Finite Group Databasebeta

← C103×#26099 #39931374

Subgroups — C103×#26099 #39931374

Order 26368.

708 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2570C211yesmaximal, characteristic, complemented
2C103×#2354C211yesmaximal, characteristic
3C103×#2094C211yesmaximal, characteristic
4C103×#2092C211yesmaximal, characteristic
5C103×#2067C211yesmaximal, characteristic
6C103×#2065C211yesmaximal, characteristic
7C103×#1949C211yesmaximal, characteristic, complemented
8C103×#1948C211yesmaximal, characteristic, complemented
9C103×#1948C211yesmaximal, characteristic, complemented
10C103×#1940C211yesmaximal, characteristic, complemented
11C103×#1919C211yesmaximal, characteristic, complemented
12C103×#1918C211yesmaximal, characteristic, complemented
13C103×#1847C211yesmaximal, characteristic, complemented
14C103×#1804C211yesmaximal, characteristic
15C103×#1762C211yesmaximal, characteristic
16C2×C4×D4×C103C2211yescharacteristic
17C2×#117×C103—21no—
18C2×#107×C103C2211yescharacteristic
19C2×#107×C103C2211yescharacteristic
20C2×#106×C103C2211yescharacteristic
21C2×#106×C103C2211yescharacteristic
22C2×#106×C103C2211yescharacteristic
23C2×#106×C103C2211yescharacteristic
24C2×C4⋊C8×C103C2211yescharacteristic
25C2×C4⋊C8×C103C2211yescharacteristic
26C2×C4⋊C8×C103C2211yescharacteristic
27C2×#102×C103C2211yescharacteristic
28C2×#102×C103C2211yescharacteristic
29C2×#102×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#97×C103C2211yescharacteristic
32#400×C103—21no—
33#398×C103—21no—
34#390×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#384×C103C2211yescharacteristic
43#384×C103C2211yescharacteristic
44#382×C103C2211yescharacteristic
45#382×C103C2211yescharacteristic
46#380×C103—21no—
47C4×C4⋊C4×C103C2211yescharacteristic
48C4×C4⋊C4×C103C2211yescharacteristic
49C4×C4⋊C4×C103C2211yescharacteristic
50C4×C4⋊C4×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×D4×C103C2311yescharacteristic
60C23×C4×C103—21no—
61C22×C8×C103C2311yescharacteristic
62C22×C8×C103C2311yescharacteristic
63C22×C8×C103C2311yescharacteristic
64C22×C8×C103C2311yescharacteristic
65C4×D4×C103—22no—
66C4×D4×C103Q814yes—
67#117×C103—44no—
68C2×C4⋊C4×C103—21no—
69C2×C4⋊C4×C103—21no—
70C2×C4⋊C4×C103—21no—
71C2×C4⋊C4×C103—21no—
72C2×C4⋊C4×C103—21no—
73C2×C4⋊C4×C103—21no—
74C2×C4⋊C4×C103D411yescharacteristic
75C2×C4⋊C4×C103D411yescharacteristic
76C2×C4⋊C4×C103C2311yescharacteristic
77C2×C4⋊C4×C103C2311yescharacteristic
78C2×C4⋊C4×C103C2311yescharacteristic
79C2×C4⋊C4×C103C2311yescharacteristic
80C2×C4⋊C4×C103C2311yescharacteristic
81C2×C4⋊C4×C103C2311yescharacteristic
82C2×C4⋊C4×C103C2311yescharacteristic
83C2×C22⋊C4×C103—21no—
84C2×C22⋊C4×C103—21no—
85C2×C22⋊C4×C103—21no—
86C2×C22⋊C4×C103—21no—
87C2×C22⋊C4×C103—21no—
88C2×C42×C103—21no—
89C2×C42×C103—21no—
90C2×C42×C103—21no—
91C2×C42×C103C2311yescharacteristic
92C2×C42×C103C2311yescharacteristic
93C2×C42×C103C2311yescharacteristic
94#107×C103—22no—
95#107×C103—41no—
96#106×C103—22no—
97#106×C103—41no—
98#106×C103—41no—
99#106×C103—41no—
100C4⋊C8×C103—22no—
101C4⋊C8×C103—22no—
102C4⋊C8×C103—22no—
103#102×C103—22no—
104#102×C103—22no—
105#102×C103—41no—
106#102×C103—41no—
107#97×C103—22no—
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×C103—21no—
117#95×C103D411yescharacteristic
118#95×C103D411yescharacteristic
119C24×C103—21no—
120C2×D4×C103—21no—
121C2×D4×C103—21no—
122C2×D4×C103—21no—
123C2×D4×C103—21no—
124C2×D4×C103—21no—
125C2×D4×C103C2×Q812yes—
126C22×C4×C103—21no—
127C22×C4×C103—24no—
128C22×C4×C103—21no—
129C22×C4×C103—21no—
130C22×C4×C103—21no—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
134C22×C4×C103—42no—
135C22×C4×C103—42no—
136C22×C4×C103C2×D411yescharacteristic
137C22×C4×C103C2×D411yescharacteristic
138C22×C4×C103C2×D411yescharacteristic
139C22×C4×C103C2×D411yescharacteristic
140C22×C4×C103C2×D411yescharacteristic
141C22×C4×C103C2×D411yescharacteristic
142C22×C4×C103C2411yescharacteristic
143C2×C8×C103—21no—
144C2×C8×C103—21no—
145C2×C8×C103—21no—
146C2×C8×C103—21no—
147C2×C8×C103—21no—
148C2×C8×C103—21no—
149C2×C8×C103—21no—
150C2×C8×C103—21no—
151C2×C8×C103—21no—
152C2×C8×C103—21no—
153C2×C8×C103#4112yes—
154C2×C8×C103#4112yes—
155C4⋊C4×C103—22no—
156C4⋊C4×C103—21no—
157C4⋊C4×C103—21no—
158C4⋊C4×C103—21no—
159C4⋊C4×C103—21no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—21no—
163C4⋊C4×C103—21no—
164C4⋊C4×C103—21no—
165C4⋊C4×C103—21no—
166C4⋊C4×C103—21no—
167C4⋊C4×C103—21no—
168C4⋊C4×C103—21no—
169C4⋊C4×C103—41no—
170C4⋊C4×C103—42no—
171C4⋊C4×C103—42no—
172C4⋊C4×C103—42no—
173C4⋊C4×C103—81no—
174C4⋊C4×C103—81no—
175C4⋊C4×C103—81no—
176C4⋊C4×C103C2×Q812yes—
177C22⋊C4×C103—24no—
178C22⋊C4×C103—42no—
179C22⋊C4×C103—42no—
180C22⋊C4×C103—81no—
181C22⋊C4×C103—81no—
182C42×C103—21no—
183C42×C103—21no—
184C42×C103—21no—
185C42×C103—21no—
186C42×C103—42no—
187C42×C103—42no—
188C42×C103—81no—
189C42×C103C2×Q812yes—
190C42×C103#4112yes—
191C23×C103—22no—
192C23×C103—41no—
193C23×C103—41no—
194C23×C103—41no—
195C23×C103—41no—
196C23×C103—41no—
197C23×C103—41no—
198C23×C103C22×D411yescharacteristic
199D4×C103—22no—
200D4×C103—22no—
201D4×C103—41no—
202D4×C103—41no—
203C2×C4×C103—21no—
204C2×C4×C103—21no—
205C2×C4×C103—21no—
206C2×C4×C103—21no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—22no—
210C2×C4×C103—21no—
211C2×C4×C103—21no—
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—21no—
219C2×C4×C103—48no—
220C2×C4×C103—41no—
221C2×C4×C103—41no—
222C2×C4×C103—41no—
223C2×C4×C103—41no—
224C2×C4×C103—41no—
225C2×C4×C103—41no—
226C2×C4×C103—41no—
227C2×C4×C103—41no—
228C2×C4×C103—41no—
229C2×C4×C103—41no—
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×C103C22⋊Q812yes—
241C2×C4×C103C22⋊Q812yes—
242C2×C4×C103AGL(1,ℤ/8)12yes—
243C2×C4×C103C22×Q811yescharacteristic
244C2×C4×C103C2×#4111yescharacteristic
245C2×C4×C103C2×#4111yescharacteristic
246C2×C4×C103C2×#4111yescharacteristic
247C2×C4×C103H(5,𝔽2)11yescharacteristic
248C2×C4×C1032−1+411yescharacteristic
249C8×C103—22no—
250C8×C103—22no—
251C8×C103—41no—
252C8×C103—41no—
253C22×C103—42no—
254C22×C103—42no—
255C22×C103—42no—
256C22×C103—81no—
257C22×C103—81no—
258C22×C103—81no—
259C22×C103—81no—
260C22×C103C2×C22⋊Q811yescharacteristic
261C22×C103#54711yescharacteristic
262C22×C103#55011yescharacteristic
263C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C103#57511yescharacteristic
265C22×C103#57711yescharacteristic
266C22×C103#57711yescharacteristic
267C4×C103—22no—
268C4×C103—22no—
269C4×C103—22no—
270C4×C103—42no—
271C4×C103—41no—
272C4×C103—41no—
273C4×C103—41no—
274C4×C103—81no—
275C4×C103—81no—
276C4×C103—81no—
277C4×C103—81no—
278C4×C103—81no—
279C4×C103—81no—
280C4×C103#53311yescharacteristic
281C4×C103#54411yescharacteristic
282C4×C103#55211yescharacteristic
283C4×C103#55311yescharacteristic
284#26099C10311yesmaximal, characteristic, direct product factor, Sylow
285C2×C103—82no—
286C2×C103#244111yescharacteristic
287C2×C103#307711yescharacteristic
288C2×C103#308411yescharacteristic
289C2×C103#334511yescharacteristic
290C2×C103#334811yescharacteristic
291C2×C103#339711yescharacteristic
292C2×C103#340111yescharacteristic
293#2570C2×C10311yescharacteristic, complemented
294#2354C2×C10311yescharacteristic
295#2094C2×C10311yescharacteristic
296#2092C2×C10311yescharacteristic
297#2067C2×C10311yescharacteristic
298#2065C2×C10311yescharacteristic
299#1949C2×C10311yescharacteristic, complemented
300#1948C2×C10311yescharacteristic, complemented
301#1948C2×C10311yescharacteristic, complemented
302#1940C2×C10311yescharacteristic, complemented
303#1919C2×C10311yescharacteristic, complemented
304#1918C2×C10311yescharacteristic, complemented
305#1847C2×C10311yescharacteristic, complemented
306#1804C2×C10311yescharacteristic
307#1762C2×C10311yescharacteristic
308C103#2609911yescharacteristic, direct product factor, Sylow
309C2×C4×D4C22×C10311yescharacteristic
310C2×#117—21no—
311C2×#107C22×C10311yescharacteristic
312C2×#107C22×C10311yescharacteristic
313C2×#106C22×C10311yescharacteristic
314C2×#106C22×C10311yescharacteristic
315C2×#106C22×C10311yescharacteristic
316C2×#106C22×C10311yescharacteristic
317C2×C4⋊C8C22×C10311yescharacteristic
318C2×C4⋊C8C22×C10311yescharacteristic
319C2×C4⋊C8C22×C10311yescharacteristic
320C2×#102C22×C10311yescharacteristic
321C2×#102C22×C10311yescharacteristic
322C2×#102C22×C10311yescharacteristic
323C2×#102C22×C10311yescharacteristic
324C2×#97C22×C10311yescharacteristic
325#400—21no—
326#398—21no—
327#390C22×C10311yescharacteristic
328#390C22×C10311yescharacteristic
329#389C22×C10311yescharacteristic
330#389C22×C10311yescharacteristic
331#388—21no—
332#388—21no—
333#387—21no—
334#387—21no—
335#384C22×C10311yescharacteristic
336#384C22×C10311yescharacteristic
337#382C22×C10311yescharacteristic
338#382C22×C10311yescharacteristic
339#380—21no—
340C4×C4⋊C4C22×C10311yescharacteristic
341C4×C4⋊C4C22×C10311yescharacteristic
342C4×C4⋊C4C22×C10311yescharacteristic
343C4×C4⋊C4C22×C10311yescharacteristic
344#340C22×C10311yescharacteristic
345#340C22×C10311yescharacteristic
346#340C22×C10311yescharacteristic
347#340C22×C10311yescharacteristic
348#340C22×C10311yescharacteristic
349#340C22×C10311yescharacteristic
350#336C22×C10311yescharacteristic
351#336C22×C10311yescharacteristic
352C22×D4C23×C10311yescharacteristic
353C23×C4—21no—
354C22×C8C23×C10311yescharacteristic
355C22×C8C23×C10311yescharacteristic
356C22×C8C23×C10311yescharacteristic
357C22×C8C23×C10311yescharacteristic
358C4×D4—22no—
359C4×D4Q8×C10314yes—
360#117—44no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C10311yescharacteristic
368C2×C4⋊C4D4×C10311yescharacteristic
369C2×C4⋊C4C23×C10311yescharacteristic
370C2×C4⋊C4C23×C10311yescharacteristic
371C2×C4⋊C4C23×C10311yescharacteristic
372C2×C4⋊C4C23×C10311yescharacteristic
373C2×C4⋊C4C23×C10311yescharacteristic
374C2×C4⋊C4C23×C10311yescharacteristic
375C2×C4⋊C4C23×C10311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42C23×C10311yescharacteristic
385C2×C42C23×C10311yescharacteristic
386C2×C42C23×C10311yescharacteristic
387#107—22no—
388#107—41no—
389#106—22no—
390#106—41no—
391#106—41no—
392#106—41no—
393C4⋊C8—22no—
394C4⋊C8—22no—
395C4⋊C8—22no—
396#102—22no—
397#102—22no—
398#102—41no—
399#102—41no—
400#97—22no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95D4×C10311yescharacteristic
411#95D4×C10311yescharacteristic
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×Q8×C10312yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4C2×D4×C10311yescharacteristic
430C22×C4C2×D4×C10311yescharacteristic
431C22×C4C2×D4×C10311yescharacteristic
432C22×C4C2×D4×C10311yescharacteristic
433C22×C4C2×D4×C10311yescharacteristic
434C22×C4C2×D4×C10311yescharacteristic
435C22×C4C24×C10311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8#41×C10312yes—
447C2×C8#41×C10312yes—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—81no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4C2×Q8×C10312yes—
470C22⋊C4—24no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—42no—
481C42—81no—
482C42C2×Q8×C10312yes—
483C42#41×C10312yes—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C22×D4×C10311yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—48no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4C22⋊Q8×C10312yes—
534C2×C4C22⋊Q8×C10312yes—
535C2×C4AGL(1,ℤ/8)×C10312yes—
536C2×C4C22×Q8×C10311yescharacteristic
537C2×C4C2×#41×C10311yescharacteristic
538C2×C4C2×#41×C10311yescharacteristic
539C2×C4C2×#41×C10311yescharacteristic
540C2×C4H(5,𝔽2)×C10311yescharacteristic
541C2×C42−1+4×C10311yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×C22⋊Q8×C10311yescharacteristic
554C22#547×C10311yescharacteristic
555C22#550×C10311yescharacteristic
556C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
557C22#575×C10311yescharacteristic
558C22#577×C10311yescharacteristic
559C22#577×C10311yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4#533×C10311yescharacteristic
574C4#544×C10311yescharacteristic
575C4#552×C10311yescharacteristic
576C4#553×C10311yescharacteristic
577C2—82no—
578C2C103×#244111yescharacteristic
579C2C103×#307711yescharacteristic
580C2C103×#308411yescharacteristic
581C2C103×#334511yescharacteristic
582C2C103×#334811yescharacteristic
583C2C103×#339711yescharacteristic
584C2C103×#340111yescharacteristic
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. C103×#2570C2semidirect
7. C103×#1949C2semidirect
8. C103×#1948C2semidirect
9. C103×#1948C2semidirect
10. C103×#1940C2semidirect
11. C103×#1919C2semidirect
12. C103×#1918C2semidirect
13. C103×#1847C2semidirect
284. #26099C103direct (N × H)
293. #2570C2×C103semidirect
299. #1949C2×C103semidirect
300. #1948C2×C103semidirect
301. #1948C2×C103semidirect
302. #1940C2×C103semidirect
303. #1919C2×C103semidirect
304. #1918C2×C103semidirect
305. #1847C2×C103semidirect
308. C103#26099direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#25702
C103×#23542
C103×#20942
C103×#20922
C103×#20672
C103×#20652
C103×#19492
C103×#19482
C103×#19402
C103×#19192
C103×#19182
C103×#18472
C103×#18042
C103×#17622
#26099103