Finite Group Databasebeta

← C103×#25533 #39930808

Subgroups — C103×#25533 #39930808

Order 26368.

1444 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C103C211yesmaximal, characteristic, complemented
2C2×#480×C103C211yesmaximal, characteristic, complemented
3C2×#466×C103C211yesmaximal, characteristic, complemented
4C103×#2416C211yesmaximal, characteristic, complemented
5C103×#2057C211yesmaximal, characteristic, complemented
6C103×#2033C211yesmaximal, characteristic, complemented
7C103×#2023C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1879C211yesmaximal, characteristic, complemented
10C103×#1874C211yesmaximal, characteristic, complemented
11C103×#1874C211yesmaximal, characteristic, complemented
12C103×#1869C211yesmaximal, characteristic, complemented
13C103×#1862C211yesmaximal, characteristic, complemented
14C103×#1852C211yesmaximal, characteristic, complemented
15C2×#340×C103C211yesmaximal, characteristic, complemented
16C22×#41×C103—21no—
17C22×D8×C103C2211yescharacteristic
18C23×C8×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×C103—21no—
26C2×#121×C103C2211yescharacteristic
27C2×#121×C103C2211yescharacteristic
28C2×#121×C103C2211yescharacteristic
29C2×#121×C103C2211yescharacteristic
30C2×C4×D4×C103C2211yescharacteristic
31C2×C4×D4×C103C2211yescharacteristic
32C22×C4⋊C4×C103C2211yescharacteristic
33C22×C4⋊C4×C103C2211yescharacteristic
34C22×C4⋊C4×C103C2211yescharacteristic
35#480×C103—24no—
36#466×C103—24no—
37C2×#107×C103C2211yescharacteristic
38C2×#107×C103C2211yescharacteristic
39C2×#107×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic
46C2×C22⋊C8×C103C2211yescharacteristic
47C2×C22⋊C8×C103C2211yescharacteristic
48C2×C22⋊C8×C103C2211yescharacteristic
49#396×C103—21no—
50#394×C103—21no—
51#390×C103C2211yescharacteristic
52#389×C103C2211yescharacteristic
53#386×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×C103—21no—
78C23×C4×C103C2311yescharacteristic
79C23×C4×C103C2311yescharacteristic
80C2×D8×C103—22no—
81C2×D8×C103—22no—
82C2×D8×C103—41no—
83C22×C8×C103—22no—
84C22×C8×C103—22no—
85C22×C8×C103—41no—
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C22×C8×C103C2311yescharacteristic
90C4⋊Q8×C103—22no—
91C4⋊Q8×C103—22no—
92#123×C103—28no—
93#123×C103—28no—
94C22⋊Q8×C103—28no—
95#121×C103—22no—
96#121×C103—22no—
97#121×C103—22no—
98#121×C103—22no—
99#121×C103—22no—
100#121×C103—22no—
101#121×C103—41no—
102#121×C103—44no—
103#121×C103D414yescomplemented
104C4×D4×C103—22no—
105C4×D4×C103—22no—
106C4×D4×C103—22no—
107C4×D4×C103—22no—
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—22no—
115C2×C4⋊C4×C103—21no—
116C2×C4⋊C4×C103—21no—
117C2×C4⋊C4×C103—41no—
118C2×C4⋊C4×C103D411yescharacteristic
119C2×C4⋊C4×C103D414yescomplemented
120C2×C4⋊C4×C103C2311yescharacteristic
121C2×C4⋊C4×C103C2311yescharacteristic
122C2×C4⋊C4×C103C2311yescharacteristic
123C2×C4⋊C4×C103C2311yescharacteristic
124C2×C4⋊C4×C103C2311yescharacteristic
125C2×C4⋊C4×C103C2311yescharacteristic
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×C103—21no—
133C2×C22⋊C4×C103—21no—
134C2×C22⋊C4×C103D411yescharacteristic
135C2×C22⋊C4×C103D411yescharacteristic
136C2×C42×C103C2311yescharacteristic
137#107×C103—22no—
138#107×C103—22no—
139#107×C103—22no—
140#102×C103—22no—
141#102×C103—22no—
142#102×C103—22no—
143#102×C103—22no—
144#102×C103—22no—
145#102×C103—41no—
146C22⋊C8×C103—22no—
147C22⋊C8×C103—22no—
148C22⋊C8×C103—41no—
149#95×C103—21no—
150#95×C103—21no—
151C24×C103—21no—
152C24×C103—21no—
153C24×C103C2×D411yescharacteristic
154C24×C103C2×D411yescharacteristic
155#41×C103—432no—
156C2×Q8×C103—24no—
157C2×Q8×C103—42no—
158C2×Q8×C103—42no—
159C2×D4×C103—22no—
160C2×D4×C103—22no—
161C2×D4×C103—24no—
162C2×D4×C103—24no—
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—42no—
182C2×D4×C103—42no—
183C2×D4×C103—81no—
184C2×D4×C103D814yescomplemented
185C2×D4×C103C2×D412yes—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—21no—
189C22×C4×C103—21no—
190C22×C4×C103—24no—
191C22×C4×C103—24no—
192C22×C4×C103—24no—
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—21no—
205C22×C4×C103—42no—
206C22×C4×C103—42no—
207C22×C4×C103—42no—
208C22×C4×C103—42no—
209C22×C4×C103—42no—
210C22×C4×C103—42no—
211C22×C4×C103—42no—
212C22×C4×C103—42no—
213C22×C4×C103—81no—
214C22×C4×C103C2×D411yescharacteristic
215C22×C4×C103C2×D411yescharacteristic
216C22×C4×C103C2×D411yescharacteristic
217C22×C4×C103C2×D412yes—
218C22×C4×C103C2×D412yes—
219C22×C4×C103C2×D411yescharacteristic
220C22×C4×C103C2411yescharacteristic
221D8×C103—44no—
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—21no—
231C2×C8×C103—21no—
232C2×C8×C103—21no—
233C2×C8×C103—44no—
234C2×C8×C103#4112yescomplemented
235C4⋊C4×C103—24no—
236C4⋊C4×C103—24no—
237C4⋊C4×C103—24no—
238C4⋊C4×C103—22no—
239C4⋊C4×C103—21no—
240C4⋊C4×C103—21no—
241C4⋊C4×C103—21no—
242C4⋊C4×C103—21no—
243C4⋊C4×C103—21no—
244C4⋊C4×C103—21no—
245C4⋊C4×C103—21no—
246C4⋊C4×C103—21no—
247C4⋊C4×C103—42no—
248C4⋊C4×C103—42no—
249C4⋊C4×C103C2×D412yes—
250C4⋊C4×C103C2×D412yes—
251C4⋊C4×C103C2×D412yes—
252C4⋊C4×C103#4112yescomplemented
253C22⋊C4×C103—24no—
254C22⋊C4×C103—24no—
255C22⋊C4×C103—22no—
256C22⋊C4×C103—24no—
257C22⋊C4×C103—22no—
258C22⋊C4×C103—42no—
259C22⋊C4×C103—42no—
260C22⋊C4×C103—42no—
261C22⋊C4×C103—42no—
262C22⋊C4×C103—81no—
263C42×C103—21no—
264C42×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—21no—
275C23×C103—22no—
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—41no—
289C23×C103#12012yes—
290C23×C103C2×D812yes—
291C23×C103C2×D812yes—
292C23×C103AGL(1,ℤ/8)12yes—
293C23×C103C22×D411yescharacteristic
294Q8×C103—48no—
295D4×C103—28no—
296D4×C103—22no—
297D4×C103—22no—
298D4×C103—48no—
299D4×C103—48no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—41no—
304D4×C103—41no—
305D4×C103—41no—
306D4×C103—84no—
307D4×C103—84no—
308C2×C4×C103—21no—
309C2×C4×C103—21no—
310C2×C4×C103—21no—
311C2×C4×C103—21no—
312C2×C4×C103—22no—
313C2×C4×C103—22no—
314C2×C4×C103—22no—
315C2×C4×C103—22no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—22no—
319C2×C4×C103—22no—
320C2×C4×C103—22no—
321C2×C4×C103—21no—
322C2×C4×C103—22no—
323C2×C4×C103—21no—
324C2×C4×C103—21no—
325C2×C4×C103—21no—
326C2×C4×C103—48no—
327C2×C4×C103—48no—
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—48no—
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—41no—
345C2×C4×C103—41no—
346C2×C4×C103—41no—
347C2×C4×C103—84no—
348C2×C4×C103#12012yes—
349C2×C4×C103C2×D812yes—
350C2×C4×C103C22×D411yescharacteristic
351C2×C4×C103C22×D411yescharacteristic
352C2×C4×C103C2×#4111yescharacteristic
353C2×C4×C103C2×#4111yescharacteristic
354C2×C4×C103H(5,𝔽2)11yescharacteristic
355C2×C4×C1032−1+411yescharacteristic
356C8×C103—22no—
357C8×C103—41no—
358C8×C103—41no—
359C8×C103—41no—
360C22×C103—22no—
361C22×C103—22no—
362C22×C103—22no—
363C22×C103—22no—
364C22×C103—22no—
365C22×C103—22no—
366C22×C103—22no—
367C22×C103—22no—
368C22×C103—22no—
369C22×C103—41no—
370C22×C103—41no—
371C22×C103—41no—
372C22×C103—41no—
373C22×C103—42no—
374C22×C103—42no—
375C22×C103—42no—
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×C103—81no—
385C22×C103—81no—
386C22×C103—81no—
387C22×C103#44714yes—
388C22×C103C2×#12011yescharacteristic
389C22×C103#54611yescharacteristic
390C22×C103#54711yescharacteristic
391C22×C103C22×D811yescharacteristic
392C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C103#57711yescharacteristic
394C22×C103#57811yescharacteristic
395C4×C103—22no—
396C4×C103—22no—
397C4×C103—41no—
398C4×C103—42no—
399C4×C103—42no—
400C4×C103—42no—
401C4×C103—41no—
402C4×C103—42no—
403C4×C103—81no—
404C4×C103—81no—
405C4×C103#53211yescharacteristic
406C4×C103#53711yescharacteristic
407C4×C103#54611yescharacteristic
408C4×C103#54711yescharacteristic
409#25533C10311yesmaximal, characteristic, direct product factor, Sylow
410C2×C103—24no—
411C2×C103—42no—
412C2×C103—82no—
413C2×C103—161no—
414C2×C103#243011yescharacteristic
415C2×C103C2×#44711yescharacteristic
416C2×C103#301311yescharacteristic
417C2×C103#329411yescharacteristic
418C2×C103#330811yescharacteristic
419C2×C103#333411yescharacteristic
420C2×C103#334511yescharacteristic
421C2×#547C2×C10311yescharacteristic, complemented
422C2×#480C2×C10311yescharacteristic, complemented
423C2×#466C2×C10311yescharacteristic, complemented
424#2416C2×C10311yescharacteristic, complemented
425#2057C2×C10311yescharacteristic, complemented
426#2033C2×C10311yescharacteristic, complemented
427#2023C2×C10311yescharacteristic, complemented
428#1999C2×C10311yescharacteristic, complemented
429#1879C2×C10311yescharacteristic, complemented
430#1874C2×C10311yescharacteristic, complemented
431#1874C2×C10311yescharacteristic, complemented
432#1869C2×C10311yescharacteristic, complemented
433#1862C2×C10311yescharacteristic, complemented
434#1852C2×C10311yescharacteristic, complemented
435C2×#340C2×C10311yescharacteristic, complemented
436C103#2553311yescharacteristic, direct product factor, Sylow
437C22×#41—21no—
438C22×D8C22×C10311yescharacteristic
439C23×C8C22×C10311yescharacteristic
440#547—24no—
441#547—24no—
442C2×C4⋊Q8C22×C10311yescharacteristic
443C2×#123—21no—
444C2×#123—21no—
445C2×C22⋊Q8—21no—
446C2×#121—21no—
447C2×#121C22×C10311yescharacteristic
448C2×#121C22×C10311yescharacteristic
449C2×#121C22×C10311yescharacteristic
450C2×#121C22×C10311yescharacteristic
451C2×C4×D4C22×C10311yescharacteristic
452C2×C4×D4C22×C10311yescharacteristic
453C22×C4⋊C4C22×C10311yescharacteristic
454C22×C4⋊C4C22×C10311yescharacteristic
455C22×C4⋊C4C22×C10311yescharacteristic
456#480—24no—
457#466—24no—
458C2×#107C22×C10311yescharacteristic
459C2×#107C22×C10311yescharacteristic
460C2×#107C22×C10311yescharacteristic
461C2×#102C22×C10311yescharacteristic
462C2×#102C22×C10311yescharacteristic
463C2×#102C22×C10311yescharacteristic
464C2×#102C22×C10311yescharacteristic
465C2×#102C22×C10311yescharacteristic
466C2×#102C22×C10311yescharacteristic
467C2×C22⋊C8C22×C10311yescharacteristic
468C2×C22⋊C8C22×C10311yescharacteristic
469C2×C22⋊C8C22×C10311yescharacteristic
470#396—21no—
471#394—21no—
472#390C22×C10311yescharacteristic
473#389C22×C10311yescharacteristic
474#386—21no—
475#380C22×C10311yescharacteristic
476#340C22×C10311yescharacteristic
477#340C22×C10311yescharacteristic
478#340C22×C10311yescharacteristic
479#340C22×C10311yescharacteristic
480#340C22×C10311yescharacteristic
481#340C22×C10311yescharacteristic
482#336C22×C10311yescharacteristic
483#336C22×C10311yescharacteristic
484C2×#41—28no—
485C2×#41—44no—
486C2×#41—44no—
487C22×Q8—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C10311yescharacteristic
493C22×D4C23×C10311yescharacteristic
494C22×D4C23×C10311yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C23×C10311yescharacteristic
500C23×C4C23×C10311yescharacteristic
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C22×C8—22no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8C23×C10311yescharacteristic
508C22×C8C23×C10311yescharacteristic
509C22×C8C23×C10311yescharacteristic
510C22×C8C23×C10311yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513#123—28no—
514#123—28no—
515C22⋊Q8—28no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—41no—
523#121—44no—
524#121D4×C10314yescomplemented
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4D4×C10311yescharacteristic
540C2×C4⋊C4D4×C10314yescomplemented
541C2×C4⋊C4C23×C10311yescharacteristic
542C2×C4⋊C4C23×C10311yescharacteristic
543C2×C4⋊C4C23×C10311yescharacteristic
544C2×C4⋊C4C23×C10311yescharacteristic
545C2×C4⋊C4C23×C10311yescharacteristic
546C2×C4⋊C4C23×C10311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C10311yescharacteristic
556C2×C22⋊C4D4×C10311yescharacteristic
557C2×C42C23×C10311yescharacteristic
558#107—22no—
559#107—22no—
560#107—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—41no—
570#95—21no—
571#95—21no—
572C24—21no—
573C24—21no—
574C24C2×D4×C10311yescharacteristic
575C24C2×D4×C10311yescharacteristic
576#41—432no—
577C2×Q8—24no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4D8×C10314yescomplemented
606C2×D4C2×D4×C10312yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—81no—
635C22×C4C2×D4×C10311yescharacteristic
636C22×C4C2×D4×C10311yescharacteristic
637C22×C4C2×D4×C10311yescharacteristic
638C22×C4C2×D4×C10312yes—
639C22×C4C2×D4×C10312yes—
640C22×C4C2×D4×C10311yescharacteristic
641C22×C4C24×C10311yescharacteristic
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8#41×C10312yescomplemented
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C10312yes—
671C4⋊C4C2×D4×C10312yes—
672C4⋊C4C2×D4×C10312yes—
673C4⋊C4#41×C10312yescomplemented
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—22no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—81no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23#120×C10312yes—
711C23C2×D8×C10312yes—
712C23C2×D8×C10312yes—
713C23AGL(1,ℤ/8)×C10312yes—
714C23C22×D4×C10311yescharacteristic
715Q8—48no—
716D4—28no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—84no—
728D4—84no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—48no—
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—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—84no—
769C2×C4#120×C10312yes—
770C2×C4C2×D8×C10312yes—
771C2×C4C22×D4×C10311yescharacteristic
772C2×C4C22×D4×C10311yescharacteristic
773C2×C4C2×#41×C10311yescharacteristic
774C2×C4C2×#41×C10311yescharacteristic
775C2×C4H(5,𝔽2)×C10311yescharacteristic
776C2×C42−1+4×C10311yescharacteristic
777C8—22no—
778C8—41no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22#447×C10314yes—
809C22C2×#120×C10311yescharacteristic
810C22#546×C10311yescharacteristic
811C22#547×C10311yescharacteristic
812C22C22×D8×C10311yescharacteristic
813C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
814C22#577×C10311yescharacteristic
815C22#578×C10311yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—41no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4#532×C10311yescharacteristic
827C4#537×C10311yescharacteristic
828C4#546×C10311yescharacteristic
829C4#547×C10311yescharacteristic
830C2—24no—
831C2—42no—
832C2—82no—
833C2—161no—
834C2C103×#243011yescharacteristic
835C2C2×#447×C10311yescharacteristic
836C2C103×#301311yescharacteristic
837C2C103×#329411yescharacteristic
838C2C103×#330811yescharacteristic
839C2C103×#333411yescharacteristic
840C2C103×#334511yescharacteristic
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×#480×C103C2semidirect
3. C2×#466×C103C2semidirect
4. C103×#2416C2semidirect
5. C103×#2057C2semidirect
6. C103×#2033C2semidirect
7. C103×#2023C2semidirect
8. C103×#1999C2semidirect
9. C103×#1879C2semidirect
10. C103×#1874C2semidirect
11. C103×#1874C2semidirect
12. C103×#1869C2semidirect
13. C103×#1862C2semidirect
14. C103×#1852C2semidirect
15. C2×#340×C103C2semidirect
103. #121×C103D4semidirect
119. C2×C4⋊C4×C103D4semidirect
184. C2×D4×C103D8semidirect
234. C2×C8×C103#41semidirect
252. C4⋊C4×C103#41semidirect
409. #25533C103direct (N × H)
421. C2×#547C2×C103semidirect
422. C2×#480C2×C103semidirect
423. C2×#466C2×C103semidirect
424. #2416C2×C103semidirect
425. #2057C2×C103semidirect
426. #2033C2×C103semidirect
427. #2023C2×C103semidirect
428. #1999C2×C103semidirect
429. #1879C2×C103semidirect
430. #1874C2×C103semidirect
431. #1874C2×C103semidirect
432. #1869C2×C103semidirect
433. #1862C2×C103semidirect
434. #1852C2×C103semidirect
435. C2×#340C2×C103semidirect
436. C103#25533direct (N × H)
524. #121D4×C103semidirect
540. C2×C4⋊C4D4×C103semidirect
605. C2×D4D8×C103semidirect
655. C2×C8#41×C103semidirect
673. 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×#480×C1032
C2×#466×C1032
C103×#24162
C103×#20572
C103×#20332
C103×#20232
C103×#19992
C103×#18792
C103×#18742
C103×#18692
C103×#18622
C103×#18522
C2×#340×C1032
#25533103