Finite Group Databasebeta

← C103×#23853 #39929128

Subgroups — C103×#23853 #39929128

Order 26368.

1800 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C103C211yesmaximal, characteristic, complemented
2C2×#547×C103C211yesmaximal, characteristic, complemented
3C2×#452×C103C211yesmaximal, characteristic, complemented
4C2×#452×C103C211yesmaximal, characteristic, complemented
5C2×#449×C103C211yesmaximal, characteristic, complemented
6C103×#2407C211yesmaximal, characteristic, complemented
7C103×#2016C211yesmaximal, characteristic, complemented
8C103×#2013C211yesmaximal, characteristic, complemented
9C103×#2001C211yesmaximal, characteristic, complemented
10C103×#2000C211yesmaximal, characteristic, complemented
11C103×#1892C211yesmaximal, characteristic, complemented
12C103×#1879C211yesmaximal, characteristic, complemented
13C103×#1877C211yesmaximal, characteristic, complemented
14C103×#1869C211yesmaximal, characteristic, complemented
15C103×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic
18C22×#41×C103C2211yescharacteristic
19C2×#135×C103—24no—
20C2×#135×C103—24no—
21C2×#135×C103—24no—
22C22×Q16×C103C2211yescharacteristic
23C22×Q16×C103C2211yescharacteristic
24C22×SD16×C103C2211yescharacteristic
25C22×SD16×C103C2211yescharacteristic
26C22×SD16×C103C2211yescharacteristic
27C22×D8×C103C2211yescharacteristic
28C23×C8×C103C2211yescharacteristic
29#547×C103—24no—
30#547×C103—24no—
31C2×C4⋊Q8×C103C2211yescharacteristic
32C2×#123×C103—21no—
33C2×#123×C103—21no—
34C2×C22⋊Q8×C103C2211yescharacteristic
35C2×C22⋊Q8×C103C2211yescharacteristic
36C2×C22⋊Q8×C103C2211yescharacteristic
37C2×#121×C103—21no—
38C2×#121×C103C2211yescharacteristic
39C2×C4×D4×C103C2211yescharacteristic
40C2×C4×D4×C103C2211yescharacteristic
41C22×C4⋊C4×C103—21no—
42#452×C103—24no—
43#452×C103—24no—
44#449×C103—24no—
45C2×#103×C103C2211yescharacteristic
46C2×#103×C103C2211yescharacteristic
47C2×#103×C103C2211yescharacteristic
48C2×#103×C103C2211yescharacteristic
49C2×#103×C103C2211yescharacteristic
50C2×#102×C103C2211yescharacteristic
51C2×#102×C103C2211yescharacteristic
52C2×#102×C103C2211yescharacteristic
53C2×C22⋊C8×C103C2211yescharacteristic
54C2×C22⋊C8×C103C2211yescharacteristic
55C2×C22⋊C8×C103C2211yescharacteristic
56#394×C103—21no—
57#392×C103—21no—
58#391×C103C2211yescharacteristic
59#390×C103C2211yescharacteristic
60#386×C103—21no—
61#385×C103—21no—
62#380×C103C2211yescharacteristic
63#340×C103C2211yescharacteristic
64#340×C103C2211yescharacteristic
65#336×C103C2211yescharacteristic
66#336×C103C2211yescharacteristic
67C2×#41×C103—22no—
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—22no—
76C2×#41×C103—22no—
77C2×#41×C103—22no—
78C2×#41×C103—41no—
79C2×#41×C103—41no—
80C2×#41×C103—41no—
81C2×#41×C103—41no—
82C2×#41×C103—41no—
83C2×#41×C103—41no—
84C2×#41×C103D414yescomplemented
85C22×Q8×C103C2311yescharacteristic
86C22×Q8×C103C2311yescharacteristic
87C22×Q8×C103C2311yescharacteristic
88C22×D4×C103—21no—
89C22×D4×C103—21no—
90C22×D4×C103—21no—
91C22×D4×C103—21no—
92C22×D4×C103D411yescharacteristic
93C22×D4×C103C2311yescharacteristic
94C22×D4×C103C2311yescharacteristic
95C23×C4×C103—21no—
96C23×C4×C103—21no—
97C23×C4×C103—21no—
98C23×C4×C103—21no—
99C23×C4×C103C2311yescharacteristic
100C23×C4×C103C2311yescharacteristic
101#135×C103—232no—
102C2×Q16×C103—22no—
103C2×Q16×C103—22no—
104C2×Q16×C103—22no—
105C2×Q16×C103—22no—
106C2×Q16×C103—22no—
107C2×Q16×C103—41no—
108C2×SD16×C103—22no—
109C2×SD16×C103—22no—
110C2×SD16×C103—22no—
111C2×SD16×C103—22no—
112C2×SD16×C103—22no—
113C2×SD16×C103—22no—
114C2×SD16×C103—22no—
115C2×SD16×C103—41no—
116C2×SD16×C103D414yescomplemented
117C2×D8×C103—22no—
118C2×D8×C103—22no—
119C2×D8×C103D414yescomplemented
120C22×C8×C103—22no—
121C22×C8×C103—22no—
122C22×C8×C103—22no—
123C22×C8×C103C2311yescharacteristic
124C22×C8×C103C2311yescharacteristic
125C22×C8×C103C2311yescharacteristic
126C22×C8×C103C2311yescharacteristic
127C4⋊Q8×C103—22no—
128C4⋊Q8×C103—22no—
129#123×C103—28no—
130#123×C103—28no—
131C22⋊Q8×C103—22no—
132C22⋊Q8×C103—22no—
133C22⋊Q8×C103—22no—
134C22⋊Q8×C103—22no—
135C22⋊Q8×C103—41no—
136C22⋊Q8×C103D414yescomplemented
137#121×C103—28no—
138#121×C103—22no—
139#121×C103—41no—
140C4×D4×C103—22no—
141C4×D4×C103—22no—
142C4×D4×C103—22no—
143C4×D4×C103—22no—
144C2×C4⋊C4×C103—28no—
145C2×C4⋊C4×C103—21no—
146C2×C4⋊C4×C103—21no—
147C2×C4⋊C4×C103—21no—
148C2×C4⋊C4×C103—21no—
149C2×C4⋊C4×C103—21no—
150C2×C4⋊C4×C103D411yescharacteristic
151C2×C4⋊C4×C103C2311yescharacteristic
152C2×C4⋊C4×C103C2311yescharacteristic
153C2×C4⋊C4×C103C2311yescharacteristic
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—22no—
167#103×C103—22no—
168#103×C103—41no—
169#103×C103—41no—
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—21no—
181C24×C103C2×D411yescharacteristic
182C24×C103C2×D411yescharacteristic
183#41×C103—28no—
184#41×C103—28no—
185#41×C103—44no—
186#41×C103—44no—
187#41×C103—44no—
188#41×C103—44no—
189#41×C103—44no—
190#41×C103—44no—
191#41×C103—44no—
192#41×C103—44no—
193#41×C103—44no—
194#41×C103—44no—
195C2×Q8×C103—21no—
196C2×Q8×C103—21no—
197C2×Q8×C103—21no—
198C2×Q8×C103—21no—
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×C103—21no—
210C2×Q8×C103C2×D412yes—
211C2×Q8×C103C2×D412yes—
212C2×Q8×C103C2×D412yes—
213C2×D4×C103—24no—
214C2×D4×C103—22no—
215C2×D4×C103—24no—
216C2×D4×C103—22no—
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—41no—
226C2×D4×C103—42no—
227C2×D4×C103—42no—
228C2×D4×C103—42no—
229C2×D4×C103—42no—
230C2×D4×C103—42no—
231C2×D4×C103—42no—
232C2×D4×C103—42no—
233C2×D4×C103—42no—
234C2×D4×C103—42no—
235C2×D4×C103—81no—
236C2×D4×C103C2×D412yes—
237C2×D4×C103C2×D412yes—
238C2×D4×C103C2×D412yes—
239C2×D4×C103C2×D412yes—
240C22×C4×C103—21no—
241C22×C4×C103—21no—
242C22×C4×C103—21no—
243C22×C4×C103—21no—
244C22×C4×C103—24no—
245C22×C4×C103—24no—
246C22×C4×C103—21no—
247C22×C4×C103—21no—
248C22×C4×C103—21no—
249C22×C4×C103—21no—
250C22×C4×C103—24no—
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—21no—
259C22×C4×C103—42no—
260C22×C4×C103—42no—
261C22×C4×C103—42no—
262C22×C4×C103—42no—
263C22×C4×C103—42no—
264C22×C4×C103—42no—
265C22×C4×C103—42no—
266C22×C4×C103—42no—
267C22×C4×C103—42no—
268C22×C4×C103C2×D411yescharacteristic
269C22×C4×C103C2×D411yescharacteristic
270C22×C4×C103C2×D411yescharacteristic
271C22×C4×C103C2×D412yes—
272C22×C4×C103C2×D412yes—
273C22×C4×C103C2×D411yescharacteristic
274C22×C4×C103C2411yescharacteristic
275Q16×C103—28no—
276Q16×C103—44no—
277SD16×C103—28no—
278SD16×C103—28no—
279SD16×C103—44no—
280D8×C103—28no—
281C2×C8×C103—28no—
282C2×C8×C103—21no—
283C2×C8×C103—21no—
284C2×C8×C103—21no—
285C2×C8×C103—21no—
286C2×C8×C103—21no—
287C2×C8×C103—21no—
288C2×C8×C103—21no—
289C2×C8×C103—21no—
290C2×C8×C103—21no—
291C2×C8×C103—21no—
292C2×C8×C103C2×D412yes—
293C2×C8×C103C2×D412yes—
294C4⋊C4×C103—24no—
295C4⋊C4×C103—24no—
296C4⋊C4×C103—24no—
297C4⋊C4×C103—22no—
298C4⋊C4×C103—24no—
299C4⋊C4×C103—21no—
300C4⋊C4×C103—21no—
301C4⋊C4×C103—21no—
302C4⋊C4×C103—21no—
303C4⋊C4×C103—21no—
304C4⋊C4×C103—42no—
305C4⋊C4×C103C2×D412yes—
306C22⋊C4×C103—24no—
307C22⋊C4×C103—24no—
308C22⋊C4×C103—24no—
309C22⋊C4×C103—22no—
310C22⋊C4×C103—22no—
311C22⋊C4×C103—42no—
312C22⋊C4×C103—42no—
313C22⋊C4×C103—42no—
314C22⋊C4×C103—81no—
315C22⋊C4×C103—81no—
316C42×C103—21no—
317C42×C103—21no—
318C23×C103—22no—
319C23×C103—21no—
320C23×C103—21no—
321C23×C103—22no—
322C23×C103—22no—
323C23×C103—21no—
324C23×C103—21no—
325C23×C103—21no—
326C23×C103—21no—
327C23×C103—21no—
328C23×C103—21no—
329C23×C103—22no—
330C23×C103—21no—
331C23×C103—21no—
332C23×C103—21no—
333C23×C103—21no—
334C23×C103—21no—
335C23×C103—41no—
336C23×C103—41no—
337C23×C103—41no—
338C23×C103—41no—
339C23×C103—41no—
340C23×C103—41no—
341C23×C103—41no—
342C23×C103—41no—
343C23×C103—41no—
344C23×C103—41no—
345C23×C103#12012yes—
346C23×C103C22×D411yescharacteristic
347Q8×C103—22no—
348Q8×C103—22no—
349Q8×C103—22no—
350Q8×C103—22no—
351Q8×C103—22no—
352Q8×C103—22no—
353Q8×C103—41no—
354Q8×C103—41no—
355Q8×C103—41no—
356Q8×C103—41no—
357Q8×C103—41no—
358Q8×C103—41no—
359D4×C103—22no—
360D4×C103—22no—
361D4×C103—22no—
362D4×C103—22no—
363D4×C103—22no—
364D4×C103—44no—
365D4×C103—48no—
366D4×C103—48no—
367D4×C103—48no—
368D4×C103—41no—
369D4×C103—41no—
370D4×C103—84no—
371D4×C103#12014yes—
372C2×C4×C103—21no—
373C2×C4×C103—21no—
374C2×C4×C103—21no—
375C2×C4×C103—21no—
376C2×C4×C103—22no—
377C2×C4×C103—22no—
378C2×C4×C103—22no—
379C2×C4×C103—22no—
380C2×C4×C103—21no—
381C2×C4×C103—22no—
382C2×C4×C103—21no—
383C2×C4×C103—22no—
384C2×C4×C103—22no—
385C2×C4×C103—21no—
386C2×C4×C103—22no—
387C2×C4×C103—21no—
388C2×C4×C103—21no—
389C2×C4×C103—21no—
390C2×C4×C103—48no—
391C2×C4×C103—48no—
392C2×C4×C103—48no—
393C2×C4×C103—48no—
394C2×C4×C103—41no—
395C2×C4×C103—41no—
396C2×C4×C103—41no—
397C2×C4×C103—41no—
398C2×C4×C103—41no—
399C2×C4×C103—41no—
400C2×C4×C103—41no—
401C2×C4×C103—41no—
402C2×C4×C103—41no—
403C2×C4×C103—41no—
404C2×C4×C103—41no—
405C2×C4×C103—41no—
406C2×C4×C103—41no—
407C2×C4×C103—41no—
408C2×C4×C103—41no—
409C2×C4×C103—41no—
410C2×C4×C103—41no—
411C2×C4×C103—41no—
412C2×C4×C103#12012yes—
413C2×C4×C103#13512yescomplemented
414C2×C4×C103C22×D411yescharacteristic
415C2×C4×C103C22×D411yescharacteristic
416C2×C4×C103C22×D411yescharacteristic
417C2×C4×C103C22×D411yescharacteristic
418C2×C4×C103H(5,𝔽2)11yescharacteristic
419C2×C4×C103H(5,𝔽2)11yescharacteristic
420C8×C103—22no—
421C8×C103—22no—
422C8×C103—41no—
423C8×C103—41no—
424C22×C103—22no—
425C22×C103—24no—
426C22×C103—22no—
427C22×C103—22no—
428C22×C103—42no—
429C22×C103—41no—
430C22×C103—42no—
431C22×C103—42no—
432C22×C103—41no—
433C22×C103—42no—
434C22×C103—41no—
435C22×C103—42no—
436C22×C103—41no—
437C22×C103—42no—
438C22×C103—42no—
439C22×C103—41no—
440C22×C103—41no—
441C22×C103—41no—
442C22×C103—42no—
443C22×C103—41no—
444C22×C103—41no—
445C22×C103—41no—
446C22×C103—42no—
447C22×C103—41no—
448C22×C103—81no—
449C22×C103—81no—
450C22×C103—81no—
451C22×C103—81no—
452C22×C103C2×#12011yescharacteristic
453C22×C103D4211yescharacteristic
454C22×C103D4211yescharacteristic
455C22×C103C2×#13511yescharacteristic
456C22×C103#57511yescharacteristic
457C22×C103#57711yescharacteristic
458C22×C103#57811yescharacteristic
459C4×C103—22no—
460C4×C103—22no—
461C4×C103—41no—
462C4×C103—42no—
463C4×C103—42no—
464C4×C103—42no—
465C4×C103—42no—
466C4×C103—41no—
467C4×C103—81no—
468C4×C103—81no—
469C4×C103C2×#12011yescharacteristic
470C4×C103#53411yescharacteristic
471C4×C103D4211yescharacteristic
472C4×C103D4211yescharacteristic
473#23853C10311yesmaximal, characteristic, direct product factor, Sylow
474C2×C103—42no—
475C2×C103—44no—
476C2×C103—81no—
477C2×C103—82no—
478C2×C103#240311yescharacteristic
479C2×C103#300211yescharacteristic
480C2×C103#301311yescharacteristic
481C2×C103#326711yescharacteristic
482C2×C103#326911yescharacteristic
483C2×C103#328311yescharacteristic
484C2×C103#328411yescharacteristic
485C22×#135C2×C10311yescharacteristic, complemented
486C2×#547C2×C10311yescharacteristic, complemented
487C2×#452C2×C10311yescharacteristic, complemented
488C2×#452C2×C10311yescharacteristic, complemented
489C2×#449C2×C10311yescharacteristic, complemented
490#2407C2×C10311yescharacteristic, complemented
491#2016C2×C10311yescharacteristic, complemented
492#2013C2×C10311yescharacteristic, complemented
493#2001C2×C10311yescharacteristic, complemented
494#2000C2×C10311yescharacteristic, complemented
495#1892C2×C10311yescharacteristic, complemented
496#1879C2×C10311yescharacteristic, complemented
497#1877C2×C10311yescharacteristic, complemented
498#1869C2×C10311yescharacteristic, complemented
499#1788C2×C10311yescharacteristic, complemented
500C103#2385311yescharacteristic, direct product factor, Sylow
501C22×#41C22×C10311yescharacteristic
502C22×#41C22×C10311yescharacteristic
503C22×#41C22×C10311yescharacteristic
504C2×#135—24no—
505C2×#135—24no—
506C2×#135—24no—
507C22×Q16C22×C10311yescharacteristic
508C22×Q16C22×C10311yescharacteristic
509C22×SD16C22×C10311yescharacteristic
510C22×SD16C22×C10311yescharacteristic
511C22×SD16C22×C10311yescharacteristic
512C22×D8C22×C10311yescharacteristic
513C23×C8C22×C10311yescharacteristic
514#547—24no—
515#547—24no—
516C2×C4⋊Q8C22×C10311yescharacteristic
517C2×#123—21no—
518C2×#123—21no—
519C2×C22⋊Q8C22×C10311yescharacteristic
520C2×C22⋊Q8C22×C10311yescharacteristic
521C2×C22⋊Q8C22×C10311yescharacteristic
522C2×#121—21no—
523C2×#121C22×C10311yescharacteristic
524C2×C4×D4C22×C10311yescharacteristic
525C2×C4×D4C22×C10311yescharacteristic
526C22×C4⋊C4—21no—
527#452—24no—
528#452—24no—
529#449—24no—
530C2×#103C22×C10311yescharacteristic
531C2×#103C22×C10311yescharacteristic
532C2×#103C22×C10311yescharacteristic
533C2×#103C22×C10311yescharacteristic
534C2×#103C22×C10311yescharacteristic
535C2×#102C22×C10311yescharacteristic
536C2×#102C22×C10311yescharacteristic
537C2×#102C22×C10311yescharacteristic
538C2×C22⋊C8C22×C10311yescharacteristic
539C2×C22⋊C8C22×C10311yescharacteristic
540C2×C22⋊C8C22×C10311yescharacteristic
541#394—21no—
542#392—21no—
543#391C22×C10311yescharacteristic
544#390C22×C10311yescharacteristic
545#386—21no—
546#385—21no—
547#380C22×C10311yescharacteristic
548#340C22×C10311yescharacteristic
549#340C22×C10311yescharacteristic
550#336C22×C10311yescharacteristic
551#336C22×C10311yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—41no—
564C2×#41—41no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C10314yescomplemented
570C22×Q8C23×C10311yescharacteristic
571C22×Q8C23×C10311yescharacteristic
572C22×Q8C23×C10311yescharacteristic
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4D4×C10311yescharacteristic
578C22×D4C23×C10311yescharacteristic
579C22×D4C23×C10311yescharacteristic
580C23×C4—21no—
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C10311yescharacteristic
585C23×C4C23×C10311yescharacteristic
586#135—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—22no—
592C2×Q16—41no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C10314yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8D4×C10314yescomplemented
605C22×C8—22no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8C23×C10311yescharacteristic
609C22×C8C23×C10311yescharacteristic
610C22×C8C23×C10311yescharacteristic
611C22×C8C23×C10311yescharacteristic
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614#123—28no—
615#123—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—41no—
621C22⋊Q8D4×C10314yescomplemented
622#121—28no—
623#121—22no—
624#121—41no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4D4×C10311yescharacteristic
636C2×C4⋊C4C23×C10311yescharacteristic
637C2×C4⋊C4C23×C10311yescharacteristic
638C2×C4⋊C4C23×C10311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4D4×C10311yescharacteristic
648C2×C22⋊C4D4×C10311yescharacteristic
649C2×C42C23×C10311yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—41no—
654#103—41no—
655#102—22no—
656#102—22no—
657#102—22no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C10311yescharacteristic
667C24C2×D4×C10311yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676#41—44no—
677#41—44no—
678#41—44no—
679#41—44no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8C2×D4×C10312yes—
696C2×Q8C2×D4×C10312yes—
697C2×Q8C2×D4×C10312yes—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—24no—
701C2×D4—22no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—41no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—81no—
721C2×D4C2×D4×C10312yes—
722C2×D4C2×D4×C10312yes—
723C2×D4C2×D4×C10312yes—
724C2×D4C2×D4×C10312yes—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—24no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C10311yescharacteristic
754C22×C4C2×D4×C10311yescharacteristic
755C22×C4C2×D4×C10311yescharacteristic
756C22×C4C2×D4×C10312yes—
757C22×C4C2×D4×C10312yes—
758C22×C4C2×D4×C10311yescharacteristic
759C22×C4C24×C10311yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C10312yes—
778C2×C8C2×D4×C10312yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—22no—
783C4⋊C4—24no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—42no—
790C4⋊C4C2×D4×C10312yes—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—42no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C42—21no—
802C42—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—22no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23#120×C10312yes—
831C23C22×D4×C10311yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844D4—22no—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—44no—
850D4—48no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—84no—
856D4#120×C10314yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—48no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4#120×C10312yes—
898C2×C4#135×C10312yescomplemented
899C2×C4C22×D4×C10311yescharacteristic
900C2×C4C22×D4×C10311yescharacteristic
901C2×C4C22×D4×C10311yescharacteristic
902C2×C4C22×D4×C10311yescharacteristic
903C2×C4H(5,𝔽2)×C10311yescharacteristic
904C2×C4H(5,𝔽2)×C10311yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—24no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—41no—
922C22—42no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—42no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C10311yescharacteristic
938C22D42×C10311yescharacteristic
939C22D42×C10311yescharacteristic
940C22C2×#135×C10311yescharacteristic
941C22#575×C10311yescharacteristic
942C22#577×C10311yescharacteristic
943C22#578×C10311yescharacteristic
944C4—22no—
945C4—22no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4C2×#120×C10311yescharacteristic
955C4#534×C10311yescharacteristic
956C4D42×C10311yescharacteristic
957C4D42×C10311yescharacteristic
958C2—42no—
959C2—44no—
960C2—81no—
961C2—82no—
962C2C103×#240311yescharacteristic
963C2C103×#300211yescharacteristic
964C2C103×#301311yescharacteristic
965C2C103×#326711yescharacteristic
966C2C103×#326911yescharacteristic
967C2C103×#328311yescharacteristic
968C2C103×#328411yescharacteristic
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×#547×C103C2semidirect
3. C2×#452×C103C2semidirect
4. C2×#452×C103C2semidirect
5. C2×#449×C103C2semidirect
6. C103×#2407C2semidirect
7. C103×#2016C2semidirect
8. C103×#2013C2semidirect
9. C103×#2001C2semidirect
10. C103×#2000C2semidirect
11. C103×#1892C2semidirect
12. C103×#1879C2semidirect
13. C103×#1877C2semidirect
14. C103×#1869C2semidirect
15. C103×#1788C2semidirect
84. C2×#41×C103D4semidirect
116. C2×SD16×C103D4semidirect
119. C2×D8×C103D4semidirect
136. C22⋊Q8×C103D4semidirect
413. C2×C4×C103#135semidirect
473. #23853C103direct (N × H)
485. C22×#135C2×C103semidirect
486. C2×#547C2×C103semidirect
487. C2×#452C2×C103semidirect
488. C2×#452C2×C103semidirect
489. C2×#449C2×C103semidirect
490. #2407C2×C103semidirect
491. #2016C2×C103semidirect
492. #2013C2×C103semidirect
493. #2001C2×C103semidirect
494. #2000C2×C103semidirect
495. #1892C2×C103semidirect
496. #1879C2×C103semidirect
497. #1877C2×C103semidirect
498. #1869C2×C103semidirect
499. #1788C2×C103semidirect
500. C103#23853direct (N × H)
569. C2×#41D4×C103semidirect
601. C2×SD16D4×C103semidirect
604. C2×D8D4×C103semidirect
621. C22⋊Q8D4×C103semidirect
898. C2×C4#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×#547×C1032
C2×#452×C1032
C2×#449×C1032
C103×#24072
C103×#20162
C103×#20132
C103×#20012
C103×#20002
C103×#18922
C103×#18792
C103×#18772
C103×#18692
C103×#17882
#23853103