Finite Group Databasebeta

← C103×#23482 #39928757

Subgroups — C103×#23482 #39928757

Order 26368.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C103C211yesmaximal, characteristic
2C2×#428×C103C211yesmaximal, characteristic, complemented
3C2×#417×C103C211yesmaximal, characteristic, complemented
4C2×#417×C103C211yesmaximal, characteristic, complemented
5C2×#407×C103C211yesmaximal, characteristic, complemented
6C2×#380×C103C211yesmaximal, characteristic, complemented
7C103×#2036C212yesmaximal, complemented
8C103×#2035C212yesmaximal, complemented
9C103×#2034C212yesmaximal, complemented
10C103×#2033C212yesmaximal, complemented
11C103×#1736C211yesmaximal, characteristic, complemented
12C22×#41×C103C2211yescharacteristic
13C24×C4×C103C2211yescharacteristic
14C22×M16×C103C2211yescharacteristic
15C22×M16×C103C2211yescharacteristic
16#525×C103—24no—
17#525×C103—24no—
18C2×#123×C103—21no—
19C2×C22⋊Q8×C103C2211yescharacteristic
20C2×C22⋊Q8×C103C2211yescharacteristic
21C2×#121×C103C2211yescharacteristic
22C2×#121×C103C2211yescharacteristic
23C2×#120×C103—21no—
24C2×C4×D4×C103—21no—
25C2×C4×D4×C103—21no—
26C2×#117×C103C2211yescharacteristic
27C22×C4⋊C4×C103C2211yescharacteristic
28C22×C4⋊C4×C103C2211yescharacteristic
29C22×C22⋊C4×C103—21no—
30#428×C103—24no—
31C2×#107×C103C2212yescomplemented
32C2×#106×C103C2212yescomplemented
33#417×C103—24no—
34#417×C103—24no—
35C2×#103×C103C2212yescomplemented
36C2×#103×C103C2212yescomplemented
37C2×#102×C103C2212yescomplemented
38C2×#102×C103C2212yescomplemented
39#407×C103—24no—
40C2×C22⋊C8×C103C2212yes—
41C2×C22⋊C8×C103C2212yes—
42#380×C103—21no—
43#380×C103—21no—
44#380×C103C2212yes—
45#380×C103C2212yes—
46C2×#95×C103—21no—
47#340×C103C2212yescomplemented
48#340×C103C2212yescomplemented
49C25×C103D411yescharacteristic
50C2×#41×C103—22no—
51C2×#41×C103—22no—
52C2×#41×C103—22no—
53C2×#41×C103—22no—
54C2×#41×C103—22no—
55C2×#41×C103D414yes—
56C22×Q8×C103C2311yescharacteristic
57C22×D4×C103—21no—
58C22×D4×C103—21no—
59C22×D4×C103—21no—
60C22×D4×C103C2311yescharacteristic
61C23×C4×C103—22no—
62C23×C4×C103—21no—
63C23×C4×C103—22no—
64C23×C4×C103—22no—
65C23×C4×C103—22no—
66C23×C4×C103—22no—
67C23×C4×C103—22no—
68C23×C4×C103—21no—
69C23×C4×C103—21no—
70C23×C4×C103D411yescharacteristic
71C23×C4×C103D411yescharacteristic
72C23×C4×C103D411yescharacteristic
73C23×C4×C103C2311yescharacteristic
74C23×C4×C103C2311yescharacteristic
75C23×C4×C103C2311yescharacteristic
76C2×M16×C103—22no—
77C2×M16×C103—22no—
78C2×M16×C103—22no—
79C2×M16×C103—22no—
80C2×M16×C103—22no—
81C2×M16×C103D414yescomplemented
82C22×C8×C103C2312yes—
83C22×C8×C103C2312yes—
84#123×C103—28no—
85C22⋊Q8×C103—22no—
86C22⋊Q8×C103—22no—
87C22⋊Q8×C103—22no—
88C22⋊Q8×C103—22no—
89#121×C103—22no—
90#121×C103—22no—
91#121×C103—22no—
92#121×C103—22no—
93#120×C103—28no—
94C4×D4×C103—28no—
95C4×D4×C103—28no—
96#117×C103—22no—
97#117×C103D414yes—
98C2×C4⋊C4×C103—21no—
99C2×C4⋊C4×C103—21no—
100C2×C4⋊C4×C103—22no—
101C2×C4⋊C4×C103—22no—
102C2×C4⋊C4×C103—22no—
103C2×C4⋊C4×C103—22no—
104C2×C4⋊C4×C103—21no—
105C2×C4⋊C4×C103—21no—
106C2×C4⋊C4×C103C2312yes—
107C2×C4⋊C4×C103C2312yes—
108C2×C4⋊C4×C103C2311yescharacteristic
109C2×C4⋊C4×C103C2311yescharacteristic
110C2×C22⋊C4×C103—21no—
111C2×C22⋊C4×C103—21no—
112C2×C22⋊C4×C103—21no—
113C2×C22⋊C4×C103—21no—
114C2×C22⋊C4×C103—21no—
115C2×C22⋊C4×C103—22no—
116C2×C22⋊C4×C103—22no—
117C2×C22⋊C4×C103—44no—
118C2×C42×C103—21no—
119#107×C103—24no—
120#106×C103—24no—
121#103×C103—24no—
122#103×C103—24no—
123#102×C103—24no—
124#102×C103—24no—
125C22⋊C8×C103—24no—
126C22⋊C8×C103—24no—
127#95×C103—22no—
128#95×C103—22no—
129C24×C103—22no—
130C24×C103—22no—
131C24×C103—22no—
132C24×C103—22no—
133C24×C103—22no—
134C24×C103—21no—
135C24×C103—41no—
136C24×C103—41no—
137C24×C103C2×D411yescharacteristic
138C24×C103C2×D411yescharacteristic
139C24×C103C2×D411yescharacteristic
140#41×C103—28no—
141#41×C103—28no—
142#41×C103—44no—
143#41×C103—44no—
144C2×Q8×C103—21no—
145C2×Q8×C103—21no—
146C2×Q8×C103—21no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
149C2×Q8×C103C2×D412yes—
150C2×D4×C103—24no—
151C2×D4×C103—24no—
152C2×D4×C103—24no—
153C2×D4×C103—21no—
154C2×D4×C103—21no—
155C2×D4×C103—21no—
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—42no—
159C2×D4×C103—42no—
160C2×D4×C103—42no—
161C2×D4×C103—42no—
162C2×D4×C103—42no—
163C2×D4×C103—42no—
164C2×D4×C103C2×D412yes—
165C22×C4×C103—22no—
166C22×C4×C103—22no—
167C22×C4×C103—22no—
168C22×C4×C103—21no—
169C22×C4×C103—21no—
170C22×C4×C103—21no—
171C22×C4×C103—22no—
172C22×C4×C103—22no—
173C22×C4×C103—24no—
174C22×C4×C103—22no—
175C22×C4×C103—22no—
176C22×C4×C103—22no—
177C22×C4×C103—22no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103—21no—
181C22×C4×C103—21no—
182C22×C4×C103—21no—
183C22×C4×C103—21no—
184C22×C4×C103—21no—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—21no—
189C22×C4×C103—21no—
190C22×C4×C103—22no—
191C22×C4×C103—22no—
192C22×C4×C103—44no—
193C22×C4×C103—44no—
194C22×C4×C103—42no—
195C22×C4×C103—44no—
196C22×C4×C103—42no—
197C22×C4×C103—44no—
198C22×C4×C103—42no—
199C22×C4×C103—42no—
200C22×C4×C103—42no—
201C22×C4×C103—42no—
202C22×C4×C103—42no—
203C22×C4×C103—42no—
204C22×C4×C103C2×D411yescharacteristic
205C22×C4×C103C2×D411yescharacteristic
206C22×C4×C103C2×D411yescharacteristic
207C22×C4×C103C2×D412yes—
208C22×C4×C103C2×D412yes—
209C22×C4×C103C2×D412yes—
210C22×C4×C103#4112yes—
211C22×C4×C103#4112yes—
212C22×C4×C103#4112yes—
213C22×C4×C103C2411yescharacteristic
214M16×C103—28no—
215M16×C103—44no—
216C2×C8×C103—22no—
217C2×C8×C103—22no—
218C2×C8×C103—22no—
219C2×C8×C103—22no—
220C2×C8×C103—22no—
221C2×C8×C103C2×D414yes—
222C4⋊C4×C103—24no—
223C4⋊C4×C103—24no—
224C4⋊C4×C103—21no—
225C4⋊C4×C103—21no—
226C4⋊C4×C103—22no—
227C4⋊C4×C103—22no—
228C4⋊C4×C103—22no—
229C4⋊C4×C103—22no—
230C4⋊C4×C103—42no—
231C4⋊C4×C103—42no—
232C4⋊C4×C103C2×D412yes—
233C4⋊C4×C103C2×D412yes—
234C22⋊C4×C103—24no—
235C22⋊C4×C103—24no—
236C22⋊C4×C103—24no—
237C22⋊C4×C103—24no—
238C22⋊C4×C103—24no—
239C22⋊C4×C103—44no—
240C22⋊C4×C103—44no—
241C42×C103—24no—
242C23×C103—21no—
243C23×C103—21no—
244C23×C103—21no—
245C23×C103—21no—
246C23×C103—28no—
247C23×C103—21no—
248C23×C103—21no—
249C23×C103—21no—
250C23×C103—21no—
251C23×C103—21no—
252C23×C103—21no—
253C23×C103—21no—
254C23×C103—21no—
255C23×C103—21no—
256C23×C103—21no—
257C23×C103—21no—
258C23×C103—21no—
259C23×C103—22no—
260C23×C103—44no—
261C23×C103—44no—
262C23×C103—44no—
263C23×C103—44no—
264C23×C103—44no—
265C23×C103—44no—
266C23×C103—41no—
267C23×C103—41no—
268C23×C103—41no—
269C23×C103—41no—
270C23×C103—41no—
271C23×C103—41no—
272C23×C103#12012yes—
273C23×C103#12112yes—
274C23×C103#12312yes—
275C23×C103AGL(1,ℤ/8)12yes—
276C23×C103#13712yes—
277C23×C103C22×D411yescharacteristic
278Q8×C103—22no—
279Q8×C103—22no—
280Q8×C103—41no—
281Q8×C103—41no—
282D4×C103—22no—
283D4×C103—22no—
284D4×C103—48no—
285D4×C103—48no—
286D4×C103—48no—
287D4×C103—41no—
288D4×C103—41no—
289C2×C4×C103—22no—
290C2×C4×C103—22no—
291C2×C4×C103—21no—
292C2×C4×C103—21no—
293C2×C4×C103—22no—
294C2×C4×C103—21no—
295C2×C4×C103—21no—
296C2×C4×C103—21no—
297C2×C4×C103—21no—
298C2×C4×C103—41no—
299C2×C4×C103—41no—
300C2×C4×C103—41no—
301C2×C4×C103—41no—
302C2×C4×C103—41no—
303C2×C4×C103—41no—
304C2×C4×C103—44no—
305C2×C4×C103—41no—
306C2×C4×C103—41no—
307C2×C4×C103—41no—
308C2×C4×C103—41no—
309C2×C4×C103—41no—
310C2×C4×C103—41no—
311C2×C4×C103—41no—
312C2×C4×C103—41no—
313C2×C4×C103—44no—
314C2×C4×C103—44no—
315C2×C4×C103—48no—
316C2×C4×C103—42no—
317C2×C4×C103—42no—
318C2×C4×C103—42no—
319C2×C4×C103—42no—
320C2×C4×C103—42no—
321C2×C4×C103—42no—
322C2×C4×C103—84no—
323C2×C4×C103—84no—
324C2×C4×C103#12012yes—
325C2×C4×C103#12114yes—
326C2×C4×C103#12114yes—
327C2×C4×C103#12112yes—
328C2×C4×C103#12314yes—
329C2×C4×C103#12312yes—
330C2×C4×C103#12414yes—
331C2×C4×C103C22×D411yescharacteristic
332C2×C4×C103C22×D411yescharacteristic
333C2×C4×C103C22×D411yescharacteristic
334C2×C4×C103C2×#4111yescharacteristic
335C2×C4×C103C2×#4111yescharacteristic
336C2×C4×C103C2×#4111yescharacteristic
337C8×C103—24no—
338C8×C103—42no—
339C22×C103—22no—
340C22×C103—22no—
341C22×C103—22no—
342C22×C103—22no—
343C22×C103—22no—
344C22×C103—22no—
345C22×C103—22no—
346C22×C103—22no—
347C22×C103—22no—
348C22×C103—22no—
349C22×C103—22no—
350C22×C103—22no—
351C22×C103—416no—
352C22×C103—41no—
353C22×C103—41no—
354C22×C103—41no—
355C22×C103—41no—
356C22×C103—41no—
357C22×C103—41no—
358C22×C103—41no—
359C22×C103—41no—
360C22×C103—42no—
361C22×C103—42no—
362C22×C103—42no—
363C22×C103—81no—
364C22×C103—81no—
365C22×C103—81no—
366C22×C103—81no—
367C22×C103#39414yes—
368C22×C103C2×#12011yescharacteristic
369C22×C103C2×#12111yescharacteristic
370C22×C103C2×#12311yescharacteristic
371C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C103C2×#13711yescharacteristic
373C22×C103#57511yescharacteristic
374C22×C103#57511yescharacteristic
375C4×C103—41no—
376C4×C103—41no—
377C4×C103—42no—
378C4×C103—42no—
379C4×C103—42no—
380C4×C103—82no—
381C4×C103—82no—
382C4×C103#39414yes—
383C4×C103C2×#12111yescharacteristic
384C4×C103C2×#12111yescharacteristic
385C4×C103C2×#12311yescharacteristic
386C4×C103C2×#12411yescharacteristic
387#23482C10311yesmaximal, characteristic, direct product factor, Sylow
388C2×C103—24no—
389C2×C103—42no—
390C2×C103—42no—
391C2×C103—82no—
392C2×C103C2×#39411yescharacteristic
393C2×C103#300611yescharacteristic
394C2×C103#300711yescharacteristic
395C2×C103#305511yescharacteristic
396C2×C103#305611yescharacteristic
397C2×C103#309211yescharacteristic
398C2×C103#309311yescharacteristic
399C2×#525C2×C10311yescharacteristic
400C2×#428C2×C10311yescharacteristic, complemented
401C2×#417C2×C10311yescharacteristic, complemented
402C2×#417C2×C10311yescharacteristic, complemented
403C2×#407C2×C10311yescharacteristic, complemented
404C2×#380C2×C10311yescharacteristic, complemented
405#2036C2×C10312yescomplemented
406#2035C2×C10312yescomplemented
407#2034C2×C10312yescomplemented
408#2033C2×C10312yescomplemented
409#1736C2×C10311yescharacteristic, complemented
410C103#2348211yescharacteristic, direct product factor, Sylow
411C22×#41C22×C10311yescharacteristic
412C24×C4C22×C10311yescharacteristic
413C22×M16C22×C10311yescharacteristic
414C22×M16C22×C10311yescharacteristic
415#525—24no—
416#525—24no—
417C2×#123—21no—
418C2×C22⋊Q8C22×C10311yescharacteristic
419C2×C22⋊Q8C22×C10311yescharacteristic
420C2×#121C22×C10311yescharacteristic
421C2×#121C22×C10311yescharacteristic
422C2×#120—21no—
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×#117C22×C10311yescharacteristic
426C22×C4⋊C4C22×C10311yescharacteristic
427C22×C4⋊C4C22×C10311yescharacteristic
428C22×C22⋊C4—21no—
429#428—24no—
430C2×#107C22×C10312yescomplemented
431C2×#106C22×C10312yescomplemented
432#417—24no—
433#417—24no—
434C2×#103C22×C10312yescomplemented
435C2×#103C22×C10312yescomplemented
436C2×#102C22×C10312yescomplemented
437C2×#102C22×C10312yescomplemented
438#407—24no—
439C2×C22⋊C8C22×C10312yes—
440C2×C22⋊C8C22×C10312yes—
441#380—21no—
442#380—21no—
443#380C22×C10312yes—
444#380C22×C10312yes—
445C2×#95—21no—
446#340C22×C10312yescomplemented
447#340C22×C10312yescomplemented
448C25D4×C10311yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41D4×C10314yes—
455C22×Q8C23×C10311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C10311yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4D4×C10311yescharacteristic
470C23×C4D4×C10311yescharacteristic
471C23×C4D4×C10311yescharacteristic
472C23×C4C23×C10311yescharacteristic
473C23×C4C23×C10311yescharacteristic
474C23×C4C23×C10311yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16D4×C10314yescomplemented
481C22×C8C23×C10312yes—
482C22×C8C23×C10312yes—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117D4×C10314yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C10312yes—
506C2×C4⋊C4C23×C10312yes—
507C2×C4⋊C4C23×C10311yescharacteristic
508C2×C4⋊C4C23×C10311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—44no—
517C2×C42—21no—
518#107—24no—
519#106—24no—
520#103—24no—
521#103—24no—
522#102—24no—
523#102—24no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×D4×C10311yescharacteristic
537C24C2×D4×C10311yescharacteristic
538C24C2×D4×C10311yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C10312yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C10312yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C10311yescharacteristic
604C22×C4C2×D4×C10311yescharacteristic
605C22×C4C2×D4×C10311yescharacteristic
606C22×C4C2×D4×C10312yes—
607C22×C4C2×D4×C10312yes—
608C22×C4C2×D4×C10312yes—
609C22×C4#41×C10312yes—
610C22×C4#41×C10312yes—
611C22×C4#41×C10312yes—
612C22×C4C24×C10311yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×D4×C10314yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C10312yes—
632C4⋊C4C2×D4×C10312yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C10312yes—
672C23#121×C10312yes—
673C23#123×C10312yes—
674C23AGL(1,ℤ/8)×C10312yes—
675C23#137×C10312yes—
676C23C22×D4×C10311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4#120×C10312yes—
724C2×C4#121×C10312yes—
725C2×C4#121×C10314yes—
726C2×C4#121×C10314yes—
727C2×C4#123×C10312yes—
728C2×C4#123×C10314yes—
729C2×C4#124×C10314yes—
730C2×C4C22×D4×C10311yescharacteristic
731C2×C4C22×D4×C10311yescharacteristic
732C2×C4C22×D4×C10311yescharacteristic
733C2×C4C2×#41×C10311yescharacteristic
734C2×C4C2×#41×C10311yescharacteristic
735C2×C4C2×#41×C10311yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#394×C10314yes—
767C22C2×#120×C10311yescharacteristic
768C22C2×#121×C10311yescharacteristic
769C22C2×#123×C10311yescharacteristic
770C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
771C22C2×#137×C10311yescharacteristic
772C22#575×C10311yescharacteristic
773C22#575×C10311yescharacteristic
774C4—42no—
775C4—42no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4#394×C10314yes—
782C4C2×#121×C10311yescharacteristic
783C4C2×#121×C10311yescharacteristic
784C4C2×#123×C10311yescharacteristic
785C4C2×#124×C10311yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#394×C10311yescharacteristic
791C2C103×#300611yescharacteristic
792C2C103×#300711yescharacteristic
793C2C103×#305511yescharacteristic
794C2C103×#305611yescharacteristic
795C2C103×#309211yescharacteristic
796C2C103×#309311yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#525×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C24×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C103C2semidirect
3. C2×#417×C103C2semidirect
4. C2×#417×C103C2semidirect
5. C2×#407×C103C2semidirect
6. C2×#380×C103C2semidirect
7. C103×#2036C2semidirect
8. C103×#2035C2semidirect
9. C103×#2034C2semidirect
10. C103×#2033C2semidirect
11. C103×#1736C2semidirect
31. C2×#107×C103C22semidirect
32. C2×#106×C103C22semidirect
35. C2×#103×C103C22semidirect
36. C2×#103×C103C22semidirect
37. C2×#102×C103C22semidirect
38. C2×#102×C103C22semidirect
47. #340×C103C22semidirect
48. #340×C103C22semidirect
81. C2×M16×C103D4semidirect
387. #23482C103direct (N × H)
400. C2×#428C2×C103semidirect
401. C2×#417C2×C103semidirect
402. C2×#417C2×C103semidirect
403. C2×#407C2×C103semidirect
404. C2×#380C2×C103semidirect
405. #2036C2×C103semidirect
406. #2035C2×C103semidirect
407. #2034C2×C103semidirect
408. #2033C2×C103semidirect
409. #1736C2×C103semidirect
410. C103#23482direct (N × H)
430. C2×#107C22×C103semidirect
431. C2×#106C22×C103semidirect
434. C2×#103C22×C103semidirect
435. C2×#103C22×C103semidirect
436. C2×#102C22×C103semidirect
437. C2×#102C22×C103semidirect
446. #340C22×C103semidirect
447. #340C22×C103semidirect
480. C2×M16D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1032
C2×#428×C1032
C2×#417×C1032
C2×#407×C1032
C2×#380×C1032
C103×#20362
C103×#20352
C103×#20342
C103×#20332
C103×#17362
#23482103