Finite Group Databasebeta

← C103×#24459 #39929734

Subgroups — C103×#24459 #39929734

Order 26368.

1362 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#576×C103C211yesmaximal, characteristic
2C2×#471×C103C211yesmaximal, characteristic, complemented
3C103×#3046C211yesmaximal, characteristic, complemented
4C2×#455×C103C211yesmaximal, characteristic, complemented
5C103×#3009C211yesmaximal, characteristic, complemented
6C103×#2897C211yesmaximal, characteristic, complemented
7C103×#2051C211yesmaximal, characteristic, complemented
8C103×#2045C211yesmaximal, characteristic, complemented
9C103×#2012C211yesmaximal, characteristic, complemented
10C103×#2003C211yesmaximal, characteristic, complemented
11C103×#1908C211yesmaximal, characteristic, complemented
12C103×#1883C211yesmaximal, characteristic, complemented
13C103×#1876C211yesmaximal, characteristic, complemented
14C103×#1866C211yesmaximal, characteristic, complemented
15C103×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C103C2211yescharacteristic
17C2×H(5,𝔽2)×C103C2211yescharacteristic
18#576×C103—24no—
19#576×C103—24no—
20C2×#137×C103C2211yescharacteristic
21C2×#137×C103C2211yescharacteristic, complemented
22C2×AGL(1,ℤ/8)×C103—21no—
23C2×AGL(1,ℤ/8)×C103—21no—
24C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
26C2×#135×C103—21no—
27C2×#135×C103C2211yescharacteristic
28C22×SD16×C103C2211yescharacteristic, complemented
29C22×D8×C103—21no—
30C22×D8×C103C2211yescharacteristic
31C2×#131×C103C2211yescharacteristic
32C2×#131×C103C2211yescharacteristic, complemented
33#536×C103C2211yescharacteristic, complemented
34C2×#124×C103C2211yescharacteristic, complemented
35#520×C103C2211yescharacteristic, complemented
36#471×C103—24no—
37#464×C103—21no—
38#463×C103—21no—
39#462×C103—21no—
40#461×C103—21no—
41#455×C103—24no—
42#452×C103—21no—
43#452×C103—21no—
44#450×C103—21no—
45#450×C103—21no—
46C2×#108×C103C2211yescharacteristic, complemented
47#424×C103C2211yescharacteristic, complemented
48C2×#104×C103C2211yescharacteristic
49C2×#104×C103C2211yescharacteristic, complemented
50C2×#104×C103C2211yescharacteristic, complemented
51#418×C103—21no—
52#418×C103C2211yescharacteristic, complemented
53#418×C103C2211yescharacteristic, complemented
54#417×C103—21no—
55#417×C103C2211yescharacteristic
56#417×C103C2211yescharacteristic, complemented
57#416×C103—21no—
58#416×C103C2211yescharacteristic
59C2×#103×C103C2211yescharacteristic, complemented
60C2×#102×C103—21no—
61C2×#102×C103C2211yescharacteristic, complemented
62C2×#101×C103C2211yescharacteristic, complemented
63C2×#100×C103C2211yescharacteristic, complemented
64C2×#100×C103C2211yescharacteristic, complemented
65#408×C103C2211yescharacteristic, complemented
66#390×C103C2211yescharacteristic, complemented
67#343×C103C2211yescharacteristic, complemented
68#341×C103C2211yescharacteristic, complemented
69#339×C103C2211yescharacteristic, complemented
70#336×C103C2211yescharacteristic, complemented
71H(5,𝔽2)×C103—22no—
72H(5,𝔽2)×C103—22no—
73H(5,𝔽2)×C103—22no—
74H(5,𝔽2)×C103—22no—
75H(5,𝔽2)×C103—22no—
76H(5,𝔽2)×C103—41no—
77H(5,𝔽2)×C103—41no—
78H(5,𝔽2)×C103D414yes—
79C2×#41×C103—21no—
80C2×#41×C103—21no—
81C2×#41×C103—21no—
82C2×#41×C103—21no—
83C2×#41×C103C2311yescharacteristic
84C2×#41×C103C2311yescharacteristic
85C2×#41×C103C2311yescharacteristic
86C22×Q8×C103C2311yescharacteristic
87C22×D4×C103—21no—
88C22×D4×C103—21no—
89C22×D4×C103—21no—
90C22×D4×C103—21no—
91C22×D4×C103—41no—
92C22×D4×C103—41no—
93C22×D4×C103C2311yescharacteristic
94C22×D4×C103C2311yescharacteristic
95#137×C103—22no—
96#137×C103—22no—
97#137×C103—22no—
98#137×C103—22no—
99AGL(1,ℤ/8)×C103—28no—
100AGL(1,ℤ/8)×C103—28no—
101AGL(1,ℤ/8)×C103—22no—
102AGL(1,ℤ/8)×C103—22no—
103AGL(1,ℤ/8)×C103—22no—
104AGL(1,ℤ/8)×C103D414yes—
105#135×C103—28no—
106#135×C103—22no—
107#135×C103—22no—
108C2×Q16×C103—21no—
109C2×Q16×C103—21no—
110C2×Q16×C103D411yescharacteristic
111C2×SD16×C103—21no—
112C2×SD16×C103—21no—
113C2×SD16×C103—21no—
114C2×SD16×C103—21no—
115C2×SD16×C103—22no—
116C2×SD16×C103—21no—
117C2×SD16×C103—21no—
118C2×SD16×C103—41no—
119C2×SD16×C103D411yescharacteristic
120C2×SD16×C103D411yescharacteristic
121C2×D8×C103—28no—
122C2×D8×C103—21no—
123C2×D8×C103—21no—
124C2×D8×C103—22no—
125C2×D8×C103—22no—
126C2×D8×C103—21no—
127C2×D8×C103—21no—
128C2×D8×C103D411yescharacteristic
129#131×C103—22no—
130#131×C103—22no—
131#131×C103—22no—
132#131×C103—41no—
133C2×M16×C103—21no—
134C2×M16×C103—21no—
135C2×M16×C103C2311yescharacteristic
136C2×M16×C103C2311yescharacteristic
137C2×M16×C103C2311yescharacteristic
138C2×M16×C103C2311yescharacteristic
139C22×C8×C103—21no—
140C22×C8×C103—21no—
141C22×C8×C103C2311yescharacteristic
142C22×C8×C103C2311yescharacteristic
143C4⋊Q8×C103—21no—
144#124×C103—22no—
145#124×C103—21no—
146#124×C103—41no—
147#123×C103—41no—
148C22⋊Q8×C103—21no—
149C22⋊Q8×C103—21no—
150C4×Q8×C103—21no—
151C4×D4×C103—21no—
152C4×D4×C103—41no—
153#117×C103—21no—
154#117×C103C2311yescharacteristic
155C2×C4⋊C4×C103—21no—
156C2×C4⋊C4×C103C2311yescharacteristic
157C2×C22⋊C4×C103—41no—
158C2×C22⋊C4×C103—41no—
159C2×C42×C103C2311yescharacteristic
160#108×C103—22no—
161C4⋊C8×C103—21no—
162C4⋊C8×C103—21no—
163#104×C103—22no—
164#104×C103—22no—
165#104×C103—41no—
166#103×C103—21no—
167#103×C103—21no—
168#103×C103—21no—
169#103×C103—21no—
170#103×C103D411yescharacteristic
171#103×C103D411yescharacteristic
172#102×C103—21no—
173#102×C103—21no—
174#102×C103—21no—
175#102×C103—21no—
176#102×C103—21no—
177#102×C103—21no—
178#102×C103—21no—
179#102×C103—21no—
180#102×C103D411yescharacteristic
181#102×C103D411yescharacteristic
182#101×C103—22no—
183#100×C103—22no—
184#100×C103—22no—
185C22⋊C8×C103—21no—
186C22⋊C8×C103—21no—
187C24×C103—21no—
188C24×C103—21no—
189C24×C103—41no—
190C24×C103—41no—
191#41×C103—21no—
192#41×C103—21no—
193#41×C103—21no—
194#41×C103—21no—
195#41×C103—24no—
196#41×C103—24no—
197#41×C103—24no—
198#41×C103—21no—
199#41×C103—21no—
200#41×C103—21no—
201#41×C103—21no—
202#41×C103—42no—
203#41×C103—42no—
204#41×C103—42no—
205#41×C103—42no—
206#41×C103—42no—
207#41×C103C2×D412yes—
208#41×C103C2×D412yes—
209#41×C103C2×D412yes—
210#41×C103#4112yes—
211C2×Q8×C103—21no—
212C2×Q8×C103—21no—
213C2×Q8×C103—21no—
214C2×Q8×C103—21no—
215C2×Q8×C103—21no—
216C2×Q8×C103—21no—
217C2×Q8×C103C2×D411yescharacteristic
218C2×Q8×C103C2×D411yescharacteristic
219C2×Q8×C103C2×D411yescharacteristic
220C2×D4×C103—21no—
221C2×D4×C103—21no—
222C2×D4×C103—24no—
223C2×D4×C103—24no—
224C2×D4×C103—24no—
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—21no—
228C2×D4×C103—21no—
229C2×D4×C103—21no—
230C2×D4×C103—21no—
231C2×D4×C103—21no—
232C2×D4×C103—21no—
233C2×D4×C103—21no—
234C2×D4×C103—21no—
235C2×D4×C103—21no—
236C2×D4×C103—42no—
237C2×D4×C103—42no—
238C2×D4×C103—42no—
239C2×D4×C103—41no—
240C2×D4×C103—41no—
241C2×D4×C103—41no—
242C2×D4×C103—41no—
243C2×D4×C103—44no—
244C2×D4×C103—42no—
245C2×D4×C103—44no—
246C2×D4×C103—44no—
247C2×D4×C103—44no—
248C2×D4×C103—42no—
249C2×D4×C103C2×D412yes—
250C2×D4×C103C2×D412yes—
251C2×D4×C103C2×D411yescharacteristic
252C2×D4×C103C2×D411yescharacteristic
253C2×D4×C103C2×D411yescharacteristic
254C22×C4×C103—21no—
255C22×C4×C103—21no—
256C22×C4×C103—21no—
257C22×C4×C103—21no—
258C22×C4×C103—21no—
259C22×C4×C103—21no—
260C22×C4×C103—41no—
261C22×C4×C103—41no—
262C22×C4×C103—41no—
263C22×C4×C103C2411yescharacteristic
264Q16×C103—22no—
265Q16×C103—42no—
266Q16×C103—42no—
267SD16×C103—24no—
268SD16×C103—24no—
269SD16×C103—22no—
270SD16×C103—22no—
271SD16×C103—42no—
272SD16×C103—42no—
273SD16×C103—42no—
274SD16×C103—42no—
275D8×C103—24no—
276D8×C103—24no—
277D8×C103—24no—
278D8×C103—22no—
279D8×C103—24no—
280M16×C103—24no—
281M16×C103—21no—
282M16×C103—21no—
283M16×C103—21no—
284M16×C103—21no—
285M16×C103—21no—
286M16×C103—21no—
287M16×C103—21no—
288M16×C103—42no—
289M16×C103C2×D412yes—
290C2×C8×C103—24no—
291C2×C8×C103—21no—
292C2×C8×C103—21no—
293C2×C8×C103—21no—
294C2×C8×C103—21no—
295C2×C8×C103—21no—
296C2×C8×C103—21no—
297C2×C8×C103—21no—
298C2×C8×C103—21no—
299C2×C8×C103—42no—
300C2×C8×C103C2×D411yescharacteristic
301C2×C8×C103C2×D411yescharacteristic
302C2×C8×C103C2×D411yescharacteristic
303C2×C8×C103C2×D411yescharacteristic
304C4⋊C4×C103—21no—
305C4⋊C4×C103—21no—
306C4⋊C4×C103—41no—
307C4⋊C4×C103—41no—
308C4⋊C4×C103—41no—
309C4⋊C4×C103C2×D411yescharacteristic
310C4⋊C4×C103C2×D411yescharacteristic
311C22⋊C4×C103—21no—
312C22⋊C4×C103—41no—
313C22⋊C4×C103—41no—
314C22⋊C4×C103—41no—
315C22⋊C4×C103—44no—
316C22⋊C4×C103—82no—
317C42×C103—21no—
318C42×C103—21no—
319C42×C103—21no—
320C42×C103—41no—
321C23×C103—21no—
322C23×C103—21no—
323C23×C103—21no—
324C23×C103—22no—
325C23×C103—22no—
326C23×C103—44no—
327C23×C103—44no—
328C23×C103—41no—
329C23×C103—41no—
330C23×C103—41no—
331C23×C103—41no—
332C23×C103—81no—
333C23×C103—81no—
334C23×C103—81no—
335C23×C103—81no—
336C23×C103—161no—
337C23×C103—161no—
338C23×C103—161no—
339C23×C103—161no—
340C23×C103H(5,𝔽2)11yescharacteristic
341Q8×C103—21no—
342Q8×C103—21no—
343Q8×C103—21no—
344Q8×C103—21no—
345Q8×C103—41no—
346Q8×C103—41no—
347Q8×C103—41no—
348Q8×C103—41no—
349Q8×C103#12012yes—
350Q8×C103#12112yes—
351D4×C103—22no—
352D4×C103—22no—
353D4×C103—22no—
354D4×C103—22no—
355D4×C103—22no—
356D4×C103—22no—
357D4×C103—21no—
358D4×C103—22no—
359D4×C103—21no—
360D4×C103—22no—
361D4×C103—21no—
362D4×C103—21no—
363D4×C103—44no—
364D4×C103—44no—
365D4×C103—44no—
366D4×C103—44no—
367D4×C103—41no—
368D4×C103—41no—
369D4×C103—41no—
370D4×C103—41no—
371D4×C103—41no—
372D4×C103—41no—
373D4×C103#12012yes—
374D4×C103#12112yes—
375C2×C4×C103—21no—
376C2×C4×C103—21no—
377C2×C4×C103—22no—
378C2×C4×C103—22no—
379C2×C4×C103—22no—
380C2×C4×C103—22no—
381C2×C4×C103—21no—
382C2×C4×C103—21no—
383C2×C4×C103—21no—
384C2×C4×C103—44no—
385C2×C4×C103—44no—
386C2×C4×C103—41no—
387C2×C4×C103—41no—
388C2×C4×C103—41no—
389C2×C4×C103—41no—
390C2×C4×C103—41no—
391C2×C4×C103—41no—
392C2×C4×C103—41no—
393C2×C4×C103—41no—
394C2×C4×C103—41no—
395C2×C4×C103—81no—
396C2×C4×C103—161no—
397C2×C4×C103C22×D411yescharacteristic
398C2×C4×C103C22×D411yescharacteristic
399C2×C4×C103C22×D411yescharacteristic
400C2×C4×C103C22×D411yescharacteristic
401C2×C4×C103C2×#4111yescharacteristic
402C2×C4×C103H(5,𝔽2)11yescharacteristic
403C8×C103—21no—
404C8×C103—22no—
405C8×C103—21no—
406C8×C103—21no—
407C8×C103—21no—
408C8×C103—41no—
409C8×C103—41no—
410C8×C103—41no—
411C22×C103—21no—
412C22×C103—21no—
413C22×C103—22no—
414C22×C103—22no—
415C22×C103—41no—
416C22×C103—41no—
417C22×C103—41no—
418C22×C103—41no—
419C22×C103—41no—
420C22×C103—42no—
421C22×C103—42no—
422C22×C103—41no—
423C22×C103—41no—
424C22×C103—82no—
425C22×C103—82no—
426C22×C103—81no—
427C22×C103—81no—
428C22×C103—81no—
429C22×C103—81no—
430C22×C103—161no—
431C22×C103—161no—
432C22×C103—164no—
433C22×C103—164no—
434C22×C103#53411yescharacteristic
435C22×C103D4211yescharacteristic
436C22×C103#54611yescharacteristic
437C4×C103—22no—
438C4×C103—22no—
439C4×C103—41no—
440C4×C103—41no—
441C4×C103—41no—
442C4×C103—81no—
443C4×C103—81no—
444C4×C103—81no—
445C4×C103C2×#12011yescharacteristic
446C4×C103C2×#12111yescharacteristic
447C4×C103D4211yescharacteristic
448C4×C103#54611yescharacteristic
449#24459C10311yesmaximal, characteristic, direct product factor, Sylow
450C2×C103—21no—
451C2×C103—21no—
452C2×C103—42no—
453C2×C103—42no—
454C2×C103—81no—
455C2×C103—82no—
456C2×C103—82no—
457C2×C103#241011yescharacteristic
458C2×C103#328811yescharacteristic
459C2×C103#329011yescharacteristic
460C2×#576C2×C10311yescharacteristic
461C2×#471C2×C10311yescharacteristic, complemented
462#3046C2×C10311yescharacteristic, complemented
463C2×#455C2×C10311yescharacteristic, complemented
464#3009C2×C10311yescharacteristic, complemented
465#2897C2×C10311yescharacteristic, complemented
466#2051C2×C10311yescharacteristic, complemented
467#2045C2×C10311yescharacteristic, complemented
468#2012C2×C10311yescharacteristic, complemented
469#2003C2×C10311yescharacteristic, complemented
470#1908C2×C10311yescharacteristic, complemented
471#1883C2×C10311yescharacteristic, complemented
472#1876C2×C10311yescharacteristic, complemented
473#1866C2×C10311yescharacteristic, complemented
474#1792C2×C10311yescharacteristic, complemented
475C103#2445911yescharacteristic, direct product factor, Sylow
476C2×H(5,𝔽2)C22×C10311yescharacteristic
477C2×H(5,𝔽2)C22×C10311yescharacteristic
478#576—24no—
479#576—24no—
480C2×#137C22×C10311yescharacteristic
481C2×#137C22×C10311yescharacteristic, complemented
482C2×AGL(1,ℤ/8)—21no—
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
485C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
486C2×#135—21no—
487C2×#135C22×C10311yescharacteristic
488C22×SD16C22×C10311yescharacteristic, complemented
489C22×D8—21no—
490C22×D8C22×C10311yescharacteristic
491C2×#131C22×C10311yescharacteristic
492C2×#131C22×C10311yescharacteristic, complemented
493#536C22×C10311yescharacteristic, complemented
494C2×#124C22×C10311yescharacteristic, complemented
495#520C22×C10311yescharacteristic, complemented
496#471—24no—
497#464—21no—
498#463—21no—
499#462—21no—
500#461—21no—
501#455—24no—
502#452—21no—
503#452—21no—
504#450—21no—
505#450—21no—
506C2×#108C22×C10311yescharacteristic, complemented
507#424C22×C10311yescharacteristic, complemented
508C2×#104C22×C10311yescharacteristic
509C2×#104C22×C10311yescharacteristic, complemented
510C2×#104C22×C10311yescharacteristic, complemented
511#418—21no—
512#418C22×C10311yescharacteristic, complemented
513#418C22×C10311yescharacteristic, complemented
514#417—21no—
515#417C22×C10311yescharacteristic
516#417C22×C10311yescharacteristic, complemented
517#416—21no—
518#416C22×C10311yescharacteristic
519C2×#103C22×C10311yescharacteristic, complemented
520C2×#102—21no—
521C2×#102C22×C10311yescharacteristic, complemented
522C2×#101C22×C10311yescharacteristic, complemented
523C2×#100C22×C10311yescharacteristic, complemented
524C2×#100C22×C10311yescharacteristic, complemented
525#408C22×C10311yescharacteristic, complemented
526#390C22×C10311yescharacteristic, complemented
527#343C22×C10311yescharacteristic, complemented
528#341C22×C10311yescharacteristic, complemented
529#339C22×C10311yescharacteristic, complemented
530#336C22×C10311yescharacteristic, complemented
531H(5,𝔽2)—22no—
532H(5,𝔽2)—22no—
533H(5,𝔽2)—22no—
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—41no—
537H(5,𝔽2)—41no—
538H(5,𝔽2)D4×C10314yes—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41C23×C10311yescharacteristic
544C2×#41C23×C10311yescharacteristic
545C2×#41C23×C10311yescharacteristic
546C22×Q8C23×C10311yescharacteristic
547C22×D4—21no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4C23×C10311yescharacteristic
554C22×D4C23×C10311yescharacteristic
555#137—22no—
556#137—22no—
557#137—22no—
558#137—22no—
559AGL(1,ℤ/8)—28no—
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)D4×C10314yes—
565#135—28no—
566#135—22no—
567#135—22no—
568C2×Q16—21no—
569C2×Q16—21no—
570C2×Q16D4×C10311yescharacteristic
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—41no—
579C2×SD16D4×C10311yescharacteristic
580C2×SD16D4×C10311yescharacteristic
581C2×D8—28no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—21no—
587C2×D8—21no—
588C2×D8D4×C10311yescharacteristic
589#131—22no—
590#131—22no—
591#131—22no—
592#131—41no—
593C2×M16—21no—
594C2×M16—21no—
595C2×M16C23×C10311yescharacteristic
596C2×M16C23×C10311yescharacteristic
597C2×M16C23×C10311yescharacteristic
598C2×M16C23×C10311yescharacteristic
599C22×C8—21no—
600C22×C8—21no—
601C22×C8C23×C10311yescharacteristic
602C22×C8C23×C10311yescharacteristic
603C4⋊Q8—21no—
604#124—22no—
605#124—21no—
606#124—41no—
607#123—41no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C4×Q8—21no—
611C4×D4—21no—
612C4×D4—41no—
613#117—21no—
614#117C23×C10311yescharacteristic
615C2×C4⋊C4—21no—
616C2×C4⋊C4C23×C10311yescharacteristic
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C42C23×C10311yescharacteristic
620#108—22no—
621C4⋊C8—21no—
622C4⋊C8—21no—
623#104—22no—
624#104—22no—
625#104—41no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103D4×C10311yescharacteristic
631#103D4×C10311yescharacteristic
632#102—21no—
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102D4×C10311yescharacteristic
641#102D4×C10311yescharacteristic
642#101—22no—
643#100—22no—
644#100—22no—
645C22⋊C8—21no—
646C22⋊C8—21no—
647C24—21no—
648C24—21no—
649C24—41no—
650C24—41no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—24no—
656#41—24no—
657#41—24no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—42no—
663#41—42no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41C2×D4×C10312yes—
668#41C2×D4×C10312yes—
669#41C2×D4×C10312yes—
670#41#41×C10312yes—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8C2×D4×C10311yescharacteristic
678C2×Q8C2×D4×C10311yescharacteristic
679C2×Q8C2×D4×C10311yescharacteristic
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—42no—
709C2×D4C2×D4×C10312yes—
710C2×D4C2×D4×C10312yes—
711C2×D4C2×D4×C10311yescharacteristic
712C2×D4C2×D4×C10311yescharacteristic
713C2×D4C2×D4×C10311yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4C24×C10311yescharacteristic
724Q16—22no—
725Q16—42no—
726Q16—42no—
727SD16—24no—
728SD16—24no—
729SD16—22no—
730SD16—22no—
731SD16—42no—
732SD16—42no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—24no—
737D8—24no—
738D8—22no—
739D8—24no—
740M16—24no—
741M16—21no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—42no—
749M16C2×D4×C10312yes—
750C2×C8—24no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—42no—
760C2×C8C2×D4×C10311yescharacteristic
761C2×C8C2×D4×C10311yescharacteristic
762C2×C8C2×D4×C10311yescharacteristic
763C2×C8C2×D4×C10311yescharacteristic
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—41no—
767C4⋊C4—41no—
768C4⋊C4—41no—
769C4⋊C4C2×D4×C10311yescharacteristic
770C4⋊C4C2×D4×C10311yescharacteristic
771C22⋊C4—21no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—41no—
775C22⋊C4—44no—
776C22⋊C4—82no—
777C42—21no—
778C42—21no—
779C42—21no—
780C42—41no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—22no—
785C23—22no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—81no—
793C23—81no—
794C23—81no—
795C23—81no—
796C23—161no—
797C23—161no—
798C23—161no—
799C23—161no—
800C23H(5,𝔽2)×C10311yescharacteristic
801Q8—21no—
802Q8—21no—
803Q8—21no—
804Q8—21no—
805Q8—41no—
806Q8—41no—
807Q8—41no—
808Q8—41no—
809Q8#120×C10312yes—
810Q8#121×C10312yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—21no—
818D4—22no—
819D4—21no—
820D4—22no—
821D4—21no—
822D4—21no—
823D4—44no—
824D4—44no—
825D4—44no—
826D4—44no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4#120×C10312yes—
834D4#121×C10312yes—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—81no—
856C2×C4—161no—
857C2×C4C22×D4×C10311yescharacteristic
858C2×C4C22×D4×C10311yescharacteristic
859C2×C4C22×D4×C10311yescharacteristic
860C2×C4C22×D4×C10311yescharacteristic
861C2×C4C2×#41×C10311yescharacteristic
862C2×C4H(5,𝔽2)×C10311yescharacteristic
863C8—21no—
864C8—22no—
865C8—21no—
866C8—21no—
867C8—21no—
868C8—41no—
869C8—41no—
870C8—41no—
871C22—21no—
872C22—21no—
873C22—22no—
874C22—22no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—42no—
884C22—82no—
885C22—82no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—161no—
891C22—161no—
892C22—164no—
893C22—164no—
894C22#534×C10311yescharacteristic
895C22D42×C10311yescharacteristic
896C22#546×C10311yescharacteristic
897C4—22no—
898C4—22no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—81no—
903C4—81no—
904C4—81no—
905C4C2×#120×C10311yescharacteristic
906C4C2×#121×C10311yescharacteristic
907C4D42×C10311yescharacteristic
908C4#546×C10311yescharacteristic
909C2—21no—
910C2—21no—
911C2—42no—
912C2—42no—
913C2—81no—
914C2—82no—
915C2—82no—
916C2C103×#241011yescharacteristic
917C2C103×#328811yescharacteristic
918C2C103×#329011yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#576×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#471×C103C2semidirect
3. C103×#3046C2semidirect
4. C2×#455×C103C2semidirect
5. C103×#3009C2semidirect
6. C103×#2897C2semidirect
7. C103×#2051C2semidirect
8. C103×#2045C2semidirect
9. C103×#2012C2semidirect
10. C103×#2003C2semidirect
11. C103×#1908C2semidirect
12. C103×#1883C2semidirect
13. C103×#1876C2semidirect
14. C103×#1866C2semidirect
15. C103×#1792C2semidirect
21. C2×#137×C103C22semidirect
28. C22×SD16×C103C22semidirect
32. C2×#131×C103C22semidirect
33. #536×C103C22semidirect
34. C2×#124×C103C22semidirect
35. #520×C103C22semidirect
46. C2×#108×C103C22semidirect
47. #424×C103C22semidirect
49. C2×#104×C103C22semidirect
50. C2×#104×C103C22semidirect
52. #418×C103C22semidirect
53. #418×C103C22semidirect
56. #417×C103C22semidirect
59. C2×#103×C103C22semidirect
61. C2×#102×C103C22semidirect
62. C2×#101×C103C22semidirect
63. C2×#100×C103C22semidirect
64. C2×#100×C103C22semidirect
65. #408×C103C22semidirect
66. #390×C103C22semidirect
67. #343×C103C22semidirect
68. #341×C103C22semidirect
69. #339×C103C22semidirect
70. #336×C103C22semidirect
449. #24459C103direct (N × H)
461. C2×#471C2×C103semidirect
462. #3046C2×C103semidirect
463. C2×#455C2×C103semidirect
464. #3009C2×C103semidirect
465. #2897C2×C103semidirect
466. #2051C2×C103semidirect
467. #2045C2×C103semidirect
468. #2012C2×C103semidirect
469. #2003C2×C103semidirect
470. #1908C2×C103semidirect
471. #1883C2×C103semidirect
472. #1876C2×C103semidirect
473. #1866C2×C103semidirect
474. #1792C2×C103semidirect
475. C103#24459direct (N × H)
481. C2×#137C22×C103semidirect
488. C22×SD16C22×C103semidirect
492. C2×#131C22×C103semidirect
493. #536C22×C103semidirect
494. C2×#124C22×C103semidirect
495. #520C22×C103semidirect
506. C2×#108C22×C103semidirect
507. #424C22×C103semidirect
509. C2×#104C22×C103semidirect
510. C2×#104C22×C103semidirect
512. #418C22×C103semidirect
513. #418C22×C103semidirect
516. #417C22×C103semidirect
519. C2×#103C22×C103semidirect
521. C2×#102C22×C103semidirect
522. C2×#101C22×C103semidirect
523. C2×#100C22×C103semidirect
524. C2×#100C22×C103semidirect
525. #408C22×C103semidirect
526. #390C22×C103semidirect
527. #343C22×C103semidirect
528. #341C22×C103semidirect
529. #339C22×C103semidirect
530. #336C22×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#576×C1032
C2×#471×C1032
C103×#30462
C2×#455×C1032
C103×#30092
C103×#28972
C103×#20512
C103×#20452
C103×#20122
C103×#20032
C103×#19082
C103×#18832
C103×#18762
C103×#18662
C103×#17922
#24459103