Finite Group Databasebeta

← C103×#25482 #39930757

Subgroups — C103×#25482 #39930757

Order 26368.

782 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#478×C103C211yesmaximal, characteristic
2C2×#446×C103C211yesmaximal, characteristic, complemented
3C103×#2584C211yesmaximal, characteristic, complemented
4C103×#2538C211yesmaximal, characteristic
5C103×#2088C211yesmaximal, characteristic, complemented
6C103×#2087C211yesmaximal, characteristic, complemented
7C103×#2067C211yesmaximal, characteristic
8C103×#2067C211yesmaximal, characteristic
9C103×#1992C211yesmaximal, characteristic, complemented
10C103×#1947C211yesmaximal, characteristic, complemented
11C103×#1943C211yesmaximal, characteristic, complemented
12C103×#1942C211yesmaximal, characteristic, complemented
13C103×#1936C211yesmaximal, characteristic
14C103×#1934C211yesmaximal, characteristic
15C103×#1762C211yesmaximal, characteristic
16C2×#125×C103C2211yescharacteristic
17C2×C22⋊Q8×C103—21no—
18C2×C4×Q8×C103C2211yescharacteristic
19C2×C4×D4×C103C2211yescharacteristic
20#478×C103—24no—
21#446×C103—24no—
22C2×#107×C103C2211yescharacteristic
23C2×#107×C103C2211yescharacteristic
24C2×#107×C103C2211yescharacteristic
25C2×#106×C103C2211yescharacteristic
26C2×C4⋊C8×C103C2211yescharacteristic
27C2×C4⋊C8×C103C2211yescharacteristic
28C2×C4⋊C8×C103C2211yescharacteristic
29C2×#102×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#97×C103C2211yescharacteristic
34C2×#97×C103C2211yescharacteristic
35C2×C4×C8×C103C2211yescharacteristic
36#398×C103—21no—
37#396×C103—21no—
38#396×C103—21no—
39#395×C103—21no—
40#390×C103C2211yescharacteristic
41#390×C103C2211yescharacteristic
42#389×C103—21no—
43#389×C103—21no—
44#389×C103C2211yescharacteristic
45#389×C103C2211yescharacteristic
46#389×C103C2211yescharacteristic
47#389×C103C2211yescharacteristic
48#389×C103C2211yescharacteristic
49#389×C103C2211yescharacteristic
50#384×C103C2211yescharacteristic
51#380×C103—21no—
52C4×C4⋊C4×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61C22×Q8×C103D411yescharacteristic
62C22×D4×C103C2311yescharacteristic
63C23×C4×C103—21no—
64C22×C8×C103C2311yescharacteristic
65C22×C8×C103C2311yescharacteristic
66C22×C8×C103C2311yescharacteristic
67C22×C8×C103C2311yescharacteristic
68#125×C103—22no—
69#125×C103—22no—
70C22⋊Q8×C103—44no—
71C4×Q8×C103—22no—
72C4×Q8×C103—22no—
73C4×D4×C103—22no—
74C4×D4×C103—22no—
75C2×C4⋊C4×C103—21no—
76C2×C4⋊C4×C103—21no—
77C2×C4⋊C4×C103—21no—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—21no—
80C2×C4⋊C4×C103—21no—
81C2×C4⋊C4×C103—21no—
82C2×C4⋊C4×C103—21no—
83C2×C4⋊C4×C103—21no—
84C2×C4⋊C4×C103—21no—
85C2×C4⋊C4×C103D411yescharacteristic
86C2×C4⋊C4×C103D411yescharacteristic
87C2×C4⋊C4×C103D411yescharacteristic
88C2×C4⋊C4×C103C2311yescharacteristic
89C2×C4⋊C4×C103C2311yescharacteristic
90C2×C4⋊C4×C103C2311yescharacteristic
91C2×C4⋊C4×C103C2311yescharacteristic
92C2×C4⋊C4×C103C2311yescharacteristic
93C2×C4⋊C4×C103C2311yescharacteristic
94C2×C4⋊C4×C103C2311yescharacteristic
95C2×C22⋊C4×C103—21no—
96C2×C22⋊C4×C103—21no—
97C2×C22⋊C4×C103—21no—
98C2×C22⋊C4×C103—21no—
99C2×C22⋊C4×C103—21no—
100C2×C42×C103—21no—
101C2×C42×C103C2311yescharacteristic
102C2×C42×C103C2311yescharacteristic
103C2×C42×C103C2311yescharacteristic
104#107×C103—22no—
105#107×C103—22no—
106#107×C103—22no—
107#106×C103—22no—
108C4⋊C8×C103—22no—
109C4⋊C8×C103—22no—
110C4⋊C8×C103D414yes—
111#102×C103—22no—
112#102×C103—22no—
113#102×C103—22no—
114#102×C103Q814yescomplemented
115#97×C103—22no—
116#97×C103—22no—
117C4×C8×C103—22no—
118#95×C103—21no—
119#95×C103—21no—
120#95×C103—21no—
121#95×C103—21no—
122#95×C103—21no—
123#95×C103—21no—
124#95×C103—21no—
125C24×C103—21no—
126C2×Q8×C103—22no—
127C2×Q8×C103—22no—
128C2×Q8×C103—41no—
129C2×D4×C103—21no—
130C2×D4×C103—21no—
131C2×D4×C103—21no—
132C2×D4×C103—21no—
133C2×D4×C103—21no—
134C2×D4×C103C2×Q812yes—
135C22×C4×C103—21no—
136C22×C4×C103—21no—
137C22×C4×C103—21no—
138C22×C4×C103—21no—
139C22×C4×C103—21no—
140C22×C4×C103—21no—
141C22×C4×C103—21no—
142C22×C4×C103—42no—
143C22×C4×C103—42no—
144C22×C4×C103—42no—
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D411yescharacteristic
147C22×C4×C103C2×D411yescharacteristic
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2×D411yescharacteristic
150C22×C4×C103C2×D411yescharacteristic
151C22×C4×C103C2411yescharacteristic
152C2×C8×C103—21no—
153C2×C8×C103—21no—
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×C103C2×D412yes—
162C2×C8×C103C2×D412yes—
163C2×C8×C103C2×Q812yes—
164C4⋊C4×C103—22no—
165C4⋊C4×C103—22no—
166C4⋊C4×C103—22no—
167C4⋊C4×C103—21no—
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—21no—
179C4⋊C4×C103—42no—
180C4⋊C4×C103—42no—
181C4⋊C4×C103—42no—
182C4⋊C4×C103—42no—
183C4⋊C4×C103—42no—
184C4⋊C4×C103—42no—
185C4⋊C4×C103—42no—
186C4⋊C4×C103—81no—
187C4⋊C4×C103—81no—
188C4⋊C4×C103—81no—
189C4⋊C4×C103C2×Q812yes—
190C4⋊C4×C103#4112yes—
191C22⋊C4×C103—42no—
192C22⋊C4×C103—42no—
193C22⋊C4×C103—42no—
194C22⋊C4×C103—81no—
195C22⋊C4×C103—81no—
196C42×C103—21no—
197C42×C103—21no—
198C42×C103—21no—
199C42×C103—21no—
200C42×C103—81no—
201C42×C103C2×D412yes—
202C42×C103#4112yes—
203C23×C103—22no—
204C23×C103—41no—
205C23×C103—41no—
206C23×C103—41no—
207C23×C103—41no—
208C23×C103—41no—
209C23×C103—41no—
210C23×C103C22×D411yescharacteristic
211Q8×C103—44no—
212D4×C103—22no—
213D4×C103—22no—
214D4×C103—41no—
215D4×C103—41no—
216C2×C4×C103—21no—
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—21no—
224C2×C4×C103—21no—
225C2×C4×C103—22no—
226C2×C4×C103—22no—
227C2×C4×C103—21no—
228C2×C4×C103—21no—
229C2×C4×C103—21no—
230C2×C4×C103—21no—
231C2×C4×C103—21no—
232C2×C4×C103—21no—
233C2×C4×C103—41no—
234C2×C4×C103—41no—
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—84no—
253C2×C4×C103#12112yes—
254C2×C4×C103#12112yes—
255C2×C4×C103AGL(1,ℤ/8)12yes—
256C2×C4×C103C22×D411yescharacteristic
257C2×C4×C103C22×Q811yescharacteristic
258C2×C4×C103C2×#4111yescharacteristic
259C2×C4×C103C2×#4111yescharacteristic
260C2×C4×C1032−1+411yescharacteristic
261C2×C4×C1032−1+411yescharacteristic
262C8×C103—22no—
263C8×C103—22no—
264C8×C103—22no—
265C8×C103—41no—
266C22×C103—42no—
267C22×C103—42no—
268C22×C103—42no—
269C22×C103—81no—
270C22×C103—81no—
271C22×C103—81no—
272C22×C103—81no—
273C22×C103C2×#12111yescharacteristic
274C22×C103#54811yescharacteristic
275C22×C103D4×Q811yescharacteristic
276C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C103#57511yescharacteristic
278C22×C103#57611yescharacteristic
279C22×C103#57811yescharacteristic
280C4×C103—22no—
281C4×C103—22no—
282C4×C103—22no—
283C4×C103—42no—
284C4×C103—42no—
285C4×C103—41no—
286C4×C103—41no—
287C4×C103—41no—
288C4×C103—81no—
289C4×C103—81no—
290C4×C103—81no—
291C4×C103—81no—
292C4×C103—81no—
293C4×C103#53311yescharacteristic
294C4×C103#54111yescharacteristic
295C4×C103#54711yescharacteristic
296C4×C103D4×Q811yescharacteristic
297#25482C10311yesmaximal, characteristic, direct product factor, Sylow
298C2×C103—82no—
299C2×C103#242911yescharacteristic
300C2×C103#305511yescharacteristic
301C2×C103#306111yescharacteristic
302C2×C103#336611yescharacteristic
303C2×C103#337711yescharacteristic
304C2×C103#338611yescharacteristic
305C2×C103#338911yescharacteristic
306C2×#478C2×C10311yescharacteristic
307C2×#446C2×C10311yescharacteristic, complemented
308#2584C2×C10311yescharacteristic, complemented
309#2538C2×C10311yescharacteristic
310#2088C2×C10311yescharacteristic, complemented
311#2087C2×C10311yescharacteristic, complemented
312#2067C2×C10311yescharacteristic
313#2067C2×C10311yescharacteristic
314#1992C2×C10311yescharacteristic, complemented
315#1947C2×C10311yescharacteristic, complemented
316#1943C2×C10311yescharacteristic, complemented
317#1942C2×C10311yescharacteristic, complemented
318#1936C2×C10311yescharacteristic
319#1934C2×C10311yescharacteristic
320#1762C2×C10311yescharacteristic
321C103#2548211yescharacteristic, direct product factor, Sylow
322C2×#125C22×C10311yescharacteristic
323C2×C22⋊Q8—21no—
324C2×C4×Q8C22×C10311yescharacteristic
325C2×C4×D4C22×C10311yescharacteristic
326#478—24no—
327#446—24no—
328C2×#107C22×C10311yescharacteristic
329C2×#107C22×C10311yescharacteristic
330C2×#107C22×C10311yescharacteristic
331C2×#106C22×C10311yescharacteristic
332C2×C4⋊C8C22×C10311yescharacteristic
333C2×C4⋊C8C22×C10311yescharacteristic
334C2×C4⋊C8C22×C10311yescharacteristic
335C2×#102C22×C10311yescharacteristic
336C2×#102C22×C10311yescharacteristic
337C2×#102C22×C10311yescharacteristic
338C2×#102C22×C10311yescharacteristic
339C2×#97C22×C10311yescharacteristic
340C2×#97C22×C10311yescharacteristic
341C2×C4×C8C22×C10311yescharacteristic
342#398—21no—
343#396—21no—
344#396—21no—
345#395—21no—
346#390C22×C10311yescharacteristic
347#390C22×C10311yescharacteristic
348#389—21no—
349#389—21no—
350#389C22×C10311yescharacteristic
351#389C22×C10311yescharacteristic
352#389C22×C10311yescharacteristic
353#389C22×C10311yescharacteristic
354#389C22×C10311yescharacteristic
355#389C22×C10311yescharacteristic
356#384C22×C10311yescharacteristic
357#380—21no—
358C4×C4⋊C4C22×C10311yescharacteristic
359#340C22×C10311yescharacteristic
360#340C22×C10311yescharacteristic
361#340C22×C10311yescharacteristic
362#340C22×C10311yescharacteristic
363#340C22×C10311yescharacteristic
364#340C22×C10311yescharacteristic
365#340C22×C10311yescharacteristic
366#340C22×C10311yescharacteristic
367C22×Q8D4×C10311yescharacteristic
368C22×D4C23×C10311yescharacteristic
369C23×C4—21no—
370C22×C8C23×C10311yescharacteristic
371C22×C8C23×C10311yescharacteristic
372C22×C8C23×C10311yescharacteristic
373C22×C8C23×C10311yescharacteristic
374#125—22no—
375#125—22no—
376C22⋊Q8—44no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×D4—22no—
380C4×D4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4D4×C10311yescharacteristic
392C2×C4⋊C4D4×C10311yescharacteristic
393C2×C4⋊C4D4×C10311yescharacteristic
394C2×C4⋊C4C23×C10311yescharacteristic
395C2×C4⋊C4C23×C10311yescharacteristic
396C2×C4⋊C4C23×C10311yescharacteristic
397C2×C4⋊C4C23×C10311yescharacteristic
398C2×C4⋊C4C23×C10311yescharacteristic
399C2×C4⋊C4C23×C10311yescharacteristic
400C2×C4⋊C4C23×C10311yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C42—21no—
407C2×C42C23×C10311yescharacteristic
408C2×C42C23×C10311yescharacteristic
409C2×C42C23×C10311yescharacteristic
410#107—22no—
411#107—22no—
412#107—22no—
413#106—22no—
414C4⋊C8—22no—
415C4⋊C8—22no—
416C4⋊C8D4×C10314yes—
417#102—22no—
418#102—22no—
419#102—22no—
420#102Q8×C10314yescomplemented
421#97—22no—
422#97—22no—
423C4×C8—22no—
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—22no—
433C2×Q8—22no—
434C2×Q8—41no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×Q8×C10312yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4C2×D4×C10311yescharacteristic
452C22×C4C2×D4×C10311yescharacteristic
453C22×C4C2×D4×C10311yescharacteristic
454C22×C4C2×D4×C10311yescharacteristic
455C22×C4C2×D4×C10311yescharacteristic
456C22×C4C2×D4×C10311yescharacteristic
457C22×C4C24×C10311yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C2×D4×C10312yes—
468C2×C8C2×D4×C10312yes—
469C2×C8C2×Q8×C10312yes—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
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—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4C2×Q8×C10312yes—
496C4⋊C4#41×C10312yes—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—81no—
507C42C2×D4×C10312yes—
508C42#41×C10312yes—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23C22×D4×C10311yescharacteristic
517Q8—44no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
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—84no—
559C2×C4#121×C10312yes—
560C2×C4#121×C10312yes—
561C2×C4AGL(1,ℤ/8)×C10312yes—
562C2×C4C22×D4×C10311yescharacteristic
563C2×C4C22×Q8×C10311yescharacteristic
564C2×C4C2×#41×C10311yescharacteristic
565C2×C4C2×#41×C10311yescharacteristic
566C2×C42−1+4×C10311yescharacteristic
567C2×C42−1+4×C10311yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22C2×#121×C10311yescharacteristic
580C22#548×C10311yescharacteristic
581C22D4×Q8×C10311yescharacteristic
582C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
583C22#575×C10311yescharacteristic
584C22#576×C10311yescharacteristic
585C22#578×C10311yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4#533×C10311yescharacteristic
600C4#541×C10311yescharacteristic
601C4#547×C10311yescharacteristic
602C4D4×Q8×C10311yescharacteristic
603C2—82no—
604C2C103×#242911yescharacteristic
605C2C103×#305511yescharacteristic
606C2C103×#306111yescharacteristic
607C2C103×#336611yescharacteristic
608C2C103×#337711yescharacteristic
609C2C103×#338611yescharacteristic
610C2C103×#338911yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C4×Q8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#446×C103C2semidirect
3. C103×#2584C2semidirect
5. C103×#2088C2semidirect
6. C103×#2087C2semidirect
9. C103×#1992C2semidirect
10. C103×#1947C2semidirect
11. C103×#1943C2semidirect
12. C103×#1942C2semidirect
114. #102×C103Q8semidirect
297. #25482C103direct (N × H)
307. C2×#446C2×C103semidirect
308. #2584C2×C103semidirect
310. #2088C2×C103semidirect
311. #2087C2×C103semidirect
314. #1992C2×C103semidirect
315. #1947C2×C103semidirect
316. #1943C2×C103semidirect
317. #1942C2×C103semidirect
321. C103#25482direct (N × H)
420. #102Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#478×C1032
C2×#446×C1032
C103×#25842
C103×#25382
C103×#20882
C103×#20872
C103×#20672
C103×#19922
C103×#19472
C103×#19432
C103×#19422
C103×#19362
C103×#19342
C103×#17622
#25482103