Finite Group Databasebeta

← C103×#23972 #39929247

Subgroups — C103×#23972 #39929247

Order 26368.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C103C211yesmaximal, characteristic, complemented
2C2×#449×C103C211yesmaximal, characteristic, complemented
3C2×#417×C103C211yesmaximal, characteristic, complemented
4C103×#2407C211yesmaximal, characteristic, complemented
5C103×#2024C211yesmaximal, characteristic, complemented
6C103×#2023C211yesmaximal, characteristic, complemented
7C103×#2000C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1895C211yesmaximal, characteristic, complemented
10C103×#1879C211yesmaximal, characteristic, complemented
11C103×#1877C211yesmaximal, characteristic, complemented
12C103×#1874C211yesmaximal, characteristic, complemented
13C103×#1872C211yesmaximal, characteristic, complemented
14C103×#1870C211yesmaximal, characteristic, complemented
15C103×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C103—21no—
17C22×#41×C103C2211yescharacteristic
18C22×SD16×C103C2211yescharacteristic
19C22×D8×C103C2211yescharacteristic
20C22×M16×C103C2211yescharacteristic
21#547×C103—24no—
22#547×C103—24no—
23C2×C4⋊Q8×C103C2211yescharacteristic
24C2×#123×C103—21no—
25C2×#123×C103—21no—
26C2×C22⋊Q8×C103—21no—
27C2×C22⋊Q8×C103C2211yescharacteristic
28C2×#121×C103C2211yescharacteristic
29C2×#121×C103C2211yescharacteristic
30C2×#121×C103C2211yescharacteristic
31C2×C4×D4×C103C2211yescharacteristic
32C2×C4×D4×C103C2211yescharacteristic
33C22×C4⋊C4×C103C2211yescharacteristic
34C22×C4⋊C4×C103C2211yescharacteristic
35#449×C103—24no—
36#417×C103—24no—
37C2×#103×C103C2211yescharacteristic
38C2×#103×C103C2211yescharacteristic
39C2×#103×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×C22⋊C8×C103C2211yescharacteristic
46C2×C22⋊C8×C103C2211yescharacteristic
47C2×C22⋊C8×C103C2211yescharacteristic
48#394×C103—21no—
49#392×C103—21no—
50#391×C103C2211yescharacteristic
51#390×C103C2211yescharacteristic
52#386×C103—21no—
53#385×C103—21no—
54#380×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C2×#41×C103—28no—
64C2×#41×C103—22no—
65C2×#41×C103—22no—
66C2×#41×C103—22no—
67C2×#41×C103—22no—
68C2×#41×C103—41no—
69C2×#41×C103—41no—
70C2×#41×C103—44no—
71C2×#41×C103—44no—
72C22×Q8×C103—21no—
73C22×Q8×C103C2311yescharacteristic
74C22×D4×C103—21no—
75C22×D4×C103—21no—
76C22×D4×C103—21no—
77C22×D4×C103—21no—
78C22×D4×C103D411yescharacteristic
79C22×D4×C103C2311yescharacteristic
80C22×D4×C103C2311yescharacteristic
81C23×C4×C103—21no—
82C23×C4×C103—21no—
83C23×C4×C103—21no—
84C23×C4×C103—21no—
85C23×C4×C103C2311yescharacteristic
86C23×C4×C103C2311yescharacteristic
87C2×SD16×C103—22no—
88C2×SD16×C103—22no—
89C2×SD16×C103—41no—
90C2×D8×C103—22no—
91C2×D8×C103—22no—
92C2×D8×C103—41no—
93C2×M16×C103—22no—
94C2×M16×C103—41no—
95C2×M16×C103—41no—
96C22×C8×C103C2311yescharacteristic
97C22×C8×C103C2311yescharacteristic
98C22×C8×C103C2311yescharacteristic
99C22×C8×C103C2311yescharacteristic
100C4⋊Q8×C103—22no—
101C4⋊Q8×C103—22no—
102#123×C103—28no—
103#123×C103—28no—
104C22⋊Q8×C103—28no—
105C22⋊Q8×C103—22no—
106C22⋊Q8×C103—41no—
107#121×C103—22no—
108#121×C103—22no—
109#121×C103—22no—
110#121×C103—22no—
111#121×C103—41no—
112#121×C103D414yescomplemented
113C4×D4×C103—22no—
114C4×D4×C103—22no—
115C4×D4×C103—22no—
116C4×D4×C103—22no—
117C2×C4⋊C4×C103—21no—
118C2×C4⋊C4×C103—21no—
119C2×C4⋊C4×C103—22no—
120C2×C4⋊C4×C103—21no—
121C2×C4⋊C4×C103—22no—
122C2×C4⋊C4×C103—22no—
123C2×C4⋊C4×C103—21no—
124C2×C4⋊C4×C103D411yescharacteristic
125C2×C4⋊C4×C103D414yescomplemented
126C2×C4⋊C4×C103C2311yescharacteristic
127C2×C4⋊C4×C103C2311yescharacteristic
128C2×C4⋊C4×C103C2311yescharacteristic
129C2×C4⋊C4×C103C2311yescharacteristic
130C2×C4⋊C4×C103C2311yescharacteristic
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103—21no—
133C2×C22⋊C4×C103—21no—
134C2×C22⋊C4×C103—21no—
135C2×C22⋊C4×C103—21no—
136C2×C22⋊C4×C103—21no—
137C2×C22⋊C4×C103—21no—
138C2×C22⋊C4×C103—21no—
139C2×C22⋊C4×C103D411yescharacteristic
140C2×C22⋊C4×C103D411yescharacteristic
141C2×C42×C103C2311yescharacteristic
142#103×C103—22no—
143#103×C103—22no—
144#103×C103—22no—
145#102×C103—22no—
146#102×C103—22no—
147#102×C103—22no—
148#102×C103—41no—
149#102×C103—41no—
150C22⋊C8×C103—22no—
151C22⋊C8×C103—41no—
152C22⋊C8×C103—41no—
153#95×C103—21no—
154#95×C103—21no—
155#95×C103—21no—
156C24×C103—21no—
157C24×C103—21no—
158C24×C103C2×D411yescharacteristic
159C24×C103C2×D411yescharacteristic
160#41×C103—28no—
161#41×C103—44no—
162#41×C103—44no—
163#41×C103—44no—
164#41×C103—432no—
165C2×Q8×C103—24no—
166C2×Q8×C103—21no—
167C2×Q8×C103—21no—
168C2×Q8×C103—21no—
169C2×Q8×C103—21no—
170C2×Q8×C103—21no—
171C2×Q8×C103—42no—
172C2×Q8×C103—42no—
173C2×Q8×C103#4112yescomplemented
174C2×D4×C103—22no—
175C2×D4×C103—22no—
176C2×D4×C103—24no—
177C2×D4×C103—24no—
178C2×D4×C103—22no—
179C2×D4×C103—21no—
180C2×D4×C103—21no—
181C2×D4×C103—21no—
182C2×D4×C103—21no—
183C2×D4×C103—21no—
184C2×D4×C103—21no—
185C2×D4×C103—21no—
186C2×D4×C103—21no—
187C2×D4×C103—21no—
188C2×D4×C103—21no—
189C2×D4×C103—42no—
190C2×D4×C103—42no—
191C2×D4×C103—42no—
192C2×D4×C103—42no—
193C2×D4×C103—42no—
194C2×D4×C103—42no—
195C2×D4×C103—42no—
196C2×D4×C103—42no—
197C2×D4×C103—42no—
198C2×D4×C103—81no—
199C2×D4×C103C2×D412yes—
200C2×D4×C103#4112yescomplemented
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—21no—
204C22×C4×C103—21no—
205C22×C4×C103—24no—
206C22×C4×C103—24no—
207C22×C4×C103—24no—
208C22×C4×C103—21no—
209C22×C4×C103—21no—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—21no—
213C22×C4×C103—21no—
214C22×C4×C103—21no—
215C22×C4×C103—21no—
216C22×C4×C103—21no—
217C22×C4×C103—21no—
218C22×C4×C103—21no—
219C22×C4×C103—21no—
220C22×C4×C103—42no—
221C22×C4×C103—42no—
222C22×C4×C103—42no—
223C22×C4×C103—42no—
224C22×C4×C103—42no—
225C22×C4×C103—42no—
226C22×C4×C103—42no—
227C22×C4×C103—42no—
228C22×C4×C103—42no—
229C22×C4×C103C2×D411yescharacteristic
230C22×C4×C103C2×D411yescharacteristic
231C22×C4×C103C2×D411yescharacteristic
232C22×C4×C103C2×D412yes—
233C22×C4×C103C2×D412yes—
234C22×C4×C103C2×D411yescharacteristic
235C22×C4×C103C2411yescharacteristic
236SD16×C103—44no—
237D8×C103—44no—
238M16×C103—44no—
239C2×C8×C103—21no—
240C2×C8×C103—21no—
241C2×C8×C103—21no—
242C2×C8×C103—21no—
243C2×C8×C103—21no—
244C2×C8×C103—21no—
245C2×C8×C103—21no—
246C2×C8×C103—21no—
247C2×C8×C103—21no—
248C2×C8×C103—21no—
249C2×C8×C103—21no—
250C2×C8×C103—21no—
251C4⋊C4×C103—24no—
252C4⋊C4×C103—24no—
253C4⋊C4×C103—24no—
254C4⋊C4×C103—22no—
255C4⋊C4×C103—21no—
256C4⋊C4×C103—21no—
257C4⋊C4×C103—21no—
258C4⋊C4×C103—21no—
259C4⋊C4×C103—21no—
260C4⋊C4×C103—21no—
261C4⋊C4×C103—21no—
262C4⋊C4×C103—42no—
263C4⋊C4×C103C2×D412yes—
264C4⋊C4×C103C2×D412yes—
265C4⋊C4×C103C2×D412yes—
266C22⋊C4×C103—24no—
267C22⋊C4×C103—24no—
268C22⋊C4×C103—22no—
269C22⋊C4×C103—24no—
270C22⋊C4×C103—22no—
271C22⋊C4×C103—42no—
272C22⋊C4×C103—42no—
273C22⋊C4×C103—42no—
274C22⋊C4×C103—81no—
275C22⋊C4×C103—81no—
276C42×C103—21no—
277C42×C103—21no—
278C23×C103—21no—
279C23×C103—21no—
280C23×C103—21no—
281C23×C103—21no—
282C23×C103—21no—
283C23×C103—21no—
284C23×C103—21no—
285C23×C103—21no—
286C23×C103—21no—
287C23×C103—21no—
288C23×C103—21no—
289C23×C103—21no—
290C23×C103—22no—
291C23×C103—22no—
292C23×C103—41no—
293C23×C103—41no—
294C23×C103—41no—
295C23×C103—41no—
296C23×C103—41no—
297C23×C103—41no—
298C23×C103—41no—
299C23×C103—41no—
300C23×C103—41no—
301C23×C103—41no—
302C23×C103—41no—
303C23×C103—41no—
304C23×C103#12012yes—
305C23×C103AGL(1,ℤ/8)12yes—
306C23×C103C22×D411yescharacteristic
307Q8×C103—22no—
308Q8×C103—22no—
309Q8×C103—48no—
310Q8×C103—41no—
311Q8×C103—41no—
312D4×C103—28no—
313D4×C103—22no—
314D4×C103—22no—
315D4×C103—22no—
316D4×C103—22no—
317D4×C103—48no—
318D4×C103—48no—
319D4×C103—48no—
320D4×C103—41no—
321D4×C103—41no—
322D4×C103—41no—
323D4×C103—41no—
324D4×C103—84no—
325C2×C4×C103—21no—
326C2×C4×C103—21no—
327C2×C4×C103—21no—
328C2×C4×C103—21no—
329C2×C4×C103—22no—
330C2×C4×C103—22no—
331C2×C4×C103—22no—
332C2×C4×C103—22no—
333C2×C4×C103—21no—
334C2×C4×C103—21no—
335C2×C4×C103—22no—
336C2×C4×C103—22no—
337C2×C4×C103—22no—
338C2×C4×C103—21no—
339C2×C4×C103—22no—
340C2×C4×C103—21no—
341C2×C4×C103—21no—
342C2×C4×C103—21no—
343C2×C4×C103—48no—
344C2×C4×C103—48no—
345C2×C4×C103—48no—
346C2×C4×C103—48no—
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—41no—
354C2×C4×C103—41no—
355C2×C4×C103—41no—
356C2×C4×C103—41no—
357C2×C4×C103—41no—
358C2×C4×C103—41no—
359C2×C4×C103—41no—
360C2×C4×C103—41no—
361C2×C4×C103—41no—
362C2×C4×C103—41no—
363C2×C4×C103—41no—
364C2×C4×C103—41no—
365C2×C4×C103#12012yes—
366C2×C4×C103AGL(1,ℤ/8)12yes—
367C2×C4×C103C22×D411yescharacteristic
368C2×C4×C103C22×D411yescharacteristic
369C2×C4×C103C2×#4111yescharacteristic
370C2×C4×C103C2×#4111yescharacteristic
371C2×C4×C103H(5,𝔽2)11yescharacteristic
372C2×C4×C103H(5,𝔽2)11yescharacteristic
373C8×C103—41no—
374C8×C103—41no—
375C8×C103—41no—
376C8×C103—41no—
377C22×C103—22no—
378C22×C103—22no—
379C22×C103—22no—
380C22×C103—22no—
381C22×C103—22no—
382C22×C103—22no—
383C22×C103—41no—
384C22×C103—41no—
385C22×C103—41no—
386C22×C103—41no—
387C22×C103—41no—
388C22×C103—41no—
389C22×C103—41no—
390C22×C103—41no—
391C22×C103—42no—
392C22×C103—42no—
393C22×C103—42no—
394C22×C103—42no—
395C22×C103—42no—
396C22×C103—42no—
397C22×C103—81no—
398C22×C103—81no—
399C22×C103—81no—
400C22×C103—81no—
401C22×C103—81no—
402C22×C103—81no—
403C22×C103—81no—
404C22×C103—81no—
405C22×C103C2×#12011yescharacteristic
406C22×C103#54611yescharacteristic
407C22×C103#54611yescharacteristic
408C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C103#57711yescharacteristic
411C22×C103#57811yescharacteristic
412C4×C103—22no—
413C4×C103—22no—
414C4×C103—41no—
415C4×C103—42no—
416C4×C103—42no—
417C4×C103—42no—
418C4×C103—42no—
419C4×C103—41no—
420C4×C103—81no—
421C4×C103—81no—
422C4×C103#52511yescharacteristic
423C4×C103#53511yescharacteristic
424C4×C103#54611yescharacteristic
425C4×C103#54611yescharacteristic
426#23972C10311yesmaximal, characteristic, direct product factor, Sylow
427C2×C103—42no—
428C2×C103—42no—
429C2×C103—82no—
430C2×C103—82no—
431C2×C103#240411yescharacteristic
432C2×C103#300311yescharacteristic
433C2×C103#301311yescharacteristic
434C2×C103#330611yescharacteristic
435C2×C103#330811yescharacteristic
436C2×C103#333011yescharacteristic
437C2×C103#333211yescharacteristic
438C2×#547C2×C10311yescharacteristic, complemented
439C2×#449C2×C10311yescharacteristic, complemented
440C2×#417C2×C10311yescharacteristic, complemented
441#2407C2×C10311yescharacteristic, complemented
442#2024C2×C10311yescharacteristic, complemented
443#2023C2×C10311yescharacteristic, complemented
444#2000C2×C10311yescharacteristic, complemented
445#1999C2×C10311yescharacteristic, complemented
446#1895C2×C10311yescharacteristic, complemented
447#1879C2×C10311yescharacteristic, complemented
448#1877C2×C10311yescharacteristic, complemented
449#1874C2×C10311yescharacteristic, complemented
450#1872C2×C10311yescharacteristic, complemented
451#1870C2×C10311yescharacteristic, complemented
452#1824C2×C10311yescharacteristic, complemented
453C103#2397211yescharacteristic, direct product factor, Sylow
454C22×#41—21no—
455C22×#41C22×C10311yescharacteristic
456C22×SD16C22×C10311yescharacteristic
457C22×D8C22×C10311yescharacteristic
458C22×M16C22×C10311yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C10311yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C10311yescharacteristic
466C2×#121C22×C10311yescharacteristic
467C2×#121C22×C10311yescharacteristic
468C2×#121C22×C10311yescharacteristic
469C2×C4×D4C22×C10311yescharacteristic
470C2×C4×D4C22×C10311yescharacteristic
471C22×C4⋊C4C22×C10311yescharacteristic
472C22×C4⋊C4C22×C10311yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C10311yescharacteristic
476C2×#103C22×C10311yescharacteristic
477C2×#103C22×C10311yescharacteristic
478C2×#102C22×C10311yescharacteristic
479C2×#102C22×C10311yescharacteristic
480C2×#102C22×C10311yescharacteristic
481C2×#102C22×C10311yescharacteristic
482C2×#102C22×C10311yescharacteristic
483C2×C22⋊C8C22×C10311yescharacteristic
484C2×C22⋊C8C22×C10311yescharacteristic
485C2×C22⋊C8C22×C10311yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C10311yescharacteristic
489#390C22×C10311yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C10311yescharacteristic
493#340C22×C10311yescharacteristic
494#340C22×C10311yescharacteristic
495#340C22×C10311yescharacteristic
496#340C22×C10311yescharacteristic
497#340C22×C10311yescharacteristic
498#340C22×C10311yescharacteristic
499#336C22×C10311yescharacteristic
500#336C22×C10311yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C10311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C10311yescharacteristic
517C22×D4C23×C10311yescharacteristic
518C22×D4C23×C10311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C10311yescharacteristic
524C23×C4C23×C10311yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C10311yescharacteristic
535C22×C8C23×C10311yescharacteristic
536C22×C8C23×C10311yescharacteristic
537C22×C8C23×C10311yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C10314yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C10311yescharacteristic
563C2×C4⋊C4D4×C10314yescomplemented
564C2×C4⋊C4C23×C10311yescharacteristic
565C2×C4⋊C4C23×C10311yescharacteristic
566C2×C4⋊C4C23×C10311yescharacteristic
567C2×C4⋊C4C23×C10311yescharacteristic
568C2×C4⋊C4C23×C10311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C10311yescharacteristic
578C2×C22⋊C4D4×C10311yescharacteristic
579C2×C42C23×C10311yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C10311yescharacteristic
597C24C2×D4×C10311yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C10312yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C10312yes—
638C2×D4#41×C10312yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C10311yescharacteristic
668C22×C4C2×D4×C10311yescharacteristic
669C22×C4C2×D4×C10311yescharacteristic
670C22×C4C2×D4×C10312yes—
671C22×C4C2×D4×C10312yes—
672C22×C4C2×D4×C10311yescharacteristic
673C22×C4C24×C10311yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C10312yes—
702C4⋊C4C2×D4×C10312yes—
703C4⋊C4C2×D4×C10312yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C10312yes—
743C23AGL(1,ℤ/8)×C10312yes—
744C23C22×D4×C10311yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C10312yes—
804C2×C4AGL(1,ℤ/8)×C10312yes—
805C2×C4C22×D4×C10311yescharacteristic
806C2×C4C22×D4×C10311yescharacteristic
807C2×C4C2×#41×C10311yescharacteristic
808C2×C4C2×#41×C10311yescharacteristic
809C2×C4H(5,𝔽2)×C10311yescharacteristic
810C2×C4H(5,𝔽2)×C10311yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C10311yescharacteristic
844C22#546×C10311yescharacteristic
845C22#546×C10311yescharacteristic
846C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
847C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
848C22#577×C10311yescharacteristic
849C22#578×C10311yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—41no—
856C4—41no—
857C4—42no—
858C4—81no—
859C4—81no—
860C4#525×C10311yescharacteristic
861C4#535×C10311yescharacteristic
862C4#546×C10311yescharacteristic
863C4#546×C10311yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C103×#240411yescharacteristic
869C2C103×#300311yescharacteristic
870C2C103×#301311yescharacteristic
871C2C103×#330611yescharacteristic
872C2C103×#330811yescharacteristic
873C2C103×#333011yescharacteristic
874C2C103×#333211yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
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
1. C2×#547×C103C2semidirect
2. C2×#449×C103C2semidirect
3. C2×#417×C103C2semidirect
4. C103×#2407C2semidirect
5. C103×#2024C2semidirect
6. C103×#2023C2semidirect
7. C103×#2000C2semidirect
8. C103×#1999C2semidirect
9. C103×#1895C2semidirect
10. C103×#1879C2semidirect
11. C103×#1877C2semidirect
12. C103×#1874C2semidirect
13. C103×#1872C2semidirect
14. C103×#1870C2semidirect
15. C103×#1824C2semidirect
112. #121×C103D4semidirect
125. C2×C4⋊C4×C103D4semidirect
173. C2×Q8×C103#41semidirect
200. C2×D4×C103#41semidirect
426. #23972C103direct (N × H)
438. C2×#547C2×C103semidirect
439. C2×#449C2×C103semidirect
440. C2×#417C2×C103semidirect
441. #2407C2×C103semidirect
442. #2024C2×C103semidirect
443. #2023C2×C103semidirect
444. #2000C2×C103semidirect
445. #1999C2×C103semidirect
446. #1895C2×C103semidirect
447. #1879C2×C103semidirect
448. #1877C2×C103semidirect
449. #1874C2×C103semidirect
450. #1872C2×C103semidirect
451. #1870C2×C103semidirect
452. #1824C2×C103semidirect
453. C103#23972direct (N × H)
550. #121D4×C103semidirect
563. C2×C4⋊C4D4×C103semidirect
611. C2×Q8#41×C103semidirect
638. C2×D4#41×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1032
C2×#449×C1032
C2×#417×C1032
C103×#24072
C103×#20242
C103×#20232
C103×#20002
C103×#19992
C103×#18952
C103×#18792
C103×#18772
C103×#18742
C103×#18722
C103×#18702
C103×#18242
#23972103