Finite Group Databasebeta

← C113×#25076 #43293096

Subgroups — C113×#25076 #43293096

Order 28928.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C113C211yesmaximal, characteristic, complemented
2C2×#459×C113C211yesmaximal, characteristic, complemented
3C2×#447×C113C211yesmaximal, characteristic, complemented
4C22×#102×C113C211yesmaximal, characteristic, complemented
5C113×#2433C211yesmaximal, characteristic, complemented
6C113×#2361C211yesmaximal, characteristic, complemented
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2054C211yesmaximal, characteristic, complemented
9C113×#2041C211yesmaximal, characteristic, complemented
10C113×#2011C211yesmaximal, characteristic, complemented
11C113×#1982C211yesmaximal, characteristic, complemented
12C113×#1925C211yesmaximal, characteristic, complemented
13C113×#1879C211yesmaximal, characteristic, complemented
14C113×#1874C211yesmaximal, characteristic, complemented
15C113×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×D8×C113C2211yescharacteristic
18C22×D8×C113C2211yescharacteristic
19C22×D8×C113C2211yescharacteristic, complemented
20C23×C8×C113C2211yescharacteristic
21C2×#127×C113C2211yescharacteristic
22C2×#127×C113C2211yescharacteristic
23C2×#121×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×#120×C113—21no—
26C2×#120×C113—21no—
27C2×C4×D4×C113—21no—
28C2×C4×D4×C113C2211yescharacteristic, complemented
29C22×C4⋊C4×C113C2211yescharacteristic
30#466×C113—24no—
31#459×C113—24no—
32#447×C113—24no—
33C2×#107×C113C2211yescharacteristic, complemented
34C2×C4⋊C8×C113C2211yescharacteristic, complemented
35C2×C4⋊C8×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×#102×C113C2211yescharacteristic, complemented
44C2×#102×C113C2211yescharacteristic, complemented
45C2×#102×C113C2211yescharacteristic, complemented
46C2×#102×C113C2211yescharacteristic, complemented
47C2×C22⋊C8×C113C2211yescharacteristic
48#392×C113—21no—
49#392×C113—21no—
50#390×C113C2211yescharacteristic
51#390×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic, complemented
53#389×C113C2211yescharacteristic, complemented
54#388×C113—21no—
55#386×C113—21no—
56#385×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×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×C113—21no—
83C23×C4×C113C2311yescharacteristic
84C2×D8×C113—22no—
85C2×D8×C113—22no—
86C2×D8×C113—22no—
87C2×D8×C113—22no—
88C2×D8×C113—22no—
89C2×D8×C113—22no—
90C2×D8×C113—41no—
91C2×D8×C113—41no—
92C2×D8×C113—41no—
93C22×C8×C113—22no—
94C22×C8×C113—22no—
95C22×C8×C113—41no—
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98C22×C8×C113C2311yescharacteristic
99C22×C8×C113C2311yescharacteristic
100#127×C113—22no—
101#127×C113—22no—
102#127×C113—41no—
103#127×C113—41no—
104#121×C113—22no—
105#121×C113—22no—
106#121×C113—22no—
107#121×C113D414yescomplemented
108#120×C113—44no—
109#120×C113—44no—
110C4×D4×C113—22no—
111C4×D4×C113—41no—
112C4×D4×C113—44no—
113C2×C4⋊C4×C113—22no—
114C2×C4⋊C4×C113—21no—
115C2×C4⋊C4×C113—21no—
116C2×C4⋊C4×C113—41no—
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
119C2×C4⋊C4×C113C2311yescharacteristic
120C2×C4⋊C4×C113C2311yescharacteristic
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×C113—21no—
130C2×C22⋊C4×C113D411yescharacteristic
131C2×C22⋊C4×C113D411yescharacteristic
132C2×C42×C113—21no—
133C2×C42×C113C2311yescharacteristic
134C2×C42×C113C2311yescharacteristic
135#107×C113—22no—
136C4⋊C8×C113—22no—
137C4⋊C8×C113—41no—
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—22no—
146#102×C113—41no—
147#102×C113D414yescomplemented
148C22⋊C8×C113—22no—
149#95×C113—21no—
150#95×C113—21no—
151#95×C113D411yescharacteristic
152#95×C113D411yescharacteristic
153C24×C113—21no—
154C24×C113—21no—
155C24×C113—21no—
156C24×C113—21no—
157C24×C113—42no—
158C24×C113—42no—
159C24×C113—42no—
160C24×C113—42no—
161C24×C113—42no—
162C24×C113—81no—
163C24×C113—81no—
164C24×C113C2×D411yescharacteristic
165C2×D4×C113—28no—
166C2×D4×C113—24no—
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—21no—
188C2×D4×C113—44no—
189C2×D4×C113—44no—
190C2×D4×C113—42no—
191C2×D4×C113—42no—
192C2×D4×C113—44no—
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—42no—
205C2×D4×C113—42no—
206C2×D4×C113—42no—
207C2×D4×C113—81no—
208C2×D4×C113—81no—
209C2×D4×C113—81no—
210C2×D4×C113—81no—
211C2×D4×C113C2×D412yes—
212C2×D4×C113C2×D412yes—
213C2×D4×C113#4112yes—
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—21no—
222C22×C4×C113—42no—
223C22×C4×C113—42no—
224C22×C4×C113—42no—
225C22×C4×C113—42no—
226C22×C4×C113—81no—
227C22×C4×C113—81no—
228C22×C4×C113C2×D411yescharacteristic
229C22×C4×C113C2×D411yescharacteristic
230C22×C4×C113C2×D411yescharacteristic
231C22×C4×C113C2×D412yes—
232C22×C4×C113C2×D411yescharacteristic
233C22×C4×C113C2×D411yescharacteristic
234C22×C4×C113#4112yes—
235C22×C4×C113C2411yescharacteristic
236D8×C113—44no—
237D8×C113—44no—
238D8×C113—44no—
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×C113—21no—
248C2×C8×C113—21no—
249C2×C8×C113—21no—
250C2×C8×C113—44no—
251C2×C8×C113C2×D412yes—
252C4⋊C4×C113—21no—
253C4⋊C4×C113—21no—
254C4⋊C4×C113—21no—
255C4⋊C4×C113—21no—
256C4⋊C4×C113—21no—
257C4⋊C4×C113—21no—
258C4⋊C4×C113—42no—
259C4⋊C4×C113—42no—
260C4⋊C4×C113C2×D412yes—
261C4⋊C4×C113C2×D412yes—
262C22⋊C4×C113—22no—
263C22⋊C4×C113—24no—
264C22⋊C4×C113—42no—
265C22⋊C4×C113—42no—
266C22⋊C4×C113—42no—
267C22⋊C4×C113—42no—
268C22⋊C4×C113—42no—
269C22⋊C4×C113—42no—
270C22⋊C4×C113—42no—
271C22⋊C4×C113—81no—
272C22⋊C4×C113D814yescomplemented
273C42×C113—21no—
274C42×C113—21no—
275C42×C113—21no—
276C42×C113—21no—
277C42×C113—42no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—21no—
281C23×C113—21no—
282C23×C113—22no—
283C23×C113—22no—
284C23×C113—22no—
285C23×C113—48no—
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—41no—
311C23×C113—84no—
312C23×C113—84no—
313C23×C113—84no—
314C23×C113—84no—
315C23×C113—84no—
316C23×C113—84no—
317C23×C113#12112yes—
318C23×C113C2×D812yes—
319C23×C113AGL(1,ℤ/8)12yes—
320C23×C113C22×D411yescharacteristic
321D4×C113—22no—
322D4×C113—22no—
323D4×C113—22no—
324D4×C113—22no—
325D4×C113—22no—
326D4×C113—22no—
327D4×C113—48no—
328D4×C113—48no—
329D4×C113—41no—
330D4×C113—41no—
331D4×C113—41no—
332D4×C113—41no—
333D4×C113—41no—
334D4×C113—41no—
335D4×C113—41no—
336D4×C113—41no—
337D4×C113—41no—
338D4×C113—41no—
339D4×C113—84no—
340D4×C113—84no—
341D4×C113—84no—
342D4×C113—84no—
343D4×C113—84no—
344C2×C4×C113—21no—
345C2×C4×C113—21no—
346C2×C4×C113—21no—
347C2×C4×C113—21no—
348C2×C4×C113—21no—
349C2×C4×C113—21no—
350C2×C4×C113—22no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—22no—
354C2×C4×C113—22no—
355C2×C4×C113—21no—
356C2×C4×C113—22no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—21no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
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—41no—
370C2×C4×C113—41no—
371C2×C4×C113—41no—
372C2×C4×C113—84no—
373C2×C4×C113—84no—
374C2×C4×C113#12112yes—
375C2×C4×C113C2×D812yes—
376C2×C4×C113C2×D812yes—
377C2×C4×C113C22×D411yescharacteristic
378C2×C4×C113C22×D411yescharacteristic
379C2×C4×C113C2×#4111yescharacteristic
380C2×C4×C113C2×#4111yescharacteristic
381C2×C4×C113H(5,𝔽2)11yescharacteristic
382C2×C4×C113H(5,𝔽2)11yescharacteristic
383C8×C113—22no—
384C8×C113—41no—
385C8×C113—41no—
386C8×C113—41no—
387C22×C113—22no—
388C22×C113—22no—
389C22×C113—22no—
390C22×C113—22no—
391C22×C113—22no—
392C22×C113—22no—
393C22×C113—42no—
394C22×C113—42no—
395C22×C113—42no—
396C22×C113—42no—
397C22×C113—42no—
398C22×C113—42no—
399C22×C113—42no—
400C22×C113—42no—
401C22×C113—42no—
402C22×C113—816no—
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×C113—81no—
420C22×C113—81no—
421C22×C113—81no—
422C22×C113#45914yescomplemented
423C22×C113C2×#12111yescharacteristic
424C22×C113D4211yescharacteristic
425C22×C113#54611yescharacteristic
426C22×C113C22×D811yescharacteristic
427C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
428C22×C113#57611yescharacteristic
429C22×C113#57711yescharacteristic
430C4×C113—22no—
431C4×C113—22no—
432C4×C113—22no—
433C4×C113—41no—
434C4×C113—42no—
435C4×C113—42no—
436C4×C113—41no—
437C4×C113—81no—
438C4×C113—81no—
439C4×C113#52511yescharacteristic
440C4×C113#53811yescharacteristic
441C4×C113D4211yescharacteristic
442C4×C113#54611yescharacteristic
443#25076C11311yesmaximal, characteristic, direct product factor, Sylow
444C2×C113—24no—
445C2×C113—82no—
446C2×C113—82no—
447C2×C113—82no—
448C2×C113—161no—
449C2×C113#242411yescharacteristic
450C2×C113C2×#45911yescharacteristic
451C2×C113#304511yescharacteristic
452C2×C113#326511yescharacteristic
453C2×C113D4×D811yescharacteristic
454C2×C113#329411yescharacteristic
455C2×C113#331811yescharacteristic
456C2×#466C2×C11311yescharacteristic, complemented
457C2×#459C2×C11311yescharacteristic, complemented
458C2×#447C2×C11311yescharacteristic, complemented
459C22×#102C2×C11311yescharacteristic, complemented
460#2433C2×C11311yescharacteristic, complemented
461#2361C2×C11311yescharacteristic, complemented
462#2067C2×C11311yescharacteristic, complemented
463#2054C2×C11311yescharacteristic, complemented
464#2041C2×C11311yescharacteristic, complemented
465#2011C2×C11311yescharacteristic, complemented
466#1982C2×C11311yescharacteristic, complemented
467#1925C2×C11311yescharacteristic, complemented
468#1879C2×C11311yescharacteristic, complemented
469#1874C2×C11311yescharacteristic, complemented
470#1850C2×C11311yescharacteristic, complemented
471C113#2507611yescharacteristic, direct product factor, Sylow
472C23×D4C22×C11311yescharacteristic
473C22×D8C22×C11311yescharacteristic
474C22×D8C22×C11311yescharacteristic
475C22×D8C22×C11311yescharacteristic, complemented
476C23×C8C22×C11311yescharacteristic
477C2×#127C22×C11311yescharacteristic
478C2×#127C22×C11311yescharacteristic
479C2×#121C22×C11311yescharacteristic
480C2×#121C22×C11311yescharacteristic
481C2×#120—21no—
482C2×#120—21no—
483C2×C4×D4—21no—
484C2×C4×D4C22×C11311yescharacteristic, complemented
485C22×C4⋊C4C22×C11311yescharacteristic
486#466—24no—
487#459—24no—
488#447—24no—
489C2×#107C22×C11311yescharacteristic, complemented
490C2×C4⋊C8C22×C11311yescharacteristic, complemented
491C2×C4⋊C8C22×C11311yescharacteristic, complemented
492C2×#102—24no—
493C2×#102C22×C11311yescharacteristic
494C2×#102C22×C11311yescharacteristic
495C2×#102C22×C11311yescharacteristic
496C2×#102C22×C11311yescharacteristic
497C2×#102C22×C11311yescharacteristic
498C2×#102C22×C11311yescharacteristic
499C2×#102C22×C11311yescharacteristic, complemented
500C2×#102C22×C11311yescharacteristic, complemented
501C2×#102C22×C11311yescharacteristic, complemented
502C2×#102C22×C11311yescharacteristic, complemented
503C2×C22⋊C8C22×C11311yescharacteristic
504#392—21no—
505#392—21no—
506#390C22×C11311yescharacteristic
507#390C22×C11311yescharacteristic
508#390C22×C11311yescharacteristic, complemented
509#389C22×C11311yescharacteristic, complemented
510#388—21no—
511#386—21no—
512#385—21no—
513C4×C4⋊C4C22×C11311yescharacteristic, complemented
514C4×C22⋊C4C22×C11311yescharacteristic
515#340C22×C11311yescharacteristic, complemented
516#340C22×C11311yescharacteristic, complemented
517#336C22×C11311yescharacteristic, complemented
518#336C22×C11311yescharacteristic, complemented
519C25—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C23×C11311yescharacteristic
534C22×D4C23×C11311yescharacteristic
535C22×D4C23×C11311yescharacteristic
536C22×D4C23×C11311yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C11311yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8C23×C11311yescharacteristic
553C22×C8C23×C11311yescharacteristic
554C22×C8C23×C11311yescharacteristic
555C22×C8C23×C11311yescharacteristic
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121D4×C11314yescomplemented
564#120—44no—
565#120—44no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4C23×C11311yescharacteristic
574C2×C4⋊C4C23×C11311yescharacteristic
575C2×C4⋊C4C23×C11311yescharacteristic
576C2×C4⋊C4C23×C11311yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4D4×C11311yescharacteristic
587C2×C22⋊C4D4×C11311yescharacteristic
588C2×C42—21no—
589C2×C42C23×C11311yescharacteristic
590C2×C42C23×C11311yescharacteristic
591#107—22no—
592C4⋊C8—22no—
593C4⋊C8—41no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102D4×C11314yescomplemented
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95D4×C11311yescharacteristic
608#95D4×C11311yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C11311yescharacteristic
621C2×D4—28no—
622C2×D4—24no—
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—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C11312yes—
668C2×D4C2×D4×C11312yes—
669C2×D4#41×C11312yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C11311yescharacteristic
685C22×C4C2×D4×C11311yescharacteristic
686C22×C4C2×D4×C11311yescharacteristic
687C22×C4C2×D4×C11312yes—
688C22×C4C2×D4×C11311yescharacteristic
689C22×C4C2×D4×C11311yescharacteristic
690C22×C4#41×C11312yes—
691C22×C4C24×C11311yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—44no—
707C2×C8C2×D4×C11312yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C11312yes—
717C4⋊C4C2×D4×C11312yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C11314yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
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—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23#121×C11312yes—
774C23C2×D8×C11312yes—
775C23AGL(1,ℤ/8)×C11312yes—
776C23C22×D4×C11311yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#121×C11312yes—
831C2×C4C2×D8×C11312yes—
832C2×C4C2×D8×C11312yes—
833C2×C4C22×D4×C11311yescharacteristic
834C2×C4C22×D4×C11311yescharacteristic
835C2×C4C2×#41×C11311yescharacteristic
836C2×C4C2×#41×C11311yescharacteristic
837C2×C4H(5,𝔽2)×C11311yescharacteristic
838C2×C4H(5,𝔽2)×C11311yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22#459×C11314yescomplemented
879C22C2×#121×C11311yescharacteristic
880C22D42×C11311yescharacteristic
881C22#546×C11311yescharacteristic
882C22C22×D8×C11311yescharacteristic
883C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
884C22#576×C11311yescharacteristic
885C22#577×C11311yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4#525×C11311yescharacteristic
896C4#538×C11311yescharacteristic
897C4D42×C11311yescharacteristic
898C4#546×C11311yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2C113×#242411yescharacteristic
905C2C2×#459×C11311yescharacteristic
906C2C113×#304511yescharacteristic
907C2C113×#326511yescharacteristic
908C2D4×D8×C11311yescharacteristic
909C2C113×#329411yescharacteristic
910C2C113×#331811yescharacteristic
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×#466×C113C2semidirect
2. C2×#459×C113C2semidirect
3. C2×#447×C113C2semidirect
4. C22×#102×C113C2semidirect
5. C113×#2433C2semidirect
6. C113×#2361C2semidirect
7. C113×#2067C2semidirect
8. C113×#2054C2semidirect
9. C113×#2041C2semidirect
10. C113×#2011C2semidirect
11. C113×#1982C2semidirect
12. C113×#1925C2semidirect
13. C113×#1879C2semidirect
14. C113×#1874C2semidirect
15. C113×#1850C2semidirect
19. C22×D8×C113C22semidirect
28. C2×C4×D4×C113C22semidirect
33. C2×#107×C113C22semidirect
34. C2×C4⋊C8×C113C22semidirect
35. C2×C4⋊C8×C113C22semidirect
43. C2×#102×C113C22semidirect
44. C2×#102×C113C22semidirect
45. C2×#102×C113C22semidirect
46. C2×#102×C113C22semidirect
52. #390×C113C22semidirect
53. #389×C113C22semidirect
57. C4×C4⋊C4×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
107. #121×C113D4semidirect
147. #102×C113D4semidirect
272. C22⋊C4×C113D8semidirect
422. C22×C113#459semidirect
443. #25076C113direct (N × H)
456. C2×#466C2×C113semidirect
457. C2×#459C2×C113semidirect
458. C2×#447C2×C113semidirect
459. C22×#102C2×C113semidirect
460. #2433C2×C113semidirect
461. #2361C2×C113semidirect
462. #2067C2×C113semidirect
463. #2054C2×C113semidirect
464. #2041C2×C113semidirect
465. #2011C2×C113semidirect
466. #1982C2×C113semidirect
467. #1925C2×C113semidirect
468. #1879C2×C113semidirect
469. #1874C2×C113semidirect
470. #1850C2×C113semidirect
471. C113#25076direct (N × H)
475. C22×D8C22×C113semidirect
484. C2×C4×D4C22×C113semidirect
489. C2×#107C22×C113semidirect
490. C2×C4⋊C8C22×C113semidirect
491. C2×C4⋊C8C22×C113semidirect
499. C2×#102C22×C113semidirect
500. C2×#102C22×C113semidirect
501. C2×#102C22×C113semidirect
502. C2×#102C22×C113semidirect
508. #390C22×C113semidirect
509. #389C22×C113semidirect
513. C4×C4⋊C4C22×C113semidirect
515. #340C22×C113semidirect
516. #340C22×C113semidirect
517. #336C22×C113semidirect
518. #336C22×C113semidirect
563. #121D4×C113semidirect
603. #102D4×C113semidirect
728. C22⋊C4D8×C113semidirect
878. C22#459×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1132
C2×#459×C1132
C2×#447×C1132
C22×#102×C1132
C113×#24332
C113×#23612
C113×#20672
C113×#20542
C113×#20412
C113×#20112
C113×#19822
C113×#19252
C113×#18792
C113×#18742
C113×#18502
#25076113