Finite Group Databasebeta

← C103×#33875 #39939150

Subgroups — C103×#33875 #39939150

Order 26368.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3334C211yesmaximal, characteristic, complemented
2C103×#3285C211yesmaximal, characteristic, complemented
3C103×#2243C211yesmaximal, characteristic, complemented
4C103×#2236C211yesmaximal, characteristic, complemented
5C103×#2232C211yesmaximal, characteristic, complemented
6C103×#2227C211yesmaximal, characteristic, complemented
7C103×#2220C211yesmaximal, characteristic, complemented
8C103×#2215C211yesmaximal, characteristic, complemented
9C103×#2210C211yesmaximal, characteristic, complemented
10C103×#2186C211yesmaximal, characteristic, complemented
11C103×#2185C211yesmaximal, characteristic, complemented
12C103×#2175C211yesmaximal, characteristic, complemented
13C103×#2168C211yesmaximal, characteristic, complemented
14C103×#2139C211yesmaximal, characteristic, complemented
15C2×#358×C103C211yesmaximal, characteristic, complemented
16C2×#135×C103C2211yescharacteristic
17C22×Q16×C103C2211yescharacteristic
18#548×C103—21no—
19#547×C103—21no—
20C2×SD32×C103C2211yescharacteristic
21C2×SD32×C103C2211yescharacteristic
22C2×D16×C103C2211yescharacteristic
23C2×M32×C103C2211yescharacteristic
24C22×C16×C103C2211yescharacteristic
25#500×C103C2211yescharacteristic
26#495×C103C2211yescharacteristic
27#480×C103—21no—
28#480×C103—21no—
29#474×C103—21no—
30#467×C103C2211yescharacteristic
31#466×C103C2211yescharacteristic
32#466×C103C2211yescharacteristic
33#466×C103C2211yescharacteristic
34#464×C103—21no—
35#452×C103—21no—
36#448×C103—21no—
37C4×Q16×C103C2211yescharacteristic
38C4×D8×C103C2211yescharacteristic
39C8×D4×C103C2211yescharacteristic
40C2×#107×C103C2211yescharacteristic
41C2×#107×C103C2211yescharacteristic
42#366×C103C2211yescharacteristic
43#366×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#357×C103C2211yescharacteristic
53#357×C103C2211yescharacteristic
54#357×C103C2211yescharacteristic
55#357×C103C2211yescharacteristic
56C22⋊C16×C103C2211yescharacteristic
57C22⋊C16×C103C2211yescharacteristic
58#346×C103C2211yescharacteristic
59C2×#41×C103—21no—
60C2×#41×C103—41no—
61C22×Q8×C103—21no—
62#135×C103—22no—
63#135×C103—41no—
64C2×Q16×C103—22no—
65C2×Q16×C103—21no—
66C2×Q16×C103—41no—
67C2×Q16×C103C2311yescharacteristic
68C2×Q16×C103C2311yescharacteristic
69C2×SD16×C103—21no—
70C2×SD16×C103—21no—
71C2×D8×C103C2311yescharacteristic
72C2×D8×C103C2311yescharacteristic
73C22×C8×C103C2311yescharacteristic
74C22×C8×C103C2311yescharacteristic
75C4⋊Q8×C103—21no—
76#124×C103—21no—
77#124×C103—41no—
78#123×C103—41no—
79#123×C103—41no—
80C22⋊Q8×C103—21no—
81C22⋊Q8×C103—41no—
82C22⋊Q8×C103—41no—
83#121×C103—21no—
84#121×C103—21no—
85#121×C103—21no—
86#121×C103—41no—
87C4×Q8×C103—21no—
88C4×D4×C103—21no—
89C4×D4×C103—41no—
90C4×D4×C103D411yescharacteristic
91C2×C4⋊C4×C103—21no—
92C2×C4⋊C4×C103—21no—
93SD32×C103—22no—
94SD32×C103—41no—
95D16×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×C103—21no—
104#107×C103—21no—
105#107×C103C2311yescharacteristic
106#107×C103C2311yescharacteristic
107#107×C103C2311yescharacteristic
108#107×C103C2311yescharacteristic
109C4⋊C8×C103D411yescharacteristic
110#103×C103—21no—
111#103×C103—21no—
112#102×C103—21no—
113#102×C103—21no—
114#102×C103—21no—
115#102×C103—21no—
116C22⋊C8×C103D411yescharacteristic
117C22⋊C8×C103D411yescharacteristic
118C4×C8×C103C2311yescharacteristic
119#41×C103—42no—
120#41×C103—81no—
121#41×C103—84no—
122C2×Q8×C103—21no—
123C2×Q8×C103—21no—
124C2×Q8×C103—42no—
125C2×Q8×C103—41no—
126C2×Q8×C103—41no—
127C2×Q8×C103—81no—
128C2×D4×C103—21no—
129C2×D4×C103—21no—
130C2×D4×C103—41no—
131C2×D4×C103—41no—
132C2×D4×C103—41no—
133C2×D4×C103—41no—
134C2×D4×C103D811yescharacteristic
135C22×C4×C103—41no—
136C22×C4×C103—41no—
137C22×C4×C103—41no—
138C22×C4×C103—41no—
139C22×C4×C103—41no—
140C22×C4×C103C2×D411yescharacteristic
141C22×C4×C103C2×D411yescharacteristic
142Q16×C103—21no—
143Q16×C103—21no—
144Q16×C103—21no—
145Q16×C103—42no—
146Q16×C103#4112yescomplemented
147SD16×C103—42no—
148SD16×C103—81no—
149D8×C103—21no—
150D8×C103—21no—
151D8×C103—21no—
152D8×C103—21no—
153C2×C8×C103—21no—
154C2×C8×C103—21no—
155C2×C8×C103—21no—
156C2×C8×C103—21no—
157C2×C8×C103C2×D411yescharacteristic
158C2×C8×C103C2×D411yescharacteristic
159C2×C8×C103C2×D411yescharacteristic
160C2×C8×C103C2411yescharacteristic
161C4⋊C4×C103—21no—
162C4⋊C4×C103—21no—
163C4⋊C4×C103—21no—
164C4⋊C4×C103—21no—
165C4⋊C4×C103—41no—
166C4⋊C4×C103—41no—
167C4⋊C4×C103—41no—
168C4⋊C4×C103—41no—
169C4⋊C4×C103—41no—
170C4⋊C4×C103D811yescharacteristic
171C22⋊C4×C103—41no—
172C22⋊C4×C103—41no—
173C22⋊C4×C103—41no—
174C22⋊C4×C103—41no—
175C22⋊C4×C103—41no—
176C22⋊C4×C103—41no—
177C22⋊C4×C103—41no—
178C22⋊C4×C103D811yescharacteristic
179C22⋊C4×C103D811yescharacteristic
180C42×C103—41no—
181C42×C103C2×D411yescharacteristic
182C16×C103—21no—
183C16×C103—21no—
184C16×C103—21no—
185C16×C103—21no—
186C23×C103—41no—
187C23×C103—41no—
188C23×C103C2×D811yescharacteristic
189C23×C103C2×D811yescharacteristic
190Q8×C103—22no—
191Q8×C103—41no—
192Q8×C103—41no—
193Q8×C103—41no—
194Q8×C103—82no—
195Q8×C103—82no—
196D4×C103—22no—
197D4×C103—41no—
198D4×C103—41no—
199D4×C103—41no—
200D4×C103—41no—
201D4×C103—82no—
202D4×C103—82no—
203D4×C103—82no—
204D4×C103—82no—
205C2×C4×C103—21no—
206C2×C4×C103—21no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—41no—
210C2×C4×C103—41no—
211C2×C4×C103—41no—
212C2×C4×C103—41no—
213C2×C4×C103—41no—
214C2×C4×C103—41no—
215C2×C4×C103—82no—
216C2×C4×C103—82no—
217C2×C4×C103—82no—
218C2×C4×C103—82no—
219C2×C4×C103—82no—
220C2×C4×C103C2×D811yescharacteristic
221C2×C4×C103C2×D811yescharacteristic
222C2×C4×C103C2×D811yescharacteristic
223C2×C4×C103C2×D811yescharacteristic
224C2×C4×C103C22×D411yescharacteristic
225C8×C103—21no—
226C8×C103—21no—
227C8×C103—21no—
228C8×C103C2×#4111yescharacteristic
229C8×C103H(5,𝔽2)11yescharacteristic
230C22×C103—21no—
231C22×C103—21no—
232C22×C103—21no—
233C22×C103—21no—
234C22×C103—21no—
235C22×C103—81no—
236C22×C103—81no—
237C22×C103—81no—
238C22×C103—81no—
239C22×C103—81no—
240C22×C103—81no—
241C22×C103#50912yes—
242C22×C103C22×D811yescharacteristic
243C4×C103—21no—
244C4×C103—21no—
245C4×C103—21no—
246C4×C103—21no—
247C4×C103—42no—
248C4×C103—81no—
249C4×C103—81no—
250C4×C103—81no—
251C4×C103—81no—
252C4×C103—81no—
253C4×C103#54611yescharacteristic
254C4×C103#57711yescharacteristic
255#33875C10311yesmaximal, characteristic, direct product factor, Sylow
256C2×C103—22no—
257C2×C103—41no—
258C2×C103—161no—
259C2×C103—161no—
260C2×C103#329411yescharacteristic
261C2×C103C2×#50911yescharacteristic
262C2×C103#341711yescharacteristic
263#3334C2×C10311yescharacteristic, complemented
264#3285C2×C10311yescharacteristic, complemented
265#2243C2×C10311yescharacteristic, complemented
266#2236C2×C10311yescharacteristic, complemented
267#2232C2×C10311yescharacteristic, complemented
268#2227C2×C10311yescharacteristic, complemented
269#2220C2×C10311yescharacteristic, complemented
270#2215C2×C10311yescharacteristic, complemented
271#2210C2×C10311yescharacteristic, complemented
272#2186C2×C10311yescharacteristic, complemented
273#2185C2×C10311yescharacteristic, complemented
274#2175C2×C10311yescharacteristic, complemented
275#2168C2×C10311yescharacteristic, complemented
276#2139C2×C10311yescharacteristic, complemented
277C2×#358C2×C10311yescharacteristic, complemented
278C103#3387511yescharacteristic, direct product factor, Sylow
279C2×#135C22×C10311yescharacteristic
280C22×Q16C22×C10311yescharacteristic
281#548—21no—
282#547—21no—
283C2×SD32C22×C10311yescharacteristic
284C2×SD32C22×C10311yescharacteristic
285C2×D16C22×C10311yescharacteristic
286C2×M32C22×C10311yescharacteristic
287C22×C16C22×C10311yescharacteristic
288#500C22×C10311yescharacteristic
289#495C22×C10311yescharacteristic
290#480—21no—
291#480—21no—
292#474—21no—
293#467C22×C10311yescharacteristic
294#466C22×C10311yescharacteristic
295#466C22×C10311yescharacteristic
296#466C22×C10311yescharacteristic
297#464—21no—
298#452—21no—
299#448—21no—
300C4×Q16C22×C10311yescharacteristic
301C4×D8C22×C10311yescharacteristic
302C8×D4C22×C10311yescharacteristic
303C2×#107C22×C10311yescharacteristic
304C2×#107C22×C10311yescharacteristic
305#366C22×C10311yescharacteristic
306#366C22×C10311yescharacteristic
307#366C22×C10311yescharacteristic
308C4⋊C16C22×C10311yescharacteristic
309#358C22×C10311yescharacteristic
310#358C22×C10311yescharacteristic
311#358C22×C10311yescharacteristic
312#358C22×C10311yescharacteristic
313#358C22×C10311yescharacteristic
314#358C22×C10311yescharacteristic
315#357C22×C10311yescharacteristic
316#357C22×C10311yescharacteristic
317#357C22×C10311yescharacteristic
318#357C22×C10311yescharacteristic
319C22⋊C16C22×C10311yescharacteristic
320C22⋊C16C22×C10311yescharacteristic
321#346C22×C10311yescharacteristic
322C2×#41—21no—
323C2×#41—41no—
324C22×Q8—21no—
325#135—22no—
326#135—41no—
327C2×Q16—22no—
328C2×Q16—21no—
329C2×Q16—41no—
330C2×Q16C23×C10311yescharacteristic
331C2×Q16C23×C10311yescharacteristic
332C2×SD16—21no—
333C2×SD16—21no—
334C2×D8C23×C10311yescharacteristic
335C2×D8C23×C10311yescharacteristic
336C22×C8C23×C10311yescharacteristic
337C22×C8C23×C10311yescharacteristic
338C4⋊Q8—21no—
339#124—21no—
340#124—41no—
341#123—41no—
342#123—41no—
343C22⋊Q8—21no—
344C22⋊Q8—41no—
345C22⋊Q8—41no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—41no—
350C4×Q8—21no—
351C4×D4—21no—
352C4×D4—41no—
353C4×D4D4×C10311yescharacteristic
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356SD32—22no—
357SD32—41no—
358D16—41no—
359M32—41no—
360C2×C16—41no—
361C2×C16C23×C10311yescharacteristic
362C2×C16C23×C10311yescharacteristic
363C2×C16C23×C10311yescharacteristic
364C2×C16C23×C10311yescharacteristic
365#107—21no—
366#107—21no—
367#107—21no—
368#107C23×C10311yescharacteristic
369#107C23×C10311yescharacteristic
370#107C23×C10311yescharacteristic
371#107C23×C10311yescharacteristic
372C4⋊C8D4×C10311yescharacteristic
373#103—21no—
374#103—21no—
375#102—21no—
376#102—21no—
377#102—21no—
378#102—21no—
379C22⋊C8D4×C10311yescharacteristic
380C22⋊C8D4×C10311yescharacteristic
381C4×C8C23×C10311yescharacteristic
382#41—42no—
383#41—81no—
384#41—84no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—42no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—81no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4D8×C10311yescharacteristic
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4C2×D4×C10311yescharacteristic
404C22×C4C2×D4×C10311yescharacteristic
405Q16—21no—
406Q16—21no—
407Q16—21no—
408Q16—42no—
409Q16#41×C10312yescomplemented
410SD16—42no—
411SD16—81no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8C2×D4×C10311yescharacteristic
421C2×C8C2×D4×C10311yescharacteristic
422C2×C8C2×D4×C10311yescharacteristic
423C2×C8C24×C10311yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4D8×C10311yescharacteristic
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4D8×C10311yescharacteristic
442C22⋊C4D8×C10311yescharacteristic
443C42—41no—
444C42C2×D4×C10311yescharacteristic
445C16—21no—
446C16—21no—
447C16—21no—
448C16—21no—
449C23—41no—
450C23—41no—
451C23C2×D8×C10311yescharacteristic
452C23C2×D8×C10311yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—82no—
458Q8—82no—
459D4—22no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—82no—
465D4—82no—
466D4—82no—
467D4—82no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4C2×D8×C10311yescharacteristic
484C2×C4C2×D8×C10311yescharacteristic
485C2×C4C2×D8×C10311yescharacteristic
486C2×C4C2×D8×C10311yescharacteristic
487C2×C4C22×D4×C10311yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8C2×#41×C10311yescharacteristic
492C8H(5,𝔽2)×C10311yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22#509×C10312yes—
505C22C22×D8×C10311yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4#546×C10311yescharacteristic
517C4#577×C10311yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—161no—
522C2C103×#329411yescharacteristic
523C2C2×#509×C10311yescharacteristic
524C2C103×#341711yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
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
1. C103×#3334C2semidirect
2. C103×#3285C2semidirect
3. C103×#2243C2semidirect
4. C103×#2236C2semidirect
5. C103×#2232C2semidirect
6. C103×#2227C2semidirect
7. C103×#2220C2semidirect
8. C103×#2215C2semidirect
9. C103×#2210C2semidirect
10. C103×#2186C2semidirect
11. C103×#2185C2semidirect
12. C103×#2175C2semidirect
13. C103×#2168C2semidirect
14. C103×#2139C2semidirect
15. C2×#358×C103C2semidirect
146. Q16×C103#41semidirect
255. #33875C103direct (N × H)
263. #3334C2×C103semidirect
264. #3285C2×C103semidirect
265. #2243C2×C103semidirect
266. #2236C2×C103semidirect
267. #2232C2×C103semidirect
268. #2227C2×C103semidirect
269. #2220C2×C103semidirect
270. #2215C2×C103semidirect
271. #2210C2×C103semidirect
272. #2186C2×C103semidirect
273. #2185C2×C103semidirect
274. #2175C2×C103semidirect
275. #2168C2×C103semidirect
276. #2139C2×C103semidirect
277. C2×#358C2×C103semidirect
278. C103#33875direct (N × H)
409. Q16#41×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#33342
C103×#32852
C103×#22432
C103×#22362
C103×#22322
C103×#22272
C103×#22202
C103×#22152
C103×#22102
C103×#21862
C103×#21852
C103×#21752
C103×#21682
C103×#21392
C2×#358×C1032
#33875103