Finite Group Databasebeta

← C103×#24471 #39929746

Subgroups — C103×#24471 #39929746

Order 26368.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3488C211yesmaximal, characteristic
2C103×#3056C211yesmaximal, characteristic, complemented
3C2×#455×C103C211yesmaximal, characteristic, complemented
4C103×#3007C211yesmaximal, characteristic, complemented
5C2×#421×C103C211yesmaximal, characteristic, complemented
6C103×#2620C211yesmaximal, characteristic, complemented
7C103×#2039C211yesmaximal, characteristic, complemented
8C103×#2037C211yesmaximal, characteristic, complemented
9C103×#2007C211yesmaximal, characteristic, complemented
10C103×#2004C211yesmaximal, characteristic, complemented
11C103×#1900C211yesmaximal, characteristic, complemented
12C103×#1897C211yesmaximal, characteristic, complemented
13C103×#1882C211yesmaximal, characteristic, complemented
14C103×#1859C211yesmaximal, characteristic, complemented
15C103×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic
18C2×#137×C103C2211yescharacteristic
19C2×#137×C103C2211yescharacteristic, complemented
20C2×#137×C103C2211yescharacteristic, complemented
21C22×M16×C103C2211yescharacteristic, complemented
22#550×C103—21no—
23#548×C103—21no—
24#546×C103—21no—
25#546×C103—22no—
26D42×C103—22no—
27D42×C103—21no—
28#537×C103—21no—
29#537×C103C2211yescharacteristic
30#535×C103—21no—
31#535×C103C2211yescharacteristic
32C2×#124×C103C2211yescharacteristic, complemented
33#525×C103—21no—
34#525×C103C2211yescharacteristic
35C2×C22⋊Q8×C103C2211yescharacteristic, complemented
36C2×#121×C103—21no—
37C2×#121×C103C2211yescharacteristic
38#520×C103C2211yescharacteristic
39C2×#117×C103C2211yescharacteristic, complemented
40#470×C103—21no—
41#468×C103—21no—
42#467×C103—21no—
43#465×C103—21no—
44#455×C103—24no—
45#452×C103—21no—
46#452×C103—21no—
47#451×C103—21no—
48#450×C103—21no—
49#428×C103C2211yescharacteristic, complemented
50#421×C103—24no—
51C2×#104×C103C2211yescharacteristic
52C2×#104×C103C2211yescharacteristic
53C2×#104×C103C2211yescharacteristic, complemented
54C2×#104×C103C2211yescharacteristic, complemented
55C2×#104×C103C2211yescharacteristic, complemented
56C2×#104×C103C2211yescharacteristic, complemented
57#419×C103C2211yescharacteristic, complemented
58#417×C103C2211yescharacteristic
59#417×C103C2211yescharacteristic, complemented
60#417×C103C2211yescharacteristic, complemented
61C2×#100×C103C2211yescharacteristic, complemented
62C2×#100×C103C2211yescharacteristic, complemented
63#407×C103C2211yescharacteristic, complemented
64#396×C103—22no—
65#394×C103—22no—
66#391×C103C2211yescharacteristic, complemented
67#390×C103C2211yescharacteristic, complemented
68#384×C103C2211yescharacteristic, complemented
69#343×C103C2211yescharacteristic, complemented
70#343×C103C2211yescharacteristic, complemented
71#339×C103C2211yescharacteristic, complemented
72#339×C103C2211yescharacteristic, complemented
73H(5,𝔽2)×C103—22no—
74H(5,𝔽2)×C103—22no—
75H(5,𝔽2)×C103—41no—
76H(5,𝔽2)×C103—41no—
77C2×#41×C103—21no—
78C2×#41×C103—21no—
79C2×#41×C103—21no—
80C2×#41×C103—21no—
81C2×#41×C103—22no—
82C2×#41×C103—22no—
83C2×#41×C103—41no—
84C2×#41×C103—41no—
85C2×#41×C103D411yescharacteristic
86C2×#41×C103D411yescharacteristic
87C2×#41×C103C2311yescharacteristic
88C2×#41×C103C2311yescharacteristic
89C2×#41×C103C2311yescharacteristic
90C22×Q8×C103D411yescharacteristic
91C22×Q8×C103C2311yescharacteristic
92C22×D4×C103—21no—
93C22×D4×C103—22no—
94C22×D4×C103—22no—
95C22×D4×C103—21no—
96C22×D4×C103—21no—
97C22×D4×C103D411yescharacteristic
98C22×D4×C103D412yes—
99C22×D4×C103C2311yescharacteristic
100C23×C4×C103—21no—
101C23×C4×C103C2311yescharacteristic
102#137×C103—22no—
103#137×C103—22no—
104#137×C103—22no—
105#137×C103—41no—
106#137×C103—41no—
107#137×C103—41no—
108C2×Q16×C103—21no—
109C2×Q16×C103—21no—
110C2×Q16×C103—21no—
111C2×SD16×C103—21no—
112C2×SD16×C103—21no—
113C2×SD16×C103—21no—
114C2×M16×C103—21no—
115C2×M16×C103—22no—
116C2×M16×C103—41no—
117C2×M16×C103C2311yescharacteristic
118C2×M16×C103C2311yescharacteristic
119C2×M16×C103C2311yescharacteristic
120C2×M16×C103C2311yescharacteristic
121C22×C8×C103—21no—
122#127×C103—22no—
123#127×C103—21no—
124#124×C103—22no—
125#124×C103—21no—
126#124×C103—22no—
127#124×C103—41no—
128#123×C103—22no—
129#123×C103—21no—
130C22⋊Q8×C103—22no—
131C22⋊Q8×C103—21no—
132C22⋊Q8×C103—21no—
133C22⋊Q8×C103—21no—
134C22⋊Q8×C103—21no—
135C22⋊Q8×C103—21no—
136C22⋊Q8×C103—21no—
137C22⋊Q8×C103D411yescharacteristic
138C22⋊Q8×C103D411yescharacteristic
139#121×C103—22no—
140#121×C103—22no—
141#121×C103—22no—
142#121×C103—22no—
143#121×C103—22no—
144#121×C103—21no—
145#121×C103—21no—
146#121×C103—21no—
147#121×C103—21no—
148#121×C103—21no—
149#121×C103—21no—
150#121×C103—22no—
151#121×C103—21no—
152#121×C103—21no—
153#121×C103D411yescharacteristic
154#121×C103D411yescharacteristic
155#120×C103—22no—
156#120×C103—22no—
157#120×C103—22no—
158#120×C103—21no—
159#120×C103—22no—
160C4×Q8×C103—21no—
161C4×D4×C103—22no—
162C4×D4×C103—22no—
163C4×D4×C103—21no—
164C4×D4×C103—22no—
165C4×D4×C103—21no—
166C4×D4×C103—21no—
167#117×C103—21no—
168#117×C103—22no—
169#117×C103—41no—
170#117×C103C2311yescharacteristic
171C2×C4⋊C4×C103—21no—
172C2×C4⋊C4×C103—21no—
173C2×C4⋊C4×C103—21no—
174C2×C4⋊C4×C103—22no—
175C2×C4⋊C4×C103C2311yescharacteristic
176C2×C4⋊C4×C103C2311yescharacteristic
177C2×C22⋊C4×C103—22no—
178C2×C22⋊C4×C103—21no—
179C2×C22⋊C4×C103—21no—
180C2×C22⋊C4×C103—22no—
181C2×C22⋊C4×C103—22no—
182C2×C22⋊C4×C103D412yes—
183C2×C42×C103C2311yescharacteristic
184C2×C42×C103C2311yescharacteristic
185#107×C103—21no—
186#106×C103—21no—
187#104×C103—22no—
188#104×C103—22no—
189#104×C103—22no—
190#104×C103—22no—
191#104×C103—41no—
192#104×C103D414yescomplemented
193#103×C103—21no—
194#103×C103—21no—
195#103×C103—21no—
196#103×C103—21no—
197#103×C103—21no—
198#102×C103—21no—
199#102×C103—21no—
200#102×C103—21no—
201#100×C103—22no—
202#100×C103—41no—
203C22⋊C8×C103—21no—
204C22⋊C8×C103—21no—
205#95×C103—22no—
206C24×C103—22no—
207C24×C103—21no—
208C24×C103C2×D412yes—
209C24×C103C2×D411yescharacteristic
210#41×C103—21no—
211#41×C103—21no—
212#41×C103—22no—
213#41×C103—22no—
214#41×C103—21no—
215#41×C103—21no—
216#41×C103—21no—
217#41×C103—21no—
218#41×C103—21no—
219#41×C103—21no—
220#41×C103—21no—
221#41×C103—21no—
222#41×C103—42no—
223#41×C103—42no—
224#41×C103—41no—
225#41×C103—41no—
226#41×C103—42no—
227#41×C103—42no—
228#41×C103—42no—
229#41×C103—42no—
230#41×C103—42no—
231#41×C103—42no—
232#41×C103C2×D412yes—
233#41×C103#4112yes—
234C2×Q8×C103—21no—
235C2×Q8×C103—22no—
236C2×Q8×C103—21no—
237C2×Q8×C103—21no—
238C2×Q8×C103—21no—
239C2×Q8×C103—21no—
240C2×Q8×C103—21no—
241C2×Q8×C103—21no—
242C2×Q8×C103—41no—
243C2×Q8×C103C2×D411yescharacteristic
244C2×Q8×C103C2×D411yescharacteristic
245C2×Q8×C103C2×D411yescharacteristic
246C2×D4×C103—21no—
247C2×D4×C103—22no—
248C2×D4×C103—22no—
249C2×D4×C103—22no—
250C2×D4×C103—22no—
251C2×D4×C103—21no—
252C2×D4×C103—21no—
253C2×D4×C103—21no—
254C2×D4×C103—21no—
255C2×D4×C103—21no—
256C2×D4×C103—22no—
257C2×D4×C103—22no—
258C2×D4×C103—22no—
259C2×D4×C103—21no—
260C2×D4×C103—22no—
261C2×D4×C103—21no—
262C2×D4×C103—21no—
263C2×D4×C103—21no—
264C2×D4×C103—21no—
265C2×D4×C103—21no—
266C2×D4×C103—21no—
267C2×D4×C103—21no—
268C2×D4×C103—41no—
269C2×D4×C103—42no—
270C2×D4×C103—42no—
271C2×D4×C103—42no—
272C2×D4×C103—42no—
273C2×D4×C103—44no—
274C2×D4×C103—44no—
275C2×D4×C103—42no—
276C2×D4×C103—42no—
277C2×D4×C103—82no—
278C2×D4×C103—84no—
279C2×D4×C103C2×D411yescharacteristic
280C2×D4×C103C2×D411yescharacteristic
281C2×D4×C103C2×D411yescharacteristic
282C22×C4×C103—21no—
283C22×C4×C103—21no—
284C22×C4×C103—21no—
285C22×C4×C103—21no—
286C22×C4×C103—21no—
287C22×C4×C103—22no—
288C22×C4×C103—21no—
289C22×C4×C103—21no—
290C22×C4×C103—22no—
291C22×C4×C103—21no—
292C22×C4×C103—21no—
293C22×C4×C103—21no—
294C22×C4×C103—21no—
295C22×C4×C103—21no—
296C22×C4×C103—21no—
297C22×C4×C103—21no—
298C22×C4×C103—42no—
299C22×C4×C103—42no—
300C22×C4×C103C2×D411yescharacteristic
301C22×C4×C103C2×D411yescharacteristic
302C22×C4×C103C2×D411yescharacteristic
303C22×C4×C103C2×D411yescharacteristic
304C22×C4×C103C2×D411yescharacteristic
305C22×C4×C103C2×D412yes—
306C22×C4×C103C2411yescharacteristic
307Q16×C103—42no—
308Q16×C103—42no—
309Q16×C103—42no—
310SD16×C103—42no—
311SD16×C103—42no—
312SD16×C103—42no—
313M16×C103—21no—
314M16×C103—21no—
315M16×C103—21no—
316M16×C103—21no—
317M16×C103—21no—
318M16×C103—21no—
319M16×C103—21no—
320M16×C103—42no—
321M16×C103C2×D412yescomplemented
322C2×C8×C103—21no—
323C2×C8×C103—21no—
324C2×C8×C103—21no—
325C2×C8×C103—21no—
326C2×C8×C103—42no—
327C4⋊C4×C103—22no—
328C4⋊C4×C103—22no—
329C4⋊C4×C103—21no—
330C4⋊C4×C103—21no—
331C4⋊C4×C103—21no—
332C4⋊C4×C103—21no—
333C4⋊C4×C103—21no—
334C4⋊C4×C103—21no—
335C4⋊C4×C103—42no—
336C4⋊C4×C103—41no—
337C4⋊C4×C103—41no—
338C4⋊C4×C103—82no—
339C4⋊C4×C103C2×D411yescharacteristic
340C4⋊C4×C103C2×D411yescharacteristic
341C22⋊C4×C103—22no—
342C22⋊C4×C103—22no—
343C22⋊C4×C103—22no—
344C22⋊C4×C103—22no—
345C22⋊C4×C103—22no—
346C22⋊C4×C103—21no—
347C22⋊C4×C103—21no—
348C22⋊C4×C103—21no—
349C22⋊C4×C103—21no—
350C22⋊C4×C103—22no—
351C22⋊C4×C103—22no—
352C22⋊C4×C103—21no—
353C22⋊C4×C103—42no—
354C22⋊C4×C103—44no—
355C22⋊C4×C103—41no—
356C22⋊C4×C103—41no—
357C22⋊C4×C103—82no—
358C42×C103—22no—
359C42×C103—21no—
360C42×C103—21no—
361C42×C103—21no—
362C42×C103—21no—
363C42×C103C2×D412yescomplemented
364C23×C103—21no—
365C23×C103—21no—
366C23×C103—21no—
367C23×C103—22no—
368C23×C103—21no—
369C23×C103—21no—
370C23×C103—22no—
371C23×C103—22no—
372C23×C103—41no—
373C23×C103—41no—
374C23×C103—42no—
375C23×C103—42no—
376C23×C103—44no—
377C23×C103—42no—
378C23×C103—42no—
379C23×C103—81no—
380C23×C103—82no—
381C23×C103—82no—
382C23×C103#12011yescharacteristic
383C23×C103#12011yescharacteristic
384C23×C103C22×D411yescharacteristic
385Q8×C103—21no—
386Q8×C103—21no—
387Q8×C103—21no—
388Q8×C103—21no—
389Q8×C103—21no—
390Q8×C103—42no—
391Q8×C103—41no—
392Q8×C103—41no—
393Q8×C103—41no—
394Q8×C103—41no—
395Q8×C103#12112yes—
396D4×C103—22no—
397D4×C103—22no—
398D4×C103—21no—
399D4×C103—21no—
400D4×C103—21no—
401D4×C103—21no—
402D4×C103—21no—
403D4×C103—42no—
404D4×C103—42no—
405D4×C103—44no—
406D4×C103—42no—
407D4×C103—44no—
408D4×C103—44no—
409D4×C103—42no—
410D4×C103—41no—
411D4×C103—41no—
412D4×C103—41no—
413D4×C103—41no—
414D4×C103—41no—
415D4×C103—41no—
416D4×C103—41no—
417D4×C103—41no—
418D4×C103—81no—
419D4×C103—82no—
420D4×C103—82no—
421D4×C103—82no—
422D4×C103—82no—
423D4×C103#12112yes—
424C2×C4×C103—21no—
425C2×C4×C103—21no—
426C2×C4×C103—21no—
427C2×C4×C103—21no—
428C2×C4×C103—21no—
429C2×C4×C103—21no—
430C2×C4×C103—21no—
431C2×C4×C103—21no—
432C2×C4×C103—21no—
433C2×C4×C103—22no—
434C2×C4×C103—21no—
435C2×C4×C103—21no—
436C2×C4×C103—22no—
437C2×C4×C103—21no—
438C2×C4×C103—22no—
439C2×C4×C103—21no—
440C2×C4×C103—21no—
441C2×C4×C103—21no—
442C2×C4×C103—22no—
443C2×C4×C103—42no—
444C2×C4×C103—42no—
445C2×C4×C103—42no—
446C2×C4×C103—44no—
447C2×C4×C103—41no—
448C2×C4×C103—41no—
449C2×C4×C103—41no—
450C2×C4×C103—41no—
451C2×C4×C103—41no—
452C2×C4×C103—41no—
453C2×C4×C103—42no—
454C2×C4×C103—41no—
455C2×C4×C103—42no—
456C2×C4×C103—41no—
457C2×C4×C103—41no—
458C2×C4×C103—41no—
459C2×C4×C103—41no—
460C2×C4×C103—41no—
461C2×C4×C103—41no—
462C2×C4×C103—82no—
463C2×C4×C103#12011yescharacteristic
464C2×C4×C103#12011yescharacteristic
465C2×C4×C103C22×D411yescharacteristic
466C2×C4×C103C22×D411yescharacteristic
467C2×C4×C103C22×D411yescharacteristic
468C2×C4×C103C2×#4111yescharacteristic
469C2×C4×C103H(5,𝔽2)11yescharacteristic
470C2×C4×C103H(5,𝔽2)11yescharacteristic
471C8×C103—22no—
472C8×C103—41no—
473C8×C103—41no—
474C8×C103—41no—
475C22×C103—21no—
476C22×C103—21no—
477C22×C103—21no—
478C22×C103—21no—
479C22×C103—22no—
480C22×C103—21no—
481C22×C103—21no—
482C22×C103—21no—
483C22×C103—21no—
484C22×C103—41no—
485C22×C103—41no—
486C22×C103—41no—
487C22×C103—41no—
488C22×C103—42no—
489C22×C103—42no—
490C22×C103—41no—
491C22×C103—41no—
492C22×C103—41no—
493C22×C103—42no—
494C22×C103—41no—
495C22×C103—81no—
496C22×C103—81no—
497C22×C103—82no—
498C22×C103—82no—
499C22×C103—84no—
500C22×C103—164no—
501C22×C103C2×#12011yescharacteristic
502C22×C103D4211yescharacteristic
503C22×C103#54611yescharacteristic
504C4×C103—21no—
505C4×C103—21no—
506C4×C103—22no—
507C4×C103—42no—
508C4×C103—41no—
509C4×C103—41no—
510C4×C103—42no—
511C4×C103—41no—
512C4×C103—41no—
513C4×C103—81no—
514C4×C103—81no—
515C4×C103—81no—
516C4×C103C2×#12111yescharacteristic
517C4×C103#53411yescharacteristic
518C4×C103D4211yescharacteristic
519C4×C103#54611yescharacteristic
520#24471C10311yesmaximal, characteristic, direct product factor, Sylow
521C2×C103—21no—
522C2×C103—21no—
523C2×C103—41no—
524C2×C103—41no—
525C2×C103—42no—
526C2×C103—81no—
527C2×C103—82no—
528C2×C103—81no—
529C2×C103#241011yescharacteristic
530C2×C103#301911yescharacteristic
531C2×C103#302211yescharacteristic
532#3488C2×C10311yescharacteristic
533#3056C2×C10311yescharacteristic, complemented
534C2×#455C2×C10311yescharacteristic, complemented
535#3007C2×C10311yescharacteristic, complemented
536C2×#421C2×C10311yescharacteristic, complemented
537#2620C2×C10311yescharacteristic, complemented
538#2039C2×C10311yescharacteristic, complemented
539#2037C2×C10311yescharacteristic, complemented
540#2007C2×C10311yescharacteristic, complemented
541#2004C2×C10311yescharacteristic, complemented
542#1900C2×C10311yescharacteristic, complemented
543#1897C2×C10311yescharacteristic, complemented
544#1882C2×C10311yescharacteristic, complemented
545#1859C2×C10311yescharacteristic, complemented
546#1792C2×C10311yescharacteristic, complemented
547C103#2447111yescharacteristic, direct product factor, Sylow
548C2×H(5,𝔽2)C22×C10311yescharacteristic
549C22×#41C22×C10311yescharacteristic
550C2×#137C22×C10311yescharacteristic
551C2×#137C22×C10311yescharacteristic, complemented
552C2×#137C22×C10311yescharacteristic, complemented
553C22×M16C22×C10311yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C10311yescharacteristic
562#535—21no—
563#535C22×C10311yescharacteristic
564C2×#124C22×C10311yescharacteristic, complemented
565#525—21no—
566#525C22×C10311yescharacteristic
567C2×C22⋊Q8C22×C10311yescharacteristic, complemented
568C2×#121—21no—
569C2×#121C22×C10311yescharacteristic
570#520C22×C10311yescharacteristic
571C2×#117C22×C10311yescharacteristic, complemented
572#470—21no—
573#468—21no—
574#467—21no—
575#465—21no—
576#455—24no—
577#452—21no—
578#452—21no—
579#451—21no—
580#450—21no—
581#428C22×C10311yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C10311yescharacteristic
584C2×#104C22×C10311yescharacteristic
585C2×#104C22×C10311yescharacteristic, complemented
586C2×#104C22×C10311yescharacteristic, complemented
587C2×#104C22×C10311yescharacteristic, complemented
588C2×#104C22×C10311yescharacteristic, complemented
589#419C22×C10311yescharacteristic, complemented
590#417C22×C10311yescharacteristic
591#417C22×C10311yescharacteristic, complemented
592#417C22×C10311yescharacteristic, complemented
593C2×#100C22×C10311yescharacteristic, complemented
594C2×#100C22×C10311yescharacteristic, complemented
595#407C22×C10311yescharacteristic, complemented
596#396—22no—
597#394—22no—
598#391C22×C10311yescharacteristic, complemented
599#390C22×C10311yescharacteristic, complemented
600#384C22×C10311yescharacteristic, complemented
601#343C22×C10311yescharacteristic, complemented
602#343C22×C10311yescharacteristic, complemented
603#339C22×C10311yescharacteristic, complemented
604#339C22×C10311yescharacteristic, complemented
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C10311yescharacteristic
618C2×#41D4×C10311yescharacteristic
619C2×#41C23×C10311yescharacteristic
620C2×#41C23×C10311yescharacteristic
621C2×#41C23×C10311yescharacteristic
622C22×Q8D4×C10311yescharacteristic
623C22×Q8C23×C10311yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C10311yescharacteristic
630C22×D4D4×C10312yes—
631C22×D4C23×C10311yescharacteristic
632C23×C4—21no—
633C23×C4C23×C10311yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C10311yescharacteristic
650C2×M16C23×C10311yescharacteristic
651C2×M16C23×C10311yescharacteristic
652C2×M16C23×C10311yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C10311yescharacteristic
670C22⋊Q8D4×C10311yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C10311yescharacteristic
686#121D4×C10311yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C10311yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C10311yescharacteristic
708C2×C4⋊C4C23×C10311yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C10312yes—
715C2×C42C23×C10311yescharacteristic
716C2×C42C23×C10311yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C10314yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C10312yes—
741C24C2×D4×C10311yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C10312yes—
765#41#41×C10312yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C10311yescharacteristic
776C2×Q8C2×D4×C10311yescharacteristic
777C2×Q8C2×D4×C10311yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C10311yescharacteristic
812C2×D4C2×D4×C10311yescharacteristic
813C2×D4C2×D4×C10311yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C10311yescharacteristic
833C22×C4C2×D4×C10311yescharacteristic
834C22×C4C2×D4×C10311yescharacteristic
835C22×C4C2×D4×C10311yescharacteristic
836C22×C4C2×D4×C10311yescharacteristic
837C22×C4C2×D4×C10312yes—
838C22×C4C24×C10311yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C10312yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C10311yescharacteristic
872C4⋊C4C2×D4×C10311yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C10312yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C10311yescharacteristic
915C23#120×C10311yescharacteristic
916C23C22×D4×C10311yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C10312yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C10312yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C10311yescharacteristic
996C2×C4#120×C10311yescharacteristic
997C2×C4C22×D4×C10311yescharacteristic
998C2×C4C22×D4×C10311yescharacteristic
999C2×C4C22×D4×C10311yescharacteristic
1000C2×C4C2×#41×C10311yescharacteristic
1001C2×C4H(5,𝔽2)×C10311yescharacteristic
1002C2×C4H(5,𝔽2)×C10311yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—42no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C10311yescharacteristic
1034C22D42×C10311yescharacteristic
1035C22#546×C10311yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C10311yescharacteristic
1049C4#534×C10311yescharacteristic
1050C4D42×C10311yescharacteristic
1051C4#546×C10311yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C103×#241011yescharacteristic
1061C2C103×#301911yescharacteristic
1062C2C103×#302211yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3056C2semidirect
3. C2×#455×C103C2semidirect
4. C103×#3007C2semidirect
5. C2×#421×C103C2semidirect
6. C103×#2620C2semidirect
7. C103×#2039C2semidirect
8. C103×#2037C2semidirect
9. C103×#2007C2semidirect
10. C103×#2004C2semidirect
11. C103×#1900C2semidirect
12. C103×#1897C2semidirect
13. C103×#1882C2semidirect
14. C103×#1859C2semidirect
15. C103×#1792C2semidirect
19. C2×#137×C103C22semidirect
20. C2×#137×C103C22semidirect
21. C22×M16×C103C22semidirect
32. C2×#124×C103C22semidirect
35. C2×C22⋊Q8×C103C22semidirect
39. C2×#117×C103C22semidirect
49. #428×C103C22semidirect
53. C2×#104×C103C22semidirect
54. C2×#104×C103C22semidirect
55. C2×#104×C103C22semidirect
56. C2×#104×C103C22semidirect
57. #419×C103C22semidirect
59. #417×C103C22semidirect
60. #417×C103C22semidirect
61. C2×#100×C103C22semidirect
62. C2×#100×C103C22semidirect
63. #407×C103C22semidirect
66. #391×C103C22semidirect
67. #390×C103C22semidirect
68. #384×C103C22semidirect
69. #343×C103C22semidirect
70. #343×C103C22semidirect
71. #339×C103C22semidirect
72. #339×C103C22semidirect
192. #104×C103D4semidirect
321. M16×C103C2×D4semidirect
363. C42×C103C2×D4semidirect
520. #24471C103direct (N × H)
533. #3056C2×C103semidirect
534. C2×#455C2×C103semidirect
535. #3007C2×C103semidirect
536. C2×#421C2×C103semidirect
537. #2620C2×C103semidirect
538. #2039C2×C103semidirect
539. #2037C2×C103semidirect
540. #2007C2×C103semidirect
541. #2004C2×C103semidirect
542. #1900C2×C103semidirect
543. #1897C2×C103semidirect
544. #1882C2×C103semidirect
545. #1859C2×C103semidirect
546. #1792C2×C103semidirect
547. C103#24471direct (N × H)
551. C2×#137C22×C103semidirect
552. C2×#137C22×C103semidirect
553. C22×M16C22×C103semidirect
564. C2×#124C22×C103semidirect
567. C2×C22⋊Q8C22×C103semidirect
571. C2×#117C22×C103semidirect
581. #428C22×C103semidirect
585. C2×#104C22×C103semidirect
586. C2×#104C22×C103semidirect
587. C2×#104C22×C103semidirect
588. C2×#104C22×C103semidirect
589. #419C22×C103semidirect
591. #417C22×C103semidirect
592. #417C22×C103semidirect
593. C2×#100C22×C103semidirect
594. C2×#100C22×C103semidirect
595. #407C22×C103semidirect
598. #391C22×C103semidirect
599. #390C22×C103semidirect
600. #384C22×C103semidirect
601. #343C22×C103semidirect
602. #343C22×C103semidirect
603. #339C22×C103semidirect
604. #339C22×C103semidirect
724. #104D4×C103semidirect
853. M16C2×D4×C103semidirect
895. C42C2×D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34882
C103×#30562
C2×#455×C1032
C103×#30072
C2×#421×C1032
C103×#26202
C103×#20392
C103×#20372
C103×#20072
C103×#20042
C103×#19002
C103×#18972
C103×#18822
C103×#18592
C103×#17922
#24471103