Finite Group Databasebeta

← C103×#25549 #39930824

Subgroups — C103×#25549 #39930824

Order 26368.

1390 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C103C211yesmaximal, characteristic, complemented
2C2×#481×C103C211yesmaximal, characteristic, complemented
3C2×#469×C103C211yesmaximal, characteristic, complemented
4C103×#2414C211yesmaximal, characteristic, complemented
5C103×#2058C211yesmaximal, characteristic, complemented
6C103×#2034C211yesmaximal, characteristic, complemented
7C103×#2023C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1879C211yesmaximal, characteristic, complemented
10C103×#1875C211yesmaximal, characteristic, complemented
11C103×#1874C211yesmaximal, characteristic, complemented
12C103×#1870C211yesmaximal, characteristic, complemented
13C103×#1864C211yesmaximal, characteristic, complemented
14C103×#1853C211yesmaximal, characteristic, complemented
15C103×#1736C211yesmaximal, characteristic, complemented
16C22×#41×C103—21no—
17C22×D8×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19#547×C103—24no—
20#547×C103—24no—
21C2×C4⋊Q8×C103C2211yescharacteristic
22C2×#123×C103—21no—
23C2×#123×C103—21no—
24C2×C22⋊Q8×C103—21no—
25C2×#121×C103C2211yescharacteristic
26C2×#121×C103C2211yescharacteristic
27C2×#121×C103C2211yescharacteristic
28C2×#121×C103C2211yescharacteristic
29C2×C4×D4×C103C2211yescharacteristic
30C2×C4×D4×C103C2211yescharacteristic
31C2×#117×C103C2211yescharacteristic
32C22×C4⋊C4×C103C2211yescharacteristic
33C22×C4⋊C4×C103C2211yescharacteristic
34#481×C103—24no—
35#469×C103—24no—
36C2×#106×C103C2211yescharacteristic
37C2×#106×C103C2211yescharacteristic
38C2×#106×C103C2211yescharacteristic
39C2×#102×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#390×C103—21no—
51#390×C103C2211yescharacteristic
52#389×C103C2211yescharacteristic
53#388×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—44no—
65C2×#41×C103—44no—
66C22×Q8×C103—21no—
67C22×D4×C103—21no—
68C22×D4×C103—21no—
69C22×D4×C103—21no—
70C22×D4×C103—21no—
71C22×D4×C103D411yescharacteristic
72C22×D4×C103C2311yescharacteristic
73C22×D4×C103C2311yescharacteristic
74C23×C4×C103—21no—
75C23×C4×C103—21no—
76C23×C4×C103—21no—
77C23×C4×C103C2311yescharacteristic
78C23×C4×C103C2311yescharacteristic
79C2×D8×C103—22no—
80C2×D8×C103—22no—
81C2×D8×C103—41no—
82C2×M16×C103—22no—
83C2×M16×C103—22no—
84C2×M16×C103—41no—
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C4⋊Q8×C103—22no—
90C4⋊Q8×C103—22no—
91#123×C103—28no—
92#123×C103—28no—
93C22⋊Q8×C103—28no—
94#121×C103—22no—
95#121×C103—22no—
96#121×C103—22no—
97#121×C103—22no—
98#121×C103—22no—
99#121×C103—22no—
100#121×C103—41no—
101#121×C103D414yescomplemented
102C4×D4×C103—22no—
103C4×D4×C103—22no—
104C4×D4×C103—22no—
105C4×D4×C103—22no—
106#117×C103—22no—
107#117×C103—41no—
108C2×C4⋊C4×C103—21no—
109C2×C4⋊C4×C103—21no—
110C2×C4⋊C4×C103—22no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103—22no—
113C2×C4⋊C4×C103—22no—
114C2×C4⋊C4×C103—21no—
115C2×C4⋊C4×C103D411yescharacteristic
116C2×C4⋊C4×C103D414yescomplemented
117C2×C4⋊C4×C103C2311yescharacteristic
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×C103—21no—
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103D411yescharacteristic
133C2×C22⋊C4×C103D411yescharacteristic
134C2×C42×C103—21no—
135C2×C42×C103C2311yescharacteristic
136#106×C103—22no—
137#106×C103—22no—
138#106×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—
145C22⋊C8×C103—22no—
146C22⋊C8×C103—22no—
147C22⋊C8×C103—41no—
148#95×C103—21no—
149#95×C103—21no—
150C24×C103—21no—
151C24×C103—21no—
152C24×C103C2×D411yescharacteristic
153C24×C103C2×D411yescharacteristic
154#41×C103—432no—
155C2×Q8×C103—24no—
156C2×Q8×C103—42no—
157C2×Q8×C103—42no—
158C2×D4×C103—22no—
159C2×D4×C103—22no—
160C2×D4×C103—24no—
161C2×D4×C103—24no—
162C2×D4×C103—22no—
163C2×D4×C103—21no—
164C2×D4×C103—21no—
165C2×D4×C103—21no—
166C2×D4×C103—21no—
167C2×D4×C103—21no—
168C2×D4×C103—21no—
169C2×D4×C103—21no—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—42no—
175C2×D4×C103—42no—
176C2×D4×C103—42no—
177C2×D4×C103—42no—
178C2×D4×C103—42no—
179C2×D4×C103—42no—
180C2×D4×C103—42no—
181C2×D4×C103—81no—
182C2×D4×C103—81no—
183C2×D4×C103—81no—
184C2×D4×C103C2×D412yes—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—21no—
189C22×C4×C103—24no—
190C22×C4×C103—24no—
191C22×C4×C103—24no—
192C22×C4×C103—21no—
193C22×C4×C103—21no—
194C22×C4×C103—21no—
195C22×C4×C103—21no—
196C22×C4×C103—21no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—21no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—21no—
204C22×C4×C103—42no—
205C22×C4×C103—42no—
206C22×C4×C103—42no—
207C22×C4×C103—42no—
208C22×C4×C103—42no—
209C22×C4×C103—42no—
210C22×C4×C103C2×D411yescharacteristic
211C22×C4×C103C2×D411yescharacteristic
212C22×C4×C103C2×D411yescharacteristic
213C22×C4×C103C2×D412yes—
214C22×C4×C103C2×D412yes—
215C22×C4×C103C2×D411yescharacteristic
216C22×C4×C103C2411yescharacteristic
217D8×C103—44no—
218M16×C103—44no—
219C2×C8×C103—21no—
220C2×C8×C103—21no—
221C2×C8×C103—21no—
222C2×C8×C103—21no—
223C2×C8×C103—21no—
224C2×C8×C103—21no—
225C2×C8×C103—21no—
226C2×C8×C103—21no—
227C2×C8×C103—21no—
228C2×C8×C103—21no—
229C2×C8×C103—21no—
230C2×C8×C103#4112yescomplemented
231C4⋊C4×C103—24no—
232C4⋊C4×C103—24no—
233C4⋊C4×C103—24no—
234C4⋊C4×C103—22no—
235C4⋊C4×C103—21no—
236C4⋊C4×C103—21no—
237C4⋊C4×C103—21no—
238C4⋊C4×C103—21no—
239C4⋊C4×C103—21no—
240C4⋊C4×C103—21no—
241C4⋊C4×C103—21no—
242C4⋊C4×C103—21no—
243C4⋊C4×C103—81no—
244C4⋊C4×C103C2×D412yes—
245C4⋊C4×C103C2×D412yes—
246C4⋊C4×C103C2×D412yes—
247C4⋊C4×C103#4112yescomplemented
248C22⋊C4×C103—24no—
249C22⋊C4×C103—24no—
250C22⋊C4×C103—22no—
251C22⋊C4×C103—24no—
252C22⋊C4×C103—22no—
253C22⋊C4×C103—42no—
254C22⋊C4×C103—42no—
255C22⋊C4×C103—42no—
256C22⋊C4×C103—42no—
257C22⋊C4×C103—81no—
258C22⋊C4×C103—81no—
259C42×C103—21no—
260C42×C103—21no—
261C42×C103—42no—
262C23×C103—21no—
263C23×C103—21no—
264C23×C103—21no—
265C23×C103—21no—
266C23×C103—21no—
267C23×C103—21no—
268C23×C103—21no—
269C23×C103—21no—
270C23×C103—21no—
271C23×C103—21no—
272C23×C103—21no—
273C23×C103—21no—
274C23×C103—22no—
275C23×C103—41no—
276C23×C103—41no—
277C23×C103—41no—
278C23×C103—41no—
279C23×C103—41no—
280C23×C103—41no—
281C23×C103—41no—
282C23×C103—41no—
283C23×C103—41no—
284C23×C103—41no—
285C23×C103—41no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103#12012yes—
289C23×C103AGL(1,ℤ/8)12yes—
290C23×C103C22×D411yescharacteristic
291Q8×C103—48no—
292D4×C103—28no—
293D4×C103—22no—
294D4×C103—22no—
295D4×C103—48no—
296D4×C103—48no—
297D4×C103—41no—
298D4×C103—41no—
299D4×C103—41no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—84no—
304D4×C103—84no—
305C2×C4×C103—21no—
306C2×C4×C103—21no—
307C2×C4×C103—21no—
308C2×C4×C103—21no—
309C2×C4×C103—22no—
310C2×C4×C103—22no—
311C2×C4×C103—22no—
312C2×C4×C103—22no—
313C2×C4×C103—21no—
314C2×C4×C103—21no—
315C2×C4×C103—22no—
316C2×C4×C103—22no—
317C2×C4×C103—22no—
318C2×C4×C103—22no—
319C2×C4×C103—21no—
320C2×C4×C103—21no—
321C2×C4×C103—21no—
322C2×C4×C103—21no—
323C2×C4×C103—48no—
324C2×C4×C103—48no—
325C2×C4×C103—48no—
326C2×C4×C103—41no—
327C2×C4×C103—41no—
328C2×C4×C103—41no—
329C2×C4×C103—41no—
330C2×C4×C103—41no—
331C2×C4×C103—41no—
332C2×C4×C103—41no—
333C2×C4×C103—41no—
334C2×C4×C103—41no—
335C2×C4×C103—41no—
336C2×C4×C103—41no—
337C2×C4×C103—41no—
338C2×C4×C103—41no—
339C2×C4×C103—41no—
340C2×C4×C103—41no—
341C2×C4×C103—41no—
342C2×C4×C103—41no—
343C2×C4×C103—41no—
344C2×C4×C103#12012yes—
345C2×C4×C103AGL(1,ℤ/8)12yes—
346C2×C4×C103C22×D411yescharacteristic
347C2×C4×C103C22×D411yescharacteristic
348C2×C4×C103C2×#4111yescharacteristic
349C2×C4×C103C2×#4111yescharacteristic
350C2×C4×C103H(5,𝔽2)11yescharacteristic
351C2×C4×C1032−1+411yescharacteristic
352C8×C103—22no—
353C8×C103—41no—
354C8×C103—41no—
355C8×C103—41no—
356C22×C103—22no—
357C22×C103—22no—
358C22×C103—22no—
359C22×C103—22no—
360C22×C103—22no—
361C22×C103—22no—
362C22×C103—41no—
363C22×C103—41no—
364C22×C103—41no—
365C22×C103—41no—
366C22×C103—41no—
367C22×C103—41no—
368C22×C103—41no—
369C22×C103—41no—
370C22×C103—42no—
371C22×C103—42no—
372C22×C103—42no—
373C22×C103—81no—
374C22×C103—81no—
375C22×C103—81no—
376C22×C103—81no—
377C22×C103—81no—
378C22×C103—81no—
379C22×C103—81no—
380C22×C103—81no—
381C22×C103—81no—
382C22×C103—81no—
383C22×C103—81no—
384C22×C103C2×#12011yescharacteristic
385C22×C103#54611yescharacteristic
386C22×C103#54711yescharacteristic
387C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C103#57711yescharacteristic
390C22×C103#57711yescharacteristic
391C4×C103—22no—
392C4×C103—22no—
393C4×C103—41no—
394C4×C103—42no—
395C4×C103—42no—
396C4×C103—42no—
397C4×C103—41no—
398C4×C103—42no—
399C4×C103—81no—
400C4×C103—81no—
401C4×C103#53211yescharacteristic
402C4×C103#53711yescharacteristic
403C4×C103#54611yescharacteristic
404C4×C103#54711yescharacteristic
405#25549C10311yesmaximal, characteristic, direct product factor, Sylow
406C2×C103—42no—
407C2×C103—42no—
408C2×C103—82no—
409C2×C103—161no—
410C2×C103#243011yescharacteristic
411C2×C103#300311yescharacteristic
412C2×C103#301011yescharacteristic
413C2×C103#330611yescharacteristic
414C2×C103#333211yescharacteristic
415C2×C103#334511yescharacteristic
416C2×C103#335411yescharacteristic
417C2×#547C2×C10311yescharacteristic, complemented
418C2×#481C2×C10311yescharacteristic, complemented
419C2×#469C2×C10311yescharacteristic, complemented
420#2414C2×C10311yescharacteristic, complemented
421#2058C2×C10311yescharacteristic, complemented
422#2034C2×C10311yescharacteristic, complemented
423#2023C2×C10311yescharacteristic, complemented
424#1999C2×C10311yescharacteristic, complemented
425#1879C2×C10311yescharacteristic, complemented
426#1875C2×C10311yescharacteristic, complemented
427#1874C2×C10311yescharacteristic, complemented
428#1870C2×C10311yescharacteristic, complemented
429#1864C2×C10311yescharacteristic, complemented
430#1853C2×C10311yescharacteristic, complemented
431#1736C2×C10311yescharacteristic, complemented
432C103#2554911yescharacteristic, direct product factor, Sylow
433C22×#41—21no—
434C22×D8C22×C10311yescharacteristic
435C22×M16C22×C10311yescharacteristic
436#547—24no—
437#547—24no—
438C2×C4⋊Q8C22×C10311yescharacteristic
439C2×#123—21no—
440C2×#123—21no—
441C2×C22⋊Q8—21no—
442C2×#121C22×C10311yescharacteristic
443C2×#121C22×C10311yescharacteristic
444C2×#121C22×C10311yescharacteristic
445C2×#121C22×C10311yescharacteristic
446C2×C4×D4C22×C10311yescharacteristic
447C2×C4×D4C22×C10311yescharacteristic
448C2×#117C22×C10311yescharacteristic
449C22×C4⋊C4C22×C10311yescharacteristic
450C22×C4⋊C4C22×C10311yescharacteristic
451#481—24no—
452#469—24no—
453C2×#106C22×C10311yescharacteristic
454C2×#106C22×C10311yescharacteristic
455C2×#106C22×C10311yescharacteristic
456C2×#102C22×C10311yescharacteristic
457C2×#102C22×C10311yescharacteristic
458C2×#102C22×C10311yescharacteristic
459C2×#102C22×C10311yescharacteristic
460C2×#102C22×C10311yescharacteristic
461C2×#102C22×C10311yescharacteristic
462C2×C22⋊C8C22×C10311yescharacteristic
463C2×C22⋊C8C22×C10311yescharacteristic
464C2×C22⋊C8C22×C10311yescharacteristic
465#394—21no—
466#392—21no—
467#390—21no—
468#390C22×C10311yescharacteristic
469#389C22×C10311yescharacteristic
470#388—21no—
471#380C22×C10311yescharacteristic
472#340C22×C10311yescharacteristic
473#340C22×C10311yescharacteristic
474#340C22×C10311yescharacteristic
475#340C22×C10311yescharacteristic
476#340C22×C10311yescharacteristic
477#340C22×C10311yescharacteristic
478#336C22×C10311yescharacteristic
479#336C22×C10311yescharacteristic
480C2×#41—28no—
481C2×#41—44no—
482C2×#41—44no—
483C22×Q8—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C10311yescharacteristic
489C22×D4C23×C10311yescharacteristic
490C22×D4C23×C10311yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C23×C10311yescharacteristic
495C23×C4C23×C10311yescharacteristic
496C2×D8—22no—
497C2×D8—22no—
498C2×D8—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8C23×C10311yescharacteristic
503C22×C8C23×C10311yescharacteristic
504C22×C8C23×C10311yescharacteristic
505C22×C8C23×C10311yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—22no—
508#123—28no—
509#123—28no—
510C22⋊Q8—28no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121D4×C10314yescomplemented
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—22no—
523#117—22no—
524#117—41no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C10311yescharacteristic
533C2×C4⋊C4D4×C10314yescomplemented
534C2×C4⋊C4C23×C10311yescharacteristic
535C2×C4⋊C4C23×C10311yescharacteristic
536C2×C4⋊C4C23×C10311yescharacteristic
537C2×C4⋊C4C23×C10311yescharacteristic
538C2×C4⋊C4C23×C10311yescharacteristic
539C2×C4⋊C4C23×C10311yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4D4×C10311yescharacteristic
550C2×C22⋊C4D4×C10311yescharacteristic
551C2×C42—21no—
552C2×C42C23×C10311yescharacteristic
553#106—22no—
554#106—22no—
555#106—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—41no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—41no—
565#95—21no—
566#95—21no—
567C24—21no—
568C24—21no—
569C24C2×D4×C10311yescharacteristic
570C24C2×D4×C10311yescharacteristic
571#41—432no—
572C2×Q8—24no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4C2×D4×C10312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4C2×D4×C10311yescharacteristic
628C22×C4C2×D4×C10311yescharacteristic
629C22×C4C2×D4×C10311yescharacteristic
630C22×C4C2×D4×C10312yes—
631C22×C4C2×D4×C10312yes—
632C22×C4C2×D4×C10311yescharacteristic
633C22×C4C24×C10311yescharacteristic
634D8—44no—
635M16—44no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8#41×C10312yescomplemented
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C10312yes—
662C4⋊C4C2×D4×C10312yes—
663C4⋊C4C2×D4×C10312yes—
664C4⋊C4#41×C10312yescomplemented
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23#120×C10312yes—
706C23AGL(1,ℤ/8)×C10312yes—
707C23C22×D4×C10311yescharacteristic
708Q8—48no—
709D4—28no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—48no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4#120×C10312yes—
762C2×C4AGL(1,ℤ/8)×C10312yes—
763C2×C4C22×D4×C10311yescharacteristic
764C2×C4C22×D4×C10311yescharacteristic
765C2×C4C2×#41×C10311yescharacteristic
766C2×C4C2×#41×C10311yescharacteristic
767C2×C4H(5,𝔽2)×C10311yescharacteristic
768C2×C42−1+4×C10311yescharacteristic
769C8—22no—
770C8—41no—
771C8—41no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#120×C10311yescharacteristic
802C22#546×C10311yescharacteristic
803C22#547×C10311yescharacteristic
804C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
805C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
806C22#577×C10311yescharacteristic
807C22#577×C10311yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—42no—
815C4—41no—
816C4—81no—
817C4—81no—
818C4#532×C10311yescharacteristic
819C4#537×C10311yescharacteristic
820C4#546×C10311yescharacteristic
821C4#547×C10311yescharacteristic
822C2—42no—
823C2—42no—
824C2—82no—
825C2—161no—
826C2C103×#243011yescharacteristic
827C2C103×#300311yescharacteristic
828C2C103×#301011yescharacteristic
829C2C103×#330611yescharacteristic
830C2C103×#333211yescharacteristic
831C2C103×#334511yescharacteristic
832C2C103×#335411yescharacteristic
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×#481×C103C2semidirect
3. C2×#469×C103C2semidirect
4. C103×#2414C2semidirect
5. C103×#2058C2semidirect
6. C103×#2034C2semidirect
7. C103×#2023C2semidirect
8. C103×#1999C2semidirect
9. C103×#1879C2semidirect
10. C103×#1875C2semidirect
11. C103×#1874C2semidirect
12. C103×#1870C2semidirect
13. C103×#1864C2semidirect
14. C103×#1853C2semidirect
15. C103×#1736C2semidirect
101. #121×C103D4semidirect
116. C2×C4⋊C4×C103D4semidirect
230. C2×C8×C103#41semidirect
247. C4⋊C4×C103#41semidirect
405. #25549C103direct (N × H)
417. C2×#547C2×C103semidirect
418. C2×#481C2×C103semidirect
419. C2×#469C2×C103semidirect
420. #2414C2×C103semidirect
421. #2058C2×C103semidirect
422. #2034C2×C103semidirect
423. #2023C2×C103semidirect
424. #1999C2×C103semidirect
425. #1879C2×C103semidirect
426. #1875C2×C103semidirect
427. #1874C2×C103semidirect
428. #1870C2×C103semidirect
429. #1864C2×C103semidirect
430. #1853C2×C103semidirect
431. #1736C2×C103semidirect
432. C103#25549direct (N × H)
518. #121D4×C103semidirect
533. C2×C4⋊C4D4×C103semidirect
647. C2×C8#41×C103semidirect
664. C4⋊C4#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×#481×C1032
C2×#469×C1032
C103×#24142
C103×#20582
C103×#20342
C103×#20232
C103×#19992
C103×#18792
C103×#18752
C103×#18742
C103×#18702
C103×#18642
C103×#18532
C103×#17362
#25549103