Finite Group Databasebeta

← C103×#23850 #39929125

Subgroups — C103×#23850 #39929125

Order 26368.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C103C211yesmaximal, characteristic, complemented
2C2×#546×C103C211yesmaximal, characteristic, complemented
3C2×#449×C103C211yesmaximal, characteristic, complemented
4C2×#450×C103C211yesmaximal, characteristic, complemented
5C2×#447×C103C211yesmaximal, characteristic, complemented
6C103×#2407C211yesmaximal, characteristic, complemented
7C103×#2015C211yesmaximal, characteristic, complemented
8C103×#2012C211yesmaximal, characteristic, complemented
9C103×#2001C211yesmaximal, characteristic, complemented
10C103×#2000C211yesmaximal, characteristic, complemented
11C103×#1893C211yesmaximal, characteristic, complemented
12C103×#1879C211yesmaximal, characteristic, complemented
13C103×#1877C211yesmaximal, characteristic, complemented
14C103×#1869C211yesmaximal, characteristic, complemented
15C103×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic, complemented
18C23×D4×C103C2211yescharacteristic
19C2×#135×C103—24no—
20C2×#135×C103—24no—
21C2×#135×C103—24no—
22C22×Q16×C103C2211yescharacteristic, complemented
23C22×SD16×C103C2211yescharacteristic
24C22×SD16×C103C2211yescharacteristic
25C22×SD16×C103C2211yescharacteristic, complemented
26C22×D8×C103C2211yescharacteristic
27C22×D8×C103C2211yescharacteristic
28C23×C8×C103C2211yescharacteristic, complemented
29#546×C103—24no—
30#546×C103—24no—
31C2×#124×C103C2211yescharacteristic
32C2×#123×C103—21no—
33C2×C22⋊Q8×C103C2211yescharacteristic
34C2×C22⋊Q8×C103C2211yescharacteristic
35C2×#121×C103—21no—
36C2×#121×C103C2211yescharacteristic
37C2×#121×C103C2211yescharacteristic
38C2×#120×C103—21no—
39C2×C4×D4×C103C2211yescharacteristic
40C2×C4×D4×C103C2211yescharacteristic
41C22×C22⋊C4×C103—21no—
42#450×C103—24no—
43#449×C103—24no—
44#447×C103—24no—
45C2×#103×C103C2211yescharacteristic, complemented
46C2×#103×C103C2211yescharacteristic, complemented
47C2×#103×C103C2211yescharacteristic, complemented
48C2×#102×C103C2211yescharacteristic
49C2×#102×C103C2211yescharacteristic
50C2×#102×C103C2211yescharacteristic
51C2×#102×C103C2211yescharacteristic
52C2×#102×C103C2211yescharacteristic, complemented
53C2×C22⋊C8×C103C2211yescharacteristic
54C2×C22⋊C8×C103C2211yescharacteristic
55C2×C22⋊C8×C103C2211yescharacteristic, complemented
56#394×C103—21no—
57#392×C103—21no—
58#391×C103C2211yescharacteristic, complemented
59#390×C103C2211yescharacteristic, complemented
60#386×C103—21no—
61#385×C103—21no—
62#380×C103C2211yescharacteristic, complemented
63#340×C103C2211yescharacteristic, complemented
64#340×C103C2211yescharacteristic, complemented
65#336×C103C2211yescharacteristic, complemented
66#336×C103C2211yescharacteristic, complemented
67C25×C103—21no—
68C2×#41×C103—22no—
69C2×#41×C103—22no—
70C2×#41×C103—22no—
71C2×#41×C103—22no—
72C2×#41×C103—22no—
73C2×#41×C103—22no—
74C2×#41×C103—22no—
75C2×#41×C103—41no—
76C2×#41×C103—41no—
77C2×#41×C103—41no—
78C2×#41×C103—41no—
79C2×#41×C103D414yescomplemented
80C22×Q8×C103C2311yescharacteristic
81C22×Q8×C103C2311yescharacteristic
82C22×D4×C103—21no—
83C22×D4×C103—21no—
84C22×D4×C103—22no—
85C22×D4×C103—22no—
86C22×D4×C103—22no—
87C22×D4×C103—22no—
88C22×D4×C103—21no—
89C22×D4×C103—21no—
90C22×D4×C103—21no—
91C22×D4×C103—41no—
92C22×D4×C103—41no—
93C22×D4×C103D411yescharacteristic
94C22×D4×C103C2311yescharacteristic
95C22×D4×C103C2311yescharacteristic
96C22×D4×C103C2311yescharacteristic
97C23×C4×C103—21no—
98C23×C4×C103—21no—
99C23×C4×C103—21no—
100C23×C4×C103C2311yescharacteristic
101C23×C4×C103C2311yescharacteristic
102#135×C103—232no—
103C2×Q16×C103—22no—
104C2×Q16×C103—22no—
105C2×Q16×C103—22no—
106C2×SD16×C103—22no—
107C2×SD16×C103—22no—
108C2×SD16×C103—22no—
109C2×SD16×C103—22no—
110C2×SD16×C103—22no—
111C2×SD16×C103—22no—
112C2×SD16×C103—22no—
113C2×SD16×C103—41no—
114C2×SD16×C103D414yescomplemented
115C2×D8×C103—22no—
116C2×D8×C103—22no—
117C2×D8×C103—22no—
118C2×D8×C103—22no—
119C2×D8×C103—41no—
120C2×D8×C103D414yescomplemented
121C22×C8×C103—22no—
122C22×C8×C103—22no—
123C22×C8×C103—22no—
124C22×C8×C103C2311yescharacteristic
125C22×C8×C103C2311yescharacteristic
126C22×C8×C103C2311yescharacteristic
127C22×C8×C103C2311yescharacteristic
128#124×C103—22no—
129#124×C103—22no—
130#123×C103—28no—
131C22⋊Q8×C103—22no—
132C22⋊Q8×C103—22no—
133C22⋊Q8×C103—22no—
134C22⋊Q8×C103—41no—
135#121×C103—28no—
136#121×C103—22no—
137#121×C103—22no—
138#121×C103—41no—
139#121×C103D414yescomplemented
140#120×C103—28no—
141C4×D4×C103—22no—
142C4×D4×C103—22no—
143C4×D4×C103—22no—
144C4×D4×C103—22no—
145C2×C4⋊C4×C103—21no—
146C2×C4⋊C4×C103—21no—
147C2×C4⋊C4×C103D411yescharacteristic
148C2×C4⋊C4×C103C2311yescharacteristic
149C2×C4⋊C4×C103C2311yescharacteristic
150C2×C4⋊C4×C103C2311yescharacteristic
151C2×C22⋊C4×C103—28no—
152C2×C22⋊C4×C103—21no—
153C2×C22⋊C4×C103—21no—
154C2×C22⋊C4×C103—21no—
155C2×C22⋊C4×C103—21no—
156C2×C22⋊C4×C103—21no—
157C2×C22⋊C4×C103—21no—
158C2×C22⋊C4×C103—21no—
159C2×C22⋊C4×C103—21no—
160C2×C22⋊C4×C103—21no—
161C2×C22⋊C4×C103—21no—
162C2×C22⋊C4×C103D411yescharacteristic
163C2×C22⋊C4×C103D411yescharacteristic
164C2×C42×C103C2311yescharacteristic
165#103×C103—22no—
166#103×C103—41no—
167#103×C103—41no—
168#102×C103—22no—
169#102×C103—22no—
170#102×C103—22no—
171#102×C103—22no—
172#102×C103—22no—
173C22⋊C8×C103—22no—
174C22⋊C8×C103—22no—
175C22⋊C8×C103—22no—
176#95×C103—21no—
177#95×C103—21no—
178#95×C103—21no—
179C24×C103—21no—
180C24×C103—24no—
181C24×C103—21no—
182C24×C103—21no—
183C24×C103—42no—
184C24×C103—42no—
185C24×C103—42no—
186C24×C103—42no—
187C24×C103—81no—
188C24×C103—81no—
189C24×C103C2×D411yescharacteristic
190C24×C103C2×D411yescharacteristic
191#41×C103—28no—
192#41×C103—28no—
193#41×C103—44no—
194#41×C103—44no—
195#41×C103—44no—
196#41×C103—44no—
197#41×C103—44no—
198#41×C103—44no—
199C2×Q8×C103—21no—
200C2×Q8×C103—21no—
201C2×Q8×C103—21no—
202C2×Q8×C103—21no—
203C2×Q8×C103—21no—
204C2×Q8×C103—21no—
205C2×Q8×C103—21no—
206C2×Q8×C103—21no—
207C2×Q8×C103—21no—
208C2×Q8×C103—21no—
209C2×Q8×C103C2×D412yes—
210C2×Q8×C103C2×D412yes—
211C2×D4×C103—24no—
212C2×D4×C103—22no—
213C2×D4×C103—24no—
214C2×D4×C103—22no—
215C2×D4×C103—24no—
216C2×D4×C103—21no—
217C2×D4×C103—21no—
218C2×D4×C103—21no—
219C2×D4×C103—21no—
220C2×D4×C103—21no—
221C2×D4×C103—21no—
222C2×D4×C103—21no—
223C2×D4×C103—21no—
224C2×D4×C103—21no—
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—21no—
228C2×D4×C103—21no—
229C2×D4×C103—41no—
230C2×D4×C103—42no—
231C2×D4×C103—42no—
232C2×D4×C103—42no—
233C2×D4×C103—44no—
234C2×D4×C103—44no—
235C2×D4×C103—44no—
236C2×D4×C103—42no—
237C2×D4×C103—42no—
238C2×D4×C103—42no—
239C2×D4×C103—42no—
240C2×D4×C103—44no—
241C2×D4×C103—42no—
242C2×D4×C103—42no—
243C2×D4×C103—81no—
244C2×D4×C103—81no—
245C2×D4×C103—81no—
246C2×D4×C103C2×D412yes—
247C2×D4×C103C2×D412yes—
248C2×D4×C103C2×D412yes—
249C2×D4×C103C2×D412yes—
250C2×D4×C103C2×D412yes—
251C22×C4×C103—21no—
252C22×C4×C103—21no—
253C22×C4×C103—21no—
254C22×C4×C103—21no—
255C22×C4×C103—21no—
256C22×C4×C103—21no—
257C22×C4×C103—21no—
258C22×C4×C103—24no—
259C22×C4×C103—24no—
260C22×C4×C103—21no—
261C22×C4×C103—21no—
262C22×C4×C103—21no—
263C22×C4×C103—21no—
264C22×C4×C103—21no—
265C22×C4×C103—21no—
266C22×C4×C103—21no—
267C22×C4×C103—21no—
268C22×C4×C103—42no—
269C22×C4×C103—42no—
270C22×C4×C103—42no—
271C22×C4×C103—42no—
272C22×C4×C103—42no—
273C22×C4×C103—81no—
274C22×C4×C103—81no—
275C22×C4×C103C2×D411yescharacteristic
276C22×C4×C103C2×D411yescharacteristic
277C22×C4×C103C2×D411yescharacteristic
278C22×C4×C103C2×D411yescharacteristic
279C22×C4×C103C2×D412yes—
280C22×C4×C103C2×D412yes—
281C22×C4×C103C2411yescharacteristic
282Q16×C103—28no—
283SD16×C103—28no—
284SD16×C103—28no—
285SD16×C103—44no—
286D8×C103—28no—
287D8×C103—44no—
288C2×C8×C103—28no—
289C2×C8×C103—21no—
290C2×C8×C103—21no—
291C2×C8×C103—21no—
292C2×C8×C103—21no—
293C2×C8×C103—21no—
294C2×C8×C103—21no—
295C2×C8×C103—21no—
296C2×C8×C103—21no—
297C2×C8×C103—21no—
298C2×C8×C103—21no—
299C2×C8×C103C2×D412yes—
300C2×C8×C103C2×D412yes—
301C4⋊C4×C103—24no—
302C4⋊C4×C103—22no—
303C4⋊C4×C103—21no—
304C4⋊C4×C103—21no—
305C4⋊C4×C103—21no—
306C4⋊C4×C103—21no—
307C4⋊C4×C103—21no—
308C4⋊C4×C103—42no—
309C4⋊C4×C103C2×D412yes—
310C22⋊C4×C103—24no—
311C22⋊C4×C103—24no—
312C22⋊C4×C103—24no—
313C22⋊C4×C103—24no—
314C22⋊C4×C103—22no—
315C22⋊C4×C103—22no—
316C22⋊C4×C103—24no—
317C22⋊C4×C103—42no—
318C22⋊C4×C103—42no—
319C22⋊C4×C103—42no—
320C22⋊C4×C103—81no—
321C22⋊C4×C103—81no—
322C42×C103—21no—
323C42×C103—21no—
324C23×C103—21no—
325C23×C103—22no—
326C23×C103—21no—
327C23×C103—21no—
328C23×C103—21no—
329C23×C103—21no—
330C23×C103—22no—
331C23×C103—22no—
332C23×C103—21no—
333C23×C103—21no—
334C23×C103—21no—
335C23×C103—21no—
336C23×C103—21no—
337C23×C103—21no—
338C23×C103—21no—
339C23×C103—22no—
340C23×C103—22no—
341C23×C103—48no—
342C23×C103—48no—
343C23×C103—41no—
344C23×C103—41no—
345C23×C103—41no—
346C23×C103—41no—
347C23×C103—41no—
348C23×C103—41no—
349C23×C103—41no—
350C23×C103—41no—
351C23×C103—41no—
352C23×C103—41no—
353C23×C103—41no—
354C23×C103—41no—
355C23×C103—41no—
356C23×C103—41no—
357C23×C103—41no—
358C23×C103—41no—
359C23×C103—84no—
360C23×C103—84no—
361C23×C103—84no—
362C23×C103—84no—
363C23×C103—84no—
364C23×C103#12012yes—
365C23×C103#13512yescomplemented
366C23×C103C22×D411yescharacteristic
367Q8×C103—22no—
368Q8×C103—22no—
369Q8×C103—22no—
370Q8×C103—22no—
371Q8×C103—41no—
372Q8×C103—41no—
373Q8×C103—41no—
374Q8×C103—41no—
375D4×C103—22no—
376D4×C103—22no—
377D4×C103—22no—
378D4×C103—22no—
379D4×C103—22no—
380D4×C103—22no—
381D4×C103—22no—
382D4×C103—44no—
383D4×C103—48no—
384D4×C103—48no—
385D4×C103—48no—
386D4×C103—41no—
387D4×C103—41no—
388D4×C103—41no—
389D4×C103—41no—
390D4×C103—84no—
391D4×C103—84no—
392D4×C103#12014yes—
393C2×C4×C103—21no—
394C2×C4×C103—21no—
395C2×C4×C103—22no—
396C2×C4×C103—22no—
397C2×C4×C103—22no—
398C2×C4×C103—22no—
399C2×C4×C103—21no—
400C2×C4×C103—21no—
401C2×C4×C103—22no—
402C2×C4×C103—22no—
403C2×C4×C103—21no—
404C2×C4×C103—21no—
405C2×C4×C103—22no—
406C2×C4×C103—21no—
407C2×C4×C103—21no—
408C2×C4×C103—21no—
409C2×C4×C103—21no—
410C2×C4×C103—21no—
411C2×C4×C103—48no—
412C2×C4×C103—48no—
413C2×C4×C103—41no—
414C2×C4×C103—41no—
415C2×C4×C103—41no—
416C2×C4×C103—41no—
417C2×C4×C103—41no—
418C2×C4×C103—41no—
419C2×C4×C103—41no—
420C2×C4×C103—41no—
421C2×C4×C103—41no—
422C2×C4×C103—41no—
423C2×C4×C103—41no—
424C2×C4×C103—41no—
425C2×C4×C103—41no—
426C2×C4×C103—41no—
427C2×C4×C103—41no—
428C2×C4×C103—41no—
429C2×C4×C103—84no—
430C2×C4×C103#12012yes—
431C2×C4×C103C22×D411yescharacteristic
432C2×C4×C103C22×D411yescharacteristic
433C2×C4×C103C22×D411yescharacteristic
434C2×C4×C103C22×D411yescharacteristic
435C2×C4×C103H(5,𝔽2)11yescharacteristic
436C2×C4×C103H(5,𝔽2)11yescharacteristic
437C8×C103—22no—
438C8×C103—22no—
439C8×C103—41no—
440C8×C103—41no—
441C22×C103—22no—
442C22×C103—24no—
443C22×C103—22no—
444C22×C103—22no—
445C22×C103—22no—
446C22×C103—22no—
447C22×C103—22no—
448C22×C103—41no—
449C22×C103—42no—
450C22×C103—41no—
451C22×C103—41no—
452C22×C103—42no—
453C22×C103—42no—
454C22×C103—41no—
455C22×C103—41no—
456C22×C103—41no—
457C22×C103—42no—
458C22×C103—41no—
459C22×C103—42no—
460C22×C103—41no—
461C22×C103—42no—
462C22×C103—42no—
463C22×C103—42no—
464C22×C103—42no—
465C22×C103—42no—
466C22×C103—42no—
467C22×C103—42no—
468C22×C103—816no—
469C22×C103—81no—
470C22×C103—81no—
471C22×C103—81no—
472C22×C103—81no—
473C22×C103—81no—
474C22×C103—81no—
475C22×C103—81no—
476C22×C103—81no—
477C22×C103C2×#12011yescharacteristic
478C22×C103D4211yescharacteristic
479C22×C103D4211yescharacteristic
480C22×C103C2×#13511yescharacteristic
481C22×C103#57511yescharacteristic
482C22×C103#57611yescharacteristic
483C22×C103#57711yescharacteristic
484C4×C103—22no—
485C4×C103—41no—
486C4×C103—42no—
487C4×C103—42no—
488C4×C103—41no—
489C4×C103—41no—
490C4×C103—42no—
491C4×C103—81no—
492C4×C103—81no—
493C4×C103C2×#12011yescharacteristic
494C4×C103#53411yescharacteristic
495C4×C103D4211yescharacteristic
496C4×C103D4211yescharacteristic
497#23850C10311yesmaximal, characteristic, direct product factor, Sylow
498C2×C103—42no—
499C2×C103—42no—
500C2×C103—44no—
501C2×C103—82no—
502C2×C103—82no—
503C2×C103#240311yescharacteristic
504C2×C103#300211yescharacteristic
505C2×C103#301211yescharacteristic
506C2×C103#326711yescharacteristic
507C2×C103#326811yescharacteristic
508C2×C103#328011yescharacteristic
509C2×C103#328211yescharacteristic
510C22×#135C2×C10311yescharacteristic, complemented
511C2×#546C2×C10311yescharacteristic, complemented
512C2×#449C2×C10311yescharacteristic, complemented
513C2×#450C2×C10311yescharacteristic, complemented
514C2×#447C2×C10311yescharacteristic, complemented
515#2407C2×C10311yescharacteristic, complemented
516#2015C2×C10311yescharacteristic, complemented
517#2012C2×C10311yescharacteristic, complemented
518#2001C2×C10311yescharacteristic, complemented
519#2000C2×C10311yescharacteristic, complemented
520#1893C2×C10311yescharacteristic, complemented
521#1879C2×C10311yescharacteristic, complemented
522#1877C2×C10311yescharacteristic, complemented
523#1869C2×C10311yescharacteristic, complemented
524#1788C2×C10311yescharacteristic, complemented
525C103#2385011yescharacteristic, direct product factor, Sylow
526C22×#41C22×C10311yescharacteristic
527C22×#41C22×C10311yescharacteristic, complemented
528C23×D4C22×C10311yescharacteristic
529C2×#135—24no—
530C2×#135—24no—
531C2×#135—24no—
532C22×Q16C22×C10311yescharacteristic, complemented
533C22×SD16C22×C10311yescharacteristic
534C22×SD16C22×C10311yescharacteristic
535C22×SD16C22×C10311yescharacteristic, complemented
536C22×D8C22×C10311yescharacteristic
537C22×D8C22×C10311yescharacteristic
538C23×C8C22×C10311yescharacteristic, complemented
539#546—24no—
540#546—24no—
541C2×#124C22×C10311yescharacteristic
542C2×#123—21no—
543C2×C22⋊Q8C22×C10311yescharacteristic
544C2×C22⋊Q8C22×C10311yescharacteristic
545C2×#121—21no—
546C2×#121C22×C10311yescharacteristic
547C2×#121C22×C10311yescharacteristic
548C2×#120—21no—
549C2×C4×D4C22×C10311yescharacteristic
550C2×C4×D4C22×C10311yescharacteristic
551C22×C22⋊C4—21no—
552#450—24no—
553#449—24no—
554#447—24no—
555C2×#103C22×C10311yescharacteristic, complemented
556C2×#103C22×C10311yescharacteristic, complemented
557C2×#103C22×C10311yescharacteristic, complemented
558C2×#102C22×C10311yescharacteristic
559C2×#102C22×C10311yescharacteristic
560C2×#102C22×C10311yescharacteristic
561C2×#102C22×C10311yescharacteristic
562C2×#102C22×C10311yescharacteristic, complemented
563C2×C22⋊C8C22×C10311yescharacteristic
564C2×C22⋊C8C22×C10311yescharacteristic
565C2×C22⋊C8C22×C10311yescharacteristic, complemented
566#394—21no—
567#392—21no—
568#391C22×C10311yescharacteristic, complemented
569#390C22×C10311yescharacteristic, complemented
570#386—21no—
571#385—21no—
572#380C22×C10311yescharacteristic, complemented
573#340C22×C10311yescharacteristic, complemented
574#340C22×C10311yescharacteristic, complemented
575#336C22×C10311yescharacteristic, complemented
576#336C22×C10311yescharacteristic, complemented
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C10314yescomplemented
590C22×Q8C23×C10311yescharacteristic
591C22×Q8C23×C10311yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4D4×C10311yescharacteristic
604C22×D4C23×C10311yescharacteristic
605C22×D4C23×C10311yescharacteristic
606C22×D4C23×C10311yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C10311yescharacteristic
611C23×C4C23×C10311yescharacteristic
612#135—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C10314yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—41no—
630C2×D8D4×C10314yescomplemented
631C22×C8—22no—
632C22×C8—22no—
633C22×C8—22no—
634C22×C8C23×C10311yescharacteristic
635C22×C8C23×C10311yescharacteristic
636C22×C8C23×C10311yescharacteristic
637C22×C8C23×C10311yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—41no—
645#121—28no—
646#121—22no—
647#121—22no—
648#121—41no—
649#121D4×C10314yescomplemented
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C10311yescharacteristic
658C2×C4⋊C4C23×C10311yescharacteristic
659C2×C4⋊C4C23×C10311yescharacteristic
660C2×C4⋊C4C23×C10311yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C10311yescharacteristic
673C2×C22⋊C4D4×C10311yescharacteristic
674C2×C42C23×C10311yescharacteristic
675#103—22no—
676#103—41no—
677#103—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—24no—
691C24—21no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C10311yescharacteristic
700C24C2×D4×C10311yescharacteristic
701#41—28no—
702#41—28no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C10312yes—
720C2×Q8C2×D4×C10312yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C10312yes—
757C2×D4C2×D4×C10312yes—
758C2×D4C2×D4×C10312yes—
759C2×D4C2×D4×C10312yes—
760C2×D4C2×D4×C10312yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C10311yescharacteristic
786C22×C4C2×D4×C10311yescharacteristic
787C22×C4C2×D4×C10311yescharacteristic
788C22×C4C2×D4×C10311yescharacteristic
789C22×C4C2×D4×C10312yes—
790C22×C4C2×D4×C10312yes—
791C22×C4C24×C10311yescharacteristic
792Q16—28no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—44no—
798C2×C8—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C10312yes—
810C2×C8C2×D4×C10312yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C10312yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—22no—
850C23—22no—
851C23—48no—
852C23—48no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23#120×C10312yes—
875C23#135×C10312yescomplemented
876C23C22×D4×C10311yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—44no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C10314yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C10312yes—
941C2×C4C22×D4×C10311yescharacteristic
942C2×C4C22×D4×C10311yescharacteristic
943C2×C4C22×D4×C10311yescharacteristic
944C2×C4C22×D4×C10311yescharacteristic
945C2×C4H(5,𝔽2)×C10311yescharacteristic
946C2×C4H(5,𝔽2)×C10311yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—24no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C10311yescharacteristic
988C22D42×C10311yescharacteristic
989C22D42×C10311yescharacteristic
990C22C2×#135×C10311yescharacteristic
991C22#575×C10311yescharacteristic
992C22#576×C10311yescharacteristic
993C22#577×C10311yescharacteristic
994C4—22no—
995C4—41no—
996C4—41no—
997C4—42no—
998C4—41no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C10311yescharacteristic
1004C4#534×C10311yescharacteristic
1005C4D42×C10311yescharacteristic
1006C4D42×C10311yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—82no—
1012C2C103×#240311yescharacteristic
1013C2C103×#300211yescharacteristic
1014C2C103×#301211yescharacteristic
1015C2C103×#326711yescharacteristic
1016C2C103×#326811yescharacteristic
1017C2C103×#328011yescharacteristic
1018C2C103×#328211yescharacteristic
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. C22×#135×C103C2semidirect
2. C2×#546×C103C2semidirect
3. C2×#449×C103C2semidirect
4. C2×#450×C103C2semidirect
5. C2×#447×C103C2semidirect
6. C103×#2407C2semidirect
7. C103×#2015C2semidirect
8. C103×#2012C2semidirect
9. C103×#2001C2semidirect
10. C103×#2000C2semidirect
11. C103×#1893C2semidirect
12. C103×#1879C2semidirect
13. C103×#1877C2semidirect
14. C103×#1869C2semidirect
15. C103×#1788C2semidirect
17. C22×#41×C103C22semidirect
22. C22×Q16×C103C22semidirect
25. C22×SD16×C103C22semidirect
28. C23×C8×C103C22semidirect
45. C2×#103×C103C22semidirect
46. C2×#103×C103C22semidirect
47. C2×#103×C103C22semidirect
52. C2×#102×C103C22semidirect
55. C2×C22⋊C8×C103C22semidirect
58. #391×C103C22semidirect
59. #390×C103C22semidirect
62. #380×C103C22semidirect
63. #340×C103C22semidirect
64. #340×C103C22semidirect
65. #336×C103C22semidirect
66. #336×C103C22semidirect
79. C2×#41×C103D4semidirect
114. C2×SD16×C103D4semidirect
120. C2×D8×C103D4semidirect
139. #121×C103D4semidirect
365. C23×C103#135semidirect
497. #23850C103direct (N × H)
510. C22×#135C2×C103semidirect
511. C2×#546C2×C103semidirect
512. C2×#449C2×C103semidirect
513. C2×#450C2×C103semidirect
514. C2×#447C2×C103semidirect
515. #2407C2×C103semidirect
516. #2015C2×C103semidirect
517. #2012C2×C103semidirect
518. #2001C2×C103semidirect
519. #2000C2×C103semidirect
520. #1893C2×C103semidirect
521. #1879C2×C103semidirect
522. #1877C2×C103semidirect
523. #1869C2×C103semidirect
524. #1788C2×C103semidirect
525. C103#23850direct (N × H)
527. C22×#41C22×C103semidirect
532. C22×Q16C22×C103semidirect
535. C22×SD16C22×C103semidirect
538. C23×C8C22×C103semidirect
555. C2×#103C22×C103semidirect
556. C2×#103C22×C103semidirect
557. C2×#103C22×C103semidirect
562. C2×#102C22×C103semidirect
565. C2×C22⋊C8C22×C103semidirect
568. #391C22×C103semidirect
569. #390C22×C103semidirect
572. #380C22×C103semidirect
573. #340C22×C103semidirect
574. #340C22×C103semidirect
575. #336C22×C103semidirect
576. #336C22×C103semidirect
589. C2×#41D4×C103semidirect
624. C2×SD16D4×C103semidirect
630. C2×D8D4×C103semidirect
649. #121D4×C103semidirect
875. C23#135×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1032
C2×#546×C1032
C2×#449×C1032
C2×#450×C1032
C2×#447×C1032
C103×#24072
C103×#20152
C103×#20122
C103×#20012
C103×#20002
C103×#18932
C103×#18792
C103×#18772
C103×#18692
C103×#17882
#23850103