Finite Group Databasebeta

← C103×#24474 #39929749

Subgroups — C103×#24474 #39929749

Order 26368.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3586C211yesmaximal, characteristic
2C103×#3069C211yesmaximal, characteristic, complemented
3C103×#3039C211yesmaximal, characteristic, complemented
4C103×#3022C211yesmaximal, characteristic, complemented
5C2×#456×C103C211yesmaximal, characteristic, complemented
6C103×#2901C211yesmaximal, characteristic, complemented
7C103×#2050C211yesmaximal, characteristic, complemented
8C103×#2049C211yesmaximal, characteristic, complemented
9C103×#2009C211yesmaximal, characteristic, complemented
10C103×#2005C211yesmaximal, characteristic, complemented
11C103×#1906C211yesmaximal, characteristic, complemented
12C103×#1902C211yesmaximal, characteristic, complemented
13C103×#1902C211yesmaximal, characteristic, complemented
14C103×#1861C211yesmaximal, characteristic, complemented
15C103×#1796C211yesmaximal, characteristic, complemented
16#585×C103C2211yescharacteristic
17C2×2−1+4×C103C2211yescharacteristic
18#578×C103—22no—
19#578×C103—22no—
20#577×C103—22no—
21#577×C103—22no—
22#575×C103—22no—
23#575×C103C2211yescharacteristic
24#575×C103C2211yescharacteristic
25C2×#137×C103—22no—
26C2×#137×C103C2211yescharacteristic
27C2×#137×C103C2211yescharacteristic
28C2×#137×C103C2211yescharacteristic
29C2×#137×C103C2211yescharacteristic
30C2×#137×C103C2211yescharacteristic, complemented
31#568×C103C2211yescharacteristic
32#568×C103C2211yescharacteristic
33#536×C103C2211yescharacteristic
34C2×C4⋊Q8×C103C2211yescharacteristic, complemented
35C4×#41×C103C2211yescharacteristic
36#473×C103—22no—
37#471×C103—22no—
38#462×C103—22no—
39#461×C103—22no—
40#456×C103—22no—
41#456×C103—22no—
42#456×C103—22no—
43#455×C103—22no—
44#430×C103C2211yescharacteristic, complemented
45#423×C103C2211yescharacteristic, complemented
46#421×C103—22no—
47#421×C103C2211yescharacteristic
48#421×C103C2211yescharacteristic
49#421×C103C2211yescharacteristic
50#421×C103C2211yescharacteristic
51C2×#104×C103—22no—
52C2×#104×C103C2211yescharacteristic
53C2×#104×C103C2211yescharacteristic
54C2×#104×C103C2211yescharacteristic, complemented
55#419×C103C2211yescharacteristic, complemented
56#419×C103C2211yescharacteristic, complemented
57#419×C103C2211yescharacteristic, complemented
58#413×C103C2211yescharacteristic
59#413×C103C2211yescharacteristic, complemented
60C2×#101×C103C2211yescharacteristic, complemented
61C2×#101×C103C2211yescharacteristic, complemented
62#410×C103C2211yescharacteristic, complemented
63#344×C103C2211yescharacteristic, complemented
64#344×C103C2211yescharacteristic, complemented
65#339×C103C2211yescharacteristic, complemented
66#338×C103C2211yescharacteristic, complemented
672−1+4×C103—22no—
682−1+4×C103—22no—
692−1+4×C103—21no—
702−1+4×C103—21no—
712−1+4×C103—22no—
722−1+4×C103—41no—
732−1+4×C103D412yes—
74H(5,𝔽2)×C103—21no—
75H(5,𝔽2)×C103—21no—
76H(5,𝔽2)×C103—41no—
77H(5,𝔽2)×C103D412yes—
78C2×#41×C103—22no—
79C2×#41×C103—22no—
80C2×#41×C103—21no—
81C2×#41×C103—21no—
82C2×#41×C103—41no—
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×Q8×C103C2311yescharacteristic
92#137×C103—24no—
93#137×C103—24no—
94#137×C103—24no—
95#137×C103—22no—
96#137×C103—22no—
97#137×C103—21no—
98#137×C103—22no—
99#137×C103—21no—
100#137×C103—21no—
101#137×C103—22no—
102#137×C103—22no—
103#137×C103—22no—
104#137×C103—22no—
105#137×C103—22no—
106#137×C103—22no—
107#137×C103—41no—
108#137×C103D412yes—
109AGL(1,ℤ/8)×C103—24no—
110AGL(1,ℤ/8)×C103—21no—
111AGL(1,ℤ/8)×C103—21no—
112AGL(1,ℤ/8)×C103—21no—
113AGL(1,ℤ/8)×C103D412yes—
114#135×C103—24no—
115#135×C103—24no—
116#135×C103—22no—
117#135×C103—22no—
118C2×Q16×C103—24no—
119C2×Q16×C103—21no—
120C2×Q16×C103—21no—
121C2×Q16×C103—21no—
122C2×Q16×C103—21no—
123C2×Q16×C103D412yes—
124C2×SD16×C103—24no—
125C2×SD16×C103—21no—
126C2×SD16×C103—21no—
127C2×SD16×C103—21no—
128C2×SD16×C103—21no—
129C2×SD16×C103D412yes—
130#131×C103—22no—
131#131×C103—22no—
132#131×C103—22no—
133#131×C103—41no—
134C2×M16×C103—22no—
135C2×M16×C103—22no—
136C2×M16×C103C2311yescharacteristic
137C2×M16×C103C2311yescharacteristic
138C2×M16×C103C2311yescharacteristic
139C2×M16×C103C2311yescharacteristic
140C2×M16×C103C2311yescharacteristic
141C2×M16×C103C2311yescharacteristic
142C4⋊Q8×C103—21no—
143C4⋊Q8×C103—22no—
144C4⋊Q8×C103—21no—
145C4⋊Q8×C103—21no—
146#124×C103—21no—
147#123×C103—41no—
148C22⋊Q8×C103—41no—
149C4×Q8×C103—21no—
150C4×D4×C103—21no—
151C4×D4×C103—41no—
152#117×C103—21no—
153#117×C103C2311yescharacteristic
154#117×C103C2311yescharacteristic
155C2×C4⋊C4×C103—41no—
156C2×C42×C103—21no—
157C2×C42×C103C2311yescharacteristic
158#108×C103—22no—
159C4⋊C8×C103—22no—
160#104×C103—22no—
161#104×C103—22no—
162#104×C103—22no—
163#104×C103—22no—
164#104×C103—21no—
165#104×C103—21no—
166#104×C103—21no—
167#104×C103—21no—
168#104×C103D412yes—
169#104×C103D412yes—
170#103×C103—22no—
171#103×C103—22no—
172#103×C103—41no—
173#101×C103—21no—
174#101×C103—21no—
175#101×C103—22no—
176#101×C103—22no—
177#100×C103—21no—
178#100×C103—21no—
179#99×C103—41no—
180#41×C103—21no—
181#41×C103—21no—
182#41×C103—21no—
183#41×C103—21no—
184#41×C103—24no—
185#41×C103—22no—
186#41×C103—22no—
187#41×C103—22no—
188#41×C103—22no—
189#41×C103—21no—
190#41×C103—21no—
191#41×C103—21no—
192#41×C103—21no—
193#41×C103—21no—
194#41×C103—21no—
195#41×C103—21no—
196#41×C103—21no—
197#41×C103—42no—
198#41×C103—42no—
199#41×C103—42no—
200#41×C103—42no—
201#41×C103—42no—
202#41×C103—44no—
203#41×C103—42no—
204#41×C103—41no—
205#41×C103—41no—
206#41×C103—44no—
207#41×C103—42no—
208#41×C103C2×D412yes—
209#41×C103C2×D412yes—
210#41×C103C2×D412yes—
211#41×C103C2×D412yes—
212C2×Q8×C103—21no—
213C2×Q8×C103—24no—
214C2×Q8×C103—22no—
215C2×Q8×C103—22no—
216C2×Q8×C103—21no—
217C2×Q8×C103—21no—
218C2×Q8×C103—21no—
219C2×Q8×C103—21no—
220C2×Q8×C103—21no—
221C2×Q8×C103—21no—
222C2×Q8×C103—21no—
223C2×Q8×C103—21no—
224C2×Q8×C103—21no—
225C2×Q8×C103—21no—
226C2×Q8×C103—41no—
227C2×Q8×C103—42no—
228C2×Q8×C103—42no—
229C2×Q8×C103—41no—
230C2×Q8×C103—42no—
231C2×Q8×C103C2×D411yescharacteristic
232C2×Q8×C103C2×D411yescharacteristic
233C2×Q8×C103C2×D412yes—
234C2×Q8×C103C2×D411yescharacteristic
235C2×Q8×C103#4111yescharacteristic
236C2×D4×C103—21no—
237C2×D4×C103—21no—
238C2×D4×C103—22no—
239C2×D4×C103—22no—
240C2×D4×C103—21no—
241C2×D4×C103—21no—
242C2×D4×C103—42no—
243C2×D4×C103—41no—
244C2×D4×C103—42no—
245C2×D4×C103—42no—
246C2×D4×C103—41no—
247C2×D4×C103C2×D411yescharacteristic
248C2×D4×C103C2×D411yescharacteristic
249C2×D4×C103C2×D411yescharacteristic
250C2×D4×C103#4111yescharacteristic
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—21no—
258C22×C4×C103—42no—
259C22×C4×C103—41no—
260C22×C4×C103—41no—
261C22×C4×C103—41no—
262C22×C4×C103C2411yescharacteristic
263Q16×C103—24no—
264Q16×C103—22no—
265Q16×C103—22no—
266Q16×C103—24no—
267Q16×C103—42no—
268Q16×C103—42no—
269Q16×C103—42no—
270SD16×C103—24no—
271SD16×C103—22no—
272SD16×C103—22no—
273SD16×C103—22no—
274SD16×C103—22no—
275SD16×C103—24no—
276SD16×C103—42no—
277SD16×C103—42no—
278SD16×C103—42no—
279D8×C103—22no—
280D8×C103—22no—
281M16×C103—24no—
282M16×C103—21no—
283M16×C103—21no—
284M16×C103—21no—
285M16×C103—21no—
286M16×C103—21no—
287M16×C103—21no—
288M16×C103—21no—
289M16×C103—21no—
290M16×C103—21no—
291M16×C103—21no—
292M16×C103—42no—
293M16×C103C2×D412yes—
294M16×C103C2×D412yes—
295C2×C8×C103—24no—
296C2×C8×C103—21no—
297C2×C8×C103—21no—
298C2×C8×C103—21no—
299C2×C8×C103—21no—
300C2×C8×C103—21no—
301C2×C8×C103—42no—
302C2×C8×C103C2×D412yes—
303C4⋊C4×C103—21no—
304C4⋊C4×C103—21no—
305C4⋊C4×C103—42no—
306C4⋊C4×C103—42no—
307C4⋊C4×C103—41no—
308C4⋊C4×C103—42no—
309C22⋊C4×C103—21no—
310C22⋊C4×C103—21no—
311C22⋊C4×C103—41no—
312C22⋊C4×C103—42no—
313C42×C103—21no—
314C42×C103—21no—
315C42×C103—21no—
316C42×C103—41no—
317C42×C103C2×D411yescharacteristic
318C42×C103C2×D411yescharacteristic
319C23×C103—21no—
320C23×C103—21no—
321C23×C103—21no—
322C23×C103—21no—
323C23×C103—42no—
324C23×C103H(5,𝔽2)11yescharacteristic
325Q8×C103—21no—
326Q8×C103—21no—
327Q8×C103—21no—
328Q8×C103—22no—
329Q8×C103—21no—
330Q8×C103—21no—
331Q8×C103—21no—
332Q8×C103—22no—
333Q8×C103—42no—
334Q8×C103—44no—
335Q8×C103—41no—
336Q8×C103—41no—
337Q8×C103—41no—
338Q8×C103—41no—
339Q8×C103—41no—
340Q8×C103—41no—
341Q8×C103#12012yes—
342Q8×C103#12112yes—
343D4×C103—22no—
344D4×C103—22no—
345D4×C103—22no—
346D4×C103—22no—
347D4×C103—21no—
348D4×C103—21no—
349D4×C103—21no—
350D4×C103—21no—
351D4×C103—21no—
352D4×C103—21no—
353D4×C103—42no—
354D4×C103—42no—
355D4×C103—42no—
356D4×C103—44no—
357D4×C103—41no—
358D4×C103—41no—
359D4×C103—41no—
360D4×C103—41no—
361D4×C103#12012yes—
362D4×C103#12112yes—
363C2×C4×C103—21no—
364C2×C4×C103—21no—
365C2×C4×C103—21no—
366C2×C4×C103—22no—
367C2×C4×C103—22no—
368C2×C4×C103—22no—
369C2×C4×C103—22no—
370C2×C4×C103—21no—
371C2×C4×C103—21no—
372C2×C4×C103—22no—
373C2×C4×C103—21no—
374C2×C4×C103—42no—
375C2×C4×C103—42no—
376C2×C4×C103—42no—
377C2×C4×C103—42no—
378C2×C4×C103—44no—
379C2×C4×C103—44no—
380C2×C4×C103—41no—
381C2×C4×C103—41no—
382C2×C4×C103—41no—
383C2×C4×C103—41no—
384C2×C4×C103—41no—
385C2×C4×C103—41no—
386C2×C4×C103—41no—
387C2×C4×C103—41no—
388C2×C4×C103—41no—
389C2×C4×C103—41no—
390C2×C4×C103—41no—
391C2×C4×C103—82no—
392C2×C4×C103C22×D411yescharacteristic
393C2×C4×C103C22×D411yescharacteristic
394C2×C4×C103C22×D411yescharacteristic
395C2×C4×C103C22×D411yescharacteristic
396C2×C4×C103C2×#4111yescharacteristic
397C2×C4×C103H(5,𝔽2)11yescharacteristic
398C8×C103—22no—
399C8×C103—22no—
400C8×C103—22no—
401C8×C103—41no—
402C8×C103—41no—
403C8×C103—41no—
404C22×C103—22no—
405C22×C103—22no—
406C22×C103—41no—
407C22×C103—41no—
408C22×C103—41no—
409C22×C103—81no—
410C22×C103—81no—
411C22×C103—81no—
412C22×C103—81no—
413C22×C103—162no—
414C22×C103#53411yescharacteristic
415C22×C103D4211yescharacteristic
416C22×C103#54611yescharacteristic
417C4×C103—22no—
418C4×C103—22no—
419C4×C103—22no—
420C4×C103—41no—
421C4×C103—41no—
422C4×C103—42no—
423C4×C103—41no—
424C4×C103—81no—
425C4×C103—81no—
426C4×C103—81no—
427C4×C103C2×#12011yescharacteristic
428C4×C103C2×#12111yescharacteristic
429C4×C103D4211yescharacteristic
430C4×C103#54611yescharacteristic
431#24474C10311yesmaximal, characteristic, direct product factor, Sylow
432C2×C103—21no—
433C2×C103—21no—
434C2×C103—21no—
435C2×C103—42no—
436C2×C103—42no—
437C2×C103—81no—
438C2×C103—81no—
439C2×C103#241011yescharacteristic
440#3586C2×C10311yescharacteristic
441#3069C2×C10311yescharacteristic, complemented
442#3039C2×C10311yescharacteristic, complemented
443#3022C2×C10311yescharacteristic, complemented
444C2×#456C2×C10311yescharacteristic, complemented
445#2901C2×C10311yescharacteristic, complemented
446#2050C2×C10311yescharacteristic, complemented
447#2049C2×C10311yescharacteristic, complemented
448#2009C2×C10311yescharacteristic, complemented
449#2005C2×C10311yescharacteristic, complemented
450#1906C2×C10311yescharacteristic, complemented
451#1902C2×C10311yescharacteristic, complemented
452#1902C2×C10311yescharacteristic, complemented
453#1861C2×C10311yescharacteristic, complemented
454#1796C2×C10311yescharacteristic, complemented
455C103#2447411yescharacteristic, direct product factor, Sylow
456#585C22×C10311yescharacteristic
457C2×2−1+4C22×C10311yescharacteristic
458#578—22no—
459#578—22no—
460#577—22no—
461#577—22no—
462#575—22no—
463#575C22×C10311yescharacteristic
464#575C22×C10311yescharacteristic
465C2×#137—22no—
466C2×#137C22×C10311yescharacteristic
467C2×#137C22×C10311yescharacteristic
468C2×#137C22×C10311yescharacteristic
469C2×#137C22×C10311yescharacteristic
470C2×#137C22×C10311yescharacteristic, complemented
471#568C22×C10311yescharacteristic
472#568C22×C10311yescharacteristic
473#536C22×C10311yescharacteristic
474C2×C4⋊Q8C22×C10311yescharacteristic, complemented
475C4×#41C22×C10311yescharacteristic
476#473—22no—
477#471—22no—
478#462—22no—
479#461—22no—
480#456—22no—
481#456—22no—
482#456—22no—
483#455—22no—
484#430C22×C10311yescharacteristic, complemented
485#423C22×C10311yescharacteristic, complemented
486#421—22no—
487#421C22×C10311yescharacteristic
488#421C22×C10311yescharacteristic
489#421C22×C10311yescharacteristic
490#421C22×C10311yescharacteristic
491C2×#104—22no—
492C2×#104C22×C10311yescharacteristic
493C2×#104C22×C10311yescharacteristic
494C2×#104C22×C10311yescharacteristic, complemented
495#419C22×C10311yescharacteristic, complemented
496#419C22×C10311yescharacteristic, complemented
497#419C22×C10311yescharacteristic, complemented
498#413C22×C10311yescharacteristic
499#413C22×C10311yescharacteristic, complemented
500C2×#101C22×C10311yescharacteristic, complemented
501C2×#101C22×C10311yescharacteristic, complemented
502#410C22×C10311yescharacteristic, complemented
503#344C22×C10311yescharacteristic, complemented
504#344C22×C10311yescharacteristic, complemented
505#339C22×C10311yescharacteristic, complemented
506#338C22×C10311yescharacteristic, complemented
5072−1+4—22no—
5082−1+4—22no—
5092−1+4—21no—
5102−1+4—21no—
5112−1+4—22no—
5122−1+4—41no—
5132−1+4D4×C10312yes—
514H(5,𝔽2)—21no—
515H(5,𝔽2)—21no—
516H(5,𝔽2)—41no—
517H(5,𝔽2)D4×C10312yes—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C10311yescharacteristic
525C2×#41C23×C10311yescharacteristic
526C2×#41C23×C10311yescharacteristic
527C2×#41C23×C10311yescharacteristic
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C10311yescharacteristic
531C22×Q8C23×C10311yescharacteristic
532#137—24no—
533#137—24no—
534#137—24no—
535#137—22no—
536#137—22no—
537#137—21no—
538#137—22no—
539#137—21no—
540#137—21no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—41no—
548#137D4×C10312yes—
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)D4×C10312yes—
554#135—24no—
555#135—24no—
556#135—22no—
557#135—22no—
558C2×Q16—24no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C10312yes—
564C2×SD16—24no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16D4×C10312yes—
570#131—22no—
571#131—22no—
572#131—22no—
573#131—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16C23×C10311yescharacteristic
577C2×M16C23×C10311yescharacteristic
578C2×M16C23×C10311yescharacteristic
579C2×M16C23×C10311yescharacteristic
580C2×M16C23×C10311yescharacteristic
581C2×M16C23×C10311yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586#124—21no—
587#123—41no—
588C22⋊Q8—41no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C10311yescharacteristic
594#117C23×C10311yescharacteristic
595C2×C4⋊C4—41no—
596C2×C42—21no—
597C2×C42C23×C10311yescharacteristic
598#108—22no—
599C4⋊C8—22no—
600#104—22no—
601#104—22no—
602#104—22no—
603#104—22no—
604#104—21no—
605#104—21no—
606#104—21no—
607#104—21no—
608#104D4×C10312yes—
609#104D4×C10312yes—
610#103—22no—
611#103—22no—
612#103—41no—
613#101—21no—
614#101—21no—
615#101—22no—
616#101—22no—
617#100—21no—
618#100—21no—
619#99—41no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—24no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—41no—
645#41—41no—
646#41—44no—
647#41—42no—
648#41C2×D4×C10312yes—
649#41C2×D4×C10312yes—
650#41C2×D4×C10312yes—
651#41C2×D4×C10312yes—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—41no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8C2×D4×C10311yescharacteristic
672C2×Q8C2×D4×C10311yescharacteristic
673C2×Q8C2×D4×C10312yes—
674C2×Q8C2×D4×C10311yescharacteristic
675C2×Q8#41×C10311yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4C2×D4×C10311yescharacteristic
688C2×D4C2×D4×C10311yescharacteristic
689C2×D4C2×D4×C10311yescharacteristic
690C2×D4#41×C10311yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C10311yescharacteristic
703Q16—24no—
704Q16—22no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710SD16—24no—
711SD16—22no—
712SD16—22no—
713SD16—22no—
714SD16—22no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719D8—22no—
720D8—22no—
721M16—24no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—42no—
733M16C2×D4×C10312yes—
734M16C2×D4×C10312yes—
735C2×C8—24no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—42no—
742C2×C8C2×D4×C10312yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—42no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—41no—
757C42C2×D4×C10311yescharacteristic
758C42C2×D4×C10311yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—42no—
764C23H(5,𝔽2)×C10311yescharacteristic
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—21no—
771Q8—21no—
772Q8—22no—
773Q8—42no—
774Q8—44no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C10312yes—
782Q8#121×C10312yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4#120×C10312yes—
802D4#121×C10312yes—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—82no—
832C2×C4C22×D4×C10311yescharacteristic
833C2×C4C22×D4×C10311yescharacteristic
834C2×C4C22×D4×C10311yescharacteristic
835C2×C4C22×D4×C10311yescharacteristic
836C2×C4C2×#41×C10311yescharacteristic
837C2×C4H(5,𝔽2)×C10311yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—162no—
854C22#534×C10311yescharacteristic
855C22D42×C10311yescharacteristic
856C22#546×C10311yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4C2×#120×C10311yescharacteristic
868C4C2×#121×C10311yescharacteristic
869C4D42×C10311yescharacteristic
870C4#546×C10311yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—42no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2C103×#241011yescharacteristic
subgroupG/H
center, socleC2×C103#2410
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3586C2
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
2. C103×#3069C2semidirect
3. C103×#3039C2semidirect
4. C103×#3022C2semidirect
5. C2×#456×C103C2semidirect
6. C103×#2901C2semidirect
7. C103×#2050C2semidirect
8. C103×#2049C2semidirect
9. C103×#2009C2semidirect
10. C103×#2005C2semidirect
11. C103×#1906C2semidirect
12. C103×#1902C2semidirect
13. C103×#1902C2semidirect
14. C103×#1861C2semidirect
15. C103×#1796C2semidirect
30. C2×#137×C103C22semidirect
34. C2×C4⋊Q8×C103C22semidirect
44. #430×C103C22semidirect
45. #423×C103C22semidirect
54. C2×#104×C103C22semidirect
55. #419×C103C22semidirect
56. #419×C103C22semidirect
57. #419×C103C22semidirect
59. #413×C103C22semidirect
60. C2×#101×C103C22semidirect
61. C2×#101×C103C22semidirect
62. #410×C103C22semidirect
63. #344×C103C22semidirect
64. #344×C103C22semidirect
65. #339×C103C22semidirect
66. #338×C103C22semidirect
431. #24474C103direct (N × H)
441. #3069C2×C103semidirect
442. #3039C2×C103semidirect
443. #3022C2×C103semidirect
444. C2×#456C2×C103semidirect
445. #2901C2×C103semidirect
446. #2050C2×C103semidirect
447. #2049C2×C103semidirect
448. #2009C2×C103semidirect
449. #2005C2×C103semidirect
450. #1906C2×C103semidirect
451. #1902C2×C103semidirect
452. #1902C2×C103semidirect
453. #1861C2×C103semidirect
454. #1796C2×C103semidirect
455. C103#24474direct (N × H)
470. C2×#137C22×C103semidirect
474. C2×C4⋊Q8C22×C103semidirect
484. #430C22×C103semidirect
485. #423C22×C103semidirect
494. C2×#104C22×C103semidirect
495. #419C22×C103semidirect
496. #419C22×C103semidirect
497. #419C22×C103semidirect
499. #413C22×C103semidirect
500. C2×#101C22×C103semidirect
501. C2×#101C22×C103semidirect
502. #410C22×C103semidirect
503. #344C22×C103semidirect
504. #344C22×C103semidirect
505. #339C22×C103semidirect
506. #338C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35862
C103×#30692
C103×#30392
C103×#30222
C2×#456×C1032
C103×#29012
C103×#20502
C103×#20492
C103×#20092
C103×#20052
C103×#19062
C103×#19022
C103×#18612
C103×#17962
#24474103