Finite Group Databasebeta

← C113×#18414 #43286434

Subgroups — C113×#18414 #43286434

Order 28928.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3534C211yesmaximal, characteristic, complemented
2C113×#3194C211yesmaximal, characteristic, complemented
3C113×#3186C211yesmaximal, characteristic, complemented
4C113×#2661C211yesmaximal, characteristic, complemented
5C113×#1612C211yesmaximal, characteristic, complemented
6C113×#1610C211yesmaximal, characteristic, complemented
7C113×#1609C211yesmaximal, characteristic, complemented
8C113×#1607C211yesmaximal, characteristic, complemented
9C113×#1600C211yesmaximal, characteristic, complemented
10C113×#1598C211yesmaximal, characteristic, complemented
11C113×#1597C211yesmaximal, characteristic, complemented
12C113×#1595C211yesmaximal, characteristic, complemented
13C113×#1507C211yesmaximal, characteristic, complemented
14C113×#1501C211yesmaximal, characteristic, complemented
15C113×#1468C211yesmaximal, characteristic, complemented
16#562×C113—21no—
17#560×C113—21no—
18#553×C113—21no—
19#551×C113—21no—
20#546×C113—21no—
21#546×C113—21no—
22#546×C113—21no—
23D42×C113—21no—
24#540×C113—21no—
25#539×C113—21no—
26#539×C113C2211yescharacteristic
27#538×C113—21no—
28#538×C113C2211yescharacteristic
29#537×C113C2211yescharacteristic
30#534×C113—21no—
31#534×C113C2211yescharacteristic
32#525×C113C2211yescharacteristic
33C2×#123×C113C2211yescharacteristic
34C2×#121×C113C2211yescharacteristic
35C2×#121×C113C2211yescharacteristic, complemented
36#483×C113C2211yescharacteristic, complemented
37#482×C113—21no—
38#480×C113—21no—
39#480×C113C2211yescharacteristic
40#480×C113C2211yescharacteristic, complemented
41#480×C113C2211yescharacteristic, complemented
42#469×C113—21no—
43#468×C113—21no—
44#466×C113—21no—
45#466×C113—21no—
46#450×C113C2211yescharacteristic, complemented
47#449×C113—21no—
48#447×C113—21no—
49#447×C113C2211yescharacteristic
50#447×C113C2211yescharacteristic, complemented
51#447×C113C2211yescharacteristic, complemented
52#407×C113C2211yescharacteristic, complemented
53C2×C22⋊C8×C113C2211yescharacteristic, complemented
54#398×C113C2211yescharacteristic, complemented
55#397×C113C2211yescharacteristic, complemented
56#394×C113—21no—
57#394×C113C2211yescharacteristic, complemented
58#392×C113—21no—
59#392×C113C2211yescharacteristic, complemented
60#390×C113—21no—
61#388×C113—21no—
62C4×C22⋊C4×C113C2211yescharacteristic, complemented
63#328×C113C2211yescharacteristic, complemented
64#328×C113C2211yescharacteristic, complemented
65#327×C113C2211yescharacteristic
66#327×C113C2211yescharacteristic
67#327×C113C2211yescharacteristic, complemented
68#327×C113C2211yescharacteristic, complemented
69#327×C113C2211yescharacteristic, complemented
70#327×C113C2211yescharacteristic, complemented
71#324×C113C2211yescharacteristic, complemented
72#324×C113C2211yescharacteristic, complemented
73#323×C113C2211yescharacteristic, complemented
74#323×C113C2211yescharacteristic, complemented
75C2×#41×C113—21no—
76C2×#41×C113D411yescharacteristic, complemented
77C22×D4×C113—21no—
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113D411yescharacteristic
83C22×D4×C113D411yescharacteristic, complemented
84C22×D4×C113C2311yescharacteristic
85C23×C4×C113C2311yescharacteristic
86C2×SD16×C113—21no—
87C2×D8×C113—21no—
88C2×D8×C113—21no—
89C2×D8×C113—21no—
90C2×M16×C113—21no—
91C22×C8×C113—21no—
92#127×C113—21no—
93#126×C113—21no—
94#126×C113—21no—
95#126×C113—21no—
96#126×C113—21no—
97#125×C113—21no—
98#125×C113—21no—
99#124×C113—21no—
100#124×C113—21no—
101#124×C113—21no—
102#123×C113—21no—
103#123×C113—21no—
104#123×C113—21no—
105#123×C113—21no—
106#123×C113—21no—
107#123×C113—21no—
108#123×C113—21no—
109#123×C113—21no—
110#123×C113—21no—
111#123×C113—21no—
112#123×C113—21no—
113#123×C113—21no—
114#123×C113—21no—
115#123×C113—21no—
116C22⋊Q8×C113—21no—
117C22⋊Q8×C113—21no—
118C22⋊Q8×C113—21no—
119C22⋊Q8×C113—21no—
120C22⋊Q8×C113—21no—
121C22⋊Q8×C113D411yescharacteristic, complemented
122C22⋊Q8×C113C2311yescharacteristic
123#121×C113—21no—
124#121×C113—21no—
125#121×C113—21no—
126#121×C113—21no—
127#121×C113—21no—
128#121×C113—21no—
129#121×C113—21no—
130#121×C113—21no—
131#121×C113—21no—
132#121×C113—21no—
133#121×C113—21no—
134#121×C113—21no—
135#121×C113—21no—
136#121×C113—21no—
137#121×C113—21no—
138#121×C113—21no—
139#121×C113—21no—
140#121×C113—21no—
141#121×C113—21no—
142#121×C113D411yescharacteristic, complemented
143#121×C113D411yescharacteristic, complemented
144#121×C113D411yescharacteristic, complemented
145#121×C113C2311yescharacteristic
146#121×C113C2311yescharacteristic
147#121×C113C2311yescharacteristic
148#120×C113—21no—
149#120×C113—21no—
150#120×C113—21no—
151#120×C113—21no—
152#120×C113—21no—
153#120×C113—21no—
154#120×C113—21no—
155#120×C113—21no—
156C4×D4×C113—21no—
157C4×D4×C113—21no—
158C4×D4×C113—21no—
159C4×D4×C113—21no—
160C4×D4×C113—21no—
161C4×D4×C113—21no—
162C4×D4×C113—21no—
163C4×D4×C113—21no—
164#117×C113—21no—
165#117×C113D411yescharacteristic, complemented
166C2×C4⋊C4×C113—21no—
167C2×C4⋊C4×C113D411yescharacteristic
168C2×C4⋊C4×C113D411yescharacteristic, complemented
169C2×C4⋊C4×C113C2311yescharacteristic
170C2×C4⋊C4×C113C2311yescharacteristic
171C2×C22⋊C4×C113—21no—
172C2×C22⋊C4×C113—21no—
173C2×C22⋊C4×C113—21no—
174C2×C22⋊C4×C113—21no—
175C2×C22⋊C4×C113—21no—
176C2×C22⋊C4×C113—21no—
177C2×C22⋊C4×C113—21no—
178C2×C22⋊C4×C113—21no—
179C2×C22⋊C4×C113—21no—
180C2×C22⋊C4×C113D411yescharacteristic
181C2×C22⋊C4×C113D411yescharacteristic
182C2×C22⋊C4×C113C2311yescharacteristic
183C2×C42×C113—21no—
184#107×C113—21no—
185#107×C113—21no—
186#107×C113—21no—
187#106×C113—21no—
188#103×C113—21no—
189#102×C113—21no—
190#102×C113—21no—
191#102×C113—21no—
192#102×C113—21no—
193#102×C113—21no—
194#102×C113—21no—
195#102×C113—21no—
196C22⋊C8×C113—21no—
197C22⋊C8×C113—21no—
198C22⋊C8×C113C2311yescharacteristic
199C22⋊C8×C113C2311yescharacteristic
200C22⋊C8×C113C2311yescharacteristic
201C22⋊C8×C113C2311yescharacteristic
202#95×C113—21no—
203#95×C113—21no—
204#95×C113C2311yescharacteristic
205#95×C113C2311yescharacteristic
206C24×C113—21no—
207C24×C113—21no—
208C24×C113—21no—
209C24×C113C2×D411yescharacteristic
210C24×C113C2×D411yescharacteristic
211#41×C113—81no—
212#41×C113—81no—
213#41×C113—81no—
214C2×Q8×C113—21no—
215C2×Q8×C113C2×D411yescharacteristic
216C2×D4×C113—21no—
217C2×D4×C113—21no—
218C2×D4×C113—21no—
219C2×D4×C113—21no—
220C2×D4×C113—21no—
221C2×D4×C113—21no—
222C2×D4×C113—21no—
223C2×D4×C113—21no—
224C2×D4×C113—21no—
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—21no—
228C2×D4×C113—21no—
229C2×D4×C113—21no—
230C2×D4×C113—21no—
231C2×D4×C113—21no—
232C2×D4×C113—21no—
233C2×D4×C113—21no—
234C2×D4×C113—21no—
235C2×D4×C113—42no—
236C2×D4×C113—41no—
237C2×D4×C113—41no—
238C2×D4×C113—81no—
239C2×D4×C113—81no—
240C2×D4×C113—81no—
241C2×D4×C113—81no—
242C2×D4×C113—81no—
243C2×D4×C113—81no—
244C2×D4×C113—81no—
245C2×D4×C113—81no—
246C2×D4×C113—81no—
247C2×D4×C113—81no—
248C2×D4×C113—81no—
249C2×D4×C113—82no—
250C2×D4×C113C2×D411yescharacteristic
251C2×D4×C113C2×D411yescharacteristic
252C2×D4×C113C2×D411yescharacteristic
253C22×C4×C113—21no—
254C22×C4×C113—21no—
255C22×C4×C113—21no—
256C22×C4×C113—21no—
257C22×C4×C113—21no—
258C22×C4×C113—21no—
259C22×C4×C113—21no—
260C22×C4×C113—21no—
261C22×C4×C113—21no—
262C22×C4×C113—21no—
263C22×C4×C113—81no—
264C22×C4×C113C2×D411yescharacteristic
265C22×C4×C113C2×D411yescharacteristic
266C22×C4×C113C2×D411yescharacteristic
267C22×C4×C113C2×D411yescharacteristic
268C22×C4×C113C2×D411yescharacteristic
269C22×C4×C113C2×D411yescharacteristic
270C22×C4×C113C2×D411yescharacteristic
271C22×C4×C113C2×D411yescharacteristic
272C22×C4×C113C2411yescharacteristic
273SD16×C113—81no—
274D8×C113—81no—
275D8×C113—81no—
276D8×C113—81no—
277M16×C113—81no—
278C2×C8×C113—21no—
279C2×C8×C113—21no—
280C2×C8×C113—21no—
281C2×C8×C113—21no—
282C2×C8×C113—81no—
283C4⋊C4×C113—21no—
284C4⋊C4×C113—21no—
285C4⋊C4×C113—21no—
286C4⋊C4×C113—21no—
287C4⋊C4×C113—21no—
288C4⋊C4×C113—21no—
289C4⋊C4×C113—21no—
290C4⋊C4×C113—21no—
291C4⋊C4×C113—21no—
292C4⋊C4×C113—21no—
293C4⋊C4×C113—21no—
294C4⋊C4×C113—21no—
295C4⋊C4×C113—21no—
296C4⋊C4×C113—21no—
297C4⋊C4×C113—21no—
298C4⋊C4×C113—81no—
299C4⋊C4×C113C2×D411yescharacteristic
300C4⋊C4×C113C2×D411yescharacteristic
301C4⋊C4×C113C2×D411yescharacteristic
302C4⋊C4×C113C2×D411yescharacteristic
303C22⋊C4×C113—21no—
304C22⋊C4×C113—21no—
305C22⋊C4×C113—21no—
306C22⋊C4×C113—21no—
307C22⋊C4×C113—21no—
308C22⋊C4×C113—21no—
309C22⋊C4×C113—21no—
310C22⋊C4×C113—21no—
311C22⋊C4×C113—21no—
312C22⋊C4×C113—21no—
313C22⋊C4×C113—21no—
314C22⋊C4×C113—21no—
315C22⋊C4×C113—21no—
316C22⋊C4×C113—21no—
317C22⋊C4×C113—21no—
318C22⋊C4×C113—21no—
319C22⋊C4×C113—21no—
320C22⋊C4×C113—21no—
321C22⋊C4×C113—21no—
322C22⋊C4×C113—21no—
323C22⋊C4×C113—21no—
324C22⋊C4×C113—21no—
325C22⋊C4×C113—21no—
326C22⋊C4×C113—21no—
327C22⋊C4×C113—21no—
328C22⋊C4×C113—42no—
329C22⋊C4×C113—42no—
330C22⋊C4×C113—41no—
331C22⋊C4×C113—41no—
332C22⋊C4×C113—81no—
333C22⋊C4×C113—81no—
334C22⋊C4×C113—81no—
335C42×C113—21no—
336C42×C113—21no—
337C42×C113—21no—
338C42×C113—81no—
339C23×C113—21no—
340C23×C113—21no—
341C23×C113—21no—
342C23×C113—21no—
343C23×C113—21no—
344C23×C113—21no—
345C23×C113—21no—
346C23×C113—21no—
347C23×C113—41no—
348C23×C113—41no—
349C23×C113—42no—
350C23×C113—41no—
351C23×C113—41no—
352C23×C113—41no—
353C23×C113—41no—
354C23×C113—41no—
355C23×C113—41no—
356C23×C113—41no—
357C23×C113—41no—
358C23×C113—41no—
359C23×C113—81no—
360C23×C113—81no—
361C23×C113—81no—
362C23×C113—81no—
363C23×C113—81no—
364C23×C113#12011yescharacteristic
365C23×C113#12011yescharacteristic
366C23×C113C22×D411yescharacteristic
367Q8×C113—41no—
368Q8×C113—81no—
369D4×C113—41no—
370D4×C113—41no—
371D4×C113—41no—
372D4×C113—41no—
373D4×C113—41no—
374D4×C113—41no—
375D4×C113—41no—
376D4×C113—42no—
377D4×C113—42no—
378D4×C113—41no—
379D4×C113—41no—
380D4×C113—41no—
381D4×C113—41no—
382D4×C113—41no—
383D4×C113—41no—
384D4×C113—81no—
385D4×C113—81no—
386D4×C113—81no—
387D4×C113—81no—
388D4×C113—81no—
389D4×C113—81no—
390D4×C113—81no—
391D4×C113—81no—
392D4×C113—81no—
393D4×C113—81no—
394D4×C113—81no—
395D4×C113—81no—
396D4×C113—84no—
397D4×C113—82no—
398D4×C113—82no—
399C2×C4×C113—22no—
400C2×C4×C113—21no—
401C2×C4×C113—21no—
402C2×C4×C113—21no—
403C2×C4×C113—21no—
404C2×C4×C113—21no—
405C2×C4×C113—21no—
406C2×C4×C113—21no—
407C2×C4×C113—21no—
408C2×C4×C113—21no—
409C2×C4×C113—21no—
410C2×C4×C113—41no—
411C2×C4×C113—41no—
412C2×C4×C113—41no—
413C2×C4×C113—41no—
414C2×C4×C113—41no—
415C2×C4×C113—41no—
416C2×C4×C113—41no—
417C2×C4×C113—41no—
418C2×C4×C113—41no—
419C2×C4×C113—41no—
420C2×C4×C113—41no—
421C2×C4×C113—41no—
422C2×C4×C113—41no—
423C2×C4×C113—41no—
424C2×C4×C113—41no—
425C2×C4×C113—41no—
426C2×C4×C113—81no—
427C2×C4×C113—81no—
428C2×C4×C113—81no—
429C2×C4×C113—81no—
430C2×C4×C113—81no—
431C2×C4×C113—81no—
432C2×C4×C113—81no—
433C2×C4×C113#12011yescharacteristic
434C2×C4×C113#12011yescharacteristic
435C2×C4×C113C22×D411yescharacteristic
436C2×C4×C113C22×D411yescharacteristic
437C8×C113—41no—
438C8×C113—41no—
439C8×C113—41no—
440C8×C113—41no—
441C22×C113—21no—
442C22×C113—21no—
443C22×C113—21no—
444C22×C113—21no—
445C22×C113—21no—
446C22×C113—21no—
447C22×C113—21no—
448C22×C113—21no—
449C22×C113—41no—
450C22×C113—41no—
451C22×C113—41no—
452C22×C113—41no—
453C22×C113—41no—
454C22×C113—41no—
455C22×C113—41no—
456C22×C113—41no—
457C22×C113—41no—
458C22×C113—41no—
459C22×C113—41no—
460C22×C113—41no—
461C22×C113—81no—
462C22×C113—81no—
463C22×C113—81no—
464C22×C113—81no—
465C22×C113—81no—
466C22×C113—81no—
467C22×C113—81no—
468C22×C113—81no—
469C22×C113—81no—
470C22×C113—81no—
471C22×C113—81no—
472C22×C113—162no—
473C22×C113—162no—
474C22×C113C2×#12011yescharacteristic
475C22×C113#57611yescharacteristic
476C22×C113#57611yescharacteristic
477C4×C113—21no—
478C4×C113—21no—
479C4×C113—21no—
480C4×C113—21no—
481C4×C113—42no—
482C4×C113—41no—
483C4×C113—41no—
484C4×C113—41no—
485C4×C113—41no—
486C4×C113—41no—
487C4×C113—41no—
488C4×C113—41no—
489C4×C113—41no—
490C4×C113—81no—
491C4×C113—81no—
492#18414C11311yesmaximal, characteristic, direct product factor, Sylow
493C2×C113—21no—
494C2×C113—21no—
495C2×C113—41no—
496C2×C113—41no—
497C2×C113—81no—
498C2×C113—81no—
499C2×C113—81no—
500C2×C113—81no—
501C2×C113—161no—
502C2×C113#300811yescharacteristic
503C2×C113#301811yescharacteristic
504C2×C113#302611yescharacteristic
505#3534C2×C11311yescharacteristic, complemented
506#3194C2×C11311yescharacteristic, complemented
507#3186C2×C11311yescharacteristic, complemented
508#2661C2×C11311yescharacteristic, complemented
509#1612C2×C11311yescharacteristic, complemented
510#1610C2×C11311yescharacteristic, complemented
511#1609C2×C11311yescharacteristic, complemented
512#1607C2×C11311yescharacteristic, complemented
513#1600C2×C11311yescharacteristic, complemented
514#1598C2×C11311yescharacteristic, complemented
515#1597C2×C11311yescharacteristic, complemented
516#1595C2×C11311yescharacteristic, complemented
517#1507C2×C11311yescharacteristic, complemented
518#1501C2×C11311yescharacteristic, complemented
519#1468C2×C11311yescharacteristic, complemented
520C113#1841411yescharacteristic, direct product factor, Sylow
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C11311yescharacteristic
532#538—21no—
533#538C22×C11311yescharacteristic
534#537C22×C11311yescharacteristic
535#534—21no—
536#534C22×C11311yescharacteristic
537#525C22×C11311yescharacteristic
538C2×#123C22×C11311yescharacteristic
539C2×#121C22×C11311yescharacteristic
540C2×#121C22×C11311yescharacteristic, complemented
541#483C22×C11311yescharacteristic, complemented
542#482—21no—
543#480—21no—
544#480C22×C11311yescharacteristic
545#480C22×C11311yescharacteristic, complemented
546#480C22×C11311yescharacteristic, complemented
547#469—21no—
548#468—21no—
549#466—21no—
550#466—21no—
551#450C22×C11311yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C11311yescharacteristic
555#447C22×C11311yescharacteristic, complemented
556#447C22×C11311yescharacteristic, complemented
557#407C22×C11311yescharacteristic, complemented
558C2×C22⋊C8C22×C11311yescharacteristic, complemented
559#398C22×C11311yescharacteristic, complemented
560#397C22×C11311yescharacteristic, complemented
561#394—21no—
562#394C22×C11311yescharacteristic, complemented
563#392—21no—
564#392C22×C11311yescharacteristic, complemented
565#390—21no—
566#388—21no—
567C4×C22⋊C4C22×C11311yescharacteristic, complemented
568#328C22×C11311yescharacteristic, complemented
569#328C22×C11311yescharacteristic, complemented
570#327C22×C11311yescharacteristic
571#327C22×C11311yescharacteristic
572#327C22×C11311yescharacteristic, complemented
573#327C22×C11311yescharacteristic, complemented
574#327C22×C11311yescharacteristic, complemented
575#327C22×C11311yescharacteristic, complemented
576#324C22×C11311yescharacteristic, complemented
577#324C22×C11311yescharacteristic, complemented
578#323C22×C11311yescharacteristic, complemented
579#323C22×C11311yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C11311yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C11311yescharacteristic
588C22×D4D4×C11311yescharacteristic, complemented
589C22×D4C23×C11311yescharacteristic
590C23×C4C23×C11311yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C11311yescharacteristic, complemented
627C22⋊Q8C23×C11311yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C11311yescharacteristic, complemented
648#121D4×C11311yescharacteristic, complemented
649#121D4×C11311yescharacteristic, complemented
650#121C23×C11311yescharacteristic
651#121C23×C11311yescharacteristic
652#121C23×C11311yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C11311yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C11311yescharacteristic
673C2×C4⋊C4D4×C11311yescharacteristic, complemented
674C2×C4⋊C4C23×C11311yescharacteristic
675C2×C4⋊C4C23×C11311yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C11311yescharacteristic
686C2×C22⋊C4D4×C11311yescharacteristic
687C2×C22⋊C4C23×C11311yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C11311yescharacteristic
704C22⋊C8C23×C11311yescharacteristic
705C22⋊C8C23×C11311yescharacteristic
706C22⋊C8C23×C11311yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C11311yescharacteristic
710#95C23×C11311yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C11311yescharacteristic
715C24C2×D4×C11311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C11311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C11311yescharacteristic
756C2×D4C2×D4×C11311yescharacteristic
757C2×D4C2×D4×C11311yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C11311yescharacteristic
770C22×C4C2×D4×C11311yescharacteristic
771C22×C4C2×D4×C11311yescharacteristic
772C22×C4C2×D4×C11311yescharacteristic
773C22×C4C2×D4×C11311yescharacteristic
774C22×C4C2×D4×C11311yescharacteristic
775C22×C4C2×D4×C11311yescharacteristic
776C22×C4C2×D4×C11311yescharacteristic
777C22×C4C24×C11311yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C11311yescharacteristic
805C4⋊C4C2×D4×C11311yescharacteristic
806C4⋊C4C2×D4×C11311yescharacteristic
807C4⋊C4C2×D4×C11311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C11311yescharacteristic
870C23#120×C11311yescharacteristic
871C23C22×D4×C11311yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C11311yescharacteristic
939C2×C4#120×C11311yescharacteristic
940C2×C4C22×D4×C11311yescharacteristic
941C2×C4C22×D4×C11311yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C11311yescharacteristic
980C22#576×C11311yescharacteristic
981C22#576×C11311yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C113×#300811yescharacteristic
1007C2C113×#301811yescharacteristic
1008C2C113×#302611yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3534C2semidirect
2. C113×#3194C2semidirect
3. C113×#3186C2semidirect
4. C113×#2661C2semidirect
5. C113×#1612C2semidirect
6. C113×#1610C2semidirect
7. C113×#1609C2semidirect
8. C113×#1607C2semidirect
9. C113×#1600C2semidirect
10. C113×#1598C2semidirect
11. C113×#1597C2semidirect
12. C113×#1595C2semidirect
13. C113×#1507C2semidirect
14. C113×#1501C2semidirect
15. C113×#1468C2semidirect
35. C2×#121×C113C22semidirect
36. #483×C113C22semidirect
40. #480×C113C22semidirect
41. #480×C113C22semidirect
46. #450×C113C22semidirect
50. #447×C113C22semidirect
51. #447×C113C22semidirect
52. #407×C113C22semidirect
53. C2×C22⋊C8×C113C22semidirect
54. #398×C113C22semidirect
55. #397×C113C22semidirect
57. #394×C113C22semidirect
59. #392×C113C22semidirect
62. C4×C22⋊C4×C113C22semidirect
63. #328×C113C22semidirect
64. #328×C113C22semidirect
67. #327×C113C22semidirect
68. #327×C113C22semidirect
69. #327×C113C22semidirect
70. #327×C113C22semidirect
71. #324×C113C22semidirect
72. #324×C113C22semidirect
73. #323×C113C22semidirect
74. #323×C113C22semidirect
76. C2×#41×C113D4semidirect
83. C22×D4×C113D4semidirect
121. C22⋊Q8×C113D4semidirect
142. #121×C113D4semidirect
143. #121×C113D4semidirect
144. #121×C113D4semidirect
165. #117×C113D4semidirect
168. C2×C4⋊C4×C113D4semidirect
492. #18414C113direct (N × H)
505. #3534C2×C113semidirect
506. #3194C2×C113semidirect
507. #3186C2×C113semidirect
508. #2661C2×C113semidirect
509. #1612C2×C113semidirect
510. #1610C2×C113semidirect
511. #1609C2×C113semidirect
512. #1607C2×C113semidirect
513. #1600C2×C113semidirect
514. #1598C2×C113semidirect
515. #1597C2×C113semidirect
516. #1595C2×C113semidirect
517. #1507C2×C113semidirect
518. #1501C2×C113semidirect
519. #1468C2×C113semidirect
520. C113#18414direct (N × H)
540. C2×#121C22×C113semidirect
541. #483C22×C113semidirect
545. #480C22×C113semidirect
546. #480C22×C113semidirect
551. #450C22×C113semidirect
555. #447C22×C113semidirect
556. #447C22×C113semidirect
557. #407C22×C113semidirect
558. C2×C22⋊C8C22×C113semidirect
559. #398C22×C113semidirect
560. #397C22×C113semidirect
562. #394C22×C113semidirect
564. #392C22×C113semidirect
567. C4×C22⋊C4C22×C113semidirect
568. #328C22×C113semidirect
569. #328C22×C113semidirect
572. #327C22×C113semidirect
573. #327C22×C113semidirect
574. #327C22×C113semidirect
575. #327C22×C113semidirect
576. #324C22×C113semidirect
577. #324C22×C113semidirect
578. #323C22×C113semidirect
579. #323C22×C113semidirect
581. C2×#41D4×C113semidirect
588. C22×D4D4×C113semidirect
626. C22⋊Q8D4×C113semidirect
647. #121D4×C113semidirect
648. #121D4×C113semidirect
649. #121D4×C113semidirect
670. #117D4×C113semidirect
673. C2×C4⋊C4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35342
C113×#31942
C113×#31862
C113×#26612
C113×#16122
C113×#16102
C113×#16092
C113×#16072
C113×#16002
C113×#15982
C113×#15972
C113×#15952
C113×#15072
C113×#15012
C113×#14682
#18414113