Finite Group Databasebeta

← C103×#22422 #39927697

Subgroups — C103×#22422 #39927697

Order 26368.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C103C211yesmaximal, characteristic
2C2×#435×C103C211yesmaximal, characteristic, complemented
3C2×#417×C103C211yesmaximal, characteristic, complemented
4C2×#416×C103C211yesmaximal, characteristic, complemented
5C103×#2352C211yesmaximal, characteristic, complemented
6C103×#1982C211yesmaximal, characteristic, complemented
7C103×#1961C211yesmaximal, characteristic, complemented
8C103×#1895C211yesmaximal, characteristic, complemented
9C103×#1893C211yesmaximal, characteristic, complemented
10C103×#1875C211yesmaximal, characteristic, complemented
11C103×#1874C211yesmaximal, characteristic, complemented
12C103×#1805C211yesmaximal, characteristic, complemented
13C103×#1788C211yesmaximal, characteristic, complemented
14C103×#1788C211yesmaximal, characteristic, complemented
15C103×#1763C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic
20#550×C103—24no—
21#550×C103C418yescomplemented
22C2×#127×C103—21no—
23C2×#127×C103C2211yescharacteristic
24C2×#121×C103—21no—
25C2×#121×C103—21no—
26C2×#121×C103C2211yescharacteristic
27C2×#121×C103C2211yescharacteristic
28C2×C4×Q8×C103C2211yescharacteristic
29C2×C4×D4×C103—21no—
30C2×C4×D4×C103C2211yescharacteristic
31C2×#117×C103C2211yescharacteristic
32C22×C4⋊C4×C103C2211yescharacteristic
33#435×C103—24no—
34C2×C4⋊C8×C103C2211yescharacteristic
35#417×C103—24no—
36#416×C103—24no—
37C2×#103×C103C2211yescharacteristic
38C2×#103×C103C2211yescharacteristic
39C2×#103×C103C2211yescharacteristic
40C2×#103×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic
46C2×#102×C103C2211yescharacteristic
47C2×#102×C103C2211yescharacteristic
48C2×#102×C103C2211yescharacteristic
49C2×C22⋊C8×C103C2211yescharacteristic
50C2×C22⋊C8×C103C2211yescharacteristic
51C2×#97×C103C2211yescharacteristic
52#388×C103—21no—
53#387×C103—21no—
54#386×C103—21no—
55#382×C103C2211yescharacteristic
56#380×C103C2211yescharacteristic
57#380×C103C2211yescharacteristic
58C4×C4⋊C4×C103C2211yescharacteristic
59C4×C22⋊C4×C103—21no—
60#340×C103C2211yescharacteristic
61#340×C103C2211yescharacteristic
62#340×C103C2211yescharacteristic
63#340×C103C2211yescharacteristic
64C2×#41×C103—22no—
65C2×#41×C103—22no—
66C2×#41×C103—22no—
67C2×#41×C103—22no—
68C2×#41×C103—22no—
69C2×#41×C103—22no—
70C2×#41×C103—41no—
71C2×#41×C103—41no—
72C2×#41×C103—41no—
73C2×#41×C103—41no—
74C2×#41×C103C2×C414yes—
75C2×#41×C103C2×C414yescomplemented
76C22×Q8×C103C2311yescharacteristic
77C22×D4×C103—21no—
78C22×D4×C103—21no—
79C22×D4×C103—21no—
80C22×D4×C103—21no—
81C22×D4×C103—21no—
82C22×D4×C103—21no—
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×M16×C103—22no—
92C2×M16×C103—22no—
93C2×M16×C103—41no—
94C22×C8×C103—22no—
95C22×C8×C103—22no—
96C22×C8×C103—41no—
97C22×C8×C103C2311yescharacteristic
98C22×C8×C103C2311yescharacteristic
99C22×C8×C103C2311yescharacteristic
100C22×C8×C103C2311yescharacteristic
101#127×C103—28no—
102#127×C103—22no—
103#127×C103C2×C414yescomplemented
104#121×C103—22no—
105#121×C103—22no—
106#121×C103—28no—
107#121×C103—28no—
108#121×C103C2×C414yes—
109#121×C103C2×C414yescomplemented
110C4×Q8×C103—22no—
111C4×Q8×C103C2×C414yescomplemented
112C4×D4×C103—28no—
113C4×D4×C103C2×C414yes—
114C4×D4×C103D414yes—
115#117×C103—22no—
116#117×C103—41no—
117C2×C4⋊C4×C103—21no—
118C2×C4⋊C4×C103—22no—
119C2×C4⋊C4×C103—21no—
120C2×C4⋊C4×C103—41no—
121C2×C4⋊C4×C103D411yescharacteristic
122C2×C4⋊C4×C103C2311yescharacteristic
123C2×C4⋊C4×C103C2311yescharacteristic
124C2×C4⋊C4×C103C2311yescharacteristic
125C2×C4⋊C4×C103C2311yescharacteristic
126C2×C4⋊C4×C103C2311yescharacteristic
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×C103—21no—
136C2×C42×C103—21no—
137C2×C42×C103C2311yescharacteristic
138C4⋊C8×C103—22no—
139#103×C103—22no—
140#103×C103—22no—
141#103×C103—22no—
142#103×C103D414yescomplemented
143#102×C103—22no—
144#102×C103—22no—
145#102×C103—22no—
146#102×C103—22no—
147#102×C103—41no—
148#102×C103—41no—
149#102×C103—41no—
150#102×C103—41no—
151C22⋊C8×C103—22no—
152C22⋊C8×C103—22no—
153#97×C103—22no—
154#95×C103—21no—
155#95×C103—21no—
156#95×C103—21no—
157#95×C103—21no—
158#95×C103—21no—
159C24×C103—21no—
160C24×C103—21no—
161C24×C103C2×D411yescharacteristic
162C24×C103C2×D411yescharacteristic
163#41×C103—28no—
164#41×C103—28no—
165#41×C103—44no—
166#41×C103—44no—
167#41×C103—44no—
168#41×C103—44no—
169#41×C103—44no—
170#41×C103—44no—
171C2×Q8×C103—21no—
172C2×Q8×C103—21no—
173C2×Q8×C103—21no—
174C2×Q8×C103C22×C412yes—
175C2×Q8×C103C2×D412yes—
176C2×Q8×C103#4112yes—
177C2×D4×C103—24no—
178C2×D4×C103—24no—
179C2×D4×C103—24no—
180C2×D4×C103—24no—
181C2×D4×C103—24no—
182C2×D4×C103—24no—
183C2×D4×C103—21no—
184C2×D4×C103—21no—
185C2×D4×C103—21no—
186C2×D4×C103—21no—
187C2×D4×C103—21no—
188C2×D4×C103—21no—
189C2×D4×C103—21no—
190C2×D4×C103—21no—
191C2×D4×C103—21no—
192C2×D4×C103—21no—
193C2×D4×C103—41no—
194C2×D4×C103—41no—
195C2×D4×C103—42no—
196C2×D4×C103—42no—
197C2×D4×C103—42no—
198C2×D4×C103—42no—
199C2×D4×C103—42no—
200C2×D4×C103—42no—
201C2×D4×C103—81no—
202C2×D4×C103—81no—
203C2×D4×C103—81no—
204C2×D4×C103—81no—
205C2×D4×C103—81no—
206C2×D4×C103—81no—
207C2×D4×C103C22⋊C414yes—
208C2×D4×C103C22×C412yes—
209C2×D4×C103C22×C412yes—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—21no—
213C22×C4×C103—21no—
214C22×C4×C103—21no—
215C22×C4×C103—21no—
216C22×C4×C103—21no—
217C22×C4×C103—21no—
218C22×C4×C103—21no—
219C22×C4×C103—21no—
220C22×C4×C103—21no—
221C22×C4×C103—24no—
222C22×C4×C103—24no—
223C22×C4×C103—21no—
224C22×C4×C103—21no—
225C22×C4×C103—21no—
226C22×C4×C103—42no—
227C22×C4×C103—42no—
228C22×C4×C103—42no—
229C22×C4×C103—42no—
230C22×C4×C103—42no—
231C22×C4×C103—42no—
232C22×C4×C103—81no—
233C22×C4×C103C22×C412yes—
234C22×C4×C103C22×C412yes—
235C22×C4×C103C2×D411yescharacteristic
236C22×C4×C103C2×D411yescharacteristic
237C22×C4×C103C2×D411yescharacteristic
238C22×C4×C103C2×D411yescharacteristic
239C22×C4×C103C2×D412yes—
240C22×C4×C103C2×D412yes—
241C22×C4×C103C2411yescharacteristic
242M16×C103—44no—
243C2×C8×C103—21no—
244C2×C8×C103—21no—
245C2×C8×C103—21no—
246C2×C8×C103—21no—
247C2×C8×C103—21no—
248C2×C8×C103—21no—
249C2×C8×C103—21no—
250C2×C8×C103—21no—
251C2×C8×C103—21no—
252C2×C8×C103—21no—
253C2×C8×C103—21no—
254C2×C8×C103—44no—
255C2×C8×C103C2×D412yes—
256C4⋊C4×C103—24no—
257C4⋊C4×C103—21no—
258C4⋊C4×C103—21no—
259C4⋊C4×C103—21no—
260C4⋊C4×C103—21no—
261C4⋊C4×C103—21no—
262C4⋊C4×C103—21no—
263C4⋊C4×C103—21no—
264C4⋊C4×C103—21no—
265C4⋊C4×C103—42no—
266C4⋊C4×C103C22⋊C414yes—
267C4⋊C4×C103C22×C412yes—
268C4⋊C4×C103C2×D412yes—
269C22⋊C4×C103—24no—
270C22⋊C4×C103—24no—
271C22⋊C4×C103—42no—
272C22⋊C4×C103—42no—
273C22⋊C4×C103—81no—
274C22⋊C4×C103C22⋊C414yes—
275C22⋊C4×C103C22⋊C414yes—
276C42×C103—24no—
277C42×C103—42no—
278C42×C103—81no—
279C42×C103C22×C412yes—
280C42×C103C2×D412yes—
281C23×C103—21no—
282C23×C103—21no—
283C23×C103—21no—
284C23×C103—21no—
285C23×C103—21no—
286C23×C103—21no—
287C23×C103—21no—
288C23×C103—21no—
289C23×C103—21no—
290C23×C103—21no—
291C23×C103—21no—
292C23×C103—21no—
293C23×C103—22no—
294C23×C103—22no—
295C23×C103—41no—
296C23×C103—41no—
297C23×C103—41no—
298C23×C103—41no—
299C23×C103—41no—
300C23×C103—41no—
301C23×C103—41no—
302C23×C103—41no—
303C23×C103—41no—
304C23×C103—41no—
305C23×C103—41no—
306C23×C103—41no—
307C23×C103C2×C22⋊C412yes—
308C23×C103C2×C22⋊C412yes—
309C23×C103C22×D411yescharacteristic
310Q8×C103—22no—
311Q8×C103—22no—
312Q8×C103—22no—
313Q8×C103C4×D414yes—
314D4×C103—22no—
315D4×C103—22no—
316D4×C103—22no—
317D4×C103—22no—
318D4×C103—44no—
319D4×C103—48no—
320D4×C103—48no—
321D4×C103—48no—
322D4×C103—41no—
323D4×C103—41no—
324D4×C103—41no—
325D4×C103—41no—
326D4×C103—84no—
327D4×C103—84no—
328D4×C103—84no—
329C2×C4×C103—22no—
330C2×C4×C103—21no—
331C2×C4×C103—21no—
332C2×C4×C103—22no—
333C2×C4×C103—21no—
334C2×C4×C103—21no—
335C2×C4×C103—22no—
336C2×C4×C103—21no—
337C2×C4×C103—21no—
338C2×C4×C103—21no—
339C2×C4×C103—21no—
340C2×C4×C103—22no—
341C2×C4×C103—22no—
342C2×C4×C103—22no—
343C2×C4×C103—22no—
344C2×C4×C103—22no—
345C2×C4×C103—22no—
346C2×C4×C103—22no—
347C2×C4×C103—22no—
348C2×C4×C103—22no—
349C2×C4×C103—22no—
350C2×C4×C103—48no—
351C2×C4×C103—48no—
352C2×C4×C103—41no—
353C2×C4×C103—41no—
354C2×C4×C103—41no—
355C2×C4×C103—41no—
356C2×C4×C103—41no—
357C2×C4×C103—41no—
358C2×C4×C103—41no—
359C2×C4×C103—41no—
360C2×C4×C103—41no—
361C2×C4×C103—41no—
362C2×C4×C103—41no—
363C2×C4×C103—41no—
364C2×C4×C103—41no—
365C2×C4×C103—84no—
366C2×C4×C103C2×C22⋊C412yes—
367C2×C4×C103C2×C22⋊C412yes—
368C2×C4×C103C2×C22⋊C412yes—
369C2×C4×C103C2×C22⋊C412yes—
370C2×C4×C103C23×C411yescharacteristic
371C2×C4×C103C22×D411yescharacteristic
372C2×C4×C103C22×D411yescharacteristic
373C2×C4×C103C2×#4111yescharacteristic
374C2×C4×C103H(5,𝔽2)11yescharacteristic
375C2×C4×C103H(5,𝔽2)11yescharacteristic
376C8×C103—22no—
377C8×C103—41no—
378C8×C103—41no—
379C8×C103—41no—
380C22×C103—22no—
381C22×C103—22no—
382C22×C103—22no—
383C22×C103—22no—
384C22×C103—22no—
385C22×C103—22no—
386C22×C103—41no—
387C22×C103—41no—
388C22×C103—41no—
389C22×C103—41no—
390C22×C103—41no—
391C22×C103—41no—
392C22×C103—41no—
393C22×C103—41no—
394C22×C103—42no—
395C22×C103—42no—
396C22×C103—42no—
397C22×C103—42no—
398C22×C103—42no—
399C22×C103—42no—
400C22×C103—81no—
401C22×C103—81no—
402C22×C103—81no—
403C22×C103—81no—
404C22×C103—81no—
405C22×C103—81no—
406C22×C103—81no—
407C22×C103—81no—
408C22×C103C22×C22⋊C411yescharacteristic
409C22×C103D4211yescharacteristic
410C22×C103#54611yescharacteristic
411C22×C103#57511yescharacteristic
412C22×C103#57511yescharacteristic
413C22×C103#57611yescharacteristic
414C22×C103#57711yescharacteristic
415C4×C103—22no—
416C4×C103—22no—
417C4×C103—24no—
418C4×C103—22no—
419C4×C103—22no—
420C4×C103—42no—
421C4×C103—42no—
422C4×C103—81no—
423C4×C103—81no—
424C4×C103—81no—
425C4×C103C2×C4×D411yescharacteristic
426C4×C103#51811yescharacteristic
427C4×C103D4211yescharacteristic
428C4×C103#54611yescharacteristic
429#22422C10311yesmaximal, characteristic, direct product factor, Sylow
430C2×C103—42no—
431C2×C103—42no—
432C2×C103—82no—
433C2×C103—82no—
434C2×C103D4×C22⋊C411yescharacteristic
435C2×C103#289611yescharacteristic
436C2×C103#289711yescharacteristic
437C2×C103#326811yescharacteristic
438C2×C103#327111yescharacteristic
439C2×C103#330911yescharacteristic
440C2×C103#331711yescharacteristic
441C2×#550C2×C10311yescharacteristic
442C2×#435C2×C10311yescharacteristic, complemented
443C2×#417C2×C10311yescharacteristic, complemented
444C2×#416C2×C10311yescharacteristic, complemented
445#2352C2×C10311yescharacteristic, complemented
446#1982C2×C10311yescharacteristic, complemented
447#1961C2×C10311yescharacteristic, complemented
448#1895C2×C10311yescharacteristic, complemented
449#1893C2×C10311yescharacteristic, complemented
450#1875C2×C10311yescharacteristic, complemented
451#1874C2×C10311yescharacteristic, complemented
452#1805C2×C10311yescharacteristic, complemented
453#1788C2×C10311yescharacteristic, complemented
454#1788C2×C10311yescharacteristic, complemented
455#1763C2×C10311yescharacteristic, complemented
456C103#2242211yescharacteristic, direct product factor, Sylow
457C22×#41C22×C10311yescharacteristic
458C22×#41C22×C10311yescharacteristic
459C22×M16C22×C10311yescharacteristic
460C23×C8C22×C10311yescharacteristic
461#550—24no—
462#550C4×C10318yescomplemented
463C2×#127—21no—
464C2×#127C22×C10311yescharacteristic
465C2×#121—21no—
466C2×#121—21no—
467C2×#121C22×C10311yescharacteristic
468C2×#121C22×C10311yescharacteristic
469C2×C4×Q8C22×C10311yescharacteristic
470C2×C4×D4—21no—
471C2×C4×D4C22×C10311yescharacteristic
472C2×#117C22×C10311yescharacteristic
473C22×C4⋊C4C22×C10311yescharacteristic
474#435—24no—
475C2×C4⋊C8C22×C10311yescharacteristic
476#417—24no—
477#416—24no—
478C2×#103C22×C10311yescharacteristic
479C2×#103C22×C10311yescharacteristic
480C2×#103C22×C10311yescharacteristic
481C2×#103C22×C10311yescharacteristic
482C2×#102C22×C10311yescharacteristic
483C2×#102C22×C10311yescharacteristic
484C2×#102C22×C10311yescharacteristic
485C2×#102C22×C10311yescharacteristic
486C2×#102C22×C10311yescharacteristic
487C2×#102C22×C10311yescharacteristic
488C2×#102C22×C10311yescharacteristic
489C2×#102C22×C10311yescharacteristic
490C2×C22⋊C8C22×C10311yescharacteristic
491C2×C22⋊C8C22×C10311yescharacteristic
492C2×#97C22×C10311yescharacteristic
493#388—21no—
494#387—21no—
495#386—21no—
496#382C22×C10311yescharacteristic
497#380C22×C10311yescharacteristic
498#380C22×C10311yescharacteristic
499C4×C4⋊C4C22×C10311yescharacteristic
500C4×C22⋊C4—21no—
501#340C22×C10311yescharacteristic
502#340C22×C10311yescharacteristic
503#340C22×C10311yescharacteristic
504#340C22×C10311yescharacteristic
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C10314yes—
516C2×#41C2×C4×C10314yescomplemented
517C22×Q8C23×C10311yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4D4×C10311yescharacteristic
525C22×D4C23×C10311yescharacteristic
526C22×D4C23×C10311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C23×C10311yescharacteristic
531C23×C4C23×C10311yescharacteristic
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8C23×C10311yescharacteristic
539C22×C8C23×C10311yescharacteristic
540C22×C8C23×C10311yescharacteristic
541C22×C8C23×C10311yescharacteristic
542#127—28no—
543#127—22no—
544#127C2×C4×C10314yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×C4×C10314yes—
550#121C2×C4×C10314yescomplemented
551C4×Q8—22no—
552C4×Q8C2×C4×C10314yescomplemented
553C4×D4—28no—
554C4×D4C2×C4×C10314yes—
555C4×D4D4×C10314yes—
556#117—22no—
557#117—41no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4D4×C10311yescharacteristic
563C2×C4⋊C4C23×C10311yescharacteristic
564C2×C4⋊C4C23×C10311yescharacteristic
565C2×C4⋊C4C23×C10311yescharacteristic
566C2×C4⋊C4C23×C10311yescharacteristic
567C2×C4⋊C4C23×C10311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4D4×C10311yescharacteristic
574C2×C22⋊C4D4×C10311yescharacteristic
575C2×C42—21no—
576C2×C42—21no—
577C2×C42—21no—
578C2×C42C23×C10311yescharacteristic
579C4⋊C8—22no—
580#103—22no—
581#103—22no—
582#103—22no—
583#103D4×C10314yescomplemented
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590#102—41no—
591#102—41no—
592C22⋊C8—22no—
593C22⋊C8—22no—
594#97—22no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600C24—21no—
601C24—21no—
602C24C2×D4×C10311yescharacteristic
603C24C2×D4×C10311yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8C22×C4×C10312yes—
616C2×Q8C2×D4×C10312yes—
617C2×Q8#41×C10312yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C10314yes—
649C2×D4C22×C4×C10312yes—
650C2×D4C22×C4×C10312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4C22×C4×C10312yes—
675C22×C4C22×C4×C10312yes—
676C22×C4C2×D4×C10311yescharacteristic
677C22×C4C2×D4×C10311yescharacteristic
678C22×C4C2×D4×C10311yescharacteristic
679C22×C4C2×D4×C10311yescharacteristic
680C22×C4C2×D4×C10312yes—
681C22×C4C2×D4×C10312yes—
682C22×C4C24×C10311yescharacteristic
683M16—44no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—44no—
696C2×C8C2×D4×C10312yes—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—42no—
707C4⋊C4C22⋊C4×C10314yes—
708C4⋊C4C22×C4×C10312yes—
709C4⋊C4C2×D4×C10312yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4C22⋊C4×C10314yes—
716C22⋊C4C22⋊C4×C10314yes—
717C42—24no—
718C42—42no—
719C42—81no—
720C42C22×C4×C10312yes—
721C42C2×D4×C10312yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊C4×C10312yes—
749C23C2×C22⋊C4×C10312yes—
750C23C22×D4×C10311yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8C4×D4×C10314yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—48no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—84no—
807C2×C4C2×C22⋊C4×C10312yes—
808C2×C4C2×C22⋊C4×C10312yes—
809C2×C4C2×C22⋊C4×C10312yes—
810C2×C4C2×C22⋊C4×C10312yes—
811C2×C4C23×C4×C10311yescharacteristic
812C2×C4C22×D4×C10311yescharacteristic
813C2×C4C22×D4×C10311yescharacteristic
814C2×C4C2×#41×C10311yescharacteristic
815C2×C4H(5,𝔽2)×C10311yescharacteristic
816C2×C4H(5,𝔽2)×C10311yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊C4×C10311yescharacteristic
850C22D42×C10311yescharacteristic
851C22#546×C10311yescharacteristic
852C22#575×C10311yescharacteristic
853C22#575×C10311yescharacteristic
854C22#576×C10311yescharacteristic
855C22#577×C10311yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4C2×C4×D4×C10311yescharacteristic
867C4#518×C10311yescharacteristic
868C4D42×C10311yescharacteristic
869C4#546×C10311yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊C4×C10311yescharacteristic
875C2C103×#289611yescharacteristic
876C2C103×#289711yescharacteristic
877C2C103×#326811yescharacteristic
878C2C103×#327111yescharacteristic
879C2C103×#330911yescharacteristic
880C2C103×#331711yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC2×#550×C103C2
LCSG ▷ C2×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×#435×C103C2semidirect
3. C2×#417×C103C2semidirect
4. C2×#416×C103C2semidirect
5. C103×#2352C2semidirect
6. C103×#1982C2semidirect
7. C103×#1961C2semidirect
8. C103×#1895C2semidirect
9. C103×#1893C2semidirect
10. C103×#1875C2semidirect
11. C103×#1874C2semidirect
12. C103×#1805C2semidirect
13. C103×#1788C2semidirect
14. C103×#1788C2semidirect
15. C103×#1763C2semidirect
21. #550×C103C4semidirect
75. C2×#41×C103C2×C4semidirect
103. #127×C103C2×C4semidirect
109. #121×C103C2×C4semidirect
111. C4×Q8×C103C2×C4semidirect
142. #103×C103D4semidirect
429. #22422C103direct (N × H)
442. C2×#435C2×C103semidirect
443. C2×#417C2×C103semidirect
444. C2×#416C2×C103semidirect
445. #2352C2×C103semidirect
446. #1982C2×C103semidirect
447. #1961C2×C103semidirect
448. #1895C2×C103semidirect
449. #1893C2×C103semidirect
450. #1875C2×C103semidirect
451. #1874C2×C103semidirect
452. #1805C2×C103semidirect
453. #1788C2×C103semidirect
454. #1788C2×C103semidirect
455. #1763C2×C103semidirect
456. C103#22422direct (N × H)
462. #550C4×C103semidirect
516. C2×#41C2×C4×C103semidirect
544. #127C2×C4×C103semidirect
550. #121C2×C4×C103semidirect
552. C4×Q8C2×C4×C103semidirect
583. #103D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1032
C2×#435×C1032
C2×#417×C1032
C2×#416×C1032
C103×#23522
C103×#19822
C103×#19612
C103×#18952
C103×#18932
C103×#18752
C103×#18742
C103×#18052
C103×#17882
C103×#17632
#22422103