⋊C8C22×C23semidirect
546. #383C22×C23semidirect
547. #382C22×C23semidirect
548. #381C22×C23semidirect
549. #380C22×C23semidirect
550. C4×C22⋊C4C22×C23semidirect
551. C2×#95C22×C23semidirect
552. #328C22×C23semidirect
553. #328C22×C23semidirect
554. #328C22×C23semidirect
555. #328C22×C23semidirect
560. #327C22×C23semidirect
561. #327C22×C23semidirect
562. #327C22×C23semidirect
563. #327C22×C23semidirect
564. #327C22×C23semidirect
565. #327C22×C23semidirect
566. #327C22×C23semidirect
567. #327C22×C23semidirect
582. C2×#41C2×C4×C23semidirect
587. C22×D4C2×C4×C23semidirect
596. C4⋊Q8C2×C4×C23semidirect
598. #127C2×C4×C23semidirect
603. #125C2×C4×C23semidirect
607. #124C2×C4×C23semidirect
618. C22⋊Q8C2×C4×C23semidirect
636. #121C2×C4×C23semidirect
637. #121C2×C4×C23semidirect
638. #121C2×C4×C23semidirect
648. C4×Q8C2×C4×C23semidirect
663. C4×D4C2×C4×C23semidirect
664. C4×D4C2×C4×C23semidirect
665. C4×D4C2×C4×C23semidirect
673. #117C2×C4×C23semidirect
677. C2×C4⋊C4C2×C4×C23semidirect
711. C23#17597direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35192
C23×#29742
C23×#23182
C23×#15212
C23×#15192
C23×#15172
C23×#15162
C23×#15142
C23×#15132
C23×#15122
C23×#15102
C23×#15072
C23×#15042
C23×#15012
C2×C23×#3272
#1759723