Finite Group Databasebeta

← C101×#7823 #38789974

Subgroups — C101×#7823 #38789974

Order 25856.

446 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2732C211yesmaximal, characteristic
2C101×#2100C211yesmaximal, characteristic, complemented
3C101×#2095C211yesmaximal, characteristic, complemented
4C101×#2094C211yesmaximal, characteristic
5C101×#1272C211yesmaximal, characteristic, complemented
6C101×#1271C211yesmaximal, characteristic, complemented
7C101×#1270C211yesmaximal, characteristic
8C2×C22⋊Q8×C101—21no—
9C2×#107×C101—21no—
10C2×#106×C101—21no—
11C2×#103×C101—21no—
12C2×#102×C101—21no—
13#399×C101—21no—
14#398×C101—21no—
15#396×C101—21no—
16#391×C101C2211yescharacteristic
17#390×C101C2211yescharacteristic
18#389×C101C2211yescharacteristic
19#386×C101—21no—
20#385×C101—21no—
21#384×C101C2211yescharacteristic
22#340×C101—21no—
23#340×C101—21no—
24#336×C101C2211yescharacteristic
25#336×C101C2211yescharacteristic
26#336×C101C2211yescharacteristic
27C22×Q8×C101D411yescharacteristic
28C22×D4×C101D411yescharacteristic
29C23×C4×C101—21no—
30C22×C8×C101—21no—
31C22×C8×C101—21no—
32C22×C8×C101—21no—
33C22⋊Q8×C101—42no—
34C22⋊Q8×C101—42no—
35C2×C4⋊C4×C101—21no—
36C2×C4⋊C4×C101—21no—
37C2×C4⋊C4×C101—21no—
38C2×C4⋊C4×C101—21no—
39C2×C4⋊C4×C101—21no—
40C2×C4⋊C4×C101—21no—
41C2×C4⋊C4×C101—21no—
42C2×C4⋊C4×C101D411yescharacteristic
43C2×C4⋊C4×C101D411yescharacteristic
44C2×C4⋊C4×C101D411yescharacteristic
45C2×C4⋊C4×C101D411yescharacteristic
46C2×C22⋊C4×C101—21no—
47C2×C22⋊C4×C101—21no—
48C2×C22⋊C4×C101—21no—
49C2×C22⋊C4×C101—21no—
50C2×C22⋊C4×C101—21no—
51C2×C42×C101C2311yescharacteristic
52#107×C101—42no—
53#106×C101—42no—
54#103×C101—42no—
55#102×C101—42no—
56#95×C101—21no—
57#95×C101—21no—
58#95×C101—21no—
59#95×C101—21no—
60C24×C101—21no—
61C2×Q8×C101—21no—
62C2×Q8×C101—41no—
63C2×Q8×C101—41no—
64C2×Q8×C101SD1612yes—
65C2×D4×C101—21no—
66C2×D4×C101—41no—
67C2×D4×C101—41no—
68C2×D4×C101Q1612yes—
69C22×C4×C101—21no—
70C22×C4×C101—21no—
71C22×C4×C101—21no—
72C22×C4×C101—21no—
73C22×C4×C101—21no—
74C22×C4×C101—42no—
75C22×C4×C101—41no—
76C22×C4×C101—81no—
77C22×C4×C101—81no—
78C22×C4×C101C2×D411yescharacteristic
79C22×C4×C101C2×D411yescharacteristic
80C22×C4×C101C2×D411yescharacteristic
81C2×C8×C101—22no—
82C2×C8×C101—22no—
83C2×C8×C101—41no—
84C2×C8×C101—41no—
85C2×C8×C101—41no—
86C2×C8×C101—41no—
87C2×C8×C101—41no—
88C2×C8×C101—41no—
89C2×C8×C101—41no—
90C4⋊C4×C101—21no—
91C4⋊C4×C101—21no—
92C4⋊C4×C101—41no—
93C4⋊C4×C101—41no—
94C4⋊C4×C101—41no—
95C4⋊C4×C101—42no—
96C4⋊C4×C101—42no—
97C4⋊C4×C101—41no—
98C4⋊C4×C101—41no—
99C4⋊C4×C101—41no—
100C4⋊C4×C101—41no—
101C4⋊C4×C101—42no—
102C4⋊C4×C101—41no—
103C4⋊C4×C101—41no—
104C4⋊C4×C101—81no—
105C22⋊C4×C101—42no—
106C22⋊C4×C101—41no—
107C22⋊C4×C101—41no—
108C22⋊C4×C101—41no—
109C22⋊C4×C101—41no—
110C22⋊C4×C101—81no—
111C22⋊C4×C101—81no—
112C42×C101—41no—
113C23×C101—22no—
114C23×C101—41no—
115C23×C101—41no—
116C23×C101—41no—
117C23×C101—41no—
118C23×C101—41no—
119C23×C101—41no—
120C23×C101#12011yescharacteristic
121Q8×C101—42no—
122Q8×C101—81no—
123D4×C101—42no—
124D4×C101—81no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—21no—
129C2×C4×C101—21no—
130C2×C4×C101—21no—
131C2×C4×C101—22no—
132C2×C4×C101—41no—
133C2×C4×C101—41no—
134C2×C4×C101—41no—
135C2×C4×C101—41no—
136C2×C4×C101—41no—
137C2×C4×C101—41no—
138C2×C4×C101—41no—
139C2×C4×C101—41no—
140C2×C4×C101—41no—
141C2×C4×C101—41no—
142C2×C4×C101—41no—
143C2×C4×C101—41no—
144C2×C4×C101—41no—
145C2×C4×C101—41no—
146C2×C4×C101—84no—
147C2×C4×C101—81no—
148C2×C4×C101—81no—
149C2×C4×C101—81no—
150C2×C4×C101C2×SD1611yescharacteristic
151C2×C4×C101C2×Q1611yescharacteristic
152C2×C4×C101#13511yescharacteristic
153C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C101#13711yescharacteristic
155C2×C4×C101#13711yescharacteristic
156C8×C101—42no—
157C8×C101—42no—
158C8×C101—81no—
159C22×C101—42no—
160C22×C101—42no—
161C22×C101—42no—
162C22×C101—81no—
163C22×C101—81no—
164C22×C101—81no—
165C22×C101—81no—
166C22×C101#45011yescharacteristic
167C22×C101#45111yescharacteristic
168C22×C101#45211yescharacteristic
169C22×C101#45311yescharacteristic
170C22×C101#45311yescharacteristic
171C22×C101#45411yescharacteristic
172C22×C101#45811yescharacteristic
173C4×C101—21no—
174C4×C101—21no—
175C4×C101—21no—
176C4×C101—21no—
177C4×C101—21no—
178C4×C101—21no—
179C4×C101—42no—
180C4×C101—81no—
181C4×C101—81no—
182C4×C101—81no—
183C4×C101—81no—
184C4×C101—161no—
185#7823C10111yesmaximal, characteristic, direct product factor, Sylow
186C2×C101—82no—
187C2×C101#161311yescharacteristic
188C2×C101#161411yescharacteristic
189C2×C101#161511yescharacteristic
190C2×C101#163111yescharacteristic
191C2×C101#163211yescharacteristic
192C2×C101#163711yescharacteristic
193C2×C101#165611yescharacteristic
194#2732C2×C10111yescharacteristic
195#2100C2×C10111yescharacteristic, complemented
196#2095C2×C10111yescharacteristic, complemented
197#2094C2×C10111yescharacteristic
198#1272C2×C10111yescharacteristic, complemented
199#1271C2×C10111yescharacteristic, complemented
200#1270C2×C10111yescharacteristic
201C101#782311yescharacteristic, direct product factor, Sylow
202C2×C22⋊Q8—21no—
203C2×#107—21no—
204C2×#106—21no—
205C2×#103—21no—
206C2×#102—21no—
207#399—21no—
208#398—21no—
209#396—21no—
210#391C22×C10111yescharacteristic
211#390C22×C10111yescharacteristic
212#389C22×C10111yescharacteristic
213#386—21no—
214#385—21no—
215#384C22×C10111yescharacteristic
216#340—21no—
217#340—21no—
218#336C22×C10111yescharacteristic
219#336C22×C10111yescharacteristic
220#336C22×C10111yescharacteristic
221C22×Q8D4×C10111yescharacteristic
222C22×D4D4×C10111yescharacteristic
223C23×C4—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22⋊Q8—42no—
228C22⋊Q8—42no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4D4×C10111yescharacteristic
237C2×C4⋊C4D4×C10111yescharacteristic
238C2×C4⋊C4D4×C10111yescharacteristic
239C2×C4⋊C4D4×C10111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C42C23×C10111yescharacteristic
246#107—42no—
247#106—42no—
248#103—42no—
249#102—42no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254C24—21no—
255C2×Q8—21no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8SD16×C10112yes—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4Q16×C10112yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—41no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4C2×D4×C10111yescharacteristic
273C22×C4C2×D4×C10111yescharacteristic
274C22×C4C2×D4×C10111yescharacteristic
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—81no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—81no—
305C22⋊C4—81no—
306C42—41no—
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23#120×C10111yescharacteristic
315Q8—42no—
316Q8—81no—
317D4—42no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4C2×SD16×C10111yescharacteristic
345C2×C4C2×Q16×C10111yescharacteristic
346C2×C4#135×C10111yescharacteristic
347C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
348C2×C4#137×C10111yescharacteristic
349C2×C4#137×C10111yescharacteristic
350C8—42no—
351C8—42no—
352C8—81no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#450×C10111yescharacteristic
361C22#451×C10111yescharacteristic
362C22#452×C10111yescharacteristic
363C22#453×C10111yescharacteristic
364C22#453×C10111yescharacteristic
365C22#454×C10111yescharacteristic
366C22#458×C10111yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—161no—
379C2—82no—
380C2C101×#161311yescharacteristic
381C2C101×#161411yescharacteristic
382C2C101×#161511yescharacteristic
383C2C101×#163111yescharacteristic
384C2C101×#163211yescharacteristic
385C2C101×#163711yescharacteristic
386C2C101×#165611yescharacteristic
subgroupG/H
center, socleC23×C101#120
commutator, Frattini, cosocleC2×C42C23×C101
prime radicalC22×D4×C101D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2100C2semidirect
3. C101×#2095C2semidirect
5. C101×#1272C2semidirect
6. C101×#1271C2semidirect
185. #7823C101direct (N × H)
195. #2100C2×C101semidirect
196. #2095C2×C101semidirect
198. #1272C2×C101semidirect
199. #1271C2×C101semidirect
201. C101#7823direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#27322
C101×#21002
C101×#20952
C101×#20942
C101×#12722
C101×#12712
C101×#12702
#7823101