Finite Group Databasebeta

← C113×#25131 #43293151

Subgroups — C113×#25131 #43293151

Order 28928.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#449×C113C211yesmaximal, characteristic, complemented
3C2×#435×C113C211yesmaximal, characteristic, complemented
4C2×#416×C113C211yesmaximal, characteristic, complemented
5C113×#2414C211yesmaximal, characteristic, complemented
6C113×#2407C211yesmaximal, characteristic, complemented
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2035C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1972C211yesmaximal, characteristic, complemented
12C113×#1935C211yesmaximal, characteristic, complemented
13C113×#1895C211yesmaximal, characteristic, complemented
14C113×#1893C211yesmaximal, characteristic, complemented
15C113×#1854C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×D8×C113C2211yescharacteristic
19C22×M16×C113C2211yescharacteristic
20C23×C8×C113C2211yescharacteristic
21C2×C22⋊Q8×C113C2211yescharacteristic
22C2×#121×C113C2211yescharacteristic
23C2×#121×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×C4×D4×C113C2211yescharacteristic
26C2×#117×C113C2211yescharacteristic
27#468×C113—24no—
28#449×C113—24no—
29#435×C113—24no—
30C2×#107×C113C2211yescharacteristic
31C2×#106×C113C2211yescharacteristic
32C2×C4⋊C8×C113C2211yescharacteristic
33#416×C113—24no—
34C2×#103×C113C2211yescharacteristic
35C2×#103×C113C2211yescharacteristic
36C2×#103×C113C2211yescharacteristic
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×C22⋊C8×C113C2211yescharacteristic
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×#97×C113C2211yescharacteristic
45#394×C113—21no—
46#394×C113—21no—
47#392×C113—21no—
48#392×C113—21no—
49#391×C113C2211yescharacteristic
50#390×C113—21no—
51#390×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic
53#389×C113C2211yescharacteristic
54#388×C113—21no—
55#386×C113—21no—
56#385×C113—21no—
57#380×C113C2211yescharacteristic
58#380×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic
62#340×C113C2211yescharacteristic
63C2×#41×C113—22no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—41no—
68C2×#41×C113—41no—
69C22×Q8×C113C2311yescharacteristic
70C22×D4×C113—21no—
71C22×D4×C113—21no—
72C22×D4×C113—21no—
73C22×D4×C113—21no—
74C22×D4×C113D411yescharacteristic
75C22×D4×C113C2311yescharacteristic
76C22×D4×C113C2311yescharacteristic
77C23×C4×C113—21no—
78C23×C4×C113C2311yescharacteristic
79C23×C4×C113C2311yescharacteristic
80C2×SD16×C113—22no—
81C2×SD16×C113—22no—
82C2×SD16×C113—41no—
83C2×D8×C113—22no—
84C2×D8×C113—22no—
85C2×D8×C113—41no—
86C2×M16×C113—22no—
87C2×M16×C113—22no—
88C2×M16×C113—41no—
89C22×C8×C113—22no—
90C22×C8×C113—22no—
91C22×C8×C113—41no—
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113—41no—
98#121×C113—22no—
99#121×C113—22no—
100#121×C113—22no—
101#121×C113—22no—
102#121×C113—41no—
103#121×C113—41no—
104C4×D4×C113—22no—
105C4×D4×C113—22no—
106#117×C113—22no—
107#117×C113—41no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113D411yescharacteristic
111C2×C4⋊C4×C113C2311yescharacteristic
112C2×C4⋊C4×C113C2311yescharacteristic
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C22⋊C4×C113—21no—
117C2×C22⋊C4×C113—21no—
118C2×C22⋊C4×C113—21no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113D411yescharacteristic
128C2×C22⋊C4×C113D411yescharacteristic
129C2×C42×C113—21no—
130C2×C42×C113C2311yescharacteristic
131#107×C113—22no—
132#106×C113—41no—
133C4⋊C8×C113—22no—
134#103×C113—22no—
135#103×C113—22no—
136#103×C113D414yescomplemented
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—41no—
142C22⋊C8×C113—22no—
143C22⋊C8×C113D414yescomplemented
144#97×C113—22no—
145#95×C113—21no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113—21no—
149#95×C113—21no—
150C24×C113—21no—
151C24×C113—21no—
152C24×C113C2×D411yescharacteristic
153C24×C113C2×D411yescharacteristic
154#41×C113—28no—
155#41×C113—44no—
156#41×C113—44no—
157#41×C113—44no—
158C2×Q8×C113—21no—
159C2×Q8×C113—21no—
160C2×Q8×C113—21no—
161C2×Q8×C113—21no—
162C2×Q8×C113—21no—
163C2×Q8×C113C2×D412yes—
164C2×D4×C113—22no—
165C2×D4×C113—21no—
166C2×D4×C113—21no—
167C2×D4×C113—21no—
168C2×D4×C113—21no—
169C2×D4×C113—21no—
170C2×D4×C113—21no—
171C2×D4×C113—21no—
172C2×D4×C113—21no—
173C2×D4×C113—21no—
174C2×D4×C113—21no—
175C2×D4×C113—21no—
176C2×D4×C113—41no—
177C2×D4×C113—41no—
178C2×D4×C113—42no—
179C2×D4×C113—42no—
180C2×D4×C113—42no—
181C2×D4×C113—42no—
182C2×D4×C113—42no—
183C2×D4×C113—42no—
184C2×D4×C113—42no—
185C2×D4×C113—42no—
186C2×D4×C113—81no—
187C2×D4×C113—81no—
188C2×D4×C113—81no—
189C2×D4×C113—81no—
190C2×D4×C113#4112yes—
191C22×C4×C113—21no—
192C22×C4×C113—21no—
193C22×C4×C113—21no—
194C22×C4×C113—21no—
195C22×C4×C113—21no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—42no—
208C22×C4×C113—42no—
209C22×C4×C113—42no—
210C22×C4×C113C2×D411yescharacteristic
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D412yes—
215C22×C4×C113#4112yes—
216C22×C4×C113C2411yescharacteristic
217SD16×C113—44no—
218D8×C113—44no—
219M16×C113—44no—
220C2×C8×C113—21no—
221C2×C8×C113—21no—
222C2×C8×C113—21no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—44no—
230C2×C8×C113C2×D412yes—
231C2×C8×C113C2×D412yes—
232C2×C8×C113C2×D412yes—
233C4⋊C4×C113—22no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—21no—
243C4⋊C4×C113—42no—
244C4⋊C4×C113—81no—
245C4⋊C4×C113C2×D412yes—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—22no—
248C22⋊C4×C113—42no—
249C22⋊C4×C113—42no—
250C22⋊C4×C113—42no—
251C22⋊C4×C113—42no—
252C22⋊C4×C113—42no—
253C22⋊C4×C113—42no—
254C22⋊C4×C113—42no—
255C22⋊C4×C113—81no—
256C22⋊C4×C113—81no—
257C22⋊C4×C113—81no—
258C22⋊C4×C113—81no—
259C42×C113—21no—
260C42×C113—21no—
261C42×C113—42no—
262C23×C113—21no—
263C23×C113—21no—
264C23×C113—21no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
269C23×C113—21no—
270C23×C113—22no—
271C23×C113—21no—
272C23×C113—21no—
273C23×C113—21no—
274C23×C113—21no—
275C23×C113—21no—
276C23×C113—41no—
277C23×C113—41no—
278C23×C113—41no—
279C23×C113—41no—
280C23×C113—41no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—41no—
285C23×C113—41no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—41no—
289C23×C113#12112yes—
290C23×C113C22×D411yescharacteristic
291Q8×C113—22no—
292Q8×C113—22no—
293Q8×C113—41no—
294Q8×C113—41no—
295D4×C113—22no—
296D4×C113—22no—
297D4×C113—44no—
298D4×C113—48no—
299D4×C113—41no—
300D4×C113—41no—
301D4×C113—41no—
302D4×C113—41no—
303D4×C113—41no—
304D4×C113—41no—
305D4×C113—84no—
306D4×C113—84no—
307D4×C113—84no—
308C2×C4×C113—21no—
309C2×C4×C113—21no—
310C2×C4×C113—22no—
311C2×C4×C113—22no—
312C2×C4×C113—22no—
313C2×C4×C113—22no—
314C2×C4×C113—21no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—22no—
318C2×C4×C113—21no—
319C2×C4×C113—22no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—21no—
325C2×C4×C113—48no—
326C2×C4×C113—41no—
327C2×C4×C113—41no—
328C2×C4×C113—41no—
329C2×C4×C113—41no—
330C2×C4×C113—41no—
331C2×C4×C113—41no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113—41no—
339C2×C4×C113—41no—
340C2×C4×C113—41no—
341C2×C4×C113—41no—
342C2×C4×C113—41no—
343C2×C4×C113—41no—
344C2×C4×C113—41no—
345C2×C4×C113—41no—
346C2×C4×C113#12112yes—
347C2×C4×C113C22×D411yescharacteristic
348C2×C4×C113C22×D411yescharacteristic
349C2×C4×C113C2×#4111yescharacteristic
350C2×C4×C113C2×#4111yescharacteristic
351C2×C4×C113H(5,𝔽2)11yescharacteristic
352C2×C4×C113H(5,𝔽2)11yescharacteristic
353C8×C113—22no—
354C8×C113—22no—
355C8×C113—22no—
356C8×C113—41no—
357C22×C113—22no—
358C22×C113—22no—
359C22×C113—22no—
360C22×C113—41no—
361C22×C113—41no—
362C22×C113—41no—
363C22×C113—41no—
364C22×C113—42no—
365C22×C113—41no—
366C22×C113—41no—
367C22×C113—41no—
368C22×C113—41no—
369C22×C113—42no—
370C22×C113—41no—
371C22×C113—41no—
372C22×C113—41no—
373C22×C113—42no—
374C22×C113—81no—
375C22×C113—81no—
376C22×C113—81no—
377C22×C113—81no—
378C22×C113—81no—
379C22×C113—81no—
380C22×C113—81no—
381C22×C113—81no—
382C22×C113—81no—
383C22×C113—81no—
384C22×C113—81no—
385C22×C113C2×#12111yescharacteristic
386C22×C113D4211yescharacteristic
387C22×C113#54611yescharacteristic
388C22×C113#57511yescharacteristic
389C22×C113#57511yescharacteristic
390C22×C113#57611yescharacteristic
391C22×C113#57711yescharacteristic
392C4×C113—22no—
393C4×C113—41no—
394C4×C113—42no—
395C4×C113—42no—
396C4×C113—41no—
397C4×C113—41no—
398C4×C113—81no—
399C4×C113—81no—
400C4×C113—81no—
401C4×C113—81no—
402C4×C113#52511yescharacteristic
403C4×C113#53811yescharacteristic
404C4×C113D4211yescharacteristic
405C4×C113#54611yescharacteristic
406#25131C11311yesmaximal, characteristic, direct product factor, Sylow
407C2×C113—42no—
408C2×C113—81no—
409C2×C113—82no—
410C2×C113—161no—
411C2×C113#242411yescharacteristic
412C2×C113#305411yescharacteristic
413C2×C113#306211yescharacteristic
414C2×C113#326811yescharacteristic
415C2×C113#327111yescharacteristic
416C2×C113#330711yescharacteristic
417C2×C113#331911yescharacteristic
418C2×#468C2×C11311yescharacteristic, complemented
419C2×#449C2×C11311yescharacteristic, complemented
420C2×#435C2×C11311yescharacteristic, complemented
421C2×#416C2×C11311yescharacteristic, complemented
422#2414C2×C11311yescharacteristic, complemented
423#2407C2×C11311yescharacteristic, complemented
424#2067C2×C11311yescharacteristic, complemented
425#2055C2×C11311yescharacteristic, complemented
426#2035C2×C11311yescharacteristic, complemented
427#1999C2×C11311yescharacteristic, complemented
428#1972C2×C11311yescharacteristic, complemented
429#1935C2×C11311yescharacteristic, complemented
430#1895C2×C11311yescharacteristic, complemented
431#1893C2×C11311yescharacteristic, complemented
432#1854C2×C11311yescharacteristic, complemented
433C113#2513111yescharacteristic, direct product factor, Sylow
434C22×#41C22×C11311yescharacteristic
435C22×SD16C22×C11311yescharacteristic
436C22×D8C22×C11311yescharacteristic
437C22×M16C22×C11311yescharacteristic
438C23×C8C22×C11311yescharacteristic
439C2×C22⋊Q8C22×C11311yescharacteristic
440C2×#121C22×C11311yescharacteristic
441C2×#121C22×C11311yescharacteristic
442C2×#121C22×C11311yescharacteristic
443C2×C4×D4C22×C11311yescharacteristic
444C2×#117C22×C11311yescharacteristic
445#468—24no—
446#449—24no—
447#435—24no—
448C2×#107C22×C11311yescharacteristic
449C2×#106C22×C11311yescharacteristic
450C2×C4⋊C8C22×C11311yescharacteristic
451#416—24no—
452C2×#103C22×C11311yescharacteristic
453C2×#103C22×C11311yescharacteristic
454C2×#103C22×C11311yescharacteristic
455C2×#102C22×C11311yescharacteristic
456C2×#102C22×C11311yescharacteristic
457C2×#102C22×C11311yescharacteristic
458C2×#102C22×C11311yescharacteristic
459C2×#102C22×C11311yescharacteristic
460C2×C22⋊C8C22×C11311yescharacteristic
461C2×C22⋊C8C22×C11311yescharacteristic
462C2×#97C22×C11311yescharacteristic
463#394—21no—
464#394—21no—
465#392—21no—
466#392—21no—
467#391C22×C11311yescharacteristic
468#390—21no—
469#390C22×C11311yescharacteristic
470#390C22×C11311yescharacteristic
471#389C22×C11311yescharacteristic
472#388—21no—
473#386—21no—
474#385—21no—
475#380C22×C11311yescharacteristic
476#380C22×C11311yescharacteristic
477#340C22×C11311yescharacteristic
478#340C22×C11311yescharacteristic
479#340C22×C11311yescharacteristic
480#340C22×C11311yescharacteristic
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8C23×C11311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C11311yescharacteristic
493C22×D4C23×C11311yescharacteristic
494C22×D4C23×C11311yescharacteristic
495C23×C4—21no—
496C23×C4C23×C11311yescharacteristic
497C23×C4C23×C11311yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C23×C11311yescharacteristic
511C22×C8C23×C11311yescharacteristic
512C22×C8C23×C11311yescharacteristic
513C22×C8C23×C11311yescharacteristic
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522C4×D4—22no—
523C4×D4—22no—
524#117—22no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C11311yescharacteristic
529C2×C4⋊C4C23×C11311yescharacteristic
530C2×C4⋊C4C23×C11311yescharacteristic
531C2×C4⋊C4C23×C11311yescharacteristic
532C2×C4⋊C4C23×C11311yescharacteristic
533C2×C4⋊C4C23×C11311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C11311yescharacteristic
546C2×C22⋊C4D4×C11311yescharacteristic
547C2×C42—21no—
548C2×C42C23×C11311yescharacteristic
549#107—22no—
550#106—41no—
551C4⋊C8—22no—
552#103—22no—
553#103—22no—
554#103D4×C11314yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8D4×C11314yescomplemented
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C11311yescharacteristic
571C24C2×D4×C11311yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C11312yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C11312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C11311yescharacteristic
629C22×C4C2×D4×C11311yescharacteristic
630C22×C4C2×D4×C11311yescharacteristic
631C22×C4C2×D4×C11311yescharacteristic
632C22×C4C2×D4×C11312yes—
633C22×C4#41×C11312yes—
634C22×C4C24×C11311yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C11312yes—
649C2×C8C2×D4×C11312yes—
650C2×C8C2×D4×C11312yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C11312yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#121×C11312yes—
708C23C22×D4×C11311yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4#121×C11312yes—
765C2×C4C22×D4×C11311yescharacteristic
766C2×C4C22×D4×C11311yescharacteristic
767C2×C4C2×#41×C11311yescharacteristic
768C2×C4C2×#41×C11311yescharacteristic
769C2×C4H(5,𝔽2)×C11311yescharacteristic
770C2×C4H(5,𝔽2)×C11311yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C11311yescharacteristic
804C22D42×C11311yescharacteristic
805C22#546×C11311yescharacteristic
806C22#575×C11311yescharacteristic
807C22#575×C11311yescharacteristic
808C22#576×C11311yescharacteristic
809C22#577×C11311yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4#525×C11311yescharacteristic
821C4#538×C11311yescharacteristic
822C4D42×C11311yescharacteristic
823C4#546×C11311yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2C113×#242411yescharacteristic
829C2C113×#305411yescharacteristic
830C2C113×#306211yescharacteristic
831C2C113×#326811yescharacteristic
832C2C113×#327111yescharacteristic
833C2C113×#330711yescharacteristic
834C2C113×#331911yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C113C2semidirect
2. C2×#449×C113C2semidirect
3. C2×#435×C113C2semidirect
4. C2×#416×C113C2semidirect
5. C113×#2414C2semidirect
6. C113×#2407C2semidirect
7. C113×#2067C2semidirect
8. C113×#2055C2semidirect
9. C113×#2035C2semidirect
10. C113×#1999C2semidirect
11. C113×#1972C2semidirect
12. C113×#1935C2semidirect
13. C113×#1895C2semidirect
14. C113×#1893C2semidirect
15. C113×#1854C2semidirect
136. #103×C113D4semidirect
143. C22⋊C8×C113D4semidirect
406. #25131C113direct (N × H)
418. C2×#468C2×C113semidirect
419. C2×#449C2×C113semidirect
420. C2×#435C2×C113semidirect
421. C2×#416C2×C113semidirect
422. #2414C2×C113semidirect
423. #2407C2×C113semidirect
424. #2067C2×C113semidirect
425. #2055C2×C113semidirect
426. #2035C2×C113semidirect
427. #1999C2×C113semidirect
428. #1972C2×C113semidirect
429. #1935C2×C113semidirect
430. #1895C2×C113semidirect
431. #1893C2×C113semidirect
432. #1854C2×C113semidirect
433. C113#25131direct (N × H)
554. #103D4×C113semidirect
561. C22⋊C8D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1132
C2×#449×C1132
C2×#435×C1132
C2×#416×C1132
C113×#24142
C113×#24072
C113×#20672
C113×#20552
C113×#20352
C113×#19992
C113×#19722
C113×#19352
C113×#18952
C113×#18932
C113×#18542
#25131113