Finite Group Databasebeta

← C101×#9952 #38792103

Subgroups — C101×#9952 #38792103

Order 25856.

692 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3186C211yesmaximal, characteristic
2C2×#480×C101C211yesmaximal, characteristic, complemented
3C101×#2501C211yesmaximal, characteristic, complemented
4C101×#1964C211yesmaximal, characteristic, complemented
5C101×#1823C211yesmaximal, characteristic, complemented
6C101×#1519C211yesmaximal, characteristic, complemented
7C101×#1282C211yesmaximal, characteristic, complemented
8C2×#123×C101—22no—
9C2×#121×C101C2211yescharacteristic
10C2×#121×C101C2211yescharacteristic
11C22×C4⋊C4×C101C2211yescharacteristic
12#480×C101—21no—
13#480×C101—21no—
14#480×C101—22no—
15#480×C101—22no—
16#466×C101—22no—
17#447×C101—21no—
18#447×C101—21no—
19C2×#107×C101—21no—
20C2×#102×C101—21no—
21C2×#99×C101—22no—
22C2×C22⋊C8×C101C2211yescharacteristic
23C2×C22⋊C8×C101C2211yescharacteristic
24#399×C101—22no—
25#390×C101—21no—
26#384×C101—21no—
27#380×C101C2211yescharacteristic
28C4×C22⋊C4×C101C2211yescharacteristic
29#340×C101—22no—
30#327×C101—22no—
31C22×D4×C101—21no—
32C22×D4×C101—21no—
33C22×D4×C101D411yescharacteristic
34C22×D4×C101D411yescharacteristic
35C23×C4×C101—21no—
36C23×C4×C101C2311yescharacteristic
37C2×D8×C101—22no—
38C22×C8×C101—21no—
39C22×C8×C101D412yes—
40#123×C101—44no—
41#123×C101—44no—
42#121×C101—21no—
43#121×C101—21no—
44#121×C101—21no—
45#121×C101—21no—
46#121×C101—21no—
47#121×C101—21no—
48#121×C101—21no—
49#121×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×C101—21no—
56C2×C4⋊C4×C101—21no—
57C2×C4⋊C4×C101D412yes—
58C2×C4⋊C4×C101D411yescharacteristic
59C2×C4⋊C4×C101D411yescharacteristic
60C2×C22⋊C4×C101—24no—
61C2×C22⋊C4×C101—21no—
62C2×C22⋊C4×C101—21no—
63C2×C22⋊C4×C101—21no—
64C2×C22⋊C4×C101D412yes—
65C2×C42×C101—21no—
66#107×C101—24no—
67#107×C101—22no—
68#102×C101—24no—
69#102×C101—22no—
70#102×C101—22no—
71#99×C101—44no—
72C22⋊C8×C101—21no—
73C22⋊C8×C101—21no—
74C22⋊C8×C101—21no—
75C22⋊C8×C101D412yes—
76#95×C101—21no—
77#95×C101—21no—
78C24×C101—21no—
79C24×C101—21no—
80C24×C101C2×D411yescharacteristic
81C2×D4×C101—21no—
82C2×D4×C101—21no—
83C2×D4×C101—21no—
84C2×D4×C101—21no—
85C2×D4×C101—42no—
86C2×D4×C101—42no—
87C2×D4×C101—41no—
88C2×D4×C101—41no—
89C2×D4×C101—41no—
90C2×D4×C101—41no—
91C2×D4×C101—42no—
92C2×D4×C101—42no—
93C2×D4×C101—42no—
94C2×D4×C101—42no—
95C22×C4×C101—22no—
96C22×C4×C101—22no—
97C22×C4×C101—21no—
98C22×C4×C101—21no—
99C22×C4×C101—42no—
100C22×C4×C101—41no—
101C22×C4×C101—41no—
102C22×C4×C101—42no—
103C22×C4×C101—42no—
104C22×C4×C101—41no—
105C22×C4×C101C2×D411yescharacteristic
106C22×C4×C101C2×D411yescharacteristic
107C22×C4×C101C2×D411yescharacteristic
108C22×C4×C101C2×D411yescharacteristic
109C22×C4×C101C2×D411yescharacteristic
110C22×C4×C101#4111yescharacteristic
111D8×C101—82no—
112C2×C8×C101—22no—
113C2×C8×C101—22no—
114C2×C8×C101—42no—
115C2×C8×C101—42no—
116C4⋊C4×C101—22no—
117C4⋊C4×C101—21no—
118C4⋊C4×C101—21no—
119C4⋊C4×C101—21no—
120C4⋊C4×C101—22no—
121C4⋊C4×C101—21no—
122C4⋊C4×C101—48no—
123C4⋊C4×C101—42no—
124C4⋊C4×C101—41no—
125C4⋊C4×C101—41no—
126C22⋊C4×C101—22no—
127C22⋊C4×C101—48no—
128C22⋊C4×C101—41no—
129C22⋊C4×C101—41no—
130C22⋊C4×C101—41no—
131C22⋊C4×C101—41no—
132C22⋊C4×C101—42no—
133C22⋊C4×C101D814yescomplemented
134C42×C101—42no—
135C23×C101—41no—
136C23×C101—41no—
137C23×C101—42no—
138C23×C101—42no—
139C23×C101—41no—
140C23×C101—41no—
141C23×C101—42no—
142C23×C101—42no—
143C23×C101—81no—
144C23×C101—81no—
145C23×C101#12011yescharacteristic
146C23×C101#12111yescharacteristic
147C23×C101#12711yescharacteristic
148C23×C101C2×D812yes—
149C23×C101AGL(1,ℤ/8)12yes—
150D4×C101—42no—
151D4×C101—42no—
152D4×C101—42no—
153D4×C101—81no—
154D4×C101—82no—
155D4×C101—82no—
156D4×C101—81no—
157D4×C101—81no—
158D4×C101—81no—
159D4×C101—81no—
160C2×C4×C101—22no—
161C2×C4×C101—22no—
162C2×C4×C101—22no—
163C2×C4×C101—24no—
164C2×C4×C101—41no—
165C2×C4×C101—41no—
166C2×C4×C101—41no—
167C2×C4×C101—42no—
168C2×C4×C101—42no—
169C2×C4×C101—41no—
170C2×C4×C101—41no—
171C2×C4×C101—42no—
172C2×C4×C101—44no—
173C2×C4×C101—42no—
174C2×C4×C101—42no—
175C2×C4×C101—82no—
176C2×C4×C101—81no—
177C2×C4×C101—81no—
178C2×C4×C101—81no—
179C2×C4×C101—81no—
180C2×C4×C101—81no—
181C2×C4×C101#12011yescharacteristic
182C2×C4×C101#12011yescharacteristic
183C2×C4×C101#12111yescharacteristic
184C2×C4×C101#12111yescharacteristic
185C8×C101—42no—
186C8×C101—42no—
187C22×C101—21no—
188C22×C101—21no—
189C22×C101—21no—
190C22×C101—21no—
191C22×C101—21no—
192C22×C101—21no—
193C22×C101—42no—
194C22×C101—42no—
195C22×C101—84no—
196C22×C101—81no—
197C22×C101—81no—
198C22×C101—81no—
199C22×C101—81no—
200C22×C101—81no—
201C22×C101—81no—
202C22×C101—162no—
203C22×C101#39211yescharacteristic
204C22×C101#44712yes—
205C22×C101#45912yes—
206C22×C101#49311yescharacteristic
207C22×C101#49611yescharacteristic
208C4×C101—21no—
209C4×C101—21no—
210C4×C101—21no—
211C4×C101—44no—
212C4×C101—82no—
213C4×C101—81no—
214C4×C101—81no—
215C4×C101—161no—
216C4×C101#45812yes—
217#9952C10111yesmaximal, characteristic, direct product factor, Sylow
218C2×C101—22no—
219C2×C101—21no—
220C2×C101—22no—
221C2×C101—21no—
222C2×C101—161no—
223C2×C101—161no—
224C2×C101#200911yescharacteristic
225C2×C101#201111yescharacteristic
226C2×C101#202211yescharacteristic
227#3186C2×C10111yescharacteristic
228C2×#480C2×C10111yescharacteristic, complemented
229#2501C2×C10111yescharacteristic, complemented
230#1964C2×C10111yescharacteristic, complemented
231#1823C2×C10111yescharacteristic, complemented
232#1519C2×C10111yescharacteristic, complemented
233#1282C2×C10111yescharacteristic, complemented
234C101#995211yescharacteristic, direct product factor, Sylow
235C2×#123—22no—
236C2×#121C22×C10111yescharacteristic
237C2×#121C22×C10111yescharacteristic
238C22×C4⋊C4C22×C10111yescharacteristic
239#480—22no—
240#480—21no—
241#480—21no—
242#480—22no—
243#466—22no—
244#447—21no—
245#447—21no—
246C2×#107—21no—
247C2×#102—21no—
248C2×#99—22no—
249C2×C22⋊C8C22×C10111yescharacteristic
250C2×C22⋊C8C22×C10111yescharacteristic
251#399—22no—
252#390—21no—
253#384—21no—
254#380C22×C10111yescharacteristic
255C4×C22⋊C4C22×C10111yescharacteristic
256#340—22no—
257#327—22no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4D4×C10111yescharacteristic
261C22×D4D4×C10111yescharacteristic
262C23×C4—21no—
263C23×C4C23×C10111yescharacteristic
264C2×D8—22no—
265C22×C8—21no—
266C22×C8D4×C10112yes—
267#123—44no—
268#123—44no—
269#121—21no—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275#121—21no—
276#121—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4D4×C10112yes—
285C2×C4⋊C4D4×C10111yescharacteristic
286C2×C4⋊C4D4×C10111yescharacteristic
287C2×C22⋊C4—24no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4D4×C10112yes—
292C2×C42—21no—
293#107—24no—
294#107—22no—
295#102—24no—
296#102—22no—
297#102—22no—
298#99—44no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8D4×C10112yes—
303#95—21no—
304#95—21no—
305C24—21no—
306C24—21no—
307C24C2×D4×C10111yescharacteristic
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—42no—
319C2×D4—42no—
320C2×D4—42no—
321C2×D4—42no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—42no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—41no—
332C22×C4C2×D4×C10111yescharacteristic
333C22×C4C2×D4×C10111yescharacteristic
334C22×C4C2×D4×C10111yescharacteristic
335C22×C4C2×D4×C10111yescharacteristic
336C22×C4C2×D4×C10111yescharacteristic
337C22×C4#41×C10111yescharacteristic
338D8—82no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—42no—
342C2×C8—42no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—48no—
350C4⋊C4—42no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C22⋊C4—22no—
354C22⋊C4—48no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—42no—
360C22⋊C4D8×C10114yescomplemented
361C42—42no—
362C23—41no—
363C23—41no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—81no—
371C23—81no—
372C23#120×C10111yescharacteristic
373C23#121×C10111yescharacteristic
374C23#127×C10111yescharacteristic
375C23C2×D8×C10112yes—
376C23AGL(1,ℤ/8)×C10112yes—
377D4—42no—
378D4—42no—
379D4—42no—
380D4—81no—
381D4—82no—
382D4—82no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—82no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4#120×C10111yescharacteristic
409C2×C4#120×C10111yescharacteristic
410C2×C4#121×C10111yescharacteristic
411C2×C4#121×C10111yescharacteristic
412C8—42no—
413C8—42no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—42no—
421C22—42no—
422C22—84no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—162no—
430C22#392×C10111yescharacteristic
431C22#447×C10112yes—
432C22#459×C10112yes—
433C22#493×C10111yescharacteristic
434C22#496×C10111yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—44no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4—161no—
443C4#458×C10112yes—
444C2—22no—
445C2—21no—
446C2—22no—
447C2—21no—
448C2—161no—
449C2—161no—
450C2C101×#200911yescharacteristic
451C2C101×#201111yescharacteristic
452C2C101×#202211yescharacteristic
subgroupG/H
center, socleC22×C101#392
commutator, Frattini, cosocleC23×C4C23×C101
prime radicalC101×#3186C2
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
2. C2×#480×C101C2semidirect
3. C101×#2501C2semidirect
4. C101×#1964C2semidirect
5. C101×#1823C2semidirect
6. C101×#1519C2semidirect
7. C101×#1282C2semidirect
133. C22⋊C4×C101D8semidirect
217. #9952C101direct (N × H)
228. C2×#480C2×C101semidirect
229. #2501C2×C101semidirect
230. #1964C2×C101semidirect
231. #1823C2×C101semidirect
232. #1519C2×C101semidirect
233. #1282C2×C101semidirect
234. C101#9952direct (N × H)
360. C22⋊C4D8×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#31862
C2×#480×C1012
C101×#25012
C101×#19642
C101×#18232
C101×#15192
C101×#12822
#9952101