Finite Group Databasebeta

← C113×#25093 #43293113

Subgroups — C113×#25093 #43293113

Order 28928.

1322 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#460×C113C211yesmaximal, characteristic, complemented
3C2×#450×C113C211yesmaximal, characteristic, complemented
4C2×#418×C113C211yesmaximal, characteristic, complemented
5C113×#2433C211yesmaximal, characteristic
6C113×#2362C211yesmaximal, characteristic, complemented
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2041C211yesmaximal, characteristic, complemented
10C113×#2014C211yesmaximal, characteristic, complemented
11C113×#1982C211yesmaximal, characteristic, complemented
12C113×#1925C211yesmaximal, characteristic, complemented
13C113×#1880C211yesmaximal, characteristic, complemented
14C113×#1875C211yesmaximal, characteristic, complemented
15C113×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic, complemented
20C22×M16×C113C2211yescharacteristic
21C2×#127×C113C2211yescharacteristic
22C2×#127×C113C2211yescharacteristic
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×#120×C113—21no—
26C2×#120×C113—21no—
27C2×C4×Q8×C113C2211yescharacteristic, complemented
28C2×#117×C113C2211yescharacteristic
29#468×C113—24no—
30#460×C113—24no—
31#450×C113—24no—
32C2×#107×C113C2211yescharacteristic, complemented
33C2×C4⋊C8×C113C2211yescharacteristic, complemented
34C2×C4⋊C8×C113C2211yescharacteristic, complemented
35#418×C113—24no—
36C2×#103×C113C2211yescharacteristic, complemented
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic, complemented
44C2×#102×C113C2211yescharacteristic, complemented
45C2×#102×C113C2211yescharacteristic, complemented
46C2×C22⋊C8×C113C2211yescharacteristic
47#392×C113—21no—
48#392×C113—21no—
49#391×C113C2211yescharacteristic, complemented
50#390×C113C2211yescharacteristic
51#390×C113C2211yescharacteristic
52#389×C113C2211yescharacteristic, complemented
53#388×C113—21no—
54#388×C113—21no—
55#387×C113—21no—
56C4×C4⋊C4×C113—21no—
57C4×C4⋊C4×C113C2211yescharacteristic, complemented
58C4×C22⋊C4×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#336×C113C2211yescharacteristic, complemented
62#336×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C22×Q8×C113C2311yescharacteristic
65C22×D4×C113—22no—
66C22×D4×C113—22no—
67C22×D4×C113—21no—
68C22×D4×C113—22no—
69C22×D4×C113—21no—
70C22×D4×C113—21no—
71C22×D4×C113—21no—
72C22×D4×C113—21no—
73C22×D4×C113—21no—
74C22×D4×C113—22no—
75C22×D4×C113—41no—
76C22×D4×C113—41no—
77C22×D4×C113C2311yescharacteristic
78C22×D4×C113C2311yescharacteristic
79C22×D4×C113C2311yescharacteristic
80C23×C4×C113C2311yescharacteristic
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—22no—
84C2×SD16×C113—22no—
85C2×SD16×C113—22no—
86C2×SD16×C113—22no—
87C2×SD16×C113—41no—
88C2×SD16×C113—41no—
89C2×SD16×C113—41no—
90C2×M16×C113—22no—
91C2×M16×C113—22no—
92C2×M16×C113—41no—
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96C22×C8×C113C2311yescharacteristic
97#127×C113—22no—
98#127×C113—22no—
99#127×C113—41no—
100#127×C113—41no—
101C22⋊Q8×C113—22no—
102C22⋊Q8×C113D414yescomplemented
103#121×C113—22no—
104#121×C113—22no—
105#120×C113—44no—
106#120×C113—44no—
107C4×Q8×C113—22no—
108C4×Q8×C113—41no—
109#117×C113—22no—
110#117×C113—41no—
111C2×C4⋊C4×C113—21no—
112C2×C4⋊C4×C113—21no—
113C2×C4⋊C4×C113—21no—
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C22⋊C4×C113—21no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113D411yescharacteristic
126C2×C22⋊C4×C113D411yescharacteristic
127C2×C42×C113—21no—
128C2×C42×C113—21no—
129C2×C42×C113—21no—
130C2×C42×C113C2311yescharacteristic
131C2×C42×C113C2311yescharacteristic
132#107×C113—22no—
133C4⋊C8×C113—22no—
134C4⋊C8×C113—41no—
135#103×C113—22no—
136#102×C113—22no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—22no—
143#102×C113—41no—
144#102×C113D414yescomplemented
145C22⋊C8×C113—22no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113—21no—
149#95×C113—21no—
150#95×C113D411yescharacteristic
151#95×C113D411yescharacteristic
152C24×C113—21no—
153C24×C113—21no—
154C24×C113—21no—
155C24×C113—42no—
156C24×C113—42no—
157C24×C113—42no—
158C24×C113—42no—
159C24×C113—42no—
160C24×C113—81no—
161C24×C113—81no—
162C24×C113C2×D411yescharacteristic
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×Q8×C113—21no—
166C2×Q8×C113—21no—
167C2×Q8×C113—21no—
168C2×Q8×C113C2×D412yes—
169C2×D4×C113—28no—
170C2×D4×C113—21no—
171C2×D4×C113—21no—
172C2×D4×C113—21no—
173C2×D4×C113—21no—
174C2×D4×C113—21no—
175C2×D4×C113—21no—
176C2×D4×C113—21no—
177C2×D4×C113—21no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—21no—
181C2×D4×C113—21no—
182C2×D4×C113—21no—
183C2×D4×C113—21no—
184C2×D4×C113—21no—
185C2×D4×C113—21no—
186C2×D4×C113—44no—
187C2×D4×C113—44no—
188C2×D4×C113—42no—
189C2×D4×C113—42no—
190C2×D4×C113—44no—
191C2×D4×C113—42no—
192C2×D4×C113—42no—
193C2×D4×C113—42no—
194C2×D4×C113—42no—
195C2×D4×C113—42no—
196C2×D4×C113—42no—
197C2×D4×C113—42no—
198C2×D4×C113—42no—
199C2×D4×C113—42no—
200C2×D4×C113—42no—
201C2×D4×C113—42no—
202C2×D4×C113—42no—
203C2×D4×C113—81no—
204C2×D4×C113—81no—
205C2×D4×C113—81no—
206C2×D4×C113—81no—
207C2×D4×C113C2×D412yes—
208C2×D4×C113#4112yes—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113C2×D411yescharacteristic
219C22×C4×C113C2×D411yescharacteristic
220C22×C4×C113C2×D411yescharacteristic
221C22×C4×C113C2×D412yes—
222C22×C4×C113C2×D411yescharacteristic
223C22×C4×C113C2×D411yescharacteristic
224C22×C4×C113#4112yes—
225C22×C4×C113C2411yescharacteristic
226SD16×C113—44no—
227SD16×C113—44no—
228SD16×C113—44no—
229M16×C113—44no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113—21no—
234C2×C8×C113—21no—
235C2×C8×C113—21no—
236C2×C8×C113—21no—
237C2×C8×C113—21no—
238C2×C8×C113—21no—
239C2×C8×C113—21no—
240C2×C8×C113—21no—
241C2×C8×C113C2×D412yes—
242C4⋊C4×C113—24no—
243C4⋊C4×C113—21no—
244C4⋊C4×C113—21no—
245C4⋊C4×C113—21no—
246C4⋊C4×C113—21no—
247C4⋊C4×C113—21no—
248C4⋊C4×C113—21no—
249C4⋊C4×C113—42no—
250C4⋊C4×C113—42no—
251C4⋊C4×C113C2×D412yes—
252C4⋊C4×C113C2×D412yes—
253C22⋊C4×C113—24no—
254C22⋊C4×C113—22no—
255C22⋊C4×C113—22no—
256C22⋊C4×C113—42no—
257C22⋊C4×C113—42no—
258C22⋊C4×C113—42no—
259C22⋊C4×C113—42no—
260C22⋊C4×C113—42no—
261C22⋊C4×C113—42no—
262C42×C113—21no—
263C42×C113—21no—
264C42×C113—21no—
265C42×C113—21no—
266C42×C113—42no—
267C42×C113—42no—
268C42×C113—42no—
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—21no—
272C23×C113—21no—
273C23×C113—21no—
274C23×C113—21no—
275C23×C113—22no—
276C23×C113—22no—
277C23×C113—48no—
278C23×C113—41no—
279C23×C113—41no—
280C23×C113—41no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—41no—
285C23×C113—41no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—41no—
289C23×C113—41no—
290C23×C113—41no—
291C23×C113—41no—
292C23×C113—41no—
293C23×C113—41no—
294C23×C113—41no—
295C23×C113—41no—
296C23×C113—41no—
297C23×C113—84no—
298C23×C113—84no—
299C23×C113—84no—
300C23×C113—84no—
301C23×C113—84no—
302C23×C113—84no—
303C23×C113#12112yes—
304C23×C113C22×D411yescharacteristic
305Q8×C113—22no—
306Q8×C113—22no—
307Q8×C113—41no—
308Q8×C113—41no—
309D4×C113—22no—
310D4×C113—22no—
311D4×C113—22no—
312D4×C113—22no—
313D4×C113—48no—
314D4×C113—41no—
315D4×C113—41no—
316D4×C113—41no—
317D4×C113—41no—
318D4×C113—41no—
319D4×C113—41no—
320D4×C113—41no—
321D4×C113—41no—
322D4×C113—84no—
323D4×C113—84no—
324D4×C113—84no—
325D4×C113—84no—
326D4×C113—84no—
327C2×C4×C113—21no—
328C2×C4×C113—21no—
329C2×C4×C113—21no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—22no—
334C2×C4×C113—22no—
335C2×C4×C113—22no—
336C2×C4×C113—22no—
337C2×C4×C113—22no—
338C2×C4×C113—22no—
339C2×C4×C113—21no—
340C2×C4×C113—22no—
341C2×C4×C113—21no—
342C2×C4×C113—21no—
343C2×C4×C113—21no—
344C2×C4×C113—21no—
345C2×C4×C113—21no—
346C2×C4×C113—41no—
347C2×C4×C113—41no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—41no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
353C2×C4×C113—41no—
354C2×C4×C113—41no—
355C2×C4×C113—41no—
356C2×C4×C113—41no—
357C2×C4×C113—41no—
358C2×C4×C113#12112yes—
359C2×C4×C113AGL(1,ℤ/8)12yes—
360C2×C4×C113AGL(1,ℤ/8)12yes—
361C2×C4×C113C22×D411yescharacteristic
362C2×C4×C113C22×D411yescharacteristic
363C2×C4×C113C2×#4111yescharacteristic
364C2×C4×C113C2×#4111yescharacteristic
365C2×C4×C113H(5,𝔽2)11yescharacteristic
366C2×C4×C113H(5,𝔽2)11yescharacteristic
367C8×C113—22no—
368C8×C113—41no—
369C8×C113—41no—
370C8×C113—41no—
371C22×C113—22no—
372C22×C113—22no—
373C22×C113—22no—
374C22×C113—41no—
375C22×C113—41no—
376C22×C113—41no—
377C22×C113—41no—
378C22×C113—42no—
379C22×C113—42no—
380C22×C113—42no—
381C22×C113—42no—
382C22×C113—42no—
383C22×C113—42no—
384C22×C113—816no—
385C22×C113—81no—
386C22×C113—81no—
387C22×C113—81no—
388C22×C113—81no—
389C22×C113—81no—
390C22×C113—81no—
391C22×C113—81no—
392C22×C113—81no—
393C22×C113—81no—
394C22×C113—81no—
395C22×C113—81no—
396C22×C113—81no—
397C22×C113—81no—
398C22×C113—81no—
399C22×C113—81no—
400C22×C113C2×#12111yescharacteristic
401C22×C113D4211yescharacteristic
402C22×C113#54611yescharacteristic
403C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
404C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C113#57711yescharacteristic
406C22×C113#57711yescharacteristic
407C4×C113—22no—
408C4×C113—22no—
409C4×C113—22no—
410C4×C113—42no—
411C4×C113—41no—
412C4×C113—42no—
413C4×C113—42no—
414C4×C113—41no—
415C4×C113—81no—
416C4×C113—81no—
417C4×C113#52511yescharacteristic
418C4×C113#53811yescharacteristic
419C4×C113D4211yescharacteristic
420C4×C113#54611yescharacteristic
421#25093C11311yesmaximal, characteristic, direct product factor, Sylow
422C2×C113—42no—
423C2×C113—82no—
424C2×C113—82no—
425C2×C113—161no—
426C2×C113#242411yescharacteristic
427C2×C113#303811yescharacteristic
428C2×C113#304311yescharacteristic
429C2×C113#326511yescharacteristic
430C2×C113#327211yescharacteristic
431C2×C113#331011yescharacteristic
432C2×C113#332411yescharacteristic
433C2×#468C2×C11311yescharacteristic, complemented
434C2×#460C2×C11311yescharacteristic, complemented
435C2×#450C2×C11311yescharacteristic, complemented
436C2×#418C2×C11311yescharacteristic, complemented
437#2433C2×C11311yescharacteristic
438#2362C2×C11311yescharacteristic, complemented
439#2067C2×C11311yescharacteristic, complemented
440#2055C2×C11311yescharacteristic, complemented
441#2041C2×C11311yescharacteristic, complemented
442#2014C2×C11311yescharacteristic, complemented
443#1982C2×C11311yescharacteristic, complemented
444#1925C2×C11311yescharacteristic, complemented
445#1880C2×C11311yescharacteristic, complemented
446#1875C2×C11311yescharacteristic, complemented
447#1851C2×C11311yescharacteristic, complemented
448C113#2509311yescharacteristic, direct product factor, Sylow
449C23×D4C22×C11311yescharacteristic
450C22×SD16C22×C11311yescharacteristic
451C22×SD16C22×C11311yescharacteristic
452C22×SD16C22×C11311yescharacteristic, complemented
453C22×M16C22×C11311yescharacteristic
454C2×#127C22×C11311yescharacteristic
455C2×#127C22×C11311yescharacteristic
456C2×C22⋊Q8C22×C11311yescharacteristic
457C2×#121C22×C11311yescharacteristic
458C2×#120—21no—
459C2×#120—21no—
460C2×C4×Q8C22×C11311yescharacteristic, complemented
461C2×#117C22×C11311yescharacteristic
462#468—24no—
463#460—24no—
464#450—24no—
465C2×#107C22×C11311yescharacteristic, complemented
466C2×C4⋊C8C22×C11311yescharacteristic, complemented
467C2×C4⋊C8C22×C11311yescharacteristic, complemented
468#418—24no—
469C2×#103C22×C11311yescharacteristic, complemented
470C2×#102C22×C11311yescharacteristic
471C2×#102C22×C11311yescharacteristic
472C2×#102C22×C11311yescharacteristic
473C2×#102C22×C11311yescharacteristic
474C2×#102C22×C11311yescharacteristic
475C2×#102C22×C11311yescharacteristic
476C2×#102C22×C11311yescharacteristic, complemented
477C2×#102C22×C11311yescharacteristic, complemented
478C2×#102C22×C11311yescharacteristic, complemented
479C2×C22⋊C8C22×C11311yescharacteristic
480#392—21no—
481#392—21no—
482#391C22×C11311yescharacteristic, complemented
483#390C22×C11311yescharacteristic
484#390C22×C11311yescharacteristic
485#389C22×C11311yescharacteristic, complemented
486#388—21no—
487#388—21no—
488#387—21no—
489C4×C4⋊C4—21no—
490C4×C4⋊C4C22×C11311yescharacteristic, complemented
491C4×C22⋊C4C22×C11311yescharacteristic
492#340C22×C11311yescharacteristic, complemented
493#340C22×C11311yescharacteristic, complemented
494#336C22×C11311yescharacteristic, complemented
495#336C22×C11311yescharacteristic, complemented
496C25—21no—
497C22×Q8C23×C11311yescharacteristic
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C11311yescharacteristic
511C22×D4C23×C11311yescharacteristic
512C22×D4C23×C11311yescharacteristic
513C23×C4C23×C11311yescharacteristic
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C22×C8C23×C11311yescharacteristic
527C22×C8C23×C11311yescharacteristic
528C22×C8C23×C11311yescharacteristic
529C22×C8C23×C11311yescharacteristic
530#127—22no—
531#127—22no—
532#127—41no—
533#127—41no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C11314yescomplemented
536#121—22no—
537#121—22no—
538#120—44no—
539#120—44no—
540C4×Q8—22no—
541C4×Q8—41no—
542#117—22no—
543#117—41no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4C23×C11311yescharacteristic
548C2×C4⋊C4C23×C11311yescharacteristic
549C2×C4⋊C4C23×C11311yescharacteristic
550C2×C4⋊C4C23×C11311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4D4×C11311yescharacteristic
559C2×C22⋊C4D4×C11311yescharacteristic
560C2×C42—21no—
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C11311yescharacteristic
564C2×C42C23×C11311yescharacteristic
565#107—22no—
566C4⋊C8—22no—
567C4⋊C8—41no—
568#103—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—41no—
577#102D4×C11314yescomplemented
578C22⋊C8—22no—
579#95—21no—
580#95—21no—
581#95—21no—
582#95—21no—
583#95D4×C11311yescharacteristic
584#95D4×C11311yescharacteristic
585C24—21no—
586C24—21no—
587C24—21no—
588C24—42no—
589C24—42no—
590C24—42no—
591C24—42no—
592C24—42no—
593C24—81no—
594C24—81no—
595C24C2×D4×C11311yescharacteristic
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C11312yes—
602C2×D4—28no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4C2×D4×C11312yes—
641C2×D4#41×C11312yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4C2×D4×C11311yescharacteristic
652C22×C4C2×D4×C11311yescharacteristic
653C22×C4C2×D4×C11311yescharacteristic
654C22×C4C2×D4×C11312yes—
655C22×C4C2×D4×C11311yescharacteristic
656C22×C4C2×D4×C11311yescharacteristic
657C22×C4#41×C11312yes—
658C22×C4C24×C11311yescharacteristic
659SD16—44no—
660SD16—44no—
661SD16—44no—
662M16—44no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8C2×D4×C11312yes—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4C2×D4×C11312yes—
685C4⋊C4C2×D4×C11312yes—
686C22⋊C4—24no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—42no—
700C42—42no—
701C42—42no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23#121×C11312yes—
737C23C22×D4×C11311yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—41no—
741Q8—41no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#121×C11312yes—
792C2×C4AGL(1,ℤ/8)×C11312yes—
793C2×C4AGL(1,ℤ/8)×C11312yes—
794C2×C4C22×D4×C11311yescharacteristic
795C2×C4C22×D4×C11311yescharacteristic
796C2×C4C2×#41×C11311yescharacteristic
797C2×C4C2×#41×C11311yescharacteristic
798C2×C4H(5,𝔽2)×C11311yescharacteristic
799C2×C4H(5,𝔽2)×C11311yescharacteristic
800C8—22no—
801C8—41no—
802C8—41no—
803C8—41no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22C2×#121×C11311yescharacteristic
834C22D42×C11311yescharacteristic
835C22#546×C11311yescharacteristic
836C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
837C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
838C22#577×C11311yescharacteristic
839C22#577×C11311yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—41no—
844C4—42no—
845C4—41no—
846C4—42no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4#525×C11311yescharacteristic
851C4#538×C11311yescharacteristic
852C4D42×C11311yescharacteristic
853C4#546×C11311yescharacteristic
854C2—42no—
855C2—82no—
856C2—82no—
857C2—161no—
858C2C113×#242411yescharacteristic
859C2C113×#303811yescharacteristic
860C2C113×#304311yescharacteristic
861C2C113×#326511yescharacteristic
862C2C113×#327211yescharacteristic
863C2C113×#331011yescharacteristic
864C2C113×#332411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2433C2
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×#460×C113C2semidirect
3. C2×#450×C113C2semidirect
4. C2×#418×C113C2semidirect
6. C113×#2362C2semidirect
7. C113×#2067C2semidirect
8. C113×#2055C2semidirect
9. C113×#2041C2semidirect
10. C113×#2014C2semidirect
11. C113×#1982C2semidirect
12. C113×#1925C2semidirect
13. C113×#1880C2semidirect
14. C113×#1875C2semidirect
15. C113×#1851C2semidirect
19. C22×SD16×C113C22semidirect
27. C2×C4×Q8×C113C22semidirect
32. C2×#107×C113C22semidirect
33. C2×C4⋊C8×C113C22semidirect
34. C2×C4⋊C8×C113C22semidirect
36. C2×#103×C113C22semidirect
43. C2×#102×C113C22semidirect
44. C2×#102×C113C22semidirect
45. C2×#102×C113C22semidirect
49. #391×C113C22semidirect
52. #389×C113C22semidirect
57. C4×C4⋊C4×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
102. C22⋊Q8×C113D4semidirect
144. #102×C113D4semidirect
421. #25093C113direct (N × H)
433. C2×#468C2×C113semidirect
434. C2×#460C2×C113semidirect
435. C2×#450C2×C113semidirect
436. C2×#418C2×C113semidirect
438. #2362C2×C113semidirect
439. #2067C2×C113semidirect
440. #2055C2×C113semidirect
441. #2041C2×C113semidirect
442. #2014C2×C113semidirect
443. #1982C2×C113semidirect
444. #1925C2×C113semidirect
445. #1880C2×C113semidirect
446. #1875C2×C113semidirect
447. #1851C2×C113semidirect
448. C113#25093direct (N × H)
452. C22×SD16C22×C113semidirect
460. C2×C4×Q8C22×C113semidirect
465. C2×#107C22×C113semidirect
466. C2×C4⋊C8C22×C113semidirect
467. C2×C4⋊C8C22×C113semidirect
469. C2×#103C22×C113semidirect
476. C2×#102C22×C113semidirect
477. C2×#102C22×C113semidirect
478. C2×#102C22×C113semidirect
482. #391C22×C113semidirect
485. #389C22×C113semidirect
490. C4×C4⋊C4C22×C113semidirect
492. #340C22×C113semidirect
493. #340C22×C113semidirect
494. #336C22×C113semidirect
495. #336C22×C113semidirect
535. C22⋊Q8D4×C113semidirect
577. #102D4×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×#460×C1132
C2×#450×C1132
C2×#418×C1132
C113×#24332
C113×#23622
C113×#20672
C113×#20552
C113×#20412
C113×#20142
C113×#19822
C113×#19252
C113×#18802
C113×#18752
C113×#18512
#25093113