Finite Group Databasebeta

← C103×#18734 #39924009

Subgroups — C103×#18734 #39924009

Order 26368.

932 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3548C211yesmaximal, characteristic
2C103×#3226C211yesmaximal, characteristic, complemented
3C103×#3206C211yesmaximal, characteristic, complemented
4C103×#3165C211yesmaximal, characteristic, complemented
5C103×#1654C214yesmaximal, complemented
6C103×#1647C214yesmaximal, complemented
7C103×#1544C211yesmaximal, characteristic, complemented
8C103×#1484C211yesmaximal, characteristic, complemented
9C103×#1484C211yesmaximal, characteristic, complemented
10#562×C103—22no—
11#554×C103—21no—
12#554×C103—21no—
13#550×C103—21no—
14#550×C103—21no—
15#547×C103C2212yes—
16#547×C103C2212yes—
17#540×C103—22no—
18#537×C103—22no—
19#537×C103—22no—
20#533×C103C2211yescharacteristic
21#532×C103C2211yescharacteristic
22#532×C103C2211yescharacteristic
23C2×C4⋊Q8×C103C2211yescharacteristic
24#501×C103—22no—
25#500×C103—21no—
26#500×C103C2212yes—
27#498×C103C2212yes—
28#492×C103—21no—
29#487×C103—21no—
30#486×C103—21no—
31#480×C103—22no—
32#474×C103C2214yes—
33#461×C103C2214yes—
34#448×C103—22no—
35#431×C103C2211yescharacteristic
36#431×C103C2211yescharacteristic
37#428×C103—22no—
38C4×M16×C103C2211yescharacteristic
39#332×C103C2212yes—
40#332×C103C2212yes—
41D4⋊C8×C103C2214yes—
42D4⋊C8×C103C2214yes—
43C2×#41×C103—22no—
44C2×#41×C103—22no—
45C2×#41×C103—21no—
46C2×#41×C103—21no—
47C22×Q8×C103—21no—
48C2×SD16×C103—24no—
49C2×M16×C103—21no—
50C4⋊Q8×C103—21no—
51C4⋊Q8×C103—21no—
52C4⋊Q8×C103—21no—
53C4⋊Q8×C103D411yescharacteristic
54C4⋊Q8×C103D411yescharacteristic
55C4⋊Q8×C103C2312yes—
56C4⋊Q8×C103C2311yescharacteristic
57C4⋊Q8×C103C2311yescharacteristic
58#127×C103—22no—
59#127×C103D411yescharacteristic
60#127×C103D411yescharacteristic
61#125×C103—22no—
62#125×C103D412yes—
63#124×C103—21no—
64#124×C103—21no—
65#123×C103—24no—
66#123×C103—24no—
67C22⋊Q8×C103—24no—
68C22⋊Q8×C103—24no—
69C22⋊Q8×C103—21no—
70C22⋊Q8×C103—21no—
71C22⋊Q8×C103—22no—
72C22⋊Q8×C103—22no—
73#121×C103—24no—
74#121×C103—24no—
75#121×C103—24no—
76#121×C103—24no—
77#121×C103—22no—
78#121×C103—22no—
79#121×C103—21no—
80#121×C103—21no—
81#121×C103D412yes—
82#121×C103D412yes—
83C4×Q8×C103—21no—
84C4×Q8×C103—21no—
85C4×D4×C103—22no—
86C4×D4×C103—22no—
87C4×D4×C103—21no—
88C4×D4×C103—21no—
89C4×D4×C103C2312yes—
90C4×D4×C103C2312yes—
91#117×C103D412yes—
92C2×C4⋊C4×C103—22no—
93C2×C4⋊C4×C103—22no—
94C2×C4⋊C4×C103—21no—
95C2×C4⋊C4×C103—21no—
96C2×C42×C103C2311yescharacteristic
97#107×C103—24no—
98#107×C103—24no—
99#106×C103—24no—
100C4⋊C8×C103C2312yes—
101C4⋊C8×C103C2312yes—
102#103×C103—24no—
103#102×C103—24no—
104C22⋊C8×C103—21no—
105C22⋊C8×C103—21no—
106#97×C103—21no—
107C4×C8×C103—21no—
108C4×C8×C103—21no—
109C4×C8×C103C2312yes—
110#41×C103—82no—
111#41×C103—82no—
112#41×C103—84no—
113#41×C103—84no—
114C2×Q8×C103—21no—
115C2×Q8×C103—21no—
116C2×Q8×C103—21no—
117C2×Q8×C103—21no—
118C2×Q8×C103—22no—
119C2×Q8×C103—41no—
120C2×Q8×C103—82no—
121C2×D4×C103—24no—
122C2×D4×C103—24no—
123C2×D4×C103—22no—
124C2×D4×C103—22no—
125C2×D4×C103—21no—
126C2×D4×C103—21no—
127C2×D4×C103—21no—
128C2×D4×C103—21no—
129C2×D4×C103C2×D412yes—
130C2×D4×C103C2×D412yes—
131C22×C4×C103—24no—
132C22×C4×C103—24no—
133C22×C4×C103—22no—
134C22×C4×C103—22no—
135C22×C4×C103—41no—
136C22×C4×C103C2×D411yescharacteristic
137C22×C4×C103C2×D411yescharacteristic
138C22×C4×C103C2×D411yescharacteristic
139SD16×C103—84no—
140M16×C103—24no—
141C2×C8×C103—22no—
142C2×C8×C103—22no—
143C2×C8×C103—22no—
144C4⋊C4×C103—24no—
145C4⋊C4×C103—24no—
146C4⋊C4×C103—21no—
147C4⋊C4×C103—21no—
148C4⋊C4×C103—22no—
149C4⋊C4×C103—22no—
150C4⋊C4×C103—21no—
151C4⋊C4×C103—21no—
152C4⋊C4×C103—22no—
153C4⋊C4×C103—22no—
154C4⋊C4×C103—41no—
155C4⋊C4×C103—41no—
156C4⋊C4×C103C2×D412yes—
157C4⋊C4×C103C2×D412yes—
158C4⋊C4×C103C2×D412yes—
159C4⋊C4×C103C2×D412yes—
160C22⋊C4×C103—24no—
161C22⋊C4×C103—24no—
162C22⋊C4×C103—22no—
163C22⋊C4×C103—22no—
164C22⋊C4×C103—22no—
165C22⋊C4×C103—22no—
166C22⋊C4×C103—22no—
167C42×C103—22no—
168C42×C103C2×D411yescharacteristic
169C42×C103C2×D411yescharacteristic
170C42×C103C2×D411yescharacteristic
171C42×C103C2411yescharacteristic
172C23×C103—22no—
173C23×C103—22no—
174C23×C103#12011yescharacteristic
175Q8×C103—42no—
176Q8×C103—42no—
177Q8×C103—44no—
178Q8×C103—81no—
179Q8×C103—81no—
180Q8×C103—82no—
181D4×C103—24no—
182D4×C103—24no—
183D4×C103—42no—
184D4×C103—42no—
185D4×C103—81no—
186D4×C103—81no—
187D4×C103—82no—
188D4×C103—82no—
189D4×C103—84no—
190D4×C103—84no—
191C2×C4×C103—22no—
192C2×C4×C103—22no—
193C2×C4×C103—22no—
194C2×C4×C103—22no—
195C2×C4×C103—22no—
196C2×C4×C103—22no—
197C2×C4×C103—22no—
198C2×C4×C103—44no—
199C2×C4×C103—44no—
200C2×C4×C103—42no—
201C2×C4×C103—84no—
202C2×C4×C103—84no—
203C2×C4×C103—82no—
204C2×C4×C103#12011yescharacteristic
205C2×C4×C103#12011yescharacteristic
206C2×C4×C103#12011yescharacteristic
207C2×C4×C103C22×D411yescharacteristic
208C2×C4×C103C22×D411yescharacteristic
209C2×C4×C103C22×D411yescharacteristic
210C8×C103—24no—
211C8×C103—42no—
212C8×C103—42no—
213C22×C103—21no—
214C22×C103—21no—
215C22×C103—21no—
216C22×C103—42no—
217C22×C103—42no—
218C22×C103—42no—
219C22×C103—42no—
220C22×C103—42no—
221C22×C103—42no—
222C22×C103C2×#12011yescharacteristic
223C4×C103—21no—
224C4×C103—21no—
225C4×C103—21no—
226C4×C103—42no—
227C4×C103—42no—
228C4×C103—42no—
229C4×C103—42no—
230C4×C103—82no—
231C4×C103#45612yes—
232C4×C103#57612yes—
233C4×C103#57712yes—
234#18734C10311yesmaximal, characteristic, direct product factor, Sylow
235C2×C103—41no—
236C2×C103—82no—
237C2×C103—82no—
238C2×C103#300811yescharacteristic
239C2×C103#300911yescharacteristic
240C2×C103C2×#45611yescharacteristic
241#3548C2×C10311yescharacteristic
242#3226C2×C10311yescharacteristic, complemented
243#3206C2×C10311yescharacteristic, complemented
244#3165C2×C10311yescharacteristic, complemented
245#1654C2×C10314yescomplemented
246#1647C2×C10314yescomplemented
247#1544C2×C10311yescharacteristic, complemented
248#1484C2×C10311yescharacteristic, complemented
249#1484C2×C10311yescharacteristic, complemented
250C103#1873411yescharacteristic, direct product factor, Sylow
251#562—22no—
252#554—21no—
253#554—21no—
254#550—21no—
255#550—21no—
256#547C22×C10312yes—
257#547C22×C10312yes—
258#540—22no—
259#537—22no—
260#537—22no—
261#533C22×C10311yescharacteristic
262#532C22×C10311yescharacteristic
263#532C22×C10311yescharacteristic
264C2×C4⋊Q8C22×C10311yescharacteristic
265#501—22no—
266#500—21no—
267#500C22×C10312yes—
268#498C22×C10312yes—
269#492—21no—
270#487—21no—
271#486—21no—
272#480—22no—
273#474C22×C10314yes—
274#461C22×C10314yes—
275#448—22no—
276#431C22×C10311yescharacteristic
277#431C22×C10311yescharacteristic
278#428—22no—
279C4×M16C22×C10311yescharacteristic
280#332C22×C10312yes—
281#332C22×C10312yes—
282D4⋊C8C22×C10314yes—
283D4⋊C8C22×C10314yes—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—21no—
287C2×#41—21no—
288C22×Q8—21no—
289C2×SD16—24no—
290C2×M16—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8D4×C10311yescharacteristic
295C4⋊Q8D4×C10311yescharacteristic
296C4⋊Q8C23×C10312yes—
297C4⋊Q8C23×C10311yescharacteristic
298C4⋊Q8C23×C10311yescharacteristic
299#127—22no—
300#127D4×C10311yescharacteristic
301#127D4×C10311yescharacteristic
302#125—22no—
303#125D4×C10312yes—
304#124—21no—
305#124—21no—
306#123—24no—
307#123—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314#121—24no—
315#121—24no—
316#121—24no—
317#121—24no—
318#121—22no—
319#121—22no—
320#121—21no—
321#121—21no—
322#121D4×C10312yes—
323#121D4×C10312yes—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4C23×C10312yes—
331C4×D4C23×C10312yes—
332#117D4×C10312yes—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C42C23×C10311yescharacteristic
338#107—24no—
339#107—24no—
340#106—24no—
341C4⋊C8C23×C10312yes—
342C4⋊C8C23×C10312yes—
343#103—24no—
344#102—24no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347#97—21no—
348C4×C8—21no—
349C4×C8—21no—
350C4×C8C23×C10312yes—
351#41—82no—
352#41—82no—
353#41—84no—
354#41—84no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—82no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4C2×D4×C10312yes—
371C2×D4C2×D4×C10312yes—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—41no—
377C22×C4C2×D4×C10311yescharacteristic
378C22×C4C2×D4×C10311yescharacteristic
379C22×C4C2×D4×C10311yescharacteristic
380SD16—84no—
381M16—24no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4C2×D4×C10312yes—
398C4⋊C4C2×D4×C10312yes—
399C4⋊C4C2×D4×C10312yes—
400C4⋊C4C2×D4×C10312yes—
401C22⋊C4—24no—
402C22⋊C4—24no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C42—22no—
409C42C2×D4×C10311yescharacteristic
410C42C2×D4×C10311yescharacteristic
411C42C2×D4×C10311yescharacteristic
412C42C24×C10311yescharacteristic
413C23—22no—
414C23—22no—
415C23#120×C10311yescharacteristic
416Q8—42no—
417Q8—42no—
418Q8—44no—
419Q8—81no—
420Q8—81no—
421Q8—82no—
422D4—24no—
423D4—24no—
424D4—42no—
425D4—42no—
426D4—81no—
427D4—81no—
428D4—82no—
429D4—82no—
430D4—84no—
431D4—84no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—84no—
443C2×C4—84no—
444C2×C4—82no—
445C2×C4#120×C10311yescharacteristic
446C2×C4#120×C10311yescharacteristic
447C2×C4#120×C10311yescharacteristic
448C2×C4C22×D4×C10311yescharacteristic
449C2×C4C22×D4×C10311yescharacteristic
450C2×C4C22×D4×C10311yescharacteristic
451C8—24no—
452C8—42no—
453C8—42no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22C2×#120×C10311yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—42no—
471C4—82no—
472C4#456×C10312yes—
473C4#576×C10312yes—
474C4#577×C10312yes—
475C2—41no—
476C2—82no—
477C2—82no—
478C2C103×#300811yescharacteristic
479C2C103×#300911yescharacteristic
480C2C2×#456×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3548C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3226C2semidirect
3. C103×#3206C2semidirect
4. C103×#3165C2semidirect
5. C103×#1654C2semidirect
6. C103×#1647C2semidirect
7. C103×#1544C2semidirect
8. C103×#1484C2semidirect
9. C103×#1484C2semidirect
234. #18734C103direct (N × H)
242. #3226C2×C103semidirect
243. #3206C2×C103semidirect
244. #3165C2×C103semidirect
245. #1654C2×C103semidirect
246. #1647C2×C103semidirect
247. #1544C2×C103semidirect
248. #1484C2×C103semidirect
249. #1484C2×C103semidirect
250. C103#18734direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#35482
C103×#32262
C103×#32062
C103×#31652
C103×#16542
C103×#16472
C103×#15442
C103×#14842
#18734103