Finite Group Databasebeta

← C103×#33913 #39939188

Subgroups — C103×#33913 #39939188

Order 26368.

484 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3339C211yesmaximal, characteristic
2C103×#3338C211yesmaximal, characteristic, complemented
3C103×#2255C211yesmaximal, characteristic, complemented
4C103×#2237C211yesmaximal, characteristic, complemented
5C103×#2236C211yesmaximal, characteristic, complemented
6C103×#2233C211yesmaximal, characteristic, complemented
7C103×#2232C211yesmaximal, characteristic, complemented
8C103×#2229C211yesmaximal, characteristic, complemented
9C103×#2224C211yesmaximal, characteristic, complemented
10C103×#2220C211yesmaximal, characteristic, complemented
11C103×#2217C211yesmaximal, characteristic, complemented
12C103×#2175C211yesmaximal, characteristic, complemented
13C103×#2168C211yesmaximal, characteristic, complemented
14C103×#2159C211yesmaximal, characteristic, complemented
15C2×#366×C103C211yesmaximal, characteristic, complemented
16#554×C103—21no—
17#553×C103—21no—
18C2×SD32×C103C2211yescharacteristic
19C2×M32×C103C2211yescharacteristic
20C22×C16×C103C2211yescharacteristic
21#500×C103C2211yescharacteristic
22#499×C103C2211yescharacteristic
23#484×C103—21no—
24#484×C103—21no—
25#482×C103—21no—
26#481×C103—21no—
27#478×C103—21no—
28#477×C103—21no—
29#467×C103C2211yescharacteristic
30#467×C103C2211yescharacteristic
31#466×C103C2211yescharacteristic
32#466×C103C2211yescharacteristic
33C4×Q16×C103C2211yescharacteristic
34C4×D8×C103C2211yescharacteristic
35C8×D4×C103C2211yescharacteristic
36#427×C103C2211yescharacteristic
37C2×#107×C103C2211yescharacteristic
38C2×#107×C103C2211yescharacteristic
39C2×#107×C103C2211yescharacteristic
40#367×C103C2211yescharacteristic
41#367×C103C2211yescharacteristic
42#367×C103C2211yescharacteristic
43#366×C103C2211yescharacteristic
44#366×C103C2211yescharacteristic
45#366×C103C2211yescharacteristic
46#366×C103C2211yescharacteristic
47#366×C103C2211yescharacteristic
48#366×C103C2211yescharacteristic
49C4⋊C16×C103C2211yescharacteristic
50#358×C103C2211yescharacteristic
51#358×C103C2211yescharacteristic
52#358×C103C2211yescharacteristic
53#357×C103C2211yescharacteristic
54#357×C103C2211yescharacteristic
55#357×C103C2211yescharacteristic
56C22⋊C16×C103C2211yescharacteristic
57C22⋊C16×C103C2211yescharacteristic
58#346×C103C2211yescharacteristic
59C2×Q16×C103C2311yescharacteristic
60C2×D8×C103C2311yescharacteristic
61C22×C8×C103C2311yescharacteristic
62C22×C8×C103C2311yescharacteristic
63C4⋊Q8×C103—21no—
64#126×C103—41no—
65#125×C103—21no—
66#125×C103—41no—
67#123×C103—41no—
68C22⋊Q8×C103—21no—
69C22⋊Q8×C103—21no—
70C22⋊Q8×C103—41no—
71C22⋊Q8×C103—41no—
72#121×C103—21no—
73#121×C103—21no—
74#121×C103—41no—
75C4×Q8×C103—21no—
76C4×D4×C103—21no—
77C4×D4×C103—41no—
78C4×D4×C103—41no—
79C4×D4×C103D411yescharacteristic
80#117×C103—21no—
81C2×C4⋊C4×C103—21no—
82C2×C4⋊C4×C103—21no—
83C2×C4⋊C4×C103—21no—
84SD32×C103—22no—
85M32×C103—22no—
86C2×C16×C103—22no—
87C2×C16×C103C2311yescharacteristic
88C2×C16×C103C2311yescharacteristic
89C2×C16×C103C2311yescharacteristic
90C2×C16×C103C2311yescharacteristic
91#107×C103—21no—
92#107×C103—21no—
93#107×C103—21no—
94#107×C103—21no—
95#107×C103C2311yescharacteristic
96#107×C103C2311yescharacteristic
97#107×C103C2311yescharacteristic
98#107×C103C2311yescharacteristic
99#107×C103C2311yescharacteristic
100#107×C103C2311yescharacteristic
101#106×C103—21no—
102#106×C103—21no—
103C4⋊C8×C103D411yescharacteristic
104#103×C103—21no—
105#103×C103—21no—
106#103×C103—21no—
107#102×C103—21no—
108#102×C103—21no—
109#102×C103—21no—
110C22⋊C8×C103D411yescharacteristic
111C22⋊C8×C103D411yescharacteristic
112C4×C8×C103C2311yescharacteristic
113C2×Q8×C103—21no—
114C2×Q8×C103—41no—
115C2×D4×C103—21no—
116C2×D4×C103—41no—
117C2×D4×C103—41no—
118C2×D4×C103D811yescharacteristic
119C22×C4×C103—41no—
120C22×C4×C103—41no—
121C22×C4×C103—41no—
122C22×C4×C103—41no—
123C22×C4×C103C2×D411yescharacteristic
124C22×C4×C103C2×D411yescharacteristic
125Q16×C103—21no—
126Q16×C103—21no—
127D8×C103—21no—
128D8×C103—21no—
129C2×C8×C103—21no—
130C2×C8×C103—21no—
131C2×C8×C103—21no—
132C2×C8×C103—21no—
133C2×C8×C103C2×D411yescharacteristic
134C2×C8×C103C2×D411yescharacteristic
135C2×C8×C103C2×D411yescharacteristic
136C2×C8×C103C2411yescharacteristic
137C4⋊C4×C103—21no—
138C4⋊C4×C103—21no—
139C4⋊C4×C103—21no—
140C4⋊C4×C103—21no—
141C4⋊C4×C103—21no—
142C4⋊C4×C103—21no—
143C4⋊C4×C103—41no—
144C4⋊C4×C103—41no—
145C4⋊C4×C103—41no—
146C4⋊C4×C103—41no—
147C4⋊C4×C103—41no—
148C4⋊C4×C103—41no—
149C4⋊C4×C103—41no—
150C4⋊C4×C103—41no—
151C4⋊C4×C103—41no—
152C4⋊C4×C103D811yescharacteristic
153C22⋊C4×C103—41no—
154C22⋊C4×C103—41no—
155C22⋊C4×C103—41no—
156C22⋊C4×C103—41no—
157C22⋊C4×C103—41no—
158C22⋊C4×C103—41no—
159C22⋊C4×C103D811yescharacteristic
160C22⋊C4×C103D811yescharacteristic
161C42×C103—41no—
162C42×C103—41no—
163C42×C103C2×D411yescharacteristic
164C16×C103—21no—
165C16×C103—21no—
166C16×C103—21no—
167C16×C103#4112yes—
168C23×C103—41no—
169C23×C103C2×D811yescharacteristic
170C23×C103C2×D811yescharacteristic
171Q8×C103—41no—
172Q8×C103—41no—
173Q8×C103—161no—
174D4×C103—22no—
175D4×C103—41no—
176D4×C103—41no—
177D4×C103—82no—
178D4×C103—161no—
179C2×C4×C103—21no—
180C2×C4×C103—21no—
181C2×C4×C103—21no—
182C2×C4×C103—21no—
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—41no—
190C2×C4×C103—161no—
191C2×C4×C103—161no—
192C2×C4×C103—161no—
193C2×C4×C103—161no—
194C2×C4×C103C2×D811yescharacteristic
195C2×C4×C103C2×D811yescharacteristic
196C2×C4×C103C2×D811yescharacteristic
197C2×C4×C103C2×D811yescharacteristic
198C2×C4×C103C22×D411yescharacteristic
199C8×C103—21no—
200C8×C103—21no—
201C8×C103—21no—
202C8×C103C2×#4111yescharacteristic
203C8×C1032−1+411yescharacteristic
204C22×C103—21no—
205C22×C103—21no—
206C22×C103—21no—
207C22×C103—21no—
208C22×C103—21no—
209C22×C103—81no—
210C22×C103—81no—
211C22×C103—81no—
212C22×C103#51012yes—
213C22×C103C22×D811yescharacteristic
214C4×C103—21no—
215C4×C103—21no—
216C4×C103—21no—
217C4×C103—21no—
218C4×C103—81no—
219C4×C103—81no—
220C4×C103—81no—
221C4×C103—81no—
222C4×C103—81no—
223C4×C103—81no—
224C4×C103—81no—
225C4×C103#54711yescharacteristic
226C4×C103#57811yescharacteristic
227#33913C10311yesmaximal, characteristic, direct product factor, Sylow
228C2×C103—22no—
229C2×C103—41no—
230C2×C103—161no—
231C2×C103#333411yescharacteristic
232C2×C103C2×#51011yescharacteristic
233C2×C103#341511yescharacteristic
234#3339C2×C10311yescharacteristic
235#3338C2×C10311yescharacteristic, complemented
236#2255C2×C10311yescharacteristic, complemented
237#2237C2×C10311yescharacteristic, complemented
238#2236C2×C10311yescharacteristic, complemented
239#2233C2×C10311yescharacteristic, complemented
240#2232C2×C10311yescharacteristic, complemented
241#2229C2×C10311yescharacteristic, complemented
242#2224C2×C10311yescharacteristic, complemented
243#2220C2×C10311yescharacteristic, complemented
244#2217C2×C10311yescharacteristic, complemented
245#2175C2×C10311yescharacteristic, complemented
246#2168C2×C10311yescharacteristic, complemented
247#2159C2×C10311yescharacteristic, complemented
248C2×#366C2×C10311yescharacteristic, complemented
249C103#3391311yescharacteristic, direct product factor, Sylow
250#554—21no—
251#553—21no—
252C2×SD32C22×C10311yescharacteristic
253C2×M32C22×C10311yescharacteristic
254C22×C16C22×C10311yescharacteristic
255#500C22×C10311yescharacteristic
256#499C22×C10311yescharacteristic
257#484—21no—
258#484—21no—
259#482—21no—
260#481—21no—
261#478—21no—
262#477—21no—
263#467C22×C10311yescharacteristic
264#467C22×C10311yescharacteristic
265#466C22×C10311yescharacteristic
266#466C22×C10311yescharacteristic
267C4×Q16C22×C10311yescharacteristic
268C4×D8C22×C10311yescharacteristic
269C8×D4C22×C10311yescharacteristic
270#427C22×C10311yescharacteristic
271C2×#107C22×C10311yescharacteristic
272C2×#107C22×C10311yescharacteristic
273C2×#107C22×C10311yescharacteristic
274#367C22×C10311yescharacteristic
275#367C22×C10311yescharacteristic
276#367C22×C10311yescharacteristic
277#366C22×C10311yescharacteristic
278#366C22×C10311yescharacteristic
279#366C22×C10311yescharacteristic
280#366C22×C10311yescharacteristic
281#366C22×C10311yescharacteristic
282#366C22×C10311yescharacteristic
283C4⋊C16C22×C10311yescharacteristic
284#358C22×C10311yescharacteristic
285#358C22×C10311yescharacteristic
286#358C22×C10311yescharacteristic
287#357C22×C10311yescharacteristic
288#357C22×C10311yescharacteristic
289#357C22×C10311yescharacteristic
290C22⋊C16C22×C10311yescharacteristic
291C22⋊C16C22×C10311yescharacteristic
292#346C22×C10311yescharacteristic
293C2×Q16C23×C10311yescharacteristic
294C2×D8C23×C10311yescharacteristic
295C22×C8C23×C10311yescharacteristic
296C22×C8C23×C10311yescharacteristic
297C4⋊Q8—21no—
298#126—41no—
299#125—21no—
300#125—41no—
301#123—41no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—41no—
305C22⋊Q8—41no—
306#121—21no—
307#121—21no—
308#121—41no—
309C4×Q8—21no—
310C4×D4—21no—
311C4×D4—41no—
312C4×D4—41no—
313C4×D4D4×C10311yescharacteristic
314#117—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318SD32—22no—
319M32—22no—
320C2×C16—22no—
321C2×C16C23×C10311yescharacteristic
322C2×C16C23×C10311yescharacteristic
323C2×C16C23×C10311yescharacteristic
324C2×C16C23×C10311yescharacteristic
325#107—21no—
326#107—21no—
327#107—21no—
328#107—21no—
329#107C23×C10311yescharacteristic
330#107C23×C10311yescharacteristic
331#107C23×C10311yescharacteristic
332#107C23×C10311yescharacteristic
333#107C23×C10311yescharacteristic
334#107C23×C10311yescharacteristic
335#106—21no—
336#106—21no—
337C4⋊C8D4×C10311yescharacteristic
338#103—21no—
339#103—21no—
340#103—21no—
341#102—21no—
342#102—21no—
343#102—21no—
344C22⋊C8D4×C10311yescharacteristic
345C22⋊C8D4×C10311yescharacteristic
346C4×C8C23×C10311yescharacteristic
347C2×Q8—21no—
348C2×Q8—41no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4D8×C10311yescharacteristic
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4C2×D4×C10311yescharacteristic
358C22×C4C2×D4×C10311yescharacteristic
359Q16—21no—
360Q16—21no—
361D8—21no—
362D8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8C2×D4×C10311yescharacteristic
368C2×C8C2×D4×C10311yescharacteristic
369C2×C8C2×D4×C10311yescharacteristic
370C2×C8C24×C10311yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4D8×C10311yescharacteristic
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4D8×C10311yescharacteristic
394C22⋊C4D8×C10311yescharacteristic
395C42—41no—
396C42—41no—
397C42C2×D4×C10311yescharacteristic
398C16—21no—
399C16—21no—
400C16—21no—
401C16#41×C10312yes—
402C23—41no—
403C23C2×D8×C10311yescharacteristic
404C23C2×D8×C10311yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—161no—
408D4—22no—
409D4—41no—
410D4—41no—
411D4—82no—
412D4—161no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—161no—
425C2×C4—161no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4C2×D8×C10311yescharacteristic
429C2×C4C2×D8×C10311yescharacteristic
430C2×C4C2×D8×C10311yescharacteristic
431C2×C4C2×D8×C10311yescharacteristic
432C2×C4C22×D4×C10311yescharacteristic
433C8—21no—
434C8—21no—
435C8—21no—
436C8C2×#41×C10311yescharacteristic
437C82−1+4×C10311yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22#510×C10312yes—
447C22C22×D8×C10311yescharacteristic
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4#547×C10311yescharacteristic
460C4#578×C10311yescharacteristic
461C2—22no—
462C2—41no—
463C2—161no—
464C2C103×#333411yescharacteristic
465C2C2×#510×C10311yescharacteristic
466C2C103×#341511yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
prime radicalC103×#3339C2
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
2. C103×#3338C2semidirect
3. C103×#2255C2semidirect
4. C103×#2237C2semidirect
5. C103×#2236C2semidirect
6. C103×#2233C2semidirect
7. C103×#2232C2semidirect
8. C103×#2229C2semidirect
9. C103×#2224C2semidirect
10. C103×#2220C2semidirect
11. C103×#2217C2semidirect
12. C103×#2175C2semidirect
13. C103×#2168C2semidirect
14. C103×#2159C2semidirect
15. C2×#366×C103C2semidirect
227. #33913C103direct (N × H)
235. #3338C2×C103semidirect
236. #2255C2×C103semidirect
237. #2237C2×C103semidirect
238. #2236C2×C103semidirect
239. #2233C2×C103semidirect
240. #2232C2×C103semidirect
241. #2229C2×C103semidirect
242. #2224C2×C103semidirect
243. #2220C2×C103semidirect
244. #2217C2×C103semidirect
245. #2175C2×C103semidirect
246. #2168C2×C103semidirect
247. #2159C2×C103semidirect
248. C2×#366C2×C103semidirect
249. C103#33913direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#33392
C103×#33382
C103×#22552
C103×#22372
C103×#22362
C103×#22332
C103×#22322
C103×#22292
C103×#22242
C103×#22202
C103×#22172
C103×#21752
C103×#21682
C103×#21592
C2×#366×C1032
#33913103