Finite Group Databasebeta

← C23×#18263 #19165889

Subgroups — C23×#18263 #19165889

Order 5888.

948 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#3535C211yesmaximal, characteristic
2C23×#3095C211yesmaximal, characteristic, complemented
3C23×#3091C211yesmaximal, characteristic, complemented
4C23×#2498C211yesmaximal, characteristic, complemented
5C23×#1618C211yesmaximal, characteristic, complemented
6C23×#1617C211yesmaximal, characteristic, complemented
7C23×#1615C211yesmaximal, characteristic, complemented
8C23×#1614C211yesmaximal, characteristic, complemented
9C23×#1612C211yesmaximal, characteristic, complemented
10C23×#1611C211yesmaximal, characteristic, complemented
11C23×#1609C211yesmaximal, characteristic, complemented
12C23×#1608C211yesmaximal, characteristic, complemented
13C23×#1504C211yesmaximal, characteristic, complemented
14C2×C23×#328C211yesmaximal, characteristic, complemented
15C23×#1468C211yesmaximal, characteristic, complemented
16C23×#563—21no—
17C23×#562—21no—
18C23×#554—21no—
19C23×#552—21no—
20C23×#551—21no—
21C23×#551—21no—
22C23×#547—21no—
23C23×#546—21no—
24C23×#544C2211yescharacteristic
25C23×#543C2211yescharacteristic
26C23×#542—21no—
27C23×#539—21no—
28C23×#539—21no—
29C23×#539C2211yescharacteristic
30C23×#538C2211yescharacteristic
31C23×#536—21no—
32C23×#525C2211yescharacteristic
33C2×C23×#123C2211yescharacteristic
34C2×C23×C22⋊Q8C2211yescharacteristic
35C2×C23×#117C2211yescharacteristic
36C23×#485—21no—
37C23×#485—21no—
38C23×#485—21no—
39C23×#484C2211yescharacteristic
40C23×#484C2211yescharacteristic
41C23×#484C2211yescharacteristic
42C23×#483C2211yescharacteristic
43C23×#483C2211yescharacteristic
44C23×#483C2211yescharacteristic
45C23×#482—21no—
46C23×#481C2211yescharacteristic
47C23×#480C2211yescharacteristic
48C23×#428—21no—
49C23×#427—21no—
50C23×#419—21no—
51C23×#416—21no—
52C23×#407C2211yescharacteristic
53C2×C23×C22⋊C8C2211yescharacteristic
54C23×#400C2211yescharacteristic
55C23×#399C2211yescharacteristic
56C23×#398C2211yescharacteristic
57C23×#397C2211yescharacteristic
58C23×#388—21no—
59C23×#387—21no—
60C23×#386—21no—
61C23×#380—21no—
62C2×C23×#95C2211yescharacteristic
63C23×#328C2211yescharacteristic
64C23×#328C2211yescharacteristic
65C23×#328C2211yescharacteristic
66C23×#328C2211yescharacteristic
67C23×#328C2211yescharacteristic
68C23×#328C2211yescharacteristic
69C23×#327C2211yescharacteristic
70C23×#327C2211yescharacteristic
71C23×#324C2211yescharacteristic
72C23×#324C2211yescharacteristic
73C23×#323C2211yescharacteristic
74C23×#323C2211yescharacteristic
75C2×#41×C23—21no—
76C2×#41×C23D411yescharacteristic
77C22×Q8×C23D411yescharacteristic
78C22×D4×C23D411yescharacteristic
79C23×C4×C23—21no—
80C23×C4×C23C2311yescharacteristic
81C2×M16×C23—21no—
82C22×C8×C23—21no—
83C23×C4⋊Q8—21no—
84C23×C4⋊Q8—21no—
85C23×C4⋊Q8—21no—
86C23×#126—21no—
87C23×#126—21no—
88C23×#126—21no—
89C23×#126—21no—
90C23×#126—21no—
91C23×#126—21no—
92C23×#125—21no—
93C23×#125—21no—
94C23×#125—21no—
95C23×#125—21no—
96C23×#125—21no—
97C23×#124—21no—
98C23×#124—21no—
99C23×#124—21no—
100C23×#124—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×#123—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⋊Q8—21no—
124C23×C22⋊Q8—21no—
125C23×C22⋊Q8—21no—
126C23×C22⋊Q8—21no—
127C23×C22⋊Q8—21no—
128C23×C22⋊Q8—21no—
129C23×C22⋊Q8D411yescharacteristic
130C23×C22⋊Q8D411yescharacteristic
131C23×C22⋊Q8D411yescharacteristic
132C23×C22⋊Q8C2311yescharacteristic
133C23×C22⋊Q8C2311yescharacteristic
134C23×C22⋊Q8C2311yescharacteristic
135C23×#121—21no—
136C23×#121—21no—
137C23×#121—21no—
138C23×#121—21no—
139C23×#121D411yescharacteristic
140C23×#121C2311yescharacteristic
141C23×#120—21no—
142C23×#120—21no—
143C4×Q8×C23—21no—
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—
151C23×#117—21no—
152C23×#117—21no—
153C23×#117—21no—
154C23×#117—21no—
155C23×#117—21no—
156C23×#117—21no—
157C23×#117—21no—
158C23×#117D411yescharacteristic
159C2×C4⋊C4×C23—21no—
160C2×C4⋊C4×C23—21no—
161C2×C4⋊C4×C23—21no—
162C2×C4⋊C4×C23—21no—
163C2×C4⋊C4×C23D411yescharacteristic
164C2×C4⋊C4×C23D411yescharacteristic
165C2×C4⋊C4×C23C2311yescharacteristic
166C2×C4⋊C4×C23C2311yescharacteristic
167C2×C4⋊C4×C23C2311yescharacteristic
168C2×C22⋊C4×C23—21no—
169C2×C22⋊C4×C23—21no—
170C2×C22⋊C4×C23—21no—
171C2×C22⋊C4×C23—21no—
172C2×C22⋊C4×C23—21no—
173C2×C22⋊C4×C23D411yescharacteristic
174C2×C22⋊C4×C23D411yescharacteristic
175C2×C22⋊C4×C23C2311yescharacteristic
176C2×C42×C23—21no—
177C23×#107—21no—
178C23×#107—21no—
179C23×#107—21no—
180C23×#107—21no—
181C23×#106—21no—
182C23×#106—21no—
183C23×#106—21no—
184C23×#106—21no—
185C23×#103—21no—
186C23×#103—21no—
187C23×#103—21no—
188C23×#103—21no—
189C23×#103—21no—
190C23×#103—21no—
191C23×#102—21no—
192C23×#102—21no—
193C23×C22⋊C8—21no—
194C23×C22⋊C8—21no—
195C23×C22⋊C8C2311yescharacteristic
196C23×C22⋊C8C2311yescharacteristic
197C23×C22⋊C8C2311yescharacteristic
198C23×C22⋊C8C2311yescharacteristic
199C23×#95—21no—
200C23×#95—21no—
201C23×#95—21no—
202C23×#95—21no—
203C23×#95—21no—
204C23×#95C2311yescharacteristic
205C23×#95C2311yescharacteristic
206C24×C23C2×D411yescharacteristic
207C24×C23C2×D411yescharacteristic
208#41×C23—42no—
209#41×C23—82no—
210C2×Q8×C23—21no—
211C2×Q8×C23—21no—
212C2×Q8×C23—21no—
213C2×Q8×C23—42no—
214C2×Q8×C23C2×D411yescharacteristic
215C2×Q8×C23C2×D411yescharacteristic
216C2×Q8×C23C2×D411yescharacteristic
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—42no—
225C2×D4×C23C2×D411yescharacteristic
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—42no—
238C22×C4×C23—42no—
239C22×C4×C23—42no—
240C22×C4×C23—81no—
241C22×C4×C23C2×D411yescharacteristic
242C22×C4×C23C2×D411yescharacteristic
243C22×C4×C23C2×D411yescharacteristic
244C22×C4×C23C2×D411yescharacteristic
245C22×C4×C23C2×D411yescharacteristic
246C22×C4×C23C2×D411yescharacteristic
247C22×C4×C23C2×D411yescharacteristic
248C22×C4×C23C2×D411yescharacteristic
249C22×C4×C23C2411yescharacteristic
250M16×C23—42no—
251C2×C8×C23—21no—
252C2×C8×C23—21no—
253C2×C8×C23—21no—
254C2×C8×C23—21no—
255C2×C8×C23—42no—
256C4⋊C4×C23—21no—
257C4⋊C4×C23—21no—
258C4⋊C4×C23—21no—
259C4⋊C4×C23—21no—
260C4⋊C4×C23—21no—
261C4⋊C4×C23—21no—
262C4⋊C4×C23—21no—
263C4⋊C4×C23—21no—
264C4⋊C4×C23—21no—
265C4⋊C4×C23—21no—
266C4⋊C4×C23—21no—
267C4⋊C4×C23—21no—
268C4⋊C4×C23—21no—
269C4⋊C4×C23—21no—
270C4⋊C4×C23—21no—
271C4⋊C4×C23—21no—
272C4⋊C4×C23—21no—
273C4⋊C4×C23—21no—
274C4⋊C4×C23—21no—
275C4⋊C4×C23—21no—
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—42no—
284C4⋊C4×C23—81no—
285C4⋊C4×C23C2×D411yescharacteristic
286C4⋊C4×C23C2×D411yescharacteristic
287C4⋊C4×C23C2×D411yescharacteristic
288C4⋊C4×C23C2×D411yescharacteristic
289C22⋊C4×C23—21no—
290C22⋊C4×C23—21no—
291C22⋊C4×C23—21no—
292C22⋊C4×C23—21no—
293C22⋊C4×C23—21no—
294C22⋊C4×C23—21no—
295C22⋊C4×C23—21no—
296C22⋊C4×C23—21no—
297C22⋊C4×C23—21no—
298C22⋊C4×C23—21no—
299C22⋊C4×C23—21no—
300C22⋊C4×C23—21no—
301C22⋊C4×C23—21no—
302C22⋊C4×C23—21no—
303C22⋊C4×C23—21no—
304C22⋊C4×C23—21no—
305C22⋊C4×C23—21no—
306C22⋊C4×C23—21no—
307C22⋊C4×C23—21no—
308C22⋊C4×C23—21no—
309C22⋊C4×C23—21no—
310C22⋊C4×C23—21no—
311C22⋊C4×C23—21no—
312C22⋊C4×C23—42no—
313C22⋊C4×C23—41no—
314C22⋊C4×C23—41no—
315C22⋊C4×C23—81no—
316C42×C23—21no—
317C42×C23—21no—
318C42×C23—21no—
319C42×C23—21no—
320C42×C23—21no—
321C42×C23—41no—
322C42×C23—41no—
323#18263C2311yesmaximal, characteristic, direct product factor, Sylow
324C23×C23—21no—
325C23×C23—21no—
326C23×C23—22no—
327C23×C23—21no—
328C23×C23—21no—
329C23×C23—21no—
330C23×C23—21no—
331C23×C23—41no—
332C23×C23—41no—
333C23×C23—41no—
334C23×C23#12011yescharacteristic
335C23×C23#12011yescharacteristic
336C23×C23C22×D411yescharacteristic
337Q8×C23—41no—
338Q8×C23—41no—
339Q8×C23—41no—
340Q8×C23—81no—
341Q8×C23—81no—
342Q8×C23—81no—
343D4×C23—41no—
344D4×C23—41no—
345D4×C23—41no—
346D4×C23—42no—
347D4×C23—42no—
348D4×C23—81no—
349D4×C23—81no—
350D4×C23—81no—
351D4×C23—81no—
352C2×C4×C23—22no—
353C2×C4×C23—22no—
354C2×C4×C23—22no—
355C2×C4×C23—21no—
356C2×C4×C23—21no—
357C2×C4×C23—21no—
358C2×C4×C23—21no—
359C2×C4×C23—21no—
360C2×C4×C23—21no—
361C2×C4×C23—21no—
362C2×C4×C23—21no—
363C2×C4×C23—21no—
364C2×C4×C23—21no—
365C2×C4×C23—21no—
366C2×C4×C23—21no—
367C2×C4×C23—41no—
368C2×C4×C23—41no—
369C2×C4×C23—41no—
370C2×C4×C23—41no—
371C2×C4×C23—41no—
372C2×C4×C23—41no—
373C2×C4×C23—42no—
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—81no—
386C2×C4×C23—81no—
387C2×C4×C23—81no—
388C2×C4×C23—81no—
389C2×C4×C23—81no—
390C2×C4×C23—81no—
391C2×C4×C23—84no—
392C2×C4×C23#12011yescharacteristic
393C2×C4×C23#12011yescharacteristic
394C2×C4×C23C22×D411yescharacteristic
395C2×C4×C23C22×D411yescharacteristic
396C8×C23—41no—
397C8×C23—41no—
398C8×C23—41no—
399C8×C23—41no—
400#3535C2×C2311yescharacteristic
401#3095C2×C2311yescharacteristic, complemented
402#3091C2×C2311yescharacteristic, complemented
403#2498C2×C2311yescharacteristic, complemented
404#1618C2×C2311yescharacteristic, complemented
405#1617C2×C2311yescharacteristic, complemented
406#1615C2×C2311yescharacteristic, complemented
407#1614C2×C2311yescharacteristic, complemented
408#1612C2×C2311yescharacteristic, complemented
409#1611C2×C2311yescharacteristic, complemented
410#1609C2×C2311yescharacteristic, complemented
411#1608C2×C2311yescharacteristic, complemented
412#1504C2×C2311yescharacteristic, complemented
413C2×#328C2×C2311yescharacteristic, complemented
414#1468C2×C2311yescharacteristic, complemented
415C22×C23—21no—
416C22×C23—21no—
417C22×C23—21no—
418C22×C23—21no—
419C22×C23—21no—
420C22×C23—21no—
421C22×C23—21no—
422C22×C23—42no—
423C22×C23—42no—
424C22×C23—41no—
425C22×C23—41no—
426C22×C23—41no—
427C22×C23—41no—
428C22×C23—41no—
429C22×C23—41no—
430C22×C23—81no—
431C22×C23—81no—
432C22×C23#45812yes—
433C22×C23C2×#12011yescharacteristic
434C22×C23#57711yescharacteristic
435C22×C23#57811yescharacteristic
436C4×C23—21no—
437C4×C23—21no—
438C4×C23—21no—
439C4×C23—21no—
440C4×C23—42no—
441C4×C23—41no—
442C4×C23—41no—
443C4×C23—41no—
444C4×C23—41no—
445C4×C23—41no—
446C4×C23—41no—
447C4×C23—41no—
448C4×C23—41no—
449C4×C23—41no—
450C4×C23—41no—
451C4×C23—81no—
452C4×C23—81no—
453C4×C23—81no—
454#563—21no—
455#562—21no—
456#554—21no—
457#552—21no—
458#551—21no—
459#551—21no—
460#547—21no—
461#546—21no—
462#544C22×C2311yescharacteristic
463#543C22×C2311yescharacteristic
464#542—21no—
465#539—21no—
466#539—21no—
467#539C22×C2311yescharacteristic
468#538C22×C2311yescharacteristic
469#536—21no—
470#525C22×C2311yescharacteristic
471C2×#123C22×C2311yescharacteristic
472C2×C22⋊Q8C22×C2311yescharacteristic
473C2×#117C22×C2311yescharacteristic
474#485—21no—
475#485—21no—
476#485—21no—
477#484C22×C2311yescharacteristic
478#484C22×C2311yescharacteristic
479#484C22×C2311yescharacteristic
480#483C22×C2311yescharacteristic
481#483C22×C2311yescharacteristic
482#483C22×C2311yescharacteristic
483#482—21no—
484#481C22×C2311yescharacteristic
485#480C22×C2311yescharacteristic
486#428—21no—
487#427—21no—
488#419—21no—
489#416—21no—
490#407C22×C2311yescharacteristic
491C2×C22⋊C8C22×C2311yescharacteristic
492#400C22×C2311yescharacteristic
493#399C22×C2311yescharacteristic
494#398C22×C2311yescharacteristic
495#397C22×C2311yescharacteristic
496#388—21no—
497#387—21no—
498#386—21no—
499#380—21no—
500C2×#95C22×C2311yescharacteristic
501#328C22×C2311yescharacteristic
502#328C22×C2311yescharacteristic
503#328C22×C2311yescharacteristic
504#328C22×C2311yescharacteristic
505#328C22×C2311yescharacteristic
506#328C22×C2311yescharacteristic
507#327C22×C2311yescharacteristic
508#327C22×C2311yescharacteristic
509#324C22×C2311yescharacteristic
510#324C22×C2311yescharacteristic
511#323C22×C2311yescharacteristic
512#323C22×C2311yescharacteristic
513C2×C23—21no—
514C2×C23—21no—
515C2×C23—22no—
516C2×C23—41no—
517C2×C23—81no—
518C2×C23—81no—
519C2×C23#301311yescharacteristic
520C2×C23#301811yescharacteristic
521C2×C23C2×#45811yescharacteristic
522C2×#41—21no—
523C2×#41D4×C2311yescharacteristic
524C22×Q8D4×C2311yescharacteristic
525C22×D4D4×C2311yescharacteristic
526C23×C4—21no—
527C23×C4C23×C2311yescharacteristic
528C2×M16—21no—
529C22×C8—21no—
530C4⋊Q8—21no—
531C4⋊Q8—21no—
532C4⋊Q8—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#125—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#124—21no—
545#124—21no—
546#124—21no—
547#124—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8D4×C2311yescharacteristic
577C22⋊Q8D4×C2311yescharacteristic
578C22⋊Q8D4×C2311yescharacteristic
579C22⋊Q8C23×C2311yescharacteristic
580C22⋊Q8C23×C2311yescharacteristic
581C22⋊Q8C23×C2311yescharacteristic
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121D4×C2311yescharacteristic
587#121C23×C2311yescharacteristic
588#120—21no—
589#120—21no—
590C4×Q8—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117D4×C2311yescharacteristic
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C2311yescharacteristic
611C2×C4⋊C4D4×C2311yescharacteristic
612C2×C4⋊C4C23×C2311yescharacteristic
613C2×C4⋊C4C23×C2311yescharacteristic
614C2×C4⋊C4C23×C2311yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4D4×C2311yescharacteristic
621C2×C22⋊C4D4×C2311yescharacteristic
622C2×C22⋊C4C23×C2311yescharacteristic
623C2×C42—21no—
624#107—21no—
625#107—21no—
626#107—21no—
627#107—21no—
628#106—21no—
629#106—21no—
630#106—21no—
631#106—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#103—21no—
637#103—21no—
638#102—21no—
639#102—21no—
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8C23×C2311yescharacteristic
643C22⋊C8C23×C2311yescharacteristic
644C22⋊C8C23×C2311yescharacteristic
645C22⋊C8C23×C2311yescharacteristic
646#95—21no—
647#95—21no—
648#95—21no—
649#95—21no—
650#95—21no—
651#95C23×C2311yescharacteristic
652#95C23×C2311yescharacteristic
653C23#1826311yescharacteristic, direct product factor, Sylow
654C24C2×D4×C2311yescharacteristic
655C24C2×D4×C2311yescharacteristic
656#41—42no—
657#41—82no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—42no—
662C2×Q8C2×D4×C2311yescharacteristic
663C2×Q8C2×D4×C2311yescharacteristic
664C2×Q8C2×D4×C2311yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—42no—
673C2×D4C2×D4×C2311yescharacteristic
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—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—81no—
689C22×C4C2×D4×C2311yescharacteristic
690C22×C4C2×D4×C2311yescharacteristic
691C22×C4C2×D4×C2311yescharacteristic
692C22×C4C2×D4×C2311yescharacteristic
693C22×C4C2×D4×C2311yescharacteristic
694C22×C4C2×D4×C2311yescharacteristic
695C22×C4C2×D4×C2311yescharacteristic
696C22×C4C2×D4×C2311yescharacteristic
697C22×C4C24×C2311yescharacteristic
698M16—42no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—42no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—42no—
732C4⋊C4—81no—
733C4⋊C4C2×D4×C2311yescharacteristic
734C4⋊C4C2×D4×C2311yescharacteristic
735C4⋊C4C2×D4×C2311yescharacteristic
736C4⋊C4C2×D4×C2311yescharacteristic
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—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—42no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C22⋊C4—81no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—21no—
769C42—41no—
770C42—41no—
771C23—21no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23C23×#12011yescharacteristic
782C23C23×#12011yescharacteristic
783C23C22×D4×C2311yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—81no—
788Q8—81no—
789Q8—81no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—42no—
794D4—42no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—81no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4—81no—
835C2×C4—81no—
836C2×C4—81no—
837C2×C4—81no—
838C2×C4—84no—
839C2×C4C23×#12011yescharacteristic
840C2×C4C23×#12011yescharacteristic
841C2×C4C22×D4×C2311yescharacteristic
842C2×C4C22×D4×C2311yescharacteristic
843C8—41no—
844C8—41no—
845C8—41no—
846C8—41no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—42no—
855C22—42no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—81no—
863C22—81no—
864C22C23×#45812yes—
865C22C2×C23×#12011yescharacteristic
866C22C23×#57711yescharacteristic
867C22C23×#57811yescharacteristic
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C2—21no—
887C2—21no—
888C2—22no—
889C2—41no—
890C2—81no—
891C2—81no—
892C2C23×#301311yescharacteristic
893C2C23×#301811yescharacteristic
894C2C2×C23×#45811yescharacteristic
subgroupG/H
center, socleC22×C23C2×#120
commutator, Frattini, cosocleC22×C4C24×C23
prime radicalC23×#3535C2
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×#3095C2semidirect
3. C23×#3091C2semidirect
4. C23×#2498C2semidirect
5. C23×#1618C2semidirect
6. C23×#1617C2semidirect
7. C23×#1615C2semidirect
8. C23×#1614C2semidirect
9. C23×#1612C2semidirect
10. C23×#1611C2semidirect
11. C23×#1609C2semidirect
12. C23×#1608C2semidirect
13. C23×#1504C2semidirect
14. C2×C23×#328C2semidirect
15. C23×#1468C2semidirect
323. #18263C23direct (N × H)
401. #3095C2×C23semidirect
402. #3091C2×C23semidirect
403. #2498C2×C23semidirect
404. #1618C2×C23semidirect
405. #1617C2×C23semidirect
406. #1615C2×C23semidirect
407. #1614C2×C23semidirect
408. #1612C2×C23semidirect
409. #1611C2×C23semidirect
410. #1609C2×C23semidirect
411. #1608C2×C23semidirect
412. #1504C2×C23semidirect
413. C2×#328C2×C23semidirect
414. #1468C2×C23semidirect
653. C23#18263direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#35352
C23×#30952
C23×#30912
C23×#24982
C23×#16182
C23×#16172
C23×#16152
C23×#16142
C23×#16122
C23×#16112
C23×#16092
C23×#16082
C23×#15042
C2×C23×#3282
C23×#14682
#1826323