Finite Group Databasebeta

← C103×#24452 #39929727

Subgroups — C103×#24452 #39929727

Order 26368.

1592 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C103C211yesmaximal, characteristic
2C2×#468×C103C211yesmaximal, characteristic, complemented
3C2×#452×C103C211yesmaximal, characteristic, complemented
4C2×#450×C103C211yesmaximal, characteristic, complemented
5C2×#417×C103C211yesmaximal, characteristic, complemented
6C103×#2417C211yesmaximal, characteristic, complemented
7C103×#2042C211yesmaximal, characteristic, complemented
8C103×#2036C211yesmaximal, characteristic, complemented
9C103×#2015C211yesmaximal, characteristic, complemented
10C103×#2001C211yesmaximal, characteristic, complemented
11C103×#1877C211yesmaximal, characteristic, complemented
12C103×#1874C211yesmaximal, characteristic, complemented
13C103×#1870C211yesmaximal, characteristic, complemented
14C103×#1862C211yesmaximal, characteristic, complemented
15C103×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C23×D4×C103C2211yescharacteristic
18C22×Q16×C103C2211yescharacteristic, complemented
19C22×SD16×C103C2211yescharacteristic
20C22×SD16×C103C2211yescharacteristic
21C22×M16×C103C2211yescharacteristic, complemented
22#546×C103—24no—
23#546×C103—24no—
24C2×#124×C103C2211yescharacteristic
25C2×#123×C103—21no—
26C2×C22⋊Q8×C103C2211yescharacteristic
27C2×C22⋊Q8×C103C2211yescharacteristic
28C2×C22⋊Q8×C103C2211yescharacteristic, complemented
29C2×#121×C103—21no—
30C2×#121×C103C2211yescharacteristic
31C2×#120×C103—21no—
32C2×C4×D4×C103C2211yescharacteristic
33C2×C4×D4×C103C2211yescharacteristic
34C22×C4⋊C4×C103C2211yescharacteristic, complemented
35C22×C22⋊C4×C103—21no—
36#468×C103—24no—
37#452×C103—24no—
38#450×C103—24no—
39C2×#107×C103C2211yescharacteristic, complemented
40#417×C103—24no—
41C2×#103×C103C2211yescharacteristic, complemented
42C2×#103×C103C2211yescharacteristic, complemented
43C2×#103×C103C2211yescharacteristic, complemented
44C2×#103×C103C2211yescharacteristic, complemented
45C2×#102×C103C2211yescharacteristic
46C2×#102×C103C2211yescharacteristic
47C2×#102×C103C2211yescharacteristic
48C2×#102×C103C2211yescharacteristic
49C2×#102×C103C2211yescharacteristic
50C2×#102×C103C2211yescharacteristic
51C2×C22⋊C8×C103C2211yescharacteristic
52C2×C22⋊C8×C103C2211yescharacteristic
53C2×C22⋊C8×C103C2211yescharacteristic, complemented
54#398×C103—21no—
55#396×C103—21no—
56#391×C103C2211yescharacteristic, complemented
57#389×C103C2211yescharacteristic, complemented
58#386×C103—21no—
59#380×C103—21no—
60#380×C103C2211yescharacteristic
61#340×C103C2211yescharacteristic, complemented
62#340×C103C2211yescharacteristic, complemented
63#336×C103C2211yescharacteristic, complemented
64#336×C103C2211yescharacteristic, complemented
65C25×C103—21no—
66C2×#41×C103—22no—
67C2×#41×C103—22no—
68C2×#41×C103—22no—
69C2×#41×C103—41no—
70C2×#41×C103—41no—
71C2×#41×C103D414yes—
72C22×Q8×C103C2311yescharacteristic
73C22×Q8×C103C2311yescharacteristic
74C22×D4×C103—21no—
75C22×D4×C103—21no—
76C22×D4×C103—22no—
77C22×D4×C103—22no—
78C22×D4×C103—22no—
79C22×D4×C103—22no—
80C22×D4×C103—21no—
81C22×D4×C103—41no—
82C22×D4×C103—41no—
83C22×D4×C103D411yescharacteristic
84C22×D4×C103C2311yescharacteristic
85C22×D4×C103C2311yescharacteristic
86C23×C4×C103—21no—
87C23×C4×C103—21no—
88C23×C4×C103—21no—
89C23×C4×C103C2311yescharacteristic
90C23×C4×C103C2311yescharacteristic
91C2×Q16×C103—22no—
92C2×Q16×C103—41no—
93C2×Q16×C103—41no—
94C2×SD16×C103—22no—
95C2×SD16×C103—22no—
96C2×SD16×C103—22no—
97C2×SD16×C103—22no—
98C2×SD16×C103—22no—
99C2×SD16×C103—41no—
100C2×M16×C103—22no—
101C2×M16×C103—22no—
102C2×M16×C103—41no—
103C22×C8×C103C2311yescharacteristic
104C22×C8×C103C2311yescharacteristic
105C22×C8×C103C2311yescharacteristic
106C22×C8×C103C2311yescharacteristic
107#124×C103—22no—
108#124×C103—22no—
109#123×C103—28no—
110C22⋊Q8×C103—22no—
111C22⋊Q8×C103—22no—
112C22⋊Q8×C103—22no—
113C22⋊Q8×C103—22no—
114C22⋊Q8×C103—22no—
115C22⋊Q8×C103—41no—
116#121×C103—28no—
117#121×C103—22no—
118#121×C103D414yes—
119#120×C103—28no—
120C4×D4×C103—22no—
121C4×D4×C103—22no—
122C4×D4×C103—22no—
123C4×D4×C103—22no—
124C2×C4⋊C4×C103—21no—
125C2×C4⋊C4×C103—22no—
126C2×C4⋊C4×C103—21no—
127C2×C4⋊C4×C103—21no—
128C2×C4⋊C4×C103—21no—
129C2×C4⋊C4×C103—21no—
130C2×C4⋊C4×C103—41no—
131C2×C4⋊C4×C103D411yescharacteristic
132C2×C4⋊C4×C103C2311yescharacteristic
133C2×C4⋊C4×C103C2311yescharacteristic
134C2×C4⋊C4×C103C2311yescharacteristic
135C2×C4⋊C4×C103C2311yescharacteristic
136C2×C22⋊C4×C103—28no—
137C2×C22⋊C4×C103—21no—
138C2×C22⋊C4×C103—21no—
139C2×C22⋊C4×C103—21no—
140C2×C22⋊C4×C103—21no—
141C2×C22⋊C4×C103—21no—
142C2×C22⋊C4×C103—21no—
143C2×C22⋊C4×C103—21no—
144C2×C22⋊C4×C103—21no—
145C2×C22⋊C4×C103D411yescharacteristic
146C2×C22⋊C4×C103D411yescharacteristic
147C2×C42×C103C2311yescharacteristic
148#107×C103—22no—
149#103×C103—22no—
150#103×C103—22no—
151#103×C103—22no—
152#103×C103—22no—
153#102×C103—22no—
154#102×C103—22no—
155#102×C103—22no—
156#102×C103—22no—
157#102×C103—41no—
158#102×C103D414yescomplemented
159C22⋊C8×C103—22no—
160C22⋊C8×C103—22no—
161C22⋊C8×C103—41no—
162#95×C103—21no—
163#95×C103—21no—
164#95×C103—21no—
165#95×C103—21no—
166C24×C103—21no—
167C24×C103—24no—
168C24×C103—21no—
169C24×C103—42no—
170C24×C103—42no—
171C24×C103—42no—
172C24×C103—42no—
173C24×C103—81no—
174C24×C103—81no—
175C24×C103C2×D411yescharacteristic
176C24×C103C2×D411yescharacteristic
177#41×C103—28no—
178#41×C103—44no—
179#41×C103—44no—
180#41×C103—44no—
181C2×Q8×C103—21no—
182C2×Q8×C103—21no—
183C2×Q8×C103—21no—
184C2×Q8×C103—21no—
185C2×Q8×C103—21no—
186C2×Q8×C103—21no—
187C2×Q8×C103—21no—
188C2×Q8×C103—21no—
189C2×Q8×C103—21no—
190C2×Q8×C103—21no—
191C2×Q8×C103—21no—
192C2×Q8×C103C2×D412yes—
193C2×D4×C103—24no—
194C2×D4×C103—22no—
195C2×D4×C103—24no—
196C2×D4×C103—22no—
197C2×D4×C103—24no—
198C2×D4×C103—21no—
199C2×D4×C103—21no—
200C2×D4×C103—21no—
201C2×D4×C103—21no—
202C2×D4×C103—21no—
203C2×D4×C103—21no—
204C2×D4×C103—21no—
205C2×D4×C103—21no—
206C2×D4×C103—41no—
207C2×D4×C103—42no—
208C2×D4×C103—42no—
209C2×D4×C103—44no—
210C2×D4×C103—44no—
211C2×D4×C103—44no—
212C2×D4×C103—42no—
213C2×D4×C103—42no—
214C2×D4×C103—44no—
215C2×D4×C103—81no—
216C2×D4×C103—81no—
217C2×D4×C103C2×D412yes—
218C2×D4×C103C2×D412yes—
219C2×D4×C103C2×D412yes—
220C2×D4×C103#4112yes—
221C22×C4×C103—21no—
222C22×C4×C103—21no—
223C22×C4×C103—21no—
224C22×C4×C103—21no—
225C22×C4×C103—21no—
226C22×C4×C103—21no—
227C22×C4×C103—21no—
228C22×C4×C103—24no—
229C22×C4×C103—24no—
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×C103—42no—
242C22×C4×C103—42no—
243C22×C4×C103—81no—
244C22×C4×C103—81no—
245C22×C4×C103—81no—
246C22×C4×C103C2×D411yescharacteristic
247C22×C4×C103C2×D411yescharacteristic
248C22×C4×C103C2×D411yescharacteristic
249C22×C4×C103C2×D411yescharacteristic
250C22×C4×C103C2×D412yes—
251C22×C4×C103C2×D412yes—
252C22×C4×C103C2411yescharacteristic
253Q16×C103—44no—
254SD16×C103—44no—
255SD16×C103—44no—
256M16×C103—44no—
257C2×C8×C103—21no—
258C2×C8×C103—21no—
259C2×C8×C103—21no—
260C2×C8×C103—21no—
261C2×C8×C103—21no—
262C2×C8×C103—21no—
263C2×C8×C103—21no—
264C2×C8×C103—21no—
265C2×C8×C103—21no—
266C2×C8×C103—21no—
267C2×C8×C103—21no—
268C2×C8×C103C2×D412yes—
269C4⋊C4×C103—24no—
270C4⋊C4×C103—22no—
271C4⋊C4×C103—21no—
272C4⋊C4×C103—21no—
273C4⋊C4×C103—21no—
274C4⋊C4×C103—21no—
275C4⋊C4×C103—21no—
276C4⋊C4×C103—21no—
277C4⋊C4×C103—42no—
278C4⋊C4×C103—42no—
279C4⋊C4×C103—42no—
280C4⋊C4×C103—81no—
281C4⋊C4×C103C2×D412yes—
282C4⋊C4×C103C2×D412yes—
283C22⋊C4×C103—24no—
284C22⋊C4×C103—24no—
285C22⋊C4×C103—24no—
286C22⋊C4×C103—24no—
287C22⋊C4×C103—22no—
288C22⋊C4×C103—22no—
289C22⋊C4×C103—24no—
290C22⋊C4×C103—42no—
291C22⋊C4×C103—42no—
292C22⋊C4×C103—81no—
293C42×C103—21no—
294C42×C103—21no—
295C23×C103—21no—
296C23×C103—22no—
297C23×C103—21no—
298C23×C103—21no—
299C23×C103—22no—
300C23×C103—21no—
301C23×C103—21no—
302C23×C103—22no—
303C23×C103—21no—
304C23×C103—21no—
305C23×C103—21no—
306C23×C103—21no—
307C23×C103—21no—
308C23×C103—21no—
309C23×C103—21no—
310C23×C103—22no—
311C23×C103—48no—
312C23×C103—48no—
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#12012yes—
329C23×C103#13712yes—
330C23×C103C22×D411yescharacteristic
331Q8×C103—22no—
332Q8×C103—22no—
333Q8×C103—41no—
334Q8×C103—41no—
335Q8×C103—41no—
336Q8×C103—41no—
337Q8×C103—41no—
338Q8×C103—41no—
339D4×C103—22no—
340D4×C103—22no—
341D4×C103—22no—
342D4×C103—22no—
343D4×C103—22no—
344D4×C103—44no—
345D4×C103—48no—
346D4×C103—48no—
347D4×C103—41no—
348D4×C103—41no—
349D4×C103—84no—
350D4×C103#12114yes—
351C2×C4×C103—21no—
352C2×C4×C103—21no—
353C2×C4×C103—22no—
354C2×C4×C103—22no—
355C2×C4×C103—22no—
356C2×C4×C103—22no—
357C2×C4×C103—21no—
358C2×C4×C103—21no—
359C2×C4×C103—22no—
360C2×C4×C103—22no—
361C2×C4×C103—21no—
362C2×C4×C103—22no—
363C2×C4×C103—21no—
364C2×C4×C103—21no—
365C2×C4×C103—21no—
366C2×C4×C103—21no—
367C2×C4×C103—21no—
368C2×C4×C103—21no—
369C2×C4×C103—48no—
370C2×C4×C103—41no—
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—84no—
390C2×C4×C103—84no—
391C2×C4×C103#12012yes—
392C2×C4×C103C22×D411yescharacteristic
393C2×C4×C103C22×D411yescharacteristic
394C2×C4×C103C22×D411yescharacteristic
395C2×C4×C103C2×#4111yescharacteristic
396C2×C4×C103H(5,𝔽2)11yescharacteristic
397C2×C4×C103H(5,𝔽2)11yescharacteristic
398C8×C103—22no—
399C8×C103—41no—
400C8×C103—41no—
401C8×C103—41no—
402C22×C103—22no—
403C22×C103—24no—
404C22×C103—22no—
405C22×C103—22no—
406C22×C103—22no—
407C22×C103—22no—
408C22×C103—22no—
409C22×C103—41no—
410C22×C103—42no—
411C22×C103—41no—
412C22×C103—42no—
413C22×C103—42no—
414C22×C103—41no—
415C22×C103—41no—
416C22×C103—41no—
417C22×C103—42no—
418C22×C103—41no—
419C22×C103—42no—
420C22×C103—41no—
421C22×C103—41no—
422C22×C103—42no—
423C22×C103—42no—
424C22×C103—42no—
425C22×C103—42no—
426C22×C103—816no—
427C22×C103—81no—
428C22×C103—81no—
429C22×C103—81no—
430C22×C103—81no—
431C22×C103C2×#12011yescharacteristic
432C22×C103D4211yescharacteristic
433C22×C103#54611yescharacteristic
434C22×C103C2×#13711yescharacteristic
435C22×C103#57511yescharacteristic
436C22×C103#57611yescharacteristic
437C22×C103#57711yescharacteristic
438C4×C103—22no—
439C4×C103—41no—
440C4×C103—42no—
441C4×C103—41no—
442C4×C103—41no—
443C4×C103—42no—
444C4×C103—42no—
445C4×C103—81no—
446C4×C103—81no—
447C4×C103—81no—
448C4×C103C2×#12111yescharacteristic
449C4×C103#53411yescharacteristic
450C4×C103D4211yescharacteristic
451C4×C103#54611yescharacteristic
452#24452C10311yesmaximal, characteristic, direct product factor, Sylow
453C2×C103—42no—
454C2×C103—42no—
455C2×C103—44no—
456C2×C103—82no—
457C2×C103#241011yescharacteristic
458C2×C103#300711yescharacteristic
459C2×C103#301211yescharacteristic
460C2×C103#326611yescharacteristic
461C2×C103#327311yescharacteristic
462C2×C103#331411yescharacteristic
463C2×C103#332311yescharacteristic
464C2×#546C2×C10311yescharacteristic
465C2×#468C2×C10311yescharacteristic, complemented
466C2×#452C2×C10311yescharacteristic, complemented
467C2×#450C2×C10311yescharacteristic, complemented
468C2×#417C2×C10311yescharacteristic, complemented
469#2417C2×C10311yescharacteristic, complemented
470#2042C2×C10311yescharacteristic, complemented
471#2036C2×C10311yescharacteristic, complemented
472#2015C2×C10311yescharacteristic, complemented
473#2001C2×C10311yescharacteristic, complemented
474#1877C2×C10311yescharacteristic, complemented
475#1874C2×C10311yescharacteristic, complemented
476#1870C2×C10311yescharacteristic, complemented
477#1862C2×C10311yescharacteristic, complemented
478#1786C2×C10311yescharacteristic, complemented
479C103#2445211yescharacteristic, direct product factor, Sylow
480C22×#41C22×C10311yescharacteristic
481C23×D4C22×C10311yescharacteristic
482C22×Q16C22×C10311yescharacteristic, complemented
483C22×SD16C22×C10311yescharacteristic
484C22×SD16C22×C10311yescharacteristic
485C22×M16C22×C10311yescharacteristic, complemented
486#546—24no—
487#546—24no—
488C2×#124C22×C10311yescharacteristic
489C2×#123—21no—
490C2×C22⋊Q8C22×C10311yescharacteristic
491C2×C22⋊Q8C22×C10311yescharacteristic
492C2×C22⋊Q8C22×C10311yescharacteristic, complemented
493C2×#121—21no—
494C2×#121C22×C10311yescharacteristic
495C2×#120—21no—
496C2×C4×D4C22×C10311yescharacteristic
497C2×C4×D4C22×C10311yescharacteristic
498C22×C4⋊C4C22×C10311yescharacteristic, complemented
499C22×C22⋊C4—21no—
500#468—24no—
501#452—24no—
502#450—24no—
503C2×#107C22×C10311yescharacteristic, complemented
504#417—24no—
505C2×#103C22×C10311yescharacteristic, complemented
506C2×#103C22×C10311yescharacteristic, complemented
507C2×#103C22×C10311yescharacteristic, complemented
508C2×#103C22×C10311yescharacteristic, complemented
509C2×#102C22×C10311yescharacteristic
510C2×#102C22×C10311yescharacteristic
511C2×#102C22×C10311yescharacteristic
512C2×#102C22×C10311yescharacteristic
513C2×#102C22×C10311yescharacteristic
514C2×#102C22×C10311yescharacteristic
515C2×C22⋊C8C22×C10311yescharacteristic
516C2×C22⋊C8C22×C10311yescharacteristic
517C2×C22⋊C8C22×C10311yescharacteristic, complemented
518#398—21no—
519#396—21no—
520#391C22×C10311yescharacteristic, complemented
521#389C22×C10311yescharacteristic, complemented
522#386—21no—
523#380—21no—
524#380C22×C10311yescharacteristic
525#340C22×C10311yescharacteristic, complemented
526#340C22×C10311yescharacteristic, complemented
527#336C22×C10311yescharacteristic, complemented
528#336C22×C10311yescharacteristic, complemented
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C10314yes—
536C22×Q8C23×C10311yescharacteristic
537C22×Q8C23×C10311yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4D4×C10311yescharacteristic
548C22×D4C23×C10311yescharacteristic
549C22×D4C23×C10311yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C23×C10311yescharacteristic
554C23×C4C23×C10311yescharacteristic
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C22×C8C23×C10311yescharacteristic
568C22×C8C23×C10311yescharacteristic
569C22×C8C23×C10311yescharacteristic
570C22×C8C23×C10311yescharacteristic
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580#121—28no—
581#121—22no—
582#121D4×C10314yes—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4D4×C10311yescharacteristic
596C2×C4⋊C4C23×C10311yescharacteristic
597C2×C4⋊C4C23×C10311yescharacteristic
598C2×C4⋊C4C23×C10311yescharacteristic
599C2×C4⋊C4C23×C10311yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C10311yescharacteristic
610C2×C22⋊C4D4×C10311yescharacteristic
611C2×C42C23×C10311yescharacteristic
612#107—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—41no—
622#102D4×C10314yescomplemented
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—41no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—21no—
631C24—24no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C10311yescharacteristic
640C24C2×D4×C10311yescharacteristic
641#41—28no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C10312yes—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—24no—
660C2×D4—22no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—41no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—44no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C10312yes—
682C2×D4C2×D4×C10312yes—
683C2×D4C2×D4×C10312yes—
684C2×D4#41×C10312yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C10311yescharacteristic
711C22×C4C2×D4×C10311yescharacteristic
712C22×C4C2×D4×C10311yescharacteristic
713C22×C4C2×D4×C10311yescharacteristic
714C22×C4C2×D4×C10312yes—
715C22×C4C2×D4×C10312yes—
716C22×C4C24×C10311yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—44no—
720M16—44no—
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—
732C2×C8C2×D4×C10312yes—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C10312yes—
746C4⋊C4C2×D4×C10312yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—22no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23#120×C10312yes—
793C23#137×C10312yes—
794C23C22×D4×C10311yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—44no—
809D4—48no—
810D4—48no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#121×C10314yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
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—84no—
854C2×C4—84no—
855C2×C4#120×C10312yes—
856C2×C4C22×D4×C10311yescharacteristic
857C2×C4C22×D4×C10311yescharacteristic
858C2×C4C22×D4×C10311yescharacteristic
859C2×C4C2×#41×C10311yescharacteristic
860C2×C4H(5,𝔽2)×C10311yescharacteristic
861C2×C4H(5,𝔽2)×C10311yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—42no—
874C22—41no—
875C22—42no—
876C22—42no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—816no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22C2×#120×C10311yescharacteristic
896C22D42×C10311yescharacteristic
897C22#546×C10311yescharacteristic
898C22C2×#137×C10311yescharacteristic
899C22#575×C10311yescharacteristic
900C22#576×C10311yescharacteristic
901C22#577×C10311yescharacteristic
902C4—22no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—42no—
907C4—41no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×#121×C10311yescharacteristic
913C4#534×C10311yescharacteristic
914C4D42×C10311yescharacteristic
915C4#546×C10311yescharacteristic
916C2—42no—
917C2—42no—
918C2—44no—
919C2—82no—
920C2C103×#241011yescharacteristic
921C2C103×#300711yescharacteristic
922C2C103×#301211yescharacteristic
923C2C103×#326611yescharacteristic
924C2C103×#327311yescharacteristic
925C2C103×#331411yescharacteristic
926C2C103×#332311yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#546×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×#468×C103C2semidirect
3. C2×#452×C103C2semidirect
4. C2×#450×C103C2semidirect
5. C2×#417×C103C2semidirect
6. C103×#2417C2semidirect
7. C103×#2042C2semidirect
8. C103×#2036C2semidirect
9. C103×#2015C2semidirect
10. C103×#2001C2semidirect
11. C103×#1877C2semidirect
12. C103×#1874C2semidirect
13. C103×#1870C2semidirect
14. C103×#1862C2semidirect
15. C103×#1786C2semidirect
18. C22×Q16×C103C22semidirect
21. C22×M16×C103C22semidirect
28. C2×C22⋊Q8×C103C22semidirect
34. C22×C4⋊C4×C103C22semidirect
39. C2×#107×C103C22semidirect
41. C2×#103×C103C22semidirect
42. C2×#103×C103C22semidirect
43. C2×#103×C103C22semidirect
44. C2×#103×C103C22semidirect
53. C2×C22⋊C8×C103C22semidirect
56. #391×C103C22semidirect
57. #389×C103C22semidirect
61. #340×C103C22semidirect
62. #340×C103C22semidirect
63. #336×C103C22semidirect
64. #336×C103C22semidirect
158. #102×C103D4semidirect
452. #24452C103direct (N × H)
465. C2×#468C2×C103semidirect
466. C2×#452C2×C103semidirect
467. C2×#450C2×C103semidirect
468. C2×#417C2×C103semidirect
469. #2417C2×C103semidirect
470. #2042C2×C103semidirect
471. #2036C2×C103semidirect
472. #2015C2×C103semidirect
473. #2001C2×C103semidirect
474. #1877C2×C103semidirect
475. #1874C2×C103semidirect
476. #1870C2×C103semidirect
477. #1862C2×C103semidirect
478. #1786C2×C103semidirect
479. C103#24452direct (N × H)
482. C22×Q16C22×C103semidirect
485. C22×M16C22×C103semidirect
492. C2×C22⋊Q8C22×C103semidirect
498. C22×C4⋊C4C22×C103semidirect
503. C2×#107C22×C103semidirect
505. C2×#103C22×C103semidirect
506. C2×#103C22×C103semidirect
507. C2×#103C22×C103semidirect
508. C2×#103C22×C103semidirect
517. C2×C22⋊C8C22×C103semidirect
520. #391C22×C103semidirect
521. #389C22×C103semidirect
525. #340C22×C103semidirect
526. #340C22×C103semidirect
527. #336C22×C103semidirect
528. #336C22×C103semidirect
622. #102D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1032
C2×#468×C1032
C2×#452×C1032
C2×#450×C1032
C2×#417×C1032
C103×#24172
C103×#20422
C103×#20362
C103×#20152
C103×#20012
C103×#18772
C103×#18742
C103×#18702
C103×#18622
C103×#17862
#24452103