Finite Group Databasebeta

← C103×#8991 #39914266

Subgroups — C103×#8991 #39914266

Order 26368.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3100C211yesmaximal, characteristic
2D4×M16×C103C211yesmaximal, characteristic, complemented
3C103×#1980C211yesmaximal, characteristic, complemented
4C4×#102×C103C211yesmaximal, characteristic, complemented
5C103×#1492C211yesmaximal, characteristic, complemented
6C103×#1303C211yesmaximal, characteristic, complemented
7C103×#1278C211yesmaximal, characteristic, complemented
8C22×M16×C103—21no—
9#532×C103C2211yescharacteristic
10C2×C4×D4×C103C2211yescharacteristic
11#480×C103—21no—
12#474×C103C411yescharacteristic, complemented
13#474×C103C411yescharacteristic, complemented
14#459×C103C411yescharacteristic, complemented
15#459×C103C411yescharacteristic, complemented
16#447×C103—21no—
17C4×D8×C103—21no—
18C4×D8×C103—21no—
19#436×C103—21no—
20#435×C103—22no—
21C8×D4×C103—21no—
22#431×C103C2211yescharacteristic
23#423×C103C2211yescharacteristic
24C2×#104×C103—21no—
25C2×#104×C103—21no—
26C2×#102×C103—21no—
27#407×C103—21no—
28C4×M16×C103C2211yescharacteristic
29C2×C4×C8×C103C2211yescharacteristic
30C4×C4⋊C4×C103C2211yescharacteristic
31#340×C103—21no—
32D4⋊C8×C103—22no—
33C2×#41×C103—21no—
34C22×D4×C103D411yescharacteristic
35C23×C4×C103—21no—
36C2×D8×C103—21no—
37C2×D8×C103—21no—
38C2×M16×C103—22no—
39C2×M16×C103—21no—
40C2×M16×C103—42no—
41C2×M16×C103—42no—
42C2×M16×C103D411yescharacteristic
43C2×M16×C103D411yescharacteristic
44C22×C8×C103—22no—
45C22×C8×C103—21no—
46C4⋊Q8×C103C2×C411yescharacteristic
47#127×C103C2×C411yescharacteristic
48#124×C103—21no—
49#121×C103—21no—
50#121×C103—21no—
51C4×D4×C103—21no—
52C4×D4×C103—21no—
53C4×D4×C103—21no—
54C4×D4×C103—21no—
55C4×D4×C103C2×C411yescharacteristic
56C4×D4×C103C2×C411yescharacteristic
57C4×D4×C103D411yescharacteristic
58C4×D4×C103D411yescharacteristic
59C2×C4⋊C4×C103—21no—
60C2×C4⋊C4×C103D411yescharacteristic
61C2×C22⋊C4×C103—21no—
62C2×C42×C103—21no—
63C2×C42×C103C2311yescharacteristic
64#107×C103—21no—
65#107×C103—21no—
66C4⋊C8×C103—21no—
67C4⋊C8×C103C2×C411yescharacteristic
68C4⋊C8×C103C2×C411yescharacteristic
69C4⋊C8×C103D412yes—
70#104×C103—42no—
71#104×C103—42no—
72#102×C103—24no—
73#102×C103—21no—
74#102×C103—21no—
75#102×C103—21no—
76#102×C103—21no—
77C22⋊C8×C103—22no—
78C22⋊C8×C103—22no—
79C22⋊C8×C103—21no—
80#97×C103—21no—
81C4×C8×C103—21no—
82C4×C8×C103—21no—
83C4×C8×C103—21no—
84C4×C8×C103—21no—
85#95×C103—21no—
86C24×C103—21no—
87#41×C103—41no—
88#41×C103—41no—
89#41×C103—41no—
90#41×C103—41no—
91C2×Q8×C103—21no—
92C2×D4×C103—22no—
93C2×D4×C103—21no—
94C2×D4×C103—21no—
95C2×D4×C103—21no—
96C2×D4×C103—21no—
97C2×D4×C103—41no—
98C2×D4×C103—41no—
99C2×D4×C103C22⋊C411yescharacteristic
100C2×D4×C103C22⋊C411yescharacteristic
101C22×C4×C103—21no—
102C22×C4×C103—21no—
103C22×C4×C103—21no—
104C22×C4×C103—21no—
105C22×C4×C103—21no—
106C22×C4×C103—41no—
107C22×C4×C103—41no—
108C22×C4×C103—41no—
109C22×C4×C103—41no—
110C22×C4×C103—41no—
111C22×C4×C103—41no—
112C22×C4×C103C2×D411yescharacteristic
113C22×C4×C103C2×D411yescharacteristic
114C22×C4×C103#4111yescharacteristic
115D8×C103—42no—
116D8×C103—42no—
117M16×C103—21no—
118M16×C103—21no—
119M16×C103—21no—
120M16×C103—44no—
121M16×C103—41no—
122M16×C103—41no—
123M16×C103D812yescomplemented
124C2×C8×C103—21no—
125C2×C8×C103—22no—
126C2×C8×C103—21no—
127C2×C8×C103—21no—
128C2×C8×C103—21no—
129C2×C8×C103—22no—
130C2×C8×C103—44no—
131C2×C8×C103—41no—
132C2×C8×C103—41no—
133C4⋊C4×C103—21no—
134C4⋊C4×C103—22no—
135C4⋊C4×C103—21no—
136C4⋊C4×C103—21no—
137C4⋊C4×C103—41no—
138C4⋊C4×C103C22⋊C411yescharacteristic
139C4⋊C4×C103C22⋊C411yescharacteristic
140C22⋊C4×C103—21no—
141C22⋊C4×C103—21no—
142C22⋊C4×C103—21no—
143C22⋊C4×C103—21no—
144C22⋊C4×C103—41no—
145C22⋊C4×C103—41no—
146C42×C103—41no—
147C42×C103—41no—
148C42×C103C22×C411yescharacteristic
149C42×C103C2×D411yescharacteristic
150C42×C103C2×D411yescharacteristic
151C42×C103#4111yescharacteristic
152C23×C103—21no—
153C23×C103—21no—
154C23×C103—42no—
155C23×C103—41no—
156C23×C103—41no—
157C23×C103—41no—
158C23×C103—81no—
159C23×C103#12111yescharacteristic
160Q8×C103—41no—
161Q8×C103—41no—
162D4×C103—21no—
163D4×C103—21no—
164D4×C103—21no—
165D4×C103—42no—
166D4×C103—42no—
167D4×C103—41no—
168D4×C103—41no—
169D4×C103—41no—
170D4×C103—41no—
171D4×C103—81no—
172D4×C103—81no—
173D4×C103#10412yescomplemented
174C2×C4×C103—21no—
175C2×C4×C103—21no—
176C2×C4×C103—21no—
177C2×C4×C103—21no—
178C2×C4×C103—41no—
179C2×C4×C103—41no—
180C2×C4×C103—41no—
181C2×C4×C103—41no—
182C2×C4×C103—41no—
183C2×C4×C103—41no—
184C2×C4×C103—41no—
185C2×C4×C103—41no—
186C2×C4×C103—41no—
187C2×C4×C103—41no—
188C2×C4×C103—41no—
189C2×C4×C103—42no—
190C2×C4×C103—41no—
191C2×C4×C103—81no—
192C2×C4×C103—81no—
193C2×C4×C103—81no—
194C2×C4×C103—81no—
195C2×C4×C103C2×C22⋊C411yescharacteristic
196C2×C4×C103C4×D411yescharacteristic
197C2×C4×C103C4×D411yescharacteristic
198C2×C4×C103#12011yescharacteristic
199C2×C4×C103#12111yescharacteristic
200C2×C4×C103#12311yescharacteristic
201C2×C4×C103C2×D811yescharacteristic
202C2×C4×C103#13511yescharacteristic
203C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
205C8×C103—22no—
206C8×C103—42no—
207C8×C103—41no—
208C8×C103—41no—
209C8×C103—42no—
210C8×C103—41no—
211C22×C103—21no—
212C22×C103—21no—
213C22×C103—22no—
214C22×C103—41no—
215C22×C103—41no—
216C22×C103—41no—
217C22×C103—41no—
218C22×C103—41no—
219C22×C103—82no—
220C22×C103—82no—
221C22×C103—81no—
222C22×C103—81no—
223C22×C103—81no—
224C22×C103#38611yescharacteristic
225C22×C103#45911yescharacteristic
226C22×C103#46311yescharacteristic
227C4×C103—21no—
228C4×C103—21no—
229C4×C103—21no—
230C4×C103—41no—
231C4×C103—41no—
232C4×C103—82no—
233C4×C103—81no—
234C4×C103C2×#10411yescharacteristic
235C4×C103#42111yescharacteristic
236C4×C103C4×D811yescharacteristic
237C4×C103#44211yescharacteristic
238C4×C103#44711yescharacteristic
239C4×C103#44911yescharacteristic
240#8991C10311yesmaximal, characteristic, direct product factor, Sylow
241C2×C103—21no—
242C2×C103—21no—
243C2×C103—42no—
244C2×C103—81no—
245C2×C103—161no—
246C2×C103#187111yescharacteristic
247C2×C103#187911yescharacteristic
248C2×C103#188111yescharacteristic
249#3100C2×C10311yescharacteristic
250D4×M16C2×C10311yescharacteristic, complemented
251#1980C2×C10311yescharacteristic, complemented
252C4×#102C2×C10311yescharacteristic, complemented
253#1492C2×C10311yescharacteristic, complemented
254#1303C2×C10311yescharacteristic, complemented
255#1278C2×C10311yescharacteristic, complemented
256C103#899111yescharacteristic, direct product factor, Sylow
257C22×M16—21no—
258#532C22×C10311yescharacteristic
259C2×C4×D4C22×C10311yescharacteristic
260#480—21no—
261#474C4×C10311yescharacteristic, complemented
262#474C4×C10311yescharacteristic, complemented
263#459C4×C10311yescharacteristic, complemented
264#459C4×C10311yescharacteristic, complemented
265#447—21no—
266C4×D8—21no—
267C4×D8—21no—
268#436—21no—
269#435—22no—
270C8×D4—21no—
271#431C22×C10311yescharacteristic
272#423C22×C10311yescharacteristic
273C2×#104—21no—
274C2×#104—21no—
275C2×#102—21no—
276#407—21no—
277C4×M16C22×C10311yescharacteristic
278C2×C4×C8C22×C10311yescharacteristic
279C4×C4⋊C4C22×C10311yescharacteristic
280#340—21no—
281D4⋊C8—22no—
282C2×#41—21no—
283C22×D4D4×C10311yescharacteristic
284C23×C4—21no—
285C2×D8—21no—
286C2×D8—21no—
287C2×M16—22no—
288C2×M16—21no—
289C2×M16—42no—
290C2×M16—42no—
291C2×M16D4×C10311yescharacteristic
292C2×M16D4×C10311yescharacteristic
293C22×C8—22no—
294C22×C8—21no—
295C4⋊Q8C2×C4×C10311yescharacteristic
296#127C2×C4×C10311yescharacteristic
297#124—21no—
298#121—21no—
299#121—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4C2×C4×C10311yescharacteristic
305C4×D4C2×C4×C10311yescharacteristic
306C4×D4D4×C10311yescharacteristic
307C4×D4D4×C10311yescharacteristic
308C2×C4⋊C4—21no—
309C2×C4⋊C4D4×C10311yescharacteristic
310C2×C22⋊C4—21no—
311C2×C42—21no—
312C2×C42C23×C10311yescharacteristic
313#107—21no—
314#107—21no—
315C4⋊C8—21no—
316C4⋊C8C2×C4×C10311yescharacteristic
317C4⋊C8C2×C4×C10311yescharacteristic
318C4⋊C8D4×C10312yes—
319#104—42no—
320#104—42no—
321#102—24no—
322#102—21no—
323#102—21no—
324#102—21no—
325#102—21no—
326C22⋊C8—22no—
327C22⋊C8—22no—
328C22⋊C8—21no—
329#97—21no—
330C4×C8—21no—
331C4×C8—21no—
332C4×C8—21no—
333C4×C8—21no—
334#95—21no—
335C24—21no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340C2×Q8—21no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4C22⋊C4×C10311yescharacteristic
349C2×D4C22⋊C4×C10311yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4C2×D4×C10311yescharacteristic
362C22×C4C2×D4×C10311yescharacteristic
363C22×C4#41×C10311yescharacteristic
364D8—42no—
365D8—42no—
366M16—21no—
367M16—21no—
368M16—21no—
369M16—44no—
370M16—41no—
371M16—41no—
372M16D8×C10312yescomplemented
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—44no—
380C2×C8—41no—
381C2×C8—41no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4C22⋊C4×C10311yescharacteristic
388C4⋊C4C22⋊C4×C10311yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—41no—
396C42—41no—
397C42C22×C4×C10311yescharacteristic
398C42C2×D4×C10311yescharacteristic
399C42C2×D4×C10311yescharacteristic
400C42#41×C10311yescharacteristic
401C23—21no—
402C23—21no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—81no—
408C23#121×C10311yescharacteristic
409Q8—41no—
410Q8—41no—
411D4—21no—
412D4—21no—
413D4—21no—
414D4—42no—
415D4—42no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—81no—
421D4—81no—
422D4#104×C10312yescomplemented
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4C2×C22⋊C4×C10311yescharacteristic
445C2×C4C4×D4×C10311yescharacteristic
446C2×C4C4×D4×C10311yescharacteristic
447C2×C4#120×C10311yescharacteristic
448C2×C4#121×C10311yescharacteristic
449C2×C4#123×C10311yescharacteristic
450C2×C4C2×D8×C10311yescharacteristic
451C2×C4#135×C10311yescharacteristic
452C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
453C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
454C8—22no—
455C8—42no—
456C8—41no—
457C8—41no—
458C8—42no—
459C8—41no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—82no—
469C22—82no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22#386×C10311yescharacteristic
474C22#459×C10311yescharacteristic
475C22#463×C10311yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—82no—
482C4—81no—
483C4C2×#104×C10311yescharacteristic
484C4#421×C10311yescharacteristic
485C4C4×D8×C10311yescharacteristic
486C4#442×C10311yescharacteristic
487C4#447×C10311yescharacteristic
488C4#449×C10311yescharacteristic
489C2—21no—
490C2—21no—
491C2—42no—
492C2—81no—
493C2—161no—
494C2C103×#187111yescharacteristic
495C2C103×#187911yescharacteristic
496C2C103×#188111yescharacteristic
subgroupG/H
centerC2×C4×C103#120
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#386
prime radicalC103×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×M16×C103C2semidirect
3. C103×#1980C2semidirect
4. C4×#102×C103C2semidirect
5. C103×#1492C2semidirect
6. C103×#1303C2semidirect
7. C103×#1278C2semidirect
12. #474×C103C4semidirect
13. #474×C103C4semidirect
14. #459×C103C4semidirect
15. #459×C103C4semidirect
123. M16×C103D8semidirect
173. D4×C103#104semidirect
240. #8991C103direct (N × H)
250. D4×M16C2×C103semidirect
251. #1980C2×C103semidirect
252. C4×#102C2×C103semidirect
253. #1492C2×C103semidirect
254. #1303C2×C103semidirect
255. #1278C2×C103semidirect
256. C103#8991direct (N × H)
261. #474C4×C103semidirect
262. #474C4×C103semidirect
263. #459C4×C103semidirect
264. #459C4×C103semidirect
372. M16D8×C103semidirect
422. D4#104×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31002
D4×M16×C1032
C103×#19802
C4×#102×C1032
C103×#14922
C103×#13032
C103×#12782
#8991103