Finite Group Databasebeta

← C113×#25128 #43293148

Subgroups — C113×#25128 #43293148

Order 28928.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#450×C113C211yesmaximal, characteristic, complemented
3C2×#435×C113C211yesmaximal, characteristic, complemented
4C22×#102×C113C211yesmaximal, characteristic, complemented
5C113×#2417C211yesmaximal, characteristic, complemented
6C113×#2408C211yesmaximal, characteristic
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2033C211yesmaximal, characteristic, complemented
10C113×#2000C211yesmaximal, characteristic, complemented
11C113×#1973C211yesmaximal, characteristic, complemented
12C113×#1936C211yesmaximal, characteristic, complemented
13C113×#1895C211yesmaximal, characteristic, complemented
14C113×#1892C211yesmaximal, characteristic, complemented
15C113×#1852C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×M16×C113C2211yescharacteristic, complemented
20C23×C8×C113C2211yescharacteristic
21C2×C22⋊Q8×C113C2211yescharacteristic
22C2×C22⋊Q8×C113C2211yescharacteristic, complemented
23C2×#121×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×#120×C113—21no—
26C2×C4×D4×C113C2211yescharacteristic
27C22×C4⋊C4×C113C2211yescharacteristic
28#468×C113—24no—
29#450×C113—24no—
30#435×C113—24no—
31C2×#107×C113C2211yescharacteristic, complemented
32C2×#107×C113C2211yescharacteristic, complemented
33C2×C4⋊C8×C113C2211yescharacteristic, complemented
34C2×#103×C113C2211yescharacteristic, complemented
35C2×#103×C113C2211yescharacteristic, complemented
36C2×#102×C113—24no—
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic, complemented
45C2×#97×C113C2211yescharacteristic, complemented
46#398×C113—21no—
47#396×C113—21no—
48#394×C113—21no—
49#392×C113—21no—
50#391×C113C2211yescharacteristic, complemented
51#390×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic
53#389×C113C2211yescharacteristic, complemented
54#386×C113—21no—
55#380×C113—21no—
56#380×C113C2211yescharacteristic
57#380×C113C2211yescharacteristic, complemented
58#379×C113—21no—
59#340×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#340×C113C2211yescharacteristic, complemented
62#340×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C22×Q8×C113C2311yescharacteristic
65C22×D4×C113—22no—
66C22×D4×C113—22no—
67C22×D4×C113—21no—
68C22×D4×C113—21no—
69C22×D4×C113—22no—
70C22×D4×C113—21no—
71C22×D4×C113—22no—
72C22×D4×C113—41no—
73C22×D4×C113—41no—
74C22×D4×C113D411yescharacteristic
75C22×D4×C113C2311yescharacteristic
76C22×D4×C113C2311yescharacteristic
77C23×C4×C113—21no—
78C23×C4×C113C2311yescharacteristic
79C23×C4×C113C2311yescharacteristic
80C2×SD16×C113—22no—
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—22no—
84C2×SD16×C113—41no—
85C2×SD16×C113—41no—
86C2×M16×C113—22no—
87C2×M16×C113—22no—
88C2×M16×C113—41no—
89C22×C8×C113—22no—
90C22×C8×C113—22no—
91C22×C8×C113—41no—
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113—22no—
99C22⋊Q8×C113—41no—
100#121×C113—22no—
101#121×C113—22no—
102#121×C113—41no—
103#121×C113—41no—
104#120×C113—44no—
105C4×D4×C113—22no—
106C4×D4×C113—22no—
107C2×C4⋊C4×C113—22no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113—21no—
112C2×C4⋊C4×C113—41no—
113C2×C4⋊C4×C113D411yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
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×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113D411yescharacteristic
130C2×C22⋊C4×C113D411yescharacteristic
131C2×C42×C113C2311yescharacteristic
132#107×C113—22no—
133#107×C113—41no—
134C4⋊C8×C113—22no—
135#103×C113—22no—
136#103×C113—41no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113D414yescomplemented
143C22⋊C8×C113—22no—
144C22⋊C8×C113D414yescomplemented
145#97×C113—22no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113—21no—
149#95×C113—21no—
150#95×C113—21no—
151C24×C113—21no—
152C24×C113—21no—
153C24×C113—42no—
154C24×C113—42no—
155C24×C113—42no—
156C24×C113—42no—
157C24×C113—42no—
158C24×C113—81no—
159C24×C113—81no—
160C24×C113C2×D411yescharacteristic
161C24×C113C2×D411yescharacteristic
162C2×Q8×C113—21no—
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×Q8×C113—21no—
166C2×Q8×C113—21no—
167C2×Q8×C113—21no—
168C2×D4×C113—28no—
169C2×D4×C113—22no—
170C2×D4×C113—22no—
171C2×D4×C113—22no—
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—44no—
183C2×D4×C113—44no—
184C2×D4×C113—42no—
185C2×D4×C113—42no—
186C2×D4×C113—44no—
187C2×D4×C113—42no—
188C2×D4×C113—42no—
189C2×D4×C113—42no—
190C2×D4×C113—42no—
191C2×D4×C113—42no—
192C2×D4×C113—81no—
193C2×D4×C113—81no—
194C2×D4×C113C2×D412yes—
195C2×D4×C113#4112yes—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—21no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—42no—
213C22×C4×C113—42no—
214C22×C4×C113—81no—
215C22×C4×C113C2×D411yescharacteristic
216C22×C4×C113C2×D411yescharacteristic
217C22×C4×C113C2×D411yescharacteristic
218C22×C4×C113C2×D411yescharacteristic
219C22×C4×C113C2×D412yes—
220C22×C4×C113#4112yes—
221C22×C4×C113C2411yescharacteristic
222SD16×C113—44no—
223SD16×C113—44no—
224M16×C113—44no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113—21no—
234C2×C8×C113—44no—
235C2×C8×C113C2×D412yes—
236C2×C8×C113C2×D412yes—
237C2×C8×C113C2×D412yes—
238C4⋊C4×C113—22no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—21no—
243C4⋊C4×C113—21no—
244C4⋊C4×C113—21no—
245C4⋊C4×C113—21no—
246C4⋊C4×C113—21no—
247C4⋊C4×C113—21no—
248C4⋊C4×C113—42no—
249C4⋊C4×C113—42no—
250C4⋊C4×C113—42no—
251C4⋊C4×C113—81no—
252C4⋊C4×C113C2×D412yes—
253C22⋊C4×C113—22no—
254C22⋊C4×C113—22no—
255C22⋊C4×C113—42no—
256C22⋊C4×C113—42no—
257C22⋊C4×C113—42no—
258C22⋊C4×C113—42no—
259C22⋊C4×C113—42no—
260C22⋊C4×C113—42no—
261C22⋊C4×C113—42no—
262C22⋊C4×C113—81no—
263C22⋊C4×C113—81no—
264C22⋊C4×C113—81no—
265C42×C113—21no—
266C42×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—21no—
272C23×C113—21no—
273C23×C113—22no—
274C23×C113—22no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—48no—
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—84no—
294C23×C113—84no—
295C23×C113—84no—
296C23×C113—84no—
297C23×C113—84no—
298C23×C113—84no—
299C23×C113#12112yes—
300C23×C113AGL(1,ℤ/8)12yes—
301C23×C113#13712yes—
302C23×C113C22×D411yescharacteristic
303Q8×C113—41no—
304Q8×C113—41no—
305Q8×C113—41no—
306Q8×C113—41no—
307D4×C113—22no—
308D4×C113—22no—
309D4×C113—22no—
310D4×C113—22no—
311D4×C113—48no—
312D4×C113—44no—
313D4×C113—41no—
314D4×C113—41no—
315D4×C113—41no—
316D4×C113—41no—
317D4×C113—84no—
318D4×C113—84no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—22no—
322C2×C4×C113—22no—
323C2×C4×C113—22no—
324C2×C4×C113—22no—
325C2×C4×C113—21no—
326C2×C4×C113—21no—
327C2×C4×C113—21no—
328C2×C4×C113—21no—
329C2×C4×C113—22no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—21no—
334C2×C4×C113—21no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113—41no—
339C2×C4×C113—41no—
340C2×C4×C113—41no—
341C2×C4×C113—41no—
342C2×C4×C113—41no—
343C2×C4×C113—41no—
344C2×C4×C113—41no—
345C2×C4×C113—41no—
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—84no—
357C2×C4×C113#12112yes—
358C2×C4×C113C22×D411yescharacteristic
359C2×C4×C113C22×D411yescharacteristic
360C2×C4×C113C2×#4111yescharacteristic
361C2×C4×C113C2×#4111yescharacteristic
362C2×C4×C113H(5,𝔽2)11yescharacteristic
363C2×C4×C113H(5,𝔽2)11yescharacteristic
364C8×C113—22no—
365C8×C113—22no—
366C8×C113—22no—
367C8×C113—41no—
368C22×C113—22no—
369C22×C113—22no—
370C22×C113—22no—
371C22×C113—22no—
372C22×C113—22no—
373C22×C113—22no—
374C22×C113—41no—
375C22×C113—42no—
376C22×C113—42no—
377C22×C113—41no—
378C22×C113—42no—
379C22×C113—41no—
380C22×C113—42no—
381C22×C113—41no—
382C22×C113—41no—
383C22×C113—42no—
384C22×C113—41no—
385C22×C113—42no—
386C22×C113—41no—
387C22×C113—816no—
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#46814yescomplemented
397C22×C113C2×#12111yescharacteristic
398C22×C113D4211yescharacteristic
399C22×C113#54611yescharacteristic
400C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C113C2×#13711yescharacteristic
402C22×C113#57611yescharacteristic
403C22×C113#57711yescharacteristic
404C4×C113—22no—
405C4×C113—41no—
406C4×C113—42no—
407C4×C113—41no—
408C4×C113—41no—
409C4×C113—81no—
410C4×C113—81no—
411C4×C113—81no—
412C4×C113—81no—
413C4×C113—81no—
414C4×C113#52511yescharacteristic
415C4×C113#53811yescharacteristic
416C4×C113D4211yescharacteristic
417C4×C113#54611yescharacteristic
418#25128C11311yesmaximal, characteristic, direct product factor, Sylow
419C2×C113—24no—
420C2×C113—81no—
421C2×C113—82no—
422C2×C113—82no—
423C2×C113#242411yescharacteristic
424C2×C113C2×#46811yescharacteristic
425C2×C113#306211yescharacteristic
426C2×C113#326411yescharacteristic
427C2×C113#326611yescharacteristic
428C2×C113#331011yescharacteristic
429C2×C113#331411yescharacteristic
430C2×#468C2×C11311yescharacteristic, complemented
431C2×#450C2×C11311yescharacteristic, complemented
432C2×#435C2×C11311yescharacteristic, complemented
433C22×#102C2×C11311yescharacteristic, complemented
434#2417C2×C11311yescharacteristic, complemented
435#2408C2×C11311yescharacteristic
436#2067C2×C11311yescharacteristic, complemented
437#2055C2×C11311yescharacteristic, complemented
438#2033C2×C11311yescharacteristic, complemented
439#2000C2×C11311yescharacteristic, complemented
440#1973C2×C11311yescharacteristic, complemented
441#1936C2×C11311yescharacteristic, complemented
442#1895C2×C11311yescharacteristic, complemented
443#1892C2×C11311yescharacteristic, complemented
444#1852C2×C11311yescharacteristic, complemented
445C113#2512811yescharacteristic, direct product factor, Sylow
446C23×D4C22×C11311yescharacteristic
447C22×SD16C22×C11311yescharacteristic
448C22×SD16C22×C11311yescharacteristic
449C22×M16C22×C11311yescharacteristic, complemented
450C23×C8C22×C11311yescharacteristic
451C2×C22⋊Q8C22×C11311yescharacteristic
452C2×C22⋊Q8C22×C11311yescharacteristic, complemented
453C2×#121C22×C11311yescharacteristic
454C2×#121C22×C11311yescharacteristic
455C2×#120—21no—
456C2×C4×D4C22×C11311yescharacteristic
457C22×C4⋊C4C22×C11311yescharacteristic
458#468—24no—
459#450—24no—
460#435—24no—
461C2×#107C22×C11311yescharacteristic, complemented
462C2×#107C22×C11311yescharacteristic, complemented
463C2×C4⋊C8C22×C11311yescharacteristic, complemented
464C2×#103C22×C11311yescharacteristic, complemented
465C2×#103C22×C11311yescharacteristic, complemented
466C2×#102—24no—
467C2×#102C22×C11311yescharacteristic
468C2×#102C22×C11311yescharacteristic
469C2×#102C22×C11311yescharacteristic
470C2×#102C22×C11311yescharacteristic
471C2×#102C22×C11311yescharacteristic
472C2×#102C22×C11311yescharacteristic
473C2×C22⋊C8C22×C11311yescharacteristic
474C2×C22⋊C8C22×C11311yescharacteristic, complemented
475C2×#97C22×C11311yescharacteristic, complemented
476#398—21no—
477#396—21no—
478#394—21no—
479#392—21no—
480#391C22×C11311yescharacteristic, complemented
481#390C22×C11311yescharacteristic
482#390C22×C11311yescharacteristic
483#389C22×C11311yescharacteristic, complemented
484#386—21no—
485#380—21no—
486#380C22×C11311yescharacteristic
487#380C22×C11311yescharacteristic, complemented
488#379—21no—
489#340C22×C11311yescharacteristic, complemented
490#340C22×C11311yescharacteristic, complemented
491#340C22×C11311yescharacteristic, complemented
492#340C22×C11311yescharacteristic, complemented
493C25—21no—
494C22×Q8C23×C11311yescharacteristic
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4D4×C11311yescharacteristic
505C22×D4C23×C11311yescharacteristic
506C22×D4C23×C11311yescharacteristic
507C23×C4—21no—
508C23×C4C23×C11311yescharacteristic
509C23×C4C23×C11311yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C23×C11311yescharacteristic
523C22×C8C23×C11311yescharacteristic
524C22×C8C23×C11311yescharacteristic
525C22×C8C23×C11311yescharacteristic
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—22no—
532#121—41no—
533#121—41no—
534#120—44no—
535C4×D4—22no—
536C4×D4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4D4×C11311yescharacteristic
544C2×C4⋊C4C23×C11311yescharacteristic
545C2×C4⋊C4C23×C11311yescharacteristic
546C2×C4⋊C4C23×C11311yescharacteristic
547C2×C4⋊C4C23×C11311yescharacteristic
548C2×C4⋊C4C23×C11311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
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⋊C4—21no—
559C2×C22⋊C4D4×C11311yescharacteristic
560C2×C22⋊C4D4×C11311yescharacteristic
561C2×C42C23×C11311yescharacteristic
562#107—22no—
563#107—41no—
564C4⋊C8—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102D4×C11314yescomplemented
573C22⋊C8—22no—
574C22⋊C8D4×C11314yescomplemented
575#97—22no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C11311yescharacteristic
591C24C2×D4×C11311yescharacteristic
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×D4—28no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
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—44no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4C2×D4×C11312yes—
625C2×D4#41×C11312yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C2×D4×C11311yescharacteristic
646C22×C4C2×D4×C11311yescharacteristic
647C22×C4C2×D4×C11311yescharacteristic
648C22×C4C2×D4×C11311yescharacteristic
649C22×C4C2×D4×C11312yes—
650C22×C4#41×C11312yes—
651C22×C4C24×C11311yescharacteristic
652SD16—44no—
653SD16—44no—
654M16—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—44no—
665C2×C8C2×D4×C11312yes—
666C2×C8C2×D4×C11312yes—
667C2×C8C2×D4×C11312yes—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4C2×D4×C11312yes—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—81no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C42—21no—
696C42—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
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—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#121×C11312yes—
730C23AGL(1,ℤ/8)×C11312yes—
731C23#137×C11312yes—
732C23C22×D4×C11311yescharacteristic
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—44no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—84no—
787C2×C4#121×C11312yes—
788C2×C4C22×D4×C11311yescharacteristic
789C2×C4C22×D4×C11311yescharacteristic
790C2×C4C2×#41×C11311yescharacteristic
791C2×C4C2×#41×C11311yescharacteristic
792C2×C4H(5,𝔽2)×C11311yescharacteristic
793C2×C4H(5,𝔽2)×C11311yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22#468×C11314yescomplemented
827C22C2×#121×C11311yescharacteristic
828C22D42×C11311yescharacteristic
829C22#546×C11311yescharacteristic
830C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
831C22C2×#137×C11311yescharacteristic
832C22#576×C11311yescharacteristic
833C22#577×C11311yescharacteristic
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—42no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4#525×C11311yescharacteristic
845C4#538×C11311yescharacteristic
846C4D42×C11311yescharacteristic
847C4#546×C11311yescharacteristic
848C2—24no—
849C2—81no—
850C2—82no—
851C2—82no—
852C2C113×#242411yescharacteristic
853C2C2×#468×C11311yescharacteristic
854C2C113×#306211yescharacteristic
855C2C113×#326411yescharacteristic
856C2C113×#326611yescharacteristic
857C2C113×#331011yescharacteristic
858C2C113×#331411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2408C2
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×#468×C113C2semidirect
2. C2×#450×C113C2semidirect
3. C2×#435×C113C2semidirect
4. C22×#102×C113C2semidirect
5. C113×#2417C2semidirect
7. C113×#2067C2semidirect
8. C113×#2055C2semidirect
9. C113×#2033C2semidirect
10. C113×#2000C2semidirect
11. C113×#1973C2semidirect
12. C113×#1936C2semidirect
13. C113×#1895C2semidirect
14. C113×#1892C2semidirect
15. C113×#1852C2semidirect
19. C22×M16×C113C22semidirect
22. C2×C22⋊Q8×C113C22semidirect
31. C2×#107×C113C22semidirect
32. C2×#107×C113C22semidirect
33. C2×C4⋊C8×C113C22semidirect
34. C2×#103×C113C22semidirect
35. C2×#103×C113C22semidirect
44. C2×C22⋊C8×C113C22semidirect
45. C2×#97×C113C22semidirect
50. #391×C113C22semidirect
53. #389×C113C22semidirect
57. #380×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #340×C113C22semidirect
62. #340×C113C22semidirect
142. #102×C113D4semidirect
144. C22⋊C8×C113D4semidirect
396. C22×C113#468semidirect
418. #25128C113direct (N × H)
430. C2×#468C2×C113semidirect
431. C2×#450C2×C113semidirect
432. C2×#435C2×C113semidirect
433. C22×#102C2×C113semidirect
434. #2417C2×C113semidirect
436. #2067C2×C113semidirect
437. #2055C2×C113semidirect
438. #2033C2×C113semidirect
439. #2000C2×C113semidirect
440. #1973C2×C113semidirect
441. #1936C2×C113semidirect
442. #1895C2×C113semidirect
443. #1892C2×C113semidirect
444. #1852C2×C113semidirect
445. C113#25128direct (N × H)
449. C22×M16C22×C113semidirect
452. C2×C22⋊Q8C22×C113semidirect
461. C2×#107C22×C113semidirect
462. C2×#107C22×C113semidirect
463. C2×C4⋊C8C22×C113semidirect
464. C2×#103C22×C113semidirect
465. C2×#103C22×C113semidirect
474. C2×C22⋊C8C22×C113semidirect
475. C2×#97C22×C113semidirect
480. #391C22×C113semidirect
483. #389C22×C113semidirect
487. #380C22×C113semidirect
489. #340C22×C113semidirect
490. #340C22×C113semidirect
491. #340C22×C113semidirect
492. #340C22×C113semidirect
572. #102D4×C113semidirect
574. C22⋊C8D4×C113semidirect
826. C22#468×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×#450×C1132
C2×#435×C1132
C22×#102×C1132
C113×#24172
C113×#24082
C113×#20672
C113×#20552
C113×#20332
C113×#20002
C113×#19732
C113×#19362
C113×#18952
C113×#18922
C113×#18522
#25128113