Finite Group Databasebeta

← C103×#25152 #39930427

Subgroups — C103×#25152 #39930427

Order 26368.

1302 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C103C211yesmaximal, characteristic, complemented
2C2×#450×C103C211yesmaximal, characteristic, complemented
3C2×#447×C103C211yesmaximal, characteristic
4C2×C4×SD16×C103C211yesmaximal, characteristic, complemented
5C103×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C103C211yesmaximal, characteristic, complemented
7C103×#2065C211yesmaximal, characteristic, complemented
8C103×#2036C211yesmaximal, characteristic, complemented
9C103×#2034C211yesmaximal, characteristic, complemented
10C103×#2012C211yesmaximal, characteristic, complemented
11C103×#1970C211yesmaximal, characteristic, complemented
12C103×#1923C211yesmaximal, characteristic, complemented
13C103×#1880C211yesmaximal, characteristic, complemented
14C103×#1879C211yesmaximal, characteristic, complemented
15C103×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C103C2211yescharacteristic
17C22×SD16×C103C2211yescharacteristic
18C22×SD16×C103C2211yescharacteristic
19C22×D8×C103C2211yescharacteristic
20C22×D8×C103C2211yescharacteristic
21C2×#124×C103C2211yescharacteristic, complemented
22C2×C22⋊Q8×C103C2211yescharacteristic
23C2×#121×C103C2211yescharacteristic
24C2×C4×Q8×C103C2211yescharacteristic, complemented
25C2×C4×D4×C103C2211yescharacteristic
26C2×C4×D4×C103C2211yescharacteristic
27C22×C22⋊C4×C103—21no—
28#463×C103—24no—
29#450×C103—24no—
30#447×C103—24no—
31C4×SD16×C103—24no—
32C2×#107×C103C2211yescharacteristic, complemented
33C2×#106×C103C2211yescharacteristic, complemented
34C2×C4⋊C8×C103C2211yescharacteristic, complemented
35C2×#103×C103C2211yescharacteristic, complemented
36C2×#103×C103C2211yescharacteristic, complemented
37C2×#102×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic
39C2×#102×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic, complemented
42C2×#102×C103C2211yescharacteristic, complemented
43C2×C22⋊C8×C103C2211yescharacteristic
44C2×C22⋊C8×C103C2211yescharacteristic
45C2×C4×C8×C103C2211yescharacteristic, complemented
46#396×C103—21no—
47#394×C103—21no—
48#390×C103—21no—
49#390×C103C2211yescharacteristic
50#390×C103C2211yescharacteristic
51#390×C103C2211yescharacteristic, complemented
52#389×C103C2211yescharacteristic, complemented
53#388×C103—21no—
54#386×C103—21no—
55#386×C103—21no—
56#380×C103C2211yescharacteristic
57#379×C103—21no—
58C4×C22⋊C4×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic, complemented
60#340×C103C2211yescharacteristic, complemented
61#336×C103C2211yescharacteristic, complemented
62#336×C103C2211yescharacteristic, complemented
63C25×C103—21no—
64C22×Q8×C103C2311yescharacteristic
65C22×D4×C103—22no—
66C22×D4×C103—22no—
67C22×D4×C103—22no—
68C22×D4×C103—22no—
69C22×D4×C103—21no—
70C22×D4×C103—21no—
71C22×D4×C103—41no—
72C22×D4×C103—41no—
73C22×D4×C103C2311yescharacteristic
74C22×D4×C103C2311yescharacteristic
75C22×D4×C103C2311yescharacteristic
76C23×C4×C103—21no—
77C23×C4×C103—21no—
78C23×C4×C103C2311yescharacteristic
79C2×SD16×C103—22no—
80C2×SD16×C103—22no—
81C2×SD16×C103—22no—
82C2×SD16×C103—22no—
83C2×SD16×C103—41no—
84C2×SD16×C103D414yescomplemented
85C2×D8×C103—22no—
86C2×D8×C103—22no—
87C2×D8×C103—22no—
88C2×D8×C103—22no—
89C2×D8×C103—22no—
90C2×D8×C103—41no—
91C22×C8×C103C2311yescharacteristic
92C22×C8×C103C2311yescharacteristic
93C22×C8×C103C2311yescharacteristic
94C22×C8×C103C2311yescharacteristic
95#124×C103—22no—
96#124×C103—41no—
97C22⋊Q8×C103—22no—
98C22⋊Q8×C103—41no—
99#121×C103—22no—
100#121×C103—41no—
101C4×Q8×C103—22no—
102C4×Q8×C103—41no—
103C4×D4×C103—22no—
104C4×D4×C103—22no—
105C4×D4×C103—41no—
106C4×D4×C103—41no—
107C2×C4⋊C4×C103—21no—
108C2×C4⋊C4×C103—21no—
109C2×C4⋊C4×C103—21no—
110C2×C4⋊C4×C103C2311yescharacteristic
111C2×C4⋊C4×C103C2311yescharacteristic
112C2×C4⋊C4×C103C2311yescharacteristic
113C2×C4⋊C4×C103C2311yescharacteristic
114C2×C22⋊C4×C103—21no—
115C2×C22⋊C4×C103—21no—
116C2×C22⋊C4×C103—21no—
117C2×C22⋊C4×C103—21no—
118C2×C22⋊C4×C103—21no—
119C2×C22⋊C4×C103—21no—
120C2×C22⋊C4×C103—21no—
121C2×C22⋊C4×C103—21no—
122C2×C22⋊C4×C103—21no—
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—44no—
128C2×C22⋊C4×C103D411yescharacteristic
129C2×C22⋊C4×C103D411yescharacteristic
130C2×C42×C103—21no—
131C2×C42×C103C2311yescharacteristic
132C2×C42×C103C2311yescharacteristic
133#107×C103—41no—
134#106×C103—22no—
135C4⋊C8×C103—22no—
136#103×C103—22no—
137#103×C103—22no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—22no—
141#102×C103—22no—
142#102×C103—41no—
143#102×C103D414yes—
144C22⋊C8×C103—22no—
145C22⋊C8×C103—22no—
146C4×C8×C103—22no—
147#95×C103—21no—
148#95×C103—21no—
149#95×C103D411yescharacteristic
150#95×C103D411yescharacteristic
151C24×C103—21no—
152C24×C103—24no—
153C24×C103—21no—
154C24×C103—21no—
155C24×C103—42no—
156C24×C103—42no—
157C24×C103—42no—
158C24×C103—42no—
159C24×C103—81no—
160C24×C103—81no—
161C24×C103C2×D411yescharacteristic
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103—21no—
166C2×Q8×C103—21no—
167C2×Q8×C103C2×D412yes—
168C2×D4×C103—24no—
169C2×D4×C103—21no—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—21no—
175C2×D4×C103—21no—
176C2×D4×C103—21no—
177C2×D4×C103—21no—
178C2×D4×C103—21no—
179C2×D4×C103—21no—
180C2×D4×C103—21no—
181C2×D4×C103—21no—
182C2×D4×C103—21no—
183C2×D4×C103—42no—
184C2×D4×C103—42no—
185C2×D4×C103—42no—
186C2×D4×C103—44no—
187C2×D4×C103—44no—
188C2×D4×C103—44no—
189C2×D4×C103—44no—
190C2×D4×C103—42no—
191C2×D4×C103—81no—
192C2×D4×C103C2×D412yes—
193C2×D4×C103C2×D412yes—
194C2×D4×C103#4112yes—
195C2×D4×C103#4112yes—
196C22×C4×C103—21no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—21no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—21no—
204C22×C4×C103—21no—
205C22×C4×C103—21no—
206C22×C4×C103—21no—
207C22×C4×C103—42no—
208C22×C4×C103—42no—
209C22×C4×C103—42no—
210C22×C4×C103—42no—
211C22×C4×C103—81no—
212C22×C4×C103—81no—
213C22×C4×C103C2×D411yescharacteristic
214C22×C4×C103C2×D411yescharacteristic
215C22×C4×C103C2×D411yescharacteristic
216C22×C4×C103C2×D411yescharacteristic
217C22×C4×C103C2×D411yescharacteristic
218C22×C4×C103C2411yescharacteristic
219SD16×C103—28no—
220SD16×C103—44no—
221D8×C103—44no—
222D8×C103—44no—
223C2×C8×C103—21no—
224C2×C8×C103—21no—
225C2×C8×C103—21no—
226C2×C8×C103—21no—
227C2×C8×C103—21no—
228C2×C8×C103—21no—
229C2×C8×C103—21no—
230C2×C8×C103—21no—
231C2×C8×C103—21no—
232C2×C8×C103—21no—
233C2×C8×C103C2×D412yes—
234C2×C8×C103C2×D412yes—
235C4⋊C4×C103—21no—
236C4⋊C4×C103—21no—
237C4⋊C4×C103—21no—
238C4⋊C4×C103—21no—
239C4⋊C4×C103—21no—
240C4⋊C4×C103—21no—
241C4⋊C4×C103—21no—
242C4⋊C4×C103—42no—
243C4⋊C4×C103—42no—
244C4⋊C4×C103—81no—
245C4⋊C4×C103C2×D412yes—
246C22⋊C4×C103—22no—
247C22⋊C4×C103—22no—
248C22⋊C4×C103—42no—
249C22⋊C4×C103—42no—
250C22⋊C4×C103—42no—
251C22⋊C4×C103—42no—
252C22⋊C4×C103—42no—
253C22⋊C4×C103—42no—
254C22⋊C4×C103—42no—
255C22⋊C4×C103—42no—
256C22⋊C4×C103—42no—
257C22⋊C4×C103—42no—
258C22⋊C4×C103—81no—
259C22⋊C4×C103—81no—
260C22⋊C4×C103—81no—
261C42×C103—21no—
262C42×C103—21no—
263C42×C103—21no—
264C42×C103—21no—
265C42×C103—42no—
266C23×C103—21no—
267C23×C103—22no—
268C23×C103—21no—
269C23×C103—22no—
270C23×C103—22no—
271C23×C103—21no—
272C23×C103—21no—
273C23×C103—21no—
274C23×C103—21no—
275C23×C103—22no—
276C23×C103—48no—
277C23×C103—48no—
278C23×C103—41no—
279C23×C103—41no—
280C23×C103—41no—
281C23×C103—41no—
282C23×C103—41no—
283C23×C103—41no—
284C23×C103—41no—
285C23×C103—41no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103—41no—
289C23×C103—41no—
290C23×C103—41no—
291C23×C103—41no—
292C23×C103—41no—
293C23×C103—41no—
294C23×C103—41no—
295C23×C103—84no—
296C23×C103—84no—
297C23×C103—84no—
298C23×C103—84no—
299C23×C103—84no—
300C23×C103#13512yes—
301C23×C103C22×D411yescharacteristic
302Q8×C103—22no—
303Q8×C103—22no—
304Q8×C103—41no—
305Q8×C103—41no—
306D4×C103—22no—
307D4×C103—22no—
308D4×C103—22no—
309D4×C103—22no—
310D4×C103—22no—
311D4×C103—48no—
312D4×C103—41no—
313D4×C103—41no—
314D4×C103—41no—
315D4×C103—41no—
316D4×C103—41no—
317D4×C103—41no—
318D4×C103—84no—
319D4×C103#12114yes—
320C2×C4×C103—21no—
321C2×C4×C103—21no—
322C2×C4×C103—21no—
323C2×C4×C103—21no—
324C2×C4×C103—21no—
325C2×C4×C103—21no—
326C2×C4×C103—22no—
327C2×C4×C103—22no—
328C2×C4×C103—21no—
329C2×C4×C103—21no—
330C2×C4×C103—21no—
331C2×C4×C103—21no—
332C2×C4×C103—21no—
333C2×C4×C103—21no—
334C2×C4×C103—21no—
335C2×C4×C103—21no—
336C2×C4×C103—41no—
337C2×C4×C103—41no—
338C2×C4×C103—41no—
339C2×C4×C103—41no—
340C2×C4×C103—41no—
341C2×C4×C103—41no—
342C2×C4×C103—41no—
343C2×C4×C103—41no—
344C2×C4×C103—41no—
345C2×C4×C103—41no—
346C2×C4×C103—41no—
347C2×C4×C103—41no—
348C2×C4×C103—41no—
349C2×C4×C103—41no—
350C2×C4×C103—41no—
351C2×C4×C103—41no—
352C2×C4×C103—41no—
353C2×C4×C103—84no—
354C2×C4×C103—84no—
355C2×C4×C103AGL(1,ℤ/8)12yes—
356C2×C4×C103C22×D411yescharacteristic
357C2×C4×C103C22×D411yescharacteristic
358C2×C4×C103C2×#4111yescharacteristic
359C2×C4×C103C2×#4111yescharacteristic
360C2×C4×C103H(5,𝔽2)11yescharacteristic
361C2×C4×C103H(5,𝔽2)11yescharacteristic
362C8×C103—22no—
363C8×C103—22no—
364C8×C103—41no—
365C8×C103—41no—
366C22×C103—22no—
367C22×C103—24no—
368C22×C103—22no—
369C22×C103—22no—
370C22×C103—42no—
371C22×C103—41no—
372C22×C103—42no—
373C22×C103—41no—
374C22×C103—42no—
375C22×C103—41no—
376C22×C103—42no—
377C22×C103—41no—
378C22×C103—42no—
379C22×C103—42no—
380C22×C103—42no—
381C22×C103—42no—
382C22×C103—42no—
383C22×C103—816no—
384C22×C103—81no—
385C22×C103—81no—
386C22×C103—81no—
387C22×C103—81no—
388C22×C103—81no—
389C22×C103—81no—
390C22×C103—81no—
391C22×C103—81no—
392C22×C103—81no—
393C22×C103—81no—
394C22×C103—81no—
395C22×C103#52511yescharacteristic
396C22×C103D4211yescharacteristic
397C22×C103D4211yescharacteristic
398C22×C103C2×#13511yescharacteristic
399C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C103#57611yescharacteristic
401C22×C103#57711yescharacteristic
402C4×C103—22no—
403C4×C103—41no—
404C4×C103—42no—
405C4×C103—41no—
406C4×C103—41no—
407C4×C103—42no—
408C4×C103—41no—
409C4×C103—81no—
410C4×C103—81no—
411C4×C103—81no—
412C4×C103C2×#12111yescharacteristic
413C4×C103#53811yescharacteristic
414C4×C103#54611yescharacteristic
415C4×C103#54611yescharacteristic
416#25152C10311yesmaximal, characteristic, direct product factor, Sylow
417C2×C103—42no—
418C2×C103—44no—
419C2×C103—82no—
420C2×C103—161no—
421C2×C103#242411yescharacteristic
422C2×C103#310511yescharacteristic
423C2×C103#311811yescharacteristic
424C2×C103#326511yescharacteristic
425C2×C103#327411yescharacteristic
426C2×C103#328011yescharacteristic
427C2×C103#328211yescharacteristic
428C2×#463C2×C10311yescharacteristic, complemented
429C2×#450C2×C10311yescharacteristic, complemented
430C2×#447C2×C10311yescharacteristic
431C2×C4×SD16C2×C10311yescharacteristic, complemented
432#2426C2×C10311yescharacteristic, complemented
433D4×C22⋊C4C2×C10311yescharacteristic, complemented
434#2065C2×C10311yescharacteristic, complemented
435#2036C2×C10311yescharacteristic, complemented
436#2034C2×C10311yescharacteristic, complemented
437#2012C2×C10311yescharacteristic, complemented
438#1970C2×C10311yescharacteristic, complemented
439#1923C2×C10311yescharacteristic, complemented
440#1880C2×C10311yescharacteristic, complemented
441#1879C2×C10311yescharacteristic, complemented
442#1862C2×C10311yescharacteristic, complemented
443C103#2515211yescharacteristic, direct product factor, Sylow
444C23×D4C22×C10311yescharacteristic
445C22×SD16C22×C10311yescharacteristic
446C22×SD16C22×C10311yescharacteristic
447C22×D8C22×C10311yescharacteristic
448C22×D8C22×C10311yescharacteristic
449C2×#124C22×C10311yescharacteristic, complemented
450C2×C22⋊Q8C22×C10311yescharacteristic
451C2×#121C22×C10311yescharacteristic
452C2×C4×Q8C22×C10311yescharacteristic, complemented
453C2×C4×D4C22×C10311yescharacteristic
454C2×C4×D4C22×C10311yescharacteristic
455C22×C22⋊C4—21no—
456#463—24no—
457#450—24no—
458#447—24no—
459C4×SD16—24no—
460C2×#107C22×C10311yescharacteristic, complemented
461C2×#106C22×C10311yescharacteristic, complemented
462C2×C4⋊C8C22×C10311yescharacteristic, complemented
463C2×#103C22×C10311yescharacteristic, complemented
464C2×#103C22×C10311yescharacteristic, complemented
465C2×#102C22×C10311yescharacteristic
466C2×#102C22×C10311yescharacteristic
467C2×#102C22×C10311yescharacteristic
468C2×#102C22×C10311yescharacteristic
469C2×#102C22×C10311yescharacteristic, complemented
470C2×#102C22×C10311yescharacteristic, complemented
471C2×C22⋊C8C22×C10311yescharacteristic
472C2×C22⋊C8C22×C10311yescharacteristic
473C2×C4×C8C22×C10311yescharacteristic, complemented
474#396—21no—
475#394—21no—
476#390—21no—
477#390C22×C10311yescharacteristic
478#390C22×C10311yescharacteristic
479#390C22×C10311yescharacteristic, complemented
480#389C22×C10311yescharacteristic, complemented
481#388—21no—
482#386—21no—
483#386—21no—
484#380C22×C10311yescharacteristic
485#379—21no—
486C4×C22⋊C4C22×C10311yescharacteristic
487#340C22×C10311yescharacteristic, complemented
488#340C22×C10311yescharacteristic, complemented
489#336C22×C10311yescharacteristic, complemented
490#336C22×C10311yescharacteristic, complemented
491C25—21no—
492C22×Q8C23×C10311yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C10311yescharacteristic
502C22×D4C23×C10311yescharacteristic
503C22×D4C23×C10311yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C10311yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C10314yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C10311yescharacteristic
520C22×C8C23×C10311yescharacteristic
521C22×C8C23×C10311yescharacteristic
522C22×C8C23×C10311yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C10311yescharacteristic
539C2×C4⋊C4C23×C10311yescharacteristic
540C2×C4⋊C4C23×C10311yescharacteristic
541C2×C4⋊C4C23×C10311yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C10311yescharacteristic
557C2×C22⋊C4D4×C10311yescharacteristic
558C2×C42—21no—
559C2×C42C23×C10311yescharacteristic
560C2×C42C23×C10311yescharacteristic
561#107—41no—
562#106—22no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C10314yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574C4×C8—22no—
575#95—21no—
576#95—21no—
577#95D4×C10311yescharacteristic
578#95D4×C10311yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C10311yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C10312yes—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C10312yes—
621C2×D4C2×D4×C10312yes—
622C2×D4#41×C10312yes—
623C2×D4#41×C10312yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C10311yescharacteristic
642C22×C4C2×D4×C10311yescharacteristic
643C22×C4C2×D4×C10311yescharacteristic
644C22×C4C2×D4×C10311yescharacteristic
645C22×C4C2×D4×C10311yescharacteristic
646C22×C4C24×C10311yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C10312yes—
662C2×C8C2×D4×C10312yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C10312yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23#135×C10312yes—
729C23C22×D4×C10311yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C10314yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4AGL(1,ℤ/8)×C10312yes—
784C2×C4C22×D4×C10311yescharacteristic
785C2×C4C22×D4×C10311yescharacteristic
786C2×C4C2×#41×C10311yescharacteristic
787C2×C4C2×#41×C10311yescharacteristic
788C2×C4H(5,𝔽2)×C10311yescharacteristic
789C2×C4H(5,𝔽2)×C10311yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—24no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22#525×C10311yescharacteristic
824C22D42×C10311yescharacteristic
825C22D42×C10311yescharacteristic
826C22C2×#135×C10311yescharacteristic
827C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
828C22#576×C10311yescharacteristic
829C22#577×C10311yescharacteristic
830C4—22no—
831C4—41no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C10311yescharacteristic
841C4#538×C10311yescharacteristic
842C4#546×C10311yescharacteristic
843C4#546×C10311yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C103×#242411yescharacteristic
849C2C103×#310511yescharacteristic
850C2C103×#311811yescharacteristic
851C2C103×#326511yescharacteristic
852C2C103×#327411yescharacteristic
853C2C103×#328011yescharacteristic
854C2C103×#328211yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#447×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C22⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C103C2semidirect
2. C2×#450×C103C2semidirect
4. C2×C4×SD16×C103C2semidirect
5. C103×#2426C2semidirect
6. D4×C22⋊C4×C103C2semidirect
7. C103×#2065C2semidirect
8. C103×#2036C2semidirect
9. C103×#2034C2semidirect
10. C103×#2012C2semidirect
11. C103×#1970C2semidirect
12. C103×#1923C2semidirect
13. C103×#1880C2semidirect
14. C103×#1879C2semidirect
15. C103×#1862C2semidirect
21. C2×#124×C103C22semidirect
24. C2×C4×Q8×C103C22semidirect
32. C2×#107×C103C22semidirect
33. C2×#106×C103C22semidirect
34. C2×C4⋊C8×C103C22semidirect
35. C2×#103×C103C22semidirect
36. C2×#103×C103C22semidirect
41. C2×#102×C103C22semidirect
42. C2×#102×C103C22semidirect
45. C2×C4×C8×C103C22semidirect
51. #390×C103C22semidirect
52. #389×C103C22semidirect
59. #340×C103C22semidirect
60. #340×C103C22semidirect
61. #336×C103C22semidirect
62. #336×C103C22semidirect
84. C2×SD16×C103D4semidirect
416. #25152C103direct (N × H)
428. C2×#463C2×C103semidirect
429. C2×#450C2×C103semidirect
431. C2×C4×SD16C2×C103semidirect
432. #2426C2×C103semidirect
433. D4×C22⋊C4C2×C103semidirect
434. #2065C2×C103semidirect
435. #2036C2×C103semidirect
436. #2034C2×C103semidirect
437. #2012C2×C103semidirect
438. #1970C2×C103semidirect
439. #1923C2×C103semidirect
440. #1880C2×C103semidirect
441. #1879C2×C103semidirect
442. #1862C2×C103semidirect
443. C103#25152direct (N × H)
449. C2×#124C22×C103semidirect
452. C2×C4×Q8C22×C103semidirect
460. C2×#107C22×C103semidirect
461. C2×#106C22×C103semidirect
462. C2×C4⋊C8C22×C103semidirect
463. C2×#103C22×C103semidirect
464. C2×#103C22×C103semidirect
469. C2×#102C22×C103semidirect
470. C2×#102C22×C103semidirect
473. C2×C4×C8C22×C103semidirect
479. #390C22×C103semidirect
480. #389C22×C103semidirect
487. #340C22×C103semidirect
488. #340C22×C103semidirect
489. #336C22×C103semidirect
490. #336C22×C103semidirect
512. C2×SD16D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1032
C2×#450×C1032
C2×#447×C1032
C2×C4×SD16×C1032
C103×#24262
D4×C22⋊C4×C1032
C103×#20652
C103×#20362
C103×#20342
C103×#20122
C103×#19702
C103×#19232
C103×#18802
C103×#18792
C103×#18622
#25152103