Finite Group Databasebeta

← C103×#29363 #39934638

Subgroups — C103×#29363 #39934638

Order 26368.

676 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
1C103×#2640C211yesmaximal, characteristic
2C103×#2330C211yesmaximal, characteristic, complemented
3C103×#2072C211yesmaximal, characteristic, complemented
4C103×#2071C211yesmaximal, characteristic
5C103×#2026C211yesmaximal, characteristic, complemented
6C103×#2025C211yesmaximal, characteristic
7C103×#1988C211yesmaximal, characteristic, complemented
8C103×#1987C211yesmaximal, characteristic, complemented
9C103×#1983C211yesmaximal, characteristic
10C103×#1983C211yesmaximal, characteristic
11C103×#1936C211yesmaximal, characteristic
12C103×#1935C211yesmaximal, characteristic, complemented
13C103×#1934C211yesmaximal, characteristic
14C103×#1933C211yesmaximal, characteristic, complemented
15C103×#1768C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C103C2211yescharacteristic
17C2×#125×C103C2211yescharacteristic
18C2×#124×C103C2211yescharacteristic
19C2×C4⋊C8×C103C2211yescharacteristic
20C2×C4⋊C8×C103C2211yescharacteristic
21C2×#103×C103C2211yescharacteristic
22C2×#103×C103C2211yescharacteristic
23C2×#103×C103C2211yescharacteristic
24C2×#103×C103C2211yescharacteristic
25C2×#102×C103C2211yescharacteristic
26C2×#102×C103C2211yescharacteristic
27C2×#102×C103C2211yescharacteristic
28C2×#102×C103C2211yescharacteristic
29C2×#97×C103C2211yescharacteristic
30C2×C4×C8×C103C2211yescharacteristic
31#397×C103—21no—
32#397×C103—21no—
33#393×C103—21no—
34#393×C103—21no—
35#391×C103C2211yescharacteristic
36#391×C103C2211yescharacteristic
37#390×C103C2211yescharacteristic
38#390×C103C2211yescharacteristic
39#389×C103—21no—
40#389×C103—21no—
41#389×C103C2211yescharacteristic
42#389×C103C2211yescharacteristic
43#387×C103—21no—
44#387×C103—21no—
45#384×C103C2211yescharacteristic
46C4×C4⋊C4×C103C2211yescharacteristic
47C4×C4⋊C4×C103C2211yescharacteristic
48#376×C103C2211yescharacteristic
49#340×C103C2211yescharacteristic
50#340×C103C2211yescharacteristic
51#340×C103C2211yescharacteristic
52#340×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#336×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59C22×Q8×C103—21no—
60C22×Q8×C103C2311yescharacteristic
61C22×D4×C103C2311yescharacteristic
62C22×C8×C103C2311yescharacteristic
63C22×C8×C103C2311yescharacteristic
64C22×C8×C103C2311yescharacteristic
65C22×C8×C103C2311yescharacteristic
66C4⋊Q8×C103—22no—
67C4⋊Q8×C103—22no—
68#125×C103—22no—
69#125×C103—22no—
70#124×C103—22no—
71#124×C103—22no—
72C2×C4⋊C4×C103—21no—
73C2×C4⋊C4×C103—21no—
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×C22⋊C4×C103—21no—
91C2×C42×C103—21no—
92C2×C42×C103—21no—
93C2×C42×C103C2311yescharacteristic
94C2×C42×C103C2311yescharacteristic
95C2×C42×C103C2311yescharacteristic
96C4⋊C8×C103—22no—
97C4⋊C8×C103—22no—
98#103×C103—22no—
99#103×C103—22no—
100#103×C103—41no—
101#103×C103—41no—
102#102×C103—22no—
103#102×C103—22no—
104#102×C103—41no—
105#102×C103—41no—
106#97×C103—41no—
107C4×C8×C103—41no—
108#95×C103—21no—
109#95×C103—21no—
110#95×C103—21no—
111#95×C103—21no—
112#95×C103—21no—
113#95×C103—21no—
114#95×C103—21no—
115#95×C103—21no—
116#95×C103D411yescharacteristic
117#95×C103D411yescharacteristic
118#95×C103D411yescharacteristic
119#95×C103D411yescharacteristic
120C24×C103—21no—
121C2×Q8×C103—21no—
122C2×Q8×C103—21no—
123C2×Q8×C103—21no—
124C2×Q8×C103—21no—
125C2×Q8×C103—21no—
126C2×Q8×C103—21no—
127C2×Q8×C103—42no—
128C2×Q8×C103—81no—
129C2×Q8×C103—81no—
130C2×D4×C103—21no—
131C2×D4×C103—21no—
132C2×D4×C103—21no—
133C2×D4×C103—21no—
134C2×D4×C103—21no—
135C2×D4×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—21no—
143C22×C4×C103C2×D411yescharacteristic
144C22×C4×C103C2×D411yescharacteristic
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D411yescharacteristic
147C22×C4×C103C2×D411yescharacteristic
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2411yescharacteristic
150C2×C8×C103—21no—
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×C103—21no—
162C4⋊C4×C103—24no—
163C4⋊C4×C103—24no—
164C4⋊C4×C103—21no—
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—42no—
175C4⋊C4×C103—81no—
176C4⋊C4×C103—81no—
177C4⋊C4×C103—81no—
178C4⋊C4×C103—81no—
179C4⋊C4×C103#4112yes—
180C4⋊C4×C103#4112yes—
181C22⋊C4×C103—42no—
182C22⋊C4×C103—42no—
183C22⋊C4×C103—81no—
184C22⋊C4×C103—81no—
185C22⋊C4×C103—81no—
186C22⋊C4×C103—81no—
187C42×C103—21no—
188C42×C103—21no—
189C42×C103—21no—
190C42×C103—21no—
191C42×C103—81no—
192C42×C103—81no—
193C42×C103#4112yes—
194C42×C103#4112yes—
195C23×C103—41no—
196C23×C103—41no—
197C23×C103—41no—
198C23×C103—41no—
199C23×C103—41no—
200C23×C103—41no—
201C23×C103—41no—
202C23×C103C22×D411yescharacteristic
203Q8×C103—41no—
204Q8×C103—41no—
205Q8×C103—41no—
206Q8×C103—41no—
207Q8×C103—84no—
208D4×C103—41no—
209D4×C103—41no—
210D4×C103—41no—
211D4×C103—41no—
212C2×C4×C103—21no—
213C2×C4×C103—21no—
214C2×C4×C103—21no—
215C2×C4×C103—21no—
216C2×C4×C103—21no—
217C2×C4×C103—21no—
218C2×C4×C103—22no—
219C2×C4×C103—22no—
220C2×C4×C103—21no—
221C2×C4×C103—21no—
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—41no—
249C2×C4×C103#12412yes—
250C2×C4×C103#12412yes—
251C2×C4×C103C2×#4111yescharacteristic
252C2×C4×C103C2×#4111yescharacteristic
253C2×C4×C103C2×#4111yescharacteristic
254C2×C4×C103C2×#4111yescharacteristic
255C2×C4×C103H(5,𝔽2)11yescharacteristic
256C2×C4×C1032−1+411yescharacteristic
257C8×C103—41no—
258C8×C103—41no—
259C8×C103—41no—
260C8×C103—41no—
261C22×C103—81no—
262C22×C103—81no—
263C22×C103—81no—
264C22×C103—81no—
265C22×C103—81no—
266C22×C103—81no—
267C22×C103—81no—
268C22×C103#52511yescharacteristic
269C22×C103C2×#12411yescharacteristic
270C22×C103#53711yescharacteristic
271C22×C103#57611yescharacteristic
272C22×C103#57711yescharacteristic
273C22×C103#57711yescharacteristic
274C22×C103#57811yescharacteristic
275C4×C103—22no—
276C4×C103—22no—
277C4×C103—41no—
278C4×C103—42no—
279C4×C103—41no—
280C4×C103—42no—
281C4×C103—41no—
282C4×C103—41no—
283C4×C103—81no—
284C4×C103—81no—
285C4×C103—81no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103#55611yescharacteristic
289C4×C103#55611yescharacteristic
290C4×C103#55911yescharacteristic
291C4×C103#55911yescharacteristic
292#29363C10311yesmaximal, characteristic, direct product factor, Sylow
293C2×C103—161no—
294C2×C103#259211yescharacteristic
295C2×C103#312411yescharacteristic
296C2×C103#312511yescharacteristic
297C2×C103#313611yescharacteristic
298C2×C103#313711yescharacteristic
299C2×C103#325711yescharacteristic
300C2×C103#325811yescharacteristic
301#2640C2×C10311yescharacteristic
302#2330C2×C10311yescharacteristic, complemented
303#2072C2×C10311yescharacteristic, complemented
304#2071C2×C10311yescharacteristic
305#2026C2×C10311yescharacteristic, complemented
306#2025C2×C10311yescharacteristic
307#1988C2×C10311yescharacteristic, complemented
308#1987C2×C10311yescharacteristic, complemented
309#1983C2×C10311yescharacteristic
310#1983C2×C10311yescharacteristic
311#1936C2×C10311yescharacteristic
312#1935C2×C10311yescharacteristic, complemented
313#1934C2×C10311yescharacteristic
314#1933C2×C10311yescharacteristic, complemented
315#1768C2×C10311yescharacteristic, complemented
316C103#2936311yescharacteristic, direct product factor, Sylow
317C2×C4⋊Q8C22×C10311yescharacteristic
318C2×#125C22×C10311yescharacteristic
319C2×#124C22×C10311yescharacteristic
320C2×C4⋊C8C22×C10311yescharacteristic
321C2×C4⋊C8C22×C10311yescharacteristic
322C2×#103C22×C10311yescharacteristic
323C2×#103C22×C10311yescharacteristic
324C2×#103C22×C10311yescharacteristic
325C2×#103C22×C10311yescharacteristic
326C2×#102C22×C10311yescharacteristic
327C2×#102C22×C10311yescharacteristic
328C2×#102C22×C10311yescharacteristic
329C2×#102C22×C10311yescharacteristic
330C2×#97C22×C10311yescharacteristic
331C2×C4×C8C22×C10311yescharacteristic
332#397—21no—
333#397—21no—
334#393—21no—
335#393—21no—
336#391C22×C10311yescharacteristic
337#391C22×C10311yescharacteristic
338#390C22×C10311yescharacteristic
339#390C22×C10311yescharacteristic
340#389—21no—
341#389—21no—
342#389C22×C10311yescharacteristic
343#389C22×C10311yescharacteristic
344#387—21no—
345#387—21no—
346#384C22×C10311yescharacteristic
347C4×C4⋊C4C22×C10311yescharacteristic
348C4×C4⋊C4C22×C10311yescharacteristic
349#376C22×C10311yescharacteristic
350#340C22×C10311yescharacteristic
351#340C22×C10311yescharacteristic
352#340C22×C10311yescharacteristic
353#340C22×C10311yescharacteristic
354#340C22×C10311yescharacteristic
355#340C22×C10311yescharacteristic
356#340C22×C10311yescharacteristic
357#340C22×C10311yescharacteristic
358#336C22×C10311yescharacteristic
359#336C22×C10311yescharacteristic
360C22×Q8—21no—
361C22×Q8C23×C10311yescharacteristic
362C22×D4C23×C10311yescharacteristic
363C22×C8C23×C10311yescharacteristic
364C22×C8C23×C10311yescharacteristic
365C22×C8C23×C10311yescharacteristic
366C22×C8C23×C10311yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369#125—22no—
370#125—22no—
371#124—22no—
372#124—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C23×C10311yescharacteristic
381C2×C4⋊C4C23×C10311yescharacteristic
382C2×C4⋊C4C23×C10311yescharacteristic
383C2×C4⋊C4C23×C10311yescharacteristic
384C2×C4⋊C4C23×C10311yescharacteristic
385C2×C4⋊C4C23×C10311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42C23×C10311yescharacteristic
395C2×C42C23×C10311yescharacteristic
396C2×C42C23×C10311yescharacteristic
397C4⋊C8—22no—
398C4⋊C8—22no—
399#103—22no—
400#103—22no—
401#103—41no—
402#103—41no—
403#102—22no—
404#102—22no—
405#102—41no—
406#102—41no—
407#97—41no—
408C4×C8—41no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95D4×C10311yescharacteristic
418#95D4×C10311yescharacteristic
419#95D4×C10311yescharacteristic
420#95D4×C10311yescharacteristic
421C24—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—42no—
429C2×Q8—81no—
430C2×Q8—81no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C2×D4×C10311yescharacteristic
445C22×C4C2×D4×C10311yescharacteristic
446C22×C4C2×D4×C10311yescharacteristic
447C22×C4C2×D4×C10311yescharacteristic
448C22×C4C2×D4×C10311yescharacteristic
449C22×C4C2×D4×C10311yescharacteristic
450C22×C4C24×C10311yescharacteristic
451C2×C8—21no—
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×C8—21no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—21no—
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—42no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4#41×C10312yes—
481C4⋊C4#41×C10312yes—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—81no—
493C42—81no—
494C42#41×C10312yes—
495C42#41×C10312yes—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C22×D4×C10311yescharacteristic
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—84no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
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—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—41no—
550C2×C4#124×C10312yes—
551C2×C4#124×C10312yes—
552C2×C4C2×#41×C10311yescharacteristic
553C2×C4C2×#41×C10311yescharacteristic
554C2×C4C2×#41×C10311yescharacteristic
555C2×C4C2×#41×C10311yescharacteristic
556C2×C4H(5,𝔽2)×C10311yescharacteristic
557C2×C42−1+4×C10311yescharacteristic
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#525×C10311yescharacteristic
570C22C2×#124×C10311yescharacteristic
571C22#537×C10311yescharacteristic
572C22#576×C10311yescharacteristic
573C22#577×C10311yescharacteristic
574C22#577×C10311yescharacteristic
575C22#578×C10311yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4#556×C10311yescharacteristic
590C4#556×C10311yescharacteristic
591C4#559×C10311yescharacteristic
592C4#559×C10311yescharacteristic
593C2—161no—
594C2C103×#259211yescharacteristic
595C2C103×#312411yescharacteristic
596C2C103×#312511yescharacteristic
597C2C103×#313611yescharacteristic
598C2C103×#313711yescharacteristic
599C2C103×#325711yescharacteristic
600C2C103×#325811yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ #376×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2330C2semidirect
3. C103×#2072C2semidirect
5. C103×#2026C2semidirect
7. C103×#1988C2semidirect
8. C103×#1987C2semidirect
12. C103×#1935C2semidirect
14. C103×#1933C2semidirect
15. C103×#1768C2semidirect
292. #29363C103direct (N × H)
302. #2330C2×C103semidirect
303. #2072C2×C103semidirect
305. #2026C2×C103semidirect
307. #1988C2×C103semidirect
308. #1987C2×C103semidirect
312. #1935C2×C103semidirect
314. #1933C2×C103semidirect
315. #1768C2×C103semidirect
316. C103#29363direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#26402
C103×#23302
C103×#20722
C103×#20712
C103×#20262
C103×#20252
C103×#19882
C103×#19872
C103×#19832
C103×#19362
C103×#19352
C103×#19342
C103×#19332
C103×#17682
#29363103