Finite Group Databasebeta

← C103×#24432 #39929707

Subgroups — C103×#24432 #39929707

Order 26368.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C103C211yesmaximal, characteristic
2C2×#465×C103C211yesmaximal, characteristic, complemented
3C2×#450×C103C211yesmaximal, characteristic, complemented
4C2×#450×C103C211yesmaximal, characteristic, complemented
5C22×#102×C103C211yesmaximal, characteristic, complemented
6C103×#2417C211yesmaximal, characteristic, complemented
7C103×#2041C211yesmaximal, characteristic, complemented
8C103×#2034C211yesmaximal, characteristic, complemented
9C103×#2014C211yesmaximal, characteristic, complemented
10C103×#2000C211yesmaximal, characteristic, complemented
11C103×#1877C211yesmaximal, characteristic, complemented
12C103×#1874C211yesmaximal, characteristic, complemented
13C103×#1869C211yesmaximal, characteristic, complemented
14C103×#1864C211yesmaximal, characteristic, complemented
15C103×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C103—21no—
17C23×D4×C103C2211yescharacteristic
18C23×D4×C103C2211yescharacteristic
19C22×SD16×C103C2211yescharacteristic
20C22×SD16×C103C2211yescharacteristic, complemented
21C22×SD16×C103C2211yescharacteristic, complemented
22C23×C8×C103C2211yescharacteristic, complemented
23D42×C103—24no—
24D42×C103—24no—
25C2×#127×C103C2211yescharacteristic
26C2×C22⋊Q8×C103C2211yescharacteristic, complemented
27C2×C22⋊Q8×C103C2211yescharacteristic, complemented
28C2×#121×C103—21no—
29C2×#121×C103C2211yescharacteristic
30C2×#121×C103C2211yescharacteristic
31C2×#120×C103—21no—
32C2×#120×C103—21no—
33C2×C4×D4×C103C2211yescharacteristic
34C2×C4×D4×C103C2211yescharacteristic
35C22×C4⋊C4×C103C2211yescharacteristic, complemented
36#465×C103—24no—
37#450×C103—24no—
38#450×C103—24no—
39C2×#106×C103C2211yescharacteristic, complemented
40C2×#103×C103C2211yescharacteristic, complemented
41C2×#102×C103—24no—
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic, complemented
46C2×#102×C103C2211yescharacteristic, complemented
47C2×#102×C103C2211yescharacteristic, complemented
48C2×#102×C103C2211yescharacteristic, complemented
49C2×#102×C103C2211yescharacteristic, complemented
50C2×#102×C103C2211yescharacteristic, complemented
51C2×C22⋊C8×C103C2211yescharacteristic, complemented
52C2×C22⋊C8×C103C2211yescharacteristic, complemented
53C2×C22⋊C8×C103C2211yescharacteristic, complemented
54#398×C103—21no—
55#396×C103—21no—
56#391×C103C2211yescharacteristic, complemented
57#389×C103C2211yescharacteristic, complemented
58#386×C103—21no—
59#380×C103—21no—
60#380×C103C2211yescharacteristic, complemented
61#340×C103C2211yescharacteristic, complemented
62#340×C103C2211yescharacteristic, complemented
63#336×C103C2211yescharacteristic, complemented
64#336×C103C2211yescharacteristic, complemented
65C25×C103—21no—
66C25×C103—21no—
67C22×Q8×C103C2311yescharacteristic
68C22×D4×C103—22no—
69C22×D4×C103—22no—
70C22×D4×C103—28no—
71C22×D4×C103—21no—
72C22×D4×C103—21no—
73C22×D4×C103—22no—
74C22×D4×C103—22no—
75C22×D4×C103—22no—
76C22×D4×C103—22no—
77C22×D4×C103—21no—
78C22×D4×C103—21no—
79C22×D4×C103—21no—
80C22×D4×C103—22no—
81C22×D4×C103—21no—
82C22×D4×C103—41no—
83C22×D4×C103—41no—
84C22×D4×C103—41no—
85C22×D4×C103—41no—
86C22×D4×C103—44no—
87C22×D4×C103—44no—
88C22×D4×C103D411yescharacteristic
89C22×D4×C103D414yes—
90C22×D4×C103C2311yescharacteristic
91C22×D4×C103C2311yescharacteristic
92C22×D4×C103C2311yescharacteristic
93C23×C4×C103—21no—
94C23×C4×C103—21no—
95C23×C4×C103C2311yescharacteristic
96C23×C4×C103C2311yescharacteristic
97C2×SD16×C103—22no—
98C2×SD16×C103—22no—
99C2×SD16×C103—22no—
100C2×SD16×C103—22no—
101C2×SD16×C103—22no—
102C2×SD16×C103—22no—
103C2×SD16×C103—41no—
104C2×SD16×C103—41no—
105C2×SD16×C103—41no—
106C22×C8×C103—22no—
107C22×C8×C103—22no—
108C22×C8×C103—41no—
109C22×C8×C103C2311yescharacteristic
110C22×C8×C103C2311yescharacteristic
111C22×C8×C103C2311yescharacteristic
112C22×C8×C103C2311yescharacteristic
113#127×C103—22no—
114#127×C103—22no—
115C22⋊Q8×C103—22no—
116C22⋊Q8×C103—22no—
117C22⋊Q8×C103—22no—
118C22⋊Q8×C103—41no—
119#121×C103—28no—
120#121×C103—22no—
121#121×C103—22no—
122#121×C103—22no—
123#121×C103D414yes—
124#120×C103—28no—
125#120×C103—28no—
126C4×D4×C103—22no—
127C4×D4×C103—22no—
128C4×D4×C103—22no—
129C4×D4×C103—22no—
130C2×C4⋊C4×C103—22no—
131C2×C4⋊C4×C103—21no—
132C2×C4⋊C4×C103—21no—
133C2×C4⋊C4×C103—21no—
134C2×C4⋊C4×C103—21no—
135C2×C4⋊C4×C103—41no—
136C2×C4⋊C4×C103D411yescharacteristic
137C2×C4⋊C4×C103C2311yescharacteristic
138C2×C4⋊C4×C103C2311yescharacteristic
139C2×C4⋊C4×C103C2311yescharacteristic
140C2×C4⋊C4×C103C2311yescharacteristic
141C2×C22⋊C4×C103—21no—
142C2×C22⋊C4×C103—21no—
143C2×C22⋊C4×C103—21no—
144C2×C22⋊C4×C103—21no—
145C2×C22⋊C4×C103—21no—
146C2×C22⋊C4×C103—21no—
147C2×C22⋊C4×C103D411yescharacteristic
148C2×C22⋊C4×C103D411yescharacteristic
149C2×C42×C103C2311yescharacteristic
150#106×C103—22no—
151#103×C103—22no—
152#102×C103—22no—
153#102×C103—22no—
154#102×C103—22no—
155#102×C103—22no—
156#102×C103—22no—
157#102×C103—22no—
158#102×C103—22no—
159#102×C103—41no—
160#102×C103D414yescomplemented
161C22⋊C8×C103—22no—
162C22⋊C8×C103—22no—
163C22⋊C8×C103—41no—
164#95×C103—21no—
165#95×C103—21no—
166#95×C103—21no—
167#95×C103—21no—
168C24×C103—21no—
169C24×C103—24no—
170C24×C103—21no—
171C24×C103—21no—
172C24×C103—24no—
173C24×C103—42no—
174C24×C103—42no—
175C24×C103—42no—
176C24×C103—42no—
177C24×C103—42no—
178C24×C103—42no—
179C24×C103—42no—
180C24×C103—42no—
181C24×C103—81no—
182C24×C103—81no—
183C24×C103—81no—
184C24×C103—81no—
185C24×C103C2×D411yescharacteristic
186C24×C103C2×D411yescharacteristic
187C2×Q8×C103—21no—
188C2×Q8×C103—21no—
189C2×Q8×C103—21no—
190C2×Q8×C103—21no—
191C2×Q8×C103—21no—
192C2×Q8×C103—21no—
193C2×D4×C103—22no—
194C2×D4×C103—22no—
195C2×D4×C103—28no—
196C2×D4×C103—24no—
197C2×D4×C103—24no—
198C2×D4×C103—24no—
199C2×D4×C103—24no—
200C2×D4×C103—24no—
201C2×D4×C103—24no—
202C2×D4×C103—21no—
203C2×D4×C103—21no—
204C2×D4×C103—21no—
205C2×D4×C103—21no—
206C2×D4×C103—21no—
207C2×D4×C103—21no—
208C2×D4×C103—21no—
209C2×D4×C103—21no—
210C2×D4×C103—21no—
211C2×D4×C103—21no—
212C2×D4×C103—21no—
213C2×D4×C103—21no—
214C2×D4×C103—21no—
215C2×D4×C103—44no—
216C2×D4×C103—44no—
217C2×D4×C103—44no—
218C2×D4×C103—42no—
219C2×D4×C103—42no—
220C2×D4×C103—42no—
221C2×D4×C103—42no—
222C2×D4×C103—42no—
223C2×D4×C103—44no—
224C2×D4×C103—44no—
225C2×D4×C103—432no—
226C2×D4×C103—44no—
227C2×D4×C103—42no—
228C2×D4×C103—42no—
229C2×D4×C103—42no—
230C2×D4×C103—42no—
231C2×D4×C103—44no—
232C2×D4×C103—42no—
233C2×D4×C103—81no—
234C2×D4×C103—81no—
235C2×D4×C103SD1614yescomplemented
236C2×D4×C103C2×D412yes—
237C2×D4×C103C2×D412yes—
238C2×D4×C103C2×D412yes—
239C2×D4×C103C2×D412yes—
240C2×D4×C103#4112yes—
241C22×C4×C103—21no—
242C22×C4×C103—21no—
243C22×C4×C103—21no—
244C22×C4×C103—21no—
245C22×C4×C103—24no—
246C22×C4×C103—21no—
247C22×C4×C103—21no—
248C22×C4×C103—21no—
249C22×C4×C103—21no—
250C22×C4×C103—21no—
251C22×C4×C103—21no—
252C22×C4×C103—21no—
253C22×C4×C103—21no—
254C22×C4×C103—21no—
255C22×C4×C103—21no—
256C22×C4×C103—21no—
257C22×C4×C103—42no—
258C22×C4×C103—42no—
259C22×C4×C103—42no—
260C22×C4×C103—42no—
261C22×C4×C103—81no—
262C22×C4×C103C2×D411yescharacteristic
263C22×C4×C103C2×D411yescharacteristic
264C22×C4×C103C2×D411yescharacteristic
265C22×C4×C103C2×D412yes—
266C22×C4×C103C2×D412yes—
267C22×C4×C103C2×D411yescharacteristic
268C22×C4×C103C2411yescharacteristic
269SD16×C103—44no—
270SD16×C103—44no—
271SD16×C103—44no—
272C2×C8×C103—21no—
273C2×C8×C103—21no—
274C2×C8×C103—21no—
275C2×C8×C103—21no—
276C2×C8×C103—21no—
277C2×C8×C103—21no—
278C2×C8×C103—21no—
279C2×C8×C103—21no—
280C2×C8×C103—21no—
281C2×C8×C103—21no—
282C2×C8×C103—21no—
283C2×C8×C103—44no—
284C2×C8×C103C2×D412yescomplemented
285C4⋊C4×C103—22no—
286C4⋊C4×C103—21no—
287C4⋊C4×C103—21no—
288C4⋊C4×C103—21no—
289C4⋊C4×C103—21no—
290C4⋊C4×C103—21no—
291C4⋊C4×C103—21no—
292C4⋊C4×C103—42no—
293C4⋊C4×C103—42no—
294C4⋊C4×C103—42no—
295C4⋊C4×C103—81no—
296C4⋊C4×C103C2×D412yes—
297C4⋊C4×C103C2×D412yescomplemented
298C22⋊C4×C103—24no—
299C22⋊C4×C103—24no—
300C22⋊C4×C103—22no—
301C22⋊C4×C103—24no—
302C22⋊C4×C103—22no—
303C22⋊C4×C103—42no—
304C22⋊C4×C103—42no—
305C22⋊C4×C103—81no—
306C42×C103—21no—
307C42×C103—21no—
308C23×C103—21no—
309C23×C103—21no—
310C23×C103—21no—
311C23×C103—21no—
312C23×C103—21no—
313C23×C103—22no—
314C23×C103—21no—
315C23×C103—22no—
316C23×C103—21no—
317C23×C103—22no—
318C23×C103—21no—
319C23×C103—21no—
320C23×C103—21no—
321C23×C103—22no—
322C23×C103—22no—
323C23×C103—48no—
324C23×C103—48no—
325C23×C103—48no—
326C23×C103—41no—
327C23×C103—41no—
328C23×C103—41no—
329C23×C103—41no—
330C23×C103—41no—
331C23×C103—41no—
332C23×C103—41no—
333C23×C103—41no—
334C23×C103—41no—
335C23×C103—41no—
336C23×C103—41no—
337C23×C103—41no—
338C23×C103—41no—
339C23×C103—41no—
340C23×C103—41no—
341C23×C103—41no—
342C23×C103—48no—
343C23×C103—84no—
344C23×C103—84no—
345C23×C103—84no—
346C23×C103—84no—
347C23×C103—84no—
348C23×C103—84no—
349C23×C103—84no—
350C23×C103—84no—
351C23×C103—84no—
352C23×C103—84no—
353C23×C103#12012yes—
354C23×C103C2×SD1612yes—
355C23×C103C2×SD1612yes—
356C23×C103AGL(1,ℤ/8)12yes—
357C23×C103C22×D411yescharacteristic
358Q8×C103—41no—
359Q8×C103—41no—
360Q8×C103—41no—
361Q8×C103—41no—
362D4×C103—28no—
363D4×C103—22no—
364D4×C103—22no—
365D4×C103—22no—
366D4×C103—22no—
367D4×C103—22no—
368D4×C103—22no—
369D4×C103—22no—
370D4×C103—48no—
371D4×C103—48no—
372D4×C103—48no—
373D4×C103—48no—
374D4×C103—48no—
375D4×C103—41no—
376D4×C103—41no—
377D4×C103—41no—
378D4×C103—41no—
379D4×C103—84no—
380D4×C103#12114yes—
381C2×C4×C103—21no—
382C2×C4×C103—21no—
383C2×C4×C103—21no—
384C2×C4×C103—21no—
385C2×C4×C103—22no—
386C2×C4×C103—22no—
387C2×C4×C103—22no—
388C2×C4×C103—22no—
389C2×C4×C103—21no—
390C2×C4×C103—21no—
391C2×C4×C103—22no—
392C2×C4×C103—22no—
393C2×C4×C103—21no—
394C2×C4×C103—21no—
395C2×C4×C103—21no—
396C2×C4×C103—21no—
397C2×C4×C103—48no—
398C2×C4×C103—41no—
399C2×C4×C103—41no—
400C2×C4×C103—41no—
401C2×C4×C103—41no—
402C2×C4×C103—41no—
403C2×C4×C103—41no—
404C2×C4×C103—41no—
405C2×C4×C103—41no—
406C2×C4×C103—41no—
407C2×C4×C103—41no—
408C2×C4×C103—41no—
409C2×C4×C103—41no—
410C2×C4×C103—41no—
411C2×C4×C103—41no—
412C2×C4×C103—41no—
413C2×C4×C103—41no—
414C2×C4×C103—41no—
415C2×C4×C103—84no—
416C2×C4×C103#12012yes—
417C2×C4×C103C2×SD1612yes—
418C2×C4×C103C22×D411yescharacteristic
419C2×C4×C103C22×D411yescharacteristic
420C2×C4×C103C22×D411yescharacteristic
421C2×C4×C103C2×#4111yescharacteristic
422C2×C4×C103H(5,𝔽2)11yescharacteristic
423C2×C4×C103H(5,𝔽2)11yescharacteristic
424C8×C103—22no—
425C8×C103—41no—
426C8×C103—41no—
427C8×C103—41no—
428C22×C103—22no—
429C22×C103—22no—
430C22×C103—22no—
431C22×C103—22no—
432C22×C103—22no—
433C22×C103—22no—
434C22×C103—24no—
435C22×C103—22no—
436C22×C103—22no—
437C22×C103—22no—
438C22×C103—41no—
439C22×C103—42no—
440C22×C103—41no—
441C22×C103—42no—
442C22×C103—41no—
443C22×C103—42no—
444C22×C103—42no—
445C22×C103—42no—
446C22×C103—41no—
447C22×C103—42no—
448C22×C103—42no—
449C22×C103—42no—
450C22×C103—42no—
451C22×C103—42no—
452C22×C103—42no—
453C22×C103—42no—
454C22×C103—816no—
455C22×C103—816no—
456C22×C103—81no—
457C22×C103—81no—
458C22×C103—81no—
459C22×C103—81no—
460C22×C103—81no—
461C22×C103—81no—
462C22×C103—81no—
463C22×C103—81no—
464C22×C103#45014yescomplemented
465C22×C103C2×#12011yescharacteristic
466C22×C103D4211yescharacteristic
467C22×C103#54611yescharacteristic
468C22×C103C22×SD1611yescharacteristic
469C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C103#57611yescharacteristic
471C22×C103#57711yescharacteristic
472C4×C103—22no—
473C4×C103—22no—
474C4×C103—41no—
475C4×C103—42no—
476C4×C103—42no—
477C4×C103—41no—
478C4×C103—81no—
479C4×C103—81no—
480C4×C103—81no—
481C4×C103C2×#12111yescharacteristic
482C4×C103#53411yescharacteristic
483C4×C103D4211yescharacteristic
484C4×C103#54611yescharacteristic
485#24432C10311yesmaximal, characteristic, direct product factor, Sylow
486C2×C103—24no—
487C2×C103—42no—
488C2×C103—44no—
489C2×C103—82no—
490C2×C103—82no—
491C2×C103#241011yescharacteristic
492C2×C103C2×#45011yescharacteristic
493C2×C103#301211yescharacteristic
494C2×C103#326411yescharacteristic
495C2×C103D4×SD1611yescharacteristic
496C2×C103#329511yescharacteristic
497C2×C103#331011yescharacteristic
498C2×D42C2×C10311yescharacteristic
499C2×#465C2×C10311yescharacteristic, complemented
500C2×#450C2×C10311yescharacteristic, complemented
501C2×#450C2×C10311yescharacteristic, complemented
502C22×#102C2×C10311yescharacteristic, complemented
503#2417C2×C10311yescharacteristic, complemented
504#2041C2×C10311yescharacteristic, complemented
505#2034C2×C10311yescharacteristic, complemented
506#2014C2×C10311yescharacteristic, complemented
507#2000C2×C10311yescharacteristic, complemented
508#1877C2×C10311yescharacteristic, complemented
509#1874C2×C10311yescharacteristic, complemented
510#1869C2×C10311yescharacteristic, complemented
511#1864C2×C10311yescharacteristic, complemented
512#1786C2×C10311yescharacteristic, complemented
513C103#2443211yescharacteristic, direct product factor, Sylow
514C23×D4—21no—
515C23×D4C22×C10311yescharacteristic
516C23×D4C22×C10311yescharacteristic
517C22×SD16C22×C10311yescharacteristic
518C22×SD16C22×C10311yescharacteristic, complemented
519C22×SD16C22×C10311yescharacteristic, complemented
520C23×C8C22×C10311yescharacteristic, complemented
521D42—24no—
522D42—24no—
523C2×#127C22×C10311yescharacteristic
524C2×C22⋊Q8C22×C10311yescharacteristic, complemented
525C2×C22⋊Q8C22×C10311yescharacteristic, complemented
526C2×#121—21no—
527C2×#121C22×C10311yescharacteristic
528C2×#121C22×C10311yescharacteristic
529C2×#120—21no—
530C2×#120—21no—
531C2×C4×D4C22×C10311yescharacteristic
532C2×C4×D4C22×C10311yescharacteristic
533C22×C4⋊C4C22×C10311yescharacteristic, complemented
534#465—24no—
535#450—24no—
536#450—24no—
537C2×#106C22×C10311yescharacteristic, complemented
538C2×#103C22×C10311yescharacteristic, complemented
539C2×#102—24no—
540C2×#102C22×C10311yescharacteristic
541C2×#102C22×C10311yescharacteristic
542C2×#102C22×C10311yescharacteristic
543C2×#102C22×C10311yescharacteristic, complemented
544C2×#102C22×C10311yescharacteristic, complemented
545C2×#102C22×C10311yescharacteristic, complemented
546C2×#102C22×C10311yescharacteristic, complemented
547C2×#102C22×C10311yescharacteristic, complemented
548C2×#102C22×C10311yescharacteristic, complemented
549C2×C22⋊C8C22×C10311yescharacteristic, complemented
550C2×C22⋊C8C22×C10311yescharacteristic, complemented
551C2×C22⋊C8C22×C10311yescharacteristic, complemented
552#398—21no—
553#396—21no—
554#391C22×C10311yescharacteristic, complemented
555#389C22×C10311yescharacteristic, complemented
556#386—21no—
557#380—21no—
558#380C22×C10311yescharacteristic, complemented
559#340C22×C10311yescharacteristic, complemented
560#340C22×C10311yescharacteristic, complemented
561#336C22×C10311yescharacteristic, complemented
562#336C22×C10311yescharacteristic, complemented
563C25—21no—
564C25—21no—
565C22×Q8C23×C10311yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C10311yescharacteristic
587C22×D4D4×C10314yes—
588C22×D4C23×C10311yescharacteristic
589C22×D4C23×C10311yescharacteristic
590C22×D4C23×C10311yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C10311yescharacteristic
594C23×C4C23×C10311yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C10311yescharacteristic
608C22×C8C23×C10311yescharacteristic
609C22×C8C23×C10311yescharacteristic
610C22×C8C23×C10311yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C10314yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C10311yescharacteristic
635C2×C4⋊C4C23×C10311yescharacteristic
636C2×C4⋊C4C23×C10311yescharacteristic
637C2×C4⋊C4C23×C10311yescharacteristic
638C2×C4⋊C4C23×C10311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C10311yescharacteristic
646C2×C22⋊C4D4×C10311yescharacteristic
647C2×C42C23×C10311yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C10314yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C10311yescharacteristic
684C24C2×D4×C10311yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C10314yescomplemented
734C2×D4C2×D4×C10312yes—
735C2×D4C2×D4×C10312yes—
736C2×D4C2×D4×C10312yes—
737C2×D4C2×D4×C10312yes—
738C2×D4#41×C10312yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C10311yescharacteristic
761C22×C4C2×D4×C10311yescharacteristic
762C22×C4C2×D4×C10311yescharacteristic
763C22×C4C2×D4×C10312yes—
764C22×C4C2×D4×C10312yes—
765C22×C4C2×D4×C10311yescharacteristic
766C22×C4C24×C10311yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C10312yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C10312yes—
795C4⋊C4C2×D4×C10312yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C10312yes—
852C23C2×SD16×C10312yes—
853C23C2×SD16×C10312yes—
854C23AGL(1,ℤ/8)×C10312yes—
855C23C22×D4×C10311yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C10314yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C10312yes—
915C2×C4C2×SD16×C10312yes—
916C2×C4C22×D4×C10311yescharacteristic
917C2×C4C22×D4×C10311yescharacteristic
918C2×C4C22×D4×C10311yescharacteristic
919C2×C4C2×#41×C10311yescharacteristic
920C2×C4H(5,𝔽2)×C10311yescharacteristic
921C2×C4H(5,𝔽2)×C10311yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—24no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—41no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#450×C10314yescomplemented
963C22C2×#120×C10311yescharacteristic
964C22D42×C10311yescharacteristic
965C22#546×C10311yescharacteristic
966C22C22×SD16×C10311yescharacteristic
967C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
968C22#576×C10311yescharacteristic
969C22#577×C10311yescharacteristic
970C4—22no—
971C4—22no—
972C4—42no—
973C4—42no—
974C4—41no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C10311yescharacteristic
980C4#534×C10311yescharacteristic
981C4D42×C10311yescharacteristic
982C4#546×C10311yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C103×#241011yescharacteristic
989C2C2×#450×C10311yescharacteristic
990C2C103×#301211yescharacteristic
991C2C103×#326411yescharacteristic
992C2D4×SD16×C10311yescharacteristic
993C2C103×#329511yescharacteristic
994C2C103×#331011yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×D42×C103C2
LCSG ▷ C22×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×#465×C103C2semidirect
3. C2×#450×C103C2semidirect
4. C2×#450×C103C2semidirect
5. C22×#102×C103C2semidirect
6. C103×#2417C2semidirect
7. C103×#2041C2semidirect
8. C103×#2034C2semidirect
9. C103×#2014C2semidirect
10. C103×#2000C2semidirect
11. C103×#1877C2semidirect
12. C103×#1874C2semidirect
13. C103×#1869C2semidirect
14. C103×#1864C2semidirect
15. C103×#1786C2semidirect
20. C22×SD16×C103C22semidirect
21. C22×SD16×C103C22semidirect
22. C23×C8×C103C22semidirect
26. C2×C22⋊Q8×C103C22semidirect
27. C2×C22⋊Q8×C103C22semidirect
35. C22×C4⋊C4×C103C22semidirect
39. C2×#106×C103C22semidirect
40. C2×#103×C103C22semidirect
45. C2×#102×C103C22semidirect
46. C2×#102×C103C22semidirect
47. C2×#102×C103C22semidirect
48. C2×#102×C103C22semidirect
49. C2×#102×C103C22semidirect
50. C2×#102×C103C22semidirect
51. C2×C22⋊C8×C103C22semidirect
52. C2×C22⋊C8×C103C22semidirect
53. C2×C22⋊C8×C103C22semidirect
56. #391×C103C22semidirect
57. #389×C103C22semidirect
60. #380×C103C22semidirect
61. #340×C103C22semidirect
62. #340×C103C22semidirect
63. #336×C103C22semidirect
64. #336×C103C22semidirect
160. #102×C103D4semidirect
235. C2×D4×C103SD16semidirect
284. C2×C8×C103C2×D4semidirect
297. C4⋊C4×C103C2×D4semidirect
464. C22×C103#450semidirect
485. #24432C103direct (N × H)
499. C2×#465C2×C103semidirect
500. C2×#450C2×C103semidirect
501. C2×#450C2×C103semidirect
502. C22×#102C2×C103semidirect
503. #2417C2×C103semidirect
504. #2041C2×C103semidirect
505. #2034C2×C103semidirect
506. #2014C2×C103semidirect
507. #2000C2×C103semidirect
508. #1877C2×C103semidirect
509. #1874C2×C103semidirect
510. #1869C2×C103semidirect
511. #1864C2×C103semidirect
512. #1786C2×C103semidirect
513. C103#24432direct (N × H)
518. C22×SD16C22×C103semidirect
519. C22×SD16C22×C103semidirect
520. C23×C8C22×C103semidirect
524. C2×C22⋊Q8C22×C103semidirect
525. C2×C22⋊Q8C22×C103semidirect
533. C22×C4⋊C4C22×C103semidirect
537. C2×#106C22×C103semidirect
538. C2×#103C22×C103semidirect
543. C2×#102C22×C103semidirect
544. C2×#102C22×C103semidirect
545. C2×#102C22×C103semidirect
546. C2×#102C22×C103semidirect
547. C2×#102C22×C103semidirect
548. C2×#102C22×C103semidirect
549. C2×C22⋊C8C22×C103semidirect
550. C2×C22⋊C8C22×C103semidirect
551. C2×C22⋊C8C22×C103semidirect
554. #391C22×C103semidirect
555. #389C22×C103semidirect
558. #380C22×C103semidirect
559. #340C22×C103semidirect
560. #340C22×C103semidirect
561. #336C22×C103semidirect
562. #336C22×C103semidirect
658. #102D4×C103semidirect
733. C2×D4SD16×C103semidirect
782. C2×C8C2×D4×C103semidirect
795. C4⋊C4C2×D4×C103semidirect
962. C22#450×C103semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1032
C2×#465×C1032
C2×#450×C1032
C22×#102×C1032
C103×#24172
C103×#20412
C103×#20342
C103×#20142
C103×#20002
C103×#18772
C103×#18742
C103×#18692
C103×#18642
C103×#17862
#24432103