Finite Group Databasebeta

← C103×#29261 #39934536

Subgroups — C103×#29261 #39934536

Order 26368.

748 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#125×C103C211yesmaximal, characteristic, complemented
2C4×#124×C103C211yesmaximal, characteristic
3C103×#2097C211yesmaximal, characteristic, complemented
4C103×#2092C211yesmaximal, characteristic
5C103×#2026C211yesmaximal, characteristic, complemented
6C103×#2025C211yesmaximal, characteristic
7C103×#1983C211yesmaximal, characteristic
8C103×#1983C211yesmaximal, characteristic
9C103×#1949C211yesmaximal, characteristic, complemented
10C103×#1949C211yesmaximal, characteristic, complemented
11C103×#1865C211yesmaximal, characteristic, complemented
12C103×#1864C211yesmaximal, characteristic
13C103×#1863C211yesmaximal, characteristic, complemented
14C103×#1862C211yesmaximal, characteristic
15C103×#1831C211yesmaximal, characteristic, complemented
16C2×#125×C103C2211yescharacteristic
17C2×#124×C103C2211yescharacteristic
18C2×C4×Q8×C103C2211yescharacteristic
19C2×C4×D4×C103C2211yescharacteristic
20C2×#107×C103C2211yescharacteristic
21C2×#107×C103C2211yescharacteristic
22C2×#106×C103C2211yescharacteristic
23C2×#106×C103C2211yescharacteristic
24C2×C4⋊C8×C103C2211yescharacteristic
25C2×C4⋊C8×C103C2211yescharacteristic
26C2×#103×C103C2211yescharacteristic
27C2×#103×C103C2211yescharacteristic
28C2×#103×C103C2211yescharacteristic
29C2×#103×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34#391×C103C2211yescharacteristic
35#390×C103C2211yescharacteristic
36#389×C103C2211yescharacteristic
37#389×C103C2211yescharacteristic
38#388×C103—21no—
39#388×C103—21no—
40#387×C103—21no—
41#387×C103—21no—
42#382×C103C2211yescharacteristic
43#382×C103C2211yescharacteristic
44C4×C4⋊C4×C103—21no—
45C4×C4⋊C4×C103—21no—
46C4×C4⋊C4×C103C2211yescharacteristic
47C4×C4⋊C4×C103C2211yescharacteristic
48C4×C22⋊C4×C103—21no—
49C4×C22⋊C4×C103—21no—
50C43×C103C2211yescharacteristic
51#340×C103C2211yescharacteristic
52#340×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#336×C103C2211yescharacteristic
56#336×C103C2211yescharacteristic
57#336×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59C22×Q8×C103C2311yescharacteristic
60C22×D4×C103C2311yescharacteristic
61C23×C4×C103—21no—
62C22×C8×C103C2311yescharacteristic
63C22×C8×C103C2311yescharacteristic
64C22×C8×C103C2311yescharacteristic
65C22×C8×C103C2311yescharacteristic
66#125×C103—22no—
67#125×C103—22no—
68#124×C103—22no—
69#124×C103Q814yes—
70C4×Q8×C103—41no—
71C4×Q8×C103—41no—
72C4×D4×C103—41no—
73C4×D4×C103—41no—
74C2×C4⋊C4×C103—21no—
75C2×C4⋊C4×C103—21no—
76C2×C4⋊C4×C103—21no—
77C2×C4⋊C4×C103—21no—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103C2311yescharacteristic
80C2×C4⋊C4×C103C2311yescharacteristic
81C2×C4⋊C4×C103C2311yescharacteristic
82C2×C4⋊C4×C103C2311yescharacteristic
83C2×C4⋊C4×C103C2311yescharacteristic
84C2×C4⋊C4×C103C2311yescharacteristic
85C2×C22⋊C4×C103—21no—
86C2×C22⋊C4×C103—21no—
87C2×C22⋊C4×C103—21no—
88C2×C22⋊C4×C103—21no—
89C2×C22⋊C4×C103—21no—
90C2×C42×C103—21no—
91C2×C42×C103—21no—
92C2×C42×C103—21no—
93C2×C42×C103D411yescharacteristic
94C2×C42×C103D411yescharacteristic
95C2×C42×C103D411yescharacteristic
96C2×C42×C103D411yescharacteristic
97C2×C42×C103C2311yescharacteristic
98C2×C42×C103C2311yescharacteristic
99C2×C42×C103C2311yescharacteristic
100#107×C103—41no—
101#107×C103—41no—
102#106×C103—41no—
103#106×C103—41no—
104C4⋊C8×C103—22no—
105C4⋊C8×C103—22no—
106#103×C103—22no—
107#103×C103—22no—
108#103×C103—41no—
109#103×C103—41no—
110#102×C103—22no—
111#102×C103—22no—
112#102×C103—41no—
113#102×C103—41no—
114#95×C103—21no—
115#95×C103—21no—
116#95×C103—21no—
117#95×C103—21no—
118#95×C103—21no—
119#95×C103—21no—
120#95×C103—21no—
121#95×C103—21no—
122#95×C103—21no—
123#95×C103—21no—
124C24×C103—21no—
125C2×Q8×C103—21no—
126C2×Q8×C103—21no—
127C2×Q8×C103—21no—
128C2×Q8×C103—21no—
129C2×Q8×C103—21no—
130C2×Q8×C103C2×Q812yes—
131C2×D4×C103—21no—
132C2×D4×C103—21no—
133C2×D4×C103—21no—
134C2×D4×C103—21no—
135C2×D4×C103—21no—
136C2×D4×C103C2×Q812yes—
137C22×C4×C103—21no—
138C22×C4×C103—21no—
139C22×C4×C103—21no—
140C22×C4×C103—21no—
141C22×C4×C103—21no—
142C22×C4×C103—21no—
143C22×C4×C103—21no—
144C22×C4×C103—42no—
145C22×C4×C103—42no—
146C22×C4×C103—42no—
147C22×C4×C103C2×D411yescharacteristic
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2×D411yescharacteristic
150C22×C4×C103C2×D411yescharacteristic
151C22×C4×C103C2×D411yescharacteristic
152C22×C4×C103C2×D411yescharacteristic
153C22×C4×C103C2411yescharacteristic
154C2×C8×C103—21no—
155C2×C8×C103—21no—
156C2×C8×C103—21no—
157C2×C8×C103—21no—
158C2×C8×C103—21no—
159C2×C8×C103—21no—
160C2×C8×C103—21no—
161C2×C8×C103—21no—
162C2×C8×C103—21no—
163C2×C8×C103—21no—
164C2×C8×C103—21no—
165C2×C8×C103—21no—
166C4⋊C4×C103—24no—
167C4⋊C4×C103—24no—
168C4⋊C4×C103—21no—
169C4⋊C4×C103—21no—
170C4⋊C4×C103—21no—
171C4⋊C4×C103—21no—
172C4⋊C4×C103—21no—
173C4⋊C4×C103—21no—
174C4⋊C4×C103—21no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—42no—
179C4⋊C4×C103—42no—
180C4⋊C4×C103—42no—
181C4⋊C4×C103#4112yes—
182C4⋊C4×C103#4112yes—
183C22⋊C4×C103—24no—
184C22⋊C4×C103—24no—
185C22⋊C4×C103—42no—
186C22⋊C4×C103—42no—
187C22⋊C4×C103—42no—
188C42×C103—22no—
189C42×C103—21no—
190C42×C103—21no—
191C42×C103—21no—
192C42×C103—21no—
193C42×C103—41no—
194C42×C103—41no—
195C42×C103—41no—
196C42×C103—42no—
197C42×C103—42no—
198C42×C103—42no—
199C42×C103C2×Q812yes—
200C42×C103#4112yes—
201C23×C103—22no—
202C23×C103—41no—
203C23×C103—41no—
204C23×C103—41no—
205C23×C103—41no—
206C23×C103—41no—
207C23×C103—41no—
208C23×C103C22×D411yescharacteristic
209Q8×C103—22no—
210Q8×C103—22no—
211Q8×C103—41no—
212Q8×C103—41no—
213D4×C103—22no—
214D4×C103—22no—
215D4×C103—41no—
216D4×C103—41no—
217C2×C4×C103—21no—
218C2×C4×C103—21no—
219C2×C4×C103—21no—
220C2×C4×C103—21no—
221C2×C4×C103—21no—
222C2×C4×C103—21no—
223C2×C4×C103—22no—
224C2×C4×C103—21no—
225C2×C4×C103—21no—
226C2×C4×C103—22no—
227C2×C4×C103—22no—
228C2×C4×C103—21no—
229C2×C4×C103—21no—
230C2×C4×C103—21no—
231C2×C4×C103—21no—
232C2×C4×C103—21no—
233C2×C4×C103—21no—
234C2×C4×C103—21no—
235C2×C4×C103—41no—
236C2×C4×C103—41no—
237C2×C4×C103—41no—
238C2×C4×C103—41no—
239C2×C4×C103—41no—
240C2×C4×C103—41no—
241C2×C4×C103—41no—
242C2×C4×C103—41no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—84no—
254C2×C4×C103C22⋊Q812yes—
255C2×C4×C103C22⋊Q812yes—
256C2×C4×C103#13512yes—
257C2×C4×C103C22×Q811yescharacteristic
258C2×C4×C103C2×#4111yescharacteristic
259C2×C4×C103C2×#4111yescharacteristic
260C2×C4×C103C2×#4111yescharacteristic
261C2×C4×C103H(5,𝔽2)11yescharacteristic
262C2×C4×C103H(5,𝔽2)11yescharacteristic
263C8×C103—41no—
264C8×C103—41no—
265C8×C103—41no—
266C8×C103—41no—
267C22×C103—42no—
268C22×C103—42no—
269C22×C103—42no—
270C22×C103—81no—
271C22×C103—81no—
272C22×C103—81no—
273C22×C103—81no—
274C22×C103C2×C22⋊Q811yescharacteristic
275C22×C103#52511yescharacteristic
276C22×C103#53511yescharacteristic
277C22×C103C2×#13511yescharacteristic
278C22×C103#57511yescharacteristic
279C22×C103#57511yescharacteristic
280C22×C103#57511yescharacteristic
281C4×C103—22no—
282C4×C103—22no—
283C4×C103—22no—
284C4×C103—42no—
285C4×C103—41no—
286C4×C103—42no—
287C4×C103—41no—
288C4×C103—42no—
289C4×C103—41no—
290C4×C103—81no—
291C4×C103—81no—
292C4×C103—81no—
293C4×C103—81no—
294C4×C103#55411yescharacteristic
295C4×C103#55411yescharacteristic
296C4×C103#55911yescharacteristic
297C4×C103#55911yescharacteristic
298#29261C10311yesmaximal, characteristic, direct product factor, Sylow
299C2×C103—82no—
300C2×C103#258011yescharacteristic
301C2×C103#307611yescharacteristic
302C2×C103#308011yescharacteristic
303C2×C103#310211yescharacteristic
304C2×C103#311111yescharacteristic
305C2×C103#321111yescharacteristic
306C2×C103#321911yescharacteristic
307C4×#125C2×C10311yescharacteristic, complemented
308C4×#124C2×C10311yescharacteristic
309#2097C2×C10311yescharacteristic, complemented
310#2092C2×C10311yescharacteristic
311#2026C2×C10311yescharacteristic, complemented
312#2025C2×C10311yescharacteristic
313#1983C2×C10311yescharacteristic
314#1983C2×C10311yescharacteristic
315#1949C2×C10311yescharacteristic, complemented
316#1949C2×C10311yescharacteristic, complemented
317#1865C2×C10311yescharacteristic, complemented
318#1864C2×C10311yescharacteristic
319#1863C2×C10311yescharacteristic, complemented
320#1862C2×C10311yescharacteristic
321#1831C2×C10311yescharacteristic, complemented
322C103#2926111yescharacteristic, direct product factor, Sylow
323C2×#125C22×C10311yescharacteristic
324C2×#124C22×C10311yescharacteristic
325C2×C4×Q8C22×C10311yescharacteristic
326C2×C4×D4C22×C10311yescharacteristic
327C2×#107C22×C10311yescharacteristic
328C2×#107C22×C10311yescharacteristic
329C2×#106C22×C10311yescharacteristic
330C2×#106C22×C10311yescharacteristic
331C2×C4⋊C8C22×C10311yescharacteristic
332C2×C4⋊C8C22×C10311yescharacteristic
333C2×#103C22×C10311yescharacteristic
334C2×#103C22×C10311yescharacteristic
335C2×#103C22×C10311yescharacteristic
336C2×#103C22×C10311yescharacteristic
337C2×#102C22×C10311yescharacteristic
338C2×#102C22×C10311yescharacteristic
339C2×#102C22×C10311yescharacteristic
340C2×#102C22×C10311yescharacteristic
341#391C22×C10311yescharacteristic
342#390C22×C10311yescharacteristic
343#389C22×C10311yescharacteristic
344#389C22×C10311yescharacteristic
345#388—21no—
346#388—21no—
347#387—21no—
348#387—21no—
349#382C22×C10311yescharacteristic
350#382C22×C10311yescharacteristic
351C4×C4⋊C4—21no—
352C4×C4⋊C4—21no—
353C4×C4⋊C4C22×C10311yescharacteristic
354C4×C4⋊C4C22×C10311yescharacteristic
355C4×C22⋊C4—21no—
356C4×C22⋊C4—21no—
357C43C22×C10311yescharacteristic
358#340C22×C10311yescharacteristic
359#340C22×C10311yescharacteristic
360#340C22×C10311yescharacteristic
361#340C22×C10311yescharacteristic
362#336C22×C10311yescharacteristic
363#336C22×C10311yescharacteristic
364#336C22×C10311yescharacteristic
365#336C22×C10311yescharacteristic
366C22×Q8C23×C10311yescharacteristic
367C22×D4C23×C10311yescharacteristic
368C23×C4—21no—
369C22×C8C23×C10311yescharacteristic
370C22×C8C23×C10311yescharacteristic
371C22×C8C23×C10311yescharacteristic
372C22×C8C23×C10311yescharacteristic
373#125—22no—
374#125—22no—
375#124—22no—
376#124Q8×C10314yes—
377C4×Q8—41no—
378C4×Q8—41no—
379C4×D4—41no—
380C4×D4—41no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4C23×C10311yescharacteristic
387C2×C4⋊C4C23×C10311yescharacteristic
388C2×C4⋊C4C23×C10311yescharacteristic
389C2×C4⋊C4C23×C10311yescharacteristic
390C2×C4⋊C4C23×C10311yescharacteristic
391C2×C4⋊C4C23×C10311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42D4×C10311yescharacteristic
401C2×C42D4×C10311yescharacteristic
402C2×C42D4×C10311yescharacteristic
403C2×C42D4×C10311yescharacteristic
404C2×C42C23×C10311yescharacteristic
405C2×C42C23×C10311yescharacteristic
406C2×C42C23×C10311yescharacteristic
407#107—41no—
408#107—41no—
409#106—41no—
410#106—41no—
411C4⋊C8—22no—
412C4⋊C8—22no—
413#103—22no—
414#103—22no—
415#103—41no—
416#103—41no—
417#102—22no—
418#102—22no—
419#102—41no—
420#102—41no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431C24—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×Q8×C10312yes—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4C2×Q8×C10312yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4C2×D4×C10311yescharacteristic
455C22×C4C2×D4×C10311yescharacteristic
456C22×C4C2×D4×C10311yescharacteristic
457C22×C4C2×D4×C10311yescharacteristic
458C22×C4C2×D4×C10311yescharacteristic
459C22×C4C2×D4×C10311yescharacteristic
460C22×C4C24×C10311yescharacteristic
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4#41×C10312yes—
489C4⋊C4#41×C10312yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C42—22no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—41no—
501C42—41no—
502C42—41no—
503C42—42no—
504C42—42no—
505C42—42no—
506C42C2×Q8×C10312yes—
507C42#41×C10312yes—
508C23—22no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×D4×C10311yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—41no—
519Q8—41no—
520D4—22no—
521D4—22no—
522D4—41no—
523D4—41no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4C22⋊Q8×C10312yes—
562C2×C4C22⋊Q8×C10312yes—
563C2×C4#135×C10312yes—
564C2×C4C22×Q8×C10311yescharacteristic
565C2×C4C2×#41×C10311yescharacteristic
566C2×C4C2×#41×C10311yescharacteristic
567C2×C4C2×#41×C10311yescharacteristic
568C2×C4H(5,𝔽2)×C10311yescharacteristic
569C2×C4H(5,𝔽2)×C10311yescharacteristic
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C2×C22⋊Q8×C10311yescharacteristic
582C22#525×C10311yescharacteristic
583C22#535×C10311yescharacteristic
584C22C2×#135×C10311yescharacteristic
585C22#575×C10311yescharacteristic
586C22#575×C10311yescharacteristic
587C22#575×C10311yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—42no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4#554×C10311yescharacteristic
602C4#554×C10311yescharacteristic
603C4#559×C10311yescharacteristic
604C4#559×C10311yescharacteristic
605C2—82no—
606C2C103×#258011yescharacteristic
607C2C103×#307611yescharacteristic
608C2C103×#308011yescharacteristic
609C2C103×#310211yescharacteristic
610C2C103×#311111yescharacteristic
611C2C103×#321111yescharacteristic
612C2C103×#321911yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C43×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×#125×C103C2semidirect
3. C103×#2097C2semidirect
5. C103×#2026C2semidirect
9. C103×#1949C2semidirect
10. C103×#1949C2semidirect
11. C103×#1865C2semidirect
13. C103×#1863C2semidirect
15. C103×#1831C2semidirect
298. #29261C103direct (N × H)
307. C4×#125C2×C103semidirect
309. #2097C2×C103semidirect
311. #2026C2×C103semidirect
315. #1949C2×C103semidirect
316. #1949C2×C103semidirect
317. #1865C2×C103semidirect
319. #1863C2×C103semidirect
321. #1831C2×C103semidirect
322. C103#29261direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#125×C1032
C4×#124×C1032
C103×#20972
C103×#20922
C103×#20262
C103×#20252
C103×#19832
C103×#19492
C103×#18652
C103×#18642
C103×#18632
C103×#18622
C103×#18312
#29261103