Finite Group Databasebeta

← C113×#25080 #43293100

Subgroups — C113×#25080 #43293100

Order 28928.

1356 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C113C211yesmaximal, characteristic, complemented
2C2×#460×C113C211yesmaximal, characteristic, complemented
3C2×#450×C113C211yesmaximal, characteristic, complemented
4C22×#102×C113C211yesmaximal, characteristic, complemented
5C113×#2433C211yesmaximal, characteristic
6C113×#2360C211yesmaximal, characteristic, complemented
7C113×#2065C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2041C211yesmaximal, characteristic, complemented
10C113×#2014C211yesmaximal, characteristic, complemented
11C113×#1982C211yesmaximal, characteristic, complemented
12C113×#1926C211yesmaximal, characteristic, complemented
13C113×#1880C211yesmaximal, characteristic, complemented
14C113×#1874C211yesmaximal, characteristic, complemented
15C113×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic, complemented
20C23×C8×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
28C22×C4⋊C4×C113C2211yescharacteristic
29#465×C113—24no—
30#460×C113—24no—
31#450×C113—24no—
32C2×#106×C113C2211yescharacteristic, complemented
33C2×C4⋊C8×C113C2211yescharacteristic, complemented
34C2×C4⋊C8×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×#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×C113—21no—
53#389×C113C2211yescharacteristic, complemented
54#387×C113—21no—
55#385×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×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×C113—21no—
81C23×C4×C113C2311yescharacteristic
82C2×SD16×C113—22no—
83C2×SD16×C113—22no—
84C2×SD16×C113—22no—
85C2×SD16×C113—22no—
86C2×SD16×C113—22no—
87C2×SD16×C113—22no—
88C2×SD16×C113—41no—
89C2×SD16×C113—41no—
90C2×SD16×C113—41no—
91C22×C8×C113—22no—
92C22×C8×C113—22no—
93C22×C8×C113—41no—
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98#127×C113—22no—
99#127×C113—22no—
100#127×C113—41no—
101#127×C113—41no—
102C22⋊Q8×C113—22no—
103C22⋊Q8×C113D414yescomplemented
104#121×C113—22no—
105#121×C113—22no—
106#120×C113—44no—
107#120×C113—44no—
108C4×Q8×C113—22no—
109C4×Q8×C113—41no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113—22no—
112C2×C4⋊C4×C113—21no—
113C2×C4⋊C4×C113—21no—
114C2×C4⋊C4×C113—21no—
115C2×C4⋊C4×C113—41no—
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
119C2×C4⋊C4×C113C2311yescharacteristic
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×C113D411yescharacteristic
127C2×C22⋊C4×C113D411yescharacteristic
128C2×C42×C113—21no—
129C2×C42×C113—21no—
130C2×C42×C113C2311yescharacteristic
131C2×C42×C113C2311yescharacteristic
132#106×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×C113—42no—
219C22×C4×C113—42no—
220C22×C4×C113—81no—
221C22×C4×C113C2×D411yescharacteristic
222C22×C4×C113C2×D411yescharacteristic
223C22×C4×C113C2×D411yescharacteristic
224C22×C4×C113C2×D412yes—
225C22×C4×C113C2×D411yescharacteristic
226C22×C4×C113C2×D411yescharacteristic
227C22×C4×C113#4112yes—
228C22×C4×C113C2411yescharacteristic
229SD16×C113—44no—
230SD16×C113—44no—
231SD16×C113—44no—
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×C113—21no—
242C2×C8×C113—21no—
243C2×C8×C113—44no—
244C2×C8×C113C2×D412yes—
245C4⋊C4×C113—24no—
246C4⋊C4×C113—21no—
247C4⋊C4×C113—21no—
248C4⋊C4×C113—21no—
249C4⋊C4×C113—21no—
250C4⋊C4×C113—21no—
251C4⋊C4×C113—21no—
252C4⋊C4×C113—42no—
253C4⋊C4×C113—42no—
254C4⋊C4×C113—81no—
255C4⋊C4×C113C2×D412yes—
256C4⋊C4×C113C2×D412yes—
257C22⋊C4×C113—24no—
258C22⋊C4×C113—22no—
259C22⋊C4×C113—42no—
260C22⋊C4×C113—42no—
261C22⋊C4×C113—42no—
262C22⋊C4×C113—42no—
263C22⋊C4×C113—42no—
264C22⋊C4×C113SD1614yescomplemented
265C42×C113—21no—
266C42×C113—21no—
267C42×C113—21no—
268C42×C113—21no—
269C42×C113—42no—
270C42×C113—81no—
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×C113C2×SD1612yes—
305C23×C113AGL(1,ℤ/8)12yes—
306C23×C113C22×D411yescharacteristic
307Q8×C113—22no—
308Q8×C113—22no—
309Q8×C113—41no—
310Q8×C113—41no—
311D4×C113—22no—
312D4×C113—22no—
313D4×C113—22no—
314D4×C113—22no—
315D4×C113—48no—
316D4×C113—41no—
317D4×C113—41no—
318D4×C113—41no—
319D4×C113—41no—
320D4×C113—41no—
321D4×C113—41no—
322D4×C113—41no—
323D4×C113—41no—
324D4×C113—84no—
325D4×C113—84no—
326D4×C113—84no—
327D4×C113—84no—
328D4×C113—84no—
329C2×C4×C113—21no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—21no—
334C2×C4×C113—21no—
335C2×C4×C113—22no—
336C2×C4×C113—22no—
337C2×C4×C113—22no—
338C2×C4×C113—22no—
339C2×C4×C113—22no—
340C2×C4×C113—22no—
341C2×C4×C113—21no—
342C2×C4×C113—22no—
343C2×C4×C113—21no—
344C2×C4×C113—21no—
345C2×C4×C113—21no—
346C2×C4×C113—21no—
347C2×C4×C113—21no—
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—41no—
359C2×C4×C113—41no—
360C2×C4×C113—84no—
361C2×C4×C113#12112yes—
362C2×C4×C113C2×SD1612yes—
363C2×C4×C113C2×SD1612yes—
364C2×C4×C113C22×D411yescharacteristic
365C2×C4×C113C22×D411yescharacteristic
366C2×C4×C113C2×#4111yescharacteristic
367C2×C4×C113C2×#4111yescharacteristic
368C2×C4×C113H(5,𝔽2)11yescharacteristic
369C2×C4×C113H(5,𝔽2)11yescharacteristic
370C8×C113—22no—
371C8×C113—41no—
372C8×C113—41no—
373C8×C113—41no—
374C22×C113—22no—
375C22×C113—22no—
376C22×C113—22no—
377C22×C113—22no—
378C22×C113—22no—
379C22×C113—22no—
380C22×C113—42no—
381C22×C113—42no—
382C22×C113—42no—
383C22×C113—42no—
384C22×C113—42no—
385C22×C113—42no—
386C22×C113—816no—
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×C113—81no—
401C22×C113—81no—
402C22×C113#46014yescomplemented
403C22×C113C2×#12111yescharacteristic
404C22×C113D4211yescharacteristic
405C22×C113#54611yescharacteristic
406C22×C113C22×SD1611yescharacteristic
407C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C113#57611yescharacteristic
409C22×C113#57711yescharacteristic
410C4×C113—22no—
411C4×C113—22no—
412C4×C113—22no—
413C4×C113—42no—
414C4×C113—41no—
415C4×C113—42no—
416C4×C113—42no—
417C4×C113—41no—
418C4×C113—81no—
419C4×C113—81no—
420C4×C113#52511yescharacteristic
421C4×C113#53811yescharacteristic
422C4×C113D4211yescharacteristic
423C4×C113#54611yescharacteristic
424#25080C11311yesmaximal, characteristic, direct product factor, Sylow
425C2×C113—24no—
426C2×C113—82no—
427C2×C113—82no—
428C2×C113—161no—
429C2×C113#242411yescharacteristic
430C2×C113C2×#46011yescharacteristic
431C2×C113#304511yescharacteristic
432C2×C113#326411yescharacteristic
433C2×C113D4×SD1611yescharacteristic
434C2×C113#329511yescharacteristic
435C2×C113#331011yescharacteristic
436C2×#465C2×C11311yescharacteristic, complemented
437C2×#460C2×C11311yescharacteristic, complemented
438C2×#450C2×C11311yescharacteristic, complemented
439C22×#102C2×C11311yescharacteristic, complemented
440#2433C2×C11311yescharacteristic
441#2360C2×C11311yescharacteristic, complemented
442#2065C2×C11311yescharacteristic, complemented
443#2055C2×C11311yescharacteristic, complemented
444#2041C2×C11311yescharacteristic, complemented
445#2014C2×C11311yescharacteristic, complemented
446#1982C2×C11311yescharacteristic, complemented
447#1926C2×C11311yescharacteristic, complemented
448#1880C2×C11311yescharacteristic, complemented
449#1874C2×C11311yescharacteristic, complemented
450#1850C2×C11311yescharacteristic, complemented
451C113#2508011yescharacteristic, direct product factor, Sylow
452C23×D4C22×C11311yescharacteristic
453C22×SD16C22×C11311yescharacteristic
454C22×SD16C22×C11311yescharacteristic
455C22×SD16C22×C11311yescharacteristic, complemented
456C23×C8C22×C11311yescharacteristic
457C2×#127C22×C11311yescharacteristic
458C2×#127C22×C11311yescharacteristic
459C2×C22⋊Q8C22×C11311yescharacteristic
460C2×#121C22×C11311yescharacteristic
461C2×#120—21no—
462C2×#120—21no—
463C2×C4×Q8C22×C11311yescharacteristic, complemented
464C22×C4⋊C4C22×C11311yescharacteristic
465#465—24no—
466#460—24no—
467#450—24no—
468C2×#106C22×C11311yescharacteristic, complemented
469C2×C4⋊C8C22×C11311yescharacteristic, complemented
470C2×C4⋊C8C22×C11311yescharacteristic, complemented
471C2×#103C22×C11311yescharacteristic, complemented
472C2×#102—24no—
473C2×#102C22×C11311yescharacteristic
474C2×#102C22×C11311yescharacteristic
475C2×#102C22×C11311yescharacteristic
476C2×#102C22×C11311yescharacteristic
477C2×#102C22×C11311yescharacteristic
478C2×#102C22×C11311yescharacteristic
479C2×#102C22×C11311yescharacteristic, complemented
480C2×#102C22×C11311yescharacteristic, complemented
481C2×#102C22×C11311yescharacteristic, complemented
482C2×C22⋊C8C22×C11311yescharacteristic
483#392—21no—
484#392—21no—
485#391C22×C11311yescharacteristic, complemented
486#390C22×C11311yescharacteristic
487#390C22×C11311yescharacteristic
488#389—21no—
489#389C22×C11311yescharacteristic, complemented
490#387—21no—
491#385—21no—
492C4×C4⋊C4C22×C11311yescharacteristic, complemented
493C4×C22⋊C4—21no—
494C4×C22⋊C4C22×C11311yescharacteristic
495#340C22×C11311yescharacteristic, complemented
496#340C22×C11311yescharacteristic, complemented
497#336C22×C11311yescharacteristic, complemented
498#336C22×C11311yescharacteristic, complemented
499C25—21no—
500C22×Q8C23×C11311yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C23×C11311yescharacteristic
514C22×D4C23×C11311yescharacteristic
515C22×D4C23×C11311yescharacteristic
516C23×C4—21no—
517C23×C4C23×C11311yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8C23×C11311yescharacteristic
531C22×C8C23×C11311yescharacteristic
532C22×C8C23×C11311yescharacteristic
533C22×C8C23×C11311yescharacteristic
534#127—22no—
535#127—22no—
536#127—41no—
537#127—41no—
538C22⋊Q8—22no—
539C22⋊Q8D4×C11314yescomplemented
540#121—22no—
541#121—22no—
542#120—44no—
543#120—44no—
544C4×Q8—22no—
545C4×Q8—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4C23×C11311yescharacteristic
553C2×C4⋊C4C23×C11311yescharacteristic
554C2×C4⋊C4C23×C11311yescharacteristic
555C2×C4⋊C4C23×C11311yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4D4×C11311yescharacteristic
563C2×C22⋊C4D4×C11311yescharacteristic
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C23×C11311yescharacteristic
567C2×C42C23×C11311yescharacteristic
568#106—22no—
569C4⋊C8—22no—
570C4⋊C8—41no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—41no—
580#102D4×C11314yescomplemented
581C22⋊C8—22no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586#95D4×C11311yescharacteristic
587#95D4×C11311yescharacteristic
588C24—21no—
589C24—21no—
590C24—21no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—81no—
597C24—81no—
598C24C2×D4×C11311yescharacteristic
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C2×D4×C11312yes—
605C2×D4—28no—
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—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
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—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4C2×D4×C11312yes—
644C2×D4#41×C11312yes—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4C2×D4×C11311yescharacteristic
658C22×C4C2×D4×C11311yescharacteristic
659C22×C4C2×D4×C11311yescharacteristic
660C22×C4C2×D4×C11312yes—
661C22×C4C2×D4×C11311yescharacteristic
662C22×C4C2×D4×C11311yescharacteristic
663C22×C4#41×C11312yes—
664C22×C4C24×C11311yescharacteristic
665SD16—44no—
666SD16—44no—
667SD16—44no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—44no—
680C2×C8C2×D4×C11312yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—81no—
691C4⋊C4C2×D4×C11312yes—
692C4⋊C4C2×D4×C11312yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4SD16×C11314yescomplemented
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—81no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—48no—
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—41no—
731C23—41no—
732C23—41no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23#121×C11312yes—
740C23C2×SD16×C11312yes—
741C23AGL(1,ℤ/8)×C11312yes—
742C23C22×D4×C11311yescharacteristic
743Q8—22no—
744Q8—22no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4—84no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4#121×C11312yes—
798C2×C4C2×SD16×C11312yes—
799C2×C4C2×SD16×C11312yes—
800C2×C4C22×D4×C11311yescharacteristic
801C2×C4C22×D4×C11311yescharacteristic
802C2×C4C2×#41×C11311yescharacteristic
803C2×C4C2×#41×C11311yescharacteristic
804C2×C4H(5,𝔽2)×C11311yescharacteristic
805C2×C4H(5,𝔽2)×C11311yescharacteristic
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22#460×C11314yescomplemented
839C22C2×#121×C11311yescharacteristic
840C22D42×C11311yescharacteristic
841C22#546×C11311yescharacteristic
842C22C22×SD16×C11311yescharacteristic
843C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
844C22#576×C11311yescharacteristic
845C22#577×C11311yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4#525×C11311yescharacteristic
857C4#538×C11311yescharacteristic
858C4D42×C11311yescharacteristic
859C4#546×C11311yescharacteristic
860C2—24no—
861C2—82no—
862C2—82no—
863C2—161no—
864C2C113×#242411yescharacteristic
865C2C2×#460×C11311yescharacteristic
866C2C113×#304511yescharacteristic
867C2C113×#326411yescharacteristic
868C2D4×SD16×C11311yescharacteristic
869C2C113×#329511yescharacteristic
870C2C113×#331011yescharacteristic
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×#465×C113C2semidirect
2. C2×#460×C113C2semidirect
3. C2×#450×C113C2semidirect
4. C22×#102×C113C2semidirect
6. C113×#2360C2semidirect
7. C113×#2065C2semidirect
8. C113×#2055C2semidirect
9. C113×#2041C2semidirect
10. C113×#2014C2semidirect
11. C113×#1982C2semidirect
12. C113×#1926C2semidirect
13. C113×#1880C2semidirect
14. C113×#1874C2semidirect
15. C113×#1850C2semidirect
19. C22×SD16×C113C22semidirect
27. C2×C4×Q8×C113C22semidirect
32. C2×#106×C113C22semidirect
33. C2×C4⋊C8×C113C22semidirect
34. C2×C4⋊C8×C113C22semidirect
35. C2×#103×C113C22semidirect
43. C2×#102×C113C22semidirect
44. C2×#102×C113C22semidirect
45. C2×#102×C113C22semidirect
49. #391×C113C22semidirect
53. #389×C113C22semidirect
56. C4×C4⋊C4×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
103. C22⋊Q8×C113D4semidirect
144. #102×C113D4semidirect
264. C22⋊C4×C113SD16semidirect
402. C22×C113#460semidirect
424. #25080C113direct (N × H)
436. C2×#465C2×C113semidirect
437. C2×#460C2×C113semidirect
438. C2×#450C2×C113semidirect
439. C22×#102C2×C113semidirect
441. #2360C2×C113semidirect
442. #2065C2×C113semidirect
443. #2055C2×C113semidirect
444. #2041C2×C113semidirect
445. #2014C2×C113semidirect
446. #1982C2×C113semidirect
447. #1926C2×C113semidirect
448. #1880C2×C113semidirect
449. #1874C2×C113semidirect
450. #1850C2×C113semidirect
451. C113#25080direct (N × H)
455. C22×SD16C22×C113semidirect
463. C2×C4×Q8C22×C113semidirect
468. C2×#106C22×C113semidirect
469. C2×C4⋊C8C22×C113semidirect
470. C2×C4⋊C8C22×C113semidirect
471. C2×#103C22×C113semidirect
479. C2×#102C22×C113semidirect
480. C2×#102C22×C113semidirect
481. C2×#102C22×C113semidirect
485. #391C22×C113semidirect
489. #389C22×C113semidirect
492. C4×C4⋊C4C22×C113semidirect
495. #340C22×C113semidirect
496. #340C22×C113semidirect
497. #336C22×C113semidirect
498. #336C22×C113semidirect
539. C22⋊Q8D4×C113semidirect
580. #102D4×C113semidirect
700. C22⋊C4SD16×C113semidirect
838. C22#460×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C1132
C2×#460×C1132
C2×#450×C1132
C22×#102×C1132
C113×#24332
C113×#23602
C113×#20652
C113×#20552
C113×#20412
C113×#20142
C113×#19822
C113×#19262
C113×#18802
C113×#18742
C113×#18502
#25080113