Finite Group Databasebeta

← C101×#9953 #38792104

Subgroups — C101×#9953 #38792104

Order 25856.

594 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3187C211yesmaximal, characteristic
2C2×#480×C101C211yesmaximal, characteristic
3C101×#2503C211yesmaximal, characteristic, complemented
4C101×#1964C211yesmaximal, characteristic
5C101×#1823C211yesmaximal, characteristic, complemented
6C101×#1520C211yesmaximal, characteristic, complemented
7C101×#1282C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C101C2211yescharacteristic
9C2×#121×C101C2211yescharacteristic
10C22×C4⋊C4×C101C2211yescharacteristic
11#483×C101—21no—
12#481×C101—21no—
13#480×C101—22no—
14#480×C101—22no—
15#465×C101—22no—
16#450×C101—21no—
17#448×C101—21no—
18C2×#107×C101—21no—
19C2×#102×C101—21no—
20C2×#99×C101—22no—
21C2×C22⋊C8×C101C2211yescharacteristic
22C2×C22⋊C8×C101C2211yescharacteristic
23#400×C101—22no—
24#391×C101—21no—
25#382×C101—21no—
26#381×C101—22no—
27#380×C101C2211yescharacteristic
28C4×C22⋊C4×C101C2211yescharacteristic
29#340×C101—22no—
30#328×C101—22no—
31C22×Q8×C101D411yescharacteristic
32C22×D4×C101—21no—
33C22×D4×C101D411yescharacteristic
34C23×C4×C101—21no—
35C23×C4×C101C2311yescharacteristic
36C2×SD16×C101—22no—
37C22×C8×C101—21no—
38C22×C8×C101D412yes—
39C22⋊Q8×C101—21no—
40C22⋊Q8×C101—21no—
41C22⋊Q8×C101—21no—
42C22⋊Q8×C101—21no—
43#121×C101—21no—
44#121×C101—21no—
45#121×C101—21no—
46#121×C101—21no—
47C2×C4⋊C4×C101—21no—
48C2×C4⋊C4×C101—21no—
49C2×C4⋊C4×C101—21no—
50C2×C4⋊C4×C101—21no—
51C2×C4⋊C4×C101—21no—
52C2×C4⋊C4×C101—21no—
53C2×C4⋊C4×C101—21no—
54C2×C4⋊C4×C101D412yes—
55C2×C4⋊C4×C101D411yescharacteristic
56C2×C4⋊C4×C101D411yescharacteristic
57C2×C22⋊C4×C101—21no—
58C2×C22⋊C4×C101—21no—
59C2×C22⋊C4×C101—21no—
60C2×C22⋊C4×C101D412yes—
61C2×C42×C101—21no—
62#107×C101—24no—
63#106×C101—22no—
64#103×C101—22no—
65#102×C101—24no—
66#102×C101—22no—
67#99×C101—44no—
68C22⋊C8×C101—21no—
69C22⋊C8×C101—21no—
70C22⋊C8×C101—21no—
71C22⋊C8×C101D412yes—
72#95×C101—24no—
73#95×C101—24no—
74#95×C101—21no—
75#95×C101—21no—
76C24×C101—21no—
77C24×C101C2×D411yescharacteristic
78C2×Q8×C101—21no—
79C2×Q8×C101—21no—
80C2×Q8×C101—42no—
81C2×D4×C101—21no—
82C2×D4×C101—21no—
83C2×D4×C101—42no—
84C2×D4×C101—41no—
85C2×D4×C101—41no—
86C2×D4×C101—42no—
87C2×D4×C101—42no—
88C22×C4×C101—22no—
89C22×C4×C101—21no—
90C22×C4×C101—21no—
91C22×C4×C101—22no—
92C22×C4×C101—21no—
93C22×C4×C101—42no—
94C22×C4×C101—41no—
95C22×C4×C101—41no—
96C22×C4×C101—42no—
97C22×C4×C101—42no—
98C22×C4×C101—41no—
99C22×C4×C101C2×D411yescharacteristic
100C22×C4×C101C2×D411yescharacteristic
101C22×C4×C101C2×D411yescharacteristic
102C22×C4×C101C2×D411yescharacteristic
103C22×C4×C101C2×D411yescharacteristic
104C22×C4×C101#4111yescharacteristic
105SD16×C101—82no—
106C2×C8×C101—22no—
107C2×C8×C101—22no—
108C2×C8×C101—42no—
109C2×C8×C101—42no—
110C4⋊C4×C101—21no—
111C4⋊C4×C101—22no—
112C4⋊C4×C101—21no—
113C4⋊C4×C101—21no—
114C4⋊C4×C101—22no—
115C4⋊C4×C101—21no—
116C4⋊C4×C101—42no—
117C4⋊C4×C101—41no—
118C4⋊C4×C101—41no—
119C4⋊C4×C101—41no—
120C4⋊C4×C101—41no—
121C22⋊C4×C101—22no—
122C22⋊C4×C101—22no—
123C22⋊C4×C101—41no—
124C22⋊C4×C101—41no—
125C22⋊C4×C101—41no—
126C22⋊C4×C101—41no—
127C22⋊C4×C101—42no—
128C42×C101—42no—
129C23×C101—41no—
130C23×C101—41no—
131C23×C101—41no—
132C23×C101—42no—
133C23×C101—81no—
134C23×C101—81no—
135C23×C101#12011yescharacteristic
136C23×C101#12111yescharacteristic
137C23×C101#12711yescharacteristic
138C23×C101#13512yes—
139C23×C101AGL(1,ℤ/8)12yes—
140Q8×C101—42no—
141Q8×C101—81no—
142D4×C101—42no—
143D4×C101—42no—
144D4×C101—82no—
145D4×C101—81no—
146D4×C101—81no—
147C2×C4×C101—22no—
148C2×C4×C101—22no—
149C2×C4×C101—22no—
150C2×C4×C101—41no—
151C2×C4×C101—41no—
152C2×C4×C101—41no—
153C2×C4×C101—42no—
154C2×C4×C101—42no—
155C2×C4×C101—42no—
156C2×C4×C101—42no—
157C2×C4×C101—41no—
158C2×C4×C101—41no—
159C2×C4×C101—41no—
160C2×C4×C101—42no—
161C2×C4×C101—42no—
162C2×C4×C101—44no—
163C2×C4×C101—42no—
164C2×C4×C101—82no—
165C2×C4×C101—81no—
166C2×C4×C101—81no—
167C2×C4×C101—81no—
168C2×C4×C101—81no—
169C2×C4×C101—81no—
170C2×C4×C101#12011yescharacteristic
171C2×C4×C101#12011yescharacteristic
172C2×C4×C101#12111yescharacteristic
173C2×C4×C101#12111yescharacteristic
174C8×C101—42no—
175C8×C101—42no—
176C22×C101—21no—
177C22×C101—21no—
178C22×C101—21no—
179C22×C101—21no—
180C22×C101—21no—
181C22×C101—21no—
182C22×C101—42no—
183C22×C101—42no—
184C22×C101—81no—
185C22×C101—81no—
186C22×C101—81no—
187C22×C101—162no—
188C22×C101#39211yescharacteristic
189C22×C101#44912yes—
190C22×C101#46312yes—
191C22×C101#49511yescharacteristic
192C22×C101#49611yescharacteristic
193C4×C101—21no—
194C4×C101—21no—
195C4×C101—21no—
196C4×C101—82no—
197C4×C101—81no—
198C4×C101—82no—
199C4×C101—81no—
200C4×C101—81no—
201C4×C101—161no—
202C4×C101#45812yes—
203#9953C10111yesmaximal, characteristic, direct product factor, Sylow
204C2×C101—22no—
205C2×C101—21no—
206C2×C101—22no—
207C2×C101—21no—
208C2×C101—161no—
209C2×C101#200911yescharacteristic
210C2×C101#201211yescharacteristic
211C2×C101#202211yescharacteristic
212#3187C2×C10111yescharacteristic
213C2×#480C2×C10111yescharacteristic
214#2503C2×C10111yescharacteristic, complemented
215#1964C2×C10111yescharacteristic
216#1823C2×C10111yescharacteristic, complemented
217#1520C2×C10111yescharacteristic, complemented
218#1282C2×C10111yescharacteristic, complemented
219C101#995311yescharacteristic, direct product factor, Sylow
220C2×C22⋊Q8C22×C10111yescharacteristic
221C2×#121C22×C10111yescharacteristic
222C22×C4⋊C4C22×C10111yescharacteristic
223#483—21no—
224#481—21no—
225#480—22no—
226#480—22no—
227#465—22no—
228#450—21no—
229#448—21no—
230C2×#107—21no—
231C2×#102—21no—
232C2×#99—22no—
233C2×C22⋊C8C22×C10111yescharacteristic
234C2×C22⋊C8C22×C10111yescharacteristic
235#400—22no—
236#391—21no—
237#382—21no—
238#381—22no—
239#380C22×C10111yescharacteristic
240C4×C22⋊C4C22×C10111yescharacteristic
241#340—22no—
242#328—22no—
243C22×Q8D4×C10111yescharacteristic
244C22×D4—21no—
245C22×D4D4×C10111yescharacteristic
246C23×C4—21no—
247C23×C4C23×C10111yescharacteristic
248C2×SD16—22no—
249C22×C8—21no—
250C22×C8D4×C10112yes—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255#121—21no—
256#121—21no—
257#121—21no—
258#121—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4D4×C10112yes—
267C2×C4⋊C4D4×C10111yescharacteristic
268C2×C4⋊C4D4×C10111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4D4×C10112yes—
273C2×C42—21no—
274#107—24no—
275#106—22no—
276#103—22no—
277#102—24no—
278#102—22no—
279#99—44no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8D4×C10112yes—
284#95—24no—
285#95—24no—
286#95—21no—
287#95—21no—
288C24—21no—
289C24C2×D4×C10111yescharacteristic
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—42no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—42no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—42no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4C2×D4×C10111yescharacteristic
312C22×C4C2×D4×C10111yescharacteristic
313C22×C4C2×D4×C10111yescharacteristic
314C22×C4C2×D4×C10111yescharacteristic
315C22×C4C2×D4×C10111yescharacteristic
316C22×C4#41×C10111yescharacteristic
317SD16—82no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—42no—
321C2×C8—42no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—42no—
340C42—42no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—42no—
345C23—81no—
346C23—81no—
347C23#120×C10111yescharacteristic
348C23#121×C10111yescharacteristic
349C23#127×C10111yescharacteristic
350C23#135×C10112yes—
351C23AGL(1,ℤ/8)×C10112yes—
352Q8—42no—
353Q8—81no—
354D4—42no—
355D4—42no—
356D4—82no—
357D4—81no—
358D4—81no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4#120×C10111yescharacteristic
383C2×C4#120×C10111yescharacteristic
384C2×C4#121×C10111yescharacteristic
385C2×C4#121×C10111yescharacteristic
386C8—42no—
387C8—42no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—42no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—162no—
400C22#392×C10111yescharacteristic
401C22#449×C10112yes—
402C22#463×C10112yes—
403C22#495×C10111yescharacteristic
404C22#496×C10111yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—82no—
409C4—81no—
410C4—82no—
411C4—81no—
412C4—81no—
413C4—161no—
414C4#458×C10112yes—
415C2—22no—
416C2—21no—
417C2—22no—
418C2—21no—
419C2—161no—
420C2C101×#200911yescharacteristic
421C2C101×#201211yescharacteristic
422C2C101×#202211yescharacteristic
subgroupG/H
center, socleC22×C101#392
commutator, Frattini, cosocleC23×C4C23×C101
prime radicalC2×#121×C101C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#2503C2semidirect
5. C101×#1823C2semidirect
6. C101×#1520C2semidirect
7. C101×#1282C2semidirect
203. #9953C101direct (N × H)
214. #2503C2×C101semidirect
216. #1823C2×C101semidirect
217. #1520C2×C101semidirect
218. #1282C2×C101semidirect
219. C101#9953direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#31872
C2×#480×C1012
C101×#25032
C101×#19642
C101×#18232
C101×#15202
C101×#12822
#9953101