Finite Group Databasebeta

← C113×#24162 #43292182

Subgroups — C113×#24162 #43292182

Order 28928.

1206 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C113C211yesmaximal, characteristic, complemented
2C2×#478×C113C211yesmaximal, characteristic, complemented
3C2×#459×C113C211yesmaximal, characteristic, complemented
4C113×#2324C211yesmaximal, characteristic, complemented
5C113×#2034C211yesmaximal, characteristic, complemented
6C113×#2033C211yesmaximal, characteristic, complemented
7C113×#1999C211yesmaximal, characteristic, complemented
8C113×#1999C211yesmaximal, characteristic, complemented
9C113×#1989C211yesmaximal, characteristic, complemented
10C113×#1982C211yesmaximal, characteristic, complemented
11C113×#1879C211yesmaximal, characteristic, complemented
12C113×#1879C211yesmaximal, characteristic, complemented
13C113×#1864C211yesmaximal, characteristic, complemented
14C113×#1862C211yesmaximal, characteristic, complemented
15C113×#1798C211yesmaximal, characteristic, complemented
16C22×D8×C113C2211yescharacteristic
17C22×D8×C113C2211yescharacteristic
18#540×C113—24no—
19#540×C113—24no—
20C2×#127×C113C2211yescharacteristic
21C2×#125×C113C2211yescharacteristic
22C2×#123×C113—21no—
23C2×#123×C113—21no—
24C2×#121×C113—21no—
25C2×#121×C113—21no—
26C2×#121×C113C2211yescharacteristic
27C2×#121×C113C2211yescharacteristic
28C2×#121×C113C2211yescharacteristic
29C2×C4×D4×C113C2211yescharacteristic
30C2×C4×D4×C113C2211yescharacteristic
31C2×C4×D4×C113C2211yescharacteristic
32C2×#117×C113C2211yescharacteristic
33#478×C113—24no—
34#459×C113—24no—
35C2×#107×C113C2211yescharacteristic
36C2×#106×C113C2211yescharacteristic
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×C4⋊C8×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×C22⋊C8×C113C2211yescharacteristic
48C2×C22⋊C8×C113C2211yescharacteristic
49#390×C113—21no—
50#390×C113C2211yescharacteristic
51#389×C113C2211yescharacteristic
52#388×C113—21no—
53#386×C113—21no—
54#385×C113—21no—
55#380×C113C2211yescharacteristic
56C4×C4⋊C4×C113C2211yescharacteristic
57#340×C113C2211yescharacteristic
58#340×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#336×C113C2211yescharacteristic
62#336×C113C2211yescharacteristic
63C22×D4×C113—21no—
64C22×D4×C113—21no—
65C22×D4×C113—21no—
66C22×D4×C113—21no—
67C22×D4×C113—21no—
68C22×D4×C113C2311yescharacteristic
69C22×D4×C113C2311yescharacteristic
70C22×D4×C113C2311yescharacteristic
71C23×C4×C113—21no—
72C23×C4×C113—21no—
73C23×C4×C113—21no—
74C23×C4×C113C2311yescharacteristic
75C2×D8×C113—22no—
76C2×D8×C113—22no—
77C2×D8×C113—22no—
78C2×D8×C113—22no—
79C2×D8×C113—41no—
80C2×D8×C113—41no—
81C22×C8×C113C2311yescharacteristic
82C22×C8×C113C2311yescharacteristic
83C22×C8×C113C2311yescharacteristic
84C22×C8×C113C2311yescharacteristic
85#127×C113—22no—
86#127×C113D414yescomplemented
87#125×C113—22no—
88#125×C113D414yescomplemented
89#123×C113—28no—
90#123×C113—28no—
91#121×C113—28no—
92#121×C113—28no—
93#121×C113—22no—
94#121×C113—22no—
95#121×C113—22no—
96#121×C113—22no—
97#121×C113—22no—
98#121×C113—22no—
99C4×D4×C113—22no—
100C4×D4×C113—22no—
101C4×D4×C113—22no—
102C4×D4×C113—22no—
103C4×D4×C113—22no—
104C4×D4×C113—22no—
105#117×C113—22no—
106#117×C113—22no—
107C2×C4⋊C4×C113—21no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113D411yescharacteristic
111C2×C4⋊C4×C113D411yescharacteristic
112C2×C4⋊C4×C113C2311yescharacteristic
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C4⋊C4×C113C2311yescharacteristic
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×C113D411yescharacteristic
127C2×C22⋊C4×C113D411yescharacteristic
128C2×C42×C113—21no—
129C2×C42×C113C2311yescharacteristic
130C2×C42×C113C2311yescharacteristic
131#107×C113—22no—
132#106×C113—22no—
133C4⋊C8×C113—22no—
134C4⋊C8×C113—22no—
135#102×C113—22no—
136#102×C113—22no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—41no—
142#102×C113—41no—
143C22⋊C8×C113—41no—
144C22⋊C8×C113—41no—
145#95×C113—21no—
146#95×C113—21no—
147#95×C113—21no—
148C24×C113—21no—
149C24×C113—21no—
150C24×C113—21no—
151C24×C113C2×D411yescharacteristic
152C2×D4×C113—24no—
153C2×D4×C113—24no—
154C2×D4×C113—24no—
155C2×D4×C113—24no—
156C2×D4×C113—24no—
157C2×D4×C113—21no—
158C2×D4×C113—21no—
159C2×D4×C113—21no—
160C2×D4×C113—21no—
161C2×D4×C113—21no—
162C2×D4×C113—21no—
163C2×D4×C113—21no—
164C2×D4×C113—21no—
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—81no—
173C2×D4×C113—81no—
174C2×D4×C113—81no—
175C2×D4×C113—81no—
176C2×D4×C113—81no—
177C2×D4×C113—81no—
178C2×D4×C113—81no—
179C2×D4×C113—81no—
180C2×D4×C113—81no—
181C2×D4×C113—81no—
182C2×D4×C113C2×D412yes—
183C2×D4×C113C2×D412yes—
184C2×D4×C113#4112yes—
185C22×C4×C113—21no—
186C22×C4×C113—21no—
187C22×C4×C113—21no—
188C22×C4×C113—24no—
189C22×C4×C113—24no—
190C22×C4×C113—21no—
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—42no—
199C22×C4×C113—81no—
200C22×C4×C113—81no—
201C22×C4×C113—81no—
202C22×C4×C113—81no—
203C22×C4×C113—81no—
204C22×C4×C113—81no—
205C22×C4×C113C2×D411yescharacteristic
206C22×C4×C113C2×D411yescharacteristic
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D411yescharacteristic
209C22×C4×C113C2×D411yescharacteristic
210C22×C4×C113C2411yescharacteristic
211D8×C113—44no—
212D8×C113—44no—
213C2×C8×C113—21no—
214C2×C8×C113—21no—
215C2×C8×C113—21no—
216C2×C8×C113—21no—
217C2×C8×C113—21no—
218C2×C8×C113—21no—
219C2×C8×C113—21no—
220C2×C8×C113—21no—
221C2×C8×C113—21no—
222C2×C8×C113—21no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C4⋊C4×C113—24no—
226C4⋊C4×C113—24no—
227C4⋊C4×C113—22no—
228C4⋊C4×C113—22no—
229C4⋊C4×C113—21no—
230C4⋊C4×C113—21no—
231C4⋊C4×C113—21no—
232C4⋊C4×C113—21no—
233C4⋊C4×C113—21no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—81no—
237C4⋊C4×C113C2×D412yes—
238C4⋊C4×C113C2×D412yes—
239C4⋊C4×C113#4112yes—
240C22⋊C4×C113—24no—
241C22⋊C4×C113—24no—
242C22⋊C4×C113—24no—
243C22⋊C4×C113—24no—
244C22⋊C4×C113—24no—
245C22⋊C4×C113—22no—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—42no—
248C22⋊C4×C113—81no—
249C22⋊C4×C113—81no—
250C22⋊C4×C113—81no—
251C42×C113—21no—
252C42×C113—21no—
253C42×C113—81no—
254C42×C113C2×D412yes—
255C42×C113C2×D412yes—
256C23×C113—21no—
257C23×C113—22no—
258C23×C113—22no—
259C23×C113—22no—
260C23×C113—21no—
261C23×C113—21no—
262C23×C113—21no—
263C23×C113—21no—
264C23×C113—21no—
265C23×C113—21no—
266C23×C113—41no—
267C23×C113—41no—
268C23×C113—41no—
269C23×C113—41no—
270C23×C113—41no—
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×C113C22×D411yescharacteristic
285D4×C113—22no—
286D4×C113—22no—
287D4×C113—22no—
288D4×C113—22no—
289D4×C113—22no—
290D4×C113—22no—
291D4×C113—41no—
292D4×C113—41no—
293D4×C113—41no—
294D4×C113—41no—
295D4×C113—41no—
296D4×C113—41no—
297D4×C113—84no—
298D4×C113—84no—
299D4×C113—84no—
300D4×C113—84no—
301D4×C113—84no—
302C2×C4×C113—21no—
303C2×C4×C113—21no—
304C2×C4×C113—21no—
305C2×C4×C113—21no—
306C2×C4×C113—21no—
307C2×C4×C113—21no—
308C2×C4×C113—21no—
309C2×C4×C113—22no—
310C2×C4×C113—22no—
311C2×C4×C113—21no—
312C2×C4×C113—22no—
313C2×C4×C113—21no—
314C2×C4×C113—21no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—21no—
318C2×C4×C113—41no—
319C2×C4×C113—41no—
320C2×C4×C113—41no—
321C2×C4×C113—41no—
322C2×C4×C113—41no—
323C2×C4×C113—41no—
324C2×C4×C113—41no—
325C2×C4×C113—41no—
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—84no—
335C2×C4×C113—84no—
336C2×C4×C113—84no—
337C2×C4×C113#12012yes—
338C2×C4×C113#12012yes—
339C2×C4×C113C22×D411yescharacteristic
340C2×C4×C113C22×D411yescharacteristic
341C2×C4×C113C2×#4111yescharacteristic
342C2×C4×C113C2×#4111yescharacteristic
343C2×C4×C113H(5,𝔽2)11yescharacteristic
344C2×C4×C1132−1+411yescharacteristic
345C8×C113—41no—
346C8×C113—41no—
347C8×C113—41no—
348C8×C113—41no—
349C22×C113—41no—
350C22×C113—42no—
351C22×C113—41no—
352C22×C113—42no—
353C22×C113—41no—
354C22×C113—42no—
355C22×C113—42no—
356C22×C113—42no—
357C22×C113—41no—
358C22×C113—41no—
359C22×C113—42no—
360C22×C113—41no—
361C22×C113—42no—
362C22×C113—42no—
363C22×C113—41no—
364C22×C113—42no—
365C22×C113—81no—
366C22×C113—81no—
367C22×C113—81no—
368C22×C113—81no—
369C22×C113—81no—
370C22×C113—81no—
371C22×C113—81no—
372C22×C113—81no—
373C22×C113—81no—
374C22×C113—81no—
375C22×C113—81no—
376C22×C113—81no—
377C22×C113C2×#12011yescharacteristic
378C22×C113#52511yescharacteristic
379C22×C113#53711yescharacteristic
380C22×C113#57611yescharacteristic
381C22×C113#57611yescharacteristic
382C22×C113#57611yescharacteristic
383C22×C113#57711yescharacteristic
384C4×C113—22no—
385C4×C113—22no—
386C4×C113—42no—
387C4×C113—41no—
388C4×C113—41no—
389C4×C113—42no—
390C4×C113—41no—
391C4×C113—42no—
392C4×C113—81no—
393C4×C113—81no—
394C4×C113#54611yescharacteristic
395C4×C113#54711yescharacteristic
396C4×C113#54811yescharacteristic
397C4×C113#55011yescharacteristic
398#24162C11311yesmaximal, characteristic, direct product factor, Sylow
399C2×C113—81no—
400C2×C113—82no—
401C2×C113—82no—
402C2×C113—82no—
403C2×C113#240711yescharacteristic
404C2×C113#300811yescharacteristic
405C2×C113#301211yescharacteristic
406C2×C113#311911yescharacteristic
407C2×C113#312211yescharacteristic
408C2×C113#325711yescharacteristic
409C2×C113#325911yescharacteristic
410C2×#540C2×C11311yescharacteristic, complemented
411C2×#478C2×C11311yescharacteristic, complemented
412C2×#459C2×C11311yescharacteristic, complemented
413#2324C2×C11311yescharacteristic, complemented
414#2034C2×C11311yescharacteristic, complemented
415#2033C2×C11311yescharacteristic, complemented
416#1999C2×C11311yescharacteristic, complemented
417#1999C2×C11311yescharacteristic, complemented
418#1989C2×C11311yescharacteristic, complemented
419#1982C2×C11311yescharacteristic, complemented
420#1879C2×C11311yescharacteristic, complemented
421#1879C2×C11311yescharacteristic, complemented
422#1864C2×C11311yescharacteristic, complemented
423#1862C2×C11311yescharacteristic, complemented
424#1798C2×C11311yescharacteristic, complemented
425C113#2416211yescharacteristic, direct product factor, Sylow
426C22×D8C22×C11311yescharacteristic
427C22×D8C22×C11311yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C11311yescharacteristic
431C2×#125C22×C11311yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C11311yescharacteristic
437C2×#121C22×C11311yescharacteristic
438C2×#121C22×C11311yescharacteristic
439C2×C4×D4C22×C11311yescharacteristic
440C2×C4×D4C22×C11311yescharacteristic
441C2×C4×D4C22×C11311yescharacteristic
442C2×#117C22×C11311yescharacteristic
443#478—24no—
444#459—24no—
445C2×#107C22×C11311yescharacteristic
446C2×#106C22×C11311yescharacteristic
447C2×C4⋊C8C22×C11311yescharacteristic
448C2×C4⋊C8C22×C11311yescharacteristic
449C2×#102C22×C11311yescharacteristic
450C2×#102C22×C11311yescharacteristic
451C2×#102C22×C11311yescharacteristic
452C2×#102C22×C11311yescharacteristic
453C2×#102C22×C11311yescharacteristic
454C2×#102C22×C11311yescharacteristic
455C2×#102C22×C11311yescharacteristic
456C2×#102C22×C11311yescharacteristic
457C2×C22⋊C8C22×C11311yescharacteristic
458C2×C22⋊C8C22×C11311yescharacteristic
459#390—21no—
460#390C22×C11311yescharacteristic
461#389C22×C11311yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C11311yescharacteristic
466C4×C4⋊C4C22×C11311yescharacteristic
467#340C22×C11311yescharacteristic
468#340C22×C11311yescharacteristic
469#340C22×C11311yescharacteristic
470#340C22×C11311yescharacteristic
471#336C22×C11311yescharacteristic
472#336C22×C11311yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C11311yescharacteristic
479C22×D4C23×C11311yescharacteristic
480C22×D4C23×C11311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C11311yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×D8—41no—
491C22×C8C23×C11311yescharacteristic
492C22×C8C23×C11311yescharacteristic
493C22×C8C23×C11311yescharacteristic
494C22×C8C23×C11311yescharacteristic
495#127—22no—
496#127D4×C11314yescomplemented
497#125—22no—
498#125D4×C11314yescomplemented
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C11311yescharacteristic
521C2×C4⋊C4D4×C11311yescharacteristic
522C2×C4⋊C4C23×C11311yescharacteristic
523C2×C4⋊C4C23×C11311yescharacteristic
524C2×C4⋊C4C23×C11311yescharacteristic
525C2×C4⋊C4C23×C11311yescharacteristic
526C2×C4⋊C4C23×C11311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C11311yescharacteristic
537C2×C22⋊C4D4×C11311yescharacteristic
538C2×C42—21no—
539C2×C42C23×C11311yescharacteristic
540C2×C42C23×C11311yescharacteristic
541#107—22no—
542#106—22no—
543C4⋊C8—22no—
544C4⋊C8—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—41no—
554C22⋊C8—41no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C11311yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C11312yes—
593C2×D4C2×D4×C11312yes—
594C2×D4#41×C11312yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C11311yescharacteristic
616C22×C4C2×D4×C11311yescharacteristic
617C22×C4C2×D4×C11311yescharacteristic
618C22×C4C2×D4×C11311yescharacteristic
619C22×C4C2×D4×C11311yescharacteristic
620C22×C4C24×C11311yescharacteristic
621D8—44no—
622D8—44no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C11312yes—
648C4⋊C4C2×D4×C11312yes—
649C4⋊C4#41×C11312yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C11312yes—
665C42C2×D4×C11312yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C11311yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C11312yes—
748C2×C4#120×C11312yes—
749C2×C4C22×D4×C11311yescharacteristic
750C2×C4C22×D4×C11311yescharacteristic
751C2×C4C2×#41×C11311yescharacteristic
752C2×C4C2×#41×C11311yescharacteristic
753C2×C4H(5,𝔽2)×C11311yescharacteristic
754C2×C42−1+4×C11311yescharacteristic
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C11311yescharacteristic
788C22#525×C11311yescharacteristic
789C22#537×C11311yescharacteristic
790C22#576×C11311yescharacteristic
791C22#576×C11311yescharacteristic
792C22#576×C11311yescharacteristic
793C22#577×C11311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4#546×C11311yescharacteristic
805C4#547×C11311yescharacteristic
806C4#548×C11311yescharacteristic
807C4#550×C11311yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C113×#240711yescharacteristic
813C2C113×#300811yescharacteristic
814C2C113×#301211yescharacteristic
815C2C113×#311911yescharacteristic
816C2C113×#312211yescharacteristic
817C2C113×#325711yescharacteristic
818C2C113×#325911yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×#117×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C113C2semidirect
2. C2×#478×C113C2semidirect
3. C2×#459×C113C2semidirect
4. C113×#2324C2semidirect
5. C113×#2034C2semidirect
6. C113×#2033C2semidirect
7. C113×#1999C2semidirect
8. C113×#1999C2semidirect
9. C113×#1989C2semidirect
10. C113×#1982C2semidirect
11. C113×#1879C2semidirect
12. C113×#1879C2semidirect
13. C113×#1864C2semidirect
14. C113×#1862C2semidirect
15. C113×#1798C2semidirect
86. #127×C113D4semidirect
88. #125×C113D4semidirect
398. #24162C113direct (N × H)
410. C2×#540C2×C113semidirect
411. C2×#478C2×C113semidirect
412. C2×#459C2×C113semidirect
413. #2324C2×C113semidirect
414. #2034C2×C113semidirect
415. #2033C2×C113semidirect
416. #1999C2×C113semidirect
417. #1999C2×C113semidirect
418. #1989C2×C113semidirect
419. #1982C2×C113semidirect
420. #1879C2×C113semidirect
421. #1879C2×C113semidirect
422. #1864C2×C113semidirect
423. #1862C2×C113semidirect
424. #1798C2×C113semidirect
425. C113#24162direct (N × H)
496. #127D4×C113semidirect
498. #125D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C1132
C2×#478×C1132
C2×#459×C1132
C113×#23242
C113×#20342
C113×#20332
C113×#19992
C113×#19892
C113×#19822
C113×#18792
C113×#18642
C113×#18622
C113×#17982
#24162113