Finite Group Databasebeta

← C103×#22419 #39927694

Subgroups — C103×#22419 #39927694

Order 26368.

1670 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×#546×C103C211yesmaximal, characteristic
2C2×#435×C103C211yesmaximal, characteristic, complemented
3C2×#417×C103C211yesmaximal, characteristic, complemented
4C22×#102×C103C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C103C211yesmaximal, characteristic, complemented
6C103×#1983C211yesmaximal, characteristic, complemented
7C103×#1959C211yesmaximal, characteristic, complemented
8C103×#1895C211yesmaximal, characteristic, complemented
9C103×#1892C211yesmaximal, characteristic, complemented
10C103×#1874C211yesmaximal, characteristic, complemented
11C103×#1872C211yesmaximal, characteristic, complemented
12C103×#1802C211yesmaximal, characteristic, complemented
13C103×#1788C211yesmaximal, characteristic, complemented
14C103×#1786C211yesmaximal, characteristic, complemented
15C103×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C23×D4×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic, complemented
19C23×C8×C103C2211yescharacteristic
20#546×C103—24no—
21#546×C103C418yescomplemented
22C2×#124×C103C2211yescharacteristic
23C2×#123×C103—21no—
24C2×C22⋊Q8×C103C2211yescharacteristic
25C2×#121×C103—21no—
26C2×#121×C103C2211yescharacteristic
27C2×#120×C103—21no—
28C2×C4×D4×C103—21no—
29C2×C4×D4×C103C2211yescharacteristic
30C2×C4×D4×C103C2211yescharacteristic
31C22×C4⋊C4×C103C2211yescharacteristic
32C22×C4⋊C4×C103C2211yescharacteristic, complemented
33C22×C22⋊C4×C103—21no—
34#435×C103—24no—
35C2×C4⋊C8×C103C2211yescharacteristic, complemented
36#417×C103—24no—
37C2×#103×C103C2211yescharacteristic, complemented
38C2×#103×C103C2211yescharacteristic, complemented
39C2×#103×C103C2211yescharacteristic, complemented
40C2×#103×C103C2211yescharacteristic, complemented
41C2×#102×C103—24no—
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic
46C2×#102×C103C2211yescharacteristic
47C2×#102×C103C2211yescharacteristic
48C2×#102×C103C2211yescharacteristic
49C2×#102×C103C2211yescharacteristic
50C2×C22⋊C8×C103C2211yescharacteristic
51C2×C22⋊C8×C103C2211yescharacteristic, complemented
52C2×#97×C103C2211yescharacteristic, complemented
53#389×C103—21no—
54#385×C103—21no—
55#385×C103—21no—
56#384×C103C2211yescharacteristic, complemented
57#380×C103C2211yescharacteristic
58#380×C103C2211yescharacteristic, complemented
59C4×C4⋊C4×C103C2211yescharacteristic, complemented
60#340×C103C2211yescharacteristic, complemented
61#340×C103C2211yescharacteristic, complemented
62#340×C103C2211yescharacteristic, complemented
63#340×C103C2211yescharacteristic, complemented
64C25×C103—21no—
65C2×#41×C103—22no—
66C2×#41×C103—22no—
67C2×#41×C103—22no—
68C2×#41×C103—41no—
69C2×#41×C103—41no—
70C2×#41×C103C2×C414yescomplemented
71C22×Q8×C103C2311yescharacteristic
72C22×D4×C103—22no—
73C22×D4×C103—22no—
74C22×D4×C103—21no—
75C22×D4×C103—21no—
76C22×D4×C103—21no—
77C22×D4×C103—22no—
78C22×D4×C103—41no—
79C22×D4×C103—41no—
80C22×D4×C103C2×C414yescomplemented
81C22×D4×C103D411yescharacteristic
82C22×D4×C103C2311yescharacteristic
83C22×D4×C103C2311yescharacteristic
84C23×C4×C103—21no—
85C23×C4×C103—21no—
86C23×C4×C103—21no—
87C23×C4×C103—21no—
88C23×C4×C103C2311yescharacteristic
89C23×C4×C103C2311yescharacteristic
90C2×M16×C103—22no—
91C2×M16×C103—22no—
92C2×M16×C103—41no—
93C22×C8×C103—22no—
94C22×C8×C103—22no—
95C22×C8×C103—41no—
96C22×C8×C103C2311yescharacteristic
97C22×C8×C103C2311yescharacteristic
98C22×C8×C103C2311yescharacteristic
99C22×C8×C103C2311yescharacteristic
100#124×C103—22no—
101#124×C103C2×C414yescomplemented
102#123×C103—28no—
103C22⋊Q8×C103—22no—
104C22⋊Q8×C103C2×C414yescomplemented
105#121×C103—22no—
106#121×C103—28no—
107#121×C103C2×C414yescomplemented
108#120×C103—28no—
109C4×D4×C103—22no—
110C4×D4×C103—44no—
111C4×D4×C103C2×C414yes—
112C4×D4×C103C2×C414yescomplemented
113C4×D4×C103D414yes—
114C2×C4⋊C4×C103—21no—
115C2×C4⋊C4×C103—22no—
116C2×C4⋊C4×C103—22no—
117C2×C4⋊C4×C103—21no—
118C2×C4⋊C4×C103—21no—
119C2×C4⋊C4×C103—21no—
120C2×C4⋊C4×C103—21no—
121C2×C4⋊C4×C103—41no—
122C2×C4⋊C4×C103—41no—
123C2×C4⋊C4×C103D411yescharacteristic
124C2×C4⋊C4×C103C2311yescharacteristic
125C2×C4⋊C4×C103C2311yescharacteristic
126C2×C4⋊C4×C103C2311yescharacteristic
127C2×C4⋊C4×C103C2311yescharacteristic
128C2×C4⋊C4×C103C2311yescharacteristic
129C2×C22⋊C4×C103—21no—
130C2×C22⋊C4×C103—21no—
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103—21no—
133C2×C22⋊C4×C103—21no—
134C2×C22⋊C4×C103—28no—
135C2×C22⋊C4×C103—21no—
136C2×C22⋊C4×C103—21no—
137C2×C22⋊C4×C103D411yescharacteristic
138C2×C22⋊C4×C103D411yescharacteristic
139C2×C42×C103—21no—
140C2×C42×C103C2311yescharacteristic
141C4⋊C8×C103—22no—
142#103×C103—22no—
143#103×C103—22no—
144#103×C103—41no—
145#103×C103—41no—
146#102×C103—22no—
147#102×C103—22no—
148#102×C103—22no—
149#102×C103—22no—
150#102×C103—22no—
151#102×C103—41no—
152#102×C103—41no—
153#102×C103D414yescomplemented
154C22⋊C8×C103—22no—
155C22⋊C8×C103—22no—
156#97×C103—22no—
157#95×C103—21no—
158#95×C103—21no—
159#95×C103—21no—
160C24×C103—21no—
161C24×C103—21no—
162C24×C103—24no—
163C24×C103—42no—
164C24×C103—42no—
165C24×C103—42no—
166C24×C103—42no—
167C24×C103—81no—
168C24×C103—81no—
169C24×C103C2×D411yescharacteristic
170C24×C103C2×D411yescharacteristic
171#41×C103—28no—
172#41×C103—44no—
173#41×C103—44no—
174#41×C103—44no—
175C2×Q8×C103—21no—
176C2×Q8×C103—21no—
177C2×Q8×C103—21no—
178C2×Q8×C103—21no—
179C2×Q8×C103—21no—
180C2×Q8×C103C22×C412yes—
181C2×D4×C103—22no—
182C2×D4×C103—22no—
183C2×D4×C103—28no—
184C2×D4×C103—24no—
185C2×D4×C103—24no—
186C2×D4×C103—24no—
187C2×D4×C103—21no—
188C2×D4×C103—21no—
189C2×D4×C103—21no—
190C2×D4×C103—21no—
191C2×D4×C103—21no—
192C2×D4×C103—21no—
193C2×D4×C103—21no—
194C2×D4×C103—21no—
195C2×D4×C103—44no—
196C2×D4×C103—44no—
197C2×D4×C103—44no—
198C2×D4×C103—42no—
199C2×D4×C103—42no—
200C2×D4×C103—42no—
201C2×D4×C103—42no—
202C2×D4×C103—81no—
203C2×D4×C103—81no—
204C2×D4×C103C22⋊C414yes—
205C2×D4×C103C22×C412yes—
206C2×D4×C103C22×C412yes—
207C2×D4×C103C2×D412yes—
208C2×D4×C103#4112yes—
209C22×C4×C103—21no—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—21no—
213C22×C4×C103—21no—
214C22×C4×C103—21no—
215C22×C4×C103—21no—
216C22×C4×C103—21no—
217C22×C4×C103—21no—
218C22×C4×C103—21no—
219C22×C4×C103—21no—
220C22×C4×C103—24no—
221C22×C4×C103—24no—
222C22×C4×C103—21no—
223C22×C4×C103—21no—
224C22×C4×C103—21no—
225C22×C4×C103—42no—
226C22×C4×C103—42no—
227C22×C4×C103—42no—
228C22×C4×C103—42no—
229C22×C4×C103—42no—
230C22×C4×C103—42no—
231C22×C4×C103—81no—
232C22×C4×C103—81no—
233C22×C4×C103—81no—
234C22×C4×C103—81no—
235C22×C4×C103C22×C412yes—
236C22×C4×C103C22×C412yes—
237C22×C4×C103C2×D411yescharacteristic
238C22×C4×C103C2×D411yescharacteristic
239C22×C4×C103C2×D411yescharacteristic
240C22×C4×C103C2×D411yescharacteristic
241C22×C4×C103C2×D412yes—
242C22×C4×C103C2×D412yes—
243C22×C4×C103C2411yescharacteristic
244M16×C103—44no—
245C2×C8×C103—21no—
246C2×C8×C103—21no—
247C2×C8×C103—21no—
248C2×C8×C103—21no—
249C2×C8×C103—21no—
250C2×C8×C103—21no—
251C2×C8×C103—21no—
252C2×C8×C103—21no—
253C2×C8×C103—21no—
254C2×C8×C103—21no—
255C2×C8×C103—21no—
256C2×C8×C103—44no—
257C2×C8×C103C2×D412yes—
258C4⋊C4×C103—24no—
259C4⋊C4×C103—21no—
260C4⋊C4×C103—21no—
261C4⋊C4×C103—21no—
262C4⋊C4×C103—21no—
263C4⋊C4×C103—21no—
264C4⋊C4×C103—21no—
265C4⋊C4×C103—21no—
266C4⋊C4×C103—21no—
267C4⋊C4×C103—42no—
268C4⋊C4×C103—42no—
269C4⋊C4×C103—42no—
270C4⋊C4×C103—81no—
271C4⋊C4×C103C22⋊C414yes—
272C4⋊C4×C103C22×C412yes—
273C4⋊C4×C103C2×D412yes—
274C22⋊C4×C103—24no—
275C22⋊C4×C103—24no—
276C22⋊C4×C103—24no—
277C22⋊C4×C103—24no—
278C22⋊C4×C103—24no—
279C22⋊C4×C103—42no—
280C22⋊C4×C103—42no—
281C22⋊C4×C103C22⋊C414yes—
282C22⋊C4×C103C22⋊C414yes—
283C42×C103—42no—
284C42×C103C22×C412yes—
285C42×C103C2×D412yes—
286C23×C103—21no—
287C23×C103—21no—
288C23×C103—21no—
289C23×C103—21no—
290C23×C103—22no—
291C23×C103—21no—
292C23×C103—22no—
293C23×C103—21no—
294C23×C103—22no—
295C23×C103—21no—
296C23×C103—21no—
297C23×C103—21no—
298C23×C103—21no—
299C23×C103—22no—
300C23×C103—48no—
301C23×C103—41no—
302C23×C103—41no—
303C23×C103—41no—
304C23×C103—41no—
305C23×C103—41no—
306C23×C103—41no—
307C23×C103—41no—
308C23×C103—41no—
309C23×C103—41no—
310C23×C103—41no—
311C23×C103—48no—
312C23×C103—84no—
313C23×C103—84no—
314C23×C103—84no—
315C23×C103—84no—
316C23×C103—84no—
317C23×C103C2×C22⋊C412yes—
318C23×C103C2×C22⋊C412yes—
319C23×C103AGL(1,ℤ/8)12yes—
320C23×C103#13712yes—
321C23×C103C22×D411yescharacteristic
322Q8×C103—22no—
323Q8×C103—22no—
324Q8×C103—41no—
325Q8×C103—41no—
326D4×C103—28no—
327D4×C103—22no—
328D4×C103—22no—
329D4×C103—22no—
330D4×C103—22no—
331D4×C103—22no—
332D4×C103—48no—
333D4×C103—48no—
334D4×C103—41no—
335D4×C103—41no—
336D4×C103—84no—
337D4×C103C4×D414yescomplemented
338C2×C4×C103—21no—
339C2×C4×C103—21no—
340C2×C4×C103—21no—
341C2×C4×C103—21no—
342C2×C4×C103—21no—
343C2×C4×C103—21no—
344C2×C4×C103—21no—
345C2×C4×C103—21no—
346C2×C4×C103—22no—
347C2×C4×C103—22no—
348C2×C4×C103—22no—
349C2×C4×C103—22no—
350C2×C4×C103—22no—
351C2×C4×C103—22no—
352C2×C4×C103—22no—
353C2×C4×C103—22no—
354C2×C4×C103—22no—
355C2×C4×C103—22no—
356C2×C4×C103—22no—
357C2×C4×C103—48no—
358C2×C4×C103—41no—
359C2×C4×C103—41no—
360C2×C4×C103—41no—
361C2×C4×C103—41no—
362C2×C4×C103—41no—
363C2×C4×C103—41no—
364C2×C4×C103—41no—
365C2×C4×C103—41no—
366C2×C4×C103—41no—
367C2×C4×C103—41no—
368C2×C4×C103—41no—
369C2×C4×C103—41no—
370C2×C4×C103—41no—
371C2×C4×C103—41no—
372C2×C4×C103—41no—
373C2×C4×C103—84no—
374C2×C4×C103—84no—
375C2×C4×C103—84no—
376C2×C4×C103C2×C22⋊C412yes—
377C2×C4×C103C2×C22⋊C412yes—
378C2×C4×C103C2×C22⋊C412yes—
379C2×C4×C103C2×C22⋊C412yes—
380C2×C4×C103C23×C411yescharacteristic
381C2×C4×C103C22×D411yescharacteristic
382C2×C4×C103C22×D411yescharacteristic
383C2×C4×C103C2×#4111yescharacteristic
384C2×C4×C103H(5,𝔽2)11yescharacteristic
385C2×C4×C103H(5,𝔽2)11yescharacteristic
386C8×C103—22no—
387C8×C103—41no—
388C8×C103—41no—
389C8×C103—41no—
390C22×C103—22no—
391C22×C103—22no—
392C22×C103—22no—
393C22×C103—22no—
394C22×C103—22no—
395C22×C103—22no—
396C22×C103—22no—
397C22×C103—24no—
398C22×C103—22no—
399C22×C103—22no—
400C22×C103—42no—
401C22×C103—42no—
402C22×C103—41no—
403C22×C103—42no—
404C22×C103—41no—
405C22×C103—42no—
406C22×C103—41no—
407C22×C103—42no—
408C22×C103—41no—
409C22×C103—42no—
410C22×C103—42no—
411C22×C103—42no—
412C22×C103—42no—
413C22×C103—816no—
414C22×C103—81no—
415C22×C103—81no—
416C22×C103—81no—
417C22×C103—81no—
418C22×C103#41714yescomplemented
419C22×C103C22×C22⋊C411yescharacteristic
420C22×C103D4211yescharacteristic
421C22×C103#54611yescharacteristic
422C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C103C2×#13711yescharacteristic
424C22×C103#57611yescharacteristic
425C22×C103#57711yescharacteristic
426C4×C103—22no—
427C4×C103—22no—
428C4×C103—22no—
429C4×C103—22no—
430C4×C103—42no—
431C4×C103—42no—
432C4×C103—42no—
433C4×C103—81no—
434C4×C103—81no—
435C4×C103—81no—
436C4×C103C2×C4×D411yescharacteristic
437C4×C103#51811yescharacteristic
438C4×C103D4211yescharacteristic
439C4×C103#54611yescharacteristic
440#22419C10311yesmaximal, characteristic, direct product factor, Sylow
441C2×C103—24no—
442C2×C103—42no—
443C2×C103—44no—
444C2×C103—82no—
445C2×C103D4×C22⋊C411yescharacteristic
446C2×C103C2×#41711yescharacteristic
447C2×C103#289711yescharacteristic
448C2×C103#326411yescharacteristic
449C2×C103#326611yescharacteristic
450C2×C103#330611yescharacteristic
451C2×C103#331411yescharacteristic
452C2×#546C2×C10311yescharacteristic
453C2×#435C2×C10311yescharacteristic, complemented
454C2×#417C2×C10311yescharacteristic, complemented
455C22×#102C2×C10311yescharacteristic, complemented
456D4×C4⋊C4C2×C10311yescharacteristic, complemented
457#1983C2×C10311yescharacteristic, complemented
458#1959C2×C10311yescharacteristic, complemented
459#1895C2×C10311yescharacteristic, complemented
460#1892C2×C10311yescharacteristic, complemented
461#1874C2×C10311yescharacteristic, complemented
462#1872C2×C10311yescharacteristic, complemented
463#1802C2×C10311yescharacteristic, complemented
464#1788C2×C10311yescharacteristic, complemented
465#1786C2×C10311yescharacteristic, complemented
466#1762C2×C10311yescharacteristic, complemented
467C103#2241911yescharacteristic, direct product factor, Sylow
468C22×#41C22×C10311yescharacteristic
469C23×D4C22×C10311yescharacteristic
470C22×M16C22×C10311yescharacteristic, complemented
471C23×C8C22×C10311yescharacteristic
472#546—24no—
473#546C4×C10318yescomplemented
474C2×#124C22×C10311yescharacteristic
475C2×#123—21no—
476C2×C22⋊Q8C22×C10311yescharacteristic
477C2×#121—21no—
478C2×#121C22×C10311yescharacteristic
479C2×#120—21no—
480C2×C4×D4—21no—
481C2×C4×D4C22×C10311yescharacteristic
482C2×C4×D4C22×C10311yescharacteristic
483C22×C4⋊C4C22×C10311yescharacteristic
484C22×C4⋊C4C22×C10311yescharacteristic, complemented
485C22×C22⋊C4—21no—
486#435—24no—
487C2×C4⋊C8C22×C10311yescharacteristic, complemented
488#417—24no—
489C2×#103C22×C10311yescharacteristic, complemented
490C2×#103C22×C10311yescharacteristic, complemented
491C2×#103C22×C10311yescharacteristic, complemented
492C2×#103C22×C10311yescharacteristic, complemented
493C2×#102—24no—
494C2×#102C22×C10311yescharacteristic
495C2×#102C22×C10311yescharacteristic
496C2×#102C22×C10311yescharacteristic
497C2×#102C22×C10311yescharacteristic
498C2×#102C22×C10311yescharacteristic
499C2×#102C22×C10311yescharacteristic
500C2×#102C22×C10311yescharacteristic
501C2×#102C22×C10311yescharacteristic
502C2×C22⋊C8C22×C10311yescharacteristic
503C2×C22⋊C8C22×C10311yescharacteristic, complemented
504C2×#97C22×C10311yescharacteristic, complemented
505#389—21no—
506#385—21no—
507#385—21no—
508#384C22×C10311yescharacteristic, complemented
509#380C22×C10311yescharacteristic
510#380C22×C10311yescharacteristic, complemented
511C4×C4⋊C4C22×C10311yescharacteristic, complemented
512#340C22×C10311yescharacteristic, complemented
513#340C22×C10311yescharacteristic, complemented
514#340C22×C10311yescharacteristic, complemented
515#340C22×C10311yescharacteristic, complemented
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×C4×C10314yescomplemented
523C22×Q8C23×C10311yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×C4×C10314yescomplemented
533C22×D4D4×C10311yescharacteristic
534C22×D4C23×C10311yescharacteristic
535C22×D4C23×C10311yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C23×C10311yescharacteristic
541C23×C4C23×C10311yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C23×C10311yescharacteristic
549C22×C8C23×C10311yescharacteristic
550C22×C8C23×C10311yescharacteristic
551C22×C8C23×C10311yescharacteristic
552#124—22no—
553#124C2×C4×C10314yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×C4×C10314yescomplemented
557#121—22no—
558#121—28no—
559#121C2×C4×C10314yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—44no—
563C4×D4C2×C4×C10314yes—
564C4×D4C2×C4×C10314yescomplemented
565C4×D4D4×C10314yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4D4×C10311yescharacteristic
576C2×C4⋊C4C23×C10311yescharacteristic
577C2×C4⋊C4C23×C10311yescharacteristic
578C2×C4⋊C4C23×C10311yescharacteristic
579C2×C4⋊C4C23×C10311yescharacteristic
580C2×C4⋊C4C23×C10311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C10311yescharacteristic
590C2×C22⋊C4D4×C10311yescharacteristic
591C2×C42—21no—
592C2×C42C23×C10311yescharacteristic
593C4⋊C8—22no—
594#103—22no—
595#103—22no—
596#103—41no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604#102—41no—
605#102D4×C10314yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C10311yescharacteristic
622C24C2×D4×C10311yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C10312yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C10314yes—
657C2×D4C22×C4×C10312yes—
658C2×D4C22×C4×C10312yes—
659C2×D4C2×D4×C10312yes—
660C2×D4#41×C10312yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C10312yes—
688C22×C4C22×C4×C10312yes—
689C22×C4C2×D4×C10311yescharacteristic
690C22×C4C2×D4×C10311yescharacteristic
691C22×C4C2×D4×C10311yescharacteristic
692C22×C4C2×D4×C10311yescharacteristic
693C22×C4C2×D4×C10312yes—
694C22×C4C2×D4×C10312yes—
695C22×C4C24×C10311yescharacteristic
696M16—44no—
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—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C10312yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C10314yes—
724C4⋊C4C22×C4×C10312yes—
725C4⋊C4C2×D4×C10312yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C10314yes—
734C22⋊C4C22⋊C4×C10314yes—
735C42—42no—
736C42C22×C4×C10312yes—
737C42C2×D4×C10312yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C10312yes—
770C23C2×C22⋊C4×C10312yes—
771C23AGL(1,ℤ/8)×C10312yes—
772C23#137×C10312yes—
773C23C22×D4×C10311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C10314yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
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—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C10312yes—
829C2×C4C2×C22⋊C4×C10312yes—
830C2×C4C2×C22⋊C4×C10312yes—
831C2×C4C2×C22⋊C4×C10312yes—
832C2×C4C23×C4×C10311yescharacteristic
833C2×C4C22×D4×C10311yescharacteristic
834C2×C4C22×D4×C10311yescharacteristic
835C2×C4C2×#41×C10311yescharacteristic
836C2×C4H(5,𝔽2)×C10311yescharacteristic
837C2×C4H(5,𝔽2)×C10311yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#417×C10314yescomplemented
871C22C22×C22⋊C4×C10311yescharacteristic
872C22D42×C10311yescharacteristic
873C22#546×C10311yescharacteristic
874C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
875C22C2×#137×C10311yescharacteristic
876C22#576×C10311yescharacteristic
877C22#577×C10311yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C10311yescharacteristic
889C4#518×C10311yescharacteristic
890C4D42×C10311yescharacteristic
891C4#546×C10311yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C10311yescharacteristic
897C2C2×#417×C10311yescharacteristic
898C2C103×#289711yescharacteristic
899C2C103×#326411yescharacteristic
900C2C103×#326611yescharacteristic
901C2C103×#330611yescharacteristic
902C2C103×#331411yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC2×#546×C103C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#435×C103C2semidirect
3. C2×#417×C103C2semidirect
4. C22×#102×C103C2semidirect
5. D4×C4⋊C4×C103C2semidirect
6. C103×#1983C2semidirect
7. C103×#1959C2semidirect
8. C103×#1895C2semidirect
9. C103×#1892C2semidirect
10. C103×#1874C2semidirect
11. C103×#1872C2semidirect
12. C103×#1802C2semidirect
13. C103×#1788C2semidirect
14. C103×#1786C2semidirect
15. C103×#1762C2semidirect
18. C22×M16×C103C22semidirect
21. #546×C103C4semidirect
32. C22×C4⋊C4×C103C22semidirect
35. C2×C4⋊C8×C103C22semidirect
37. C2×#103×C103C22semidirect
38. C2×#103×C103C22semidirect
39. C2×#103×C103C22semidirect
40. C2×#103×C103C22semidirect
51. C2×C22⋊C8×C103C22semidirect
52. C2×#97×C103C22semidirect
56. #384×C103C22semidirect
58. #380×C103C22semidirect
59. C4×C4⋊C4×C103C22semidirect
60. #340×C103C22semidirect
61. #340×C103C22semidirect
62. #340×C103C22semidirect
63. #340×C103C22semidirect
70. C2×#41×C103C2×C4semidirect
80. C22×D4×C103C2×C4semidirect
101. #124×C103C2×C4semidirect
104. C22⋊Q8×C103C2×C4semidirect
107. #121×C103C2×C4semidirect
112. C4×D4×C103C2×C4semidirect
153. #102×C103D4semidirect
337. D4×C103C4×D4semidirect
418. C22×C103#417semidirect
440. #22419C103direct (N × H)
453. C2×#435C2×C103semidirect
454. C2×#417C2×C103semidirect
455. C22×#102C2×C103semidirect
456. D4×C4⋊C4C2×C103semidirect
457. #1983C2×C103semidirect
458. #1959C2×C103semidirect
459. #1895C2×C103semidirect
460. #1892C2×C103semidirect
461. #1874C2×C103semidirect
462. #1872C2×C103semidirect
463. #1802C2×C103semidirect
464. #1788C2×C103semidirect
465. #1786C2×C103semidirect
466. #1762C2×C103semidirect
467. C103#22419direct (N × H)
470. C22×M16C22×C103semidirect
473. #546C4×C103semidirect
484. C22×C4⋊C4C22×C103semidirect
487. C2×C4⋊C8C22×C103semidirect
489. C2×#103C22×C103semidirect
490. C2×#103C22×C103semidirect
491. C2×#103C22×C103semidirect
492. C2×#103C22×C103semidirect
503. C2×C22⋊C8C22×C103semidirect
504. C2×#97C22×C103semidirect
508. #384C22×C103semidirect
510. #380C22×C103semidirect
511. C4×C4⋊C4C22×C103semidirect
512. #340C22×C103semidirect
513. #340C22×C103semidirect
514. #340C22×C103semidirect
515. #340C22×C103semidirect
522. C2×#41C2×C4×C103semidirect
532. C22×D4C2×C4×C103semidirect
553. #124C2×C4×C103semidirect
556. C22⋊Q8C2×C4×C103semidirect
559. #121C2×C4×C103semidirect
564. C4×D4C2×C4×C103semidirect
605. #102D4×C103semidirect
789. D4C4×D4×C103semidirect
870. C22#417×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1032
C2×#435×C1032
C2×#417×C1032
C22×#102×C1032
D4×C4⋊C4×C1032
C103×#19832
C103×#19592
C103×#18952
C103×#18922
C103×#18742
C103×#18722
C103×#18022
C103×#17882
C103×#17862
C103×#17622
#22419103