Finite Group Databasebeta

← C113×#25087 #43293107

Subgroups — C113×#25087 #43293107

Order 28928.

1192 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C113C211yesmaximal, characteristic, complemented
2C2×#463×C113C211yesmaximal, characteristic, complemented
3C2×#449×C113C211yesmaximal, characteristic, complemented
4C2×#416×C113C211yesmaximal, characteristic, complemented
5C113×#2431C211yesmaximal, characteristic, complemented
6C113×#2363C211yesmaximal, characteristic, complemented
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2042C211yesmaximal, characteristic, complemented
10C113×#2011C211yesmaximal, characteristic, complemented
11C113×#1982C211yesmaximal, characteristic, complemented
12C113×#1928C211yesmaximal, characteristic, complemented
13C113×#1879C211yesmaximal, characteristic, complemented
14C113×#1875C211yesmaximal, characteristic, complemented
15C113×#1850C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×D8×C113C2211yescharacteristic
19C22×D8×C113C2211yescharacteristic
20C23×C8×C113C2211yescharacteristic
21C2×#127×C113C2211yescharacteristic
22C2×#124×C113C2211yescharacteristic
23C2×#121×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×C4×D4×C113C2211yescharacteristic
26C2×#117×C113C2211yescharacteristic
27#466×C113—24no—
28#463×C113—24no—
29#449×C113—24no—
30C2×#107×C113C2211yescharacteristic
31C2×C4⋊C8×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×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45#392×C113—21no—
46#392×C113—21no—
47#391×C113C2211yescharacteristic
48#390×C113—21no—
49#390×C113C2211yescharacteristic
50#390×C113C2211yescharacteristic
51#389×C113C2211yescharacteristic
52#388×C113—21no—
53#386×C113—21no—
54#386×C113—21no—
55#386×C113—21no—
56C4×C4⋊C4×C113C2211yescharacteristic
57C4×C22⋊C4×C113—21no—
58C4×C22⋊C4×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#336×C113C2211yescharacteristic
62#336×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×C113—21no—
75C22×D4×C113C2311yescharacteristic
76C22×D4×C113C2311yescharacteristic
77C22×D4×C113C2311yescharacteristic
78C23×C4×C113—21no—
79C23×C4×C113—21no—
80C23×C4×C113C2311yescharacteristic
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—41no—
84C2×D8×C113—22no—
85C2×D8×C113—22no—
86C2×D8×C113—22no—
87C2×D8×C113—22no—
88C2×D8×C113—41no—
89C2×D8×C113—41no—
90C22×C8×C113—22no—
91C22×C8×C113—22no—
92C22×C8×C113—41no—
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96C22×C8×C113C2311yescharacteristic
97#127×C113—22no—
98#127×C113—41no—
99#124×C113—22no—
100#124×C113—41no—
101#121×C113—22no—
102#121×C113—22no—
103#121×C113—22no—
104#121×C113D414yescomplemented
105C4×D4×C113—22no—
106C4×D4×C113—41no—
107#117×C113—22no—
108#117×C113—41no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113C2311yescharacteristic
111C2×C4⋊C4×C113C2311yescharacteristic
112C2×C4⋊C4×C113C2311yescharacteristic
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C22⋊C4×C113—21no—
115C2×C22⋊C4×C113—21no—
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×C113D411yescharacteristic
125C2×C22⋊C4×C113D411yescharacteristic
126C2×C42×C113—21no—
127C2×C42×C113—21no—
128C2×C42×C113C2311yescharacteristic
129C2×C42×C113C2311yescharacteristic
130#107×C113—22no—
131C4⋊C8×C113—22no—
132C4⋊C8×C113—41no—
133#103×C113—22no—
134#103×C113—22no—
135#103×C113D414yescomplemented
136#102×C113—22no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—41no—
143C22⋊C8×C113—22no—
144#95×C113—21no—
145#95×C113—21no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113D411yescharacteristic
149#95×C113D411yescharacteristic
150C24×C113—21no—
151C24×C113—21no—
152C24×C113—21no—
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—24no—
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—21no—
177C2×D4×C113—21no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—21no—
181C2×D4×C113—42no—
182C2×D4×C113—42no—
183C2×D4×C113—42no—
184C2×D4×C113—42no—
185C2×D4×C113—42no—
186C2×D4×C113—42no—
187C2×D4×C113—42no—
188C2×D4×C113—42no—
189C2×D4×C113—81no—
190C2×D4×C113—81no—
191C2×D4×C113—81no—
192C2×D4×C113—81no—
193C2×D4×C113—81no—
194C2×D4×C113—81no—
195C2×D4×C113C2×D412yes—
196C2×D4×C113#4112yes—
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—42no—
207C22×C4×C113—42no—
208C22×C4×C113—42no—
209C22×C4×C113—42no—
210C22×C4×C113—42no—
211C22×C4×C113—81no—
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D411yescharacteristic
216C22×C4×C113C2×D412yes—
217C22×C4×C113C2×D411yescharacteristic
218C22×C4×C113#4112yes—
219C22×C4×C113C2411yescharacteristic
220SD16×C113—44no—
221D8×C113—44no—
222D8×C113—44no—
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—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113—21no—
234C2×C8×C113—44no—
235C2×C8×C113C2×D412yes—
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—81no—
243C4⋊C4×C113C2×D412yes—
244C4⋊C4×C113C2×D412yes—
245C22⋊C4×C113—24no—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—41no—
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—81no—
255C22⋊C4×C113—81no—
256C22⋊C4×C113—81no—
257C42×C113—21no—
258C42×C113—21no—
259C42×C113—21no—
260C42×C113—21no—
261C42×C113—42no—
262C42×C113—81no—
263C23×C113—21no—
264C23×C113—21no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
269C23×C113—22no—
270C23×C113—22no—
271C23×C113—41no—
272C23×C113—41no—
273C23×C113—41no—
274C23×C113—41no—
275C23×C113—41no—
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—41no—
290C23×C113#12112yes—
291C23×C113C22×D411yescharacteristic
292Q8×C113—22no—
293Q8×C113—22no—
294Q8×C113—41no—
295Q8×C113—41no—
296D4×C113—22no—
297D4×C113—22no—
298D4×C113—22no—
299D4×C113—22no—
300D4×C113—48no—
301D4×C113—41no—
302D4×C113—41no—
303D4×C113—41no—
304D4×C113—41no—
305D4×C113—41no—
306D4×C113—41no—
307D4×C113—41no—
308D4×C113—41no—
309D4×C113—84no—
310D4×C113—84no—
311D4×C113—84no—
312D4×C113—84no—
313C2×C4×C113—21no—
314C2×C4×C113—21no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—22no—
318C2×C4×C113—22no—
319C2×C4×C113—22no—
320C2×C4×C113—22no—
321C2×C4×C113—22no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—22no—
325C2×C4×C113—22no—
326C2×C4×C113—21no—
327C2×C4×C113—21no—
328C2×C4×C113—21no—
329C2×C4×C113—21no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—48no—
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—84no—
347C2×C4×C113#12112yes—
348C2×C4×C113#13512yes—
349C2×C4×C113C22×D411yescharacteristic
350C2×C4×C113C22×D411yescharacteristic
351C2×C4×C113C2×#4111yescharacteristic
352C2×C4×C113C2×#4111yescharacteristic
353C2×C4×C113H(5,𝔽2)11yescharacteristic
354C2×C4×C113H(5,𝔽2)11yescharacteristic
355C8×C113—22no—
356C8×C113—41no—
357C8×C113—41no—
358C8×C113—41no—
359C22×C113—22no—
360C22×C113—22no—
361C22×C113—22no—
362C22×C113—41no—
363C22×C113—41no—
364C22×C113—41no—
365C22×C113—41no—
366C22×C113—42no—
367C22×C113—42no—
368C22×C113—42no—
369C22×C113—42no—
370C22×C113—42no—
371C22×C113—42no—
372C22×C113—81no—
373C22×C113—81no—
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×C113—81no—
386C22×C113—81no—
387C22×C113C2×#12111yescharacteristic
388C22×C113D4211yescharacteristic
389C22×C113#54611yescharacteristic
390C22×C113C2×#13511yescharacteristic
391C22×C113#57511yescharacteristic
392C22×C113#57611yescharacteristic
393C22×C113#57611yescharacteristic
394C4×C113—22no—
395C4×C113—22no—
396C4×C113—42no—
397C4×C113—41no—
398C4×C113—42no—
399C4×C113—41no—
400C4×C113—42no—
401C4×C113—41no—
402C4×C113—81no—
403C4×C113—81no—
404C4×C113#52511yescharacteristic
405C4×C113#53811yescharacteristic
406C4×C113D4211yescharacteristic
407C4×C113#54611yescharacteristic
408#25087C11311yesmaximal, characteristic, direct product factor, Sylow
409C2×C113—42no—
410C2×C113—82no—
411C2×C113—82no—
412C2×C113—161no—
413C2×C113#242411yescharacteristic
414C2×C113#303511yescharacteristic
415C2×C113#304111yescharacteristic
416C2×C113#326811yescharacteristic
417C2×C113#328711yescharacteristic
418C2×C113#329711yescharacteristic
419C2×C113#331911yescharacteristic
420C2×#466C2×C11311yescharacteristic, complemented
421C2×#463C2×C11311yescharacteristic, complemented
422C2×#449C2×C11311yescharacteristic, complemented
423C2×#416C2×C11311yescharacteristic, complemented
424#2431C2×C11311yescharacteristic, complemented
425#2363C2×C11311yescharacteristic, complemented
426#2067C2×C11311yescharacteristic, complemented
427#2055C2×C11311yescharacteristic, complemented
428#2042C2×C11311yescharacteristic, complemented
429#2011C2×C11311yescharacteristic, complemented
430#1982C2×C11311yescharacteristic, complemented
431#1928C2×C11311yescharacteristic, complemented
432#1879C2×C11311yescharacteristic, complemented
433#1875C2×C11311yescharacteristic, complemented
434#1850C2×C11311yescharacteristic, complemented
435C113#2508711yescharacteristic, direct product factor, Sylow
436C22×#41C22×C11311yescharacteristic
437C22×SD16C22×C11311yescharacteristic
438C22×D8C22×C11311yescharacteristic
439C22×D8C22×C11311yescharacteristic
440C23×C8C22×C11311yescharacteristic
441C2×#127C22×C11311yescharacteristic
442C2×#124C22×C11311yescharacteristic
443C2×#121C22×C11311yescharacteristic
444C2×#121C22×C11311yescharacteristic
445C2×C4×D4C22×C11311yescharacteristic
446C2×#117C22×C11311yescharacteristic
447#466—24no—
448#463—24no—
449#449—24no—
450C2×#107C22×C11311yescharacteristic
451C2×C4⋊C8C22×C11311yescharacteristic
452C2×C4⋊C8C22×C11311yescharacteristic
453#416—24no—
454C2×#103C22×C11311yescharacteristic
455C2×#103C22×C11311yescharacteristic
456C2×#103C22×C11311yescharacteristic
457C2×#102C22×C11311yescharacteristic
458C2×#102C22×C11311yescharacteristic
459C2×#102C22×C11311yescharacteristic
460C2×#102C22×C11311yescharacteristic
461C2×#102C22×C11311yescharacteristic
462C2×#102C22×C11311yescharacteristic
463C2×#102C22×C11311yescharacteristic
464C2×C22⋊C8C22×C11311yescharacteristic
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#386—21no—
475#386—21no—
476C4×C4⋊C4C22×C11311yescharacteristic
477C4×C22⋊C4—21no—
478C4×C22⋊C4C22×C11311yescharacteristic
479#340C22×C11311yescharacteristic
480#340C22×C11311yescharacteristic
481#336C22×C11311yescharacteristic
482#336C22×C11311yescharacteristic
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8C23×C11311yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C23×C11311yescharacteristic
496C22×D4C23×C11311yescharacteristic
497C22×D4C23×C11311yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C11311yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C23×C11311yescharacteristic
514C22×C8C23×C11311yescharacteristic
515C22×C8C23×C11311yescharacteristic
516C22×C8C23×C11311yescharacteristic
517#127—22no—
518#127—41no—
519#124—22no—
520#124—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121D4×C11314yescomplemented
525C4×D4—22no—
526C4×D4—41no—
527#117—22no—
528#117—41no—
529C2×C4⋊C4—21no—
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⋊C4D4×C11311yescharacteristic
545C2×C22⋊C4D4×C11311yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C11311yescharacteristic
549C2×C42C23×C11311yescharacteristic
550#107—22no—
551C4⋊C8—22no—
552C4⋊C8—41no—
553#103—22no—
554#103—22no—
555#103D4×C11314yescomplemented
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—41no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95D4×C11311yescharacteristic
569#95D4×C11311yescharacteristic
570C24—21no—
571C24—21no—
572C24—21no—
573C24C2×D4×C11311yescharacteristic
574#41—28no—
575#41—44no—
576#41—44no—
577#41—44no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8C2×D4×C11312yes—
584C2×D4—24no—
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—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C11312yes—
616C2×D4#41×C11312yes—
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—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4C2×D4×C11311yescharacteristic
633C22×C4C2×D4×C11311yescharacteristic
634C22×C4C2×D4×C11311yescharacteristic
635C22×C4C2×D4×C11311yescharacteristic
636C22×C4C2×D4×C11312yes—
637C22×C4C2×D4×C11311yescharacteristic
638C22×C4#41×C11312yes—
639C22×C4C24×C11311yescharacteristic
640SD16—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8C2×D4×C11312yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C11312yes—
664C4⋊C4C2×D4×C11312yes—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—81no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
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—41no—
708C23—41no—
709C23—41no—
710C23#121×C11312yes—
711C23C22×D4×C11311yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—84no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—48no—
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—41no—
765C2×C4—41no—
766C2×C4—84no—
767C2×C4#121×C11312yes—
768C2×C4#135×C11312yes—
769C2×C4C22×D4×C11311yescharacteristic
770C2×C4C22×D4×C11311yescharacteristic
771C2×C4C2×#41×C11311yescharacteristic
772C2×C4C2×#41×C11311yescharacteristic
773C2×C4H(5,𝔽2)×C11311yescharacteristic
774C2×C4H(5,𝔽2)×C11311yescharacteristic
775C8—22no—
776C8—41no—
777C8—41no—
778C8—41no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C11311yescharacteristic
808C22D42×C11311yescharacteristic
809C22#546×C11311yescharacteristic
810C22C2×#135×C11311yescharacteristic
811C22#575×C11311yescharacteristic
812C22#576×C11311yescharacteristic
813C22#576×C11311yescharacteristic
814C4—22no—
815C4—22no—
816C4—41no—
817C4—42no—
818C4—41no—
819C4—42no—
820C4—41no—
821C4—42no—
822C4—81no—
823C4—81no—
824C4#525×C11311yescharacteristic
825C4#538×C11311yescharacteristic
826C4D42×C11311yescharacteristic
827C4#546×C11311yescharacteristic
828C2—42no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C113×#242411yescharacteristic
833C2C113×#303511yescharacteristic
834C2C113×#304111yescharacteristic
835C2C113×#326811yescharacteristic
836C2C113×#328711yescharacteristic
837C2C113×#329711yescharacteristic
838C2C113×#331911yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#466×C113C2semidirect
2. C2×#463×C113C2semidirect
3. C2×#449×C113C2semidirect
4. C2×#416×C113C2semidirect
5. C113×#2431C2semidirect
6. C113×#2363C2semidirect
7. C113×#2067C2semidirect
8. C113×#2055C2semidirect
9. C113×#2042C2semidirect
10. C113×#2011C2semidirect
11. C113×#1982C2semidirect
12. C113×#1928C2semidirect
13. C113×#1879C2semidirect
14. C113×#1875C2semidirect
15. C113×#1850C2semidirect
104. #121×C113D4semidirect
135. #103×C113D4semidirect
408. #25087C113direct (N × H)
420. C2×#466C2×C113semidirect
421. C2×#463C2×C113semidirect
422. C2×#449C2×C113semidirect
423. C2×#416C2×C113semidirect
424. #2431C2×C113semidirect
425. #2363C2×C113semidirect
426. #2067C2×C113semidirect
427. #2055C2×C113semidirect
428. #2042C2×C113semidirect
429. #2011C2×C113semidirect
430. #1982C2×C113semidirect
431. #1928C2×C113semidirect
432. #1879C2×C113semidirect
433. #1875C2×C113semidirect
434. #1850C2×C113semidirect
435. C113#25087direct (N × H)
524. #121D4×C113semidirect
555. #103D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1132
C2×#463×C1132
C2×#449×C1132
C2×#416×C1132
C113×#24312
C113×#23632
C113×#20672
C113×#20552
C113×#20422
C113×#20112
C113×#19822
C113×#19282
C113×#18792
C113×#18752
C113×#18502
#25087113