Finite Group Databasebeta

← C103×#22414 #39927689

Subgroups — C103×#22414 #39927689

Order 26368.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C103C211yesmaximal, characteristic
2C2×C8×D4×C103C211yesmaximal, characteristic, complemented
3C2×#416×C103C211yesmaximal, characteristic, complemented
4C22×#102×C103C211yesmaximal, characteristic, complemented
5C103×#2352C211yesmaximal, characteristic, complemented
6C103×#1983C211yesmaximal, characteristic, complemented
7C103×#1958C211yesmaximal, characteristic, complemented
8C103×#1893C211yesmaximal, characteristic, complemented
9C103×#1892C211yesmaximal, characteristic, complemented
10C103×#1875C211yesmaximal, characteristic, complemented
11C103×#1872C211yesmaximal, characteristic, complemented
12C103×#1804C211yesmaximal, characteristic, complemented
13C103×#1788C211yesmaximal, characteristic, complemented
14C103×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C103C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C23×D4×C103C2211yescharacteristic
18C23×C8×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic, complemented
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×C103C2211yescharacteristic
29C2×C4×D4×C103C2211yescharacteristic
30C2×#117×C103C2211yescharacteristic, complemented
31C22×C4⋊C4×C103C2211yescharacteristic
32C22×C22⋊C4×C103—21no—
33C8×D4×C103—24no—
34C2×C4⋊C8×C103C2211yescharacteristic, complemented
35#416×C103—24no—
36C2×#103×C103C2211yescharacteristic, complemented
37C2×#103×C103C2211yescharacteristic, complemented
38C2×#103×C103C2211yescharacteristic, complemented
39C2×#103×C103C2211yescharacteristic, complemented
40C2×#102×C103—24no—
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic
46C2×#102×C103C2211yescharacteristic
47C2×#102×C103C2211yescharacteristic
48C2×#102×C103C2211yescharacteristic
49C2×C22⋊C8×C103C2211yescharacteristic
50C2×C22⋊C8×C103C2211yescharacteristic, complemented
51C2×C4×C8×C103C2211yescharacteristic, complemented
52#388×C103—21no—
53#387×C103—21no—
54#386×C103—21no—
55#382×C103C2211yescharacteristic, complemented
56#380×C103C2211yescharacteristic
57#380×C103C2211yescharacteristic, complemented
58C4×C4⋊C4×C103C2211yescharacteristic, complemented
59C4×C22⋊C4×C103—21no—
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×C414yes—
81C22×D4×C103D411yescharacteristic
82C22×D4×C103C2311yescharacteristic
83C22×D4×C103C2311yescharacteristic
84C23×C4×C103—21no—
85C23×C4×C103—21no—
86C23×C4×C103—21no—
87C23×C4×C103C2311yescharacteristic
88C23×C4×C103C2311yescharacteristic
89C22×C8×C103—22no—
90C22×C8×C103—22no—
91C22×C8×C103—22no—
92C22×C8×C103—22no—
93C22×C8×C103—41no—
94C22×C8×C103—41no—
95C22×C8×C103C2311yescharacteristic
96C22×C8×C103C2311yescharacteristic
97C22×C8×C103C2311yescharacteristic
98C22×C8×C103C2311yescharacteristic
99#124×C103—22no—
100#124×C103C2×C414yescomplemented
101#123×C103—28no—
102C22⋊Q8×C103—22no—
103C22⋊Q8×C103C2×C414yes—
104#121×C103—22no—
105#121×C103—28no—
106#121×C103C2×C414yescomplemented
107#120×C103—28no—
108C4×D4×C103—22no—
109C4×D4×C103C2×C414yes—
110C4×D4×C103C2×C414yescomplemented
111C4×D4×C103D414yes—
112#117×C103—22no—
113#117×C103—41no—
114C2×C4⋊C4×C103—21no—
115C2×C4⋊C4×C103—22no—
116C2×C4⋊C4×C103—21no—
117C2×C4⋊C4×C103—41no—
118C2×C4⋊C4×C103D411yescharacteristic
119C2×C4⋊C4×C103C2311yescharacteristic
120C2×C4⋊C4×C103C2311yescharacteristic
121C2×C4⋊C4×C103C2311yescharacteristic
122C2×C4⋊C4×C103C2311yescharacteristic
123C2×C4⋊C4×C103C2311yescharacteristic
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103—21no—
129C2×C22⋊C4×C103—28no—
130C2×C22⋊C4×C103—21no—
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103—21no—
133C2×C22⋊C4×C103D411yescharacteristic
134C2×C22⋊C4×C103D411yescharacteristic
135C2×C42×C103—21no—
136C2×C42×C103—21no—
137C2×C42×C103C2311yescharacteristic
138C4⋊C8×C103—22no—
139#103×C103—22no—
140#103×C103—22no—
141#103×C103—41no—
142#103×C103—41no—
143#102×C103—22no—
144#102×C103—22no—
145#102×C103—22no—
146#102×C103—22no—
147#102×C103—22no—
148#102×C103—41no—
149#102×C103—41no—
150#102×C103D414yescomplemented
151C22⋊C8×C103—22no—
152C22⋊C8×C103—22no—
153C4×C8×C103—22no—
154#95×C103—21no—
155#95×C103—21no—
156#95×C103—21no—
157#95×C103—21no—
158#95×C103—21no—
159C24×C103—21no—
160C24×C103—21no—
161C24×C103—24no—
162C24×C103—42no—
163C24×C103—42no—
164C24×C103—42no—
165C24×C103—42no—
166C24×C103—81no—
167C24×C103—81no—
168C24×C103C2×D411yescharacteristic
169C24×C103C2×D411yescharacteristic
170#41×C103—28no—
171#41×C103—44no—
172#41×C103—44no—
173#41×C103—44no—
174C2×Q8×C103—21no—
175C2×Q8×C103—21no—
176C2×Q8×C103—21no—
177C2×Q8×C103—21no—
178C2×Q8×C103—21no—
179C2×Q8×C103C22×C412yes—
180C2×D4×C103—22no—
181C2×D4×C103—22no—
182C2×D4×C103—28no—
183C2×D4×C103—24no—
184C2×D4×C103—24no—
185C2×D4×C103—24no—
186C2×D4×C103—21no—
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—44no—
195C2×D4×C103—44no—
196C2×D4×C103—44no—
197C2×D4×C103—42no—
198C2×D4×C103—42no—
199C2×D4×C103—42no—
200C2×D4×C103—42no—
201C2×D4×C103—81no—
202C2×D4×C103—81no—
203C2×D4×C103C22⋊C414yes—
204C2×D4×C103C22×C412yes—
205C2×D4×C103C22×C412yes—
206C2×D4×C103C2×D412yes—
207C2×D4×C103#4112yes—
208C22×C4×C103—21no—
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—24no—
220C22×C4×C103—24no—
221C22×C4×C103—21no—
222C22×C4×C103—21no—
223C22×C4×C103—21no—
224C22×C4×C103—42no—
225C22×C4×C103—42no—
226C22×C4×C103—42no—
227C22×C4×C103—42no—
228C22×C4×C103—81no—
229C22×C4×C103—81no—
230C22×C4×C103—81no—
231C22×C4×C103C22×C412yes—
232C22×C4×C103C22×C412yes—
233C22×C4×C103C2×D411yescharacteristic
234C22×C4×C103C2×D411yescharacteristic
235C22×C4×C103C2×D411yescharacteristic
236C22×C4×C103C2×D411yescharacteristic
237C22×C4×C103C2×D412yes—
238C22×C4×C103C2×D412yes—
239C22×C4×C103C2411yescharacteristic
240C2×C8×C103—21no—
241C2×C8×C103—21no—
242C2×C8×C103—21no—
243C2×C8×C103—21no—
244C2×C8×C103—21no—
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—44no—
252C2×C8×C103—44no—
253C2×C8×C103C2×D412yes—
254C4⋊C4×C103—24no—
255C4⋊C4×C103—21no—
256C4⋊C4×C103—21no—
257C4⋊C4×C103—21no—
258C4⋊C4×C103—21no—
259C4⋊C4×C103—21no—
260C4⋊C4×C103—21no—
261C4⋊C4×C103—21no—
262C4⋊C4×C103—21no—
263C4⋊C4×C103—42no—
264C4⋊C4×C103C22⋊C414yes—
265C4⋊C4×C103C22×C412yes—
266C4⋊C4×C103C2×D412yes—
267C22⋊C4×C103—24no—
268C22⋊C4×C103—24no—
269C22⋊C4×C103—24no—
270C22⋊C4×C103—24no—
271C22⋊C4×C103—24no—
272C22⋊C4×C103—42no—
273C22⋊C4×C103—42no—
274C22⋊C4×C103—81no—
275C22⋊C4×C103C22⋊C414yes—
276C22⋊C4×C103C22⋊C414yes—
277C42×C103—42no—
278C42×C103—81no—
279C42×C103C22×C412yes—
280C42×C103C2×D412yes—
281C23×C103—21no—
282C23×C103—21no—
283C23×C103—21no—
284C23×C103—21no—
285C23×C103—22no—
286C23×C103—21no—
287C23×C103—22no—
288C23×C103—21no—
289C23×C103—22no—
290C23×C103—21no—
291C23×C103—21no—
292C23×C103—21no—
293C23×C103—21no—
294C23×C103—22no—
295C23×C103—48no—
296C23×C103—41no—
297C23×C103—41no—
298C23×C103—41no—
299C23×C103—41no—
300C23×C103—41no—
301C23×C103—41no—
302C23×C103—41no—
303C23×C103—41no—
304C23×C103—41no—
305C23×C103—41no—
306C23×C103—48no—
307C23×C103—84no—
308C23×C103—84no—
309C23×C103—84no—
310C23×C103—84no—
311C23×C103—84no—
312C23×C103C2×C22⋊C412yes—
313C23×C103C2×C22⋊C412yes—
314C23×C103#13512yes—
315C23×C103#13512yes—
316C23×C103C22×D411yescharacteristic
317Q8×C103—22no—
318Q8×C103—22no—
319Q8×C103—41no—
320Q8×C103—41no—
321D4×C103—28no—
322D4×C103—22no—
323D4×C103—22no—
324D4×C103—22no—
325D4×C103—22no—
326D4×C103—22no—
327D4×C103—48no—
328D4×C103—48no—
329D4×C103—41no—
330D4×C103—41no—
331D4×C103—84no—
332D4×C103C4×D414yes—
333C2×C4×C103—21no—
334C2×C4×C103—21no—
335C2×C4×C103—21no—
336C2×C4×C103—21no—
337C2×C4×C103—21no—
338C2×C4×C103—21no—
339C2×C4×C103—21no—
340C2×C4×C103—21no—
341C2×C4×C103—22no—
342C2×C4×C103—22no—
343C2×C4×C103—22no—
344C2×C4×C103—22no—
345C2×C4×C103—22no—
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—48no—
353C2×C4×C103—41no—
354C2×C4×C103—41no—
355C2×C4×C103—41no—
356C2×C4×C103—41no—
357C2×C4×C103—41no—
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—84no—
369C2×C4×C103—84no—
370C2×C4×C103C2×C22⋊C412yes—
371C2×C4×C103C2×C22⋊C412yes—
372C2×C4×C103C2×C22⋊C412yes—
373C2×C4×C103C2×C22⋊C412yes—
374C2×C4×C103C23×C411yescharacteristic
375C2×C4×C103C22×D411yescharacteristic
376C2×C4×C103C22×D411yescharacteristic
377C2×C4×C103C2×#4111yescharacteristic
378C2×C4×C103H(5,𝔽2)11yescharacteristic
379C2×C4×C103H(5,𝔽2)11yescharacteristic
380C8×C103—22no—
381C8×C103—41no—
382C8×C103—41no—
383C8×C103—41no—
384C22×C103—22no—
385C22×C103—22no—
386C22×C103—22no—
387C22×C103—22no—
388C22×C103—22no—
389C22×C103—22no—
390C22×C103—22no—
391C22×C103—24no—
392C22×C103—22no—
393C22×C103—22no—
394C22×C103—42no—
395C22×C103—42no—
396C22×C103—41no—
397C22×C103—42no—
398C22×C103—41no—
399C22×C103—42no—
400C22×C103—41no—
401C22×C103—42no—
402C22×C103—41no—
403C22×C103—42no—
404C22×C103—42no—
405C22×C103—42no—
406C22×C103—42no—
407C22×C103—816no—
408C22×C103—81no—
409C22×C103—81no—
410C22×C103—81no—
411C22×C103—81no—
412C22×C103#41614yescomplemented
413C22×C103C22×C22⋊C411yescharacteristic
414C22×C103D4211yescharacteristic
415C22×C103#54611yescharacteristic
416C22×C103C2×#13511yescharacteristic
417C22×C103C2×#13511yescharacteristic
418C22×C103#57611yescharacteristic
419C22×C103#57711yescharacteristic
420C4×C103—22no—
421C4×C103—22no—
422C4×C103—22no—
423C4×C103—22no—
424C4×C103—42no—
425C4×C103—42no—
426C4×C103—42no—
427C4×C103—81no—
428C4×C103—81no—
429C4×C103—81no—
430C4×C103C2×C4×D411yescharacteristic
431C4×C103#51811yescharacteristic
432C4×C103D4211yescharacteristic
433C4×C103#54611yescharacteristic
434#22414C10311yesmaximal, characteristic, direct product factor, Sylow
435C2×C103—24no—
436C2×C103—42no—
437C2×C103—44no—
438C2×C103—82no—
439C2×C103D4×C22⋊C411yescharacteristic
440C2×C103C2×#41611yescharacteristic
441C2×C103#289711yescharacteristic
442C2×C103#328011yescharacteristic
443C2×C103#328211yescharacteristic
444C2×C103#329611yescharacteristic
445C2×C103#329711yescharacteristic
446C2×#546C2×C10311yescharacteristic
447C2×C8×D4C2×C10311yescharacteristic, complemented
448C2×#416C2×C10311yescharacteristic, complemented
449C22×#102C2×C10311yescharacteristic, complemented
450#2352C2×C10311yescharacteristic, complemented
451#1983C2×C10311yescharacteristic, complemented
452#1958C2×C10311yescharacteristic, complemented
453#1893C2×C10311yescharacteristic, complemented
454#1892C2×C10311yescharacteristic, complemented
455#1875C2×C10311yescharacteristic, complemented
456#1872C2×C10311yescharacteristic, complemented
457#1804C2×C10311yescharacteristic, complemented
458#1788C2×C10311yescharacteristic, complemented
459#1786C2×C10311yescharacteristic, complemented
460C4×#102C2×C10311yescharacteristic, complemented
461C103#2241411yescharacteristic, direct product factor, Sylow
462C22×#41C22×C10311yescharacteristic
463C23×D4C22×C10311yescharacteristic
464C23×C8C22×C10311yescharacteristic
465C23×C8C22×C10311yescharacteristic, complemented
466#546—24no—
467#546C4×C10318yescomplemented
468C2×#124C22×C10311yescharacteristic
469C2×#123—21no—
470C2×C22⋊Q8C22×C10311yescharacteristic
471C2×#121—21no—
472C2×#121C22×C10311yescharacteristic
473C2×#120—21no—
474C2×C4×D4C22×C10311yescharacteristic
475C2×C4×D4C22×C10311yescharacteristic
476C2×#117C22×C10311yescharacteristic, complemented
477C22×C4⋊C4C22×C10311yescharacteristic
478C22×C22⋊C4—21no—
479C8×D4—24no—
480C2×C4⋊C8C22×C10311yescharacteristic, complemented
481#416—24no—
482C2×#103C22×C10311yescharacteristic, complemented
483C2×#103C22×C10311yescharacteristic, complemented
484C2×#103C22×C10311yescharacteristic, complemented
485C2×#103C22×C10311yescharacteristic, complemented
486C2×#102—24no—
487C2×#102C22×C10311yescharacteristic
488C2×#102C22×C10311yescharacteristic
489C2×#102C22×C10311yescharacteristic
490C2×#102C22×C10311yescharacteristic
491C2×#102C22×C10311yescharacteristic
492C2×#102C22×C10311yescharacteristic
493C2×#102C22×C10311yescharacteristic
494C2×#102C22×C10311yescharacteristic
495C2×C22⋊C8C22×C10311yescharacteristic
496C2×C22⋊C8C22×C10311yescharacteristic, complemented
497C2×C4×C8C22×C10311yescharacteristic, complemented
498#388—21no—
499#387—21no—
500#386—21no—
501#382C22×C10311yescharacteristic, complemented
502#380C22×C10311yescharacteristic
503#380C22×C10311yescharacteristic, complemented
504C4×C4⋊C4C22×C10311yescharacteristic, complemented
505C4×C22⋊C4—21no—
506#340C22×C10311yescharacteristic, complemented
507#340C22×C10311yescharacteristic, complemented
508#340C22×C10311yescharacteristic, complemented
509#340C22×C10311yescharacteristic, complemented
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×C4×C10314yescomplemented
517C22×Q8C23×C10311yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×C4×C10314yes—
527C22×D4D4×C10311yescharacteristic
528C22×D4C23×C10311yescharacteristic
529C22×D4C23×C10311yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C23×C10311yescharacteristic
534C23×C4C23×C10311yescharacteristic
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8C23×C10311yescharacteristic
542C22×C8C23×C10311yescharacteristic
543C22×C8C23×C10311yescharacteristic
544C22×C8C23×C10311yescharacteristic
545#124—22no—
546#124C2×C4×C10314yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×C4×C10314yes—
550#121—22no—
551#121—28no—
552#121C2×C4×C10314yescomplemented
553#120—28no—
554C4×D4—22no—
555C4×D4C2×C4×C10314yes—
556C4×D4C2×C4×C10314yescomplemented
557C4×D4D4×C10314yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C10311yescharacteristic
565C2×C4⋊C4C23×C10311yescharacteristic
566C2×C4⋊C4C23×C10311yescharacteristic
567C2×C4⋊C4C23×C10311yescharacteristic
568C2×C4⋊C4C23×C10311yescharacteristic
569C2×C4⋊C4C23×C10311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C10311yescharacteristic
580C2×C22⋊C4D4×C10311yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C10311yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—22no—
587#103—41no—
588#103—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102—41no—
596#102D4×C10314yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×D4×C10311yescharacteristic
615C24C2×D4×C10311yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×C4×C10312yes—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—28no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—24no—
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—44no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊C4×C10314yes—
650C2×D4C22×C4×C10312yes—
651C2×D4C22×C4×C10312yes—
652C2×D4C2×D4×C10312yes—
653C2×D4#41×C10312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4C22×C4×C10312yes—
678C22×C4C22×C4×C10312yes—
679C22×C4C2×D4×C10311yescharacteristic
680C22×C4C2×D4×C10311yescharacteristic
681C22×C4C2×D4×C10311yescharacteristic
682C22×C4C2×D4×C10311yescharacteristic
683C22×C4C2×D4×C10312yes—
684C22×C4C2×D4×C10312yes—
685C22×C4C24×C10311yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—44no—
698C2×C8—44no—
699C2×C8C2×D4×C10312yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4C22⋊C4×C10314yes—
711C4⋊C4C22×C4×C10312yes—
712C4⋊C4C2×D4×C10312yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4C22⋊C4×C10314yes—
722C22⋊C4C22⋊C4×C10314yes—
723C42—42no—
724C42—81no—
725C42C22×C4×C10312yes—
726C42C2×D4×C10312yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—48no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23C2×C22⋊C4×C10312yes—
759C23C2×C22⋊C4×C10312yes—
760C23#135×C10312yes—
761C23#135×C10312yes—
762C23C22×D4×C10311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—28no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4C4×D4×C10314yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×C22⋊C4×C10312yes—
817C2×C4C2×C22⋊C4×C10312yes—
818C2×C4C2×C22⋊C4×C10312yes—
819C2×C4C2×C22⋊C4×C10312yes—
820C2×C4C23×C4×C10311yescharacteristic
821C2×C4C22×D4×C10311yescharacteristic
822C2×C4C22×D4×C10311yescharacteristic
823C2×C4C2×#41×C10311yescharacteristic
824C2×C4H(5,𝔽2)×C10311yescharacteristic
825C2×C4H(5,𝔽2)×C10311yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—24no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—816no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22#416×C10314yescomplemented
859C22C22×C22⋊C4×C10311yescharacteristic
860C22D42×C10311yescharacteristic
861C22#546×C10311yescharacteristic
862C22C2×#135×C10311yescharacteristic
863C22C2×#135×C10311yescharacteristic
864C22#576×C10311yescharacteristic
865C22#577×C10311yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4C2×C4×D4×C10311yescharacteristic
877C4#518×C10311yescharacteristic
878C4D42×C10311yescharacteristic
879C4#546×C10311yescharacteristic
880C2—24no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊C4×C10311yescharacteristic
885C2C2×#416×C10311yescharacteristic
886C2C103×#289711yescharacteristic
887C2C103×#328011yescharacteristic
888C2C103×#328211yescharacteristic
889C2C103×#329611yescharacteristic
890C2C103×#329711yescharacteristic
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×C8×D4×C103C2semidirect
3. C2×#416×C103C2semidirect
4. C22×#102×C103C2semidirect
5. C103×#2352C2semidirect
6. C103×#1983C2semidirect
7. C103×#1958C2semidirect
8. C103×#1893C2semidirect
9. C103×#1892C2semidirect
10. C103×#1875C2semidirect
11. C103×#1872C2semidirect
12. C103×#1804C2semidirect
13. C103×#1788C2semidirect
14. C103×#1786C2semidirect
15. C4×#102×C103C2semidirect
19. C23×C8×C103C22semidirect
21. #546×C103C4semidirect
30. C2×#117×C103C22semidirect
34. C2×C4⋊C8×C103C22semidirect
36. C2×#103×C103C22semidirect
37. C2×#103×C103C22semidirect
38. C2×#103×C103C22semidirect
39. C2×#103×C103C22semidirect
50. C2×C22⋊C8×C103C22semidirect
51. C2×C4×C8×C103C22semidirect
55. #382×C103C22semidirect
57. #380×C103C22semidirect
58. C4×C4⋊C4×C103C22semidirect
60. #340×C103C22semidirect
61. #340×C103C22semidirect
62. #340×C103C22semidirect
63. #340×C103C22semidirect
70. C2×#41×C103C2×C4semidirect
100. #124×C103C2×C4semidirect
106. #121×C103C2×C4semidirect
110. C4×D4×C103C2×C4semidirect
150. #102×C103D4semidirect
412. C22×C103#416semidirect
434. #22414C103direct (N × H)
447. C2×C8×D4C2×C103semidirect
448. C2×#416C2×C103semidirect
449. C22×#102C2×C103semidirect
450. #2352C2×C103semidirect
451. #1983C2×C103semidirect
452. #1958C2×C103semidirect
453. #1893C2×C103semidirect
454. #1892C2×C103semidirect
455. #1875C2×C103semidirect
456. #1872C2×C103semidirect
457. #1804C2×C103semidirect
458. #1788C2×C103semidirect
459. #1786C2×C103semidirect
460. C4×#102C2×C103semidirect
461. C103#22414direct (N × H)
465. C23×C8C22×C103semidirect
467. #546C4×C103semidirect
476. C2×#117C22×C103semidirect
480. C2×C4⋊C8C22×C103semidirect
482. C2×#103C22×C103semidirect
483. C2×#103C22×C103semidirect
484. C2×#103C22×C103semidirect
485. C2×#103C22×C103semidirect
496. C2×C22⋊C8C22×C103semidirect
497. C2×C4×C8C22×C103semidirect
501. #382C22×C103semidirect
503. #380C22×C103semidirect
504. C4×C4⋊C4C22×C103semidirect
506. #340C22×C103semidirect
507. #340C22×C103semidirect
508. #340C22×C103semidirect
509. #340C22×C103semidirect
516. C2×#41C2×C4×C103semidirect
546. #124C2×C4×C103semidirect
552. #121C2×C4×C103semidirect
556. C4×D4C2×C4×C103semidirect
596. #102D4×C103semidirect
858. C22#416×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×C8×D4×C1032
C2×#416×C1032
C22×#102×C1032
C103×#23522
C103×#19832
C103×#19582
C103×#18932
C103×#18922
C103×#18752
C103×#18722
C103×#18042
C103×#17882
C103×#17862
C4×#102×C1032
#22414103