Finite Group Databasebeta

← C101×#13232 #38795383

Subgroups — C101×#13232 #38795383

Order 25856.

448 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3057C211yesmaximal, characteristic
2C101×#2135C211yesmaximal, characteristic, complemented
3C101×#2134C211yesmaximal, characteristic
4C101×#2123C211yesmaximal, characteristic, complemented
5C101×#2122C211yesmaximal, characteristic
6C101×#1813C211yesmaximal, characteristic, complemented
7C101×#1757C211yesmaximal, characteristic, complemented
8C22×SD16×C101C411yescharacteristic, complemented
9C2×#131×C101C2211yescharacteristic
10#536×C101C2211yescharacteristic
11#535×C101C2211yescharacteristic
12#468×C101—21no—
13#468×C101—21no—
14#465×C101—21no—
15#465×C101—21no—
16C2×#108×C101—21no—
17#427×C101C411yescharacteristic, complemented
18#419×C101C411yescharacteristic, complemented
19#418×C101C411yescharacteristic, complemented
20#413×C101C2211yescharacteristic
21#413×C101C2211yescharacteristic
22#413×C101C2211yescharacteristic
23#410×C101C2211yescharacteristic
24#405×C101—21no—
25#356×C101—22no—
26#355×C101—22no—
27#352×C101—22no—
28AΣL(1,𝔽16)×C101—22no—
29#344×C101—21no—
30#338×C101—21no—
31C2×#41×C101C2311yescharacteristic
32C22×Q8×C101C2×C411yescharacteristic
33C22×D4×C101C2×C411yescharacteristic
34C2×SD16×C101—21no—
35C2×SD16×C101—21no—
36C2×SD16×C101—41no—
37C2×SD16×C101—41no—
38#131×C101—41no—
39#131×C101—41no—
40C2×M16×C101—21no—
41C2×M16×C101—21no—
42C2×M16×C101—21no—
43C2×M16×C101C2×C411yescharacteristic
44C2×M16×C101D411yescharacteristic
45C2×M16×C101D411yescharacteristic
46C22×C8×C101C2×C411yescharacteristic
47C22×C8×C101D411yescharacteristic
48C22×C8×C101D411yescharacteristic
49C4⋊Q8×C101—21no—
50#127×C101—21no—
51#124×C101—21no—
52#124×C101—21no—
53#123×C101—21no—
54#123×C101—21no—
55C22⋊Q8×C101—21no—
56C22⋊Q8×C101—21no—
57#121×C101—21no—
58#121×C101—21no—
59#120×C101—21no—
60#120×C101—21no—
61#117×C101—21no—
62#117×C101C2×C411yescharacteristic
63#117×C101C2×C411yescharacteristic
64#108×C101—41no—
65#108×C101—41no—
66#107×C101—21no—
67#106×C101—21no—
68#103×C101—21no—
69#103×C101—21no—
70#102×C101—21no—
71#102×C101—21no—
72#101×C101—21no—
73#101×C101—21no—
74#101×C101D412yes—
75#100×C101—21no—
76#100×C101—21no—
77#100×C101—21no—
78#99×C101—21no—
79#99×C101D412yes—
80#97×C101—41no—
81C4×C8×C101—41no—
82C24×C101—21no—
83#41×C101—41no—
84#41×C101—41no—
85C2×Q8×C101—21no—
86C2×Q8×C101—21no—
87C2×Q8×C101—41no—
88C2×Q8×C101—41no—
89C2×Q8×C101C2×D411yescharacteristic
90C2×D4×C101—21no—
91C2×D4×C101—21no—
92C2×D4×C101—41no—
93C2×D4×C101—41no—
94C2×D4×C101—41no—
95C2×D4×C101—41no—
96C2×D4×C101C2×D411yescharacteristic
97C2×D4×C101#4111yescharacteristic
98C2×D4×C101#4111yescharacteristic
99C22×C4×C101—21no—
100C22×C4×C101C22×C411yescharacteristic
101C22×C4×C101C2×D411yescharacteristic
102C22×C4×C101C2×D411yescharacteristic
103SD16×C101—42no—
104SD16×C101—41no—
105SD16×C101—41no—
106M16×C101—22no—
107M16×C101—41no—
108M16×C101—41no—
109M16×C101—41no—
110M16×C101—41no—
111M16×C101—41no—
112M16×C101—41no—
113M16×C101—41no—
114M16×C101—41no—
115C2×C8×C101—21no—
116C2×C8×C101—21no—
117C2×C8×C101—21no—
118C2×C8×C101—21no—
119C2×C8×C101—21no—
120C2×C8×C101—21no—
121C2×C8×C101—41no—
122C2×C8×C101—41no—
123C2×C8×C101—41no—
124C2×C8×C101C22⋊C411yescharacteristic
125C2×C8×C101C22⋊C411yescharacteristic
126C2×C8×C101C22⋊C411yescharacteristic
127C2×C8×C101C22⋊C411yescharacteristic
128C4⋊C4×C101—21no—
129C4⋊C4×C101—21no—
130C4⋊C4×C101—41no—
131C4⋊C4×C101—41no—
132C4⋊C4×C101—41no—
133C22⋊C4×C101—21no—
134C22⋊C4×C101—21no—
135C22⋊C4×C101—22no—
136C22⋊C4×C101—41no—
137C22⋊C4×C101—41no—
138C22⋊C4×C101—41no—
139C22⋊C4×C101—41no—
140C42×C101—21no—
141C42×C101—21no—
142C42×C101—41no—
143C23×C101—41no—
144C23×C101—81no—
145C23×C101—161no—
146C23×C101C4×D411yescharacteristic
147C23×C101#12111yescharacteristic
148C23×C101#12411yescharacteristic
149Q8×C101—41no—
150Q8×C101—41no—
151Q8×C101—41no—
152Q8×C101—81no—
153D4×C101—41no—
154D4×C101—41no—
155D4×C101—41no—
156D4×C101—41no—
157D4×C101—41no—
158D4×C101—81no—
159D4×C101—161no—
160D4×C101—161no—
161C2×C4×C101—21no—
162C2×C4×C101—21no—
163C2×C4×C101—21no—
164C2×C4×C101—21no—
165C2×C4×C101—21no—
166C2×C4×C101—21no—
167C2×C4×C101—42no—
168C2×C4×C101—41no—
169C2×C4×C101—41no—
170C2×C4×C101—41no—
171C2×C4×C101—81no—
172C2×C4×C101C2×C22⋊C411yescharacteristic
173C2×C4×C101C4×D411yescharacteristic
174C2×C4×C101#12111yescharacteristic
175C2×C4×C101#12711yescharacteristic
176C8×C101—21no—
177C8×C101—21no—
178C8×C101—21no—
179C8×C101—42no—
180C8×C101—81no—
181C8×C101—81no—
182C8×C101#9911yescharacteristic
183C8×C101#9911yescharacteristic
184C22×C101—21no—
185C22×C101—21no—
186C22×C101—21no—
187C22×C101—41no—
188C22×C101—41no—
189C22×C101—41no—
190C22×C101—81no—
191C22×C101—81no—
192C22×C101—81no—
193C22×C101—162no—
194C22×C101#39011yescharacteristic
195C4×C101—21no—
196C4×C101—21no—
197C4×C101—21no—
198C4×C101—81no—
199C4×C101—81no—
200C4×C101—82no—
201C4×C101—81no—
202C4×C101C2×#9911yescharacteristic
203C4×C101#41011yescharacteristic
204#13232C10111yesmaximal, characteristic, direct product factor, Sylow
205C2×C101—21no—
206C2×C101—41no—
207C2×C101—41no—
208C2×C101—41no—
209C2×C101—161no—
210C2×C101#196411yescharacteristic
211#3057C2×C10111yescharacteristic
212#2135C2×C10111yescharacteristic, complemented
213#2134C2×C10111yescharacteristic
214#2123C2×C10111yescharacteristic, complemented
215#2122C2×C10111yescharacteristic
216#1813C2×C10111yescharacteristic, complemented
217#1757C2×C10111yescharacteristic, complemented
218C101#1323211yescharacteristic, direct product factor, Sylow
219C22×SD16C4×C10111yescharacteristic, complemented
220C2×#131C22×C10111yescharacteristic
221#536C22×C10111yescharacteristic
222#535C22×C10111yescharacteristic
223#468—21no—
224#468—21no—
225#465—21no—
226#465—21no—
227C2×#108—21no—
228#427C4×C10111yescharacteristic, complemented
229#419C4×C10111yescharacteristic, complemented
230#418C4×C10111yescharacteristic, complemented
231#413C22×C10111yescharacteristic
232#413C22×C10111yescharacteristic
233#413C22×C10111yescharacteristic
234#410C22×C10111yescharacteristic
235#405—21no—
236#356—22no—
237#355—22no—
238#352—22no—
239AΣL(1,𝔽16)—22no—
240#344—21no—
241#338—21no—
242C2×#41C23×C10111yescharacteristic
243C22×Q8C2×C4×C10111yescharacteristic
244C22×D4C2×C4×C10111yescharacteristic
245C2×SD16—21no—
246C2×SD16—21no—
247C2×SD16—41no—
248C2×SD16—41no—
249#131—41no—
250#131—41no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16C2×C4×C10111yescharacteristic
255C2×M16D4×C10111yescharacteristic
256C2×M16D4×C10111yescharacteristic
257C22×C8C2×C4×C10111yescharacteristic
258C22×C8D4×C10111yescharacteristic
259C22×C8D4×C10111yescharacteristic
260C4⋊Q8—21no—
261#127—21no—
262#124—21no—
263#124—21no—
264#123—21no—
265#123—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—21no—
269#121—21no—
270#120—21no—
271#120—21no—
272#117—21no—
273#117C2×C4×C10111yescharacteristic
274#117C2×C4×C10111yescharacteristic
275#108—41no—
276#108—41no—
277#107—21no—
278#106—21no—
279#103—21no—
280#103—21no—
281#102—21no—
282#102—21no—
283#101—21no—
284#101—21no—
285#101D4×C10112yes—
286#100—21no—
287#100—21no—
288#100—21no—
289#99—21no—
290#99D4×C10112yes—
291#97—41no—
292C4×C8—41no—
293C24—21no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8C2×D4×C10111yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4C2×D4×C10111yescharacteristic
308C2×D4#41×C10111yescharacteristic
309C2×D4#41×C10111yescharacteristic
310C22×C4—21no—
311C22×C4C22×C4×C10111yescharacteristic
312C22×C4C2×D4×C10111yescharacteristic
313C22×C4C2×D4×C10111yescharacteristic
314SD16—42no—
315SD16—41no—
316SD16—41no—
317M16—22no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—41no—
324M16—41no—
325M16—41no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8C22⋊C4×C10111yescharacteristic
336C2×C8C22⋊C4×C10111yescharacteristic
337C2×C8C22⋊C4×C10111yescharacteristic
338C2×C8C22⋊C4×C10111yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—22no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—21no—
352C42—21no—
353C42—41no—
354C23—41no—
355C23—81no—
356C23—161no—
357C23C4×D4×C10111yescharacteristic
358C23#121×C10111yescharacteristic
359C23#124×C10111yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—161no—
371D4—161no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4C2×C22⋊C4×C10111yescharacteristic
384C2×C4C4×D4×C10111yescharacteristic
385C2×C4#121×C10111yescharacteristic
386C2×C4#127×C10111yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—42no—
391C8—81no—
392C8—81no—
393C8#99×C10111yescharacteristic
394C8#99×C10111yescharacteristic
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—162no—
405C22#390×C10111yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—81no—
411C4—82no—
412C4—81no—
413C4C2×#99×C10111yescharacteristic
414C4#410×C10111yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—161no—
420C2C101×#196411yescharacteristic
subgroupG/H
center, socleC2×C101#1964
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×#41C23×C101
prime radical#535×C101C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C2×C4×C101 ◁ C2×#131×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2135C2semidirect
4. C101×#2123C2semidirect
6. C101×#1813C2semidirect
7. C101×#1757C2semidirect
8. C22×SD16×C101C4semidirect
17. #427×C101C4semidirect
18. #419×C101C4semidirect
19. #418×C101C4semidirect
204. #13232C101direct (N × H)
212. #2135C2×C101semidirect
214. #2123C2×C101semidirect
216. #1813C2×C101semidirect
217. #1757C2×C101semidirect
218. C101#13232direct (N × H)
219. C22×SD16C4×C101semidirect
228. #427C4×C101semidirect
229. #419C4×C101semidirect
230. #418C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30572
C101×#21352
C101×#21342
C101×#21232
C101×#21222
C101×#18132
C101×#17572
#13232101