Finite Group Databasebeta

← C103×#33879 #39939154

Subgroups — C103×#33879 #39939154

Order 26368.

536 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3336C211yesmaximal, characteristic
2D4×Q16×C103C211yesmaximal, characteristic
3C103×#2245C211yesmaximal, characteristic, complemented
4C103×#2237C211yesmaximal, characteristic, complemented
5C103×#2235C211yesmaximal, characteristic, complemented
6C103×#2229C211yesmaximal, characteristic, complemented
7C103×#2219C211yesmaximal, characteristic, complemented
8C103×#2216C211yesmaximal, characteristic, complemented
9C103×#2209C211yesmaximal, characteristic, complemented
10C103×#2188C211yesmaximal, characteristic, complemented
11C103×#2188C211yesmaximal, characteristic, complemented
12C103×#2176C211yesmaximal, characteristic, complemented
13C103×#2168C211yesmaximal, characteristic
14C103×#2141C211yesmaximal, characteristic, complemented
15C2×#358×C103C211yesmaximal, characteristic, complemented
16C22×Q16×C103C2211yescharacteristic
17C22×Q16×C103C2211yescharacteristic
18#552×C103—21no—
19D4×Q8×C103—21no—
20C2×Q32×C103C2211yescharacteristic
21C2×Q32×C103C2211yescharacteristic
22C2×Q32×C103C2211yescharacteristic
23C2×M32×C103C2211yescharacteristic
24C22×C16×C103C2211yescharacteristic
25#499×C103C2211yescharacteristic
26#494×C103C2211yescharacteristic
27#485×C103—21no—
28#483×C103—21no—
29#479×C103—21no—
30#467×C103C2211yescharacteristic
31#467×C103C2211yescharacteristic
32#467×C103C2211yescharacteristic
33#467×C103C2211yescharacteristic
34#462×C103—21no—
35#451×C103—21no—
36#451×C103—21no—
37C4×Q16×C103C2211yescharacteristic
38C4×Q16×C103C2211yescharacteristic
39C8×D4×C103C2211yescharacteristic
40#427×C103C2211yescharacteristic
41C2×#107×C103C2211yescharacteristic
42#367×C103C2211yescharacteristic
43#367×C103C2211yescharacteristic
44#366×C103C2211yescharacteristic
45C4⋊C16×C103C2211yescharacteristic
46#358×C103C2211yescharacteristic
47#358×C103C2211yescharacteristic
48#358×C103C2211yescharacteristic
49#358×C103C2211yescharacteristic
50#358×C103C2211yescharacteristic
51#358×C103C2211yescharacteristic
52#358×C103C2211yescharacteristic
53#358×C103C2211yescharacteristic
54#358×C103C2211yescharacteristic
55#358×C103C2211yescharacteristic
56C22⋊C16×C103C2211yescharacteristic
57C22⋊C16×C103C2211yescharacteristic
58#346×C103C2211yescharacteristic
59C22×Q8×C103—21no—
60C22×Q8×C103—21no—
61C2×Q16×C103—22no—
62C2×Q16×C103—22no—
63C2×Q16×C103—21no—
64C2×Q16×C103—21no—
65C2×Q16×C103—21no—
66C2×Q16×C103—41no—
67C2×Q16×C103—41no—
68C2×Q16×C103C2311yescharacteristic
69C2×Q16×C103C2311yescharacteristic
70C2×Q16×C103C2311yescharacteristic
71C2×Q16×C103C2311yescharacteristic
72C22×C8×C103C2311yescharacteristic
73C22×C8×C103C2311yescharacteristic
74C4⋊Q8×C103—21no—
75C4⋊Q8×C103—41no—
76#126×C103—41no—
77#125×C103—21no—
78#125×C103—41no—
79#123×C103—41no—
80C22⋊Q8×C103—21no—
81C22⋊Q8×C103—21no—
82C22⋊Q8×C103—21no—
83C22⋊Q8×C103—21no—
84C22⋊Q8×C103—41no—
85C22⋊Q8×C103—41no—
86C4×Q8×C103—21no—
87C4×Q8×C103—21no—
88C4×D4×C103—41no—
89C4×D4×C103D411yescharacteristic
90#117×C103—21no—
91#117×C103—41no—
92C2×C4⋊C4×C103—21no—
93Q32×C103—22no—
94Q32×C103—41no—
95Q32×C103—41no—
96M32×C103—41no—
97C2×C16×C103—41no—
98C2×C16×C103C2311yescharacteristic
99C2×C16×C103C2311yescharacteristic
100C2×C16×C103C2311yescharacteristic
101C2×C16×C103C2311yescharacteristic
102#107×C103—21no—
103#107×C103C2311yescharacteristic
104#107×C103C2311yescharacteristic
105#107×C103C2311yescharacteristic
106#107×C103C2311yescharacteristic
107#106×C103—21no—
108#106×C103—21no—
109C4⋊C8×C103D411yescharacteristic
110#103×C103—21no—
111#103×C103—21no—
112#103×C103—21no—
113#103×C103—21no—
114#103×C103—21no—
115#103×C103—21no—
116C22⋊C8×C103D411yescharacteristic
117C22⋊C8×C103D411yescharacteristic
118C4×C8×C103C2311yescharacteristic
119C2×Q8×C103—21no—
120C2×Q8×C103—21no—
121C2×Q8×C103—21no—
122C2×Q8×C103—21no—
123C2×Q8×C103—42no—
124C2×Q8×C103—42no—
125C2×Q8×C103—41no—
126C2×Q8×C103—41no—
127C2×Q8×C103—81no—
128C2×Q8×C103—81no—
129C2×D4×C103D811yescharacteristic
130C22×C4×C103—41no—
131C22×C4×C103—41no—
132C22×C4×C103—41no—
133C22×C4×C103C2×D411yescharacteristic
134C22×C4×C103C2×D411yescharacteristic
135Q16×C103—21no—
136Q16×C103—21no—
137Q16×C103—21no—
138Q16×C103—21no—
139Q16×C103—21no—
140Q16×C103—21no—
141Q16×C103—21no—
142Q16×C103—42no—
143Q16×C103—42no—
144Q16×C103—81no—
145Q16×C103#4112yes—
146C2×C8×C103—21no—
147C2×C8×C103—21no—
148C2×C8×C103—21no—
149C2×C8×C103—21no—
150C2×C8×C103C2×D411yescharacteristic
151C2×C8×C103C2×D411yescharacteristic
152C2×C8×C103C2×D411yescharacteristic
153C2×C8×C103C2411yescharacteristic
154C4⋊C4×C103—21no—
155C4⋊C4×C103—21no—
156C4⋊C4×C103—21no—
157C4⋊C4×C103—21no—
158C4⋊C4×C103—41no—
159C4⋊C4×C103—41no—
160C4⋊C4×C103—41no—
161C4⋊C4×C103—41no—
162C4⋊C4×C103—41no—
163C4⋊C4×C103—41no—
164C4⋊C4×C103—41no—
165C4⋊C4×C103—41no—
166C4⋊C4×C103—41no—
167C4⋊C4×C103—41no—
168C4⋊C4×C103—41no—
169C4⋊C4×C103D811yescharacteristic
170C22⋊C4×C103—41no—
171C22⋊C4×C103—41no—
172C22⋊C4×C103—41no—
173C22⋊C4×C103—41no—
174C22⋊C4×C103—41no—
175C22⋊C4×C103D811yescharacteristic
176C22⋊C4×C103D811yescharacteristic
177C42×C103—41no—
178C42×C103—41no—
179C42×C103—41no—
180C42×C103C2×D411yescharacteristic
181C16×C103—21no—
182C16×C103—21no—
183C16×C103—21no—
184C16×C103—21no—
185C23×C103C2×D811yescharacteristic
186C23×C103C2×D811yescharacteristic
187Q8×C103—22no—
188Q8×C103—41no—
189Q8×C103—41no—
190Q8×C103—41no—
191Q8×C103—41no—
192Q8×C103—41no—
193Q8×C103—41no—
194Q8×C103—41no—
195Q8×C103—82no—
196Q8×C103—82no—
197D4×C103—22no—
198C2×C4×C103—21no—
199C2×C4×C103—21no—
200C2×C4×C103—21no—
201C2×C4×C103—21no—
202C2×C4×C103—41no—
203C2×C4×C103—41no—
204C2×C4×C103—41no—
205C2×C4×C103—41no—
206C2×C4×C103—41no—
207C2×C4×C103—41no—
208C2×C4×C103—41no—
209C2×C4×C103—41no—
210C2×C4×C103—82no—
211C2×C4×C103—82no—
212C2×C4×C103—82no—
213C2×C4×C103C2×D811yescharacteristic
214C2×C4×C103C2×D811yescharacteristic
215C2×C4×C103C2×D811yescharacteristic
216C2×C4×C103C2×D811yescharacteristic
217C2×C4×C103C22×D411yescharacteristic
218C8×C103—21no—
219C8×C103—21no—
220C8×C103—21no—
221C8×C103C2×#4111yescharacteristic
222C8×C103H(5,𝔽2)11yescharacteristic
223C22×C103—21no—
224C22×C103—21no—
225C22×C103—21no—
226C22×C103—21no—
227C22×C103—21no—
228C22×C103#51012yes—
229C22×C103C22×D811yescharacteristic
230C4×C103—21no—
231C4×C103—21no—
232C4×C103—21no—
233C4×C103—21no—
234C4×C103—42no—
235C4×C103—81no—
236C4×C103—81no—
237C4×C103—81no—
238C4×C103—81no—
239C4×C103—81no—
240C4×C103—81no—
241C4×C103—81no—
242C4×C103#54611yescharacteristic
243C4×C103#57711yescharacteristic
244#33879C10311yesmaximal, characteristic, direct product factor, Sylow
245C2×C103—22no—
246C2×C103—41no—
247C2×C103#329411yescharacteristic
248C2×C103C2×#51011yescharacteristic
249C2×C103#341711yescharacteristic
250#3336C2×C10311yescharacteristic
251D4×Q16C2×C10311yescharacteristic
252#2245C2×C10311yescharacteristic, complemented
253#2237C2×C10311yescharacteristic, complemented
254#2235C2×C10311yescharacteristic, complemented
255#2229C2×C10311yescharacteristic, complemented
256#2219C2×C10311yescharacteristic, complemented
257#2216C2×C10311yescharacteristic, complemented
258#2209C2×C10311yescharacteristic, complemented
259#2188C2×C10311yescharacteristic, complemented
260#2188C2×C10311yescharacteristic, complemented
261#2176C2×C10311yescharacteristic, complemented
262#2168C2×C10311yescharacteristic
263#2141C2×C10311yescharacteristic, complemented
264C2×#358C2×C10311yescharacteristic, complemented
265C103#3387911yescharacteristic, direct product factor, Sylow
266C22×Q16C22×C10311yescharacteristic
267C22×Q16C22×C10311yescharacteristic
268#552—21no—
269D4×Q8—21no—
270C2×Q32C22×C10311yescharacteristic
271C2×Q32C22×C10311yescharacteristic
272C2×Q32C22×C10311yescharacteristic
273C2×M32C22×C10311yescharacteristic
274C22×C16C22×C10311yescharacteristic
275#499C22×C10311yescharacteristic
276#494C22×C10311yescharacteristic
277#485—21no—
278#483—21no—
279#479—21no—
280#467C22×C10311yescharacteristic
281#467C22×C10311yescharacteristic
282#467C22×C10311yescharacteristic
283#467C22×C10311yescharacteristic
284#462—21no—
285#451—21no—
286#451—21no—
287C4×Q16C22×C10311yescharacteristic
288C4×Q16C22×C10311yescharacteristic
289C8×D4C22×C10311yescharacteristic
290#427C22×C10311yescharacteristic
291C2×#107C22×C10311yescharacteristic
292#367C22×C10311yescharacteristic
293#367C22×C10311yescharacteristic
294#366C22×C10311yescharacteristic
295C4⋊C16C22×C10311yescharacteristic
296#358C22×C10311yescharacteristic
297#358C22×C10311yescharacteristic
298#358C22×C10311yescharacteristic
299#358C22×C10311yescharacteristic
300#358C22×C10311yescharacteristic
301#358C22×C10311yescharacteristic
302#358C22×C10311yescharacteristic
303#358C22×C10311yescharacteristic
304#358C22×C10311yescharacteristic
305#358C22×C10311yescharacteristic
306C22⋊C16C22×C10311yescharacteristic
307C22⋊C16C22×C10311yescharacteristic
308#346C22×C10311yescharacteristic
309C22×Q8—21no—
310C22×Q8—21no—
311C2×Q16—22no—
312C2×Q16—22no—
313C2×Q16—21no—
314C2×Q16—21no—
315C2×Q16—21no—
316C2×Q16—41no—
317C2×Q16—41no—
318C2×Q16C23×C10311yescharacteristic
319C2×Q16C23×C10311yescharacteristic
320C2×Q16C23×C10311yescharacteristic
321C2×Q16C23×C10311yescharacteristic
322C22×C8C23×C10311yescharacteristic
323C22×C8C23×C10311yescharacteristic
324C4⋊Q8—21no—
325C4⋊Q8—41no—
326#126—41no—
327#125—21no—
328#125—41no—
329#123—41no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—41no—
335C22⋊Q8—41no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×D4—41no—
339C4×D4D4×C10311yescharacteristic
340#117—21no—
341#117—41no—
342C2×C4⋊C4—21no—
343Q32—22no—
344Q32—41no—
345Q32—41no—
346M32—41no—
347C2×C16—41no—
348C2×C16C23×C10311yescharacteristic
349C2×C16C23×C10311yescharacteristic
350C2×C16C23×C10311yescharacteristic
351C2×C16C23×C10311yescharacteristic
352#107—21no—
353#107C23×C10311yescharacteristic
354#107C23×C10311yescharacteristic
355#107C23×C10311yescharacteristic
356#107C23×C10311yescharacteristic
357#106—21no—
358#106—21no—
359C4⋊C8D4×C10311yescharacteristic
360#103—21no—
361#103—21no—
362#103—21no—
363#103—21no—
364#103—21no—
365#103—21no—
366C22⋊C8D4×C10311yescharacteristic
367C22⋊C8D4×C10311yescharacteristic
368C4×C8C23×C10311yescharacteristic
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—42no—
374C2×Q8—42no—
375C2×Q8—41no—
376C2×Q8—41no—
377C2×Q8—81no—
378C2×Q8—81no—
379C2×D4D8×C10311yescharacteristic
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4C2×D4×C10311yescharacteristic
384C22×C4C2×D4×C10311yescharacteristic
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—21no—
390Q16—21no—
391Q16—21no—
392Q16—42no—
393Q16—42no—
394Q16—81no—
395Q16#41×C10312yes—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8C2×D4×C10311yescharacteristic
401C2×C8C2×D4×C10311yescharacteristic
402C2×C8C2×D4×C10311yescharacteristic
403C2×C8C24×C10311yescharacteristic
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4D8×C10311yescharacteristic
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4D8×C10311yescharacteristic
426C22⋊C4D8×C10311yescharacteristic
427C42—41no—
428C42—41no—
429C42—41no—
430C42C2×D4×C10311yescharacteristic
431C16—21no—
432C16—21no—
433C16—21no—
434C16—21no—
435C23C2×D8×C10311yescharacteristic
436C23C2×D8×C10311yescharacteristic
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—82no—
446Q8—82no—
447D4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—82no—
463C2×C4C2×D8×C10311yescharacteristic
464C2×C4C2×D8×C10311yescharacteristic
465C2×C4C2×D8×C10311yescharacteristic
466C2×C4C2×D8×C10311yescharacteristic
467C2×C4C22×D4×C10311yescharacteristic
468C8—21no—
469C8—21no—
470C8—21no—
471C8C2×#41×C10311yescharacteristic
472C8H(5,𝔽2)×C10311yescharacteristic
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22#510×C10312yes—
479C22C22×D8×C10311yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—81no—
492C4#546×C10311yescharacteristic
493C4#577×C10311yescharacteristic
494C2—22no—
495C2—41no—
496C2C103×#329411yescharacteristic
497C2C2×#510×C10311yescharacteristic
498C2C103×#341711yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
prime radicalC2×D4×C103D8
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
3. C103×#2245C2semidirect
4. C103×#2237C2semidirect
5. C103×#2235C2semidirect
6. C103×#2229C2semidirect
7. C103×#2219C2semidirect
8. C103×#2216C2semidirect
9. C103×#2209C2semidirect
10. C103×#2188C2semidirect
11. C103×#2188C2semidirect
12. C103×#2176C2semidirect
14. C103×#2141C2semidirect
15. C2×#358×C103C2semidirect
244. #33879C103direct (N × H)
252. #2245C2×C103semidirect
253. #2237C2×C103semidirect
254. #2235C2×C103semidirect
255. #2229C2×C103semidirect
256. #2219C2×C103semidirect
257. #2216C2×C103semidirect
258. #2209C2×C103semidirect
259. #2188C2×C103semidirect
260. #2188C2×C103semidirect
261. #2176C2×C103semidirect
263. #2141C2×C103semidirect
264. C2×#358C2×C103semidirect
265. C103#33879direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#33362
D4×Q16×C1032
C103×#22452
C103×#22372
C103×#22352
C103×#22292
C103×#22192
C103×#22162
C103×#22092
C103×#21882
C103×#21762
C103×#21682
C103×#21412
C2×#358×C1032
#33879103