Finite Group Databasebeta

← C103×#19519 #39924794

Subgroups — C103×#19519 #39924794

Order 26368.

602 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3253C211yesmaximal, characteristic
2C103×#3246C211yesmaximal, characteristic, complemented
3C103×#3228C211yesmaximal, characteristic, complemented
4C103×#2981C211yesmaximal, characteristic, complemented
5C103×#1697C212yesmaximal, complemented
6C103×#1691C212yesmaximal, complemented
7C103×#1681C212yesmaximal, complemented
8C103×#1675C212yesmaximal, complemented
9C103×#1571C211yesmaximal, characteristic, complemented
10C103×#1559C211yesmaximal, characteristic, complemented
11C103×#1551C211yesmaximal, characteristic, complemented
12#533×C103C2211yescharacteristic
13#532×C103C2211yescharacteristic
14#532×C103C2211yescharacteristic
15#500×C103C2211yescharacteristic
16#498×C103C2211yescharacteristic
17#486×C103C2211yescharacteristic
18#486×C103C2211yescharacteristic
19#482×C103—22no—
20#478×C103—22no—
21#476×C103—21no—
22#476×C103C2212yes—
23#476×C103C2212yes—
24#475×C103—21no—
25#469×C103—22no—
26#465×C103—22no—
27#461×C103C2212yes—
28#460×C103—21no—
29#459×C103—21no—
30#459×C103C2212yes—
31#436×C103C2212yes—
32#435×C103—22no—
33C8×D4×C103C2212yes—
34#432×C103C2211yescharacteristic
35#431×C103C2211yescharacteristic
36#423×C103C2211yescharacteristic
37C2×C4⋊C8×C103C2211yescharacteristic
38#408×C103—22no—
39#335×C103C2212yes—
40#335×C103C2212yes—
41#333×C103C2212yes—
42#333×C103C2212yes—
43#332×C103C2212yes—
44#331×C103C2212yes—
45C2×#41×C103—21no—
46C2×#41×C103—21no—
47C2×SD16×C103—22no—
48C2×D8×C103—22no—
49C2×M16×C103—21no—
50C2×M16×C103—22no—
51C22×C8×C103—21no—
52C22×C8×C103—22no—
53C4⋊Q8×C103D411yescharacteristic
54C4⋊Q8×C103C2311yescharacteristic
55C4⋊Q8×C103C2311yescharacteristic
56C4⋊Q8×C103C2311yescharacteristic
57#127×C103D411yescharacteristic
58#127×C103C2311yescharacteristic
59#125×C103—21no—
60#124×C103—21no—
61#124×C103—21no—
62C22⋊Q8×C103—21no—
63C22⋊Q8×C103—21no—
64#121×C103—21no—
65#121×C103—21no—
66#121×C103—21no—
67#121×C103D412yes—
68C4×Q8×C103—21no—
69C4×Q8×C103—21no—
70C4×D4×C103—21no—
71C4×D4×C103—21no—
72C4×D4×C103—21no—
73C4×D4×C103C2312yes—
74#117×C103—21no—
75C2×C42×C103C2311yescharacteristic
76#107×C103—22no—
77#106×C103—22no—
78#106×C103—22no—
79#106×C103—22no—
80C4⋊C8×C103—21no—
81C4⋊C8×C103—21no—
82C4⋊C8×C103D412yes—
83C4⋊C8×C103C2312yes—
84C4⋊C8×C103C2312yes—
85C4⋊C8×C103C2312yes—
86#103×C103—22no—
87#102×C103—22no—
88#102×C103—22no—
89#102×C103—22no—
90#102×C103—22no—
91#102×C103—22no—
92C22⋊C8×C103—21no—
93C22⋊C8×C103—22no—
94C22⋊C8×C103—22no—
95C22⋊C8×C103D412yes—
96#97×C103—21no—
97C4×C8×C103C2311yescharacteristic
98C4×C8×C103C2311yescharacteristic
99#41×C103—82no—
100#41×C103—82no—
101C2×Q8×C103—21no—
102C2×Q8×C103—21no—
103C2×Q8×C103—21no—
104C2×Q8×C103—21no—
105C2×D4×C103—22no—
106C2×D4×C103—21no—
107C2×D4×C103—21no—
108C2×D4×C103—21no—
109C2×D4×C103—21no—
110C2×D4×C103—21no—
111C2×D4×C103—41no—
112C2×D4×C103C2×D412yes—
113C22×C4×C103—22no—
114C22×C4×C103—41no—
115C22×C4×C103C2×D411yescharacteristic
116C22×C4×C103C2×D411yescharacteristic
117C22×C4×C103#4111yescharacteristic
118SD16×C103—82no—
119D8×C103—82no—
120M16×C103—82no—
121M16×C103—81no—
122C2×C8×C103—22no—
123C2×C8×C103—22no—
124C2×C8×C103—22no—
125C2×C8×C103—82no—
126C2×C8×C103—81no—
127C2×C8×C103C2×D412yes—
128C2×C8×C103C2×D412yes—
129C4⋊C4×C103—21no—
130C4⋊C4×C103—21no—
131C4⋊C4×C103—21no—
132C4⋊C4×C103—21no—
133C4⋊C4×C103—21no—
134C4⋊C4×C103—21no—
135C4⋊C4×C103—21no—
136C4⋊C4×C103—41no—
137C4⋊C4×C103—41no—
138C4⋊C4×C103C2×D412yes—
139C22⋊C4×C103—22no—
140C22⋊C4×C103—22no—
141C22⋊C4×C103—41no—
142C22⋊C4×C103—41no—
143C22⋊C4×C103—41no—
144C42×C103—41no—
145C42×C103C2×D411yescharacteristic
146C42×C103C2×D411yescharacteristic
147C42×C103#4111yescharacteristic
148C42×C103C2411yescharacteristic
149C23×C103—22no—
150C23×C103—41no—
151C23×C103#12111yescharacteristic
152Q8×C103—41no—
153Q8×C103—41no—
154Q8×C103—81no—
155Q8×C103—81no—
156Q8×C103—81no—
157D4×C103—22no—
158D4×C103—22no—
159D4×C103—41no—
160D4×C103—42no—
161D4×C103—41no—
162D4×C103—81no—
163D4×C103—81no—
164D4×C103—81no—
165D4×C103—82no—
166D4×C103—82no—
167C2×C4×C103—21no—
168C2×C4×C103—22no—
169C2×C4×C103—21no—
170C2×C4×C103—22no—
171C2×C4×C103—41no—
172C2×C4×C103—42no—
173C2×C4×C103—42no—
174C2×C4×C103—41no—
175C2×C4×C103—41no—
176C2×C4×C103—41no—
177C2×C4×C103—82no—
178C2×C4×C103#12111yescharacteristic
179C2×C4×C103#12111yescharacteristic
180C2×C4×C103#12111yescharacteristic
181C2×C4×C103C22×D411yescharacteristic
182C2×C4×C103C22×D411yescharacteristic
183C2×C4×C103C2×#4111yescharacteristic
184C8×C103—22no—
185C8×C103—22no—
186C8×C103—42no—
187C8×C103—42no—
188C8×C103—42no—
189C22×C103—21no—
190C22×C103—21no—
191C22×C103—21no—
192C22×C103—42no—
193C22×C103—42no—
194C22×C103—42no—
195C22×C103—81no—
196C22×C103—81no—
197C22×C103—81no—
198C22×C103C2×#12111yescharacteristic
199C4×C103—21no—
200C4×C103—21no—
201C4×C103—21no—
202C4×C103—21no—
203C4×C103—42no—
204C4×C103—81no—
205C4×C103—81no—
206C4×C103—81no—
207C4×C103#57611yescharacteristic
208C4×C103#57712yes—
209C4×C103#57811yescharacteristic
210#19519C10311yesmaximal, characteristic, direct product factor, Sylow
211C2×C103—41no—
212C2×C103—82no—
213C2×C103—161no—
214C2×C103#304211yescharacteristic
215C2×C103#306111yescharacteristic
216C2×C103#306811yescharacteristic
217#3253C2×C10311yescharacteristic
218#3246C2×C10311yescharacteristic, complemented
219#3228C2×C10311yescharacteristic, complemented
220#2981C2×C10311yescharacteristic, complemented
221#1697C2×C10312yescomplemented
222#1691C2×C10312yescomplemented
223#1681C2×C10312yescomplemented
224#1675C2×C10312yescomplemented
225#1571C2×C10311yescharacteristic, complemented
226#1559C2×C10311yescharacteristic, complemented
227#1551C2×C10311yescharacteristic, complemented
228C103#1951911yescharacteristic, direct product factor, Sylow
229#533C22×C10311yescharacteristic
230#532C22×C10311yescharacteristic
231#532C22×C10311yescharacteristic
232#500C22×C10311yescharacteristic
233#498C22×C10311yescharacteristic
234#486C22×C10311yescharacteristic
235#486C22×C10311yescharacteristic
236#482—22no—
237#478—22no—
238#476—21no—
239#476C22×C10312yes—
240#476C22×C10312yes—
241#475—21no—
242#469—22no—
243#465—22no—
244#461C22×C10312yes—
245#460—21no—
246#459—21no—
247#459C22×C10312yes—
248#436C22×C10312yes—
249#435—22no—
250C8×D4C22×C10312yes—
251#432C22×C10311yescharacteristic
252#431C22×C10311yescharacteristic
253#423C22×C10311yescharacteristic
254C2×C4⋊C8C22×C10311yescharacteristic
255#408—22no—
256#335C22×C10312yes—
257#335C22×C10312yes—
258#333C22×C10312yes—
259#333C22×C10312yes—
260#332C22×C10312yes—
261#331C22×C10312yes—
262C2×#41—21no—
263C2×#41—21no—
264C2×SD16—22no—
265C2×D8—22no—
266C2×M16—21no—
267C2×M16—22no—
268C22×C8—21no—
269C22×C8—22no—
270C4⋊Q8D4×C10311yescharacteristic
271C4⋊Q8C23×C10311yescharacteristic
272C4⋊Q8C23×C10311yescharacteristic
273C4⋊Q8C23×C10311yescharacteristic
274#127D4×C10311yescharacteristic
275#127C23×C10311yescharacteristic
276#125—21no—
277#124—21no—
278#124—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281#121—21no—
282#121—21no—
283#121—21no—
284#121D4×C10312yes—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4C23×C10312yes—
291#117—21no—
292C2×C42C23×C10311yescharacteristic
293#107—22no—
294#106—22no—
295#106—22no—
296#106—22no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8D4×C10312yes—
300C4⋊C8C23×C10312yes—
301C4⋊C8C23×C10312yes—
302C4⋊C8C23×C10312yes—
303#103—22no—
304#102—22no—
305#102—22no—
306#102—22no—
307#102—22no—
308#102—22no—
309C22⋊C8—21no—
310C22⋊C8—22no—
311C22⋊C8—22no—
312C22⋊C8D4×C10312yes—
313#97—21no—
314C4×C8C23×C10311yescharacteristic
315C4×C8C23×C10311yescharacteristic
316#41—82no—
317#41—82no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×D4—22no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4C2×D4×C10312yes—
330C22×C4—22no—
331C22×C4—41no—
332C22×C4C2×D4×C10311yescharacteristic
333C22×C4C2×D4×C10311yescharacteristic
334C22×C4#41×C10311yescharacteristic
335SD16—82no—
336D8—82no—
337M16—82no—
338M16—81no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—82no—
343C2×C8—81no—
344C2×C8C2×D4×C10312yes—
345C2×C8C2×D4×C10312yes—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4C2×D4×C10312yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C42—41no—
362C42C2×D4×C10311yescharacteristic
363C42C2×D4×C10311yescharacteristic
364C42#41×C10311yescharacteristic
365C42C24×C10311yescharacteristic
366C23—22no—
367C23—41no—
368C23#121×C10311yescharacteristic
369Q8—41no—
370Q8—41no—
371Q8—81no—
372Q8—81no—
373Q8—81no—
374D4—22no—
375D4—22no—
376D4—41no—
377D4—42no—
378D4—41no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—82no—
383D4—82no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4#121×C10311yescharacteristic
396C2×C4#121×C10311yescharacteristic
397C2×C4#121×C10311yescharacteristic
398C2×C4C22×D4×C10311yescharacteristic
399C2×C4C22×D4×C10311yescharacteristic
400C2×C4C2×#41×C10311yescharacteristic
401C8—22no—
402C8—22no—
403C8—42no—
404C8—42no—
405C8—42no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22C2×#121×C10311yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—42no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4#576×C10311yescharacteristic
425C4#577×C10312yes—
426C4#578×C10311yescharacteristic
427C2—41no—
428C2—82no—
429C2—161no—
430C2C103×#304211yescharacteristic
431C2C103×#306111yescharacteristic
432C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC103×#3253C2
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×#3246C2semidirect
3. C103×#3228C2semidirect
4. C103×#2981C2semidirect
5. C103×#1697C2semidirect
6. C103×#1691C2semidirect
7. C103×#1681C2semidirect
8. C103×#1675C2semidirect
9. C103×#1571C2semidirect
10. C103×#1559C2semidirect
11. C103×#1551C2semidirect
210. #19519C103direct (N × H)
218. #3246C2×C103semidirect
219. #3228C2×C103semidirect
220. #2981C2×C103semidirect
221. #1697C2×C103semidirect
222. #1691C2×C103semidirect
223. #1681C2×C103semidirect
224. #1675C2×C103semidirect
225. #1571C2×C103semidirect
226. #1559C2×C103semidirect
227. #1551C2×C103semidirect
228. C103#19519direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32532
C103×#32462
C103×#32282
C103×#29812
C103×#16972
C103×#16912
C103×#16812
C103×#16752
C103×#15712
C103×#15592
C103×#15512
#19519103