Finite Group Databasebeta

← C113×#25097 #43293117

Subgroups — C113×#25097 #43293117

Order 28928.

1378 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C113C211yesmaximal, characteristic, complemented
2C2×#459×C113C211yesmaximal, characteristic, complemented
3C2×#447×C113C211yesmaximal, characteristic, complemented
4C2×#418×C113C211yesmaximal, characteristic, complemented
5C113×#2433C211yesmaximal, characteristic, complemented
6C113×#2363C211yesmaximal, characteristic, complemented
7C113×#2065C211yesmaximal, characteristic, complemented
8C113×#2054C211yesmaximal, characteristic, complemented
9C113×#2041C211yesmaximal, characteristic, complemented
10C113×#2011C211yesmaximal, characteristic, complemented
11C113×#1982C211yesmaximal, characteristic, complemented
12C113×#1926C211yesmaximal, characteristic, complemented
13C113×#1879C211yesmaximal, characteristic, complemented
14C113×#1875C211yesmaximal, characteristic, complemented
15C113×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×D8×C113C2211yescharacteristic
18C22×D8×C113C2211yescharacteristic
19C22×D8×C113C2211yescharacteristic, complemented
20C22×M16×C113C2211yescharacteristic
21C2×#127×C113C2211yescharacteristic
22C2×#127×C113C2211yescharacteristic
23C2×#121×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×#120×C113—21no—
26C2×#120×C113—21no—
27C2×C4×D4×C113C2211yescharacteristic, complemented
28C2×#117×C113C2211yescharacteristic
29#469×C113—24no—
30#459×C113—24no—
31#447×C113—24no—
32C2×#106×C113C2211yescharacteristic, complemented
33C2×C4⋊C8×C113C2211yescharacteristic, complemented
34C2×C4⋊C8×C113C2211yescharacteristic, complemented
35#418×C113—24no—
36C2×#102×C113C2211yescharacteristic
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic, complemented
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#390×C113—21no—
50#390×C113C2211yescharacteristic
51#390×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic, complemented
53#389×C113C2211yescharacteristic, complemented
54#388×C113—21no—
55#386×C113—21no—
56C4×C4⋊C4×C113C2211yescharacteristic, complemented
57C4×C22⋊C4×C113—21no—
58C4×C22⋊C4×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#336×C113C2211yescharacteristic, complemented
62#336×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C22×D4×C113—22no—
65C22×D4×C113—22no—
66C22×D4×C113—21no—
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
80C22×D4×C113C2311yescharacteristic
81C23×C4×C113—21no—
82C23×C4×C113C2311yescharacteristic
83C2×D8×C113—22no—
84C2×D8×C113—22no—
85C2×D8×C113—22no—
86C2×D8×C113—22no—
87C2×D8×C113—22no—
88C2×D8×C113—22no—
89C2×D8×C113—41no—
90C2×D8×C113—41no—
91C2×D8×C113—41no—
92C2×M16×C113—22no—
93C2×M16×C113—22no—
94C2×M16×C113—41no—
95C22×C8×C113C2311yescharacteristic
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98C22×C8×C113C2311yescharacteristic
99#127×C113—22no—
100#127×C113—22no—
101#127×C113—41no—
102#127×C113—41no—
103#121×C113—22no—
104#121×C113—22no—
105#121×C113—22no—
106#121×C113D414yescomplemented
107#120×C113—44no—
108#120×C113—44no—
109C4×D4×C113—22no—
110C4×D4×C113—41no—
111#117×C113—22no—
112#117×C113—41no—
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×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113D411yescharacteristic
129C2×C22⋊C4×C113D411yescharacteristic
130C2×C42×C113—21no—
131C2×C42×C113—21no—
132C2×C42×C113C2311yescharacteristic
133C2×C42×C113C2311yescharacteristic
134#106×C113—22no—
135C4⋊C8×C113—22no—
136C4⋊C8×C113—41no—
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—22no—
144#102×C113—22no—
145#102×C113—41no—
146#102×C113D414yescomplemented
147C22⋊C8×C113—22no—
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—21no—
156C24×C113—42no—
157C24×C113—42no—
158C24×C113—42no—
159C24×C113—42no—
160C24×C113—42no—
161C24×C113—81no—
162C24×C113—81no—
163C24×C113C2×D411yescharacteristic
164C2×D4×C113—28no—
165C2×D4×C113—24no—
166C2×D4×C113—21no—
167C2×D4×C113—21no—
168C2×D4×C113—21no—
169C2×D4×C113—21no—
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—21no—
187C2×D4×C113—44no—
188C2×D4×C113—44no—
189C2×D4×C113—42no—
190C2×D4×C113—42no—
191C2×D4×C113—44no—
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—42no—
204C2×D4×C113—81no—
205C2×D4×C113—81no—
206C2×D4×C113—81no—
207C2×D4×C113—81no—
208C2×D4×C113—81no—
209C2×D4×C113—81no—
210C2×D4×C113C2×D412yes—
211C2×D4×C113C2×D412yes—
212C2×D4×C113#4112yes—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—42no—
222C22×C4×C113—42no—
223C22×C4×C113—81no—
224C22×C4×C113C2×D411yescharacteristic
225C22×C4×C113C2×D411yescharacteristic
226C22×C4×C113C2×D411yescharacteristic
227C22×C4×C113C2×D412yes—
228C22×C4×C113C2×D411yescharacteristic
229C22×C4×C113C2×D411yescharacteristic
230C22×C4×C113#4112yes—
231C22×C4×C113C2411yescharacteristic
232D8×C113—44no—
233D8×C113—44no—
234D8×C113—44no—
235M16×C113—44no—
236C2×C8×C113—21no—
237C2×C8×C113—21no—
238C2×C8×C113—21no—
239C2×C8×C113—21no—
240C2×C8×C113—21no—
241C2×C8×C113—21no—
242C2×C8×C113—21no—
243C2×C8×C113—21no—
244C2×C8×C113—21no—
245C2×C8×C113—21no—
246C2×C8×C113—21no—
247C2×C8×C113C2×D412yes—
248C4⋊C4×C113—21no—
249C4⋊C4×C113—21no—
250C4⋊C4×C113—21no—
251C4⋊C4×C113—21no—
252C4⋊C4×C113—21no—
253C4⋊C4×C113—21no—
254C4⋊C4×C113—81no—
255C4⋊C4×C113C2×D412yes—
256C4⋊C4×C113C2×D412yes—
257C22⋊C4×C113—24no—
258C22⋊C4×C113—22no—
259C22⋊C4×C113—22no—
260C22⋊C4×C113—42no—
261C22⋊C4×C113—42no—
262C22⋊C4×C113—42no—
263C22⋊C4×C113—42no—
264C22⋊C4×C113—42no—
265C22⋊C4×C113—42no—
266C22⋊C4×C113—42no—
267C22⋊C4×C113—42no—
268C22⋊C4×C113—81no—
269C42×C113—21no—
270C42×C113—21no—
271C42×C113—21no—
272C42×C113—21no—
273C42×C113—42no—
274C42×C113—81no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—21no—
281C23×C113—22no—
282C23×C113—22no—
283C23×C113—22no—
284C23×C113—48no—
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—41no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113—41no—
302C23×C113—41no—
303C23×C113—41no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—41no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—84no—
311C23×C113—84no—
312C23×C113—84no—
313C23×C113—84no—
314C23×C113—84no—
315C23×C113—84no—
316C23×C113#12112yes—
317C23×C113C22×D411yescharacteristic
318D4×C113—22no—
319D4×C113—22no—
320D4×C113—22no—
321D4×C113—22no—
322D4×C113—22no—
323D4×C113—22no—
324D4×C113—48no—
325D4×C113—41no—
326D4×C113—41no—
327D4×C113—41no—
328D4×C113—41no—
329D4×C113—41no—
330D4×C113—41no—
331D4×C113—41no—
332D4×C113—41no—
333D4×C113—41no—
334D4×C113—41no—
335D4×C113—84no—
336D4×C113—84no—
337D4×C113—84no—
338D4×C113—84no—
339D4×C113—84no—
340D4×C113—84no—
341C2×C4×C113—21no—
342C2×C4×C113—21no—
343C2×C4×C113—21no—
344C2×C4×C113—21no—
345C2×C4×C113—21no—
346C2×C4×C113—21no—
347C2×C4×C113—22no—
348C2×C4×C113—22no—
349C2×C4×C113—22no—
350C2×C4×C113—22no—
351C2×C4×C113—22no—
352C2×C4×C113—21no—
353C2×C4×C113—22no—
354C2×C4×C113—21no—
355C2×C4×C113—21no—
356C2×C4×C113—21no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—41no—
360C2×C4×C113—41no—
361C2×C4×C113—41no—
362C2×C4×C113—41no—
363C2×C4×C113—41no—
364C2×C4×C113—41no—
365C2×C4×C113—41no—
366C2×C4×C113—41no—
367C2×C4×C113—41no—
368C2×C4×C113—41no—
369C2×C4×C113—84no—
370C2×C4×C113#12112yes—
371C2×C4×C113AGL(1,ℤ/8)12yes—
372C2×C4×C113AGL(1,ℤ/8)12yes—
373C2×C4×C113C22×D411yescharacteristic
374C2×C4×C113C22×D411yescharacteristic
375C2×C4×C113C2×#4111yescharacteristic
376C2×C4×C113C2×#4111yescharacteristic
377C2×C4×C113H(5,𝔽2)11yescharacteristic
378C2×C4×C113H(5,𝔽2)11yescharacteristic
379C8×C113—22no—
380C8×C113—41no—
381C8×C113—41no—
382C8×C113—41no—
383C22×C113—22no—
384C22×C113—22no—
385C22×C113—22no—
386C22×C113—41no—
387C22×C113—41no—
388C22×C113—41no—
389C22×C113—41no—
390C22×C113—42no—
391C22×C113—42no—
392C22×C113—42no—
393C22×C113—42no—
394C22×C113—42no—
395C22×C113—42no—
396C22×C113—42no—
397C22×C113—42no—
398C22×C113—42no—
399C22×C113—816no—
400C22×C113—81no—
401C22×C113—81no—
402C22×C113—81no—
403C22×C113—81no—
404C22×C113—81no—
405C22×C113—81no—
406C22×C113—81no—
407C22×C113—81no—
408C22×C113—81no—
409C22×C113—81no—
410C22×C113—81no—
411C22×C113—81no—
412C22×C113—81no—
413C22×C113—81no—
414C22×C113—81no—
415C22×C113—81no—
416C22×C113—81no—
417C22×C113—81no—
418C22×C113—81no—
419C22×C113C2×#12111yescharacteristic
420C22×C113D4211yescharacteristic
421C22×C113#54611yescharacteristic
422C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C113#57611yescharacteristic
425C22×C113#57611yescharacteristic
426C4×C113—22no—
427C4×C113—22no—
428C4×C113—22no—
429C4×C113—42no—
430C4×C113—41no—
431C4×C113—42no—
432C4×C113—41no—
433C4×C113—81no—
434C4×C113—81no—
435C4×C113#52511yescharacteristic
436C4×C113#53811yescharacteristic
437C4×C113D4211yescharacteristic
438C4×C113#54611yescharacteristic
439#25097C11311yesmaximal, characteristic, direct product factor, Sylow
440C2×C113—42no—
441C2×C113—82no—
442C2×C113—82no—
443C2×C113—82no—
444C2×C113—161no—
445C2×C113#242411yescharacteristic
446C2×C113#303811yescharacteristic
447C2×C113#304111yescharacteristic
448C2×C113#326411yescharacteristic
449C2×C113#327411yescharacteristic
450C2×C113#331811yescharacteristic
451C2×C113#332511yescharacteristic
452C2×#469C2×C11311yescharacteristic, complemented
453C2×#459C2×C11311yescharacteristic, complemented
454C2×#447C2×C11311yescharacteristic, complemented
455C2×#418C2×C11311yescharacteristic, complemented
456#2433C2×C11311yescharacteristic, complemented
457#2363C2×C11311yescharacteristic, complemented
458#2065C2×C11311yescharacteristic, complemented
459#2054C2×C11311yescharacteristic, complemented
460#2041C2×C11311yescharacteristic, complemented
461#2011C2×C11311yescharacteristic, complemented
462#1982C2×C11311yescharacteristic, complemented
463#1926C2×C11311yescharacteristic, complemented
464#1879C2×C11311yescharacteristic, complemented
465#1875C2×C11311yescharacteristic, complemented
466#1851C2×C11311yescharacteristic, complemented
467C113#2509711yescharacteristic, direct product factor, Sylow
468C23×D4C22×C11311yescharacteristic
469C22×D8C22×C11311yescharacteristic
470C22×D8C22×C11311yescharacteristic
471C22×D8C22×C11311yescharacteristic, complemented
472C22×M16C22×C11311yescharacteristic
473C2×#127C22×C11311yescharacteristic
474C2×#127C22×C11311yescharacteristic
475C2×#121C22×C11311yescharacteristic
476C2×#121C22×C11311yescharacteristic
477C2×#120—21no—
478C2×#120—21no—
479C2×C4×D4C22×C11311yescharacteristic, complemented
480C2×#117C22×C11311yescharacteristic
481#469—24no—
482#459—24no—
483#447—24no—
484C2×#106C22×C11311yescharacteristic, complemented
485C2×C4⋊C8C22×C11311yescharacteristic, complemented
486C2×C4⋊C8C22×C11311yescharacteristic, complemented
487#418—24no—
488C2×#102C22×C11311yescharacteristic
489C2×#102C22×C11311yescharacteristic
490C2×#102C22×C11311yescharacteristic
491C2×#102C22×C11311yescharacteristic
492C2×#102C22×C11311yescharacteristic
493C2×#102C22×C11311yescharacteristic
494C2×#102C22×C11311yescharacteristic, complemented
495C2×#102C22×C11311yescharacteristic, complemented
496C2×#102C22×C11311yescharacteristic, complemented
497C2×#102C22×C11311yescharacteristic, complemented
498C2×C22⋊C8C22×C11311yescharacteristic
499#392—21no—
500#392—21no—
501#390—21no—
502#390C22×C11311yescharacteristic
503#390C22×C11311yescharacteristic
504#390C22×C11311yescharacteristic, complemented
505#389C22×C11311yescharacteristic, complemented
506#388—21no—
507#386—21no—
508C4×C4⋊C4C22×C11311yescharacteristic, complemented
509C4×C22⋊C4—21no—
510C4×C22⋊C4C22×C11311yescharacteristic
511#340C22×C11311yescharacteristic, complemented
512#340C22×C11311yescharacteristic, complemented
513#336C22×C11311yescharacteristic, complemented
514#336C22×C11311yescharacteristic, complemented
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C23×C11311yescharacteristic
530C22×D4C23×C11311yescharacteristic
531C22×D4C23×C11311yescharacteristic
532C22×D4C23×C11311yescharacteristic
533C23×C4—21no—
534C23×C4C23×C11311yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C22×C8C23×C11311yescharacteristic
548C22×C8C23×C11311yescharacteristic
549C22×C8C23×C11311yescharacteristic
550C22×C8C23×C11311yescharacteristic
551#127—22no—
552#127—22no—
553#127—41no—
554#127—41no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121D4×C11314yescomplemented
559#120—44no—
560#120—44no—
561C4×D4—22no—
562C4×D4—41no—
563#117—22no—
564#117—41no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4C23×C11311yescharacteristic
567C2×C4⋊C4C23×C11311yescharacteristic
568C2×C4⋊C4C23×C11311yescharacteristic
569C2×C4⋊C4C23×C11311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4D4×C11311yescharacteristic
581C2×C22⋊C4D4×C11311yescharacteristic
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C11311yescharacteristic
585C2×C42C23×C11311yescharacteristic
586#106—22no—
587C4⋊C8—22no—
588C4⋊C8—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—41no—
598#102D4×C11314yescomplemented
599C22⋊C8—22no—
600#95—21no—
601#95—21no—
602#95D4×C11311yescharacteristic
603#95D4×C11311yescharacteristic
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C11311yescharacteristic
616C2×D4—28no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—81no—
659C2×D4—81no—
660C2×D4—81no—
661C2×D4—81no—
662C2×D4C2×D4×C11312yes—
663C2×D4C2×D4×C11312yes—
664C2×D4#41×C11312yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4C2×D4×C11311yescharacteristic
677C22×C4C2×D4×C11311yescharacteristic
678C22×C4C2×D4×C11311yescharacteristic
679C22×C4C2×D4×C11312yes—
680C22×C4C2×D4×C11311yescharacteristic
681C22×C4C2×D4×C11311yescharacteristic
682C22×C4#41×C11312yes—
683C22×C4C24×C11311yescharacteristic
684D8—44no—
685D8—44no—
686D8—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C11312yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—81no—
707C4⋊C4C2×D4×C11312yes—
708C4⋊C4C2×D4×C11312yes—
709C22⋊C4—24no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—42no—
726C42—81no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23#121×C11312yes—
769C23C22×D4×C11311yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—48no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4—84no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4#121×C11312yes—
823C2×C4AGL(1,ℤ/8)×C11312yes—
824C2×C4AGL(1,ℤ/8)×C11312yes—
825C2×C4C22×D4×C11311yescharacteristic
826C2×C4C22×D4×C11311yescharacteristic
827C2×C4C2×#41×C11311yescharacteristic
828C2×C4C2×#41×C11311yescharacteristic
829C2×C4H(5,𝔽2)×C11311yescharacteristic
830C2×C4H(5,𝔽2)×C11311yescharacteristic
831C8—22no—
832C8—41no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C2×#121×C11311yescharacteristic
872C22D42×C11311yescharacteristic
873C22#546×C11311yescharacteristic
874C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
875C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
876C22#576×C11311yescharacteristic
877C22#576×C11311yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—41no—
882C4—42no—
883C4—41no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4#525×C11311yescharacteristic
888C4#538×C11311yescharacteristic
889C4D42×C11311yescharacteristic
890C4#546×C11311yescharacteristic
891C2—42no—
892C2—82no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2C113×#242411yescharacteristic
897C2C113×#303811yescharacteristic
898C2C113×#304111yescharacteristic
899C2C113×#326411yescharacteristic
900C2C113×#327411yescharacteristic
901C2C113×#331811yescharacteristic
902C2C113×#332511yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
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×#469×C113C2semidirect
2. C2×#459×C113C2semidirect
3. C2×#447×C113C2semidirect
4. C2×#418×C113C2semidirect
5. C113×#2433C2semidirect
6. C113×#2363C2semidirect
7. C113×#2065C2semidirect
8. C113×#2054C2semidirect
9. C113×#2041C2semidirect
10. C113×#2011C2semidirect
11. C113×#1982C2semidirect
12. C113×#1926C2semidirect
13. C113×#1879C2semidirect
14. C113×#1875C2semidirect
15. C113×#1851C2semidirect
19. C22×D8×C113C22semidirect
27. C2×C4×D4×C113C22semidirect
32. C2×#106×C113C22semidirect
33. C2×C4⋊C8×C113C22semidirect
34. C2×C4⋊C8×C113C22semidirect
42. C2×#102×C113C22semidirect
43. C2×#102×C113C22semidirect
44. C2×#102×C113C22semidirect
45. C2×#102×C113C22semidirect
52. #390×C113C22semidirect
53. #389×C113C22semidirect
56. C4×C4⋊C4×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
106. #121×C113D4semidirect
146. #102×C113D4semidirect
439. #25097C113direct (N × H)
452. C2×#469C2×C113semidirect
453. C2×#459C2×C113semidirect
454. C2×#447C2×C113semidirect
455. C2×#418C2×C113semidirect
456. #2433C2×C113semidirect
457. #2363C2×C113semidirect
458. #2065C2×C113semidirect
459. #2054C2×C113semidirect
460. #2041C2×C113semidirect
461. #2011C2×C113semidirect
462. #1982C2×C113semidirect
463. #1926C2×C113semidirect
464. #1879C2×C113semidirect
465. #1875C2×C113semidirect
466. #1851C2×C113semidirect
467. C113#25097direct (N × H)
471. C22×D8C22×C113semidirect
479. C2×C4×D4C22×C113semidirect
484. C2×#106C22×C113semidirect
485. C2×C4⋊C8C22×C113semidirect
486. C2×C4⋊C8C22×C113semidirect
494. C2×#102C22×C113semidirect
495. C2×#102C22×C113semidirect
496. C2×#102C22×C113semidirect
497. C2×#102C22×C113semidirect
504. #390C22×C113semidirect
505. #389C22×C113semidirect
508. C4×C4⋊C4C22×C113semidirect
511. #340C22×C113semidirect
512. #340C22×C113semidirect
513. #336C22×C113semidirect
514. #336C22×C113semidirect
558. #121D4×C113semidirect
598. #102D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1132
C2×#459×C1132
C2×#447×C1132
C2×#418×C1132
C113×#24332
C113×#23632
C113×#20652
C113×#20542
C113×#20412
C113×#20112
C113×#19822
C113×#19262
C113×#18792
C113×#18752
C113×#18512
#25097113