Finite Group Databasebeta

← C113×#26987 #43295007

Subgroups — C113×#26987 #43295007

Order 28928.

974 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#440×C113C211yesmaximal, characteristic, complemented
3C113×#2428C211yesmaximal, characteristic
4C113×#2423C211yesmaximal, characteristic, complemented
5C113×#2083C211yesmaximal, characteristic, complemented
6C113×#2033C211yesmaximal, characteristic, complemented
7C113×#2014C211yesmaximal, characteristic, complemented
8C113×#2000C211yesmaximal, characteristic, complemented
9C113×#1957C211yesmaximal, characteristic, complemented
10C113×#1936C211yesmaximal, characteristic, complemented
11C113×#1933C211yesmaximal, characteristic, complemented
12C113×#1895C211yesmaximal, characteristic, complemented
13C113×#1880C211yesmaximal, characteristic, complemented
14C113×#1862C211yesmaximal, characteristic, complemented
15C113×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×M16×C113C2211yescharacteristic
19C2×#127×C113C2211yescharacteristic
20C2×C22⋊Q8×C113C2211yescharacteristic
21C2×#121×C113—21no—
22C2×#121×C113C2211yescharacteristic
23C2×#121×C113C2211yescharacteristic
24C2×C4×Q8×C113C2211yescharacteristic
25C2×C4×D4×C113C2211yescharacteristic
26#468×C113—24no—
27#440×C113—24no—
28C2×#107×C113C2211yescharacteristic
29C2×#107×C113C2211yescharacteristic
30C2×#103×C113C2211yescharacteristic
31C2×#103×C113C2211yescharacteristic
32C2×#102×C113C2211yescharacteristic
33C2×#102×C113C2211yescharacteristic
34C2×#102×C113C2211yescharacteristic
35C2×#102×C113C2211yescharacteristic
36C2×#102×C113C2211yescharacteristic
37C2×#102×C113C2211yescharacteristic
38C2×C22⋊C8×C113C2211yescharacteristic
39C2×#97×C113C2211yescharacteristic
40C2×C4×C8×C113C2211yescharacteristic
41#399×C113—21no—
42#398×C113—21no—
43#394×C113—21no—
44#392×C113—21no—
45#391×C113C2211yescharacteristic
46#390×C113C2211yescharacteristic
47#389×C113C2211yescharacteristic
48#389×C113C2211yescharacteristic
49#388×C113—21no—
50#387×C113—21no—
51#386×C113—21no—
52#384×C113C2211yescharacteristic
53#380×C113C2211yescharacteristic
54C4×C22⋊C4×C113C2211yescharacteristic
55#340×C113C2211yescharacteristic
56#340×C113C2211yescharacteristic
57#340×C113C2211yescharacteristic
58#340×C113C2211yescharacteristic
59#336×C113C2211yescharacteristic
60#336×C113C2211yescharacteristic
61C22×Q8×C113C2311yescharacteristic
62C22×D4×C113—21no—
63C22×D4×C113—21no—
64C22×D4×C113—21no—
65C22×D4×C113—21no—
66C22×D4×C113C2311yescharacteristic
67C22×D4×C113C2311yescharacteristic
68C23×C4×C113—21no—
69C23×C4×C113C2311yescharacteristic
70C2×SD16×C113—22no—
71C2×SD16×C113—22no—
72C2×SD16×C113—22no—
73C2×SD16×C113—22no—
74C2×SD16×C113—22no—
75C2×SD16×C113—41no—
76C2×M16×C113—22no—
77C2×M16×C113—22no—
78C2×M16×C113—41no—
79C22×C8×C113C2311yescharacteristic
80C22×C8×C113C2311yescharacteristic
81C22×C8×C113C2311yescharacteristic
82C22×C8×C113C2311yescharacteristic
83#127×C113—22no—
84#127×C113—41no—
85C22⋊Q8×C113—22no—
86C22⋊Q8×C113—41no—
87#121×C113—22no—
88#121×C113—22no—
89#121×C113—44no—
90#121×C113—41no—
91#121×C113—41no—
92C4×Q8×C113—22no—
93C4×Q8×C113—41no—
94C4×D4×C113—22no—
95C4×D4×C113—41no—
96C2×C4⋊C4×C113—21no—
97C2×C4⋊C4×C113—21no—
98C2×C4⋊C4×C113—21no—
99C2×C4⋊C4×C113—21no—
100C2×C4⋊C4×C113—21no—
101C2×C4⋊C4×C113—21no—
102C2×C4⋊C4×C113C2311yescharacteristic
103C2×C4⋊C4×C113C2311yescharacteristic
104C2×C4⋊C4×C113C2311yescharacteristic
105C2×C4⋊C4×C113C2311yescharacteristic
106C2×C4⋊C4×C113C2311yescharacteristic
107C2×C22⋊C4×C113—21no—
108C2×C22⋊C4×C113—21no—
109C2×C22⋊C4×C113—21no—
110C2×C22⋊C4×C113—21no—
111C2×C22⋊C4×C113—21no—
112C2×C22⋊C4×C113—21no—
113C2×C22⋊C4×C113—21no—
114C2×C22⋊C4×C113D411yescharacteristic
115C2×C22⋊C4×C113D411yescharacteristic
116C2×C42×C113—21no—
117C2×C42×C113C2311yescharacteristic
118C2×C42×C113C2311yescharacteristic
119#107×C113—22no—
120#107×C113—22no—
121#103×C113—41no—
122#103×C113D414yescomplemented
123#102×C113—22no—
124#102×C113—22no—
125#102×C113—22no—
126#102×C113—22no—
127#102×C113—41no—
128#102×C113—41no—
129C22⋊C8×C113—22no—
130#97×C113—22no—
131C4×C8×C113—41no—
132#95×C113—21no—
133#95×C113—21no—
134#95×C113—21no—
135#95×C113—21no—
136#95×C113—21no—
137#95×C113D411yescharacteristic
138#95×C113D411yescharacteristic
139C24×C113—21no—
140C24×C113—21no—
141C24×C113C2×D411yescharacteristic
142C2×Q8×C113—21no—
143C2×Q8×C113—21no—
144C2×Q8×C113—21no—
145C2×Q8×C113—21no—
146C2×Q8×C113—21no—
147C2×Q8×C113C2×D412yes—
148C2×D4×C113—21no—
149C2×D4×C113—21no—
150C2×D4×C113—21no—
151C2×D4×C113—21no—
152C2×D4×C113—21no—
153C2×D4×C113—21no—
154C2×D4×C113—21no—
155C2×D4×C113—21no—
156C2×D4×C113—21no—
157C2×D4×C113—21no—
158C2×D4×C113—21no—
159C2×D4×C113—42no—
160C2×D4×C113—42no—
161C2×D4×C113—42no—
162C2×D4×C113—42no—
163C2×D4×C113—42no—
164C2×D4×C113—42no—
165C2×D4×C113—42no—
166C2×D4×C113—42no—
167C2×D4×C113—81no—
168C2×D4×C113—81no—
169C2×D4×C113—81no—
170C2×D4×C113—81no—
171C2×D4×C113#4112yes—
172C22×C4×C113—21no—
173C22×C4×C113—21no—
174C22×C4×C113—21no—
175C22×C4×C113—21no—
176C22×C4×C113—21no—
177C22×C4×C113—21no—
178C22×C4×C113—21no—
179C22×C4×C113—21no—
180C22×C4×C113—21no—
181C22×C4×C113—21no—
182C22×C4×C113—21no—
183C22×C4×C113—21no—
184C22×C4×C113—42no—
185C22×C4×C113—42no—
186C22×C4×C113—81no—
187C22×C4×C113C2×D411yescharacteristic
188C22×C4×C113C2×D411yescharacteristic
189C22×C4×C113C2×D411yescharacteristic
190C22×C4×C113C2×D411yescharacteristic
191C22×C4×C113C2×D411yescharacteristic
192C22×C4×C113C2411yescharacteristic
193SD16×C113—28no—
194SD16×C113—44no—
195M16×C113—44no—
196C2×C8×C113—21no—
197C2×C8×C113—21no—
198C2×C8×C113—21no—
199C2×C8×C113—21no—
200C2×C8×C113—21no—
201C2×C8×C113—21no—
202C2×C8×C113—21no—
203C2×C8×C113—21no—
204C2×C8×C113—21no—
205C2×C8×C113C2×D412yes—
206C2×C8×C113#4112yes—
207C2×C8×C113#4112yes—
208C4⋊C4×C113—21no—
209C4⋊C4×C113—21no—
210C4⋊C4×C113—21no—
211C4⋊C4×C113—21no—
212C4⋊C4×C113—21no—
213C4⋊C4×C113—21no—
214C4⋊C4×C113—21no—
215C4⋊C4×C113—21no—
216C4⋊C4×C113—21no—
217C4⋊C4×C113—42no—
218C4⋊C4×C113—42no—
219C4⋊C4×C113—42no—
220C4⋊C4×C113—42no—
221C4⋊C4×C113—81no—
222C4⋊C4×C113—81no—
223C4⋊C4×C113C2×D412yes—
224C22⋊C4×C113—22no—
225C22⋊C4×C113—22no—
226C22⋊C4×C113—42no—
227C22⋊C4×C113—42no—
228C22⋊C4×C113—42no—
229C22⋊C4×C113—42no—
230C22⋊C4×C113—42no—
231C22⋊C4×C113—81no—
232C22⋊C4×C113—81no—
233C42×C113—21no—
234C42×C113—21no—
235C42×C113—21no—
236C42×C113—21no—
237C42×C113—42no—
238C23×C113—21no—
239C23×C113—21no—
240C23×C113—22no—
241C23×C113—21no—
242C23×C113—21no—
243C23×C113—21no—
244C23×C113—21no—
245C23×C113—21no—
246C23×C113—41no—
247C23×C113—41no—
248C23×C113—41no—
249C23×C113—41no—
250C23×C113—41no—
251C23×C113—41no—
252C23×C113—41no—
253C23×C113—41no—
254C23×C113—41no—
255C23×C113—41no—
256C23×C113—41no—
257C23×C113—41no—
258C23×C113—41no—
259C23×C113C22×D411yescharacteristic
260Q8×C113—22no—
261Q8×C113—22no—
262Q8×C113—41no—
263Q8×C113—41no—
264D4×C113—22no—
265D4×C113—22no—
266D4×C113—41no—
267D4×C113—41no—
268D4×C113—41no—
269D4×C113—41no—
270D4×C113—41no—
271D4×C113—41no—
272D4×C113—84no—
273D4×C113—84no—
274D4×C113—84no—
275D4×C113—84no—
276C2×C4×C113—21no—
277C2×C4×C113—21no—
278C2×C4×C113—21no—
279C2×C4×C113—21no—
280C2×C4×C113—21no—
281C2×C4×C113—21no—
282C2×C4×C113—21no—
283C2×C4×C113—22no—
284C2×C4×C113—22no—
285C2×C4×C113—21no—
286C2×C4×C113—21no—
287C2×C4×C113—21no—
288C2×C4×C113—21no—
289C2×C4×C113—21no—
290C2×C4×C113—21no—
291C2×C4×C113—41no—
292C2×C4×C113—41no—
293C2×C4×C113—41no—
294C2×C4×C113—41no—
295C2×C4×C113—41no—
296C2×C4×C113—41no—
297C2×C4×C113—41no—
298C2×C4×C113—41no—
299C2×C4×C113—41no—
300C2×C4×C113—41no—
301C2×C4×C113—41no—
302C2×C4×C113—41no—
303C2×C4×C113—41no—
304C2×C4×C113—41no—
305C2×C4×C113—41no—
306C2×C4×C113—41no—
307C2×C4×C113—41no—
308C2×C4×C113—41no—
309C2×C4×C113—41no—
310C2×C4×C113—41no—
311C2×C4×C113—84no—
312C2×C4×C113AGL(1,ℤ/8)12yes—
313C2×C4×C113#13712yes—
314C2×C4×C113C22×D411yescharacteristic
315C2×C4×C113C2×#4111yescharacteristic
316C2×C4×C113C2×#4111yescharacteristic
317C2×C4×C113C2×#4111yescharacteristic
318C2×C4×C113H(5,𝔽2)11yescharacteristic
319C2×C4×C113H(5,𝔽2)11yescharacteristic
320C8×C113—22no—
321C8×C113—22no—
322C8×C113—22no—
323C8×C113—41no—
324C22×C113—41no—
325C22×C113—41no—
326C22×C113—41no—
327C22×C113—42no—
328C22×C113—41no—
329C22×C113—41no—
330C22×C113—41no—
331C22×C113—42no—
332C22×C113—42no—
333C22×C113—41no—
334C22×C113—81no—
335C22×C113—81no—
336C22×C113—81no—
337C22×C113—81no—
338C22×C113—81no—
339C22×C113—81no—
340C22×C113—81no—
341C22×C113—81no—
342C22×C113—81no—
343C22×C113—81no—
344C22×C113—81no—
345C22×C113#53211yescharacteristic
346C22×C113D4211yescharacteristic
347C22×C113#54611yescharacteristic
348C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C113C2×#13711yescharacteristic
350C22×C113#57611yescharacteristic
351C22×C113#57711yescharacteristic
352C4×C113—22no—
353C4×C113—22no—
354C4×C113—41no—
355C4×C113—42no—
356C4×C113—41no—
357C4×C113—42no—
358C4×C113—41no—
359C4×C113—81no—
360C4×C113—81no—
361C4×C113—81no—
362C4×C113—81no—
363C4×C113#52511yescharacteristic
364C4×C113#54011yescharacteristic
365C4×C113#54611yescharacteristic
366C4×C113#55311yescharacteristic
367#26987C11311yesmaximal, characteristic, direct product factor, Sylow
368C2×C113—81no—
369C2×C113—82no—
370C2×C113—161no—
371C2×C113#246411yescharacteristic
372C2×C113#317911yescharacteristic
373C2×C113#318211yescharacteristic
374C2×C113#327411yescharacteristic
375C2×C113#327811yescharacteristic
376C2×C113#331011yescharacteristic
377C2×C113#331411yescharacteristic
378C2×#468C2×C11311yescharacteristic, complemented
379C2×#440C2×C11311yescharacteristic, complemented
380#2428C2×C11311yescharacteristic
381#2423C2×C11311yescharacteristic, complemented
382#2083C2×C11311yescharacteristic, complemented
383#2033C2×C11311yescharacteristic, complemented
384#2014C2×C11311yescharacteristic, complemented
385#2000C2×C11311yescharacteristic, complemented
386#1957C2×C11311yescharacteristic, complemented
387#1936C2×C11311yescharacteristic, complemented
388#1933C2×C11311yescharacteristic, complemented
389#1895C2×C11311yescharacteristic, complemented
390#1880C2×C11311yescharacteristic, complemented
391#1862C2×C11311yescharacteristic, complemented
392#1753C2×C11311yescharacteristic, complemented
393C113#2698711yescharacteristic, direct product factor, Sylow
394C22×SD16C22×C11311yescharacteristic
395C22×SD16C22×C11311yescharacteristic
396C22×M16C22×C11311yescharacteristic
397C2×#127C22×C11311yescharacteristic
398C2×C22⋊Q8C22×C11311yescharacteristic
399C2×#121—21no—
400C2×#121C22×C11311yescharacteristic
401C2×#121C22×C11311yescharacteristic
402C2×C4×Q8C22×C11311yescharacteristic
403C2×C4×D4C22×C11311yescharacteristic
404#468—24no—
405#440—24no—
406C2×#107C22×C11311yescharacteristic
407C2×#107C22×C11311yescharacteristic
408C2×#103C22×C11311yescharacteristic
409C2×#103C22×C11311yescharacteristic
410C2×#102C22×C11311yescharacteristic
411C2×#102C22×C11311yescharacteristic
412C2×#102C22×C11311yescharacteristic
413C2×#102C22×C11311yescharacteristic
414C2×#102C22×C11311yescharacteristic
415C2×#102C22×C11311yescharacteristic
416C2×C22⋊C8C22×C11311yescharacteristic
417C2×#97C22×C11311yescharacteristic
418C2×C4×C8C22×C11311yescharacteristic
419#399—21no—
420#398—21no—
421#394—21no—
422#392—21no—
423#391C22×C11311yescharacteristic
424#390C22×C11311yescharacteristic
425#389C22×C11311yescharacteristic
426#389C22×C11311yescharacteristic
427#388—21no—
428#387—21no—
429#386—21no—
430#384C22×C11311yescharacteristic
431#380C22×C11311yescharacteristic
432C4×C22⋊C4C22×C11311yescharacteristic
433#340C22×C11311yescharacteristic
434#340C22×C11311yescharacteristic
435#340C22×C11311yescharacteristic
436#340C22×C11311yescharacteristic
437#336C22×C11311yescharacteristic
438#336C22×C11311yescharacteristic
439C22×Q8C23×C11311yescharacteristic
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4C23×C11311yescharacteristic
445C22×D4C23×C11311yescharacteristic
446C23×C4—21no—
447C23×C4C23×C11311yescharacteristic
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—41no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8C23×C11311yescharacteristic
458C22×C8C23×C11311yescharacteristic
459C22×C8C23×C11311yescharacteristic
460C22×C8C23×C11311yescharacteristic
461#127—22no—
462#127—41no—
463C22⋊Q8—22no—
464C22⋊Q8—41no—
465#121—22no—
466#121—22no—
467#121—44no—
468#121—41no—
469#121—41no—
470C4×Q8—22no—
471C4×Q8—41no—
472C4×D4—22no—
473C4×D4—41no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4C23×C11311yescharacteristic
481C2×C4⋊C4C23×C11311yescharacteristic
482C2×C4⋊C4C23×C11311yescharacteristic
483C2×C4⋊C4C23×C11311yescharacteristic
484C2×C4⋊C4C23×C11311yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C11311yescharacteristic
493C2×C22⋊C4D4×C11311yescharacteristic
494C2×C42—21no—
495C2×C42C23×C11311yescharacteristic
496C2×C42C23×C11311yescharacteristic
497#107—22no—
498#107—22no—
499#103—41no—
500#103D4×C11314yescomplemented
501#102—22no—
502#102—22no—
503#102—22no—
504#102—22no—
505#102—41no—
506#102—41no—
507C22⋊C8—22no—
508#97—22no—
509C4×C8—41no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95D4×C11311yescharacteristic
516#95D4×C11311yescharacteristic
517C24—21no—
518C24—21no—
519C24C2×D4×C11311yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8C2×D4×C11312yes—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4#41×C11312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4C2×D4×C11311yescharacteristic
566C22×C4C2×D4×C11311yescharacteristic
567C22×C4C2×D4×C11311yescharacteristic
568C22×C4C2×D4×C11311yescharacteristic
569C22×C4C2×D4×C11311yescharacteristic
570C22×C4C24×C11311yescharacteristic
571SD16—28no—
572SD16—44no—
573M16—44no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8C2×D4×C11312yes—
584C2×C8#41×C11312yes—
585C2×C8#41×C11312yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—81no—
600C4⋊C4—81no—
601C4⋊C4C2×D4×C11312yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—42no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23C22×D4×C11311yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—41no—
641Q8—41no—
642D4—22no—
643D4—22no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—84no—
651D4—84no—
652D4—84no—
653D4—84no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4AGL(1,ℤ/8)×C11312yes—
691C2×C4#137×C11312yes—
692C2×C4C22×D4×C11311yescharacteristic
693C2×C4C2×#41×C11311yescharacteristic
694C2×C4C2×#41×C11311yescharacteristic
695C2×C4C2×#41×C11311yescharacteristic
696C2×C4H(5,𝔽2)×C11311yescharacteristic
697C2×C4H(5,𝔽2)×C11311yescharacteristic
698C8—22no—
699C8—22no—
700C8—22no—
701C8—41no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—41no—
711C22—41no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22#532×C11311yescharacteristic
724C22D42×C11311yescharacteristic
725C22#546×C11311yescharacteristic
726C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
727C22C2×#137×C11311yescharacteristic
728C22#576×C11311yescharacteristic
729C22#577×C11311yescharacteristic
730C4—22no—
731C4—22no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4#525×C11311yescharacteristic
742C4#540×C11311yescharacteristic
743C4#546×C11311yescharacteristic
744C4#553×C11311yescharacteristic
745C2—81no—
746C2—82no—
747C2—161no—
748C2C113×#246411yescharacteristic
749C2C113×#317911yescharacteristic
750C2C113×#318211yescharacteristic
751C2C113×#327411yescharacteristic
752C2C113×#327811yescharacteristic
753C2C113×#331011yescharacteristic
754C2C113×#331411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2428C2
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×#468×C113C2semidirect
2. C2×#440×C113C2semidirect
4. C113×#2423C2semidirect
5. C113×#2083C2semidirect
6. C113×#2033C2semidirect
7. C113×#2014C2semidirect
8. C113×#2000C2semidirect
9. C113×#1957C2semidirect
10. C113×#1936C2semidirect
11. C113×#1933C2semidirect
12. C113×#1895C2semidirect
13. C113×#1880C2semidirect
14. C113×#1862C2semidirect
15. C113×#1753C2semidirect
122. #103×C113D4semidirect
367. #26987C113direct (N × H)
378. C2×#468C2×C113semidirect
379. C2×#440C2×C113semidirect
381. #2423C2×C113semidirect
382. #2083C2×C113semidirect
383. #2033C2×C113semidirect
384. #2014C2×C113semidirect
385. #2000C2×C113semidirect
386. #1957C2×C113semidirect
387. #1936C2×C113semidirect
388. #1933C2×C113semidirect
389. #1895C2×C113semidirect
390. #1880C2×C113semidirect
391. #1862C2×C113semidirect
392. #1753C2×C113semidirect
393. C113#26987direct (N × H)
500. #103D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1132
C2×#440×C1132
C113×#24282
C113×#24232
C113×#20832
C113×#20332
C113×#20142
C113×#20002
C113×#19572
C113×#19362
C113×#19332
C113×#18952
C113×#18802
C113×#18622
C113×#17532
#26987113