Finite Group Databasebeta

← C101×#9951 #38792102

Subgroups — C101×#9951 #38792102

Order 25856.

610 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×#3187C211yesmaximal, characteristic
2C2×#481×C101C211yesmaximal, characteristic
3C101×#2502C211yesmaximal, characteristic, complemented
4C101×#1964C211yesmaximal, characteristic
5C101×#1824C211yesmaximal, 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#481×C101—22no—
14#481×C101—22no—
15#465×C101—22no—
16#450×C101—21no—
17#448×C101—21no—
18C2×#106×C101—21no—
19C2×#102×C101—21no—
20C2×#99×C101—22no—
21C2×C22⋊C8×C101C2211yescharacteristic
22C2×C22⋊C8×C101C2211yescharacteristic
23#398×C101—22no—
24#391×C101—21no—
25#385×C101—22no—
26#384×C101—21no—
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×C101—24no—
55C2×C4⋊C4×C101D412yes—
56C2×C4⋊C4×C101D411yescharacteristic
57C2×C4⋊C4×C101D411yescharacteristic
58C2×C22⋊C4×C101—21no—
59C2×C22⋊C4×C101—21no—
60C2×C22⋊C4×C101—21no—
61C2×C22⋊C4×C101D412yes—
62C2×C42×C101—21no—
63#106×C101—24no—
64#106×C101—22no—
65#103×C101—22no—
66#102×C101—24no—
67#102×C101—22no—
68#99×C101—44no—
69C22⋊C8×C101—21no—
70C22⋊C8×C101—21no—
71C22⋊C8×C101—21no—
72C22⋊C8×C101D412yes—
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—22no—
91C22×C4×C101—21no—
92C22×C4×C101—21no—
93C22×C4×C101—42no—
94C22×C4×C101—41no—
95C22×C4×C101—41no—
96C22×C4×C101—41no—
97C22×C4×C101—82no—
98C22×C4×C101C2×D411yescharacteristic
99C22×C4×C101C2×D411yescharacteristic
100C22×C4×C101C2×D411yescharacteristic
101C22×C4×C101C2×D411yescharacteristic
102C22×C4×C101C2×D411yescharacteristic
103C22×C4×C101#4111yescharacteristic
104SD16×C101—82no—
105C2×C8×C101—22no—
106C2×C8×C101—22no—
107C2×C8×C101—42no—
108C2×C8×C101—42no—
109C4⋊C4×C101—22no—
110C4⋊C4×C101—21no—
111C4⋊C4×C101—21no—
112C4⋊C4×C101—21no—
113C4⋊C4×C101—22no—
114C4⋊C4×C101—21no—
115C4⋊C4×C101—42no—
116C4⋊C4×C101—41no—
117C4⋊C4×C101—41no—
118C4⋊C4×C101—41no—
119C4⋊C4×C101—41no—
120C4⋊C4×C101—84no—
121C22⋊C4×C101—22no—
122C22⋊C4×C101—41no—
123C22⋊C4×C101—41no—
124C22⋊C4×C101—41no—
125C22⋊C4×C101—41no—
126C22⋊C4×C101—42no—
127C22⋊C4×C101SD1614yescomplemented
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×C101C2×SD1612yes—
139C23×C101#13712yes—
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—24no—
151C2×C4×C101—41no—
152C2×C4×C101—41no—
153C2×C4×C101—41no—
154C2×C4×C101—42no—
155C2×C4×C101—42no—
156C2×C4×C101—42no—
157C2×C4×C101—44no—
158C2×C4×C101—42no—
159C2×C4×C101—41no—
160C2×C4×C101—41no—
161C2×C4×C101—41no—
162C2×C4×C101—42no—
163C2×C4×C101—42no—
164C2×C4×C101—82no—
165C2×C4×C101—82no—
166C2×C4×C101—81no—
167C2×C4×C101—81no—
168C2×C4×C101—81no—
169C2×C4×C101#12011yescharacteristic
170C2×C4×C101#12011yescharacteristic
171C2×C4×C101#12111yescharacteristic
172C2×C4×C101#12111yescharacteristic
173C8×C101—42no—
174C8×C101—42no—
175C22×C101—21no—
176C22×C101—21no—
177C22×C101—21no—
178C22×C101—21no—
179C22×C101—21no—
180C22×C101—21no—
181C22×C101—42no—
182C22×C101—42no—
183C22×C101—81no—
184C22×C101—81no—
185C22×C101—81no—
186C22×C101—162no—
187C22×C101#39211yescharacteristic
188C22×C101#44812yes—
189C22×C101#46112yes—
190C22×C101#49211yescharacteristic
191C22×C101#49711yescharacteristic
192C4×C101—21no—
193C4×C101—21no—
194C4×C101—21no—
195C4×C101—44no—
196C4×C101—81no—
197C4×C101—82no—
198C4×C101—81no—
199C4×C101—81no—
200C4×C101—161no—
201C4×C101#45812yes—
202#9951C10111yesmaximal, characteristic, direct product factor, Sylow
203C2×C101—22no—
204C2×C101—21no—
205C2×C101—22no—
206C2×C101—21no—
207C2×C101—161no—
208C2×C101#200811yescharacteristic
209C2×C101#201311yescharacteristic
210C2×C101#202211yescharacteristic
211#3187C2×C10111yescharacteristic
212C2×#481C2×C10111yescharacteristic
213#2502C2×C10111yescharacteristic, complemented
214#1964C2×C10111yescharacteristic
215#1824C2×C10111yescharacteristic, complemented
216#1520C2×C10111yescharacteristic, complemented
217#1282C2×C10111yescharacteristic, complemented
218C101#995111yescharacteristic, direct product factor, Sylow
219C2×C22⋊Q8C22×C10111yescharacteristic
220C2×#121C22×C10111yescharacteristic
221C22×C4⋊C4C22×C10111yescharacteristic
222#483—21no—
223#481—22no—
224#481—21no—
225#481—22no—
226#465—22no—
227#450—21no—
228#448—21no—
229C2×#106—21no—
230C2×#102—21no—
231C2×#99—22no—
232C2×C22⋊C8C22×C10111yescharacteristic
233C2×C22⋊C8C22×C10111yescharacteristic
234#398—22no—
235#391—21no—
236#385—22no—
237#384—21no—
238#380C22×C10111yescharacteristic
239C4×C22⋊C4C22×C10111yescharacteristic
240#340—22no—
241#328—22no—
242C22×Q8D4×C10111yescharacteristic
243C22×D4—21no—
244C22×D4D4×C10111yescharacteristic
245C23×C4—21no—
246C23×C4C23×C10111yescharacteristic
247C2×SD16—22no—
248C22×C8—21no—
249C22×C8D4×C10112yes—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254#121—21no—
255#121—21no—
256#121—21no—
257#121—21no—
258C2×C4⋊C4—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—24no—
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#106—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—21no—
286#95—21no—
287C24—21no—
288C24C2×D4×C10111yescharacteristic
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—42no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—42no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—82no—
309C22×C4C2×D4×C10111yescharacteristic
310C22×C4C2×D4×C10111yescharacteristic
311C22×C4C2×D4×C10111yescharacteristic
312C22×C4C2×D4×C10111yescharacteristic
313C22×C4C2×D4×C10111yescharacteristic
314C22×C4#41×C10111yescharacteristic
315SD16—82no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—42no—
319C2×C8—42no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—84no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—42no—
338C22⋊C4SD16×C10114yescomplemented
339C42—42no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—42no—
344C23—81no—
345C23—81no—
346C23#120×C10111yescharacteristic
347C23#121×C10111yescharacteristic
348C23#127×C10111yescharacteristic
349C23C2×SD16×C10112yes—
350C23#137×C10112yes—
351Q8—42no—
352Q8—81no—
353D4—42no—
354D4—42no—
355D4—82no—
356D4—81no—
357D4—81no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4#120×C10111yescharacteristic
381C2×C4#120×C10111yescharacteristic
382C2×C4#121×C10111yescharacteristic
383C2×C4#121×C10111yescharacteristic
384C8—42no—
385C8—42no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—162no—
398C22#392×C10111yescharacteristic
399C22#448×C10112yes—
400C22#461×C10112yes—
401C22#492×C10111yescharacteristic
402C22#497×C10111yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—44no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—161no—
412C4#458×C10112yes—
413C2—22no—
414C2—21no—
415C2—22no—
416C2—21no—
417C2—161no—
418C2C101×#200811yescharacteristic
419C2C101×#201311yescharacteristic
420C2C101×#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×#2502C2semidirect
5. C101×#1824C2semidirect
6. C101×#1520C2semidirect
7. C101×#1282C2semidirect
127. C22⋊C4×C101SD16semidirect
202. #9951C101direct (N × H)
213. #2502C2×C101semidirect
215. #1824C2×C101semidirect
216. #1520C2×C101semidirect
217. #1282C2×C101semidirect
218. C101#9951direct (N × H)
338. C22⋊C4SD16×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31872
C2×#481×C1012
C101×#25022
C101×#19642
C101×#18242
C101×#15202
C101×#12822
#9951101