Finite Group Databasebeta

← C103×#23878 #39929153

Subgroups — C103×#23878 #39929153

Order 26368.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C103C211yesmaximal, characteristic, complemented
2C103×#3488C211yesmaximal, characteristic, complemented
3C2×#455×C103C211yesmaximal, characteristic, complemented
4C2×#453×C103C211yesmaximal, characteristic, complemented
5C103×#3005C211yesmaximal, characteristic, complemented
6C103×#2431C211yesmaximal, characteristic, complemented
7C103×#2007C211yesmaximal, characteristic, complemented
8C103×#2006C211yesmaximal, characteristic, complemented
9C103×#2004C211yesmaximal, characteristic, complemented
10C103×#2002C211yesmaximal, characteristic, complemented
11C103×#1900C211yesmaximal, characteristic, complemented
12C103×#1883C211yesmaximal, characteristic, complemented
13C103×#1882C211yesmaximal, characteristic, complemented
14C103×#1871C211yesmaximal, characteristic, complemented
15C103×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic
18C22×#41×C103C2211yescharacteristic, complemented
19#575×C103—24no—
20#575×C103—24no—
21C2×#137×C103—21no—
22C2×#137×C103C2211yescharacteristic
23C2×#137×C103C2211yescharacteristic, complemented
24C2×#137×C103C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C103—21no—
26C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C103C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C103C2211yescharacteristic, complemented
29C2×#135×C103—21no—
30C2×#135×C103—21no—
31C22×M16×C103C2211yescharacteristic, complemented
32#550×C103—21no—
33#548×C103—21no—
34#546×C103—21no—
35#546×C103—22no—
36D42×C103—22no—
37D42×C103—21no—
38#537×C103—21no—
39#537×C103C2211yescharacteristic
40#535×C103—21no—
41#535×C103C2211yescharacteristic
42C2×#127×C103C2211yescharacteristic, complemented
43C2×#124×C103C2211yescharacteristic, complemented
44#525×C103—21no—
45#525×C103C2211yescharacteristic
46C2×#121×C103—21no—
47C2×#121×C103C2211yescharacteristic
48#520×C103C2211yescharacteristic
49#455×C103—24no—
50#453×C103—24no—
51#452×C103—21no—
52#452×C103—21no—
53#449×C103—21no—
54#449×C103—21no—
55C2×#104×C103C2211yescharacteristic
56C2×#104×C103C2211yescharacteristic
57C2×#104×C103C2211yescharacteristic, complemented
58C2×#104×C103C2211yescharacteristic, complemented
59C2×#104×C103C2211yescharacteristic, complemented
60C2×#104×C103C2211yescharacteristic, complemented
61#419×C103C2211yescharacteristic, complemented
62#418×C103C2211yescharacteristic, complemented
63C2×#100×C103C2211yescharacteristic, complemented
64C2×#100×C103C2211yescharacteristic, complemented
65#407×C103C2211yescharacteristic, complemented
66#392×C103—22no—
67#391×C103C2211yescharacteristic, complemented
68#390×C103C2211yescharacteristic, complemented
69#386×C103—22no—
70C4×C22⋊C4×C103C2211yescharacteristic, complemented
71#343×C103C2211yescharacteristic, complemented
72#343×C103C2211yescharacteristic, complemented
73#339×C103C2211yescharacteristic, complemented
74#339×C103C2211yescharacteristic, complemented
75H(5,𝔽2)×C103—22no—
76H(5,𝔽2)×C103—22no—
77H(5,𝔽2)×C103—41no—
78H(5,𝔽2)×C103—41no—
79C2×#41×C103—21no—
80C2×#41×C103—21no—
81C2×#41×C103—21no—
82C2×#41×C103—21no—
83C2×#41×C103—22no—
84C2×#41×C103—22no—
85C2×#41×C103—22no—
86C2×#41×C103—22no—
87C2×#41×C103—21no—
88C2×#41×C103—21no—
89C2×#41×C103—21no—
90C2×#41×C103—21no—
91C2×#41×C103—41no—
92C2×#41×C103—41no—
93C2×#41×C103—41no—
94C2×#41×C103—41no—
95C2×#41×C103D411yescharacteristic, complemented
96C2×#41×C103D411yescharacteristic, complemented
97C2×#41×C103C2311yescharacteristic
98C2×#41×C103C2311yescharacteristic
99C2×#41×C103C2311yescharacteristic
100C22×Q8×C103D411yescharacteristic, complemented
101C22×Q8×C103C2311yescharacteristic
102C22×D4×C103—21no—
103C22×D4×C103—22no—
104C22×D4×C103—22no—
105C22×D4×C103—21no—
106C22×D4×C103—21no—
107C22×D4×C103—21no—
108C22×D4×C103—22no—
109C22×D4×C103D412yes—
110C22×D4×C103D411yescharacteristic, complemented
111C22×D4×C103C2311yescharacteristic
112C22×D4×C103C2311yescharacteristic
113C23×C4×C103—21no—
114C23×C4×C103—21no—
115C23×C4×C103C2311yescharacteristic
116#137×C103—28no—
117#137×C103—22no—
118#137×C103—22no—
119#137×C103—22no—
120#137×C103—22no—
121#137×C103—41no—
122#137×C103D414yescomplemented
123AGL(1,ℤ/8)×C103—28no—
124AGL(1,ℤ/8)×C103—22no—
125AGL(1,ℤ/8)×C103—22no—
126AGL(1,ℤ/8)×C103—22no—
127AGL(1,ℤ/8)×C103—22no—
128AGL(1,ℤ/8)×C103—41no—
129AGL(1,ℤ/8)×C103D414yescomplemented
130#135×C103—28no—
131#135×C103—28no—
132C2×Q16×C103—21no—
133C2×Q16×C103—21no—
134C2×Q16×C103—21no—
135C2×SD16×C103—21no—
136C2×SD16×C103—21no—
137C2×SD16×C103—21no—
138C2×SD16×C103—21no—
139C2×SD16×C103—21no—
140C2×SD16×C103—21no—
141C2×D8×C103—21no—
142C2×D8×C103—21no—
143C2×D8×C103—21no—
144C2×M16×C103—21no—
145C2×M16×C103—22no—
146C2×M16×C103—22no—
147C2×M16×C103C2311yescharacteristic
148C2×M16×C103C2311yescharacteristic
149C2×M16×C103C2311yescharacteristic
150C2×M16×C103C2311yescharacteristic
151C22×C8×C103—21no—
152#127×C103—22no—
153#127×C103—21no—
154#127×C103—22no—
155#127×C103—41no—
156#124×C103—22no—
157#124×C103—21no—
158#124×C103—22no—
159#124×C103—41no—
160#123×C103—22no—
161#123×C103—21no—
162C22⋊Q8×C103—22no—
163C22⋊Q8×C103—21no—
164C22⋊Q8×C103—21no—
165C22⋊Q8×C103D411yescharacteristic, complemented
166C22⋊Q8×C103D411yescharacteristic, complemented
167#121×C103—22no—
168#121×C103—22no—
169#121×C103—22no—
170#121×C103—22no—
171#121×C103—22no—
172#121×C103—21no—
173#121×C103—21no—
174#121×C103—21no—
175#121×C103—21no—
176#121×C103—21no—
177#121×C103—21no—
178#121×C103—22no—
179#121×C103—21no—
180#121×C103—21no—
181#121×C103D411yescharacteristic, complemented
182#121×C103D411yescharacteristic, complemented
183#120×C103—22no—
184#120×C103—22no—
185#120×C103—22no—
186#120×C103—21no—
187#120×C103—22no—
188C4×Q8×C103—21no—
189C4×D4×C103—22no—
190C4×D4×C103—22no—
191C4×D4×C103—21no—
192C4×D4×C103—22no—
193C4×D4×C103—21no—
194C4×D4×C103—21no—
195#117×C103—21no—
196#117×C103C2311yescharacteristic
197C2×C4⋊C4×C103—21no—
198C2×C4⋊C4×C103C2311yescharacteristic
199C2×C22⋊C4×C103—22no—
200C2×C22⋊C4×C103—21no—
201C2×C22⋊C4×C103—22no—
202C2×C22⋊C4×C103—22no—
203C2×C22⋊C4×C103D412yes—
204C2×C42×C103C2311yescharacteristic
205C2×C42×C103C2311yescharacteristic
206#104×C103—22no—
207#104×C103—22no—
208#104×C103—22no—
209#104×C103—22no—
210#104×C103—41no—
211#104×C103—41no—
212#103×C103—21no—
213#103×C103—21no—
214#102×C103—21no—
215#102×C103—21no—
216#100×C103—22no—
217#100×C103—22no—
218C22⋊C8×C103—21no—
219C22⋊C8×C103—21no—
220#95×C103—21no—
221#95×C103—22no—
222C24×C103—22no—
223C24×C103—21no—
224C24×C103—21no—
225C24×C103C2×D412yes—
226C24×C103C2×D411yescharacteristic
227#41×C103—21no—
228#41×C103—21no—
229#41×C103—24no—
230#41×C103—24no—
231#41×C103—22no—
232#41×C103—22no—
233#41×C103—21no—
234#41×C103—21no—
235#41×C103—21no—
236#41×C103—21no—
237#41×C103—21no—
238#41×C103—21no—
239#41×C103—21no—
240#41×C103—21no—
241#41×C103—42no—
242#41×C103—42no—
243#41×C103—41no—
244#41×C103—41no—
245#41×C103—42no—
246#41×C103—42no—
247#41×C103—42no—
248#41×C103—42no—
249#41×C103—42no—
250#41×C103—42no—
251#41×C103—42no—
252#41×C103—42no—
253#41×C103—42no—
254#41×C103—42no—
255#41×C103—42no—
256#41×C103—42no—
257#41×C103C2×D412yes—
258#41×C103C2×D412yes—
259C2×Q8×C103—21no—
260C2×Q8×C103—21no—
261C2×Q8×C103—22no—
262C2×Q8×C103—21no—
263C2×Q8×C103—21no—
264C2×Q8×C103—21no—
265C2×Q8×C103—21no—
266C2×Q8×C103—41no—
267C2×Q8×C103C2×D411yescharacteristic
268C2×Q8×C103C2×D411yescharacteristic
269C2×Q8×C103C2×D411yescharacteristic
270C2×Q8×C103C2×D412yescomplemented
271C2×D4×C103—21no—
272C2×D4×C103—22no—
273C2×D4×C103—22no—
274C2×D4×C103—22no—
275C2×D4×C103—22no—
276C2×D4×C103—21no—
277C2×D4×C103—21no—
278C2×D4×C103—21no—
279C2×D4×C103—21no—
280C2×D4×C103—21no—
281C2×D4×C103—22no—
282C2×D4×C103—22no—
283C2×D4×C103—22no—
284C2×D4×C103—21no—
285C2×D4×C103—22no—
286C2×D4×C103—21no—
287C2×D4×C103—21no—
288C2×D4×C103—21no—
289C2×D4×C103—21no—
290C2×D4×C103—21no—
291C2×D4×C103—21no—
292C2×D4×C103—21no—
293C2×D4×C103—21no—
294C2×D4×C103—21no—
295C2×D4×C103—21no—
296C2×D4×C103—21no—
297C2×D4×C103—21no—
298C2×D4×C103—41no—
299C2×D4×C103—42no—
300C2×D4×C103—42no—
301C2×D4×C103—42no—
302C2×D4×C103—44no—
303C2×D4×C103—42no—
304C2×D4×C103—42no—
305C2×D4×C103—44no—
306C2×D4×C103—44no—
307C2×D4×C103—42no—
308C2×D4×C103—42no—
309C2×D4×C103—41no—
310C2×D4×C103—41no—
311C2×D4×C103—42no—
312C2×D4×C103—44no—
313C2×D4×C103—82no—
314C2×D4×C103—82no—
315C2×D4×C103—84no—
316C2×D4×C103C2×D411yescharacteristic
317C2×D4×C103C2×D411yescharacteristic
318C2×D4×C103C2×D411yescharacteristic
319C2×D4×C103C2×D412yescomplemented
320C22×C4×C103—21no—
321C22×C4×C103—21no—
322C22×C4×C103—21no—
323C22×C4×C103—21no—
324C22×C4×C103—21no—
325C22×C4×C103—22no—
326C22×C4×C103—21no—
327C22×C4×C103—21no—
328C22×C4×C103—21no—
329C22×C4×C103—22no—
330C22×C4×C103—21no—
331C22×C4×C103—21no—
332C22×C4×C103—21no—
333C22×C4×C103—21no—
334C22×C4×C103—21no—
335C22×C4×C103—42no—
336C22×C4×C103—42no—
337C22×C4×C103—42no—
338C22×C4×C103—42no—
339C22×C4×C103—41no—
340C22×C4×C103—41no—
341C22×C4×C103C2×D411yescharacteristic
342C22×C4×C103C2×D411yescharacteristic
343C22×C4×C103C2×D411yescharacteristic
344C22×C4×C103C2×D411yescharacteristic
345C22×C4×C103C2×D411yescharacteristic
346C22×C4×C103C2×D412yes—
347C22×C4×C103C2411yescharacteristic
348Q16×C103—24no—
349Q16×C103—24no—
350Q16×C103—42no—
351SD16×C103—24no—
352SD16×C103—24no—
353SD16×C103—24no—
354SD16×C103—24no—
355SD16×C103—42no—
356SD16×C103—42no—
357D8×C103—24no—
358D8×C103—24no—
359D8×C103—42no—
360M16×C103—24no—
361M16×C103—21no—
362M16×C103—21no—
363M16×C103—21no—
364M16×C103—21no—
365M16×C103—21no—
366M16×C103—21no—
367M16×C103C2×D412yescomplemented
368M16×C103C2×D412yescomplemented
369C2×C8×C103—24no—
370C2×C8×C103—21no—
371C2×C8×C103—21no—
372C2×C8×C103—21no—
373C2×C8×C103—21no—
374C4⋊C4×C103—22no—
375C4⋊C4×C103—22no—
376C4⋊C4×C103—21no—
377C4⋊C4×C103—21no—
378C4⋊C4×C103—21no—
379C4⋊C4×C103—21no—
380C4⋊C4×C103C2×D411yescharacteristic
381C4⋊C4×C103C2×D411yescharacteristic
382C22⋊C4×C103—22no—
383C22⋊C4×C103—22no—
384C22⋊C4×C103—22no—
385C22⋊C4×C103—22no—
386C22⋊C4×C103—22no—
387C22⋊C4×C103—21no—
388C22⋊C4×C103—21no—
389C22⋊C4×C103—21no—
390C22⋊C4×C103—21no—
391C22⋊C4×C103—22no—
392C22⋊C4×C103—22no—
393C22⋊C4×C103—21no—
394C22⋊C4×C103—44no—
395C22⋊C4×C103—42no—
396C22⋊C4×C103—82no—
397C42×C103—22no—
398C42×C103—21no—
399C42×C103—21no—
400C42×C103—21no—
401C42×C103—21no—
402C42×C103—21no—
403C23×C103—21no—
404C23×C103—21no—
405C23×C103—21no—
406C23×C103—22no—
407C23×C103—21no—
408C23×C103—21no—
409C23×C103—22no—
410C23×C103—22no—
411C23×C103—22no—
412C23×C103—41no—
413C23×C103—41no—
414C23×C103—42no—
415C23×C103—42no—
416C23×C103—42no—
417C23×C103—42no—
418C23×C103—44no—
419C23×C103—42no—
420C23×C103—42no—
421C23×C103—41no—
422C23×C103—41no—
423C23×C103—81no—
424C23×C103—82no—
425C23×C103—82no—
426C23×C103#12011yescharacteristic
427C23×C103#12011yescharacteristic
428C23×C103C22×D411yescharacteristic
429Q8×C103—21no—
430Q8×C103—21no—
431Q8×C103—22no—
432Q8×C103—21no—
433Q8×C103—21no—
434Q8×C103—22no—
435Q8×C103—21no—
436Q8×C103—42no—
437Q8×C103—41no—
438Q8×C103—41no—
439Q8×C103#12012yes—
440D4×C103—22no—
441D4×C103—22no—
442D4×C103—21no—
443D4×C103—22no—
444D4×C103—21no—
445D4×C103—21no—
446D4×C103—21no—
447D4×C103—22no—
448D4×C103—21no—
449D4×C103—42no—
450D4×C103—42no—
451D4×C103—44no—
452D4×C103—42no—
453D4×C103—44no—
454D4×C103—44no—
455D4×C103—42no—
456D4×C103—44no—
457D4×C103—44no—
458D4×C103—41no—
459D4×C103—41no—
460D4×C103—41no—
461D4×C103—41no—
462D4×C103—41no—
463D4×C103—41no—
464D4×C103—41no—
465D4×C103—41no—
466D4×C103—41no—
467D4×C103—41no—
468D4×C103—81no—
469D4×C103—82no—
470D4×C103—82no—
471D4×C103—82no—
472D4×C103—82no—
473D4×C103—88no—
474D4×C103#12012yes—
475C2×C4×C103—21no—
476C2×C4×C103—21no—
477C2×C4×C103—21no—
478C2×C4×C103—21no—
479C2×C4×C103—21no—
480C2×C4×C103—21no—
481C2×C4×C103—21no—
482C2×C4×C103—21no—
483C2×C4×C103—21no—
484C2×C4×C103—21no—
485C2×C4×C103—21no—
486C2×C4×C103—22no—
487C2×C4×C103—22no—
488C2×C4×C103—22no—
489C2×C4×C103—21no—
490C2×C4×C103—22no—
491C2×C4×C103—21no—
492C2×C4×C103—21no—
493C2×C4×C103—21no—
494C2×C4×C103—22no—
495C2×C4×C103—42no—
496C2×C4×C103—42no—
497C2×C4×C103—42no—
498C2×C4×C103—44no—
499C2×C4×C103—44no—
500C2×C4×C103—44no—
501C2×C4×C103—41no—
502C2×C4×C103—41no—
503C2×C4×C103—41no—
504C2×C4×C103—41no—
505C2×C4×C103—41no—
506C2×C4×C103—41no—
507C2×C4×C103—41no—
508C2×C4×C103—41no—
509C2×C4×C103—42no—
510C2×C4×C103—41no—
511C2×C4×C103—41no—
512C2×C4×C103—41no—
513C2×C4×C103—82no—
514C2×C4×C103#12011yescharacteristic
515C2×C4×C103#12011yescharacteristic
516C2×C4×C103C22×D411yescharacteristic
517C2×C4×C103C22×D411yescharacteristic
518C2×C4×C103C22×D411yescharacteristic
519C2×C4×C103C22×D411yescharacteristic
520C2×C4×C103H(5,𝔽2)11yescharacteristic
521C2×C4×C103H(5,𝔽2)11yescharacteristic
522C8×C103—22no—
523C8×C103—22no—
524C8×C103—41no—
525C8×C103—41no—
526C22×C103—21no—
527C22×C103—21no—
528C22×C103—21no—
529C22×C103—21no—
530C22×C103—22no—
531C22×C103—21no—
532C22×C103—21no—
533C22×C103—21no—
534C22×C103—21no—
535C22×C103—44no—
536C22×C103—41no—
537C22×C103—41no—
538C22×C103—41no—
539C22×C103—42no—
540C22×C103—41no—
541C22×C103—42no—
542C22×C103—41no—
543C22×C103—42no—
544C22×C103—41no—
545C22×C103—42no—
546C22×C103—41no—
547C22×C103—41no—
548C22×C103—81no—
549C22×C103—81no—
550C22×C103—82no—
551C22×C103—82no—
552C22×C103—82no—
553C22×C103—84no—
554C22×C103—81no—
555C22×C103—81no—
556C22×C103—164no—
557C22×C103C2×#12011yescharacteristic
558C22×C103D4211yescharacteristic
559C22×C103D4211yescharacteristic
560C4×C103—21no—
561C4×C103—21no—
562C4×C103—22no—
563C4×C103—42no—
564C4×C103—41no—
565C4×C103—41no—
566C4×C103—42no—
567C4×C103—41no—
568C4×C103—42no—
569C4×C103—41no—
570C4×C103—81no—
571C4×C103C2×#12011yescharacteristic
572C4×C103#53411yescharacteristic
573C4×C103D4211yescharacteristic
574C4×C103D4211yescharacteristic
575#23878C10311yesmaximal, characteristic, direct product factor, Sylow
576C2×C103—21no—
577C2×C103—21no—
578C2×C103—41no—
579C2×C103—41no—
580C2×C103—42no—
581C2×C103—82no—
582C2×C103—81no—
583C2×C103—82no—
584C2×C103—81no—
585C2×C103#240311yescharacteristic
586C2×C103#301811yescharacteristic
587C2×C103#301911yescharacteristic
588C2×#575C2×C10311yescharacteristic, complemented
589#3488C2×C10311yescharacteristic, complemented
590C2×#455C2×C10311yescharacteristic, complemented
591C2×#453C2×C10311yescharacteristic, complemented
592#3005C2×C10311yescharacteristic, complemented
593#2431C2×C10311yescharacteristic, complemented
594#2007C2×C10311yescharacteristic, complemented
595#2006C2×C10311yescharacteristic, complemented
596#2004C2×C10311yescharacteristic, complemented
597#2002C2×C10311yescharacteristic, complemented
598#1900C2×C10311yescharacteristic, complemented
599#1883C2×C10311yescharacteristic, complemented
600#1882C2×C10311yescharacteristic, complemented
601#1871C2×C10311yescharacteristic, complemented
602#1789C2×C10311yescharacteristic, complemented
603C103#2387811yescharacteristic, direct product factor, Sylow
604C2×H(5,𝔽2)C22×C10311yescharacteristic
605C22×#41C22×C10311yescharacteristic
606C22×#41C22×C10311yescharacteristic, complemented
607#575—24no—
608#575—24no—
609C2×#137—21no—
610C2×#137C22×C10311yescharacteristic
611C2×#137C22×C10311yescharacteristic, complemented
612C2×#137C22×C10311yescharacteristic, complemented
613C2×AGL(1,ℤ/8)—21no—
614C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
615C2×AGL(1,ℤ/8)C22×C10311yescharacteristic, complemented
616C2×AGL(1,ℤ/8)C22×C10311yescharacteristic, complemented
617C2×#135—21no—
618C2×#135—21no—
619C22×M16C22×C10311yescharacteristic, complemented
620#550—21no—
621#548—21no—
622#546—21no—
623#546—22no—
624D42—22no—
625D42—21no—
626#537—21no—
627#537C22×C10311yescharacteristic
628#535—21no—
629#535C22×C10311yescharacteristic
630C2×#127C22×C10311yescharacteristic, complemented
631C2×#124C22×C10311yescharacteristic, complemented
632#525—21no—
633#525C22×C10311yescharacteristic
634C2×#121—21no—
635C2×#121C22×C10311yescharacteristic
636#520C22×C10311yescharacteristic
637#455—24no—
638#453—24no—
639#452—21no—
640#452—21no—
641#449—21no—
642#449—21no—
643C2×#104C22×C10311yescharacteristic
644C2×#104C22×C10311yescharacteristic
645C2×#104C22×C10311yescharacteristic, complemented
646C2×#104C22×C10311yescharacteristic, complemented
647C2×#104C22×C10311yescharacteristic, complemented
648C2×#104C22×C10311yescharacteristic, complemented
649#419C22×C10311yescharacteristic, complemented
650#418C22×C10311yescharacteristic, complemented
651C2×#100C22×C10311yescharacteristic, complemented
652C2×#100C22×C10311yescharacteristic, complemented
653#407C22×C10311yescharacteristic, complemented
654#392—22no—
655#391C22×C10311yescharacteristic, complemented
656#390C22×C10311yescharacteristic, complemented
657#386—22no—
658C4×C22⋊C4C22×C10311yescharacteristic, complemented
659#343C22×C10311yescharacteristic, complemented
660#343C22×C10311yescharacteristic, complemented
661#339C22×C10311yescharacteristic, complemented
662#339C22×C10311yescharacteristic, complemented
663H(5,𝔽2)—22no—
664H(5,𝔽2)—22no—
665H(5,𝔽2)—41no—
666H(5,𝔽2)—41no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—21no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—22no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—21no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41—41no—
683C2×#41D4×C10311yescharacteristic, complemented
684C2×#41D4×C10311yescharacteristic, complemented
685C2×#41C23×C10311yescharacteristic
686C2×#41C23×C10311yescharacteristic
687C2×#41C23×C10311yescharacteristic
688C22×Q8D4×C10311yescharacteristic, complemented
689C22×Q8C23×C10311yescharacteristic
690C22×D4—21no—
691C22×D4—22no—
692C22×D4—22no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—21no—
696C22×D4—22no—
697C22×D4D4×C10312yes—
698C22×D4D4×C10311yescharacteristic, complemented
699C22×D4C23×C10311yescharacteristic
700C22×D4C23×C10311yescharacteristic
701C23×C4—21no—
702C23×C4—21no—
703C23×C4C23×C10311yescharacteristic
704#137—28no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—22no—
709#137—41no—
710#137D4×C10314yescomplemented
711AGL(1,ℤ/8)—28no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—22no—
716AGL(1,ℤ/8)—41no—
717AGL(1,ℤ/8)D4×C10314yescomplemented
718#135—28no—
719#135—28no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×Q16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×D8—21no—
732C2×M16—21no—
733C2×M16—22no—
734C2×M16—22no—
735C2×M16C23×C10311yescharacteristic
736C2×M16C23×C10311yescharacteristic
737C2×M16C23×C10311yescharacteristic
738C2×M16C23×C10311yescharacteristic
739C22×C8—21no—
740#127—22no—
741#127—21no—
742#127—22no—
743#127—41no—
744#124—22no—
745#124—21no—
746#124—22no—
747#124—41no—
748#123—22no—
749#123—21no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8D4×C10311yescharacteristic, complemented
754C22⋊Q8D4×C10311yescharacteristic, complemented
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—22no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—22no—
767#121—21no—
768#121—21no—
769#121D4×C10311yescharacteristic, complemented
770#121D4×C10311yescharacteristic, complemented
771#120—22no—
772#120—22no—
773#120—22no—
774#120—21no—
775#120—22no—
776C4×Q8—21no—
777C4×D4—22no—
778C4×D4—22no—
779C4×D4—21no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—21no—
783#117—21no—
784#117C23×C10311yescharacteristic
785C2×C4⋊C4—21no—
786C2×C4⋊C4C23×C10311yescharacteristic
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4D4×C10312yes—
792C2×C42C23×C10311yescharacteristic
793C2×C42C23×C10311yescharacteristic
794#104—22no—
795#104—22no—
796#104—22no—
797#104—22no—
798#104—41no—
799#104—41no—
800#103—21no—
801#103—21no—
802#102—21no—
803#102—21no—
804#100—22no—
805#100—22no—
806C22⋊C8—21no—
807C22⋊C8—21no—
808#95—21no—
809#95—22no—
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C10312yes—
814C24C2×D4×C10311yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C10312yes—
846#41C2×D4×C10312yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C10311yescharacteristic
856C2×Q8C2×D4×C10311yescharacteristic
857C2×Q8C2×D4×C10311yescharacteristic
858C2×Q8C2×D4×C10312yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C10311yescharacteristic
905C2×D4C2×D4×C10311yescharacteristic
906C2×D4C2×D4×C10311yescharacteristic
907C2×D4C2×D4×C10312yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C10311yescharacteristic
930C22×C4C2×D4×C10311yescharacteristic
931C22×C4C2×D4×C10311yescharacteristic
932C22×C4C2×D4×C10311yescharacteristic
933C22×C4C2×D4×C10311yescharacteristic
934C22×C4C2×D4×C10312yes—
935C22×C4C24×C10311yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C10312yescomplemented
956M16C2×D4×C10312yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C10311yescharacteristic
969C4⋊C4C2×D4×C10311yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23#120×C10311yescharacteristic
1015C23#120×C10311yescharacteristic
1016C23C22×D4×C10311yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—22no—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8#120×C10312yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—22no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—82no—
1057D4—81no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4#120×C10312yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4#120×C10311yescharacteristic
1103C2×C4#120×C10311yescharacteristic
1104C2×C4C22×D4×C10311yescharacteristic
1105C2×C4C22×D4×C10311yescharacteristic
1106C2×C4C22×D4×C10311yescharacteristic
1107C2×C4C22×D4×C10311yescharacteristic
1108C2×C4H(5,𝔽2)×C10311yescharacteristic
1109C2×C4H(5,𝔽2)×C10311yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—22no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—42no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×#120×C10311yescharacteristic
1146C22D42×C10311yescharacteristic
1147C22D42×C10311yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—42no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—81no—
1159C4C2×#120×C10311yescharacteristic
1160C4#534×C10311yescharacteristic
1161C4D42×C10311yescharacteristic
1162C4D42×C10311yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C103×#240311yescharacteristic
1173C2C103×#301811yescharacteristic
1174C2C103×#301911yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C103C2semidirect
2. C103×#3488C2semidirect
3. C2×#455×C103C2semidirect
4. C2×#453×C103C2semidirect
5. C103×#3005C2semidirect
6. C103×#2431C2semidirect
7. C103×#2007C2semidirect
8. C103×#2006C2semidirect
9. C103×#2004C2semidirect
10. C103×#2002C2semidirect
11. C103×#1900C2semidirect
12. C103×#1883C2semidirect
13. C103×#1882C2semidirect
14. C103×#1871C2semidirect
15. C103×#1789C2semidirect
18. C22×#41×C103C22semidirect
23. C2×#137×C103C22semidirect
24. C2×#137×C103C22semidirect
27. C2×AGL(1,ℤ/8)×C103C22semidirect
28. C2×AGL(1,ℤ/8)×C103C22semidirect
31. C22×M16×C103C22semidirect
42. C2×#127×C103C22semidirect
43. C2×#124×C103C22semidirect
57. C2×#104×C103C22semidirect
58. C2×#104×C103C22semidirect
59. C2×#104×C103C22semidirect
60. C2×#104×C103C22semidirect
61. #419×C103C22semidirect
62. #418×C103C22semidirect
63. C2×#100×C103C22semidirect
64. C2×#100×C103C22semidirect
65. #407×C103C22semidirect
67. #391×C103C22semidirect
68. #390×C103C22semidirect
70. C4×C22⋊C4×C103C22semidirect
71. #343×C103C22semidirect
72. #343×C103C22semidirect
73. #339×C103C22semidirect
74. #339×C103C22semidirect
95. C2×#41×C103D4semidirect
96. C2×#41×C103D4semidirect
100. C22×Q8×C103D4semidirect
110. C22×D4×C103D4semidirect
122. #137×C103D4semidirect
129. AGL(1,ℤ/8)×C103D4semidirect
165. C22⋊Q8×C103D4semidirect
166. C22⋊Q8×C103D4semidirect
181. #121×C103D4semidirect
182. #121×C103D4semidirect
270. C2×Q8×C103C2×D4semidirect
319. C2×D4×C103C2×D4semidirect
367. M16×C103C2×D4semidirect
368. M16×C103C2×D4semidirect
575. #23878C103direct (N × H)
588. C2×#575C2×C103semidirect
589. #3488C2×C103semidirect
590. C2×#455C2×C103semidirect
591. C2×#453C2×C103semidirect
592. #3005C2×C103semidirect
593. #2431C2×C103semidirect
594. #2007C2×C103semidirect
595. #2006C2×C103semidirect
596. #2004C2×C103semidirect
597. #2002C2×C103semidirect
598. #1900C2×C103semidirect
599. #1883C2×C103semidirect
600. #1882C2×C103semidirect
601. #1871C2×C103semidirect
602. #1789C2×C103semidirect
603. C103#23878direct (N × H)
606. C22×#41C22×C103semidirect
611. C2×#137C22×C103semidirect
612. C2×#137C22×C103semidirect
615. C2×AGL(1,ℤ/8)C22×C103semidirect
616. C2×AGL(1,ℤ/8)C22×C103semidirect
619. C22×M16C22×C103semidirect
630. C2×#127C22×C103semidirect
631. C2×#124C22×C103semidirect
645. C2×#104C22×C103semidirect
646. C2×#104C22×C103semidirect
647. C2×#104C22×C103semidirect
648. C2×#104C22×C103semidirect
649. #419C22×C103semidirect
650. #418C22×C103semidirect
651. C2×#100C22×C103semidirect
652. C2×#100C22×C103semidirect
653. #407C22×C103semidirect
655. #391C22×C103semidirect
656. #390C22×C103semidirect
658. C4×C22⋊C4C22×C103semidirect
659. #343C22×C103semidirect
660. #343C22×C103semidirect
661. #339C22×C103semidirect
662. #339C22×C103semidirect
683. C2×#41D4×C103semidirect
684. C2×#41D4×C103semidirect
688. C22×Q8D4×C103semidirect
698. C22×D4D4×C103semidirect
710. #137D4×C103semidirect
717. AGL(1,ℤ/8)D4×C103semidirect
753. C22⋊Q8D4×C103semidirect
754. C22⋊Q8D4×C103semidirect
769. #121D4×C103semidirect
770. #121D4×C103semidirect
858. C2×Q8C2×D4×C103semidirect
907. C2×D4C2×D4×C103semidirect
955. M16C2×D4×C103semidirect
956. M16C2×D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1032
C103×#34882
C2×#455×C1032
C2×#453×C1032
C103×#30052
C103×#24312
C103×#20072
C103×#20062
C103×#20042
C103×#20022
C103×#19002
C103×#18832
C103×#18822
C103×#18712
C103×#17892
#23878103