Finite Group Databasebeta

← C103×#33874 #39939149

Subgroups — C103×#33874 #39939149

Order 26368.

554 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3339C211yesmaximal, characteristic, complemented
2C103×#3283C211yesmaximal, characteristic, complemented
3C103×#2245C211yesmaximal, characteristic, complemented
4C103×#2237C211yesmaximal, characteristic, complemented
5C103×#2235C211yesmaximal, characteristic, complemented
6C103×#2228C211yesmaximal, characteristic, complemented
7C103×#2220C211yesmaximal, characteristic, complemented
8C103×#2217C211yesmaximal, characteristic, complemented
9C103×#2208C211yesmaximal, characteristic, complemented
10C103×#2186C211yesmaximal, characteristic, complemented
11C103×#2186C211yesmaximal, characteristic, complemented
12C103×#2177C211yesmaximal, characteristic, complemented
13C103×#2168C211yesmaximal, characteristic, complemented
14C103×#2139C211yesmaximal, characteristic, complemented
15C103×#2138C211yesmaximal, characteristic, complemented
16C2×#135×C103C2211yescharacteristic
17C2×#135×C103C2211yescharacteristic
18#553×C103—21no—
19#547×C103—21no—
20C2×SD32×C103C2211yescharacteristic
21C2×SD32×C103C2211yescharacteristic
22C2×D16×C103C2211yescharacteristic
23C2×M32×C103C2211yescharacteristic
24C22×C16×C103C2211yescharacteristic
25#499×C103C2211yescharacteristic
26#494×C103C2211yescharacteristic
27#482×C103—21no—
28#481×C103—21no—
29#478×C103—21no—
30#467×C103C2211yescharacteristic
31#467×C103C2211yescharacteristic
32#466×C103C2211yescharacteristic
33#466×C103C2211yescharacteristic
34#461×C103—21no—
35#452×C103—21no—
36#452×C103—21no—
37C4×D8×C103C2211yescharacteristic
38C4×D8×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#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—21no—
61#135×C103—22no—
62#135×C103—22no—
63#135×C103—41no—
64#135×C103—41no—
65C2×Q16×C103—21no—
66C2×Q16×C103C2311yescharacteristic
67C2×Q16×C103C2311yescharacteristic
68C2×SD16×C103—21no—
69C2×SD16×C103—21no—
70C2×D8×C103C2311yescharacteristic
71C2×D8×C103C2311yescharacteristic
72C22×C8×C103C2311yescharacteristic
73C22×C8×C103C2311yescharacteristic
74C4⋊Q8×C103—21no—
75#126×C103—41no—
76#125×C103—21no—
77#123×C103—41no—
78#123×C103—41no—
79#123×C103—41no—
80C22⋊Q8×C103—21no—
81C22⋊Q8×C103—21no—
82#121×C103—21no—
83#121×C103—21no—
84#121×C103—41no—
85#121×C103—41no—
86C4×D4×C103—21no—
87C4×D4×C103—21no—
88C4×D4×C103—41no—
89C4×D4×C103D411yescharacteristic
90#117×C103—21no—
91C2×C4⋊C4×C103—21no—
92C2×C4⋊C4×C103—41no—
93SD32×C103—41no—
94SD32×C103—41no—
95D16×C103—22no—
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#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—42no—
121#41×C103—81no—
122#41×C103—81no—
123C2×Q8×C103—21no—
124C2×Q8×C103—21no—
125C2×D4×C103—21no—
126C2×D4×C103—21no—
127C2×D4×C103—41no—
128C2×D4×C103—41no—
129C2×D4×C103—41no—
130C2×D4×C103—41no—
131C2×D4×C103D811yescharacteristic
132C22×C4×C103—41no—
133C22×C4×C103—41no—
134C22×C4×C103—41no—
135C22×C4×C103—41no—
136C22×C4×C103—41no—
137C22×C4×C103C2×D411yescharacteristic
138C22×C4×C103C2×D411yescharacteristic
139Q16×C103—21no—
140Q16×C103—21no—
141Q16×C103—21no—
142Q16×C103—21no—
143Q16×C103—81no—
144SD16×C103—42no—
145SD16×C103—42no—
146D8×C103—21no—
147D8×C103—21no—
148D8×C103—21no—
149D8×C103#4112yes—
150C2×C8×C103—21no—
151C2×C8×C103—21no—
152C2×C8×C103—21no—
153C2×C8×C103—21no—
154C2×C8×C103C2×D411yescharacteristic
155C2×C8×C103C2×D411yescharacteristic
156C2×C8×C103C2×D411yescharacteristic
157C2×C8×C103C2411yescharacteristic
158C4⋊C4×C103—21no—
159C4⋊C4×C103—21no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
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×C103—41no—
176C22⋊C4×C103—41no—
177C22⋊C4×C103D811yescharacteristic
178C22⋊C4×C103D811yescharacteristic
179C42×C103—41no—
180C42×C103C2×D411yescharacteristic
181C16×C103—21no—
182C16×C103—21no—
183C16×C103—21no—
184C16×C103—21no—
185C23×C103—41no—
186C23×C103—41no—
187C23×C103C2×D811yescharacteristic
188C23×C103C2×D811yescharacteristic
189Q8×C103—41no—
190Q8×C103—41no—
191Q8×C103—41no—
192Q8×C103—41no—
193D4×C103—22no—
194D4×C103—41no—
195D4×C103—41no—
196D4×C103—41no—
197D4×C103—41no—
198D4×C103—82no—
199D4×C103—82no—
200D4×C103—82no—
201D4×C103—161no—
202C2×C4×C103—21no—
203C2×C4×C103—21no—
204C2×C4×C103—21no—
205C2×C4×C103—21no—
206C2×C4×C103—41no—
207C2×C4×C103—41no—
208C2×C4×C103—41no—
209C2×C4×C103—41no—
210C2×C4×C103—41no—
211C2×C4×C103—41no—
212C2×C4×C103—82no—
213C2×C4×C103—82no—
214C2×C4×C103—82no—
215C2×C4×C103—161no—
216C2×C4×C103—161no—
217C2×C4×C103C2×D811yescharacteristic
218C2×C4×C103C2×D811yescharacteristic
219C2×C4×C103C2×D811yescharacteristic
220C2×C4×C103C2×D811yescharacteristic
221C2×C4×C103C22×D411yescharacteristic
222C8×C103—21no—
223C8×C103—21no—
224C8×C103—21no—
225C8×C103C2×#4111yescharacteristic
226C8×C103H(5,𝔽2)11yescharacteristic
227C22×C103—21no—
228C22×C103—21no—
229C22×C103—21no—
230C22×C103—21no—
231C22×C103—21no—
232C22×C103—21no—
233C22×C103—42no—
234C22×C103—81no—
235C22×C103—81no—
236C22×C103—81no—
237C22×C103—81no—
238C22×C103—81no—
239C22×C103C22×D811yescharacteristic
240C4×C103—21no—
241C4×C103—21no—
242C4×C103—21no—
243C4×C103—21no—
244C4×C103—81no—
245C4×C103—81no—
246C4×C103—81no—
247C4×C103—81no—
248C4×C103—81no—
249C4×C103—81no—
250C4×C103#54611yescharacteristic
251C4×C103#57711yescharacteristic
252#33874C10311yesmaximal, characteristic, direct product factor, Sylow
253C2×C103—41no—
254C2×C103—41no—
255C2×C103—82no—
256C2×C103—161no—
257C2×C103#329411yescharacteristic
258C2×C103#341411yescharacteristic
259C2×C103#341611yescharacteristic
260#3339C2×C10311yescharacteristic, complemented
261#3283C2×C10311yescharacteristic, complemented
262#2245C2×C10311yescharacteristic, complemented
263#2237C2×C10311yescharacteristic, complemented
264#2235C2×C10311yescharacteristic, complemented
265#2228C2×C10311yescharacteristic, complemented
266#2220C2×C10311yescharacteristic, complemented
267#2217C2×C10311yescharacteristic, complemented
268#2208C2×C10311yescharacteristic, complemented
269#2186C2×C10311yescharacteristic, complemented
270#2186C2×C10311yescharacteristic, complemented
271#2177C2×C10311yescharacteristic, complemented
272#2168C2×C10311yescharacteristic, complemented
273#2139C2×C10311yescharacteristic, complemented
274#2138C2×C10311yescharacteristic, complemented
275C103#3387411yescharacteristic, direct product factor, Sylow
276C2×#135C22×C10311yescharacteristic
277C2×#135C22×C10311yescharacteristic
278#553—21no—
279#547—21no—
280C2×SD32C22×C10311yescharacteristic
281C2×SD32C22×C10311yescharacteristic
282C2×D16C22×C10311yescharacteristic
283C2×M32C22×C10311yescharacteristic
284C22×C16C22×C10311yescharacteristic
285#499C22×C10311yescharacteristic
286#494C22×C10311yescharacteristic
287#482—21no—
288#481—21no—
289#478—21no—
290#467C22×C10311yescharacteristic
291#467C22×C10311yescharacteristic
292#466C22×C10311yescharacteristic
293#466C22×C10311yescharacteristic
294#461—21no—
295#452—21no—
296#452—21no—
297C4×D8C22×C10311yescharacteristic
298C4×D8C22×C10311yescharacteristic
299C8×D4C22×C10311yescharacteristic
300#427C22×C10311yescharacteristic
301C2×#107C22×C10311yescharacteristic
302#367C22×C10311yescharacteristic
303#367C22×C10311yescharacteristic
304#366C22×C10311yescharacteristic
305C4⋊C16C22×C10311yescharacteristic
306#358C22×C10311yescharacteristic
307#358C22×C10311yescharacteristic
308#358C22×C10311yescharacteristic
309#358C22×C10311yescharacteristic
310#358C22×C10311yescharacteristic
311#358C22×C10311yescharacteristic
312#357C22×C10311yescharacteristic
313#357C22×C10311yescharacteristic
314#357C22×C10311yescharacteristic
315#357C22×C10311yescharacteristic
316C22⋊C16C22×C10311yescharacteristic
317C22⋊C16C22×C10311yescharacteristic
318#346C22×C10311yescharacteristic
319C2×#41—21no—
320C2×#41—21no—
321#135—22no—
322#135—22no—
323#135—41no—
324#135—41no—
325C2×Q16—21no—
326C2×Q16C23×C10311yescharacteristic
327C2×Q16C23×C10311yescharacteristic
328C2×SD16—21no—
329C2×SD16—21no—
330C2×D8C23×C10311yescharacteristic
331C2×D8C23×C10311yescharacteristic
332C22×C8C23×C10311yescharacteristic
333C22×C8C23×C10311yescharacteristic
334C4⋊Q8—21no—
335#126—41no—
336#125—21no—
337#123—41no—
338#123—41no—
339#123—41no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342#121—21no—
343#121—21no—
344#121—41no—
345#121—41no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—41no—
349C4×D4D4×C10311yescharacteristic
350#117—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—41no—
353SD32—41no—
354SD32—41no—
355D16—22no—
356M32—41no—
357C2×C16—41no—
358C2×C16C23×C10311yescharacteristic
359C2×C16C23×C10311yescharacteristic
360C2×C16C23×C10311yescharacteristic
361C2×C16C23×C10311yescharacteristic
362#107—21no—
363#107C23×C10311yescharacteristic
364#107C23×C10311yescharacteristic
365#107C23×C10311yescharacteristic
366#107C23×C10311yescharacteristic
367#106—21no—
368#106—21no—
369C4⋊C8D4×C10311yescharacteristic
370#103—21no—
371#103—21no—
372#102—21no—
373#102—21no—
374#102—21no—
375#102—21no—
376C22⋊C8D4×C10311yescharacteristic
377C22⋊C8D4×C10311yescharacteristic
378C4×C8C23×C10311yescharacteristic
379#41—42no—
380#41—42no—
381#41—81no—
382#41—81no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4D8×C10311yescharacteristic
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4C2×D4×C10311yescharacteristic
398C22×C4C2×D4×C10311yescharacteristic
399Q16—21no—
400Q16—21no—
401Q16—21no—
402Q16—21no—
403Q16—81no—
404SD16—42no—
405SD16—42no—
406D8—21no—
407D8—21no—
408D8—21no—
409D8#41×C10312yes—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8C2×D4×C10311yescharacteristic
415C2×C8C2×D4×C10311yescharacteristic
416C2×C8C2×D4×C10311yescharacteristic
417C2×C8C24×C10311yescharacteristic
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4D8×C10311yescharacteristic
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4D8×C10311yescharacteristic
438C22⋊C4D8×C10311yescharacteristic
439C42—41no—
440C42C2×D4×C10311yescharacteristic
441C16—21no—
442C16—21no—
443C16—21no—
444C16—21no—
445C23—41no—
446C23—41no—
447C23C2×D8×C10311yescharacteristic
448C23C2×D8×C10311yescharacteristic
449Q8—41no—
450Q8—41no—
451Q8—41no—
452Q8—41no—
453D4—22no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—82no—
459D4—82no—
460D4—82no—
461D4—161no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—161no—
476C2×C4—161no—
477C2×C4C2×D8×C10311yescharacteristic
478C2×C4C2×D8×C10311yescharacteristic
479C2×C4C2×D8×C10311yescharacteristic
480C2×C4C2×D8×C10311yescharacteristic
481C2×C4C22×D4×C10311yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8C2×#41×C10311yescharacteristic
486C8H(5,𝔽2)×C10311yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22C22×D8×C10311yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4#546×C10311yescharacteristic
511C4#577×C10311yescharacteristic
512C2—41no—
513C2—41no—
514C2—82no—
515C2—161no—
516C2C103×#329411yescharacteristic
517C2C103×#341411yescharacteristic
518C2C103×#341611yescharacteristic
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×#3339C2semidirect
2. C103×#3283C2semidirect
3. C103×#2245C2semidirect
4. C103×#2237C2semidirect
5. C103×#2235C2semidirect
6. C103×#2228C2semidirect
7. C103×#2220C2semidirect
8. C103×#2217C2semidirect
9. C103×#2208C2semidirect
10. C103×#2186C2semidirect
11. C103×#2186C2semidirect
12. C103×#2177C2semidirect
13. C103×#2168C2semidirect
14. C103×#2139C2semidirect
15. C103×#2138C2semidirect
252. #33874C103direct (N × H)
260. #3339C2×C103semidirect
261. #3283C2×C103semidirect
262. #2245C2×C103semidirect
263. #2237C2×C103semidirect
264. #2235C2×C103semidirect
265. #2228C2×C103semidirect
266. #2220C2×C103semidirect
267. #2217C2×C103semidirect
268. #2208C2×C103semidirect
269. #2186C2×C103semidirect
270. #2186C2×C103semidirect
271. #2177C2×C103semidirect
272. #2168C2×C103semidirect
273. #2139C2×C103semidirect
274. #2138C2×C103semidirect
275. C103#33874direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#33392
C103×#32832
C103×#22452
C103×#22372
C103×#22352
C103×#22282
C103×#22202
C103×#22172
C103×#22082
C103×#21862
C103×#21772
C103×#21682
C103×#21392
C103×#21382
#33874103