Finite Group Databasebeta

← C23×#18447 #19166073

Subgroups — C23×#18447 #19166073

Order 5888.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3534C211yesmaximal, characteristic
2C23×#3193C211yesmaximal, characteristic, complemented
3C23×#3190C211yesmaximal, characteristic, complemented
4C23×#2814C211yesmaximal, characteristic, complemented
5C23×#1612C211yesmaximal, characteristic, complemented
6C23×#1610C211yesmaximal, characteristic, complemented
7C23×#1609C211yesmaximal, characteristic, complemented
8C23×#1607C211yesmaximal, characteristic, complemented
9C23×#1606C211yesmaximal, characteristic, complemented
10C23×#1604C211yesmaximal, characteristic, complemented
11C23×#1603C211yesmaximal, characteristic, complemented
12C23×#1601C211yesmaximal, characteristic, complemented
13C23×#1519C211yesmaximal, characteristic, complemented
14C23×#1513C211yesmaximal, characteristic, complemented
15C23×#1468C211yesmaximal, characteristic, complemented
16C23×#562—21no—
17C23×#560—21no—
18C23×#553—21no—
19C23×#551—21no—
20C23×#546—21no—
21C23×#546—21no—
22C23×#546—21no—
23D42×C23—21no—
24C23×#540—21no—
25C23×#539—21no—
26C23×#539C2211yescharacteristic
27C23×#538—21no—
28C23×#538C2211yescharacteristic
29C23×#537C2211yescharacteristic
30C23×#534—21no—
31C23×#534C2211yescharacteristic
32C23×#525C2211yescharacteristic
33C2×C23×#123C2211yescharacteristic
34C2×C23×C22⋊Q8C2211yescharacteristic, complemented
35C2×C23×#121C2211yescharacteristic
36C23×#485—21no—
37C23×#484—21no—
38C23×#483C2211yescharacteristic, complemented
39C23×#480C2211yescharacteristic
40C23×#480C2211yescharacteristic, complemented
41C23×#480C2211yescharacteristic, complemented
42C23×#468—21no—
43C23×#468—21no—
44C23×#467—21no—
45C23×#465—21no—
46C23×#452—21no—
47C23×#451C2211yescharacteristic, complemented
48C23×#450—21no—
49C23×#448C2211yescharacteristic
50C23×#448C2211yescharacteristic, complemented
51C23×#448C2211yescharacteristic, complemented
52C23×#407C2211yescharacteristic, complemented
53C2×C23×C22⋊C8C2211yescharacteristic, complemented
54C23×#398—21no—
55C23×#398C2211yescharacteristic, complemented
56C23×#397—21no—
57C23×#397C2211yescharacteristic, complemented
58C23×#396—21no—
59C23×#395C2211yescharacteristic, complemented
60C23×#394—21no—
61C23×#393C2211yescharacteristic, complemented
62C23×#380C2211yescharacteristic, complemented
63C23×#328C2211yescharacteristic, complemented
64C23×#328C2211yescharacteristic, complemented
65C23×#327C2211yescharacteristic
66C23×#327C2211yescharacteristic
67C23×#327C2211yescharacteristic, complemented
68C23×#327C2211yescharacteristic, complemented
69C23×#327C2211yescharacteristic, complemented
70C23×#327C2211yescharacteristic, complemented
71C23×#324C2211yescharacteristic, complemented
72C23×#324C2211yescharacteristic, complemented
73C23×#323C2211yescharacteristic, complemented
74C23×#323C2211yescharacteristic, complemented
75C2×#41×C23—21no—
76C2×#41×C23D411yescharacteristic
77C22×Q8×C23C2311yescharacteristic
78C22×D4×C23—21no—
79C22×D4×C23—21no—
80C22×D4×C23—21no—
81C22×D4×C23D411yescharacteristic
82C22×D4×C23D411yescharacteristic
83C23×C4×C23C2311yescharacteristic
84C2×Q16×C23—21no—
85C2×SD16×C23—21no—
86C2×SD16×C23—21no—
87C2×SD16×C23—21no—
88C2×M16×C23—21no—
89C22×C8×C23—21no—
90C23×#127—21no—
91C23×#126—21no—
92C23×#126—21no—
93C23×#126—21no—
94C23×#126—21no—
95C23×#125—21no—
96C23×#125—21no—
97C23×#124—21no—
98C23×#124—21no—
99C23×#124—21no—
100C23×#123—21no—
101C23×#123—21no—
102C23×#123—21no—
103C23×#123—21no—
104C23×#123—21no—
105C23×#123—21no—
106C23×#123—21no—
107C23×#123—21no—
108C23×#123—21no—
109C23×#123—21no—
110C23×#123—21no—
111C23×#123—21no—
112C23×#123—21no—
113C23×#123—21no—
114C23×C22⋊Q8—21no—
115C23×C22⋊Q8—21no—
116C23×C22⋊Q8—21no—
117C23×C22⋊Q8—21no—
118C23×C22⋊Q8—21no—
119C23×C22⋊Q8—21no—
120C23×C22⋊Q8—21no—
121C23×C22⋊Q8—21no—
122C23×C22⋊Q8—21no—
123C23×C22⋊Q8D411yescharacteristic
124C23×C22⋊Q8C2311yescharacteristic
125C23×#121—21no—
126C23×#121—21no—
127C23×#121—21no—
128C23×#121—21no—
129C23×#121—21no—
130C23×#121—21no—
131C23×#121—21no—
132C23×#121—21no—
133C23×#121—21no—
134C23×#121—21no—
135C23×#121—21no—
136C23×#121—21no—
137C23×#121—21no—
138C23×#121—21no—
139C23×#121—21no—
140C23×#121D411yescharacteristic
141C23×#121D411yescharacteristic
142C23×#121D411yescharacteristic
143C23×#121C2311yescharacteristic
144C23×#121C2311yescharacteristic
145C23×#121C2311yescharacteristic
146C23×#120—21no—
147C23×#120—21no—
148C23×#120—21no—
149C23×#120—21no—
150C23×#120—21no—
151C23×#120—21no—
152C23×#120—21no—
153C23×#120—21no—
154C4×D4×C23—21no—
155C4×D4×C23—21no—
156C4×D4×C23—21no—
157C4×D4×C23—21no—
158C4×D4×C23—21no—
159C4×D4×C23—21no—
160C4×D4×C23—21no—
161C4×D4×C23—21no—
162C23×#117—21no—
163C23×#117D411yescharacteristic
164C2×C4⋊C4×C23—21no—
165C2×C4⋊C4×C23—21no—
166C2×C4⋊C4×C23—21no—
167C2×C4⋊C4×C23—21no—
168C2×C4⋊C4×C23D411yescharacteristic
169C2×C4⋊C4×C23D411yescharacteristic
170C2×C4⋊C4×C23C2311yescharacteristic
171C2×C4⋊C4×C23C2311yescharacteristic
172C2×C22⋊C4×C23—21no—
173C2×C22⋊C4×C23—21no—
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×C23D411yescharacteristic
180C2×C22⋊C4×C23D411yescharacteristic
181C2×C22⋊C4×C23C2311yescharacteristic
182C23×#107—21no—
183C23×#107—21no—
184C23×#107—21no—
185C23×#106—21no—
186C23×#103—21no—
187C23×#103—21no—
188C23×#103—21no—
189C23×#103—21no—
190C23×#103—21no—
191C23×#102—21no—
192C23×#102—21no—
193C23×#102—21no—
194C23×C22⋊C8—21no—
195C23×C22⋊C8—21no—
196C23×C22⋊C8C2311yescharacteristic
197C23×C22⋊C8C2311yescharacteristic
198C23×C22⋊C8C2311yescharacteristic
199C23×C22⋊C8C2311yescharacteristic
200C23×#95—21no—
201C23×#95—21no—
202C23×#95—21no—
203C23×#95—21no—
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—
213C2×Q8×C23—21no—
214C2×Q8×C23—21no—
215C2×Q8×C23—21no—
216C2×Q8×C23—81no—
217C2×Q8×C23C2×D411yescharacteristic
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—21no—
232C2×D4×C23—21no—
233C2×D4×C23—21no—
234C2×D4×C23—21no—
235C2×D4×C23—81no—
236C2×D4×C23—81no—
237C2×D4×C23—81no—
238C2×D4×C23—81no—
239C2×D4×C23—81no—
240C2×D4×C23—81no—
241C2×D4×C23—82no—
242C2×D4×C23C2×D411yescharacteristic
243C2×D4×C23C2×D411yescharacteristic
244C2×D4×C23C2×D411yescharacteristic
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—81no—
257C22×C4×C23C2×D411yescharacteristic
258C22×C4×C23C2×D411yescharacteristic
259C22×C4×C23C2×D411yescharacteristic
260C22×C4×C23C2×D411yescharacteristic
261C22×C4×C23C2×D411yescharacteristic
262C22×C4×C23C2×D411yescharacteristic
263C22×C4×C23C2×D411yescharacteristic
264C22×C4×C23C2×D411yescharacteristic
265C22×C4×C23C2411yescharacteristic
266Q16×C23—81no—
267SD16×C23—81no—
268SD16×C23—81no—
269SD16×C23—81no—
270M16×C23—81no—
271C2×C8×C23—21no—
272C2×C8×C23—21no—
273C2×C8×C23—21no—
274C2×C8×C23—21no—
275C2×C8×C23—81no—
276C4⋊C4×C23—21no—
277C4⋊C4×C23—21no—
278C4⋊C4×C23—21no—
279C4⋊C4×C23—21no—
280C4⋊C4×C23—21no—
281C4⋊C4×C23—21no—
282C4⋊C4×C23—21no—
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—41no—
292C4⋊C4×C23—41no—
293C4⋊C4×C23—81no—
294C4⋊C4×C23—81no—
295C4⋊C4×C23—81no—
296C4⋊C4×C23C2×D411yescharacteristic
297C4⋊C4×C23C2×D411yescharacteristic
298C4⋊C4×C23C2×D411yescharacteristic
299C4⋊C4×C23C2×D411yescharacteristic
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—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—21no—
322C22⋊C4×C23—21no—
323C22⋊C4×C23—21no—
324C22⋊C4×C23—21no—
325C22⋊C4×C23—41no—
326C22⋊C4×C23—41no—
327C22⋊C4×C23—81no—
328C22⋊C4×C23—81no—
329C22⋊C4×C23—81no—
330C42×C23—21no—
331C42×C23—21no—
332C42×C23—21no—
333#18447C2311yesmaximal, characteristic, direct product factor, Sylow
334C23×C23—21no—
335C23×C23—21no—
336C23×C23—21no—
337C23×C23—21no—
338C23×C23—21no—
339C23×C23—21no—
340C23×C23—21no—
341C23×C23—21no—
342C23×C23—41no—
343C23×C23—41no—
344C23×C23—42no—
345C23×C23—41no—
346C23×C23—41no—
347C23×C23—81no—
348C23×C23—81no—
349C23×C23—81no—
350C23×C23—81no—
351C23×C23—81no—
352C23×C23#12011yescharacteristic
353C23×C23#12011yescharacteristic
354C23×C23C22×D411yescharacteristic
355Q8×C23—41no—
356Q8×C23—41no—
357Q8×C23—41no—
358Q8×C23—41no—
359Q8×C23—41no—
360Q8×C23—81no—
361D4×C23—41no—
362D4×C23—41no—
363D4×C23—41no—
364D4×C23—42no—
365D4×C23—42no—
366D4×C23—41no—
367D4×C23—41no—
368D4×C23—41no—
369D4×C23—41no—
370D4×C23—41no—
371D4×C23—41no—
372D4×C23—81no—
373D4×C23—81no—
374D4×C23—81no—
375D4×C23—81no—
376D4×C23—81no—
377D4×C23—81no—
378D4×C23—81no—
379D4×C23—81no—
380D4×C23—81no—
381D4×C23—81no—
382D4×C23—81no—
383D4×C23—81no—
384C2×C4×C23—21no—
385C2×C4×C23—21no—
386C2×C4×C23—21no—
387C2×C4×C23—21no—
388C2×C4×C23—21no—
389C2×C4×C23—21no—
390C2×C4×C23—21no—
391C2×C4×C23—21no—
392C2×C4×C23—21no—
393C2×C4×C23—21no—
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—81no—
415C2×C4×C23—81no—
416C2×C4×C23—81no—
417C2×C4×C23—81no—
418C2×C4×C23—81no—
419C2×C4×C23—81no—
420C2×C4×C23—81no—
421C2×C4×C23#12011yescharacteristic
422C2×C4×C23#12011yescharacteristic
423C2×C4×C23C22×D411yescharacteristic
424C2×C4×C23C22×D411yescharacteristic
425C8×C23—41no—
426C8×C23—41no—
427C8×C23—41no—
428C8×C23—41no—
429#3534C2×C2311yescharacteristic
430#3193C2×C2311yescharacteristic, complemented
431#3190C2×C2311yescharacteristic, complemented
432#2814C2×C2311yescharacteristic, complemented
433#1612C2×C2311yescharacteristic, complemented
434#1610C2×C2311yescharacteristic, complemented
435#1609C2×C2311yescharacteristic, complemented
436#1607C2×C2311yescharacteristic, complemented
437#1606C2×C2311yescharacteristic, complemented
438#1604C2×C2311yescharacteristic, complemented
439#1603C2×C2311yescharacteristic, complemented
440#1601C2×C2311yescharacteristic, complemented
441#1519C2×C2311yescharacteristic, complemented
442#1513C2×C2311yescharacteristic, complemented
443#1468C2×C2311yescharacteristic, complemented
444C22×C23—21no—
445C22×C23—21no—
446C22×C23—21no—
447C22×C23—21no—
448C22×C23—21no—
449C22×C23—21no—
450C22×C23—21no—
451C22×C23—21no—
452C22×C23—41no—
453C22×C23—41no—
454C22×C23—41no—
455C22×C23—41no—
456C22×C23—41no—
457C22×C23—41no—
458C22×C23—41no—
459C22×C23—41no—
460C22×C23—41no—
461C22×C23—41no—
462C22×C23—41no—
463C22×C23—41no—
464C22×C23—81no—
465C22×C23—81no—
466C22×C23—81no—
467C22×C23—81no—
468C22×C23—162no—
469C22×C23—162no—
470C22×C23C2×#12011yescharacteristic
471C22×C23#57611yescharacteristic
472C22×C23#57711yescharacteristic
473C4×C23—21no—
474C4×C23—21no—
475C4×C23—21no—
476C4×C23—21no—
477C4×C23—41no—
478C4×C23—41no—
479C4×C23—41no—
480C4×C23—41no—
481C4×C23—41no—
482C4×C23—41no—
483C4×C23—41no—
484C4×C23—41no—
485C4×C23—81no—
486C4×C23—81no—
487C4×C23—81no—
488C4×C23—81no—
489#562—21no—
490#560—21no—
491#553—21no—
492#551—21no—
493#546—21no—
494#546—21no—
495#546—21no—
496D42—21no—
497#540—21no—
498#539—21no—
499#539C22×C2311yescharacteristic
500#538—21no—
501#538C22×C2311yescharacteristic
502#537C22×C2311yescharacteristic
503#534—21no—
504#534C22×C2311yescharacteristic
505#525C22×C2311yescharacteristic
506C2×#123C22×C2311yescharacteristic
507C2×C22⋊Q8C22×C2311yescharacteristic, complemented
508C2×#121C22×C2311yescharacteristic
509#485—21no—
510#484—21no—
511#483C22×C2311yescharacteristic, complemented
512#480C22×C2311yescharacteristic
513#480C22×C2311yescharacteristic, complemented
514#480C22×C2311yescharacteristic, complemented
515#468—21no—
516#468—21no—
517#467—21no—
518#465—21no—
519#452—21no—
520#451C22×C2311yescharacteristic, complemented
521#450—21no—
522#448C22×C2311yescharacteristic
523#448C22×C2311yescharacteristic, complemented
524#448C22×C2311yescharacteristic, complemented
525#407C22×C2311yescharacteristic, complemented
526C2×C22⋊C8C22×C2311yescharacteristic, complemented
527#398—21no—
528#398C22×C2311yescharacteristic, complemented
529#397—21no—
530#397C22×C2311yescharacteristic, complemented
531#396—21no—
532#395C22×C2311yescharacteristic, complemented
533#394—21no—
534#393C22×C2311yescharacteristic, complemented
535#380C22×C2311yescharacteristic, complemented
536#328C22×C2311yescharacteristic, complemented
537#328C22×C2311yescharacteristic, complemented
538#327C22×C2311yescharacteristic
539#327C22×C2311yescharacteristic
540#327C22×C2311yescharacteristic, complemented
541#327C22×C2311yescharacteristic, complemented
542#327C22×C2311yescharacteristic, complemented
543#327C22×C2311yescharacteristic, complemented
544#324C22×C2311yescharacteristic, complemented
545#324C22×C2311yescharacteristic, complemented
546#323C22×C2311yescharacteristic, complemented
547#323C22×C2311yescharacteristic, complemented
548C2×C23—21no—
549C2×C23—21no—
550C2×C23—41no—
551C2×C23—41no—
552C2×C23—81no—
553C2×C23—81no—
554C2×C23—81no—
555C2×C23—81no—
556C2×C23#301211yescharacteristic
557C2×C23#302211yescharacteristic
558C2×C23#302611yescharacteristic
559C2×#41—21no—
560C2×#41D4×C2311yescharacteristic
561C22×Q8C23×C2311yescharacteristic
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C2311yescharacteristic
566C22×D4D4×C2311yescharacteristic
567C23×C4C23×C2311yescharacteristic
568C2×Q16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×M16—21no—
573C22×C8—21no—
574#127—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#125—21no—
580#125—21no—
581#124—21no—
582#124—21no—
583#124—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8D4×C2311yescharacteristic
608C22⋊Q8C23×C2311yescharacteristic
609#121—21no—
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C2311yescharacteristic
625#121D4×C2311yescharacteristic
626#121D4×C2311yescharacteristic
627#121C23×C2311yescharacteristic
628#121C23×C2311yescharacteristic
629#121C23×C2311yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646#117—21no—
647#117D4×C2311yescharacteristic
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C2311yescharacteristic
653C2×C4⋊C4D4×C2311yescharacteristic
654C2×C4⋊C4C23×C2311yescharacteristic
655C2×C4⋊C4C23×C2311yescharacteristic
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C2311yescharacteristic
664C2×C22⋊C4D4×C2311yescharacteristic
665C2×C22⋊C4C23×C2311yescharacteristic
666#107—21no—
667#107—21no—
668#107—21no—
669#106—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8—21no—
679C22⋊C8—21no—
680C22⋊C8C23×C2311yescharacteristic
681C22⋊C8C23×C2311yescharacteristic
682C22⋊C8C23×C2311yescharacteristic
683C22⋊C8C23×C2311yescharacteristic
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95C23×C2311yescharacteristic
689#95C23×C2311yescharacteristic
690C23#1844711yescharacteristic, direct product factor, Sylow
691C24—21no—
692C24—21no—
693C24C2×D4×C2311yescharacteristic
694C24C2×D4×C2311yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C2311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C2311yescharacteristic
728C2×D4C2×D4×C2311yescharacteristic
729C2×D4C2×D4×C2311yescharacteristic
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—81no—
742C22×C4C2×D4×C2311yescharacteristic
743C22×C4C2×D4×C2311yescharacteristic
744C22×C4C2×D4×C2311yescharacteristic
745C22×C4C2×D4×C2311yescharacteristic
746C22×C4C2×D4×C2311yescharacteristic
747C22×C4C2×D4×C2311yescharacteristic
748C22×C4C2×D4×C2311yescharacteristic
749C22×C4C2×D4×C2311yescharacteristic
750C22×C4C24×C2311yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C2311yescharacteristic
782C4⋊C4C2×D4×C2311yescharacteristic
783C4⋊C4C2×D4×C2311yescharacteristic
784C4⋊C4C2×D4×C2311yescharacteristic
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23C23×#12011yescharacteristic
837C23C23×#12011yescharacteristic
838C23C22×D4×C2311yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
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—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4C23×#12011yescharacteristic
906C2×C4C23×#12011yescharacteristic
907C2×C4C22×D4×C2311yescharacteristic
908C2×C4C22×D4×C2311yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×C23×#12011yescharacteristic
940C22C23×#57611yescharacteristic
941C22C23×#57711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C23×#301211yescharacteristic
967C2C23×#302211yescharacteristic
968C2C23×#302611yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC23×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×#3193C2semidirect
3. C23×#3190C2semidirect
4. C23×#2814C2semidirect
5. C23×#1612C2semidirect
6. C23×#1610C2semidirect
7. C23×#1609C2semidirect
8. C23×#1607C2semidirect
9. C23×#1606C2semidirect
10. C23×#1604C2semidirect
11. C23×#1603C2semidirect
12. C23×#1601C2semidirect
13. C23×#1519C2semidirect
14. C23×#1513C2semidirect
15. C23×#1468C2semidirect
34. C2×C23×C22⋊Q8C22semidirect
38. C23×#483C22semidirect
40. C23×#480C22semidirect
41. C23×#480C22semidirect
47. C23×#451C22semidirect
50. C23×#448C22semidirect
51. C23×#448C22semidirect
52. C23×#407C22semidirect
53. C2×C23×C22⋊C8C22semidirect
55. C23×#398C22semidirect
57. C23×#397C22semidirect
59. C23×#395C22semidirect
61. C23×#393C22semidirect
62. C23×#380C22semidirect
63. C23×#328C22semidirect
64. C23×#328C22semidirect
67. C23×#327C22semidirect
68. C23×#327C22semidirect
69. C23×#327C22semidirect
70. C23×#327C22semidirect
71. C23×#324C22semidirect
72. C23×#324C22semidirect
73. C23×#323C22semidirect
74. C23×#323C22semidirect
333. #18447C23direct (N × H)
430. #3193C2×C23semidirect
431. #3190C2×C23semidirect
432. #2814C2×C23semidirect
433. #1612C2×C23semidirect
434. #1610C2×C23semidirect
435. #1609C2×C23semidirect
436. #1607C2×C23semidirect
437. #1606C2×C23semidirect
438. #1604C2×C23semidirect
439. #1603C2×C23semidirect
440. #1601C2×C23semidirect
441. #1519C2×C23semidirect
442. #1513C2×C23semidirect
443. #1468C2×C23semidirect
507. C2×C22⋊Q8C22×C23semidirect
511. #483C22×C23semidirect
513. #480C22×C23semidirect
514. #480C22×C23semidirect
520. #451C22×C23semidirect
523. #448C22×C23semidirect
524. #448C22×C23semidirect
525. #407C22×C23semidirect
526. C2×C22⋊C8C22×C23semidirect
528. #398C22×C23semidirect
530. #397C22×C23semidirect
532. #395C22×C23semidirect
534. #393C22×C23semidirect
535. #380C22×C23semidirect
536. #328C22×C23semidirect
537. #328C22×C23semidirect
540. #327C22×C23semidirect
541. #327C22×C23semidirect
542. #327C22×C23semidirect
543. #327C22×C23semidirect
544. #324C22×C23semidirect
545. #324C22×C23semidirect
546. #323C22×C23semidirect
547. #323C22×C23semidirect
690. C23#18447direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35342
C23×#31932
C23×#31902
C23×#28142
C23×#16122
C23×#16102
C23×#16092
C23×#16072
C23×#16062
C23×#16042
C23×#16032
C23×#16012
C23×#15192
C23×#15132
C23×#14682
#1844723