Finite Group Databasebeta

← C113×#24142 #43292162

Subgroups — C113×#24142 #43292162

Order 28928.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3505C211yesmaximal, characteristic, complemented
2C113×#2626C211yesmaximal, characteristic, complemented
3C113×#2617C211yesmaximal, characteristic, complemented
4C113×#2321C211yesmaximal, characteristic, complemented
5C113×#2044C212yesmaximal, complemented
6C113×#2021C212yesmaximal, complemented
7C113×#1996C211yesmaximal, characteristic, complemented
8C113×#1964C211yesmaximal, characteristic, complemented
9C113×#1889C212yesmaximal, complemented
10C113×#1867C212yesmaximal, complemented
11C113×#1799C211yesmaximal, characteristic, complemented
12#553×C113—22no—
13#553×C113—21no—
14#552×C113—21no—
15#551×C113—22no—
16#548×C113—21no—
17#546×C113—21no—
18#539×C113—21no—
19#538×C113—21no—
20#534×C113C2212yes—
21#529×C113—21no—
22#525×C113—21no—
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×#120×C113C2211yescharacteristic
26C2×#120×C113C2212yes—
27#518×C113C2212yes—
28C2×C4×D4×C113C2211yescharacteristic
29C22×C22⋊C4×C113C2211yescharacteristic
30C2×#99×C113C2212yes—
31C2×#99×C113C2212yes—
32C2×#99×C113C2212yes—
33#399×C113—21no—
34#397×C113—21no—
35#396×C113—22no—
36#394×C113—22no—
37#393×C113—21no—
38#392×C113—21no—
39#390×C113—21no—
40#388×C113—21no—
41#388×C113—21no—
42#386×C113—21no—
43#386×C113C2211yescharacteristic
44#386×C113C2212yes—
45#385×C113C2212yes—
46#385×C113C2211yescharacteristic
47#380×C113C2211yescharacteristic
48#380×C113C2211yescharacteristic
49#379×C113C2212yes—
50#379×C113C2211yescharacteristic
51C4×C22⋊C4×C113C2211yescharacteristic
52#342×C113C2212yes—
53#342×C113C2212yes—
54#342×C113C2212yes—
55C25×C113C2311yescharacteristic
56C2×#41×C113—21no—
57C22×Q8×C113D411yescharacteristic, complemented
58C22×D4×C113—21no—
59C22×D4×C113—22no—
60C22×D4×C113D411yescharacteristic, complemented
61C22×D4×C113C2311yescharacteristic
62C22×D4×C113C2312yes—
63C23×C4×C113D411yescharacteristic, complemented
64C23×C4×C113C2311yescharacteristic
65C23×C4×C113C2311yescharacteristic
66#126×C113—22no—
67#126×C113—22no—
68#126×C113—22no—
69#125×C113—21no—
70#125×C113—22no—
71#124×C113—21no—
72#124×C113—22no—
73#123×C113—22no—
74#123×C113—22no—
75#123×C113—22no—
76#123×C113—22no—
77#123×C113—22no—
78C22⋊Q8×C113—21no—
79C22⋊Q8×C113—22no—
80C22⋊Q8×C113—21no—
81C22⋊Q8×C113—21no—
82C22⋊Q8×C113—21no—
83C22⋊Q8×C113—21no—
84#121×C113—21no—
85#121×C113—22no—
86#121×C113—21no—
87#121×C113—21no—
88#121×C113—21no—
89#121×C113—21no—
90#121×C113—22no—
91#121×C113—22no—
92#120×C113—22no—
93#120×C113—22no—
94#120×C113—22no—
95#120×C113—22no—
96#120×C113—24no—
97#120×C113—42no—
98C4×Q8×C113—21no—
99C4×D4×C113—22no—
100C4×D4×C113—21no—
101C4×D4×C113—21no—
102C4×D4×C113—21no—
103C4×D4×C113—21no—
104C4×D4×C113—21no—
105C4×D4×C113—22no—
106C4×D4×C113—22no—
107C4×D4×C113—22no—
108C4×D4×C113—22no—
109#117×C113—21no—
110#117×C113—22no—
111#117×C113—22no—
112C2×C4⋊C4×C113—21no—
113C2×C4⋊C4×C113—21no—
114C2×C4⋊C4×C113—21no—
115C2×C4⋊C4×C113—22no—
116C2×C4⋊C4×C113D411yescharacteristic, complemented
117C2×C4⋊C4×C113D411yescharacteristic, complemented
118C2×C4⋊C4×C113D412yescomplemented
119C2×C4⋊C4×C113D411yescharacteristic, complemented
120C2×C22⋊C4×C113—22no—
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×C113—21no—
128C2×C22⋊C4×C113—22no—
129C2×C22⋊C4×C113—21no—
130C2×C22⋊C4×C113—22no—
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—22no—
134C2×C22⋊C4×C113—22no—
135C2×C22⋊C4×C113D411yescharacteristic, complemented
136C2×C22⋊C4×C113D412yescomplemented
137C2×C22⋊C4×C113C2312yes—
138C2×C22⋊C4×C113C2311yescharacteristic
139C2×C22⋊C4×C113C2312yes—
140C2×C22⋊C4×C113C2311yescharacteristic
141C2×C22⋊C4×C113C2312yes—
142C2×C22⋊C4×C113C2311yescharacteristic
143C2×C42×C113—21no—
144C2×C42×C113D411yescharacteristic, complemented
145#99×C113—24no—
146#99×C113—42no—
147#99×C113—42no—
148#95×C113—21no—
149#95×C113—21no—
150#95×C113—21no—
151#95×C113—21no—
152#95×C113—22no—
153#95×C113—21no—
154#95×C113—22no—
155C24×C113—21no—
156C24×C113—21no—
157C24×C113—21no—
158C24×C113—21no—
159C24×C113—21no—
160C24×C113—21no—
161C24×C113—81no—
162C24×C113—81no—
163C24×C113C2×D412yes—
164C24×C113C2×D411yescharacteristic
165C24×C113#4112yescomplemented
166C24×C113C2411yescharacteristic
167#41×C113—82no—
168C2×Q8×C113—21no—
169C2×Q8×C113—21no—
170C2×Q8×C113—81no—
171C2×D4×C113—21no—
172C2×D4×C113—22no—
173C2×D4×C113—21no—
174C2×D4×C113—22no—
175C2×D4×C113—22no—
176C2×D4×C113—21no—
177C2×D4×C113—21no—
178C2×D4×C113—22no—
179C2×D4×C113—21no—
180C2×D4×C113—22no—
181C2×D4×C113—21no—
182C2×D4×C113—22no—
183C2×D4×C113—22no—
184C2×D4×C113—22no—
185C2×D4×C113—24no—
186C2×D4×C113—21no—
187C2×D4×C113—21no—
188C2×D4×C113—44no—
189C2×D4×C113—81no—
190C2×D4×C113—81no—
191C2×D4×C113—81no—
192C2×D4×C113—82no—
193C2×D4×C113—82no—
194C22×C4×C113—21no—
195C22×C4×C113—22no—
196C22×C4×C113—22no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—22no—
203C22×C4×C113—22no—
204C22×C4×C113—21no—
205C22×C4×C113—81no—
206C22×C4×C113—81no—
207C22×C4×C113—81no—
208C22×C4×C113C2×D411yescharacteristic
209C22×C4×C113C2×D412yes—
210C22×C4×C113C2×D411yescharacteristic
211C22×C4×C113C2×D412yes—
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D412yes—
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D411yescharacteristic
216C22×C4×C113C2×D411yescharacteristic
217C22×C4×C113C2×D411yescharacteristic
218C22×C4×C113C2×D411yescharacteristic
219C22×C4×C113C2×D411yescharacteristic
220C4⋊C4×C113—22no—
221C4⋊C4×C113—22no—
222C4⋊C4×C113—22no—
223C4⋊C4×C113—22no—
224C4⋊C4×C113—21no—
225C4⋊C4×C113—22no—
226C4⋊C4×C113—21no—
227C4⋊C4×C113—21no—
228C4⋊C4×C113—21no—
229C4⋊C4×C113—21no—
230C4⋊C4×C113—22no—
231C4⋊C4×C113—21no—
232C4⋊C4×C113—81no—
233C4⋊C4×C113—81no—
234C4⋊C4×C113—81no—
235C4⋊C4×C113—82no—
236C22⋊C4×C113—22no—
237C22⋊C4×C113—22no—
238C22⋊C4×C113—24no—
239C22⋊C4×C113—22no—
240C22⋊C4×C113—22no—
241C22⋊C4×C113—22no—
242C22⋊C4×C113—22no—
243C22⋊C4×C113—21no—
244C22⋊C4×C113—22no—
245C22⋊C4×C113—21no—
246C22⋊C4×C113—22no—
247C22⋊C4×C113—21no—
248C22⋊C4×C113—22no—
249C22⋊C4×C113—21no—
250C22⋊C4×C113—21no—
251C22⋊C4×C113—22no—
252C22⋊C4×C113—22no—
253C22⋊C4×C113—22no—
254C22⋊C4×C113—21no—
255C22⋊C4×C113—22no—
256C22⋊C4×C113—22no—
257C22⋊C4×C113—21no—
258C22⋊C4×C113—44no—
259C22⋊C4×C113—41no—
260C22⋊C4×C113—41no—
261C22⋊C4×C113—41no—
262C22⋊C4×C113—41no—
263C22⋊C4×C113—81no—
264C22⋊C4×C113—82no—
265C22⋊C4×C113—81no—
266C22⋊C4×C113—82no—
267C22⋊C4×C113—81no—
268C22⋊C4×C113—82no—
269C22⋊C4×C113#4112yescomplemented
270C42×C113—22no—
271C42×C113—22no—
272C42×C113—21no—
273C42×C113—21no—
274C42×C113—81no—
275C23×C113—21no—
276C23×C113—22no—
277C23×C113—22no—
278C23×C113—21no—
279C23×C113—22no—
280C23×C113—22no—
281C23×C113—21no—
282C23×C113—22no—
283C23×C113—22no—
284C23×C113—41no—
285C23×C113—41no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—42no—
289C23×C113—41no—
290C23×C113—42no—
291C23×C113—41no—
292C23×C113—41no—
293C23×C113—42no—
294C23×C113—41no—
295C23×C113—42no—
296C23×C113—42no—
297C23×C113—42no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113—41no—
302C23×C113—82no—
303C23×C113—82no—
304C23×C113—82no—
305C23×C113—82no—
306C23×C113C22×D411yescharacteristic
307C23×C113C22×D411yescharacteristic
308C23×C113C22×D411yescharacteristic
309C23×C113C2×#4111yescharacteristic
310C23×C113C2×#4111yescharacteristic
311C23×C113H(5,𝔽2)11yescharacteristic
312C23×C1132−1+411yescharacteristic
313Q8×C113—42no—
314Q8×C113—81no—
315D4×C113—42no—
316D4×C113—42no—
317D4×C113—42no—
318D4×C113—41no—
319D4×C113—41no—
320D4×C113—41no—
321D4×C113—42no—
322D4×C113—42no—
323D4×C113—41no—
324D4×C113—81no—
325D4×C113—82no—
326D4×C113—84no—
327D4×C113—82no—
328D4×C113—88no—
329C2×C4×C113—21no—
330C2×C4×C113—22no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—22no—
334C2×C4×C113—22no—
335C2×C4×C113—21no—
336C2×C4×C113—22no—
337C2×C4×C113—21no—
338C2×C4×C113—22no—
339C2×C4×C113—22no—
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—42no—
347C2×C4×C113—41no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—42no—
351C2×C4×C113—41no—
352C2×C4×C113—42no—
353C2×C4×C113—41no—
354C2×C4×C113—41no—
355C2×C4×C113—42no—
356C2×C4×C113—42no—
357C2×C4×C113—41no—
358C2×C4×C113—42no—
359C2×C4×C113—42no—
360C2×C4×C113—42no—
361C2×C4×C113—41no—
362C2×C4×C113—42no—
363C2×C4×C113—41no—
364C2×C4×C113—41no—
365C2×C4×C113—42no—
366C2×C4×C113—42no—
367C2×C4×C113—81no—
368C2×C4×C113—82no—
369C2×C4×C113—82no—
370C2×C4×C113#12011yescharacteristic
371C2×C4×C113#12011yescharacteristic
372C2×C4×C113#12011yescharacteristic
373C2×C4×C113#12011yescharacteristic
374C22×C113—21no—
375C22×C113—21no—
376C22×C113—21no—
377C22×C113—21no—
378C22×C113—21no—
379C22×C113—21no—
380C22×C113—41no—
381C22×C113—41no—
382C22×C113—41no—
383C22×C113—41no—
384C22×C113—42no—
385C22×C113—42no—
386C22×C113—44no—
387C22×C113—42no—
388C22×C113—44no—
389C22×C113—41no—
390C22×C113—42no—
391C22×C113—42no—
392C22×C113—41no—
393C22×C113—42no—
394C22×C113—42no—
395C22×C113—41no—
396C22×C113—82no—
397C22×C113—81no—
398C22×C113—82no—
399C22×C113—82no—
400C22×C113—81no—
401C22×C113—81no—
402C22×C113—82no—
403C22×C113—81no—
404C22×C113—81no—
405C22×C113C2×#12011yescharacteristic
406C22×C113#52511yescharacteristic
407C22×C113#53711yescharacteristic
408C22×C113#54611yescharacteristic
409C22×C113#54711yescharacteristic
410C22×C113#54811yescharacteristic
411C22×C113#55011yescharacteristic
412C4×C113—21no—
413C4×C113—21no—
414C4×C113—21no—
415C4×C113—21no—
416C4×C113—42no—
417C4×C113—41no—
418C4×C113—42no—
419C4×C113—41no—
420C4×C113—42no—
421C4×C113—41no—
422C4×C113—42no—
423C4×C113—82no—
424C4×C113—81no—
425C4×C113—82no—
426C4×C113—81no—
427#24142C11311yesmaximal, characteristic, direct product factor, Sylow
428C2×C113—21no—
429C2×C113—21no—
430C2×C113—21no—
431C2×C113—21no—
432C2×C113—21no—
433C2×C113—21no—
434C2×C113—82no—
435C2×C113—81no—
436C2×C113—82no—
437C2×C113#240711yescharacteristic
438C2×C113#302611yescharacteristic
439C2×C113#302711yescharacteristic
440#3505C2×C11311yescharacteristic, complemented
441#2626C2×C11311yescharacteristic, complemented
442#2617C2×C11311yescharacteristic, complemented
443#2321C2×C11311yescharacteristic, complemented
444#2044C2×C11312yescomplemented
445#2021C2×C11312yescomplemented
446#1996C2×C11311yescharacteristic, complemented
447#1964C2×C11311yescharacteristic, complemented
448#1889C2×C11312yescomplemented
449#1867C2×C11312yescomplemented
450#1799C2×C11311yescharacteristic, complemented
451C113#2414211yescharacteristic, direct product factor, Sylow
452#553—22no—
453#553—21no—
454#552—21no—
455#551—22no—
456#548—21no—
457#546—21no—
458#539—21no—
459#538—21no—
460#534C22×C11312yes—
461#529—21no—
462#525—21no—
463C2×C22⋊Q8C22×C11311yescharacteristic
464C2×#121C22×C11311yescharacteristic
465C2×#120C22×C11311yescharacteristic
466C2×#120C22×C11312yes—
467#518C22×C11312yes—
468C2×C4×D4C22×C11311yescharacteristic
469C22×C22⋊C4C22×C11311yescharacteristic
470C2×#99C22×C11312yes—
471C2×#99C22×C11312yes—
472C2×#99C22×C11312yes—
473#399—21no—
474#397—21no—
475#396—22no—
476#394—22no—
477#393—21no—
478#392—21no—
479#390—21no—
480#388—21no—
481#388—21no—
482#386—21no—
483#386C22×C11311yescharacteristic
484#386C22×C11312yes—
485#385C22×C11311yescharacteristic
486#385C22×C11312yes—
487#380C22×C11311yescharacteristic
488#380C22×C11311yescharacteristic
489#379C22×C11311yescharacteristic
490#379C22×C11312yes—
491C4×C22⋊C4C22×C11311yescharacteristic
492#342C22×C11312yes—
493#342C22×C11312yes—
494#342C22×C11312yes—
495C25C23×C11311yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C11311yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C11311yescharacteristic, complemented
501C22×D4C23×C11311yescharacteristic
502C22×D4C23×C11312yes—
503C23×C4D4×C11311yescharacteristic, complemented
504C23×C4C23×C11311yescharacteristic
505C23×C4C23×C11311yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C11311yescharacteristic, complemented
557C2×C4⋊C4D4×C11311yescharacteristic, complemented
558C2×C4⋊C4D4×C11312yescomplemented
559C2×C4⋊C4D4×C11311yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C11311yescharacteristic, complemented
576C2×C22⋊C4D4×C11312yescomplemented
577C2×C22⋊C4C23×C11312yes—
578C2×C22⋊C4C23×C11311yescharacteristic
579C2×C22⋊C4C23×C11312yes—
580C2×C22⋊C4C23×C11311yescharacteristic
581C2×C22⋊C4C23×C11312yes—
582C2×C22⋊C4C23×C11311yescharacteristic
583C2×C42—21no—
584C2×C42D4×C11311yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C11312yes—
604C24C2×D4×C11311yescharacteristic
605C24#41×C11312yescomplemented
606C24C24×C11311yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C11311yescharacteristic
649C22×C4C2×D4×C11312yes—
650C22×C4C2×D4×C11311yescharacteristic
651C22×C4C2×D4×C11312yes—
652C22×C4C2×D4×C11311yescharacteristic
653C22×C4C2×D4×C11312yes—
654C22×C4C2×D4×C11311yescharacteristic
655C22×C4C2×D4×C11311yescharacteristic
656C22×C4C2×D4×C11311yescharacteristic
657C22×C4C2×D4×C11311yescharacteristic
658C22×C4C2×D4×C11311yescharacteristic
659C22×C4C2×D4×C11311yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C11312yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C11311yescharacteristic
747C23C22×D4×C11311yescharacteristic
748C23C22×D4×C11311yescharacteristic
749C23C2×#41×C11311yescharacteristic
750C23C2×#41×C11311yescharacteristic
751C23H(5,𝔽2)×C11311yescharacteristic
752C232−1+4×C11311yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C11311yescharacteristic
811C2×C4#120×C11311yescharacteristic
812C2×C4#120×C11311yescharacteristic
813C2×C4#120×C11311yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C11311yescharacteristic
846C22#525×C11311yescharacteristic
847C22#537×C11311yescharacteristic
848C22#546×C11311yescharacteristic
849C22#547×C11311yescharacteristic
850C22#548×C11311yescharacteristic
851C22#550×C11311yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C113×#240711yescharacteristic
877C2C113×#302611yescharacteristic
878C2C113×#302711yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3505C2semidirect
2. C113×#2626C2semidirect
3. C113×#2617C2semidirect
4. C113×#2321C2semidirect
5. C113×#2044C2semidirect
6. C113×#2021C2semidirect
7. C113×#1996C2semidirect
8. C113×#1964C2semidirect
9. C113×#1889C2semidirect
10. C113×#1867C2semidirect
11. C113×#1799C2semidirect
57. C22×Q8×C113D4semidirect
60. C22×D4×C113D4semidirect
63. C23×C4×C113D4semidirect
116. C2×C4⋊C4×C113D4semidirect
117. C2×C4⋊C4×C113D4semidirect
118. C2×C4⋊C4×C113D4semidirect
119. C2×C4⋊C4×C113D4semidirect
135. C2×C22⋊C4×C113D4semidirect
136. C2×C22⋊C4×C113D4semidirect
144. C2×C42×C113D4semidirect
165. C24×C113#41semidirect
269. C22⋊C4×C113#41semidirect
427. #24142C113direct (N × H)
440. #3505C2×C113semidirect
441. #2626C2×C113semidirect
442. #2617C2×C113semidirect
443. #2321C2×C113semidirect
444. #2044C2×C113semidirect
445. #2021C2×C113semidirect
446. #1996C2×C113semidirect
447. #1964C2×C113semidirect
448. #1889C2×C113semidirect
449. #1867C2×C113semidirect
450. #1799C2×C113semidirect
451. C113#24142direct (N × H)
497. C22×Q8D4×C113semidirect
500. C22×D4D4×C113semidirect
503. C23×C4D4×C113semidirect
556. C2×C4⋊C4D4×C113semidirect
557. C2×C4⋊C4D4×C113semidirect
558. C2×C4⋊C4D4×C113semidirect
559. C2×C4⋊C4D4×C113semidirect
575. C2×C22⋊C4D4×C113semidirect
576. C2×C22⋊C4D4×C113semidirect
584. C2×C42D4×C113semidirect
605. C24#41×C113semidirect
709. C22⋊C4#41×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35052
C113×#26262
C113×#26172
C113×#23212
C113×#20442
C113×#20212
C113×#19962
C113×#19642
C113×#18892
C113×#18672
C113×#17992
#24142113