Finite Group Databasebeta

← C103×#24295 #39929570

Subgroups — C103×#24295 #39929570

Order 26368.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C103C211yesmaximal, characteristic, complemented
2C103×#3067C211yesmaximal, characteristic, complemented
3C103×#3057C211yesmaximal, characteristic, complemented
4C103×#3020C211yesmaximal, characteristic, complemented
5C103×#3019C211yesmaximal, characteristic, complemented
6C103×#2955C211yesmaximal, characteristic, complemented
7C103×#2049C211yesmaximal, characteristic, complemented
8C103×#2048C211yesmaximal, characteristic, complemented
9C103×#2009C211yesmaximal, characteristic, complemented
10C103×#2008C211yesmaximal, characteristic, complemented
11C103×#1977C211yesmaximal, characteristic, complemented
12C103×#1976C211yesmaximal, characteristic, complemented
13C103×#1814C211yesmaximal, characteristic, complemented
14C103×#1796C211yesmaximal, characteristic, complemented
15C103×#1795C211yesmaximal, characteristic, complemented
16C2×2−1+4×C103C2211yescharacteristic
17C2×H(5,𝔽2)×C103C2211yescharacteristic
18#577×C103—22no—
19#577×C103—22no—
20#577×C103—22no—
21#577×C103—22no—
22#575×C103C2211yescharacteristic
23#575×C103C2211yescharacteristic
24#575×C103C2211yescharacteristic, complemented
25C2×#137×C103—21no—
26C2×#137×C103C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C103—21no—
28C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
29C2×#135×C103—21no—
30C2×#135×C103C2211yescharacteristic
31C22×SD16×C103—21no—
32C22×SD16×C103C2211yescharacteristic
33C2×#131×C103C2211yescharacteristic
34C2×#131×C103C2211yescharacteristic, complemented
35#536×C103C2211yescharacteristic, complemented
36#535×C103C2211yescharacteristic
37#473×C103—21no—
38#472×C103—21no—
39#471×C103—21no—
40#471×C103—21no—
41#468×C103—22no—
42#465×C103—22no—
43#456×C103—22no—
44#455×C103—22no—
45#454×C103—22no—
46#453×C103—22no—
47#444×C103—22no—
48#443×C103—22no—
49#430×C103C2211yescharacteristic, complemented
50C2×#108×C103C2211yescharacteristic, complemented
51#427×C103C2211yescharacteristic, complemented
52#421×C103C2211yescharacteristic
53#421×C103C2211yescharacteristic
54#421×C103C2211yescharacteristic
55#421×C103C2211yescharacteristic
56#421×C103C2211yescharacteristic, complemented
57#421×C103C2211yescharacteristic, complemented
58#419×C103C2211yescharacteristic, complemented
59#419×C103C2211yescharacteristic, complemented
60#418×C103C2211yescharacteristic
61#418×C103C2211yescharacteristic
62#413×C103C2211yescharacteristic
63#413×C103C2211yescharacteristic, complemented
64C2×#101×C103C2211yescharacteristic, complemented
65C2×#100×C103C2211yescharacteristic
66#410×C103C2211yescharacteristic
67#410×C103C2211yescharacteristic, complemented
68#405×C103C2211yescharacteristic, complemented
69#344×C103C2211yescharacteristic, complemented
70#344×C103C2211yescharacteristic, complemented
712−1+4×C103—22no—
722−1+4×C103—22no—
732−1+4×C103—22no—
742−1+4×C103—41no—
75H(5,𝔽2)×C103—22no—
76H(5,𝔽2)×C103—22no—
77H(5,𝔽2)×C103—22no—
78H(5,𝔽2)×C103—41no—
79C2×#41×C103—21no—
80C2×#41×C103—21no—
81C2×#41×C103—21no—
82C2×#41×C103—21no—
83C2×#41×C103—41no—
84C2×#41×C103C2311yescharacteristic
85C2×#41×C103C2311yescharacteristic
86C2×#41×C103C2311yescharacteristic
87C2×#41×C103C2311yescharacteristic
88C22×Q8×C103—21no—
89C22×Q8×C103—21no—
90C22×Q8×C103C2311yescharacteristic
91C22×D4×C103—21no—
92C22×D4×C103—21no—
93C22×D4×C103—41no—
94C22×D4×C103C2311yescharacteristic
95#137×C103—24no—
96#137×C103—24no—
97#137×C103—22no—
98#137×C103—21no—
99#137×C103—21no—
100#137×C103—21no—
101#137×C103—21no—
102#137×C103—21no—
103#137×C103—22no—
104#137×C103D412yes—
105AGL(1,ℤ/8)×C103—24no—
106AGL(1,ℤ/8)×C103—24no—
107AGL(1,ℤ/8)×C103—22no—
108AGL(1,ℤ/8)×C103—21no—
109AGL(1,ℤ/8)×C103—21no—
110AGL(1,ℤ/8)×C103—21no—
111AGL(1,ℤ/8)×C103—21no—
112AGL(1,ℤ/8)×C103—21no—
113AGL(1,ℤ/8)×C103—22no—
114AGL(1,ℤ/8)×C103D412yes—
115#135×C103—24no—
116#135×C103—24no—
117#135×C103—22no—
118#135×C103—21no—
119#135×C103—21no—
120#135×C103—21no—
121#135×C103—21no—
122#135×C103—41no—
123#135×C103—41no—
124C2×Q16×C103—21no—
125C2×Q16×C103D411yescharacteristic, complemented
126C2×SD16×C103—24no—
127C2×SD16×C103—24no—
128C2×SD16×C103—21no—
129C2×SD16×C103—21no—
130C2×SD16×C103—21no—
131C2×SD16×C103—21no—
132C2×SD16×C103—21no—
133C2×SD16×C103—21no—
134C2×SD16×C103D412yes—
135C2×SD16×C103D412yes—
136C2×SD16×C103D411yescharacteristic, complemented
137C2×SD16×C103D411yescharacteristic, complemented
138C2×D8×C103—21no—
139C2×D8×C103D411yescharacteristic, complemented
140#131×C103—21no—
141#131×C103—21no—
142#131×C103—21no—
143#131×C103—21no—
144#131×C103—21no—
145#131×C103—21no—
146#131×C103D412yescomplemented
147#131×C103D412yescomplemented
148C2×M16×C103—21no—
149C2×M16×C103—21no—
150C2×M16×C103C2311yescharacteristic
151C2×M16×C103C2311yescharacteristic
152C2×M16×C103C2311yescharacteristic
153C2×M16×C103C2311yescharacteristic
154C2×M16×C103C2311yescharacteristic
155C22×C8×C103—21no—
156C22×C8×C103—21no—
157C22×C8×C103C2311yescharacteristic
158C4⋊Q8×C103—21no—
159#127×C103—21no—
160#124×C103—21no—
161#124×C103—21no—
162#123×C103—41no—
163C22⋊Q8×C103—22no—
164#121×C103—22no—
165#120×C103—41no—
166#117×C103C2311yescharacteristic
167#117×C103C2311yescharacteristic
168#117×C103C2311yescharacteristic
169#108×C103—22no—
170#108×C103—21no—
171#108×C103—21no—
172#107×C103—21no—
173#106×C103—21no—
174#104×C103—22no—
175#104×C103—22no—
176#104×C103—22no—
177#104×C103—22no—
178#104×C103—22no—
179#104×C103—22no—
180#103×C103—22no—
181#103×C103—41no—
182#102×C103—22no—
183#102×C103—41no—
184#101×C103—21no—
185#101×C103—21no—
186#101×C103—22no—
187#100×C103—21no—
188#100×C103—21no—
189#100×C103—22no—
190#99×C103—41no—
191#99×C103—41no—
192#97×C103—21no—
193C4×C8×C103—21no—
194C24×C103—21no—
195C24×C103—41no—
196#41×C103—21no—
197#41×C103—21no—
198#41×C103—24no—
199#41×C103—24no—
200#41×C103—21no—
201#41×C103—21no—
202#41×C103—21no—
203#41×C103—21no—
204#41×C103—21no—
205#41×C103—21no—
206#41×C103—21no—
207#41×C103—21no—
208#41×C103—21no—
209#41×C103—21no—
210#41×C103—21no—
211#41×C103—21no—
212#41×C103—42no—
213#41×C103—44no—
214#41×C103—42no—
215#41×C103—42no—
216#41×C103—42no—
217#41×C103—44no—
218#41×C103—42no—
219#41×C103—42no—
220#41×C103C2×D412yes—
221#41×C103C2×D412yes—
222C2×Q8×C103—21no—
223C2×Q8×C103—24no—
224C2×Q8×C103—21no—
225C2×Q8×C103—21no—
226C2×Q8×C103—21no—
227C2×Q8×C103—21no—
228C2×Q8×C103—41no—
229C2×Q8×C103—42no—
230C2×Q8×C103—42no—
231C2×Q8×C103—42no—
232C2×Q8×C103C2×D411yescharacteristic
233C2×Q8×C103C2×D411yescharacteristic
234C2×Q8×C103C2×D412yes—
235C2×Q8×C103C2×D411yescharacteristic
236C2×Q8×C103#4111yescharacteristic
237C2×D4×C103—21no—
238C2×D4×C103—24no—
239C2×D4×C103—21no—
240C2×D4×C103—21no—
241C2×D4×C103—21no—
242C2×D4×C103—21no—
243C2×D4×C103—21no—
244C2×D4×C103—21no—
245C2×D4×C103—21no—
246C2×D4×C103—21no—
247C2×D4×C103—42no—
248C2×D4×C103—41no—
249C2×D4×C103—41no—
250C2×D4×C103—42no—
251C2×D4×C103—44no—
252C2×D4×C103—44no—
253C2×D4×C103—41no—
254C2×D4×C103—42no—
255C2×D4×C103—42no—
256C2×D4×C103C2×D411yescharacteristic
257C2×D4×C103C2×D411yescharacteristic
258C2×D4×C103C2×D412yes—
259C2×D4×C103C2×D411yescharacteristic
260C2×D4×C103#4111yescharacteristic
261C22×C4×C103—21no—
262C22×C4×C103—21no—
263C22×C4×C103—21no—
264C22×C4×C103—21no—
265C22×C4×C103—21no—
266C22×C4×C103—41no—
267C22×C4×C103—41no—
268C22×C4×C103—41no—
269C22×C4×C103C2411yescharacteristic
270Q16×C103—24no—
271Q16×C103—22no—
272Q16×C103—21no—
273Q16×C103—21no—
274Q16×C103—41no—
275Q16×C103—41no—
276SD16×C103—24no—
277SD16×C103—24no—
278SD16×C103—22no—
279SD16×C103—22no—
280SD16×C103—22no—
281SD16×C103—22no—
282SD16×C103—21no—
283SD16×C103—21no—
284SD16×C103—22no—
285SD16×C103—22no—
286SD16×C103—21no—
287SD16×C103—21no—
288SD16×C103—41no—
289SD16×C103—41no—
290SD16×C103—41no—
291SD16×C103—41no—
292D8×C103—24no—
293D8×C103—22no—
294D8×C103—21no—
295D8×C103—21no—
296D8×C103—41no—
297D8×C103—41no—
298M16×C103—21no—
299M16×C103—21no—
300M16×C103—22no—
301M16×C103—22no—
302M16×C103—21no—
303M16×C103—21no—
304M16×C103—21no—
305M16×C103—21no—
306M16×C103—21no—
307M16×C103—21no—
308M16×C103—41no—
309M16×C103—41no—
310M16×C103C2×D412yes—
311M16×C103C2×D412yes—
312C2×C8×C103—21no—
313C2×C8×C103—21no—
314C2×C8×C103—22no—
315C2×C8×C103—22no—
316C2×C8×C103—21no—
317C2×C8×C103—21no—
318C2×C8×C103—21no—
319C2×C8×C103—41no—
320C2×C8×C103—41no—
321C2×C8×C103C2×D411yescharacteristic
322C2×C8×C103C2×D411yescharacteristic
323C2×C8×C103C2×D411yescharacteristic
324C2×C8×C103C2×D411yescharacteristic
325C2×C8×C103C2×D411yescharacteristic
326C2×C8×C103C2×D411yescharacteristic
327C4⋊C4×C103—21no—
328C4⋊C4×C103—21no—
329C4⋊C4×C103—21no—
330C4⋊C4×C103—42no—
331C22⋊C4×C103—21no—
332C22⋊C4×C103—21no—
333C22⋊C4×C103—21no—
334C22⋊C4×C103—42no—
335C22⋊C4×C103—42no—
336C42×C103—21no—
337C42×C103—21no—
338C42×C103—21no—
339C23×C103—21no—
340C23×C103—21no—
341C23×C103—22no—
342C23×C103—21no—
343C23×C103—21no—
344C23×C103—44no—
345C23×C103—41no—
346C23×C103—41no—
347C23×C103—161no—
348C23×C103—162no—
349C23×C103H(5,𝔽2)11yescharacteristic
350Q8×C103—21no—
351Q8×C103—21no—
352Q8×C103—22no—
353Q8×C103—21no—
354Q8×C103—21no—
355Q8×C103—21no—
356Q8×C103—21no—
357Q8×C103—21no—
358Q8×C103—22no—
359Q8×C103—44no—
360Q8×C103—41no—
361Q8×C103—41no—
362Q8×C103#12112yes—
363D4×C103—22no—
364D4×C103—22no—
365D4×C103—21no—
366D4×C103—22no—
367D4×C103—21no—
368D4×C103—21no—
369D4×C103—21no—
370D4×C103—21no—
371D4×C103—21no—
372D4×C103—21no—
373D4×C103—22no—
374D4×C103—44no—
375D4×C103—44no—
376D4×C103—44no—
377D4×C103—41no—
378D4×C103—41no—
379D4×C103—41no—
380D4×C103—41no—
381D4×C103—41no—
382D4×C103—41no—
383D4×C103—41no—
384D4×C103—41no—
385D4×C103—162no—
386D4×C103#12112yes—
387C2×C4×C103—21no—
388C2×C4×C103—22no—
389C2×C4×C103—22no—
390C2×C4×C103—21no—
391C2×C4×C103—22no—
392C2×C4×C103—21no—
393C2×C4×C103—21no—
394C2×C4×C103—44no—
395C2×C4×C103—44no—
396C2×C4×C103—44no—
397C2×C4×C103—41no—
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×C103C22×D411yescharacteristic
409C2×C4×C103C22×D411yescharacteristic
410C2×C4×C103C22×D411yescharacteristic
411C2×C4×C103C22×D411yescharacteristic
412C2×C4×C103C2×#4111yescharacteristic
413C2×C4×C103H(5,𝔽2)11yescharacteristic
414C8×C103—22no—
415C8×C103—22no—
416C8×C103—41no—
417C8×C103—41no—
418C8×C103—41no—
419C8×C103#12011yescharacteristic
420C8×C103#12011yescharacteristic
421C8×C103#12011yescharacteristic
422C8×C103#12011yescharacteristic
423C22×C103—22no—
424C22×C103—41no—
425C22×C103—42no—
426C22×C103—42no—
427C22×C103—41no—
428C22×C103—42no—
429C22×C103—41no—
430C22×C103—41no—
431C22×C103—82no—
432C22×C103—81no—
433C22×C103—81no—
434C22×C103—82no—
435C22×C103—161no—
436C22×C103—164no—
437C22×C103#53511yescharacteristic
438C22×C103D4211yescharacteristic
439C22×C103#54611yescharacteristic
440C4×C103—22no—
441C4×C103—41no—
442C4×C103—42no—
443C4×C103—41no—
444C4×C103—41no—
445C4×C103—81no—
446C4×C103—81no—
447C4×C103—81no—
448C4×C103C2×#12011yescharacteristic
449C4×C103C2×#12111yescharacteristic
450C4×C103D4211yescharacteristic
451C4×C103#54611yescharacteristic
452#24295C10311yesmaximal, characteristic, direct product factor, Sylow
453C2×C103—21no—
454C2×C103—21no—
455C2×C103—21no—
456C2×C103—42no—
457C2×C103—81no—
458C2×C103—81no—
459C2×C103—82no—
460C2×C103—81no—
461C2×C103#240811yescharacteristic
462C2×#577C2×C10311yescharacteristic, complemented
463#3067C2×C10311yescharacteristic, complemented
464#3057C2×C10311yescharacteristic, complemented
465#3020C2×C10311yescharacteristic, complemented
466#3019C2×C10311yescharacteristic, complemented
467#2955C2×C10311yescharacteristic, complemented
468#2049C2×C10311yescharacteristic, complemented
469#2048C2×C10311yescharacteristic, complemented
470#2009C2×C10311yescharacteristic, complemented
471#2008C2×C10311yescharacteristic, complemented
472#1977C2×C10311yescharacteristic, complemented
473#1976C2×C10311yescharacteristic, complemented
474#1814C2×C10311yescharacteristic, complemented
475#1796C2×C10311yescharacteristic, complemented
476#1795C2×C10311yescharacteristic, complemented
477C103#2429511yescharacteristic, direct product factor, Sylow
478C2×2−1+4C22×C10311yescharacteristic
479C2×H(5,𝔽2)C22×C10311yescharacteristic
480#577—22no—
481#577—22no—
482#577—22no—
483#577—22no—
484#575C22×C10311yescharacteristic
485#575C22×C10311yescharacteristic
486#575C22×C10311yescharacteristic, complemented
487C2×#137—21no—
488C2×#137C22×C10311yescharacteristic
489C2×AGL(1,ℤ/8)—21no—
490C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
491C2×#135—21no—
492C2×#135C22×C10311yescharacteristic
493C22×SD16—21no—
494C22×SD16C22×C10311yescharacteristic
495C2×#131C22×C10311yescharacteristic
496C2×#131C22×C10311yescharacteristic, complemented
497#536C22×C10311yescharacteristic, complemented
498#535C22×C10311yescharacteristic
499#473—21no—
500#472—21no—
501#471—21no—
502#471—21no—
503#468—22no—
504#465—22no—
505#456—22no—
506#455—22no—
507#454—22no—
508#453—22no—
509#444—22no—
510#443—22no—
511#430C22×C10311yescharacteristic, complemented
512C2×#108C22×C10311yescharacteristic, complemented
513#427C22×C10311yescharacteristic, complemented
514#421C22×C10311yescharacteristic
515#421C22×C10311yescharacteristic
516#421C22×C10311yescharacteristic
517#421C22×C10311yescharacteristic
518#421C22×C10311yescharacteristic, complemented
519#421C22×C10311yescharacteristic, complemented
520#419C22×C10311yescharacteristic, complemented
521#419C22×C10311yescharacteristic, complemented
522#418C22×C10311yescharacteristic
523#418C22×C10311yescharacteristic
524#413C22×C10311yescharacteristic
525#413C22×C10311yescharacteristic, complemented
526C2×#101C22×C10311yescharacteristic, complemented
527C2×#100C22×C10311yescharacteristic
528#410C22×C10311yescharacteristic
529#410C22×C10311yescharacteristic, complemented
530#405C22×C10311yescharacteristic, complemented
531#344C22×C10311yescharacteristic, complemented
532#344C22×C10311yescharacteristic, complemented
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C10311yescharacteristic
547C2×#41C23×C10311yescharacteristic
548C2×#41C23×C10311yescharacteristic
549C2×#41C23×C10311yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C10311yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C10311yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C10312yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C10312yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C10311yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C10312yes—
597C2×SD16D4×C10312yes—
598C2×SD16D4×C10311yescharacteristic, complemented
599C2×SD16D4×C10311yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C10311yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C10312yescomplemented
609#131D4×C10312yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C10311yescharacteristic
613C2×M16C23×C10311yescharacteristic
614C2×M16C23×C10311yescharacteristic
615C2×M16C23×C10311yescharacteristic
616C2×M16C23×C10311yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C10311yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C10311yescharacteristic
629#117C23×C10311yescharacteristic
630#117C23×C10311yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C10312yes—
683#41C2×D4×C10312yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C10311yescharacteristic
695C2×Q8C2×D4×C10311yescharacteristic
696C2×Q8C2×D4×C10312yes—
697C2×Q8C2×D4×C10311yescharacteristic
698C2×Q8#41×C10311yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
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—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C10311yescharacteristic
719C2×D4C2×D4×C10311yescharacteristic
720C2×D4C2×D4×C10312yes—
721C2×D4C2×D4×C10311yescharacteristic
722C2×D4#41×C10311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C10311yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C10312yes—
773M16C2×D4×C10312yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C10311yescharacteristic
784C2×C8C2×D4×C10311yescharacteristic
785C2×C8C2×D4×C10311yescharacteristic
786C2×C8C2×D4×C10311yescharacteristic
787C2×C8C2×D4×C10311yescharacteristic
788C2×C8C2×D4×C10311yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C10311yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—21no—
816Q8—21no—
817Q8—21no—
818Q8—21no—
819Q8—21no—
820Q8—22no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C10312yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—22no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C10312yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C10311yescharacteristic
871C2×C4C22×D4×C10311yescharacteristic
872C2×C4C22×D4×C10311yescharacteristic
873C2×C4C22×D4×C10311yescharacteristic
874C2×C4C2×#41×C10311yescharacteristic
875C2×C4H(5,𝔽2)×C10311yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C10311yescharacteristic
882C8#120×C10311yescharacteristic
883C8#120×C10311yescharacteristic
884C8#120×C10311yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22#535×C10311yescharacteristic
900C22D42×C10311yescharacteristic
901C22#546×C10311yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C10311yescharacteristic
911C4C2×#121×C10311yescharacteristic
912C4D42×C10311yescharacteristic
913C4#546×C10311yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2C103×#240811yescharacteristic
subgroupG/H
center, socleC2×C103#2408
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C103C2semidirect
2. C103×#3067C2semidirect
3. C103×#3057C2semidirect
4. C103×#3020C2semidirect
5. C103×#3019C2semidirect
6. C103×#2955C2semidirect
7. C103×#2049C2semidirect
8. C103×#2048C2semidirect
9. C103×#2009C2semidirect
10. C103×#2008C2semidirect
11. C103×#1977C2semidirect
12. C103×#1976C2semidirect
13. C103×#1814C2semidirect
14. C103×#1796C2semidirect
15. C103×#1795C2semidirect
24. #575×C103C22semidirect
34. C2×#131×C103C22semidirect
35. #536×C103C22semidirect
49. #430×C103C22semidirect
50. C2×#108×C103C22semidirect
51. #427×C103C22semidirect
56. #421×C103C22semidirect
57. #421×C103C22semidirect
58. #419×C103C22semidirect
59. #419×C103C22semidirect
63. #413×C103C22semidirect
64. C2×#101×C103C22semidirect
67. #410×C103C22semidirect
68. #405×C103C22semidirect
69. #344×C103C22semidirect
70. #344×C103C22semidirect
125. C2×Q16×C103D4semidirect
136. C2×SD16×C103D4semidirect
137. C2×SD16×C103D4semidirect
139. C2×D8×C103D4semidirect
146. #131×C103D4semidirect
147. #131×C103D4semidirect
452. #24295C103direct (N × H)
462. C2×#577C2×C103semidirect
463. #3067C2×C103semidirect
464. #3057C2×C103semidirect
465. #3020C2×C103semidirect
466. #3019C2×C103semidirect
467. #2955C2×C103semidirect
468. #2049C2×C103semidirect
469. #2048C2×C103semidirect
470. #2009C2×C103semidirect
471. #2008C2×C103semidirect
472. #1977C2×C103semidirect
473. #1976C2×C103semidirect
474. #1814C2×C103semidirect
475. #1796C2×C103semidirect
476. #1795C2×C103semidirect
477. C103#24295direct (N × H)
486. #575C22×C103semidirect
496. C2×#131C22×C103semidirect
497. #536C22×C103semidirect
511. #430C22×C103semidirect
512. C2×#108C22×C103semidirect
513. #427C22×C103semidirect
518. #421C22×C103semidirect
519. #421C22×C103semidirect
520. #419C22×C103semidirect
521. #419C22×C103semidirect
525. #413C22×C103semidirect
526. C2×#101C22×C103semidirect
529. #410C22×C103semidirect
530. #405C22×C103semidirect
531. #344C22×C103semidirect
532. #344C22×C103semidirect
587. C2×Q16D4×C103semidirect
598. C2×SD16D4×C103semidirect
599. C2×SD16D4×C103semidirect
601. C2×D8D4×C103semidirect
608. #131D4×C103semidirect
609. #131D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1032
C103×#30672
C103×#30572
C103×#30202
C103×#30192
C103×#29552
C103×#20492
C103×#20482
C103×#20092
C103×#20082
C103×#19772
C103×#19762
C103×#18142
C103×#17962
C103×#17952
#24295103