Finite Group Databasebeta

← C113×#18262 #43286282

Subgroups — C113×#18262 #43286282

Order 28928.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3534C211yesmaximal, characteristic
2C113×#3094C211yesmaximal, characteristic, complemented
3C113×#3091C211yesmaximal, characteristic, complemented
4C113×#2498C211yesmaximal, characteristic, complemented
5C113×#1618C211yesmaximal, characteristic, complemented
6C113×#1616C211yesmaximal, characteristic, complemented
7C113×#1615C211yesmaximal, characteristic, complemented
8C113×#1613C211yesmaximal, characteristic, complemented
9C113×#1612C211yesmaximal, characteristic, complemented
10C113×#1610C211yesmaximal, characteristic, complemented
11C113×#1609C211yesmaximal, characteristic, complemented
12C113×#1607C211yesmaximal, characteristic, complemented
13C113×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C113C211yesmaximal, 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×#117×C113C2211yescharacteristic, complemented
36#485×C113—21no—
37#484×C113C2211yescharacteristic, complemented
38#483×C113C2211yescharacteristic, complemented
39#482×C113—21no—
40#482×C113—21no—
41#482×C113—21no—
42#481×C113C2211yescharacteristic
43#481×C113C2211yescharacteristic, complemented
44#481×C113C2211yescharacteristic, complemented
45#480×C113C2211yescharacteristic
46#480×C113C2211yescharacteristic, complemented
47#480×C113C2211yescharacteristic, complemented
48#428×C113—21no—
49#427×C113—21no—
50#418×C113—21no—
51#416×C113—21no—
52#407×C113C2211yescharacteristic, complemented
53C2×C22⋊C8×C113C2211yescharacteristic, complemented
54#400×C113C2211yescharacteristic, complemented
55#399×C113C2211yescharacteristic, complemented
56#398×C113C2211yescharacteristic, complemented
57#397×C113C2211yescharacteristic, complemented
58#388×C113—21no—
59#387×C113—21no—
60#386×C113—21no—
61#380×C113—21no—
62C2×#95×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
77C22×D4×C113—21no—
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113D411yescharacteristic
81C22×D4×C113D411yescharacteristic
82C23×C4×C113—21no—
83C23×C4×C113C2311yescharacteristic
84C2×M16×C113—21no—
85C22×C8×C113—21no—
86#127×C113—21no—
87#126×C113—21no—
88#126×C113—21no—
89#126×C113—21no—
90#126×C113—21no—
91#125×C113—21no—
92#125×C113—21no—
93#124×C113—21no—
94#124×C113—21no—
95#124×C113—21no—
96#123×C113—21no—
97#123×C113—21no—
98#123×C113—21no—
99#123×C113—21no—
100#123×C113—21no—
101#123×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—
110C22⋊Q8×C113—21no—
111C22⋊Q8×C113—21no—
112C22⋊Q8×C113—21no—
113C22⋊Q8×C113—21no—
114C22⋊Q8×C113—21no—
115C22⋊Q8×C113D411yescharacteristic
116C22⋊Q8×C113C2311yescharacteristic
117#121×C113—21no—
118#121×C113—21no—
119#121×C113—21no—
120#121×C113—21no—
121#121×C113—21no—
122#121×C113—21no—
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×C113D411yescharacteristic
133#121×C113D411yescharacteristic
134#121×C113D411yescharacteristic
135#121×C113C2311yescharacteristic
136#121×C113C2311yescharacteristic
137#121×C113C2311yescharacteristic
138#120×C113—21no—
139#120×C113—21no—
140#120×C113—21no—
141#120×C113—21no—
142#120×C113—21no—
143#120×C113—21no—
144#120×C113—21no—
145#120×C113—21no—
146C4×D4×C113—21no—
147C4×D4×C113—21no—
148C4×D4×C113—21no—
149C4×D4×C113—21no—
150C4×D4×C113—21no—
151C4×D4×C113—21no—
152C4×D4×C113—21no—
153C4×D4×C113—21no—
154#117×C113—21no—
155#117×C113—21no—
156#117×C113—21no—
157#117×C113—21no—
158#117×C113—21no—
159#117×C113D411yescharacteristic
160C2×C4⋊C4×C113—21no—
161C2×C4⋊C4×C113—21no—
162C2×C4⋊C4×C113D411yescharacteristic
163C2×C4⋊C4×C113D411yescharacteristic
164C2×C4⋊C4×C113C2311yescharacteristic
165C2×C4⋊C4×C113C2311yescharacteristic
166C2×C4⋊C4×C113C2311yescharacteristic
167C2×C22⋊C4×C113—21no—
168C2×C22⋊C4×C113—21no—
169C2×C22⋊C4×C113—21no—
170C2×C22⋊C4×C113—21no—
171C2×C22⋊C4×C113—21no—
172C2×C22⋊C4×C113—21no—
173C2×C22⋊C4×C113D411yescharacteristic
174C2×C22⋊C4×C113D411yescharacteristic
175C2×C22⋊C4×C113C2311yescharacteristic
176C2×C42×C113—21no—
177#107×C113—21no—
178#107×C113—21no—
179#107×C113—21no—
180#107×C113—21no—
181#106×C113—21no—
182#106×C113—21no—
183#106×C113—21no—
184#106×C113—21no—
185#103×C113—21no—
186#103×C113—21no—
187#102×C113—21no—
188#102×C113—21no—
189#102×C113—21no—
190#102×C113—21no—
191#102×C113—21no—
192#102×C113—21no—
193C22⋊C8×C113—21no—
194C22⋊C8×C113—21no—
195C22⋊C8×C113C2311yescharacteristic
196C22⋊C8×C113C2311yescharacteristic
197C22⋊C8×C113C2311yescharacteristic
198C22⋊C8×C113C2311yescharacteristic
199#95×C113—21no—
200#95×C113—21no—
201#95×C113—21no—
202#95×C113—21no—
203#95×C113—21no—
204#95×C113C2311yescharacteristic
205#95×C113C2311yescharacteristic
206C24×C113—21no—
207C24×C113—21no—
208C24×C113C2×D411yescharacteristic
209C24×C113C2×D411yescharacteristic
210#41×C113—42no—
211#41×C113—81no—
212#41×C113—81no—
213C2×Q8×C113—21no—
214C2×Q8×C113C2×D411yescharacteristic
215C2×D4×C113—21no—
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—42no—
233C2×D4×C113—42no—
234C2×D4×C113—81no—
235C2×D4×C113—81no—
236C2×D4×C113—81no—
237C2×D4×C113—81no—
238C2×D4×C113—82no—
239C2×D4×C113C2×D411yescharacteristic
240C2×D4×C113C2×D411yescharacteristic
241C2×D4×C113C2×D411yescharacteristic
242C22×C4×C113—21no—
243C22×C4×C113—21no—
244C22×C4×C113—21no—
245C22×C4×C113—21no—
246C22×C4×C113—21no—
247C22×C4×C113—21no—
248C22×C4×C113—21no—
249C22×C4×C113—21no—
250C22×C4×C113—21no—
251C22×C4×C113—21no—
252C22×C4×C113—21no—
253C22×C4×C113—42no—
254C22×C4×C113—42no—
255C22×C4×C113—42no—
256C22×C4×C113—81no—
257C22×C4×C113C2×D411yescharacteristic
258C22×C4×C113C2×D411yescharacteristic
259C22×C4×C113C2×D411yescharacteristic
260C22×C4×C113C2×D411yescharacteristic
261C22×C4×C113C2×D411yescharacteristic
262C22×C4×C113C2×D411yescharacteristic
263C22×C4×C113C2×D411yescharacteristic
264C22×C4×C113C2×D411yescharacteristic
265C22×C4×C113C2411yescharacteristic
266M16×C113—42no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—21no—
270C2×C8×C113—21no—
271C2×C8×C113—42no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—21no—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
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—42no—
290C4⋊C4×C113—81no—
291C4⋊C4×C113C2×D411yescharacteristic
292C4⋊C4×C113C2×D411yescharacteristic
293C4⋊C4×C113C2×D411yescharacteristic
294C4⋊C4×C113C2×D411yescharacteristic
295C22⋊C4×C113—21no—
296C22⋊C4×C113—21no—
297C22⋊C4×C113—21no—
298C22⋊C4×C113—21no—
299C22⋊C4×C113—21no—
300C22⋊C4×C113—21no—
301C22⋊C4×C113—21no—
302C22⋊C4×C113—21no—
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—42no—
321C22⋊C4×C113—41no—
322C22⋊C4×C113—41no—
323C22⋊C4×C113—81no—
324C42×C113—21no—
325C42×C113—21no—
326C42×C113—21no—
327C42×C113—41no—
328C42×C113—41no—
329C23×C113—21no—
330C23×C113—21no—
331C23×C113—22no—
332C23×C113—21no—
333C23×C113—21no—
334C23×C113—21no—
335C23×C113—21no—
336C23×C113—21no—
337C23×C113—21no—
338C23×C113—41no—
339C23×C113—41no—
340C23×C113—41no—
341C23×C113—42no—
342C23×C113—81no—
343C23×C113—81no—
344C23×C113—81no—
345C23×C113—81no—
346C23×C113—81no—
347C23×C113#12011yescharacteristic
348C23×C113#12011yescharacteristic
349C23×C113C22×D411yescharacteristic
350Q8×C113—41no—
351Q8×C113—81no—
352D4×C113—41no—
353D4×C113—41no—
354D4×C113—41no—
355D4×C113—41no—
356D4×C113—41no—
357D4×C113—41no—
358D4×C113—41no—
359D4×C113—41no—
360D4×C113—41no—
361D4×C113—42no—
362D4×C113—42no—
363D4×C113—81no—
364D4×C113—81no—
365D4×C113—81no—
366D4×C113—81no—
367D4×C113—81no—
368D4×C113—81no—
369D4×C113—81no—
370D4×C113—81no—
371D4×C113—81no—
372D4×C113—81no—
373D4×C113—81no—
374D4×C113—81no—
375C2×C4×C113—22no—
376C2×C4×C113—22no—
377C2×C4×C113—22no—
378C2×C4×C113—21no—
379C2×C4×C113—21no—
380C2×C4×C113—21no—
381C2×C4×C113—21no—
382C2×C4×C113—21no—
383C2×C4×C113—21no—
384C2×C4×C113—21no—
385C2×C4×C113—21no—
386C2×C4×C113—21no—
387C2×C4×C113—21no—
388C2×C4×C113—41no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—41no—
393C2×C4×C113—41no—
394C2×C4×C113—41no—
395C2×C4×C113—41no—
396C2×C4×C113—41no—
397C2×C4×C113—41no—
398C2×C4×C113—41no—
399C2×C4×C113—41no—
400C2×C4×C113—41no—
401C2×C4×C113—41no—
402C2×C4×C113—41no—
403C2×C4×C113—41no—
404C2×C4×C113—41no—
405C2×C4×C113—81no—
406C2×C4×C113—81no—
407C2×C4×C113—81no—
408C2×C4×C113—81no—
409C2×C4×C113—81no—
410C2×C4×C113—81no—
411C2×C4×C113—81no—
412C2×C4×C113—84no—
413C2×C4×C113#12011yescharacteristic
414C2×C4×C113#12011yescharacteristic
415C2×C4×C113C22×D411yescharacteristic
416C2×C4×C113C22×D411yescharacteristic
417C8×C113—41no—
418C8×C113—41no—
419C8×C113—41no—
420C8×C113—41no—
421C22×C113—21no—
422C22×C113—21no—
423C22×C113—21no—
424C22×C113—21no—
425C22×C113—21no—
426C22×C113—21no—
427C22×C113—21no—
428C22×C113—42no—
429C22×C113—42no—
430C22×C113—41no—
431C22×C113—41no—
432C22×C113—41no—
433C22×C113—41no—
434C22×C113—41no—
435C22×C113—41no—
436C22×C113—41no—
437C22×C113—41no—
438C22×C113—41no—
439C22×C113—41no—
440C22×C113—41no—
441C22×C113—41no—
442C22×C113—81no—
443C22×C113—81no—
444C22×C113—162no—
445C22×C113—162no—
446C22×C113#45812yes—
447C22×C113C2×#12011yescharacteristic
448C22×C113#57611yescharacteristic
449C22×C113#57711yescharacteristic
450C4×C113—21no—
451C4×C113—21no—
452C4×C113—21no—
453C4×C113—21no—
454C4×C113—42no—
455C4×C113—41no—
456C4×C113—41no—
457C4×C113—41no—
458C4×C113—41no—
459C4×C113—41no—
460C4×C113—41no—
461C4×C113—41no—
462C4×C113—41no—
463C4×C113—81no—
464C4×C113—81no—
465C4×C113—81no—
466#18262C11311yesmaximal, characteristic, direct product factor, Sylow
467C2×C113—21no—
468C2×C113—21no—
469C2×C113—22no—
470C2×C113—41no—
471C2×C113—81no—
472C2×C113—81no—
473C2×C113—81no—
474C2×C113—81no—
475C2×C113#301211yescharacteristic
476C2×C113#301811yescharacteristic
477C2×C113C2×#45811yescharacteristic
478#3534C2×C11311yescharacteristic
479#3094C2×C11311yescharacteristic, complemented
480#3091C2×C11311yescharacteristic, complemented
481#2498C2×C11311yescharacteristic, complemented
482#1618C2×C11311yescharacteristic, complemented
483#1616C2×C11311yescharacteristic, complemented
484#1615C2×C11311yescharacteristic, complemented
485#1613C2×C11311yescharacteristic, complemented
486#1612C2×C11311yescharacteristic, complemented
487#1610C2×C11311yescharacteristic, complemented
488#1609C2×C11311yescharacteristic, complemented
489#1607C2×C11311yescharacteristic, complemented
490#1504C2×C11311yescharacteristic, complemented
491C2×#327C2×C11311yescharacteristic, complemented
492#1468C2×C11311yescharacteristic, complemented
493C113#1826211yescharacteristic, direct product factor, Sylow
494#562—21no—
495#560—21no—
496#553—21no—
497#551—21no—
498#546—21no—
499#546—21no—
500#546—21no—
501D42—21no—
502#540—21no—
503#539—21no—
504#539C22×C11311yescharacteristic
505#538—21no—
506#538C22×C11311yescharacteristic
507#537C22×C11311yescharacteristic
508#534—21no—
509#534C22×C11311yescharacteristic
510#525C22×C11311yescharacteristic
511C2×#123C22×C11311yescharacteristic
512C2×#121C22×C11311yescharacteristic
513C2×#117C22×C11311yescharacteristic, complemented
514#485—21no—
515#484C22×C11311yescharacteristic, complemented
516#483C22×C11311yescharacteristic, complemented
517#482—21no—
518#482—21no—
519#482—21no—
520#481C22×C11311yescharacteristic
521#481C22×C11311yescharacteristic, complemented
522#481C22×C11311yescharacteristic, complemented
523#480C22×C11311yescharacteristic
524#480C22×C11311yescharacteristic, complemented
525#480C22×C11311yescharacteristic, complemented
526#428—21no—
527#427—21no—
528#418—21no—
529#416—21no—
530#407C22×C11311yescharacteristic, complemented
531C2×C22⋊C8C22×C11311yescharacteristic, complemented
532#400C22×C11311yescharacteristic, complemented
533#399C22×C11311yescharacteristic, complemented
534#398C22×C11311yescharacteristic, complemented
535#397C22×C11311yescharacteristic, complemented
536#388—21no—
537#387—21no—
538#386—21no—
539#380—21no—
540C2×#95C22×C11311yescharacteristic, complemented
541#328C22×C11311yescharacteristic, complemented
542#328C22×C11311yescharacteristic, complemented
543#327C22×C11311yescharacteristic
544#327C22×C11311yescharacteristic
545#327C22×C11311yescharacteristic, complemented
546#327C22×C11311yescharacteristic, complemented
547#327C22×C11311yescharacteristic, complemented
548#327C22×C11311yescharacteristic, complemented
549#324C22×C11311yescharacteristic, complemented
550#324C22×C11311yescharacteristic, complemented
551#323C22×C11311yescharacteristic, complemented
552#323C22×C11311yescharacteristic, complemented
553C2×#41—21no—
554C2×#41D4×C11311yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C11311yescharacteristic
559C22×D4D4×C11311yescharacteristic
560C23×C4—21no—
561C23×C4C23×C11311yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C11311yescharacteristic
594C22⋊Q8C23×C11311yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C11311yescharacteristic
611#121D4×C11311yescharacteristic
612#121D4×C11311yescharacteristic
613#121C23×C11311yescharacteristic
614#121C23×C11311yescharacteristic
615#121C23×C11311yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C11311yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C11311yescharacteristic
641C2×C4⋊C4D4×C11311yescharacteristic
642C2×C4⋊C4C23×C11311yescharacteristic
643C2×C4⋊C4C23×C11311yescharacteristic
644C2×C4⋊C4C23×C11311yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C11311yescharacteristic
652C2×C22⋊C4D4×C11311yescharacteristic
653C2×C22⋊C4C23×C11311yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C11311yescharacteristic
674C22⋊C8C23×C11311yescharacteristic
675C22⋊C8C23×C11311yescharacteristic
676C22⋊C8C23×C11311yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C11311yescharacteristic
683#95C23×C11311yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C11311yescharacteristic
687C24C2×D4×C11311yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C11311yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C11311yescharacteristic
718C2×D4C2×D4×C11311yescharacteristic
719C2×D4C2×D4×C11311yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C11311yescharacteristic
736C22×C4C2×D4×C11311yescharacteristic
737C22×C4C2×D4×C11311yescharacteristic
738C22×C4C2×D4×C11311yescharacteristic
739C22×C4C2×D4×C11311yescharacteristic
740C22×C4C2×D4×C11311yescharacteristic
741C22×C4C2×D4×C11311yescharacteristic
742C22×C4C2×D4×C11311yescharacteristic
743C22×C4C24×C11311yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C11311yescharacteristic
770C4⋊C4C2×D4×C11311yescharacteristic
771C4⋊C4C2×D4×C11311yescharacteristic
772C4⋊C4C2×D4×C11311yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C11311yescharacteristic
826C23#120×C11311yescharacteristic
827C23C22×D4×C11311yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C11311yescharacteristic
892C2×C4#120×C11311yescharacteristic
893C2×C4C22×D4×C11311yescharacteristic
894C2×C4C22×D4×C11311yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22#458×C11312yes—
925C22C2×#120×C11311yescharacteristic
926C22#576×C11311yescharacteristic
927C22#577×C11311yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C113×#301211yescharacteristic
953C2C113×#301811yescharacteristic
954C2C2×#458×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3534C2
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
2. C113×#3094C2semidirect
3. C113×#3091C2semidirect
4. C113×#2498C2semidirect
5. C113×#1618C2semidirect
6. C113×#1616C2semidirect
7. C113×#1615C2semidirect
8. C113×#1613C2semidirect
9. C113×#1612C2semidirect
10. C113×#1610C2semidirect
11. C113×#1609C2semidirect
12. C113×#1607C2semidirect
13. C113×#1504C2semidirect
14. C2×#327×C113C2semidirect
15. C113×#1468C2semidirect
35. C2×#117×C113C22semidirect
37. #484×C113C22semidirect
38. #483×C113C22semidirect
43. #481×C113C22semidirect
44. #481×C113C22semidirect
46. #480×C113C22semidirect
47. #480×C113C22semidirect
52. #407×C113C22semidirect
53. C2×C22⋊C8×C113C22semidirect
54. #400×C113C22semidirect
55. #399×C113C22semidirect
56. #398×C113C22semidirect
57. #397×C113C22semidirect
62. C2×#95×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
466. #18262C113direct (N × H)
479. #3094C2×C113semidirect
480. #3091C2×C113semidirect
481. #2498C2×C113semidirect
482. #1618C2×C113semidirect
483. #1616C2×C113semidirect
484. #1615C2×C113semidirect
485. #1613C2×C113semidirect
486. #1612C2×C113semidirect
487. #1610C2×C113semidirect
488. #1609C2×C113semidirect
489. #1607C2×C113semidirect
490. #1504C2×C113semidirect
491. C2×#327C2×C113semidirect
492. #1468C2×C113semidirect
493. C113#18262direct (N × H)
513. C2×#117C22×C113semidirect
515. #484C22×C113semidirect
516. #483C22×C113semidirect
521. #481C22×C113semidirect
522. #481C22×C113semidirect
524. #480C22×C113semidirect
525. #480C22×C113semidirect
530. #407C22×C113semidirect
531. C2×C22⋊C8C22×C113semidirect
532. #400C22×C113semidirect
533. #399C22×C113semidirect
534. #398C22×C113semidirect
535. #397C22×C113semidirect
540. C2×#95C22×C113semidirect
541. #328C22×C113semidirect
542. #328C22×C113semidirect
545. #327C22×C113semidirect
546. #327C22×C113semidirect
547. #327C22×C113semidirect
548. #327C22×C113semidirect
549. #324C22×C113semidirect
550. #324C22×C113semidirect
551. #323C22×C113semidirect
552. #323C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35342
C113×#30942
C113×#30912
C113×#24982
C113×#16182
C113×#16162
C113×#16152
C113×#16132
C113×#16122
C113×#16102
C113×#16092
C113×#16072
C113×#15042
C2×#327×C1132
C113×#14682
#18262113