Finite Group Databasebeta

← C103×#25489 #39930764

Subgroups — C103×#25489 #39930764

Order 26368.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3165C211yesmaximal, characteristic, complemented
2C103×#3077C211yesmaximal, characteristic
3C2×#474×C103C211yesmaximal, characteristic
4C103×#2962C211yesmaximal, characteristic, complemented
5C103×#2089C212yesmaximal, complemented
6C103×#2063C212yesmaximal
7C103×#1997C211yesmaximal, characteristic, complemented
8C103×#1952C212yesmaximal, complemented
9C103×#1950C211yesmaximal, characteristic, complemented
10C103×#1931C212yesmaximal
11C4×#100×C103C211yesmaximal, characteristic
12#533×C103C2211yescharacteristic
13C2×C4⋊Q8×C103C2211yescharacteristic
14C2×C4×D4×C103C2211yescharacteristic
15#501×C103—22no—
16#500×C103—21no—
17#498×C103—21no—
18#478×C103—22no—
19#476×C103—21no—
20#474×C103—21no—
21#474×C103—21no—
22#474×C103—22no—
23#474×C103—21no—
24#446×C103—22no—
25#446×C103—21no—
26C8×Q8×C103—21no—
27C2×#108×C103C2212yes—
28#428×C103C2212yes—
29#428×C103C2212yes—
30#428×C103C2212yes—
31C2×#107×C103C2212yes—
32#424×C103C2212yes—
33#423×C103C2211yescharacteristic
34C2×C4⋊C8×C103C2211yescharacteristic
35#418×C103C2212yes—
36C2×#102×C103C2212yes—
37C2×#100×C103C2211yescharacteristic
38C2×#100×C103C2211yescharacteristic
39#405×C103C2212yes—
40C4×M16×C103C2211yescharacteristic
41C4×M16×C103C2211yescharacteristic
42#343×C103C2212yes—
43#343×C103C2211yescharacteristic
44#343×C103C2212yes—
45#343×C103C2211yescharacteristic
46#341×C103C2212yes—
47C22×Q8×C103—21no—
48C22×D4×C103C2311yescharacteristic
49C23×C4×C103—21no—
50C2×M16×C103C2312yes—
51C2×M16×C103C2311yescharacteristic
52C2×M16×C103C2311yescharacteristic
53C2×M16×C103C2311yescharacteristic
54C2×M16×C103C2311yescharacteristic
55C22×C8×C103C2312yes—
56C4⋊Q8×C103—21no—
57C4⋊Q8×C103—21no—
58C4⋊Q8×C103—21no—
59C4⋊Q8×C103—21no—
60C4⋊Q8×C103D411yescharacteristic
61C4⋊Q8×C103D411yescharacteristic
62#125×C103D412yes—
63C22⋊Q8×C103—21no—
64C22⋊Q8×C103—21no—
65C4×Q8×C103—21no—
66C4×Q8×C103—21no—
67C4×D4×C103—21no—
68C4×D4×C103—21no—
69C4×D4×C103—21no—
70C4×D4×C103—21no—
71#117×C103C2312yes—
72C2×C4⋊C4×C103—21no—
73C2×C4⋊C4×C103C2312yes—
74C2×C4⋊C4×C103C2311yescharacteristic
75C2×C22⋊C4×C103—21no—
76C2×C42×C103C2311yescharacteristic
77#108×C103—24no—
78#107×C103—22no—
79#107×C103—22no—
80#107×C103—22no—
81#107×C103—22no—
82#107×C103—22no—
83#106×C103—22no—
84#106×C103—22no—
85#106×C103—22no—
86C4⋊C8×C103—22no—
87C4⋊C8×C103—22no—
88C4⋊C8×C103—21no—
89C4⋊C8×C103—21no—
90C4⋊C8×C103D411yescharacteristic
91C4⋊C8×C103D411yescharacteristic
92C4⋊C8×C103D412yes—
93#102×C103—22no—
94#102×C103—22no—
95#102×C103—22no—
96#102×C103—22no—
97#100×C103—22no—
98#100×C103Q814yescomplemented
99#97×C103—22no—
100#97×C103—21no—
101#97×C103—21no—
102C4×C8×C103—22no—
103C4×C8×C103—21no—
104C4×C8×C103—21no—
105C24×C103—21no—
106C2×Q8×C103—21no—
107C2×Q8×C103—21no—
108C2×Q8×C103—41no—
109C2×Q8×C103—41no—
110C2×Q8×C103—82no—
111C2×D4×C103—21no—
112C2×D4×C103—21no—
113C2×D4×C103—21no—
114C2×D4×C103—21no—
115C2×D4×C103—21no—
116C2×D4×C103C2×Q812yes—
117C22×C4×C103—21no—
118C22×C4×C103—22no—
119C22×C4×C103—41no—
120C22×C4×C103—41no—
121C22×C4×C103—82no—
122C22×C4×C103#4111yescharacteristic
123C22×C4×C103#4111yescharacteristic
124C22×C4×C103C2411yescharacteristic
125M16×C103—21no—
126M16×C103—21no—
127M16×C103—21no—
128M16×C103—21no—
129M16×C103—22no—
130M16×C103—21no—
131M16×C103—22no—
132M16×C103C2×Q812yes—
133M16×C103C2×Q812yes—
134M16×C103#4112yes—
135C2×C8×C103—21no—
136C2×C8×C103—21no—
137C2×C8×C103—21no—
138C2×C8×C103—22no—
139C2×C8×C103—22no—
140C2×C8×C103—21no—
141C2×C8×C103—22no—
142C2×C8×C103C2×D412yes—
143C2×C8×C103C2×D412yes—
144C4⋊C4×C103—22no—
145C4⋊C4×C103—22no—
146C4⋊C4×C103—21no—
147C4⋊C4×C103—21no—
148C4⋊C4×C103—22no—
149C4⋊C4×C103—21no—
150C4⋊C4×C103—22no—
151C4⋊C4×C103—21no—
152C4⋊C4×C103—41no—
153C4⋊C4×C103—41no—
154C4⋊C4×C103C2×D412yes—
155C4⋊C4×C103C2×D412yes—
156C22⋊C4×C103—22no—
157C22⋊C4×C103—41no—
158C22⋊C4×C103—41no—
159C42×C103—22no—
160C42×C103C2×D411yescharacteristic
161C42×C103C2×D411yescharacteristic
162C42×C103C2×D411yescharacteristic
163C42×C103C2×D411yescharacteristic
164C23×C103—22no—
165C23×C103—41no—
166C23×C103—41no—
167C23×C103—81no—
168C23×C103—81no—
169C23×C103C2×#4111yescharacteristic
170Q8×C103—42no—
171Q8×C103—81no—
172Q8×C103—82no—
173Q8×C103—82no—
174D4×C103—22no—
175D4×C103—22no—
176D4×C103—41no—
177D4×C103—41no—
178C2×C4×C103—22no—
179C2×C4×C103—22no—
180C2×C4×C103—22no—
181C2×C4×C103—41no—
182C2×C4×C103—41no—
183C2×C4×C103—42no—
184C2×C4×C103—82no—
185C2×C4×C103—82no—
186C2×C4×C103—81no—
187C2×C4×C103—82no—
188C2×C4×C103#12111yescharacteristic
189C2×C4×C103#12111yescharacteristic
190C2×C4×C103#12111yescharacteristic
191C2×C4×C103#12111yescharacteristic
192C2×C4×C103C22×D411yescharacteristic
193C2×C4×C103C22×D411yescharacteristic
194C2×C4×C103C22×Q811yescharacteristic
195C2×C4×C103C2×#4111yescharacteristic
196C2×C4×C1032−1+411yescharacteristic
197C2×C4×C1032−1+411yescharacteristic
198C8×C103—22no—
199C8×C103—22no—
200C8×C103—22no—
201C8×C103—22no—
202C8×C103—22no—
203C8×C103—41no—
204C8×C103—42no—
205C22×C103—21no—
206C22×C103—21no—
207C22×C103—42no—
208C22×C103—82no—
209C22×C103—82no—
210C22×C103—81no—
211C22×C103—81no—
212C22×C103C2×#12111yescharacteristic
213C22×C103#53311yescharacteristic
214C22×C103#54111yescharacteristic
215C4×C103—21no—
216C4×C103—21no—
217C4×C103—21no—
218C4×C103—42no—
219C4×C103—42no—
220C4×C103—81no—
221C4×C103—82no—
222C4×C103#47212yes—
223C4×C103#54711yescharacteristic
224C4×C103#54811yescharacteristic
225C4×C103D4×Q811yescharacteristic
226C4×C103D4×Q811yescharacteristic
227#25489C10311yesmaximal, characteristic, direct product factor, Sylow
228C2×C103—21no—
229C2×C103—21no—
230C2×C103—82no—
231C2×C103#242911yescharacteristic
232C2×C103C2×#47211yescharacteristic
233C2×C103#306911yescharacteristic
234#3165C2×C10311yescharacteristic, complemented
235#3077C2×C10311yescharacteristic
236C2×#474C2×C10311yescharacteristic
237#2962C2×C10311yescharacteristic, complemented
238#2089C2×C10312yescomplemented
239#2063C2×C10312yes—
240#1997C2×C10311yescharacteristic, complemented
241#1952C2×C10312yescomplemented
242#1950C2×C10311yescharacteristic, complemented
243#1931C2×C10312yes—
244C4×#100C2×C10311yescharacteristic
245C103#2548911yescharacteristic, direct product factor, Sylow
246#533C22×C10311yescharacteristic
247C2×C4⋊Q8C22×C10311yescharacteristic
248C2×C4×D4C22×C10311yescharacteristic
249#501—22no—
250#500—21no—
251#498—21no—
252#478—22no—
253#476—21no—
254#474—21no—
255#474—21no—
256#474—22no—
257#474—21no—
258#446—22no—
259#446—21no—
260C8×Q8—21no—
261C2×#108C22×C10312yes—
262#428C22×C10312yes—
263#428C22×C10312yes—
264#428C22×C10312yes—
265C2×#107C22×C10312yes—
266#424C22×C10312yes—
267#423C22×C10311yescharacteristic
268C2×C4⋊C8C22×C10311yescharacteristic
269#418C22×C10312yes—
270C2×#102C22×C10312yes—
271C2×#100C22×C10311yescharacteristic
272C2×#100C22×C10311yescharacteristic
273#405C22×C10312yes—
274C4×M16C22×C10311yescharacteristic
275C4×M16C22×C10311yescharacteristic
276#343C22×C10312yes—
277#343C22×C10311yescharacteristic
278#343C22×C10312yes—
279#343C22×C10311yescharacteristic
280#341C22×C10312yes—
281C22×Q8—21no—
282C22×D4C23×C10311yescharacteristic
283C23×C4—21no—
284C2×M16C23×C10312yes—
285C2×M16C23×C10311yescharacteristic
286C2×M16C23×C10311yescharacteristic
287C2×M16C23×C10311yescharacteristic
288C2×M16C23×C10311yescharacteristic
289C22×C8C23×C10312yes—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8D4×C10311yescharacteristic
295C4⋊Q8D4×C10311yescharacteristic
296#125D4×C10312yes—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305#117C23×C10312yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4C23×C10311yescharacteristic
308C2×C4⋊C4C23×C10312yes—
309C2×C22⋊C4—21no—
310C2×C42C23×C10311yescharacteristic
311#108—24no—
312#107—22no—
313#107—22no—
314#107—22no—
315#107—22no—
316#107—22no—
317#106—22no—
318#106—22no—
319#106—22no—
320C4⋊C8—22no—
321C4⋊C8—22no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8D4×C10311yescharacteristic
325C4⋊C8D4×C10311yescharacteristic
326C4⋊C8D4×C10312yes—
327#102—22no—
328#102—22no—
329#102—22no—
330#102—22no—
331#100—22no—
332#100Q8×C10314yescomplemented
333#97—22no—
334#97—21no—
335#97—21no—
336C4×C8—22no—
337C4×C8—21no—
338C4×C8—21no—
339C24—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4C2×Q8×C10312yes—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—82no—
356C22×C4#41×C10311yescharacteristic
357C22×C4#41×C10311yescharacteristic
358C22×C4C24×C10311yescharacteristic
359M16—21no—
360M16—21no—
361M16—21no—
362M16—21no—
363M16—22no—
364M16—21no—
365M16—22no—
366M16C2×Q8×C10312yes—
367M16C2×Q8×C10312yes—
368M16#41×C10312yes—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8C2×D4×C10312yes—
377C2×C8C2×D4×C10312yes—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4C2×D4×C10312yes—
389C4⋊C4C2×D4×C10312yes—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C42—22no—
394C42C2×D4×C10311yescharacteristic
395C42C2×D4×C10311yescharacteristic
396C42C2×D4×C10311yescharacteristic
397C42C2×D4×C10311yescharacteristic
398C23—22no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23C2×#41×C10311yescharacteristic
404Q8—42no—
405Q8—81no—
406Q8—82no—
407Q8—82no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—81no—
421C2×C4—82no—
422C2×C4#121×C10311yescharacteristic
423C2×C4#121×C10311yescharacteristic
424C2×C4#121×C10311yescharacteristic
425C2×C4#121×C10311yescharacteristic
426C2×C4C22×D4×C10311yescharacteristic
427C2×C4C22×D4×C10311yescharacteristic
428C2×C4C22×Q8×C10311yescharacteristic
429C2×C4C2×#41×C10311yescharacteristic
430C2×C42−1+4×C10311yescharacteristic
431C2×C42−1+4×C10311yescharacteristic
432C8—22no—
433C8—22no—
434C8—22no—
435C8—22no—
436C8—22no—
437C8—41no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—82no—
443C22—82no—
444C22—81no—
445C22—81no—
446C22C2×#121×C10311yescharacteristic
447C22#533×C10311yescharacteristic
448C22#541×C10311yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—81no—
455C4—82no—
456C4#472×C10312yes—
457C4#547×C10311yescharacteristic
458C4#548×C10311yescharacteristic
459C4D4×Q8×C10311yescharacteristic
460C4D4×Q8×C10311yescharacteristic
461C2—21no—
462C2—21no—
463C2—82no—
464C2C103×#242911yescharacteristic
465C2C2×#472×C10311yescharacteristic
466C2C103×#306911yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3165C2semidirect
4. C103×#2962C2semidirect
5. C103×#2089C2semidirect
7. C103×#1997C2semidirect
8. C103×#1952C2semidirect
9. C103×#1950C2semidirect
98. #100×C103Q8semidirect
227. #25489C103direct (N × H)
234. #3165C2×C103semidirect
237. #2962C2×C103semidirect
238. #2089C2×C103semidirect
240. #1997C2×C103semidirect
241. #1952C2×C103semidirect
242. #1950C2×C103semidirect
245. C103#25489direct (N × H)
332. #100Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#31652
C103×#30772
C2×#474×C1032
C103×#29622
C103×#20892
C103×#20632
C103×#19972
C103×#19522
C103×#19502
C103×#19312
C4×#100×C1032
#25489103