Finite Group Databasebeta

← C113×#24451 #43292471

Subgroups — C113×#24451 #43292471

Order 28928.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C113C211yesmaximal, characteristic, complemented
2C2×#469×C113C211yesmaximal, characteristic, complemented
3C2×#449×C113C211yesmaximal, characteristic, complemented
4C2×#449×C113C211yesmaximal, characteristic, complemented
5C2×#417×C113C211yesmaximal, characteristic, complemented
6C113×#2416C211yesmaximal, characteristic, complemented
7C113×#2041C211yesmaximal, characteristic, complemented
8C113×#2034C211yesmaximal, characteristic, complemented
9C113×#2011C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1880C211yesmaximal, characteristic, complemented
12C113×#1874C211yesmaximal, characteristic, complemented
13C113×#1870C211yesmaximal, characteristic, complemented
14C113×#1865C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×D8×C113C2211yescharacteristic
20C22×D8×C113C2211yescharacteristic
21C22×M16×C113C2211yescharacteristic
22#550×C113—24no—
23#550×C113—24no—
24C2×#127×C113—21no—
25C2×#127×C113C2211yescharacteristic
26C2×#121×C113—21no—
27C2×#121×C113—21no—
28C2×#121×C113—21no—
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic
31C2×#121×C113C2211yescharacteristic
32C2×#121×C113C2211yescharacteristic
33C2×C4×Q8×C113C2211yescharacteristic
34C2×C4×D4×C113—21no—
35C2×C4×D4×C113C2211yescharacteristic
36C22×C4⋊C4×C113C2211yescharacteristic
37#469×C113—24no—
38#449×C113—24no—
39#449×C113—24no—
40C2×#106×C113C2211yescharacteristic
41#417×C113—24no—
42C2×#103×C113C2211yescharacteristic
43C2×#103×C113C2211yescharacteristic
44C2×#103×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×#102×C113C2211yescharacteristic
52C2×C22⋊C8×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54C2×C22⋊C8×C113C2211yescharacteristic
55#396×C113—21no—
56#394×C113—21no—
57#390×C113C2211yescharacteristic
58#389×C113C2211yescharacteristic
59#386×C113—21no—
60#380×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic
62#340×C113C2211yescharacteristic
63#336×C113C2211yescharacteristic
64#336×C113C2211yescharacteristic
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—22no—
71C2×#41×C113—22no—
72C2×#41×C113—41no—
73C2×#41×C113—41no—
74C2×#41×C113—41no—
75C2×#41×C113—41no—
76C2×#41×C113D414yescomplemented
77C22×Q8×C113C2311yescharacteristic
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—21no—
83C22×D4×C113—21no—
84C22×D4×C113—21no—
85C22×D4×C113—21no—
86C22×D4×C113D411yescharacteristic
87C22×D4×C113C2311yescharacteristic
88C22×D4×C113C2311yescharacteristic
89C22×D4×C113C2311yescharacteristic
90C23×C4×C113—21no—
91C23×C4×C113—21no—
92C23×C4×C113—21no—
93C23×C4×C113C2311yescharacteristic
94C23×C4×C113C2311yescharacteristic
95C2×SD16×C113—22no—
96C2×SD16×C113—22no—
97C2×SD16×C113—22no—
98C2×D8×C113—22no—
99C2×D8×C113—22no—
100C2×D8×C113—22no—
101C2×D8×C113—41no—
102C2×D8×C113—41no—
103C2×D8×C113—41no—
104C2×M16×C113—22no—
105C2×M16×C113—22no—
106C2×M16×C113—41no—
107C22×C8×C113C2311yescharacteristic
108C22×C8×C113C2311yescharacteristic
109C22×C8×C113C2311yescharacteristic
110C22×C8×C113C2311yescharacteristic
111#127×C113—28no—
112#127×C113—22no—
113#127×C113—22no—
114#121×C113—28no—
115#121×C113—28no—
116#121×C113—22no—
117#121×C113—22no—
118#121×C113—22no—
119#121×C113—22no—
120#121×C113—22no—
121#121×C113—22no—
122#121×C113—41no—
123#121×C113—44no—
124#121×C113D414yescomplemented
125C4×Q8×C113—22no—
126C4×Q8×C113—22no—
127C4×D4×C113—28no—
128C4×D4×C113—22no—
129C4×D4×C113—22no—
130C2×C4⋊C4×C113—21no—
131C2×C4⋊C4×C113—22no—
132C2×C4⋊C4×C113—21no—
133C2×C4⋊C4×C113—21no—
134C2×C4⋊C4×C113—41no—
135C2×C4⋊C4×C113D411yescharacteristic
136C2×C4⋊C4×C113C2311yescharacteristic
137C2×C4⋊C4×C113C2311yescharacteristic
138C2×C4⋊C4×C113C2311yescharacteristic
139C2×C4⋊C4×C113C2311yescharacteristic
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113—21no—
142C2×C22⋊C4×C113—21no—
143C2×C22⋊C4×C113—21no—
144C2×C22⋊C4×C113—21no—
145C2×C22⋊C4×C113—21no—
146C2×C22⋊C4×C113—21no—
147C2×C22⋊C4×C113D411yescharacteristic
148C2×C22⋊C4×C113D411yescharacteristic
149C2×C42×C113—21no—
150C2×C42×C113C2311yescharacteristic
151#106×C113—22no—
152#103×C113—22no—
153#103×C113—22no—
154#103×C113D414yescomplemented
155#102×C113—22no—
156#102×C113—22no—
157#102×C113—22no—
158#102×C113—22no—
159#102×C113—22no—
160#102×C113—22no—
161#102×C113—41no—
162C22⋊C8×C113—22no—
163C22⋊C8×C113—22no—
164C22⋊C8×C113—41no—
165#95×C113—21no—
166#95×C113—21no—
167C24×C113—21no—
168C24×C113—21no—
169C24×C113—21no—
170C24×C113C2×D411yescharacteristic
171C24×C113C2×D411yescharacteristic
172#41×C113—28no—
173#41×C113—44no—
174#41×C113—44no—
175#41×C113—44no—
176#41×C113—44no—
177#41×C113—44no—
178#41×C113—44no—
179#41×C113—44no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113C2×D412yes—
184C2×Q8×C113C2×D412yes—
185C2×Q8×C113#4112yes—
186C2×D4×C113—24no—
187C2×D4×C113—24no—
188C2×D4×C113—22no—
189C2×D4×C113—24no—
190C2×D4×C113—24no—
191C2×D4×C113—24no—
192C2×D4×C113—24no—
193C2×D4×C113—22no—
194C2×D4×C113—21no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—21no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—21no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—21no—
207C2×D4×C113—21no—
208C2×D4×C113—21no—
209C2×D4×C113—21no—
210C2×D4×C113—41no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—42no—
215C2×D4×C113—42no—
216C2×D4×C113—42no—
217C2×D4×C113—42no—
218C2×D4×C113—42no—
219C2×D4×C113—42no—
220C2×D4×C113—42no—
221C2×D4×C113—42no—
222C2×D4×C113—81no—
223C2×D4×C113—81no—
224C2×D4×C113—81no—
225C2×D4×C113—81no—
226C2×D4×C113—81no—
227C2×D4×C113—81no—
228C2×D4×C113—81no—
229C2×D4×C113C2×D412yes—
230C2×D4×C113C2×D412yes—
231C22×C4×C113—21no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—24no—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—24no—
240C22×C4×C113—21no—
241C22×C4×C113—21no—
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—42no—
249C22×C4×C113—42no—
250C22×C4×C113—42no—
251C22×C4×C113—42no—
252C22×C4×C113—42no—
253C22×C4×C113—42no—
254C22×C4×C113—81no—
255C22×C4×C113C2×D411yescharacteristic
256C22×C4×C113C2×D411yescharacteristic
257C22×C4×C113C2×D411yescharacteristic
258C22×C4×C113C2×D412yes—
259C22×C4×C113C2×D412yes—
260C22×C4×C113C2×D411yescharacteristic
261C22×C4×C113C2411yescharacteristic
262SD16×C113—44no—
263D8×C113—44no—
264D8×C113—44no—
265M16×C113—44no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—21no—
270C2×C8×C113—21no—
271C2×C8×C113—21no—
272C2×C8×C113—21no—
273C2×C8×C113—21no—
274C2×C8×C113—21no—
275C2×C8×C113—21no—
276C2×C8×C113—21no—
277C2×C8×C113C2×D412yes—
278C4⋊C4×C113—24no—
279C4⋊C4×C113—22no—
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—42no—
287C4⋊C4×C113—42no—
288C4⋊C4×C113C2×D412yes—
289C4⋊C4×C113C2×D412yes—
290C22⋊C4×C113—24no—
291C22⋊C4×C113—22no—
292C22⋊C4×C113—24no—
293C22⋊C4×C113—22no—
294C22⋊C4×C113—42no—
295C22⋊C4×C113—42no—
296C22⋊C4×C113—42no—
297C22⋊C4×C113—42no—
298C22⋊C4×C113—81no—
299C42×C113—24no—
300C42×C113—21no—
301C42×C113—21no—
302C23×C113—21no—
303C23×C113—21no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
307C23×C113—21no—
308C23×C113—21no—
309C23×C113—22no—
310C23×C113—22no—
311C23×C113—21no—
312C23×C113—21no—
313C23×C113—21no—
314C23×C113—21no—
315C23×C113—21no—
316C23×C113—21no—
317C23×C113—41no—
318C23×C113—41no—
319C23×C113—41no—
320C23×C113—41no—
321C23×C113—41no—
322C23×C113—41no—
323C23×C113—41no—
324C23×C113—41no—
325C23×C113—41no—
326C23×C113—41no—
327C23×C113—41no—
328C23×C113—41no—
329C23×C113—41no—
330C23×C113—41no—
331C23×C113—41no—
332C23×C113—41no—
333C23×C113—41no—
334C23×C113—41no—
335C23×C113—41no—
336C23×C113#12012yes—
337C23×C113C22×D411yescharacteristic
338Q8×C113—22no—
339Q8×C113—22no—
340Q8×C113—22no—
341Q8×C113#12114yescomplemented
342D4×C113—22no—
343D4×C113—22no—
344D4×C113—22no—
345D4×C113—22no—
346D4×C113—44no—
347D4×C113—48no—
348D4×C113—48no—
349D4×C113—48no—
350D4×C113—41no—
351D4×C113—41no—
352D4×C113—41no—
353D4×C113—41no—
354D4×C113—41no—
355D4×C113—41no—
356D4×C113—41no—
357D4×C113—41no—
358D4×C113—84no—
359D4×C113—84no—
360D4×C113—84no—
361D4×C113—84no—
362D4×C113—84no—
363C2×C4×C113—21no—
364C2×C4×C113—22no—
365C2×C4×C113—21no—
366C2×C4×C113—22no—
367C2×C4×C113—21no—
368C2×C4×C113—22no—
369C2×C4×C113—21no—
370C2×C4×C113—22no—
371C2×C4×C113—22no—
372C2×C4×C113—22no—
373C2×C4×C113—22no—
374C2×C4×C113—21no—
375C2×C4×C113—22no—
376C2×C4×C113—21no—
377C2×C4×C113—21no—
378C2×C4×C113—22no—
379C2×C4×C113—21no—
380C2×C4×C113—21no—
381C2×C4×C113—21no—
382C2×C4×C113—48no—
383C2×C4×C113—48no—
384C2×C4×C113—41no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—41no—
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—84no—
399C2×C4×C113#12012yes—
400C2×C4×C113AGL(1,ℤ/8)12yes—
401C2×C4×C113C22×D411yescharacteristic
402C2×C4×C113C22×D411yescharacteristic
403C2×C4×C113C22×D411yescharacteristic
404C2×C4×C113C2×#4111yescharacteristic
405C2×C4×C113H(5,𝔽2)11yescharacteristic
406C2×C4×C113H(5,𝔽2)11yescharacteristic
407C8×C113—22no—
408C8×C113—41no—
409C8×C113—41no—
410C8×C113—41no—
411C22×C113—22no—
412C22×C113—22no—
413C22×C113—22no—
414C22×C113—41no—
415C22×C113—41no—
416C22×C113—41no—
417C22×C113—41no—
418C22×C113—41no—
419C22×C113—42no—
420C22×C113—42no—
421C22×C113—41no—
422C22×C113—41no—
423C22×C113—42no—
424C22×C113—42no—
425C22×C113—41no—
426C22×C113—42no—
427C22×C113—42no—
428C22×C113—41no—
429C22×C113—41no—
430C22×C113—41no—
431C22×C113—81no—
432C22×C113—81no—
433C22×C113—81no—
434C22×C113—81no—
435C22×C113—81no—
436C22×C113—81no—
437C22×C113—81no—
438C22×C113—81no—
439C22×C113—81no—
440C22×C113—81no—
441C22×C113—81no—
442C22×C113—81no—
443C22×C113—81no—
444C22×C113—81no—
445C22×C113—81no—
446C22×C113C2×#12011yescharacteristic
447C22×C113D4211yescharacteristic
448C22×C113#54611yescharacteristic
449C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C113#57511yescharacteristic
451C22×C113#57611yescharacteristic
452C22×C113#57711yescharacteristic
453C4×C113—22no—
454C4×C113—24no—
455C4×C113—22no—
456C4×C113—41no—
457C4×C113—41no—
458C4×C113—42no—
459C4×C113—42no—
460C4×C113—81no—
461C4×C113—81no—
462C4×C113C2×#12111yescharacteristic
463C4×C113#53411yescharacteristic
464C4×C113D4211yescharacteristic
465C4×C113#54611yescharacteristic
466#24451C11311yesmaximal, characteristic, direct product factor, Sylow
467C2×C113—42no—
468C2×C113—81no—
469C2×C113—82no—
470C2×C113—82no—
471C2×C113—161no—
472C2×C113#241011yescharacteristic
473C2×C113#300611yescharacteristic
474C2×C113#301211yescharacteristic
475C2×C113#327111yescharacteristic
476C2×C113#327411yescharacteristic
477C2×C113#330911yescharacteristic
478C2×C113#333211yescharacteristic
479C2×#550C2×C11311yescharacteristic, complemented
480C2×#469C2×C11311yescharacteristic, complemented
481C2×#449C2×C11311yescharacteristic, complemented
482C2×#449C2×C11311yescharacteristic, complemented
483C2×#417C2×C11311yescharacteristic, complemented
484#2416C2×C11311yescharacteristic, complemented
485#2041C2×C11311yescharacteristic, complemented
486#2034C2×C11311yescharacteristic, complemented
487#2011C2×C11311yescharacteristic, complemented
488#1999C2×C11311yescharacteristic, complemented
489#1880C2×C11311yescharacteristic, complemented
490#1874C2×C11311yescharacteristic, complemented
491#1870C2×C11311yescharacteristic, complemented
492#1865C2×C11311yescharacteristic, complemented
493#1788C2×C11311yescharacteristic, complemented
494C113#2445111yescharacteristic, direct product factor, Sylow
495C22×#41C22×C11311yescharacteristic
496C22×#41C22×C11311yescharacteristic
497C22×SD16C22×C11311yescharacteristic
498C22×D8C22×C11311yescharacteristic
499C22×D8C22×C11311yescharacteristic
500C22×M16C22×C11311yescharacteristic
501#550—24no—
502#550—24no—
503C2×#127—21no—
504C2×#127C22×C11311yescharacteristic
505C2×#121—21no—
506C2×#121—21no—
507C2×#121—21no—
508C2×#121C22×C11311yescharacteristic
509C2×#121C22×C11311yescharacteristic
510C2×#121C22×C11311yescharacteristic
511C2×#121C22×C11311yescharacteristic
512C2×C4×Q8C22×C11311yescharacteristic
513C2×C4×D4—21no—
514C2×C4×D4C22×C11311yescharacteristic
515C22×C4⋊C4C22×C11311yescharacteristic
516#469—24no—
517#449—24no—
518#449—24no—
519C2×#106C22×C11311yescharacteristic
520#417—24no—
521C2×#103C22×C11311yescharacteristic
522C2×#103C22×C11311yescharacteristic
523C2×#103C22×C11311yescharacteristic
524C2×#102C22×C11311yescharacteristic
525C2×#102C22×C11311yescharacteristic
526C2×#102C22×C11311yescharacteristic
527C2×#102C22×C11311yescharacteristic
528C2×#102C22×C11311yescharacteristic
529C2×#102C22×C11311yescharacteristic
530C2×#102C22×C11311yescharacteristic
531C2×C22⋊C8C22×C11311yescharacteristic
532C2×C22⋊C8C22×C11311yescharacteristic
533C2×C22⋊C8C22×C11311yescharacteristic
534#396—21no—
535#394—21no—
536#390C22×C11311yescharacteristic
537#389C22×C11311yescharacteristic
538#386—21no—
539#380C22×C11311yescharacteristic
540#340C22×C11311yescharacteristic
541#340C22×C11311yescharacteristic
542#336C22×C11311yescharacteristic
543#336C22×C11311yescharacteristic
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C11314yescomplemented
556C22×Q8C23×C11311yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C11311yescharacteristic
566C22×D4C23×C11311yescharacteristic
567C22×D4C23×C11311yescharacteristic
568C22×D4C23×C11311yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C11311yescharacteristic
573C23×C4C23×C11311yescharacteristic
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×M16—22no—
584C2×M16—22no—
585C2×M16—41no—
586C22×C8C23×C11311yescharacteristic
587C22×C8C23×C11311yescharacteristic
588C22×C8C23×C11311yescharacteristic
589C22×C8C23×C11311yescharacteristic
590#127—28no—
591#127—22no—
592#127—22no—
593#121—28no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—44no—
603#121D4×C11314yescomplemented
604C4×Q8—22no—
605C4×Q8—22no—
606C4×D4—28no—
607C4×D4—22no—
608C4×D4—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4D4×C11311yescharacteristic
615C2×C4⋊C4C23×C11311yescharacteristic
616C2×C4⋊C4C23×C11311yescharacteristic
617C2×C4⋊C4C23×C11311yescharacteristic
618C2×C4⋊C4C23×C11311yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C11311yescharacteristic
627C2×C22⋊C4D4×C11311yescharacteristic
628C2×C42—21no—
629C2×C42C23×C11311yescharacteristic
630#106—22no—
631#103—22no—
632#103—22no—
633#103D4×C11314yescomplemented
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×D4×C11311yescharacteristic
650C24C2×D4×C11311yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658#41—44no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C11312yes—
663C2×Q8C2×D4×C11312yes—
664C2×Q8#41×C11312yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4C2×D4×C11312yes—
709C2×D4C2×D4×C11312yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4C2×D4×C11311yescharacteristic
735C22×C4C2×D4×C11311yescharacteristic
736C22×C4C2×D4×C11311yescharacteristic
737C22×C4C2×D4×C11312yes—
738C22×C4C2×D4×C11312yes—
739C22×C4C2×D4×C11311yescharacteristic
740C22×C4C24×C11311yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744M16—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8C2×D4×C11312yes—
757C4⋊C4—24no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4C2×D4×C11312yes—
768C4⋊C4C2×D4×C11312yes—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—81no—
778C42—24no—
779C42—21no—
780C42—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23#120×C11312yes—
816C23C22×D4×C11311yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8#121×C11314yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841D4—84no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
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—84no—
878C2×C4#120×C11312yes—
879C2×C4AGL(1,ℤ/8)×C11312yes—
880C2×C4C22×D4×C11311yescharacteristic
881C2×C4C22×D4×C11311yescharacteristic
882C2×C4C22×D4×C11311yescharacteristic
883C2×C4C2×#41×C11311yescharacteristic
884C2×C4H(5,𝔽2)×C11311yescharacteristic
885C2×C4H(5,𝔽2)×C11311yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×#120×C11311yescharacteristic
926C22D42×C11311yescharacteristic
927C22#546×C11311yescharacteristic
928C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
929C22#575×C11311yescharacteristic
930C22#576×C11311yescharacteristic
931C22#577×C11311yescharacteristic
932C4—22no—
933C4—24no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4C2×#121×C11311yescharacteristic
942C4#534×C11311yescharacteristic
943C4D42×C11311yescharacteristic
944C4#546×C11311yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2C113×#241011yescharacteristic
951C2C113×#300611yescharacteristic
952C2C113×#301211yescharacteristic
953C2C113×#327111yescharacteristic
954C2C113×#327411yescharacteristic
955C2C113×#330911yescharacteristic
956C2C113×#333211yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#550×C113C2semidirect
2. C2×#469×C113C2semidirect
3. C2×#449×C113C2semidirect
4. C2×#449×C113C2semidirect
5. C2×#417×C113C2semidirect
6. C113×#2416C2semidirect
7. C113×#2041C2semidirect
8. C113×#2034C2semidirect
9. C113×#2011C2semidirect
10. C113×#1999C2semidirect
11. C113×#1880C2semidirect
12. C113×#1874C2semidirect
13. C113×#1870C2semidirect
14. C113×#1865C2semidirect
15. C113×#1788C2semidirect
76. C2×#41×C113D4semidirect
124. #121×C113D4semidirect
154. #103×C113D4semidirect
341. Q8×C113#121semidirect
466. #24451C113direct (N × H)
479. C2×#550C2×C113semidirect
480. C2×#469C2×C113semidirect
481. C2×#449C2×C113semidirect
482. C2×#449C2×C113semidirect
483. C2×#417C2×C113semidirect
484. #2416C2×C113semidirect
485. #2041C2×C113semidirect
486. #2034C2×C113semidirect
487. #2011C2×C113semidirect
488. #1999C2×C113semidirect
489. #1880C2×C113semidirect
490. #1874C2×C113semidirect
491. #1870C2×C113semidirect
492. #1865C2×C113semidirect
493. #1788C2×C113semidirect
494. C113#24451direct (N × H)
555. C2×#41D4×C113semidirect
603. #121D4×C113semidirect
633. #103D4×C113semidirect
820. Q8#121×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1132
C2×#469×C1132
C2×#449×C1132
C2×#417×C1132
C113×#24162
C113×#20412
C113×#20342
C113×#20112
C113×#19992
C113×#18802
C113×#18742
C113×#18702
C113×#18652
C113×#17882
#24451113