Finite Group Databasebeta

← C103×#24044 #39929319

Subgroups — C103×#24044 #39929319

Order 26368.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C103C211yesmaximal, characteristic
2C2×#482×C103C211yesmaximal, characteristic, complemented
3C2×#418×C103C211yesmaximal, characteristic, complemented
4C103×#2485C211yesmaximal, characteristic, complemented
5C103×#2041C211yesmaximal, characteristic, complemented
6C103×#2041C211yesmaximal, characteristic, complemented
7C103×#2034C211yesmaximal, characteristic, complemented
8C103×#2033C211yesmaximal, characteristic, complemented
9C103×#1895C211yesmaximal, characteristic, complemented
10C103×#1870C211yesmaximal, characteristic, complemented
11C103×#1864C211yesmaximal, characteristic, complemented
12C103×#1862C211yesmaximal, characteristic, complemented
13C103×#1786C211yesmaximal, characteristic, complemented
14C103×#1786C211yesmaximal, characteristic, complemented
15C103×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C103—21no—
17C23×D4×C103C2211yescharacteristic
18C23×D4×C103C2211yescharacteristic
19C22×M16×C103C2211yescharacteristic, complemented
20D42×C103—24no—
21D42×C103—24no—
22C2×#127×C103C2211yescharacteristic
23C2×#121×C103—21no—
24C2×#121×C103C2211yescharacteristic
25C2×#121×C103C2211yescharacteristic
26C2×#120×C103—21no—
27C2×#120×C103—21no—
28C2×C4×D4×C103C2211yescharacteristic
29C2×C4×D4×C103C2211yescharacteristic
30C2×#117×C103C2211yescharacteristic, complemented
31#482×C103—24no—
32C2×#107×C103C2211yescharacteristic, complemented
33C2×#106×C103C2211yescharacteristic, complemented
34#418×C103—24no—
35C2×#102×C103C2211yescharacteristic
36C2×#102×C103C2211yescharacteristic
37C2×#102×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic
39C2×#102×C103C2211yescharacteristic, complemented
40C2×#102×C103C2211yescharacteristic, complemented
41C2×#102×C103C2211yescharacteristic, complemented
42C2×#102×C103C2211yescharacteristic, complemented
43C2×#102×C103C2211yescharacteristic, complemented
44C2×#102×C103C2211yescharacteristic, complemented
45C2×#102×C103C2211yescharacteristic, complemented
46C2×#102×C103C2211yescharacteristic, complemented
47C2×C22⋊C8×C103C2211yescharacteristic, complemented
48C2×C22⋊C8×C103C2211yescharacteristic, complemented
49C2×C22⋊C8×C103C2211yescharacteristic, complemented
50#397×C103—21no—
51#394×C103—21no—
52#389×C103C2211yescharacteristic, complemented
53#389×C103C2211yescharacteristic, complemented
54#388×C103—21no—
55#387×C103—21no—
56#380×C103C2211yescharacteristic, complemented
57#380×C103C2211yescharacteristic, complemented
58#380×C103C2211yescharacteristic, complemented
59#340×C103C2211yescharacteristic, complemented
60#340×C103C2211yescharacteristic, complemented
61#336×C103C2211yescharacteristic, complemented
62#336×C103C2211yescharacteristic, complemented
63C25×C103—21no—
64C25×C103—21no—
65C22×D4×C103—22no—
66C22×D4×C103—22no—
67C22×D4×C103—28no—
68C22×D4×C103—21no—
69C22×D4×C103—21no—
70C22×D4×C103—22no—
71C22×D4×C103—22no—
72C22×D4×C103—22no—
73C22×D4×C103—22no—
74C22×D4×C103—21no—
75C22×D4×C103—21no—
76C22×D4×C103—21no—
77C22×D4×C103—22no—
78C22×D4×C103—21no—
79C22×D4×C103—41no—
80C22×D4×C103—41no—
81C22×D4×C103—41no—
82C22×D4×C103—41no—
83C22×D4×C103—44no—
84C22×D4×C103—44no—
85C22×D4×C103D411yescharacteristic
86C22×D4×C103D414yes—
87C22×D4×C103C2311yescharacteristic
88C22×D4×C103C2311yescharacteristic
89C22×D4×C103C2311yescharacteristic
90C23×C4×C103—21no—
91C23×C4×C103C2311yescharacteristic
92C23×C4×C103C2311yescharacteristic
93C2×M16×C103—22no—
94C2×M16×C103—41no—
95C2×M16×C103—41no—
96C22×C8×C103C2311yescharacteristic
97C22×C8×C103C2311yescharacteristic
98C22×C8×C103C2311yescharacteristic
99C22×C8×C103C2311yescharacteristic
100#127×C103—22no—
101#127×C103—22no—
102#121×C103—28no—
103#121×C103—22no—
104#121×C103—22no—
105#121×C103—22no—
106#121×C103D414yes—
107#120×C103—28no—
108#120×C103—28no—
109C4×D4×C103—22no—
110C4×D4×C103—22no—
111C4×D4×C103—22no—
112C4×D4×C103—22no—
113#117×C103—22no—
114#117×C103—22no—
115C2×C4⋊C4×C103—21no—
116C2×C4⋊C4×C103—21no—
117C2×C4⋊C4×C103D411yescharacteristic
118C2×C4⋊C4×C103C2311yescharacteristic
119C2×C4⋊C4×C103C2311yescharacteristic
120C2×C4⋊C4×C103C2311yescharacteristic
121C2×C4⋊C4×C103C2311yescharacteristic
122C2×C4⋊C4×C103C2311yescharacteristic
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103—21no—
129C2×C22⋊C4×C103—21no—
130C2×C22⋊C4×C103D411yescharacteristic
131C2×C22⋊C4×C103D411yescharacteristic
132C2×C42×C103—21no—
133C2×C42×C103C2311yescharacteristic
134#107×C103—22no—
135#106×C103—22no—
136#102×C103—22no—
137#102×C103—22no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—22no—
141#102×C103—22no—
142#102×C103—22no—
143#102×C103—22no—
144#102×C103—41no—
145#102×C103—41no—
146#102×C103—41no—
147#102×C103—41no—
148C22⋊C8×C103—22no—
149C22⋊C8×C103—41no—
150C22⋊C8×C103—41no—
151#95×C103—21no—
152#95×C103—21no—
153#95×C103—21no—
154#95×C103—21no—
155#95×C103—21no—
156C24×C103—21no—
157C24×C103—24no—
158C24×C103—21no—
159C24×C103—21no—
160C24×C103—24no—
161C24×C103—42no—
162C24×C103—42no—
163C24×C103—42no—
164C24×C103—42no—
165C24×C103—42no—
166C24×C103—42no—
167C24×C103—42no—
168C24×C103—42no—
169C24×C103—81no—
170C24×C103—81no—
171C24×C103—81no—
172C24×C103—81no—
173C24×C103C2×D411yescharacteristic
174C24×C103C2×D411yescharacteristic
175C2×D4×C103—22no—
176C2×D4×C103—22no—
177C2×D4×C103—28no—
178C2×D4×C103—24no—
179C2×D4×C103—24no—
180C2×D4×C103—24no—
181C2×D4×C103—24no—
182C2×D4×C103—24no—
183C2×D4×C103—24no—
184C2×D4×C103—22no—
185C2×D4×C103—21no—
186C2×D4×C103—21no—
187C2×D4×C103—21no—
188C2×D4×C103—21no—
189C2×D4×C103—21no—
190C2×D4×C103—21no—
191C2×D4×C103—21no—
192C2×D4×C103—21no—
193C2×D4×C103—21no—
194C2×D4×C103—21no—
195C2×D4×C103—21no—
196C2×D4×C103—21no—
197C2×D4×C103—21no—
198C2×D4×C103—44no—
199C2×D4×C103—44no—
200C2×D4×C103—44no—
201C2×D4×C103—42no—
202C2×D4×C103—42no—
203C2×D4×C103—42no—
204C2×D4×C103—42no—
205C2×D4×C103—42no—
206C2×D4×C103—44no—
207C2×D4×C103—44no—
208C2×D4×C103—432no—
209C2×D4×C103—44no—
210C2×D4×C103—42no—
211C2×D4×C103—42no—
212C2×D4×C103—42no—
213C2×D4×C103—42no—
214C2×D4×C103—44no—
215C2×D4×C103—42no—
216C2×D4×C103—81no—
217C2×D4×C103—81no—
218C2×D4×C103C2×D412yes—
219C2×D4×C103C2×D412yes—
220C2×D4×C103C2×D412yes—
221C2×D4×C103#4112yes—
222C2×D4×C103#4112yes—
223C22×C4×C103—21no—
224C22×C4×C103—21no—
225C22×C4×C103—21no—
226C22×C4×C103—21no—
227C22×C4×C103—24no—
228C22×C4×C103—21no—
229C22×C4×C103—21no—
230C22×C4×C103—21no—
231C22×C4×C103—21no—
232C22×C4×C103—21no—
233C22×C4×C103—21no—
234C22×C4×C103—21no—
235C22×C4×C103—21no—
236C22×C4×C103—21no—
237C22×C4×C103—21no—
238C22×C4×C103—21no—
239C22×C4×C103—42no—
240C22×C4×C103—42no—
241C22×C4×C103C2×D411yescharacteristic
242C22×C4×C103C2×D411yescharacteristic
243C22×C4×C103C2×D411yescharacteristic
244C22×C4×C103C2×D412yes—
245C22×C4×C103C2×D412yes—
246C22×C4×C103C2×D411yescharacteristic
247C22×C4×C103C2411yescharacteristic
248M16×C103—44no—
249C2×C8×C103—21no—
250C2×C8×C103—21no—
251C2×C8×C103—21no—
252C2×C8×C103—21no—
253C2×C8×C103—21no—
254C2×C8×C103—21no—
255C2×C8×C103—21no—
256C2×C8×C103—21no—
257C2×C8×C103—21no—
258C2×C8×C103—21no—
259C2×C8×C103—21no—
260C2×C8×C103—21no—
261C4⋊C4×C103—22no—
262C4⋊C4×C103—21no—
263C4⋊C4×C103—21no—
264C4⋊C4×C103—21no—
265C4⋊C4×C103—21no—
266C4⋊C4×C103—21no—
267C4⋊C4×C103—21no—
268C4⋊C4×C103—21no—
269C4⋊C4×C103—21no—
270C4⋊C4×C103—21no—
271C4⋊C4×C103—42no—
272C4⋊C4×C103—81no—
273C4⋊C4×C103C2×D412yes—
274C22⋊C4×C103—24no—
275C22⋊C4×C103—24no—
276C22⋊C4×C103—22no—
277C22⋊C4×C103—24no—
278C22⋊C4×C103—22no—
279C22⋊C4×C103—42no—
280C22⋊C4×C103—42no—
281C22⋊C4×C103—81no—
282C22⋊C4×C103—81no—
283C42×C103—21no—
284C42×C103—21no—
285C42×C103—42no—
286C23×C103—21no—
287C23×C103—22no—
288C23×C103—21no—
289C23×C103—21no—
290C23×C103—21no—
291C23×C103—21no—
292C23×C103—22no—
293C23×C103—22no—
294C23×C103—21no—
295C23×C103—21no—
296C23×C103—21no—
297C23×C103—21no—
298C23×C103—21no—
299C23×C103—21no—
300C23×C103—21no—
301C23×C103—22no—
302C23×C103—22no—
303C23×C103—48no—
304C23×C103—48no—
305C23×C103—48no—
306C23×C103—48no—
307C23×C103—41no—
308C23×C103—41no—
309C23×C103—41no—
310C23×C103—41no—
311C23×C103—41no—
312C23×C103—41no—
313C23×C103—41no—
314C23×C103—41no—
315C23×C103—41no—
316C23×C103—41no—
317C23×C103—41no—
318C23×C103—41no—
319C23×C103—41no—
320C23×C103—41no—
321C23×C103—41no—
322C23×C103—41no—
323C23×C103—84no—
324C23×C103—84no—
325C23×C103—84no—
326C23×C103—84no—
327C23×C103—84no—
328C23×C103—84no—
329C23×C103—84no—
330C23×C103—84no—
331C23×C103—84no—
332C23×C103—84no—
333C23×C103#12012yes—
334C23×C103AGL(1,ℤ/8)12yes—
335C23×C103C22×D411yescharacteristic
336D4×C103—28no—
337D4×C103—22no—
338D4×C103—22no—
339D4×C103—22no—
340D4×C103—22no—
341D4×C103—22no—
342D4×C103—22no—
343D4×C103—22no—
344D4×C103—48no—
345D4×C103—48no—
346D4×C103—48no—
347D4×C103—48no—
348D4×C103—48no—
349D4×C103—41no—
350D4×C103—41no—
351D4×C103—41no—
352D4×C103—41no—
353D4×C103—84no—
354D4×C103#12314yes—
355C2×C4×C103—21no—
356C2×C4×C103—21no—
357C2×C4×C103—21no—
358C2×C4×C103—21no—
359C2×C4×C103—22no—
360C2×C4×C103—22no—
361C2×C4×C103—22no—
362C2×C4×C103—22no—
363C2×C4×C103—21no—
364C2×C4×C103—21no—
365C2×C4×C103—22no—
366C2×C4×C103—21no—
367C2×C4×C103—21no—
368C2×C4×C103—21no—
369C2×C4×C103—21no—
370C2×C4×C103—48no—
371C2×C4×C103—41no—
372C2×C4×C103—41no—
373C2×C4×C103—41no—
374C2×C4×C103—41no—
375C2×C4×C103—41no—
376C2×C4×C103—41no—
377C2×C4×C103—41no—
378C2×C4×C103—41no—
379C2×C4×C103—41no—
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#12012yes—
390C2×C4×C103AGL(1,ℤ/8)12yes—
391C2×C4×C103C22×D411yescharacteristic
392C2×C4×C103C22×D411yescharacteristic
393C2×C4×C103C2×#4111yescharacteristic
394C2×C4×C103C2×#4111yescharacteristic
395C2×C4×C103H(5,𝔽2)11yescharacteristic
396C2×C4×C103H(5,𝔽2)11yescharacteristic
397C8×C103—41no—
398C8×C103—41no—
399C8×C103—41no—
400C8×C103—41no—
401C22×C103—22no—
402C22×C103—24no—
403C22×C103—22no—
404C22×C103—22no—
405C22×C103—22no—
406C22×C103—22no—
407C22×C103—22no—
408C22×C103—41no—
409C22×C103—42no—
410C22×C103—41no—
411C22×C103—42no—
412C22×C103—41no—
413C22×C103—42no—
414C22×C103—41no—
415C22×C103—42no—
416C22×C103—41no—
417C22×C103—41no—
418C22×C103—42no—
419C22×C103—41no—
420C22×C103—41no—
421C22×C103—42no—
422C22×C103—42no—
423C22×C103—42no—
424C22×C103—42no—
425C22×C103—42no—
426C22×C103—42no—
427C22×C103—42no—
428C22×C103—816no—
429C22×C103—816no—
430C22×C103—81no—
431C22×C103—81no—
432C22×C103—81no—
433C22×C103—81no—
434C22×C103—81no—
435C22×C103—81no—
436C22×C103—81no—
437C22×C103—81no—
438C22×C103C2×#12011yescharacteristic
439C22×C103#54611yescharacteristic
440C22×C103#54611yescharacteristic
441C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C103#57611yescharacteristic
444C22×C103#57711yescharacteristic
445C4×C103—22no—
446C4×C103—22no—
447C4×C103—41no—
448C4×C103—42no—
449C4×C103—41no—
450C4×C103—81no—
451C4×C103—81no—
452C4×C103—81no—
453C4×C103—81no—
454C4×C103C2×#12311yescharacteristic
455C4×C103#53411yescharacteristic
456C4×C103#54611yescharacteristic
457C4×C103#54611yescharacteristic
458#24044C10311yesmaximal, characteristic, direct product factor, Sylow
459C2×C103—42no—
460C2×C103—42no—
461C2×C103—44no—
462C2×C103—82no—
463C2×C103—82no—
464C2×C103#240511yescharacteristic
465C2×C103#300311yescharacteristic
466C2×C103#301211yescharacteristic
467C2×C103#331011yescharacteristic
468C2×C103#331811yescharacteristic
469C2×C103#332411yescharacteristic
470C2×C103#332511yescharacteristic
471C2×D42C2×C10311yescharacteristic
472C2×#482C2×C10311yescharacteristic, complemented
473C2×#418C2×C10311yescharacteristic, complemented
474#2485C2×C10311yescharacteristic, complemented
475#2041C2×C10311yescharacteristic, complemented
476#2041C2×C10311yescharacteristic, complemented
477#2034C2×C10311yescharacteristic, complemented
478#2033C2×C10311yescharacteristic, complemented
479#1895C2×C10311yescharacteristic, complemented
480#1870C2×C10311yescharacteristic, complemented
481#1864C2×C10311yescharacteristic, complemented
482#1862C2×C10311yescharacteristic, complemented
483#1786C2×C10311yescharacteristic, complemented
484#1786C2×C10311yescharacteristic, complemented
485#1786C2×C10311yescharacteristic, complemented
486C103#2404411yescharacteristic, direct product factor, Sylow
487C23×D4—21no—
488C23×D4C22×C10311yescharacteristic
489C23×D4C22×C10311yescharacteristic
490C22×M16C22×C10311yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C10311yescharacteristic
494C2×#121—21no—
495C2×#121C22×C10311yescharacteristic
496C2×#121C22×C10311yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C10311yescharacteristic
500C2×C4×D4C22×C10311yescharacteristic
501C2×#117C22×C10311yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C10311yescharacteristic, complemented
504C2×#106C22×C10311yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C10311yescharacteristic
507C2×#102C22×C10311yescharacteristic
508C2×#102C22×C10311yescharacteristic
509C2×#102C22×C10311yescharacteristic
510C2×#102C22×C10311yescharacteristic, complemented
511C2×#102C22×C10311yescharacteristic, complemented
512C2×#102C22×C10311yescharacteristic, complemented
513C2×#102C22×C10311yescharacteristic, complemented
514C2×#102C22×C10311yescharacteristic, complemented
515C2×#102C22×C10311yescharacteristic, complemented
516C2×#102C22×C10311yescharacteristic, complemented
517C2×#102C22×C10311yescharacteristic, complemented
518C2×C22⋊C8C22×C10311yescharacteristic, complemented
519C2×C22⋊C8C22×C10311yescharacteristic, complemented
520C2×C22⋊C8C22×C10311yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C10311yescharacteristic, complemented
524#389C22×C10311yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C10311yescharacteristic, complemented
528#380C22×C10311yescharacteristic, complemented
529#380C22×C10311yescharacteristic, complemented
530#340C22×C10311yescharacteristic, complemented
531#340C22×C10311yescharacteristic, complemented
532#336C22×C10311yescharacteristic, complemented
533#336C22×C10311yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C10311yescharacteristic
557C22×D4D4×C10314yes—
558C22×D4C23×C10311yescharacteristic
559C22×D4C23×C10311yescharacteristic
560C22×D4C23×C10311yescharacteristic
561C23×C4—21no—
562C23×C4C23×C10311yescharacteristic
563C23×C4C23×C10311yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C10311yescharacteristic
568C22×C8C23×C10311yescharacteristic
569C22×C8C23×C10311yescharacteristic
570C22×C8C23×C10311yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C10314yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C10311yescharacteristic
589C2×C4⋊C4C23×C10311yescharacteristic
590C2×C4⋊C4C23×C10311yescharacteristic
591C2×C4⋊C4C23×C10311yescharacteristic
592C2×C4⋊C4C23×C10311yescharacteristic
593C2×C4⋊C4C23×C10311yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C10311yescharacteristic
602C2×C22⋊C4D4×C10311yescharacteristic
603C2×C42—21no—
604C2×C42C23×C10311yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C10311yescharacteristic
645C24C2×D4×C10311yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C10312yes—
690C2×D4C2×D4×C10312yes—
691C2×D4C2×D4×C10312yes—
692C2×D4#41×C10312yes—
693C2×D4#41×C10312yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C10311yescharacteristic
713C22×C4C2×D4×C10311yescharacteristic
714C22×C4C2×D4×C10311yescharacteristic
715C22×C4C2×D4×C10312yes—
716C22×C4C2×D4×C10312yes—
717C22×C4C2×D4×C10311yescharacteristic
718C22×C4C24×C10311yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C10312yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C10312yes—
805C23AGL(1,ℤ/8)×C10312yes—
806C23C22×D4×C10311yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C10314yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C10312yes—
861C2×C4AGL(1,ℤ/8)×C10312yes—
862C2×C4C22×D4×C10311yescharacteristic
863C2×C4C22×D4×C10311yescharacteristic
864C2×C4C2×#41×C10311yescharacteristic
865C2×C4C2×#41×C10311yescharacteristic
866C2×C4H(5,𝔽2)×C10311yescharacteristic
867C2×C4H(5,𝔽2)×C10311yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—24no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C10311yescharacteristic
910C22#546×C10311yescharacteristic
911C22#546×C10311yescharacteristic
912C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
913C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
914C22#576×C10311yescharacteristic
915C22#577×C10311yescharacteristic
916C4—22no—
917C4—22no—
918C4—42no—
919C4—41no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C10311yescharacteristic
926C4#534×C10311yescharacteristic
927C4#546×C10311yescharacteristic
928C4#546×C10311yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C103×#240511yescharacteristic
935C2C103×#300311yescharacteristic
936C2C103×#301211yescharacteristic
937C2C103×#331011yescharacteristic
938C2C103×#331811yescharacteristic
939C2C103×#332411yescharacteristic
940C2C103×#332511yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×D42×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#482×C103C2semidirect
3. C2×#418×C103C2semidirect
4. C103×#2485C2semidirect
5. C103×#2041C2semidirect
6. C103×#2041C2semidirect
7. C103×#2034C2semidirect
8. C103×#2033C2semidirect
9. C103×#1895C2semidirect
10. C103×#1870C2semidirect
11. C103×#1864C2semidirect
12. C103×#1862C2semidirect
13. C103×#1786C2semidirect
14. C103×#1786C2semidirect
15. C103×#1786C2semidirect
19. C22×M16×C103C22semidirect
30. C2×#117×C103C22semidirect
32. C2×#107×C103C22semidirect
33. C2×#106×C103C22semidirect
39. C2×#102×C103C22semidirect
40. C2×#102×C103C22semidirect
41. C2×#102×C103C22semidirect
42. C2×#102×C103C22semidirect
43. C2×#102×C103C22semidirect
44. C2×#102×C103C22semidirect
45. C2×#102×C103C22semidirect
46. C2×#102×C103C22semidirect
47. C2×C22⋊C8×C103C22semidirect
48. C2×C22⋊C8×C103C22semidirect
49. C2×C22⋊C8×C103C22semidirect
52. #389×C103C22semidirect
53. #389×C103C22semidirect
56. #380×C103C22semidirect
57. #380×C103C22semidirect
58. #380×C103C22semidirect
59. #340×C103C22semidirect
60. #340×C103C22semidirect
61. #336×C103C22semidirect
62. #336×C103C22semidirect
458. #24044C103direct (N × H)
472. C2×#482C2×C103semidirect
473. C2×#418C2×C103semidirect
474. #2485C2×C103semidirect
475. #2041C2×C103semidirect
476. #2041C2×C103semidirect
477. #2034C2×C103semidirect
478. #2033C2×C103semidirect
479. #1895C2×C103semidirect
480. #1870C2×C103semidirect
481. #1864C2×C103semidirect
482. #1862C2×C103semidirect
483. #1786C2×C103semidirect
484. #1786C2×C103semidirect
485. #1786C2×C103semidirect
486. C103#24044direct (N × H)
490. C22×M16C22×C103semidirect
501. C2×#117C22×C103semidirect
503. C2×#107C22×C103semidirect
504. C2×#106C22×C103semidirect
510. C2×#102C22×C103semidirect
511. C2×#102C22×C103semidirect
512. C2×#102C22×C103semidirect
513. C2×#102C22×C103semidirect
514. C2×#102C22×C103semidirect
515. C2×#102C22×C103semidirect
516. C2×#102C22×C103semidirect
517. C2×#102C22×C103semidirect
518. C2×C22⋊C8C22×C103semidirect
519. C2×C22⋊C8C22×C103semidirect
520. C2×C22⋊C8C22×C103semidirect
523. #389C22×C103semidirect
524. #389C22×C103semidirect
527. #380C22×C103semidirect
528. #380C22×C103semidirect
529. #380C22×C103semidirect
530. #340C22×C103semidirect
531. #340C22×C103semidirect
532. #336C22×C103semidirect
533. #336C22×C103semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1032
C2×#482×C1032
C2×#418×C1032
C103×#24852
C103×#20412
C103×#20342
C103×#20332
C103×#18952
C103×#18702
C103×#18642
C103×#18622
C103×#17862
#24044103