Finite Group Databasebeta

← C103×#23889 #39929164

Subgroups — C103×#23889 #39929164

Order 26368.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C103C211yesmaximal, characteristic, complemented
2C2×#577×C103C211yesmaximal, characteristic, complemented
3C2×#454×C103C211yesmaximal, characteristic, complemented
4C2×#455×C103C211yesmaximal, characteristic, complemented
5C103×#3013C211yesmaximal, characteristic, complemented
6C103×#3012C211yesmaximal, characteristic, complemented
7C103×#2020C211yesmaximal, characteristic, complemented
8C103×#2019C211yesmaximal, characteristic, complemented
9C103×#2015C211yesmaximal, characteristic, complemented
10C103×#2007C211yesmaximal, characteristic, complemented
11C103×#1908C211yesmaximal, characteristic, complemented
12C103×#1907C211yesmaximal, characteristic, complemented
13C103×#1876C211yesmaximal, characteristic, complemented
14C103×#1876C211yesmaximal, characteristic, complemented
15C103×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C103C2211yescharacteristic
17C2×2−1+4×C103C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C103C2211yescharacteristic
19#578×C103—24no—
20#578×C103—24no—
21#577×C103—24no—
22#577×C103—24no—
23C2×#137×C103—21no—
24C2×#137×C103—21no—
25C2×#137×C103—21no—
26C2×#137×C103C2211yescharacteristic
27C2×#137×C103C2211yescharacteristic
28C2×#137×C103C2211yescharacteristic
29C2×#137×C103C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C103—21no—
31C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C103C2211yescharacteristic
33C2×#135×C103—21no—
34C2×#135×C103—21no—
35C2×#135×C103C2211yescharacteristic
36C2×#135×C103C2211yescharacteristic
37C22×Q16×C103—21no—
38C22×Q16×C103C2211yescharacteristic, complemented
39C22×SD16×C103—21no—
40C22×SD16×C103C2211yescharacteristic
41C2×#131×C103C2211yescharacteristic
42C2×#131×C103C2211yescharacteristic, complemented
43#537×C103C2211yescharacteristic
44C2×#124×C103C2211yescharacteristic
45#455×C103—24no—
46#454×C103—24no—
47#452×C103—21no—
48#452×C103—21no—
49#451×C103—21no—
50#450×C103—21no—
51#449×C103—21no—
52#449×C103—21no—
53#448×C103—21no—
54#447×C103—21no—
55C2×#104×C103C2211yescharacteristic
56C2×#104×C103C2211yescharacteristic
57C2×#104×C103C2211yescharacteristic, complemented
58C2×#104×C103C2211yescharacteristic, complemented
59#417×C103C2211yescharacteristic
60#417×C103C2211yescharacteristic, complemented
61C2×#103×C103C2211yescharacteristic, complemented
62C2×#102×C103C2211yescharacteristic
63C2×#101×C103C2211yescharacteristic, complemented
64C2×#101×C103C2211yescharacteristic, complemented
65C2×#100×C103C2211yescharacteristic
66#408×C103C2211yescharacteristic
67#408×C103C2211yescharacteristic, complemented
68#391×C103C2211yescharacteristic, complemented
69#343×C103C2211yescharacteristic, complemented
70#341×C103C2211yescharacteristic, complemented
71#341×C103C2211yescharacteristic, complemented
72#336×C103C2211yescharacteristic, complemented
732−1+4×C103—22no—
742−1+4×C103—22no—
752−1+4×C103—22no—
762−1+4×C103—22no—
772−1+4×C103—22no—
782−1+4×C103—41no—
792−1+4×C103—41no—
802−1+4×C103D414yescomplemented
81H(5,𝔽2)×C103—22no—
82H(5,𝔽2)×C103—22no—
83H(5,𝔽2)×C103—22no—
84H(5,𝔽2)×C103—41no—
85C2×#41×C103—21no—
86C2×#41×C103—21no—
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×C103C2311yescharacteristic
94C2×#41×C103C2311yescharacteristic
95C2×#41×C103C2311yescharacteristic
96C2×#41×C103C2311yescharacteristic
97C22×Q8×C103—21no—
98C22×Q8×C103—21no—
99C22×Q8×C103—21no—
100C22×Q8×C103—21no—
101C22×Q8×C103C2311yescharacteristic
102C22×Q8×C103C2311yescharacteristic
103C22×D4×C103—21no—
104C22×D4×C103—21no—
105C22×D4×C103—41no—
106C22×D4×C103C2311yescharacteristic
107#137×C103—28no—
108#137×C103—28no—
109#137×C103—28no—
110#137×C103—22no—
111#137×C103—22no—
112#137×C103—22no—
113#137×C103—22no—
114#137×C103—22no—
115#137×C103—22no—
116#137×C103—41no—
117#137×C103D414yescomplemented
118AGL(1,ℤ/8)×C103—28no—
119AGL(1,ℤ/8)×C103—22no—
120AGL(1,ℤ/8)×C103—22no—
121AGL(1,ℤ/8)×C103—41no—
122AGL(1,ℤ/8)×C103D414yescomplemented
123#135×C103—28no—
124#135×C103—28no—
125#135×C103—22no—
126#135×C103—22no—
127#135×C103—22no—
128#135×C103—22no—
129C2×Q16×C103—28no—
130C2×Q16×C103—21no—
131C2×Q16×C103—21no—
132C2×Q16×C103—22no—
133C2×Q16×C103—22no—
134C2×Q16×C103—21no—
135C2×Q16×C103—21no—
136C2×Q16×C103—21no—
137C2×Q16×C103—21no—
138C2×Q16×C103D411yescharacteristic
139C2×Q16×C103D411yescharacteristic
140C2×SD16×C103—28no—
141C2×SD16×C103—21no—
142C2×SD16×C103—22no—
143C2×SD16×C103—21no—
144C2×SD16×C103—22no—
145C2×SD16×C103—21no—
146C2×SD16×C103—21no—
147C2×SD16×C103—21no—
148C2×SD16×C103—21no—
149C2×SD16×C103—21no—
150C2×SD16×C103—21no—
151C2×SD16×C103D411yescharacteristic
152C2×SD16×C103D411yescharacteristic
153C2×SD16×C103D411yescharacteristic
154C2×SD16×C103D411yescharacteristic
155C2×D8×C103—21no—
156C2×D8×C103—21no—
157C2×D8×C103D411yescharacteristic
158C2×D8×C103D411yescharacteristic
159#131×C103—22no—
160#131×C103—22no—
161#131×C103—22no—
162#131×C103—22no—
163C2×M16×C103—21no—
164C2×M16×C103—21no—
165C2×M16×C103C2311yescharacteristic
166C2×M16×C103C2311yescharacteristic
167C2×M16×C103C2311yescharacteristic
168C2×M16×C103C2311yescharacteristic
169C22×C8×C103—21no—
170C22×C8×C103—21no—
171C22×C8×C103C2311yescharacteristic
172C22×C8×C103C2311yescharacteristic
173#124×C103—22no—
174#124×C103—22no—
175C22⋊Q8×C103—21no—
176C22⋊Q8×C103—21no—
177#121×C103—21no—
178#121×C103—21no—
179#121×C103—41no—
180C2×C4⋊C4×C103C2311yescharacteristic
181C2×C22⋊C4×C103—41no—
182C2×C42×C103C2311yescharacteristic
183#104×C103—22no—
184#104×C103—22no—
185#104×C103—22no—
186#104×C103—22no—
187#103×C103—21no—
188#103×C103—21no—
189#103×C103—21no—
190#103×C103—21no—
191#102×C103—21no—
192#102×C103—21no—
193#102×C103—21no—
194#102×C103—21no—
195#101×C103—22no—
196#101×C103—41no—
197#100×C103—22no—
198C22⋊C8×C103—21no—
199C22⋊C8×C103—21no—
200C22⋊C8×C103—21no—
201C22⋊C8×C103—21no—
202#95×C103—41no—
203C24×C103—21no—
204C24×C103—41no—
205#41×C103—21no—
206#41×C103—21no—
207#41×C103—21no—
208#41×C103—21no—
209#41×C103—24no—
210#41×C103—24no—
211#41×C103—24no—
212#41×C103—24no—
213#41×C103—21no—
214#41×C103—21no—
215#41×C103—21no—
216#41×C103—21no—
217#41×C103—21no—
218#41×C103—21no—
219#41×C103—21no—
220#41×C103—21no—
221#41×C103—44no—
222#41×C103—42no—
223#41×C103—42no—
224#41×C103—42no—
225#41×C103—44no—
226#41×C103—42no—
227#41×C103—44no—
228#41×C103—42no—
229#41×C103—42no—
230#41×C103—44no—
231#41×C103—42no—
232#41×C103—42no—
233#41×C103C2×D412yes—
234#41×C103C2×D412yes—
235#41×C103C2×D412yes—
236#41×C103C2×D412yes—
237C2×Q8×C103—21no—
238C2×Q8×C103—21no—
239C2×Q8×C103—24no—
240C2×Q8×C103—24no—
241C2×Q8×C103—24no—
242C2×Q8×C103—21no—
243C2×Q8×C103—21no—
244C2×Q8×C103—21no—
245C2×Q8×C103—21no—
246C2×Q8×C103—21no—
247C2×Q8×C103—21no—
248C2×Q8×C103—21no—
249C2×Q8×C103—21no—
250C2×Q8×C103—41no—
251C2×Q8×C103—41no—
252C2×Q8×C103—42no—
253C2×Q8×C103—42no—
254C2×Q8×C103—42no—
255C2×Q8×C103—42no—
256C2×Q8×C103—42no—
257C2×Q8×C103C2×D411yescharacteristic
258C2×Q8×C103C2×D411yescharacteristic
259C2×Q8×C103C2×D412yes—
260C2×Q8×C103C2×D412yes—
261C2×Q8×C103C2×D411yescharacteristic
262C2×Q8×C103C2×D411yescharacteristic
263C2×D4×C103—21no—
264C2×D4×C103—21no—
265C2×D4×C103—24no—
266C2×D4×C103—21no—
267C2×D4×C103—21no—
268C2×D4×C103—21no—
269C2×D4×C103—21no—
270C2×D4×C103—21no—
271C2×D4×C103—21no—
272C2×D4×C103—21no—
273C2×D4×C103—42no—
274C2×D4×C103—41no—
275C2×D4×C103—41no—
276C2×D4×C103—42no—
277C2×D4×C103—44no—
278C2×D4×C103—44no—
279C2×D4×C103—41no—
280C2×D4×C103—41no—
281C2×D4×C103—42no—
282C2×D4×C103—41no—
283C2×D4×C103C2×D411yescharacteristic
284C2×D4×C103C2×D411yescharacteristic
285C2×D4×C103C2×D412yes—
286C2×D4×C103C2×D411yescharacteristic
287C2×D4×C103C2×D411yescharacteristic
288C22×C4×C103—21no—
289C22×C4×C103—21no—
290C22×C4×C103—21no—
291C22×C4×C103—21no—
292C22×C4×C103—21no—
293C22×C4×C103—21no—
294C22×C4×C103—21no—
295C22×C4×C103—21no—
296C22×C4×C103—41no—
297C22×C4×C103—41no—
298C22×C4×C103—41no—
299C22×C4×C103—41no—
300C22×C4×C103—41no—
301C22×C4×C103C2411yescharacteristic
302Q16×C103—24no—
303Q16×C103—24no—
304Q16×C103—24no—
305Q16×C103—24no—
306Q16×C103—22no—
307Q16×C103—24no—
308Q16×C103—22no—
309Q16×C103—42no—
310SD16×C103—24no—
311SD16×C103—24no—
312SD16×C103—24no—
313SD16×C103—24no—
314SD16×C103—22no—
315SD16×C103—24no—
316SD16×C103—22no—
317SD16×C103—24no—
318SD16×C103—22no—
319SD16×C103—22no—
320SD16×C103—42no—
321SD16×C103—42no—
322D8×C103—24no—
323D8×C103—22no—
324D8×C103—22no—
325D8×C103—42no—
326M16×C103—24no—
327M16×C103—24no—
328M16×C103—21no—
329M16×C103—21no—
330M16×C103—21no—
331M16×C103—21no—
332M16×C103—21no—
333M16×C103—21no—
334M16×C103C2×D412yes—
335M16×C103C2×D412yes—
336C2×C8×C103—24no—
337C2×C8×C103—24no—
338C2×C8×C103—21no—
339C2×C8×C103—21no—
340C2×C8×C103—21no—
341C2×C8×C103—21no—
342C2×C8×C103—21no—
343C2×C8×C103—21no—
344C2×C8×C103—21no—
345C2×C8×C103—21no—
346C2×C8×C103C2×D411yescharacteristic
347C2×C8×C103C2×D411yescharacteristic
348C2×C8×C103C2×D411yescharacteristic
349C2×C8×C103C2×D411yescharacteristic
350C4⋊C4×C103—21no—
351C4⋊C4×C103—21no—
352C4⋊C4×C103—41no—
353C22⋊C4×C103—44no—
354C22⋊C4×C103—41no—
355C22⋊C4×C103—41no—
356C42×C103—21no—
357C42×C103—21no—
358C23×C103—21no—
359C23×C103—21no—
360C23×C103—21no—
361C23×C103—21no—
362C23×C103—22no—
363C23×C103—44no—
364C23×C103—41no—
365C23×C103—41no—
366C23×C103—81no—
367C23×C103—81no—
368C23×C103—161no—
369C23×C103—161no—
370C23×C103H(5,𝔽2)11yescharacteristic
371Q8×C103—21no—
372Q8×C103—21no—
373Q8×C103—22no—
374Q8×C103—22no—
375Q8×C103—22no—
376Q8×C103—21no—
377Q8×C103—21no—
378Q8×C103—21no—
379Q8×C103—22no—
380Q8×C103—21no—
381Q8×C103—44no—
382Q8×C103—44no—
383Q8×C103—41no—
384Q8×C103—41no—
385Q8×C103—41no—
386Q8×C103—41no—
387Q8×C103#12012yes—
388Q8×C103#12012yes—
389D4×C103—22no—
390D4×C103—22no—
391D4×C103—22no—
392D4×C103—22no—
393D4×C103—22no—
394D4×C103—21no—
395D4×C103—21no—
396D4×C103—21no—
397D4×C103—21no—
398D4×C103—21no—
399D4×C103—22no—
400D4×C103—21no—
401D4×C103—44no—
402D4×C103—44no—
403D4×C103—44no—
404D4×C103—44no—
405D4×C103—41no—
406D4×C103—41no—
407D4×C103—41no—
408D4×C103—41no—
409D4×C103—41no—
410D4×C103—41no—
411D4×C103—161no—
412D4×C103#12012yes—
413D4×C103#12012yes—
414C2×C4×C103—21no—
415C2×C4×C103—21no—
416C2×C4×C103—22no—
417C2×C4×C103—22no—
418C2×C4×C103—22no—
419C2×C4×C103—22no—
420C2×C4×C103—22no—
421C2×C4×C103—22no—
422C2×C4×C103—21no—
423C2×C4×C103—21no—
424C2×C4×C103—44no—
425C2×C4×C103—44no—
426C2×C4×C103—44no—
427C2×C4×C103—44no—
428C2×C4×C103—44no—
429C2×C4×C103—41no—
430C2×C4×C103—41no—
431C2×C4×C103—41no—
432C2×C4×C103—41no—
433C2×C4×C103—41no—
434C2×C4×C103—41no—
435C2×C4×C103—41no—
436C2×C4×C103—41no—
437C2×C4×C103—41no—
438C2×C4×C103—41no—
439C2×C4×C103—41no—
440C2×C4×C103—41no—
441C2×C4×C103—81no—
442C2×C4×C103C22×D411yescharacteristic
443C2×C4×C103C22×D411yescharacteristic
444C2×C4×C103C22×D411yescharacteristic
445C2×C4×C103C22×D411yescharacteristic
446C2×C4×C103C22×D411yescharacteristic
447C2×C4×C103H(5,𝔽2)11yescharacteristic
448C8×C103—21no—
449C8×C103—21no—
450C8×C103—22no—
451C8×C103—22no—
452C8×C103—21no—
453C8×C103—21no—
454C8×C103—41no—
455C8×C103—41no—
456C22×C103—21no—
457C22×C103—21no—
458C22×C103—22no—
459C22×C103—22no—
460C22×C103—41no—
461C22×C103—41no—
462C22×C103—41no—
463C22×C103—41no—
464C22×C103—41no—
465C22×C103—41no—
466C22×C103—42no—
467C22×C103—41no—
468C22×C103—41no—
469C22×C103—41no—
470C22×C103—41no—
471C22×C103—82no—
472C22×C103—81no—
473C22×C103—81no—
474C22×C103—161no—
475C22×C103—164no—
476C22×C103#53411yescharacteristic
477C22×C103D4211yescharacteristic
478C22×C103D4211yescharacteristic
479C4×C103—22no—
480C4×C103—22no—
481C4×C103—41no—
482C4×C103—42no—
483C4×C103—42no—
484C4×C103—41no—
485C4×C103—81no—
486C4×C103—81no—
487C4×C103C2×#12011yescharacteristic
488C4×C103C2×#12011yescharacteristic
489C4×C103D4211yescharacteristic
490C4×C103D4211yescharacteristic
491#23889C10311yesmaximal, characteristic, direct product factor, Sylow
492C2×C103—21no—
493C2×C103—21no—
494C2×C103—42no—
495C2×C103—42no—
496C2×C103—81no—
497C2×C103—81no—
498C2×C103—82no—
499C2×C103#240311yescharacteristic
500C2×C103#328911yescharacteristic
501C2×C103#329011yescharacteristic
502C2×#578C2×C10311yescharacteristic, complemented
503C2×#577C2×C10311yescharacteristic, complemented
504C2×#454C2×C10311yescharacteristic, complemented
505C2×#455C2×C10311yescharacteristic, complemented
506#3013C2×C10311yescharacteristic, complemented
507#3012C2×C10311yescharacteristic, complemented
508#2020C2×C10311yescharacteristic, complemented
509#2019C2×C10311yescharacteristic, complemented
510#2015C2×C10311yescharacteristic, complemented
511#2007C2×C10311yescharacteristic, complemented
512#1908C2×C10311yescharacteristic, complemented
513#1907C2×C10311yescharacteristic, complemented
514#1876C2×C10311yescharacteristic, complemented
515#1876C2×C10311yescharacteristic, complemented
516#1793C2×C10311yescharacteristic, complemented
517C103#2388911yescharacteristic, direct product factor, Sylow
518C2×2−1+4C22×C10311yescharacteristic
519C2×2−1+4C22×C10311yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C10311yescharacteristic
521#578—24no—
522#578—24no—
523#577—24no—
524#577—24no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137—21no—
528C2×#137C22×C10311yescharacteristic
529C2×#137C22×C10311yescharacteristic
530C2×#137C22×C10311yescharacteristic
531C2×#137C22×C10311yescharacteristic, complemented
532C2×AGL(1,ℤ/8)—21no—
533C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
534C2×AGL(1,ℤ/8)C22×C10311yescharacteristic
535C2×#135—21no—
536C2×#135—21no—
537C2×#135C22×C10311yescharacteristic
538C2×#135C22×C10311yescharacteristic
539C22×Q16—21no—
540C22×Q16C22×C10311yescharacteristic, complemented
541C22×SD16—21no—
542C22×SD16C22×C10311yescharacteristic
543C2×#131C22×C10311yescharacteristic
544C2×#131C22×C10311yescharacteristic, complemented
545#537C22×C10311yescharacteristic
546C2×#124C22×C10311yescharacteristic
547#455—24no—
548#454—24no—
549#452—21no—
550#452—21no—
551#451—21no—
552#450—21no—
553#449—21no—
554#449—21no—
555#448—21no—
556#447—21no—
557C2×#104C22×C10311yescharacteristic
558C2×#104C22×C10311yescharacteristic
559C2×#104C22×C10311yescharacteristic, complemented
560C2×#104C22×C10311yescharacteristic, complemented
561#417C22×C10311yescharacteristic
562#417C22×C10311yescharacteristic, complemented
563C2×#103C22×C10311yescharacteristic, complemented
564C2×#102C22×C10311yescharacteristic
565C2×#101C22×C10311yescharacteristic, complemented
566C2×#101C22×C10311yescharacteristic, complemented
567C2×#100C22×C10311yescharacteristic
568#408C22×C10311yescharacteristic
569#408C22×C10311yescharacteristic, complemented
570#391C22×C10311yescharacteristic, complemented
571#343C22×C10311yescharacteristic, complemented
572#341C22×C10311yescharacteristic, complemented
573#341C22×C10311yescharacteristic, complemented
574#336C22×C10311yescharacteristic, complemented
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C10314yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C10311yescharacteristic
596C2×#41C23×C10311yescharacteristic
597C2×#41C23×C10311yescharacteristic
598C2×#41C23×C10311yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C10311yescharacteristic
604C22×Q8C23×C10311yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C10311yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C10314yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C10314yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C10311yescharacteristic
641C2×Q16D4×C10311yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C10311yescharacteristic
654C2×SD16D4×C10311yescharacteristic
655C2×SD16D4×C10311yescharacteristic
656C2×SD16D4×C10311yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C10311yescharacteristic
660C2×D8D4×C10311yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C10311yescharacteristic
668C2×M16C23×C10311yescharacteristic
669C2×M16C23×C10311yescharacteristic
670C2×M16C23×C10311yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C10311yescharacteristic
674C22×C8C23×C10311yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C10311yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C10311yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C10312yes—
736#41C2×D4×C10312yes—
737#41C2×D4×C10312yes—
738#41C2×D4×C10312yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C10311yescharacteristic
760C2×Q8C2×D4×C10311yescharacteristic
761C2×Q8C2×D4×C10312yes—
762C2×Q8C2×D4×C10312yes—
763C2×Q8C2×D4×C10311yescharacteristic
764C2×Q8C2×D4×C10311yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C10311yescharacteristic
786C2×D4C2×D4×C10311yescharacteristic
787C2×D4C2×D4×C10312yes—
788C2×D4C2×D4×C10311yescharacteristic
789C2×D4C2×D4×C10311yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C10311yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C10312yes—
837M16C2×D4×C10312yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C10311yescharacteristic
849C2×C8C2×D4×C10311yescharacteristic
850C2×C8C2×D4×C10311yescharacteristic
851C2×C8C2×D4×C10311yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C10311yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C10312yes—
890Q8#120×C10312yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C10312yes—
915D4#120×C10312yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C10311yescharacteristic
945C2×C4C22×D4×C10311yescharacteristic
946C2×C4C22×D4×C10311yescharacteristic
947C2×C4C22×D4×C10311yescharacteristic
948C2×C4C22×D4×C10311yescharacteristic
949C2×C4H(5,𝔽2)×C10311yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—42no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22#534×C10311yescharacteristic
979C22D42×C10311yescharacteristic
980C22D42×C10311yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C10311yescharacteristic
990C4C2×#120×C10311yescharacteristic
991C4D42×C10311yescharacteristic
992C4D42×C10311yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C103×#240311yescharacteristic
1001C2C103×#328911yescharacteristic
1002C2C103×#329011yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC22×C4C24×C103
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
1. C2×#578×C103C2semidirect
2. C2×#577×C103C2semidirect
3. C2×#454×C103C2semidirect
4. C2×#455×C103C2semidirect
5. C103×#3013C2semidirect
6. C103×#3012C2semidirect
7. C103×#2020C2semidirect
8. C103×#2019C2semidirect
9. C103×#2015C2semidirect
10. C103×#2007C2semidirect
11. C103×#1908C2semidirect
12. C103×#1907C2semidirect
13. C103×#1876C2semidirect
14. C103×#1876C2semidirect
15. C103×#1793C2semidirect
17. C2×2−1+4×C103C22semidirect
29. C2×#137×C103C22semidirect
38. C22×Q16×C103C22semidirect
42. C2×#131×C103C22semidirect
57. C2×#104×C103C22semidirect
58. C2×#104×C103C22semidirect
60. #417×C103C22semidirect
61. C2×#103×C103C22semidirect
63. C2×#101×C103C22semidirect
64. C2×#101×C103C22semidirect
67. #408×C103C22semidirect
68. #391×C103C22semidirect
69. #343×C103C22semidirect
70. #341×C103C22semidirect
71. #341×C103C22semidirect
72. #336×C103C22semidirect
80. 2−1+4×C103D4semidirect
117. #137×C103D4semidirect
122. AGL(1,ℤ/8)×C103D4semidirect
491. #23889C103direct (N × H)
502. C2×#578C2×C103semidirect
503. C2×#577C2×C103semidirect
504. C2×#454C2×C103semidirect
505. C2×#455C2×C103semidirect
506. #3013C2×C103semidirect
507. #3012C2×C103semidirect
508. #2020C2×C103semidirect
509. #2019C2×C103semidirect
510. #2015C2×C103semidirect
511. #2007C2×C103semidirect
512. #1908C2×C103semidirect
513. #1907C2×C103semidirect
514. #1876C2×C103semidirect
515. #1876C2×C103semidirect
516. #1793C2×C103semidirect
517. C103#23889direct (N × H)
519. C2×2−1+4C22×C103semidirect
531. C2×#137C22×C103semidirect
540. C22×Q16C22×C103semidirect
544. C2×#131C22×C103semidirect
559. C2×#104C22×C103semidirect
560. C2×#104C22×C103semidirect
562. #417C22×C103semidirect
563. C2×#103C22×C103semidirect
565. C2×#101C22×C103semidirect
566. C2×#101C22×C103semidirect
569. #408C22×C103semidirect
570. #391C22×C103semidirect
571. #343C22×C103semidirect
572. #341C22×C103semidirect
573. #341C22×C103semidirect
574. #336C22×C103semidirect
582. 2−1+4D4×C103semidirect
619. #137D4×C103semidirect
624. AGL(1,ℤ/8)D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#578×C1032
C2×#577×C1032
C2×#454×C1032
C2×#455×C1032
C103×#30132
C103×#30122
C103×#20202
C103×#20192
C103×#20152
C103×#20072
C103×#19082
C103×#19072
C103×#18762
C103×#17932
#23889103