Finite Group Databasebeta

← C103×#8336 #39913611

Subgroups — C103×#8336 #39913611

Order 26368.

846 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C103C211yesmaximal, characteristic
2C103×#1749C211yesmaximal, characteristic, complemented
3C103×#1749C211yesmaximal, characteristic, complemented
4C2×#330×C103C212yesmaximal, complemented
5C2×#329×C103C212yesmaximal, complemented
6#529×C103—24no—
7#529×C103—24no—
8C2×#126×C103—21no—
9C2×#125×C103C2211yescharacteristic
10C2×#124×C103C2211yescharacteristic
11C2×#123×C103—21no—
12C2×C22⋊Q8×C103C411yescharacteristic
13C2×#121×C103C411yescharacteristic
14C2×C4×Q8×C103C411yescharacteristic
15C2×C4×D4×C103—21no—
16C2×C4×D4×C103C411yescharacteristic
17C2×#117×C103—21no—
18C22×C42×C103C2211yescharacteristic
19C2×C22⋊C8×C103—21no—
20C2×C22⋊C8×C103—21no—
21C2×#97×C103C2212yes—
22C2×#97×C103C2212yes—
23#336×C103—21no—
24#336×C103—21no—
25#330×C103—24no—
26#329×C103—24no—
27C22×Q8×C103C2×C411yescharacteristic
28C22×D4×C103—21no—
29C22×D4×C103C2×C411yescharacteristic
30C23×C4×C103—21no—
31C23×C4×C103C2×C411yescharacteristic
32C23×C4×C103D411yescharacteristic
33C23×C4×C103D411yescharacteristic
34C22×C8×C103—22no—
35C22×C8×C103—22no—
36#126×C103—28no—
37#125×C103—22no—
38#125×C103D414yes—
39#124×C103—22no—
40#124×C103D414yes—
41#123×C103—28no—
42C22⋊Q8×C103—22no—
43C22⋊Q8×C103—22no—
44#121×C103—22no—
45#121×C103—22no—
46C4×Q8×C103—22no—
47C4×Q8×C103—22no—
48C4×D4×C103—28no—
49C4×D4×C103—22no—
50C4×D4×C103—22no—
51#117×C103—28no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103—21no—
54C2×C4⋊C4×C103—21no—
55C2×C4⋊C4×C103—21no—
56C2×C4⋊C4×C103C2×C411yescharacteristic
57C2×C4⋊C4×C103C2×C411yescharacteristic
58C2×C22⋊C4×C103—21no—
59C2×C22⋊C4×C103—21no—
60C2×C22⋊C4×C103—21no—
61C2×C22⋊C4×C103—21no—
62C2×C22⋊C4×C103—21no—
63C2×C42×C103—21no—
64C2×C42×C103—22no—
65C2×C42×C103—22no—
66C2×C42×C103C2×C411yescharacteristic
67C2×C42×C103D411yescharacteristic
68C2×C42×C103D411yescharacteristic
69C2×C42×C103C2311yescharacteristic
70C22⋊C8×C103—24no—
71C22⋊C8×C103—24no—
72#97×C103—22no—
73#97×C103—22no—
74#97×C103—22no—
75#97×C103—22no—
76C24×C103—21no—
77C24×C103C22⋊C411yescharacteristic
78C2×Q8×C103—21no—
79C2×Q8×C103—41no—
80C2×Q8×C103—41no—
81C2×Q8×C103C22⋊C412yes—
82C2×D4×C103—24no—
83C2×D4×C103—21no—
84C2×D4×C103—41no—
85C2×D4×C103—41no—
86C2×D4×C103—42no—
87C2×D4×C103—42no—
88C2×D4×C103C22⋊C412yes—
89C22×C4×C103—24no—
90C22×C4×C103—22no—
91C22×C4×C103—21no—
92C22×C4×C103—21no—
93C22×C4×C103—21no—
94C22×C4×C103—22no—
95C22×C4×C103—21no—
96C22×C4×C103—21no—
97C22×C4×C103—22no—
98C22×C4×C103—22no—
99C22×C4×C103—41no—
100C22×C4×C103—41no—
101C22×C4×C103—41no—
102C22×C4×C103—41no—
103C22×C4×C103—42no—
104C22×C4×C103—42no—
105C22×C4×C103C22⋊C411yescharacteristic
106C22×C4×C103C22⋊C411yescharacteristic
107C22×C4×C103C22⋊C411yescharacteristic
108C22×C4×C103C22×C411yescharacteristic
109C22×C4×C103C2×D411yescharacteristic
110C22×C4×C103C2×D411yescharacteristic
111C2×C8×C103—24no—
112C2×C8×C103—24no—
113C2×C8×C103—42no—
114C2×C8×C103—42no—
115C2×C8×C103—42no—
116C2×C8×C103—42no—
117C4⋊C4×C103—24no—
118C4⋊C4×C103—24no—
119C4⋊C4×C103—21no—
120C4⋊C4×C103—21no—
121C4⋊C4×C103—24no—
122C4⋊C4×C103—24no—
123C4⋊C4×C103C22⋊C412yes—
124C4⋊C4×C103C22⋊C412yes—
125C22⋊C4×C103—24no—
126C22⋊C4×C103—24no—
127C22⋊C4×C103—24no—
128C22⋊C4×C103—24no—
129C22⋊C4×C103—24no—
130C42×C103—24no—
131C42×C103—21no—
132C42×C103—21no—
133C42×C103—22no—
134C42×C103—22no—
135C42×C103C2×D412yes—
136C42×C103C2×D412yes—
137C23×C103—21no—
138C23×C103—21no—
139C23×C103—21no—
140C23×C103—21no—
141C23×C103—21no—
142C23×C103—21no—
143C23×C103—22no—
144C23×C103—41no—
145C23×C103—41no—
146C23×C103—41no—
147C23×C103—41no—
148C23×C103—41no—
149C23×C103—41no—
150C23×C103#10412yes—
151C23×C103C2×C22⋊C411yescharacteristic
152Q8×C103—42no—
153Q8×C103—42no—
154D4×C103—42no—
155D4×C103—42no—
156D4×C103—48no—
157C2×C4×C103—21no—
158C2×C4×C103—21no—
159C2×C4×C103—21no—
160C2×C4×C103—21no—
161C2×C4×C103—21no—
162C2×C4×C103—21no—
163C2×C4×C103—21no—
164C2×C4×C103—21no—
165C2×C4×C103—21no—
166C2×C4×C103—21no—
167C2×C4×C103—22no—
168C2×C4×C103—22no—
169C2×C4×C103—22no—
170C2×C4×C103—21no—
171C2×C4×C103—21no—
172C2×C4×C103—21no—
173C2×C4×C103—21no—
174C2×C4×C103—44no—
175C2×C4×C103—44no—
176C2×C4×C103—42no—
177C2×C4×C103—42no—
178C2×C4×C103—48no—
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#10412yes—
186C2×C4×C103C2×C22⋊C411yescharacteristic
187C2×C4×C103C2×C22⋊C411yescharacteristic
188C2×C4×C103#12012yes—
189C2×C4×C103#12012yes—
190C8×C103—44no—
191C8×C103—44no—
192C22×C103—22no—
193C22×C103—22no—
194C22×C103—22no—
195C22×C103—41no—
196C22×C103—41no—
197C22×C103—41no—
198C22×C103—41no—
199C22×C103—42no—
200C22×C103—42no—
201C22×C103—42no—
202C22×C103—81no—
203C22×C103—81no—
204C22×C103—81no—
205C22×C103—81no—
206C22×C103#37911yescharacteristic
207C22×C103#41311yescharacteristic
208C22×C103#41311yescharacteristic
209C22×C103C2×#10411yescharacteristic
210C22×C103C2×#10411yescharacteristic
211C22×C103#42111yescharacteristic
212C22×C103#42111yescharacteristic
213C4×C103—21no—
214C4×C103—21no—
215C4×C103—22no—
216C4×C103—22no—
217C4×C103—22no—
218C4×C103—41no—
219C4×C103—42no—
220C4×C103—41no—
221C4×C103—42no—
222C4×C103—42no—
223#8336C10311yesmaximal, characteristic, direct product factor, Sylow
224C2×C103—42no—
225C2×C103—82no—
226C2×C103#152411yescharacteristic
227C2×C103#152911yescharacteristic
228C2×C103#153211yescharacteristic
229C2×C103#153511yescharacteristic
230C2×C103#178511yescharacteristic
231C2×C103#178911yescharacteristic
232C2×C103#178911yescharacteristic
233C2×#529C2×C10311yescharacteristic
234#1749C2×C10311yescharacteristic, complemented
235#1749C2×C10311yescharacteristic, complemented
236C2×#330C2×C10312yescomplemented
237C2×#329C2×C10312yescomplemented
238C103#833611yescharacteristic, direct product factor, Sylow
239#529—24no—
240#529—24no—
241C2×#126—21no—
242C2×#125C22×C10311yescharacteristic
243C2×#124C22×C10311yescharacteristic
244C2×#123—21no—
245C2×C22⋊Q8C4×C10311yescharacteristic
246C2×#121C4×C10311yescharacteristic
247C2×C4×Q8C4×C10311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4C4×C10311yescharacteristic
250C2×#117—21no—
251C22×C42C22×C10311yescharacteristic
252C2×C22⋊C8—21no—
253C2×C22⋊C8—21no—
254C2×#97C22×C10312yes—
255C2×#97C22×C10312yes—
256#336—21no—
257#336—21no—
258#330—24no—
259#329—24no—
260C22×Q8C2×C4×C10311yescharacteristic
261C22×D4—21no—
262C22×D4C2×C4×C10311yescharacteristic
263C23×C4—21no—
264C23×C4C2×C4×C10311yescharacteristic
265C23×C4D4×C10311yescharacteristic
266C23×C4D4×C10311yescharacteristic
267C22×C8—22no—
268C22×C8—22no—
269#126—28no—
270#125—22no—
271#125D4×C10314yes—
272#124—22no—
273#124D4×C10314yes—
274#123—28no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277#121—22no—
278#121—22no—
279C4×Q8—22no—
280C4×Q8—22no—
281C4×D4—28no—
282C4×D4—22no—
283C4×D4—22no—
284#117—28no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4C2×C4×C10311yescharacteristic
290C2×C4⋊C4C2×C4×C10311yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C42—21no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42C2×C4×C10311yescharacteristic
300C2×C42D4×C10311yescharacteristic
301C2×C42D4×C10311yescharacteristic
302C2×C42C23×C10311yescharacteristic
303C22⋊C8—24no—
304C22⋊C8—24no—
305#97—22no—
306#97—22no—
307#97—22no—
308#97—22no—
309C24—21no—
310C24C22⋊C4×C10311yescharacteristic
311C2×Q8—21no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8C22⋊C4×C10312yes—
315C2×D4—24no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—42no—
320C2×D4—42no—
321C2×D4C22⋊C4×C10312yes—
322C22×C4—24no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4C22⋊C4×C10311yescharacteristic
339C22×C4C22⋊C4×C10311yescharacteristic
340C22×C4C22⋊C4×C10311yescharacteristic
341C22×C4C22×C4×C10311yescharacteristic
342C22×C4C2×D4×C10311yescharacteristic
343C22×C4C2×D4×C10311yescharacteristic
344C2×C8—24no—
345C2×C8—24no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—42no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4C22⋊C4×C10312yes—
357C4⋊C4C22⋊C4×C10312yes—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—24no—
363C42—24no—
364C42—21no—
365C42—21no—
366C42—22no—
367C42—22no—
368C42C2×D4×C10312yes—
369C42C2×D4×C10312yes—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—22no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23#104×C10312yes—
384C23C2×C22⋊C4×C10311yescharacteristic
385Q8—42no—
386Q8—42no—
387D4—42no—
388D4—42no—
389D4—48no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—48no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4#104×C10312yes—
419C2×C4C2×C22⋊C4×C10311yescharacteristic
420C2×C4C2×C22⋊C4×C10311yescharacteristic
421C2×C4#120×C10312yes—
422C2×C4#120×C10312yes—
423C8—44no—
424C8—44no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22#379×C10311yescharacteristic
440C22#413×C10311yescharacteristic
441C22#413×C10311yescharacteristic
442C22C2×#104×C10311yescharacteristic
443C22C2×#104×C10311yescharacteristic
444C22#421×C10311yescharacteristic
445C22#421×C10311yescharacteristic
446C4—21no—
447C4—21no—
448C4—22no—
449C4—22no—
450C4—22no—
451C4—41no—
452C4—42no—
453C4—41no—
454C4—42no—
455C4—42no—
456C2—42no—
457C2—82no—
458C2C103×#152411yescharacteristic
459C2C103×#152911yescharacteristic
460C2C103×#153211yescharacteristic
461C2C103×#153511yescharacteristic
462C2C103×#178511yescharacteristic
463C2C103×#178911yescharacteristic
464C2C103×#178911yescharacteristic
subgroupG/H
center, socleC23×C103C2×C22⋊C4
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC2×#121×C103C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1749C2semidirect
3. C103×#1749C2semidirect
4. C2×#330×C103C2semidirect
5. C2×#329×C103C2semidirect
223. #8336C103direct (N × H)
234. #1749C2×C103semidirect
235. #1749C2×C103semidirect
236. C2×#330C2×C103semidirect
237. C2×#329C2×C103semidirect
238. C103#8336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#529×C1032
C103×#17492
C2×#330×C1032
C2×#329×C1032
#8336103