Finite Group Databasebeta

← C103×#33864 #39939139

Subgroups — C103×#33864 #39939139

Order 26368.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3339C211yesmaximal, characteristic, complemented
2C103×#3280C211yesmaximal, characteristic, complemented
3C103×#2242C211yesmaximal, characteristic, complemented
4C103×#2236C211yesmaximal, characteristic, complemented
5C103×#2234C211yesmaximal, characteristic, complemented
6C103×#2228C211yesmaximal, characteristic, complemented
7C103×#2217C211yesmaximal, characteristic, complemented
8C103×#2215C211yesmaximal, characteristic, complemented
9C103×#2210C211yesmaximal, characteristic, complemented
10C103×#2186C211yesmaximal, characteristic, complemented
11C103×#2184C211yesmaximal, characteristic, complemented
12C4×D16×C103C211yesmaximal, characteristic, complemented
13D4×C16×C103C211yesmaximal, characteristic, complemented
14C103×#2138C211yesmaximal, characteristic, complemented
15C2×#357×C103C211yesmaximal, characteristic, complemented
16C2×#135×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18#553×C103—21no—
19#546×C103—21no—
20C2×SD32×C103C2211yescharacteristic, complemented
21C2×D16×C103C2211yescharacteristic
22C2×D16×C103C2211yescharacteristic
23C22×C16×C103C2211yescharacteristic
24C22×C16×C103C2211yescharacteristic, complemented
25#499×C103C2211yescharacteristic, complemented
26#495×C103C2211yescharacteristic
27#482×C103—21no—
28#481×C103—21no—
29#478×C103—21no—
30#467×C103C2211yescharacteristic
31#466×C103C2211yescharacteristic
32#466×C103C2211yescharacteristic
33#466×C103C2211yescharacteristic, complemented
34#463×C103—21no—
35#450×C103—21no—
36#449×C103—21no—
37C4×D8×C103C2211yescharacteristic
38C4×D8×C103C2211yescharacteristic, complemented
39C8×D4×C103C2211yescharacteristic
40#427×C103C2211yescharacteristic, complemented
41C2×#107×C103C2211yescharacteristic
42#367×C103C2211yescharacteristic, complemented
43#366×C103C2211yescharacteristic, complemented
44#366×C103C2211yescharacteristic, complemented
45C4⋊C16×C103C2211yescharacteristic, complemented
46#358×C103C2211yescharacteristic, complemented
47#358×C103C2211yescharacteristic, complemented
48#358×C103C2211yescharacteristic, complemented
49#357×C103C2211yescharacteristic
50#357×C103C2211yescharacteristic
51#357×C103C2211yescharacteristic
52#357×C103C2211yescharacteristic
53#357×C103C2211yescharacteristic
54#357×C103C2211yescharacteristic
55#357×C103C2211yescharacteristic, complemented
56C22⋊C16×C103C2211yescharacteristic
57C22⋊C16×C103C2211yescharacteristic, complemented
58C4×C16×C103C2211yescharacteristic, complemented
59C2×#41×C103—21no—
60C22×D4×C103—21no—
61#135×C103—22no—
62#135×C103—41no—
63C2×Q16×C103C2311yescharacteristic
64C2×SD16×C103—21no—
65C2×SD16×C103—21no—
66C2×D8×C103—22no—
67C2×D8×C103—21no—
68C2×D8×C103—41no—
69C2×D8×C103C2311yescharacteristic
70C2×D8×C103C2311yescharacteristic
71C2×D8×C103C2311yescharacteristic
72C22×C8×C103C2311yescharacteristic
73C22×C8×C103C2311yescharacteristic
74#126×C103—41no—
75#125×C103—21no—
76#124×C103—21no—
77#123×C103—41no—
78#123×C103—41no—
79C22⋊Q8×C103—21no—
80#121×C103—21no—
81#121×C103—21no—
82#121×C103—21no—
83#121×C103—41no—
84#121×C103—41no—
85#120×C103—41no—
86C4×D4×C103—21no—
87C4×D4×C103—21no—
88C4×D4×C103—41no—
89C4×D4×C103D411yescharacteristic
90#117×C103—21no—
91C2×C4⋊C4×C103—21no—
92C2×C22⋊C4×C103—41no—
93SD32×C103—41no—
94D16×C103—22no—
95D16×C103—41no—
96C2×C16×C103—41no—
97C2×C16×C103—41no—
98C2×C16×C103C2311yescharacteristic
99C2×C16×C103C2311yescharacteristic
100C2×C16×C103C2311yescharacteristic
101C2×C16×C103C2311yescharacteristic
102#107×C103—21no—
103#107×C103C2311yescharacteristic
104#107×C103C2311yescharacteristic
105#107×C103C2311yescharacteristic
106#107×C103C2311yescharacteristic
107#106×C103—21no—
108#106×C103—21no—
109C4⋊C8×C103D411yescharacteristic
110#103×C103—21no—
111#102×C103—21no—
112#102×C103—21no—
113#102×C103—21no—
114#102×C103—21no—
115#102×C103—21no—
116C22⋊C8×C103D411yescharacteristic
117C22⋊C8×C103D411yescharacteristic
118C4×C8×C103C2311yescharacteristic
119C24×C103—41no—
120#41×C103—42no—
121#41×C103—81no—
122C2×Q8×C103—21no—
123C2×D4×C103—21no—
124C2×D4×C103—21no—
125C2×D4×C103—21no—
126C2×D4×C103—42no—
127C2×D4×C103—41no—
128C2×D4×C103—41no—
129C2×D4×C103—41no—
130C2×D4×C103—41no—
131C2×D4×C103—41no—
132C2×D4×C103—81no—
133C2×D4×C103D811yescharacteristic
134C22×C4×C103—41no—
135C22×C4×C103—41no—
136C22×C4×C103—41no—
137C22×C4×C103—41no—
138C22×C4×C103C2×D411yescharacteristic
139C22×C4×C103C2×D411yescharacteristic
140Q16×C103—21no—
141Q16×C103—21no—
142SD16×C103—42no—
143SD16×C103—81no—
144D8×C103—21no—
145D8×C103—21no—
146D8×C103—21no—
147D8×C103—21no—
148D8×C103—21no—
149D8×C103—42no—
150D8×C103#4112yes—
151C2×C8×C103—21no—
152C2×C8×C103—21no—
153C2×C8×C103—21no—
154C2×C8×C103—21no—
155C2×C8×C103C2×D411yescharacteristic
156C2×C8×C103C2×D411yescharacteristic
157C2×C8×C103C2×D411yescharacteristic
158C2×C8×C103C2411yescharacteristic
159C4⋊C4×C103—21no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—21no—
163C4⋊C4×C103—41no—
164C4⋊C4×C103—41no—
165C4⋊C4×C103—41no—
166C4⋊C4×C103—41no—
167C4⋊C4×C103D811yescharacteristic
168C22⋊C4×C103—41no—
169C22⋊C4×C103—41no—
170C22⋊C4×C103—41no—
171C22⋊C4×C103—41no—
172C22⋊C4×C103—41no—
173C22⋊C4×C103—41no—
174C22⋊C4×C103—41no—
175C22⋊C4×C103—41no—
176C22⋊C4×C103—41no—
177C22⋊C4×C103D811yescharacteristic
178C22⋊C4×C103D811yescharacteristic
179C42×C103—41no—
180C42×C103C2×D411yescharacteristic
181C16×C103—21no—
182C16×C103—21no—
183C16×C103—21no—
184C16×C103—21no—
185C23×C103—41no—
186C23×C103—41no—
187C23×C103—41no—
188C23×C103—82no—
189C23×C103—82no—
190C23×C103—161no—
191C23×C103C2×D811yescharacteristic
192C23×C103C2×D811yescharacteristic
193Q8×C103—41no—
194Q8×C103—41no—
195D4×C103—22no—
196D4×C103—22no—
197D4×C103—41no—
198D4×C103—41no—
199D4×C103—41no—
200D4×C103—41no—
201D4×C103—41no—
202D4×C103—82no—
203D4×C103—82no—
204D4×C103—82no—
205D4×C103—161no—
206D4×C103—161no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—21no—
210C2×C4×C103—21no—
211C2×C4×C103—41no—
212C2×C4×C103—41no—
213C2×C4×C103—41no—
214C2×C4×C103—41no—
215C2×C4×C103—41no—
216C2×C4×C103—82no—
217C2×C4×C103—161no—
218C2×C4×C103—161no—
219C2×C4×C103—161no—
220C2×C4×C103C2×D811yescharacteristic
221C2×C4×C103C2×D811yescharacteristic
222C2×C4×C103C2×D811yescharacteristic
223C2×C4×C103C2×D811yescharacteristic
224C2×C4×C103C22×D411yescharacteristic
225C8×C103—21no—
226C8×C103—21no—
227C8×C103—21no—
228C8×C103C2×#4111yescharacteristic
229C8×C103H(5,𝔽2)11yescharacteristic
230C22×C103—21no—
231C22×C103—21no—
232C22×C103—21no—
233C22×C103—21no—
234C22×C103—21no—
235C22×C103—42no—
236C22×C103—81no—
237C22×C103—81no—
238C22×C103—81no—
239C22×C103—81no—
240C22×C103—81no—
241C22×C103—81no—
242C22×C103—81no—
243C22×C103—81no—
244C22×C103—164no—
245C22×C103#50812yes—
246C22×C103C22×D811yescharacteristic
247C4×C103—21no—
248C4×C103—21no—
249C4×C103—21no—
250C4×C103—21no—
251C4×C103—81no—
252C4×C103—81no—
253C4×C103—81no—
254C4×C103—81no—
255C4×C103—81no—
256C4×C103#54611yescharacteristic
257C4×C103#57711yescharacteristic
258#33864C10311yesmaximal, characteristic, direct product factor, Sylow
259C2×C103—22no—
260C2×C103—41no—
261C2×C103—82no—
262C2×C103—161no—
263C2×C103—161no—
264C2×C103#329411yescharacteristic
265C2×C103C2×#50811yescharacteristic
266C2×C103#341511yescharacteristic
267#3339C2×C10311yescharacteristic, complemented
268#3280C2×C10311yescharacteristic, complemented
269#2242C2×C10311yescharacteristic, complemented
270#2236C2×C10311yescharacteristic, complemented
271#2234C2×C10311yescharacteristic, complemented
272#2228C2×C10311yescharacteristic, complemented
273#2217C2×C10311yescharacteristic, complemented
274#2215C2×C10311yescharacteristic, complemented
275#2210C2×C10311yescharacteristic, complemented
276#2186C2×C10311yescharacteristic, complemented
277#2184C2×C10311yescharacteristic, complemented
278C4×D16C2×C10311yescharacteristic, complemented
279D4×C16C2×C10311yescharacteristic, complemented
280#2138C2×C10311yescharacteristic, complemented
281C2×#357C2×C10311yescharacteristic, complemented
282C103#3386411yescharacteristic, direct product factor, Sylow
283C2×#135C22×C10311yescharacteristic
284C22×D8C22×C10311yescharacteristic
285#553—21no—
286#546—21no—
287C2×SD32C22×C10311yescharacteristic, complemented
288C2×D16C22×C10311yescharacteristic
289C2×D16C22×C10311yescharacteristic
290C22×C16C22×C10311yescharacteristic
291C22×C16C22×C10311yescharacteristic, complemented
292#499C22×C10311yescharacteristic, complemented
293#495C22×C10311yescharacteristic
294#482—21no—
295#481—21no—
296#478—21no—
297#467C22×C10311yescharacteristic
298#466C22×C10311yescharacteristic
299#466C22×C10311yescharacteristic
300#466C22×C10311yescharacteristic, complemented
301#463—21no—
302#450—21no—
303#449—21no—
304C4×D8C22×C10311yescharacteristic
305C4×D8C22×C10311yescharacteristic, complemented
306C8×D4C22×C10311yescharacteristic
307#427C22×C10311yescharacteristic, complemented
308C2×#107C22×C10311yescharacteristic
309#367C22×C10311yescharacteristic, complemented
310#366C22×C10311yescharacteristic, complemented
311#366C22×C10311yescharacteristic, complemented
312C4⋊C16C22×C10311yescharacteristic, complemented
313#358C22×C10311yescharacteristic, complemented
314#358C22×C10311yescharacteristic, complemented
315#358C22×C10311yescharacteristic, complemented
316#357C22×C10311yescharacteristic
317#357C22×C10311yescharacteristic
318#357C22×C10311yescharacteristic
319#357C22×C10311yescharacteristic
320#357C22×C10311yescharacteristic
321#357C22×C10311yescharacteristic
322#357C22×C10311yescharacteristic, complemented
323C22⋊C16C22×C10311yescharacteristic
324C22⋊C16C22×C10311yescharacteristic, complemented
325C4×C16C22×C10311yescharacteristic, complemented
326C2×#41—21no—
327C22×D4—21no—
328#135—22no—
329#135—41no—
330C2×Q16C23×C10311yescharacteristic
331C2×SD16—21no—
332C2×SD16—21no—
333C2×D8—22no—
334C2×D8—21no—
335C2×D8—41no—
336C2×D8C23×C10311yescharacteristic
337C2×D8C23×C10311yescharacteristic
338C2×D8C23×C10311yescharacteristic
339C22×C8C23×C10311yescharacteristic
340C22×C8C23×C10311yescharacteristic
341#126—41no—
342#125—21no—
343#124—21no—
344#123—41no—
345#123—41no—
346C22⋊Q8—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—41no—
351#121—41no—
352#120—41no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—41no—
356C4×D4D4×C10311yescharacteristic
357#117—21no—
358C2×C4⋊C4—21no—
359C2×C22⋊C4—41no—
360SD32—41no—
361D16—22no—
362D16—41no—
363C2×C16—41no—
364C2×C16—41no—
365C2×C16C23×C10311yescharacteristic
366C2×C16C23×C10311yescharacteristic
367C2×C16C23×C10311yescharacteristic
368C2×C16C23×C10311yescharacteristic
369#107—21no—
370#107C23×C10311yescharacteristic
371#107C23×C10311yescharacteristic
372#107C23×C10311yescharacteristic
373#107C23×C10311yescharacteristic
374#106—21no—
375#106—21no—
376C4⋊C8D4×C10311yescharacteristic
377#103—21no—
378#102—21no—
379#102—21no—
380#102—21no—
381#102—21no—
382#102—21no—
383C22⋊C8D4×C10311yescharacteristic
384C22⋊C8D4×C10311yescharacteristic
385C4×C8C23×C10311yescharacteristic
386C24—41no—
387#41—42no—
388#41—81no—
389C2×Q8—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—42no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—81no—
400C2×D4D8×C10311yescharacteristic
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4C2×D4×C10311yescharacteristic
406C22×C4C2×D4×C10311yescharacteristic
407Q16—21no—
408Q16—21no—
409SD16—42no—
410SD16—81no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—42no—
417D8#41×C10312yes—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8C2×D4×C10311yescharacteristic
423C2×C8C2×D4×C10311yescharacteristic
424C2×C8C2×D4×C10311yescharacteristic
425C2×C8C24×C10311yescharacteristic
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4D8×C10311yescharacteristic
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4D8×C10311yescharacteristic
445C22⋊C4D8×C10311yescharacteristic
446C42—41no—
447C42C2×D4×C10311yescharacteristic
448C16—21no—
449C16—21no—
450C16—21no—
451C16—21no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—82no—
456C23—82no—
457C23—161no—
458C23C2×D8×C10311yescharacteristic
459C23C2×D8×C10311yescharacteristic
460Q8—41no—
461Q8—41no—
462D4—22no—
463D4—22no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—41no—
469D4—82no—
470D4—82no—
471D4—82no—
472D4—161no—
473D4—161no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—161no—
485C2×C4—161no—
486C2×C4—161no—
487C2×C4C2×D8×C10311yescharacteristic
488C2×C4C2×D8×C10311yescharacteristic
489C2×C4C2×D8×C10311yescharacteristic
490C2×C4C2×D8×C10311yescharacteristic
491C2×C4C22×D4×C10311yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8C2×#41×C10311yescharacteristic
496C8H(5,𝔽2)×C10311yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—164no—
512C22#508×C10312yes—
513C22C22×D8×C10311yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4#546×C10311yescharacteristic
524C4#577×C10311yescharacteristic
525C2—22no—
526C2—41no—
527C2—82no—
528C2—161no—
529C2—161no—
530C2C103×#329411yescharacteristic
531C2C2×#508×C10311yescharacteristic
532C2C103×#341511yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C4×D4×C103 ◁ C8×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3339C2semidirect
2. C103×#3280C2semidirect
3. C103×#2242C2semidirect
4. C103×#2236C2semidirect
5. C103×#2234C2semidirect
6. C103×#2228C2semidirect
7. C103×#2217C2semidirect
8. C103×#2215C2semidirect
9. C103×#2210C2semidirect
10. C103×#2186C2semidirect
11. C103×#2184C2semidirect
12. C4×D16×C103C2semidirect
13. D4×C16×C103C2semidirect
14. C103×#2138C2semidirect
15. C2×#357×C103C2semidirect
20. C2×SD32×C103C22semidirect
24. C22×C16×C103C22semidirect
25. #499×C103C22semidirect
33. #466×C103C22semidirect
38. C4×D8×C103C22semidirect
40. #427×C103C22semidirect
42. #367×C103C22semidirect
43. #366×C103C22semidirect
44. #366×C103C22semidirect
45. C4⋊C16×C103C22semidirect
46. #358×C103C22semidirect
47. #358×C103C22semidirect
48. #358×C103C22semidirect
55. #357×C103C22semidirect
57. C22⋊C16×C103C22semidirect
58. C4×C16×C103C22semidirect
258. #33864C103direct (N × H)
267. #3339C2×C103semidirect
268. #3280C2×C103semidirect
269. #2242C2×C103semidirect
270. #2236C2×C103semidirect
271. #2234C2×C103semidirect
272. #2228C2×C103semidirect
273. #2217C2×C103semidirect
274. #2215C2×C103semidirect
275. #2210C2×C103semidirect
276. #2186C2×C103semidirect
277. #2184C2×C103semidirect
278. C4×D16C2×C103semidirect
279. D4×C16C2×C103semidirect
280. #2138C2×C103semidirect
281. C2×#357C2×C103semidirect
282. C103#33864direct (N × H)
287. C2×SD32C22×C103semidirect
291. C22×C16C22×C103semidirect
292. #499C22×C103semidirect
300. #466C22×C103semidirect
305. C4×D8C22×C103semidirect
307. #427C22×C103semidirect
309. #367C22×C103semidirect
310. #366C22×C103semidirect
311. #366C22×C103semidirect
312. C4⋊C16C22×C103semidirect
313. #358C22×C103semidirect
314. #358C22×C103semidirect
315. #358C22×C103semidirect
322. #357C22×C103semidirect
324. C22⋊C16C22×C103semidirect
325. C4×C16C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33392
C103×#32802
C103×#22422
C103×#22362
C103×#22342
C103×#22282
C103×#22172
C103×#22152
C103×#22102
C103×#21862
C103×#21842
C4×D16×C1032
D4×C16×C1032
C103×#21382
C2×#357×C1032
#33864103