Finite Group Databasebeta

← C113×#17592 #43285612

Subgroups — C113×#17592 #43285612

Order 28928.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C113C211yesmaximal, characteristic
2C2×#407×C113C211yesmaximal, characteristic, complemented
3C2×#380×C113C211yesmaximal, characteristic, complemented
4C113×#1520C212yesmaximal, complemented
5C113×#1519C212yesmaximal, complemented
6C113×#1513C214yesmaximal, complemented
7C113×#1504C214yesmaximal, complemented
8C22×#41×C113C411yescharacteristic, complemented
9C24×C4×C113C2211yescharacteristic
10C22×M16×C113—21no—
11#525×C113—21no—
12#525×C113—21no—
13#525×C113—21no—
14#525×C113—21no—
15#525×C113C412yescomplemented
16#525×C113C412yescomplemented
17#525×C113C2212yes—
18#525×C113C2212yes—
19C2×#123×C113—21no—
20C2×C22⋊Q8×C113C411yescharacteristic, complemented
21C2×C22⋊Q8×C113C2211yescharacteristic
22C2×#121×C113C411yescharacteristic, complemented
23C2×#121×C113C2211yescharacteristic
24C2×#120×C113—21no—
25C2×C4×D4×C113—21no—
26C2×C4×D4×C113—21no—
27C2×#117×C113C411yescharacteristic, complemented
28C22×C4⋊C4×C113—21no—
29C22×C22⋊C4×C113—21no—
30#407×C113—21no—
31#407×C113—21no—
32#407×C113C2212yescomplemented
33#407×C113C2212yescomplemented
34C2×C22⋊C8×C113—21no—
35C2×C22⋊C8×C113C2212yes—
36#380×C113—21no—
37#380×C113—21no—
38#380×C113C2212yes—
39#380×C113C2212yescomplemented
40C2×#95×C113C2212yescomplemented
41#328×C113C2218yescomplemented
42#327×C113C2218yescomplemented
43C25×C113D411yescharacteristic
44C2×#41×C113—21no—
45C2×#41×C113—21no—
46C2×#41×C113—44no—
47C2×#41×C113C2×C412yes—
48C2×#41×C113C2×C412yescomplemented
49C22×Q8×C113C2×C411yescharacteristic, complemented
50C22×D4×C113—21no—
51C22×D4×C113—21no—
52C22×D4×C113—21no—
53C22×D4×C113C2×C411yescharacteristic, complemented
54C23×C4×C113—21no—
55C23×C4×C113—22no—
56C23×C4×C113—44no—
57C23×C4×C113C2×C411yescharacteristic
58C23×C4×C113C2×C411yescharacteristic
59C23×C4×C113C2×C411yescharacteristic
60C23×C4×C113C2×C411yescharacteristic
61C23×C4×C113D411yescharacteristic
62C23×C4×C113D411yescharacteristic
63C23×C4×C113D411yescharacteristic
64C23×C4×C113D411yescharacteristic
65C23×C4×C113D411yescharacteristic
66C23×C4×C113D411yescharacteristic
67C23×C4×C113D411yescharacteristic
68C23×C4×C113C2311yescharacteristic
69C23×C4×C113C2311yescharacteristic
70C23×C4×C113C2311yescharacteristic
71C2×M16×C113—22no—
72C2×M16×C113—22no—
73C2×M16×C113—44no—
74C22×C8×C113—22no—
75#123×C113—22no—
76#123×C113—22no—
77#123×C113—22no—
78#123×C113—22no—
79C22⋊Q8×C113—21no—
80C22⋊Q8×C113—21no—
81C22⋊Q8×C113—21no—
82C22⋊Q8×C113—21no—
83C22⋊Q8×C113C2×C412yes—
84C22⋊Q8×C113C2×C412yescomplemented
85C22⋊Q8×C113C2×C412yescomplemented
86C22⋊Q8×C113C2312yes—
87#121×C113—21no—
88#121×C113—21no—
89#121×C113—21no—
90#121×C113—21no—
91#121×C113C2×C412yes—
92#121×C113C2×C412yescomplemented
93#121×C113C2×C412yescomplemented
94#121×C113C2312yes—
95#120×C113—22no—
96#120×C113—22no—
97#120×C113—22no—
98#120×C113—22no—
99C4×D4×C113—22no—
100C4×D4×C113—22no—
101C4×D4×C113—22no—
102C4×D4×C113—22no—
103C4×D4×C113—22no—
104C4×D4×C113—22no—
105C4×D4×C113—22no—
106C4×D4×C113—22no—
107#117×C113—21no—
108#117×C113—21no—
109#117×C113C2×C412yes—
110#117×C113C2×C412yescomplemented
111C2×C4⋊C4×C113—21no—
112C2×C4⋊C4×C113—21no—
113C2×C4⋊C4×C113—22no—
114C2×C4⋊C4×C113—22no—
115C2×C4⋊C4×C113—44no—
116C2×C4⋊C4×C113C2×C411yescharacteristic, complemented
117C2×C4⋊C4×C113C2×C411yescharacteristic, complemented
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—22no—
124C2×C22⋊C4×C113—22no—
125C2×C22⋊C4×C113—44no—
126C2×C42×C113—21no—
127C22⋊C8×C113—22no—
128C22⋊C8×C113—22no—
129C22⋊C8×C113—22no—
130C22⋊C8×C113C2314yes—
131#95×C113—22no—
132#95×C113C2314yes—
133C24×C113—22no—
134C24×C113—22no—
135C24×C113—21no—
136C24×C113—42no—
137C24×C113—42no—
138C24×C113C22⋊C411yescharacteristic
139C24×C113C22⋊C411yescharacteristic
140C24×C113C22⋊C411yescharacteristic
141C24×C113C22⋊C411yescharacteristic
142C24×C113C2×D411yescharacteristic
143C24×C113C2×D411yescharacteristic
144C24×C113C2×D411yescharacteristic
145#41×C113—44no—
146#41×C113—44no—
147#41×C113—44no—
148#41×C113—44no—
149C2×Q8×C113—21no—
150C2×Q8×C113—42no—
151C2×Q8×C113C22×C412yes—
152C2×D4×C113—22no—
153C2×D4×C113—22no—
154C2×D4×C113—22no—
155C2×D4×C113—22no—
156C2×D4×C113—22no—
157C2×D4×C113—22no—
158C2×D4×C113—21no—
159C2×D4×C113—42no—
160C2×D4×C113—44no—
161C2×D4×C113—44no—
162C2×D4×C113—42no—
163C2×D4×C113—42no—
164C2×D4×C113C22×C412yes—
165C22×C4×C113—24no—
166C22×C4×C113—24no—
167C22×C4×C113—24no—
168C22×C4×C113—21no—
169C22×C4×C113—21no—
170C22×C4×C113—21no—
171C22×C4×C113—22no—
172C22×C4×C113—22no—
173C22×C4×C113—24no—
174C22×C4×C113—42no—
175C22×C4×C113—42no—
176C22×C4×C113—42no—
177C22×C4×C113—42no—
178C22×C4×C113—42no—
179C22×C4×C113—42no—
180C22×C4×C113—42no—
181C22×C4×C113—42no—
182C22×C4×C113—42no—
183C22×C4×C113—42no—
184C22×C4×C113—42no—
185C22×C4×C113—44no—
186C22×C4×C113—44no—
187C22×C4×C113—44no—
188C22×C4×C113—44no—
189C22×C4×C113C22⋊C411yescharacteristic
190C22×C4×C113C22⋊C411yescharacteristic
191C22×C4×C113C22⋊C411yescharacteristic
192C22×C4×C113C22⋊C411yescharacteristic
193C22×C4×C113C22⋊C411yescharacteristic
194C22×C4×C113C22⋊C411yescharacteristic
195C22×C4×C113C22⋊C411yescharacteristic
196C22×C4×C113C22⋊C411yescharacteristic
197C22×C4×C113C22⋊C411yescharacteristic
198C22×C4×C113C22⋊C411yescharacteristic
199C22×C4×C113C22⋊C411yescharacteristic
200C22×C4×C113C22⋊C411yescharacteristic
201C22×C4×C113C22×C411yescharacteristic
202C22×C4×C113C22×C411yescharacteristic
203C22×C4×C113C22×C411yescharacteristic
204C22×C4×C113C22×C411yescharacteristic
205C22×C4×C113C22×C411yescharacteristic
206C22×C4×C113C22×C411yescharacteristic
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D411yescharacteristic
209C22×C4×C113C2×D411yescharacteristic
210C22×C4×C113C2×D411yescharacteristic
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D411yescharacteristic
216C22×C4×C113C2411yescharacteristic
217M16×C113—44no—
218M16×C113—44no—
219C2×C8×C113—24no—
220C2×C8×C113—44no—
221C4⋊C4×C113—22no—
222C4⋊C4×C113—22no—
223C4⋊C4×C113—22no—
224C4⋊C4×C113—21no—
225C4⋊C4×C113—21no—
226C4⋊C4×C113—22no—
227C4⋊C4×C113—44no—
228C4⋊C4×C113—44no—
229C4⋊C4×C113C22×C412yes—
230C4⋊C4×C113C22×C412yes—
231C22⋊C4×C113—22no—
232C22⋊C4×C113—22no—
233C22⋊C4×C113—22no—
234C22⋊C4×C113—22no—
235C22⋊C4×C113—22no—
236C22⋊C4×C113—22no—
237C22⋊C4×C113—22no—
238C22⋊C4×C113—22no—
239C22⋊C4×C113—22no—
240C22⋊C4×C113—22no—
241C22⋊C4×C113—44no—
242C22⋊C4×C113—44no—
243C42×C113—22no—
244C42×C113—22no—
245C23×C113—21no—
246C23×C113—21no—
247C23×C113—22no—
248C23×C113—22no—
249C23×C113—21no—
250C23×C113—21no—
251C23×C113—22no—
252C23×C113—22no—
253C23×C113—22no—
254C23×C113—22no—
255C23×C113—22no—
256C23×C113—22no—
257C23×C113—22no—
258C23×C113—22no—
259C23×C113—22no—
260C23×C113—41no—
261C23×C113—41no—
262C23×C113—41no—
263C23×C113—41no—
264C23×C113—41no—
265C23×C113—41no—
266C23×C113—41no—
267C23×C113—41no—
268C23×C113—48no—
269C23×C113—48no—
270C23×C113—42no—
271C23×C113—42no—
272C23×C113—42no—
273C23×C113C2×C22⋊C411yescharacteristic
274C23×C113C2×C22⋊C411yescharacteristic
275C23×C113C2×C22⋊C411yescharacteristic
276C23×C113C2×C22⋊C411yescharacteristic
277C23×C113C2×C22⋊C411yescharacteristic
278C23×C113C2×C22⋊C411yescharacteristic
279C23×C113AGL(1,ℤ/8)12yes—
280C23×C113#13712yes—
281C23×C113C22×D411yescharacteristic
282Q8×C113—42no—
283Q8×C113—42no—
284D4×C113—42no—
285D4×C113—44no—
286D4×C113—44no—
287D4×C113—42no—
288D4×C113—42no—
289D4×C113—44no—
290D4×C113—44no—
291D4×C113—44no—
292D4×C113—42no—
293C2×C4×C113—22no—
294C2×C4×C113—22no—
295C2×C4×C113—22no—
296C2×C4×C113—22no—
297C2×C4×C113—22no—
298C2×C4×C113—22no—
299C2×C4×C113—22no—
300C2×C4×C113—22no—
301C2×C4×C113—22no—
302C2×C4×C113—22no—
303C2×C4×C113—22no—
304C2×C4×C113—22no—
305C2×C4×C113—22no—
306C2×C4×C113—22no—
307C2×C4×C113—22no—
308C2×C4×C113—22no—
309C2×C4×C113—22no—
310C2×C4×C113—22no—
311C2×C4×C113—41no—
312C2×C4×C113—41no—
313C2×C4×C113—41no—
314C2×C4×C113—41no—
315C2×C4×C113—41no—
316C2×C4×C113—41no—
317C2×C4×C113—41no—
318C2×C4×C113—41no—
319C2×C4×C113—41no—
320C2×C4×C113—41no—
321C2×C4×C113—41no—
322C2×C4×C113—41no—
323C2×C4×C113—44no—
324C2×C4×C113—42no—
325C2×C4×C113—42no—
326C2×C4×C113—42no—
327C2×C4×C113—44no—
328C2×C4×C113—44no—
329C2×C4×C113—44no—
330C2×C4×C113—44no—
331C2×C4×C113—88no—
332C2×C4×C113#9914yes—
333C2×C4×C113C2×C22⋊C411yescharacteristic
334C2×C4×C113C2×C22⋊C411yescharacteristic
335C2×C4×C113C2×C22⋊C411yescharacteristic
336C2×C4×C113C2×C22⋊C411yescharacteristic
337C2×C4×C113C2×C22⋊C411yescharacteristic
338C2×C4×C113C2×C22⋊C411yescharacteristic
339C2×C4×C113C23×C411yescharacteristic
340C2×C4×C113C22×D411yescharacteristic
341C8×C113—44no—
342C22×C113—24no—
343C22×C113—24no—
344C22×C113—21no—
345C22×C113—21no—
346C22×C113—21no—
347C22×C113—21no—
348C22×C113—21no—
349C22×C113—21no—
350C22×C113—21no—
351C22×C113—21no—
352C22×C113—21no—
353C22×C113—21no—
354C22×C113—21no—
355C22×C113—21no—
356C22×C113—21no—
357C22×C113—21no—
358C22×C113—21no—
359C22×C113—21no—
360C22×C113—42no—
361C22×C113—42no—
362C22×C113—44no—
363C22×C113—44no—
364C22×C113—44no—
365C22×C113—44no—
366C22×C113—42no—
367C22×C113—42no—
368C22×C113—42no—
369C22×C113—42no—
370C22×C113—42no—
371C22×C113—84no—
372C22×C113C2×#9912yes—
373C22×C113#41712yes—
374C22×C113#41712yes—
375C22×C113#42112yes—
376C22×C113C22×C22⋊C411yescharacteristic
377C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C113C2×#13711yescharacteristic
379C4×C113—21no—
380C4×C113—21no—
381C4×C113—21no—
382C4×C113—21no—
383C4×C113—21no—
384C4×C113—21no—
385C4×C113—42no—
386C4×C113—42no—
387C4×C113—42no—
388C4×C113—84no—
389C4×C113C2×#9912yes—
390C4×C113C2×#9912yes—
391#17592C11311yesmaximal, characteristic, direct product factor, Sylow
392C2×C113—21no—
393C2×C113—21no—
394C2×C113—22no—
395C2×C113—22no—
396C2×C113—22no—
397C2×C113—22no—
398C2×C113—41no—
399C2×C113—41no—
400C2×C113—82no—
401C2×C113C22×#9911yescharacteristic
402C2×C113C2×#41711yescharacteristic
403C2×C113C2×#42111yescharacteristic
404C2×#525C2×C11311yescharacteristic
405C2×#407C2×C11311yescharacteristic, complemented
406C2×#380C2×C11311yescharacteristic, complemented
407#1520C2×C11312yescomplemented
408#1519C2×C11312yescomplemented
409#1513C2×C11314yescomplemented
410#1504C2×C11314yescomplemented
411C113#1759211yescharacteristic, direct product factor, Sylow
412C22×#41C4×C11311yescharacteristic, complemented
413C24×C4C22×C11311yescharacteristic
414C22×M16—21no—
415#525—21no—
416#525—21no—
417#525—21no—
418#525—21no—
419#525C4×C11312yescomplemented
420#525C4×C11312yescomplemented
421#525C22×C11312yes—
422#525C22×C11312yes—
423C2×#123—21no—
424C2×C22⋊Q8C4×C11311yescharacteristic, complemented
425C2×C22⋊Q8C22×C11311yescharacteristic
426C2×#121C4×C11311yescharacteristic, complemented
427C2×#121C22×C11311yescharacteristic
428C2×#120—21no—
429C2×C4×D4—21no—
430C2×C4×D4—21no—
431C2×#117C4×C11311yescharacteristic, complemented
432C22×C4⋊C4—21no—
433C22×C22⋊C4—21no—
434#407—21no—
435#407—21no—
436#407C22×C11312yescomplemented
437#407C22×C11312yescomplemented
438C2×C22⋊C8—21no—
439C2×C22⋊C8C22×C11312yes—
440#380—21no—
441#380—21no—
442#380C22×C11312yes—
443#380C22×C11312yescomplemented
444C2×#95C22×C11312yescomplemented
445#328C22×C11318yescomplemented
446#327C22×C11318yescomplemented
447C25D4×C11311yescharacteristic
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—44no—
451C2×#41C2×C4×C11312yes—
452C2×#41C2×C4×C11312yescomplemented
453C22×Q8C2×C4×C11311yescharacteristic, complemented
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C2×C4×C11311yescharacteristic, complemented
458C23×C4—21no—
459C23×C4—22no—
460C23×C4—44no—
461C23×C4C2×C4×C11311yescharacteristic
462C23×C4C2×C4×C11311yescharacteristic
463C23×C4C2×C4×C11311yescharacteristic
464C23×C4C2×C4×C11311yescharacteristic
465C23×C4D4×C11311yescharacteristic
466C23×C4D4×C11311yescharacteristic
467C23×C4D4×C11311yescharacteristic
468C23×C4D4×C11311yescharacteristic
469C23×C4D4×C11311yescharacteristic
470C23×C4D4×C11311yescharacteristic
471C23×C4D4×C11311yescharacteristic
472C23×C4C23×C11311yescharacteristic
473C23×C4C23×C11311yescharacteristic
474C23×C4C23×C11311yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—44no—
478C22×C8—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8C2×C4×C11312yes—
488C22⋊Q8C2×C4×C11312yescomplemented
489C22⋊Q8C2×C4×C11312yescomplemented
490C22⋊Q8C23×C11312yes—
491#121—21no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121C2×C4×C11312yes—
496#121C2×C4×C11312yescomplemented
497#121C2×C4×C11312yescomplemented
498#121C23×C11312yes—
499#120—22no—
500#120—22no—
501#120—22no—
502#120—22no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511#117—21no—
512#117—21no—
513#117C2×C4×C11312yes—
514#117C2×C4×C11312yescomplemented
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—44no—
520C2×C4⋊C4C2×C4×C11311yescharacteristic, complemented
521C2×C4⋊C4C2×C4×C11311yescharacteristic, complemented
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—44no—
530C2×C42—21no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8C23×C11314yes—
535#95—22no—
536#95C23×C11314yes—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—42no—
541C24—42no—
542C24C22⋊C4×C11311yescharacteristic
543C24C22⋊C4×C11311yescharacteristic
544C24C22⋊C4×C11311yescharacteristic
545C24C22⋊C4×C11311yescharacteristic
546C24C2×D4×C11311yescharacteristic
547C24C2×D4×C11311yescharacteristic
548C24C2×D4×C11311yescharacteristic
549#41—44no—
550#41—44no—
551#41—44no—
552#41—44no—
553C2×Q8—21no—
554C2×Q8—42no—
555C2×Q8C22×C4×C11312yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4C22×C4×C11312yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4C22⋊C4×C11311yescharacteristic
594C22×C4C22⋊C4×C11311yescharacteristic
595C22×C4C22⋊C4×C11311yescharacteristic
596C22×C4C22⋊C4×C11311yescharacteristic
597C22×C4C22⋊C4×C11311yescharacteristic
598C22×C4C22⋊C4×C11311yescharacteristic
599C22×C4C22⋊C4×C11311yescharacteristic
600C22×C4C22⋊C4×C11311yescharacteristic
601C22×C4C22⋊C4×C11311yescharacteristic
602C22×C4C22⋊C4×C11311yescharacteristic
603C22×C4C22⋊C4×C11311yescharacteristic
604C22×C4C22⋊C4×C11311yescharacteristic
605C22×C4C22×C4×C11311yescharacteristic
606C22×C4C22×C4×C11311yescharacteristic
607C22×C4C22×C4×C11311yescharacteristic
608C22×C4C22×C4×C11311yescharacteristic
609C22×C4C22×C4×C11311yescharacteristic
610C22×C4C22×C4×C11311yescharacteristic
611C22×C4C2×D4×C11311yescharacteristic
612C22×C4C2×D4×C11311yescharacteristic
613C22×C4C2×D4×C11311yescharacteristic
614C22×C4C2×D4×C11311yescharacteristic
615C22×C4C2×D4×C11311yescharacteristic
616C22×C4C2×D4×C11311yescharacteristic
617C22×C4C2×D4×C11311yescharacteristic
618C22×C4C2×D4×C11311yescharacteristic
619C22×C4C2×D4×C11311yescharacteristic
620C22×C4C24×C11311yescharacteristic
621M16—44no—
622M16—44no—
623C2×C8—24no—
624C2×C8—44no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4C22×C4×C11312yes—
634C4⋊C4C22×C4×C11312yes—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C42—22no—
648C42—22no—
649C23—21no—
650C23—21no—
651C23—22no—
652C23—22no—
653C23—21no—
654C23—21no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—48no—
673C23—48no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C2×C22⋊C4×C11311yescharacteristic
678C23C2×C22⋊C4×C11311yescharacteristic
679C23C2×C22⋊C4×C11311yescharacteristic
680C23C2×C22⋊C4×C11311yescharacteristic
681C23C2×C22⋊C4×C11311yescharacteristic
682C23C2×C22⋊C4×C11311yescharacteristic
683C23AGL(1,ℤ/8)×C11312yes—
684C23#137×C11312yes—
685C23C22×D4×C11311yescharacteristic
686Q8—42no—
687Q8—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—44no—
694D4—44no—
695D4—44no—
696D4—42no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—88no—
736C2×C4#99×C11314yes—
737C2×C4C2×C22⋊C4×C11311yescharacteristic
738C2×C4C2×C22⋊C4×C11311yescharacteristic
739C2×C4C2×C22⋊C4×C11311yescharacteristic
740C2×C4C2×C22⋊C4×C11311yescharacteristic
741C2×C4C2×C22⋊C4×C11311yescharacteristic
742C2×C4C2×C22⋊C4×C11311yescharacteristic
743C2×C4C23×C4×C11311yescharacteristic
744C2×C4C22×D4×C11311yescharacteristic
745C8—44no—
746C22—24no—
747C22—24no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—84no—
776C22C2×#99×C11312yes—
777C22#417×C11312yes—
778C22#417×C11312yes—
779C22#421×C11312yes—
780C22C22×C22⋊C4×C11311yescharacteristic
781C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
782C22C2×#137×C11311yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—84no—
793C4C2×#99×C11312yes—
794C4C2×#99×C11312yes—
795C2—21no—
796C2—21no—
797C2—22no—
798C2—22no—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—41no—
803C2—82no—
804C2C22×#99×C11311yescharacteristic
805C2C2×#417×C11311yescharacteristic
806C2C2×#421×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C22×C22⋊C4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC2×#525×C113C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C24×C4×C113 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#407×C113C2semidirect
3. C2×#380×C113C2semidirect
4. C113×#1520C2semidirect
5. C113×#1519C2semidirect
6. C113×#1513C2semidirect
7. C113×#1504C2semidirect
8. C22×#41×C113C4semidirect
15. #525×C113C4semidirect
16. #525×C113C4semidirect
20. C2×C22⋊Q8×C113C4semidirect
22. C2×#121×C113C4semidirect
27. C2×#117×C113C4semidirect
32. #407×C113C22semidirect
33. #407×C113C22semidirect
39. #380×C113C22semidirect
40. C2×#95×C113C22semidirect
41. #328×C113C22semidirect
42. #327×C113C22semidirect
48. C2×#41×C113C2×C4semidirect
49. C22×Q8×C113C2×C4semidirect
53. C22×D4×C113C2×C4semidirect
84. C22⋊Q8×C113C2×C4semidirect
85. C22⋊Q8×C113C2×C4semidirect
92. #121×C113C2×C4semidirect
93. #121×C113C2×C4semidirect
110. #117×C113C2×C4semidirect
116. C2×C4⋊C4×C113C2×C4semidirect
117. C2×C4⋊C4×C113C2×C4semidirect
391. #17592C113direct (N × H)
405. C2×#407C2×C113semidirect
406. C2×#380C2×C113semidirect
407. #1520C2×C113semidirect
408. #1519C2×C113semidirect
409. #1513C2×C113semidirect
410. #1504C2×C113semidirect
411. C113#17592direct (N × H)
412. C22×#41C4×C113semidirect
419. #525C4×C113semidirect
420. #525C4×C113semidirect
424. C2×C22⋊Q8C4×C113semidirect
426. C2×#121C4×C113semidirect
431. C2×#117C4×C113semidirect
436. #407C22×C113semidirect
437. #407C22×C113semidirect
443. #380C22×C113semidirect
444. C2×#95C22×C113semidirect
445. #328C22×C113semidirect
446. #327C22×C113semidirect
452. C2×#41C2×C4×C113semidirect
453. C22×Q8C2×C4×C113semidirect
457. C22×D4C2×C4×C113semidirect
488. C22⋊Q8C2×C4×C113semidirect
489. C22⋊Q8C2×C4×C113semidirect
496. #121C2×C4×C113semidirect
497. #121C2×C4×C113semidirect
514. #117C2×C4×C113semidirect
520. C2×C4⋊C4C2×C4×C113semidirect
521. C2×C4⋊C4C2×C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1132
C2×#407×C1132
C2×#380×C1132
C113×#15202
C113×#15192
C113×#15132
C113×#15042
#17592113