Finite Group Databasebeta

← C101×#9958 #38792109

Subgroups — C101×#9958 #38792109

Order 25856.

594 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3187C211yesmaximal, characteristic
2C2×#484×C101C211yesmaximal, characteristic, complemented
3C101×#2504C211yesmaximal, characteristic
4C101×#1996C211yesmaximal, characteristic, complemented
5C101×#1824C211yesmaximal, characteristic, complemented
6C101×#1519C211yesmaximal, characteristic
7C101×#1282C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C101C2211yescharacteristic
9C2×#121×C101C2211yescharacteristic
10C22×C4⋊C4×C101C2211yescharacteristic
11#484×C101—22no—
12#484×C101—22no—
13#483×C101—21no—
14#481×C101—21no—
15#465×C101—22no—
16#450×C101—21no—
17#448×C101—21no—
18C2×#107×C101—21no—
19C2×#103×C101—21no—
20C2×C22⋊C8×C101C2211yescharacteristic
21C2×C22⋊C8×C101C2211yescharacteristic
22#397×C101—22no—
23#390×C101—21no—
24#386×C101—22no—
25#382×C101—21no—
26#380×C101C2211yescharacteristic
27C4×C22⋊C4×C101C2211yescharacteristic
28#342×C101—22no—
29#340×C101—22no—
30#327×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×C101—24no—
61C2×C22⋊C4×C101D412yes—
62C2×C42×C101—21no—
63#107×C101—24no—
64#106×C101—22no—
65#103×C101—24no—
66#103×C101—22no—
67#102×C101—22no—
68C22⋊C8×C101—21no—
69C22⋊C8×C101—21no—
70C22⋊C8×C101—21no—
71C22⋊C8×C101D412yes—
72#95×C101—24no—
73#95×C101—21no—
74#95×C101—21no—
75C24×C101—21no—
76C24×C101C2×D411yescharacteristic
77C2×Q8×C101—21no—
78C2×Q8×C101—21no—
79C2×Q8×C101—42no—
80C2×D4×C101—21no—
81C2×D4×C101—21no—
82C2×D4×C101—42no—
83C2×D4×C101—41no—
84C2×D4×C101—41no—
85C2×D4×C101—42no—
86C2×D4×C101—42no—
87C22×C4×C101—21no—
88C22×C4×C101—22no—
89C22×C4×C101—22no—
90C22×C4×C101—21no—
91C22×C4×C101—21no—
92C22×C4×C101—42no—
93C22×C4×C101—41no—
94C22×C4×C101—41no—
95C22×C4×C101—41no—
96C22×C4×C101—82no—
97C22×C4×C101C2×D411yescharacteristic
98C22×C4×C101C2×D411yescharacteristic
99C22×C4×C101C2×D411yescharacteristic
100C22×C4×C101C2×D411yescharacteristic
101C22×C4×C101C2×D411yescharacteristic
102C22×C4×C101#4111yescharacteristic
103SD16×C101—82no—
104C2×C8×C101—22no—
105C2×C8×C101—22no—
106C2×C8×C101—42no—
107C2×C8×C101—42no—
108C4⋊C4×C101—21no—
109C4⋊C4×C101—21no—
110C4⋊C4×C101—22no—
111C4⋊C4×C101—21no—
112C4⋊C4×C101—22no—
113C4⋊C4×C101—21no—
114C4⋊C4×C101—42no—
115C4⋊C4×C101—41no—
116C4⋊C4×C101—41no—
117C4⋊C4×C101—41no—
118C4⋊C4×C101—41no—
119C22⋊C4×C101—22no—
120C22⋊C4×C101—22no—
121C22⋊C4×C101—41no—
122C22⋊C4×C101—41no—
123C22⋊C4×C101—41no—
124C22⋊C4×C101—41no—
125C22⋊C4×C101—42no—
126C22⋊C4×C101—84no—
127C42×C101—42no—
128C23×C101—41no—
129C23×C101—41no—
130C23×C101—42no—
131C23×C101—42no—
132C23×C101—41no—
133C23×C101—42no—
134C23×C101#12011yescharacteristic
135C23×C101#12111yescharacteristic
136C23×C101#12711yescharacteristic
137C23×C101#13512yes—
138C23×C101#13712yes—
139Q8×C101—42no—
140Q8×C101—42no—
141D4×C101—42no—
142D4×C101—81no—
143D4×C101—82no—
144D4×C101—81no—
145D4×C101—81no—
146C2×C4×C101—22no—
147C2×C4×C101—22no—
148C2×C4×C101—22no—
149C2×C4×C101—41no—
150C2×C4×C101—41no—
151C2×C4×C101—41no—
152C2×C4×C101—42no—
153C2×C4×C101—42no—
154C2×C4×C101—44no—
155C2×C4×C101—41no—
156C2×C4×C101—41no—
157C2×C4×C101—41no—
158C2×C4×C101—42no—
159C2×C4×C101—42no—
160C2×C4×C101—42no—
161C2×C4×C101—82no—
162C2×C4×C101—82no—
163C2×C4×C101—81no—
164C2×C4×C101—81no—
165C2×C4×C101—81no—
166C2×C4×C101—81no—
167C2×C4×C101—81no—
168C2×C4×C101#12011yescharacteristic
169C2×C4×C101#12011yescharacteristic
170C2×C4×C101#12111yescharacteristic
171C2×C4×C101#12111yescharacteristic
172C8×C101—42no—
173C8×C101—42no—
174C22×C101—21no—
175C22×C101—21no—
176C22×C101—21no—
177C22×C101—21no—
178C22×C101—21no—
179C22×C101—21no—
180C22×C101—42no—
181C22×C101—42no—
182C22×C101—84no—
183C22×C101—81no—
184C22×C101—81no—
185C22×C101—81no—
186C22×C101#39211yescharacteristic
187C22×C101#45212yes—
188C22×C101#46412yes—
189C22×C101#49511yescharacteristic
190C22×C101#49711yescharacteristic
191C4×C101—21no—
192C4×C101—21no—
193C4×C101—21no—
194C4×C101—82no—
195C4×C101—82no—
196C4×C101—81no—
197C4×C101—81no—
198C4×C101—81no—
199C4×C101—161no—
200C4×C101#45812yes—
201#9958C10111yesmaximal, characteristic, direct product factor, Sylow
202C2×C101—22no—
203C2×C101—21no—
204C2×C101—22no—
205C2×C101—21no—
206C2×C101—161no—
207C2×C101#200811yescharacteristic
208C2×C101#201511yescharacteristic
209C2×C101#202211yescharacteristic
210#3187C2×C10111yescharacteristic
211C2×#484C2×C10111yescharacteristic, complemented
212#2504C2×C10111yescharacteristic
213#1996C2×C10111yescharacteristic, complemented
214#1824C2×C10111yescharacteristic, complemented
215#1519C2×C10111yescharacteristic
216#1282C2×C10111yescharacteristic, complemented
217C101#995811yescharacteristic, direct product factor, Sylow
218C2×C22⋊Q8C22×C10111yescharacteristic
219C2×#121C22×C10111yescharacteristic
220C22×C4⋊C4C22×C10111yescharacteristic
221#484—22no—
222#484—22no—
223#483—21no—
224#481—21no—
225#465—22no—
226#450—21no—
227#448—21no—
228C2×#107—21no—
229C2×#103—21no—
230C2×C22⋊C8C22×C10111yescharacteristic
231C2×C22⋊C8C22×C10111yescharacteristic
232#397—22no—
233#390—21no—
234#386—22no—
235#382—21no—
236#380C22×C10111yescharacteristic
237C4×C22⋊C4C22×C10111yescharacteristic
238#342—22no—
239#340—22no—
240#327—22no—
241C22×Q8D4×C10111yescharacteristic
242C22×D4—21no—
243C22×D4D4×C10111yescharacteristic
244C23×C4—21no—
245C23×C4C23×C10111yescharacteristic
246C2×SD16—22no—
247C22×C8—21no—
248C22×C8D4×C10112yes—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253#121—21no—
254#121—21no—
255#121—21no—
256#121—21no—
257C2×C4⋊C4—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⋊C4D4×C10112yes—
265C2×C4⋊C4D4×C10111yescharacteristic
266C2×C4⋊C4D4×C10111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4D4×C10112yes—
272C2×C42—21no—
273#107—24no—
274#106—22no—
275#103—24no—
276#103—22no—
277#102—22no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8D4×C10112yes—
282#95—24no—
283#95—21no—
284#95—21no—
285C24—21no—
286C24C2×D4×C10111yescharacteristic
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—42no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—42no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—82no—
307C22×C4C2×D4×C10111yescharacteristic
308C22×C4C2×D4×C10111yescharacteristic
309C22×C4C2×D4×C10111yescharacteristic
310C22×C4C2×D4×C10111yescharacteristic
311C22×C4C2×D4×C10111yescharacteristic
312C22×C4#41×C10111yescharacteristic
313SD16—82no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—42no—
317C2×C8—42no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—42no—
336C22⋊C4—84no—
337C42—42no—
338C23—41no—
339C23—41no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—41no—
344C23#120×C10111yescharacteristic
345C23#121×C10111yescharacteristic
346C23#127×C10111yescharacteristic
347C23#135×C10112yes—
348C23#137×C10112yes—
349Q8—42no—
350Q8—42no—
351D4—42no—
352D4—81no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4#120×C10111yescharacteristic
379C2×C4#120×C10111yescharacteristic
380C2×C4#121×C10111yescharacteristic
381C2×C4#121×C10111yescharacteristic
382C8—42no—
383C8—42no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—42no—
392C22—84no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#392×C10111yescharacteristic
397C22#452×C10112yes—
398C22#464×C10112yes—
399C22#495×C10111yescharacteristic
400C22#497×C10111yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—82no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—161no—
410C4#458×C10112yes—
411C2—22no—
412C2—21no—
413C2—22no—
414C2—21no—
415C2—161no—
416C2C101×#200811yescharacteristic
417C2C101×#201511yescharacteristic
418C2C101×#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
2. C2×#484×C101C2semidirect
4. C101×#1996C2semidirect
5. C101×#1824C2semidirect
7. C101×#1282C2semidirect
201. #9958C101direct (N × H)
211. C2×#484C2×C101semidirect
213. #1996C2×C101semidirect
214. #1824C2×C101semidirect
216. #1282C2×C101semidirect
217. C101#9958direct (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×#484×C1012
C101×#25042
C101×#19962
C101×#18242
C101×#15192
C101×#12822
#9958101