Finite Group Databasebeta

← C103×#26079 #39931354

Subgroups — C103×#26079 #39931354

Order 26368.

782 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#501×C103C211yesmaximal, characteristic, complemented
2C2×#428×C103C211yesmaximal, characteristic
3C103×#2442C211yesmaximal, characteristic
4C103×#2439C211yesmaximal, characteristic
5C103×#2085C211yesmaximal, characteristic, complemented
6C103×#2085C211yesmaximal, characteristic, complemented
7C103×#2059C211yesmaximal, characteristic, complemented
8C103×#2057C211yesmaximal, characteristic, complemented
9C103×#1943C211yesmaximal, characteristic, complemented
10C103×#1942C211yesmaximal, characteristic, complemented
11C103×#1854C211yesmaximal, characteristic
12C103×#1852C211yesmaximal, characteristic
13C103×#1846C211yesmaximal, characteristic, complemented
14C103×#1809C211yesmaximal, characteristic
15C103×#1753C211yesmaximal, characteristic
16C22×M16×C103C2211yescharacteristic
17C2×C4⋊Q8×C103C2211yescharacteristic
18C2×#125×C103C2211yescharacteristic
19C2×#117×C103C2211yescharacteristic
20C22×C4⋊C4×C103C2211yescharacteristic
21#501×C103—24no—
22#428×C103—24no—
23C2×#107×C103C2211yescharacteristic
24C2×#107×C103C2211yescharacteristic
25C2×#107×C103C2211yescharacteristic
26C2×#107×C103C2211yescharacteristic
27C2×#107×C103C2211yescharacteristic
28C2×#107×C103C2211yescharacteristic
29C2×#106×C103C2211yescharacteristic
30C2×#106×C103C2211yescharacteristic
31C2×#106×C103C2211yescharacteristic
32C2×#106×C103C2211yescharacteristic
33C2×C22⋊C8×C103C2211yescharacteristic
34C2×#97×C103C2211yescharacteristic
35C2×C4×C8×C103C2211yescharacteristic
36#400×C103—21no—
37#398×C103—21no—
38#396×C103—21no—
39#393×C103—21no—
40#391×C103—21no—
41#389×C103C2211yescharacteristic
42#389×C103C2211yescharacteristic
43#389×C103C2211yescharacteristic
44#389×C103C2211yescharacteristic
45#387×C103—21no—
46#385×C103—21no—
47#382×C103C2211yescharacteristic
48#382×C103C2211yescharacteristic
49#380×C103—21no—
50#380×C103C2211yescharacteristic
51#380×C103C2211yescharacteristic
52C4×C22⋊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—
62C23×C4×C103—21no—
63C23×C4×C103C2311yescharacteristic
64C2×M16×C103—22no—
65C2×M16×C103—22no—
66C2×M16×C103Q814yescomplemented
67C22×C8×C103C2311yescharacteristic
68C22×C8×C103C2311yescharacteristic
69C22×C8×C103C2311yescharacteristic
70C22×C8×C103C2311yescharacteristic
71C4⋊Q8×C103—22no—
72C4⋊Q8×C103—41no—
73#125×C103—22no—
74#125×C103—41no—
75#117×C103—22no—
76#117×C103—41no—
77C2×C4⋊C4×C103—22no—
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×C103—21no—
86C2×C4⋊C4×C103—41no—
87C2×C4⋊C4×C103C2311yescharacteristic
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×C103D411yescharacteristic
99C2×C22⋊C4×C103D411yescharacteristic
100C2×C42×C103—21no—
101C2×C42×C103C2311yescharacteristic
102C2×C42×C103C2311yescharacteristic
103#107×C103—22no—
104#107×C103—22no—
105#107×C103—22no—
106#107×C103—41no—
107#107×C103—41no—
108#107×C103D414yes—
109#106×C103—22no—
110#106×C103—22no—
111#106×C103—22no—
112#106×C103—22no—
113C22⋊C8×C103Q814yescomplemented
114#97×C103—22no—
115C4×C8×C103—22no—
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—
124#95×C103—21no—
125#95×C103—21no—
126#95×C103D411yescharacteristic
127#95×C103D411yescharacteristic
128C24×C103C2×D411yescharacteristic
129C2×Q8×C103—42no—
130C2×Q8×C103—42no—
131C2×Q8×C103—81no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
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—21no—
142C22×C4×C103—21no—
143C22×C4×C103—21no—
144C22×C4×C103—42no—
145C22×C4×C103—42no—
146C22×C4×C103—81no—
147C22×C4×C103C2×D411yescharacteristic
148C22×C4×C103C2×D411yescharacteristic
149C22×C4×C103C2×D411yescharacteristic
150C22×C4×C103C2×D411yescharacteristic
151C22×C4×C103C2×D411yescharacteristic
152C22×C4×C103C2×Q812yes—
153C22×C4×C103C2×Q812yes—
154C22×C4×C103C2411yescharacteristic
155M16×C103—28no—
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×C103C2×D412yes—
163C2×C8×C103C2×Q812yes—
164C2×C8×C103C2×Q812yes—
165C2×C8×C103C2×Q812yes—
166C2×C8×C103C2×Q812yes—
167C2×C8×C103#4112yes—
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—21no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—21no—
182C4⋊C4×C103—42no—
183C4⋊C4×C103—42no—
184C4⋊C4×C103—42no—
185C4⋊C4×C103—42no—
186C4⋊C4×C103—42no—
187C4⋊C4×C103—81no—
188C4⋊C4×C103—81no—
189C4⋊C4×C103—81no—
190C4⋊C4×C103C2×D412yes—
191C4⋊C4×C103C2×D412yes—
192C22⋊C4×C103—41no—
193C22⋊C4×C103—41no—
194C22⋊C4×C103—42no—
195C22⋊C4×C103—42no—
196C22⋊C4×C103—81no—
197C42×C103—21no—
198C42×C103—21no—
199C42×C103—21no—
200C42×C103—21no—
201C42×C103—42no—
202C23×C103—21no—
203C23×C103—21no—
204C23×C103—21no—
205C23×C103—21no—
206C23×C103—21no—
207C23×C103—21no—
208C23×C103C4⋊Q812yes—
209C23×C103C22×D411yescharacteristic
210Q8×C103—84no—
211C2×C4×C103—21no—
212C2×C4×C103—21no—
213C2×C4×C103—22no—
214C2×C4×C103—22no—
215C2×C4×C103—22no—
216C2×C4×C103—22no—
217C2×C4×C103—21no—
218C2×C4×C103—21no—
219C2×C4×C103—22no—
220C2×C4×C103—22no—
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—21no—
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—41no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—84no—
254C2×C4×C103C4⋊Q812yes—
255C2×C4×C103C22×D411yescharacteristic
256C2×C4×C103C22×Q811yescharacteristic
257C2×C4×C103C22×Q811yescharacteristic
258C2×C4×C103C2×#4111yescharacteristic
259C2×C4×C103H(5,𝔽2)11yescharacteristic
260C2×C4×C1032−1+411yescharacteristic
261C8×C103—22no—
262C8×C103—22no—
263C8×C103—22no—
264C8×C103C22⋊Q814yes—
265C22×C103—22no—
266C22×C103—22no—
267C22×C103—22no—
268C22×C103—41no—
269C22×C103—41no—
270C22×C103—41no—
271C22×C103—41no—
272C22×C103C2×C4⋊Q811yescharacteristic
273C22×C103D4211yescharacteristic
274C22×C103#54711yescharacteristic
275C22×C103#57511yescharacteristic
276C22×C103#57511yescharacteristic
277C22×C103#57611yescharacteristic
278C22×C103#57811yescharacteristic
279C4×C103—22no—
280C4×C103—41no—
281C4×C103—41no—
282C4×C103—41no—
283C4×C103—42no—
284C4×C103—42no—
285C4×C103—41no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103—81no—
289C4×C103—81no—
290C4×C103—81no—
291C4×C103—81no—
292C4×C103C2×C22⋊Q811yescharacteristic
293C4×C103#54411yescharacteristic
294C4×C103D4×Q811yescharacteristic
295C4×C103#55411yescharacteristic
296#26079C10311yesmaximal, characteristic, direct product factor, Sylow
297C2×C103—42no—
298C2×C103#244011yescharacteristic
299C2×C103#316411yescharacteristic
300C2×C103#316611yescharacteristic
301C2×C103#327311yescharacteristic
302C2×C103#327711yescharacteristic
303C2×C103#334711yescharacteristic
304C2×C103#334911yescharacteristic
305C2×#501C2×C10311yescharacteristic, complemented
306C2×#428C2×C10311yescharacteristic
307#2442C2×C10311yescharacteristic
308#2439C2×C10311yescharacteristic
309#2085C2×C10311yescharacteristic, complemented
310#2085C2×C10311yescharacteristic, complemented
311#2059C2×C10311yescharacteristic, complemented
312#2057C2×C10311yescharacteristic, complemented
313#1943C2×C10311yescharacteristic, complemented
314#1942C2×C10311yescharacteristic, complemented
315#1854C2×C10311yescharacteristic
316#1852C2×C10311yescharacteristic
317#1846C2×C10311yescharacteristic, complemented
318#1809C2×C10311yescharacteristic
319#1753C2×C10311yescharacteristic
320C103#2607911yescharacteristic, direct product factor, Sylow
321C22×M16C22×C10311yescharacteristic
322C2×C4⋊Q8C22×C10311yescharacteristic
323C2×#125C22×C10311yescharacteristic
324C2×#117C22×C10311yescharacteristic
325C22×C4⋊C4C22×C10311yescharacteristic
326#501—24no—
327#428—24no—
328C2×#107C22×C10311yescharacteristic
329C2×#107C22×C10311yescharacteristic
330C2×#107C22×C10311yescharacteristic
331C2×#107C22×C10311yescharacteristic
332C2×#107C22×C10311yescharacteristic
333C2×#107C22×C10311yescharacteristic
334C2×#106C22×C10311yescharacteristic
335C2×#106C22×C10311yescharacteristic
336C2×#106C22×C10311yescharacteristic
337C2×#106C22×C10311yescharacteristic
338C2×C22⋊C8C22×C10311yescharacteristic
339C2×#97C22×C10311yescharacteristic
340C2×C4×C8C22×C10311yescharacteristic
341#400—21no—
342#398—21no—
343#396—21no—
344#393—21no—
345#391—21no—
346#389C22×C10311yescharacteristic
347#389C22×C10311yescharacteristic
348#389C22×C10311yescharacteristic
349#389C22×C10311yescharacteristic
350#387—21no—
351#385—21no—
352#382C22×C10311yescharacteristic
353#382C22×C10311yescharacteristic
354#380—21no—
355#380C22×C10311yescharacteristic
356#380C22×C10311yescharacteristic
357C4×C22⋊C4C22×C10311yescharacteristic
358#340C22×C10311yescharacteristic
359#340C22×C10311yescharacteristic
360#340C22×C10311yescharacteristic
361#340C22×C10311yescharacteristic
362#340C22×C10311yescharacteristic
363#340C22×C10311yescharacteristic
364#336C22×C10311yescharacteristic
365#336C22×C10311yescharacteristic
366C22×Q8—21no—
367C23×C4—21no—
368C23×C4C23×C10311yescharacteristic
369C2×M16—22no—
370C2×M16—22no—
371C2×M16Q8×C10314yescomplemented
372C22×C8C23×C10311yescharacteristic
373C22×C8C23×C10311yescharacteristic
374C22×C8C23×C10311yescharacteristic
375C22×C8C23×C10311yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—41no—
378#125—22no—
379#125—41no—
380#117—22no—
381#117—41no—
382C2×C4⋊C4—22no—
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⋊C4—41no—
392C2×C4⋊C4C23×C10311yescharacteristic
393C2×C4⋊C4C23×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×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4D4×C10311yescharacteristic
404C2×C22⋊C4D4×C10311yescharacteristic
405C2×C42—21no—
406C2×C42C23×C10311yescharacteristic
407C2×C42C23×C10311yescharacteristic
408#107—22no—
409#107—22no—
410#107—22no—
411#107—41no—
412#107—41no—
413#107D4×C10314yes—
414#106—22no—
415#106—22no—
416#106—22no—
417#106—22no—
418C22⋊C8Q8×C10314yescomplemented
419#97—22no—
420C4×C8—22no—
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—
431#95D4×C10311yescharacteristic
432#95D4×C10311yescharacteristic
433C24C2×D4×C10311yescharacteristic
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—81no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—81no—
452C22×C4C2×D4×C10311yescharacteristic
453C22×C4C2×D4×C10311yescharacteristic
454C22×C4C2×D4×C10311yescharacteristic
455C22×C4C2×D4×C10311yescharacteristic
456C22×C4C2×D4×C10311yescharacteristic
457C22×C4C2×Q8×C10312yes—
458C22×C4C2×Q8×C10312yes—
459C22×C4C24×C10311yescharacteristic
460M16—28no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C2×D4×C10312yes—
468C2×C8C2×Q8×C10312yes—
469C2×C8C2×Q8×C10312yes—
470C2×C8C2×Q8×C10312yes—
471C2×C8C2×Q8×C10312yes—
472C2×C8#41×C10312yes—
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—21no—
486C4⋊C4—21no—
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×D4×C10312yes—
496C4⋊C4C2×D4×C10312yes—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C22⋊C4—81no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23C4⋊Q8×C10312yes—
514C23C22×D4×C10311yescharacteristic
515Q8—84no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
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—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×C4C4⋊Q8×C10312yes—
560C2×C4C22×D4×C10311yescharacteristic
561C2×C4C22×Q8×C10311yescharacteristic
562C2×C4C22×Q8×C10311yescharacteristic
563C2×C4C2×#41×C10311yescharacteristic
564C2×C4H(5,𝔽2)×C10311yescharacteristic
565C2×C42−1+4×C10311yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8C22⋊Q8×C10314yes—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22C2×C4⋊Q8×C10311yescharacteristic
578C22D42×C10311yescharacteristic
579C22#547×C10311yescharacteristic
580C22#575×C10311yescharacteristic
581C22#575×C10311yescharacteristic
582C22#576×C10311yescharacteristic
583C22#578×C10311yescharacteristic
584C4—22no—
585C4—41no—
586C4—42no—
587C4—42no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C2×C22⋊Q8×C10311yescharacteristic
598C4#544×C10311yescharacteristic
599C4D4×Q8×C10311yescharacteristic
600C4#554×C10311yescharacteristic
601C2—42no—
602C2C103×#244011yescharacteristic
603C2C103×#316411yescharacteristic
604C2C103×#316611yescharacteristic
605C2C103×#327311yescharacteristic
606C2C103×#327711yescharacteristic
607C2C103×#334711yescharacteristic
608C2C103×#334911yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C22⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#501×C103C2semidirect
5. C103×#2085C2semidirect
6. C103×#2085C2semidirect
7. C103×#2059C2semidirect
8. C103×#2057C2semidirect
9. C103×#1943C2semidirect
10. C103×#1942C2semidirect
13. C103×#1846C2semidirect
66. C2×M16×C103Q8semidirect
113. C22⋊C8×C103Q8semidirect
296. #26079C103direct (N × H)
305. C2×#501C2×C103semidirect
309. #2085C2×C103semidirect
310. #2085C2×C103semidirect
311. #2059C2×C103semidirect
312. #2057C2×C103semidirect
313. #1943C2×C103semidirect
314. #1942C2×C103semidirect
317. #1846C2×C103semidirect
320. C103#26079direct (N × H)
371. C2×M16Q8×C103semidirect
418. C22⋊C8Q8×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×#428×C1032
C103×#24422
C103×#24392
C103×#20852
C103×#20592
C103×#20572
C103×#19432
C103×#19422
C103×#18542
C103×#18522
C103×#18462
C103×#18092
C103×#17532
#26079103