Finite Group Databasebeta

← C103×#25466 #39930741

Subgroups — C103×#25466 #39930741

Order 26368.

756 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#501×C103C211yesmaximal, characteristic, complemented
2C2×#478×C103C211yesmaximal, characteristic
3C103×#2563C211yesmaximal, characteristic
4C103×#2370C211yesmaximal, characteristic, complemented
5C103×#2085C211yesmaximal, characteristic, complemented
6C103×#2085C211yesmaximal, characteristic, complemented
7C103×#2067C211yesmaximal, characteristic
8C103×#2065C211yesmaximal, characteristic
9C103×#1988C211yesmaximal, characteristic, complemented
10C103×#1949C211yesmaximal, characteristic, complemented
11C103×#1949C211yesmaximal, characteristic, complemented
12C103×#1940C211yesmaximal, characteristic, complemented
13C103×#1926C211yesmaximal, characteristic
14C103×#1925C211yesmaximal, characteristic
15C103×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C103C2211yescharacteristic
17C2×#125×C103C2211yescharacteristic
18C2×C4×D4×C103C2211yescharacteristic
19#501×C103—24no—
20#478×C103—24no—
21C2×#107×C103C2211yescharacteristic
22C2×#107×C103C2211yescharacteristic
23C2×#107×C103C2211yescharacteristic
24C2×#106×C103C2211yescharacteristic
25C2×#106×C103C2211yescharacteristic
26C2×#106×C103C2211yescharacteristic
27C2×C4⋊C8×C103C2211yescharacteristic
28C2×C4⋊C8×C103C2211yescharacteristic
29C2×C4⋊C8×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×#97×C103C2211yescharacteristic
35#393×C103—21no—
36#393×C103—21no—
37#390×C103C2211yescharacteristic
38#390×C103C2211yescharacteristic
39#389×C103—21no—
40#389×C103C2211yescharacteristic
41#389×C103C2211yescharacteristic
42#387×C103—21no—
43#387×C103—21no—
44#382×C103C2211yescharacteristic
45#382×C103C2211yescharacteristic
46#380×C103—21no—
47#380×C103—21no—
48C4×C4⋊C4×C103—21no—
49C4×C4⋊C4×C103C2211yescharacteristic
50C4×C4⋊C4×C103C2211yescharacteristic
51C4×C4⋊C4×C103C2211yescharacteristic
52C4×C4⋊C4×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#336×C103C2211yescharacteristic
60#336×C103C2211yescharacteristic
61C22×Q8×C103—21no—
62C22×D4×C103C2311yescharacteristic
63C23×C4×C103—21no—
64C22×C8×C103C2311yescharacteristic
65C22×C8×C103C2311yescharacteristic
66C22×C8×C103C2311yescharacteristic
67C22×C8×C103C2311yescharacteristic
68C4⋊Q8×C103—22no—
69C4⋊Q8×C103—22no—
70#125×C103—22no—
71#125×C103D414yes—
72C4×D4×C103—22no—
73C4×D4×C103—22no—
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×C103D411yescharacteristic
80C2×C4⋊C4×C103D411yescharacteristic
81C2×C4⋊C4×C103C2311yescharacteristic
82C2×C4⋊C4×C103C2311yescharacteristic
83C2×C4⋊C4×C103C2311yescharacteristic
84C2×C4⋊C4×C103C2311yescharacteristic
85C2×C4⋊C4×C103C2311yescharacteristic
86C2×C4⋊C4×C103C2311yescharacteristic
87C2×C4⋊C4×C103C2311yescharacteristic
88C2×C22⋊C4×C103—21no—
89C2×C22⋊C4×C103—21no—
90C2×C22⋊C4×C103—21no—
91C2×C22⋊C4×C103—21no—
92C2×C22⋊C4×C103—21no—
93C2×C42×C103—21no—
94C2×C42×C103—21no—
95C2×C42×C103—21no—
96C2×C42×C103C2311yescharacteristic
97C2×C42×C103C2311yescharacteristic
98C2×C42×C103C2311yescharacteristic
99#107×C103—22no—
100#107×C103—22no—
101#107×C103—22no—
102#106×C103—22no—
103#106×C103—22no—
104#106×C103—22no—
105C4⋊C8×C103—22no—
106C4⋊C8×C103—22no—
107C4⋊C8×C103—22no—
108#102×C103—22no—
109#102×C103—22no—
110#102×C103—22no—
111#102×C103Q814yescomplemented
112#97×C103—22no—
113#95×C103—21no—
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×C103D411yescharacteristic
123#95×C103D411yescharacteristic
124C24×C103—21no—
125C2×Q8×C103—42no—
126C2×Q8×C103—81no—
127C2×Q8×C103—81no—
128C2×D4×C103—21no—
129C2×D4×C103—21no—
130C2×D4×C103—21no—
131C2×D4×C103—21no—
132C2×D4×C103—21no—
133C2×D4×C103C2×Q812yes—
134C22×C4×C103—21no—
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—42no—
142C22×C4×C103—42no—
143C22×C4×C103—42no—
144C22×C4×C103C2×D411yescharacteristic
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D411yescharacteristic
147C22×C4×C103C2×D411yescharacteristic
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2×D411yescharacteristic
150C22×C4×C103C2411yescharacteristic
151C2×C8×C103—21no—
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×Q812yes—
162C2×C8×C103#4112yes—
163C4⋊C4×C103—24no—
164C4⋊C4×C103—24no—
165C4⋊C4×C103—21no—
166C4⋊C4×C103—21no—
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—41no—
177C4⋊C4×C103—41no—
178C4⋊C4×C103—42no—
179C4⋊C4×C103—42no—
180C4⋊C4×C103—81no—
181C4⋊C4×C103C2×D412yes—
182C4⋊C4×C103C2×D412yes—
183C4⋊C4×C103C2×Q812yes—
184C22⋊C4×C103—42no—
185C22⋊C4×C103—81no—
186C22⋊C4×C103—81no—
187C22⋊C4×C103—81no—
188C22⋊C4×C103—81no—
189C42×C103—21no—
190C42×C103—21no—
191C42×C103—21no—
192C42×C103—21no—
193C42×C103—42no—
194C42×C103—81no—
195C42×C103—81no—
196C42×C103C2×D412yes—
197C42×C103#4112yes—
198C23×C103—22no—
199C23×C103—41no—
200C23×C103—41no—
201C23×C103—41no—
202C23×C103—41no—
203C23×C103—41no—
204C23×C103—41no—
205C23×C103C22×D411yescharacteristic
206Q8×C103—84no—
207D4×C103—22no—
208D4×C103—22no—
209D4×C103—41no—
210D4×C103—41no—
211C2×C4×C103—21no—
212C2×C4×C103—21no—
213C2×C4×C103—21no—
214C2×C4×C103—21no—
215C2×C4×C103—22no—
216C2×C4×C103—22no—
217C2×C4×C103—21no—
218C2×C4×C103—21no—
219C2×C4×C103—21no—
220C2×C4×C103—21no—
221C2×C4×C103—22no—
222C2×C4×C103—21no—
223C2×C4×C103—21no—
224C2×C4×C103—21no—
225C2×C4×C103—21no—
226C2×C4×C103—21no—
227C2×C4×C103—21no—
228C2×C4×C103—21no—
229C2×C4×C103—21no—
230C2×C4×C103—41no—
231C2×C4×C103—41no—
232C2×C4×C103—41no—
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—84no—
249C2×C4×C103#12112yes—
250C2×C4×C103#12112yes—
251C2×C4×C103C22×D411yescharacteristic
252C2×C4×C103C22×Q811yescharacteristic
253C2×C4×C103C2×#4111yescharacteristic
254C2×C4×C103C2×#4111yescharacteristic
255C2×C4×C1032−1+411yescharacteristic
256C2×C4×C1032−1+411yescharacteristic
257C8×C103—22no—
258C8×C103—22no—
259C8×C103—41no—
260C8×C103—41no—
261C22×C103—42no—
262C22×C103—42no—
263C22×C103—42no—
264C22×C103—81no—
265C22×C103—81no—
266C22×C103—81no—
267C22×C103—81no—
268C22×C103C2×#12111yescharacteristic
269C22×C103#54711yescharacteristic
270C22×C103D4×Q811yescharacteristic
271C22×C103#57511yescharacteristic
272C22×C103#57511yescharacteristic
273C22×C103#57611yescharacteristic
274C22×C103#57711yescharacteristic
275C4×C103—22no—
276C4×C103—22no—
277C4×C103—41no—
278C4×C103—41no—
279C4×C103—41no—
280C4×C103—41no—
281C4×C103—42no—
282C4×C103—42no—
283C4×C103—42no—
284C4×C103—81no—
285C4×C103—81no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103#53311yescharacteristic
289C4×C103#54111yescharacteristic
290C4×C103#54811yescharacteristic
291C4×C103D4×Q811yescharacteristic
292#25466C10311yesmaximal, characteristic, direct product factor, Sylow
293C2×C103—82no—
294C2×C103#242911yescharacteristic
295C2×C103#304011yescharacteristic
296C2×C103#304511yescharacteristic
297C2×C103#334711yescharacteristic
298C2×C103#334811yescharacteristic
299C2×C103#338811yescharacteristic
300C2×C103#338911yescharacteristic
301C2×#501C2×C10311yescharacteristic, complemented
302C2×#478C2×C10311yescharacteristic
303#2563C2×C10311yescharacteristic
304#2370C2×C10311yescharacteristic, complemented
305#2085C2×C10311yescharacteristic, complemented
306#2085C2×C10311yescharacteristic, complemented
307#2067C2×C10311yescharacteristic
308#2065C2×C10311yescharacteristic
309#1988C2×C10311yescharacteristic, complemented
310#1949C2×C10311yescharacteristic, complemented
311#1949C2×C10311yescharacteristic, complemented
312#1940C2×C10311yescharacteristic, complemented
313#1926C2×C10311yescharacteristic
314#1925C2×C10311yescharacteristic
315#1762C2×C10311yescharacteristic
316C103#2546611yescharacteristic, direct product factor, Sylow
317C2×C4⋊Q8C22×C10311yescharacteristic
318C2×#125C22×C10311yescharacteristic
319C2×C4×D4C22×C10311yescharacteristic
320#501—24no—
321#478—24no—
322C2×#107C22×C10311yescharacteristic
323C2×#107C22×C10311yescharacteristic
324C2×#107C22×C10311yescharacteristic
325C2×#106C22×C10311yescharacteristic
326C2×#106C22×C10311yescharacteristic
327C2×#106C22×C10311yescharacteristic
328C2×C4⋊C8C22×C10311yescharacteristic
329C2×C4⋊C8C22×C10311yescharacteristic
330C2×C4⋊C8C22×C10311yescharacteristic
331C2×#102C22×C10311yescharacteristic
332C2×#102C22×C10311yescharacteristic
333C2×#102C22×C10311yescharacteristic
334C2×#102C22×C10311yescharacteristic
335C2×#97C22×C10311yescharacteristic
336#393—21no—
337#393—21no—
338#390C22×C10311yescharacteristic
339#390C22×C10311yescharacteristic
340#389—21no—
341#389C22×C10311yescharacteristic
342#389C22×C10311yescharacteristic
343#387—21no—
344#387—21no—
345#382C22×C10311yescharacteristic
346#382C22×C10311yescharacteristic
347#380—21no—
348#380—21no—
349C4×C4⋊C4—21no—
350C4×C4⋊C4C22×C10311yescharacteristic
351C4×C4⋊C4C22×C10311yescharacteristic
352C4×C4⋊C4C22×C10311yescharacteristic
353C4×C4⋊C4C22×C10311yescharacteristic
354#340C22×C10311yescharacteristic
355#340C22×C10311yescharacteristic
356#340C22×C10311yescharacteristic
357#340C22×C10311yescharacteristic
358#340C22×C10311yescharacteristic
359#340C22×C10311yescharacteristic
360#336C22×C10311yescharacteristic
361#336C22×C10311yescharacteristic
362C22×Q8—21no—
363C22×D4C23×C10311yescharacteristic
364C23×C4—21no—
365C22×C8C23×C10311yescharacteristic
366C22×C8C23×C10311yescharacteristic
367C22×C8C23×C10311yescharacteristic
368C22×C8C23×C10311yescharacteristic
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371#125—22no—
372#125D4×C10314yes—
373C4×D4—22no—
374C4×D4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4D4×C10311yescharacteristic
381C2×C4⋊C4D4×C10311yescharacteristic
382C2×C4⋊C4C23×C10311yescharacteristic
383C2×C4⋊C4C23×C10311yescharacteristic
384C2×C4⋊C4C23×C10311yescharacteristic
385C2×C4⋊C4C23×C10311yescharacteristic
386C2×C4⋊C4C23×C10311yescharacteristic
387C2×C4⋊C4C23×C10311yescharacteristic
388C2×C4⋊C4C23×C10311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C10311yescharacteristic
398C2×C42C23×C10311yescharacteristic
399C2×C42C23×C10311yescharacteristic
400#107—22no—
401#107—22no—
402#107—22no—
403#106—22no—
404#106—22no—
405#106—22no—
406C4⋊C8—22no—
407C4⋊C8—22no—
408C4⋊C8—22no—
409#102—22no—
410#102—22no—
411#102—22no—
412#102Q8×C10314yescomplemented
413#97—22no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95D4×C10311yescharacteristic
424#95D4×C10311yescharacteristic
425C24—21no—
426C2×Q8—42no—
427C2×Q8—81no—
428C2×Q8—81no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×Q8×C10312yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C2×D4×C10311yescharacteristic
446C22×C4C2×D4×C10311yescharacteristic
447C22×C4C2×D4×C10311yescharacteristic
448C22×C4C2×D4×C10311yescharacteristic
449C22×C4C2×D4×C10311yescharacteristic
450C22×C4C2×D4×C10311yescharacteristic
451C22×C4C24×C10311yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8C2×Q8×C10312yes—
463C2×C8#41×C10312yes—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4C2×D4×C10312yes—
483C4⋊C4C2×D4×C10312yes—
484C4⋊C4C2×Q8×C10312yes—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—42no—
495C42—81no—
496C42—81no—
497C42C2×D4×C10312yes—
498C42#41×C10312yes—
499C23—22no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23C22×D4×C10311yescharacteristic
507Q8—84no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
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—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
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—84no—
550C2×C4#121×C10312yes—
551C2×C4#121×C10312yes—
552C2×C4C22×D4×C10311yescharacteristic
553C2×C4C22×Q8×C10311yescharacteristic
554C2×C4C2×#41×C10311yescharacteristic
555C2×C4C2×#41×C10311yescharacteristic
556C2×C42−1+4×C10311yescharacteristic
557C2×C42−1+4×C10311yescharacteristic
558C8—22no—
559C8—22no—
560C8—41no—
561C8—41no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22C2×#121×C10311yescharacteristic
570C22#547×C10311yescharacteristic
571C22D4×Q8×C10311yescharacteristic
572C22#575×C10311yescharacteristic
573C22#575×C10311yescharacteristic
574C22#576×C10311yescharacteristic
575C22#577×C10311yescharacteristic
576C4—22no—
577C4—22no—
578C4—42no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—42no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4#533×C10311yescharacteristic
590C4#541×C10311yescharacteristic
591C4#548×C10311yescharacteristic
592C4D4×Q8×C10311yescharacteristic
593C2—82no—
594C2C103×#242911yescharacteristic
595C2C103×#304011yescharacteristic
596C2C103×#304511yescharacteristic
597C2C103×#334711yescharacteristic
598C2C103×#334811yescharacteristic
599C2C103×#338811yescharacteristic
600C2C103×#338911yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C4⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#501×C103C2semidirect
4. C103×#2370C2semidirect
5. C103×#2085C2semidirect
6. C103×#2085C2semidirect
9. C103×#1988C2semidirect
10. C103×#1949C2semidirect
11. C103×#1949C2semidirect
12. C103×#1940C2semidirect
111. #102×C103Q8semidirect
292. #25466C103direct (N × H)
301. C2×#501C2×C103semidirect
304. #2370C2×C103semidirect
305. #2085C2×C103semidirect
306. #2085C2×C103semidirect
309. #1988C2×C103semidirect
310. #1949C2×C103semidirect
311. #1949C2×C103semidirect
312. #1940C2×C103semidirect
316. C103#25466direct (N × H)
412. #102Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#501×C1032
C2×#478×C1032
C103×#25632
C103×#23702
C103×#20852
C103×#20672
C103×#20652
C103×#19882
C103×#19492
C103×#19402
C103×#19262
C103×#19252
C103×#17622
#25466103