Finite Group Databasebeta

← C101×#7718 #38789869

Subgroups — C101×#7718 #38789869

Order 25856.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2854C211yesmaximal, characteristic
2C101×#1817C211yesmaximal, characteristic, complemented
3C101×#1817C211yesmaximal, characteristic, complemented
4C101×#1271C212yesmaximal, complemented
5C101×#1270C212yesmaximal, complemented
6C2×#123×C101—21no—
7C2×#121×C101C411yescharacteristic
8C22×C42×C101C2211yescharacteristic
9C2×C22⋊C8×C101—21no—
10C2×C22⋊C8×C101—21no—
11#390×C101C411yescharacteristic
12#390×C101C2211yescharacteristic
13#389×C101C411yescharacteristic
14#389×C101C2211yescharacteristic
15#388×C101—21no—
16#388×C101—21no—
17#386×C101—21no—
18#380×C101C411yescharacteristic
19#336×C101—21no—
20#336×C101—21no—
21#336×C101C2212yes—
22#336×C101C2212yes—
23C22×D4×C101—21no—
24C22×D4×C101C2×C411yescharacteristic
25C23×C4×C101C2×C411yescharacteristic
26C23×C4×C101D411yescharacteristic
27C23×C4×C101D411yescharacteristic
28C22×C8×C101—22no—
29C22×C8×C101—22no—
30#123×C101—44no—
31#121×C101—42no—
32C2×C4⋊C4×C101—21no—
33C2×C4⋊C4×C101—21no—
34C2×C4⋊C4×C101C2×C411yescharacteristic
35C2×C4⋊C4×C101C2×C411yescharacteristic
36C2×C4⋊C4×C101C2×C411yescharacteristic
37C2×C22⋊C4×C101—21no—
38C2×C22⋊C4×C101—21no—
39C2×C22⋊C4×C101—21no—
40C2×C22⋊C4×C101—21no—
41C2×C22⋊C4×C101—21no—
42C2×C22⋊C4×C101—21no—
43C2×C42×C101—42no—
44C2×C42×C101C2×C411yescharacteristic
45C2×C42×C101D411yescharacteristic
46C2×C42×C101D411yescharacteristic
47C2×C42×C101C2311yescharacteristic
48C22⋊C8×C101—42no—
49C22⋊C8×C101—42no—
50#95×C101—21no—
51#95×C101—21no—
52#95×C101—21no—
53C24×C101—21no—
54C24×C101C22⋊C411yescharacteristic
55C2×D4×C101—22no—
56C2×D4×C101—41no—
57C2×D4×C101—41no—
58C2×D4×C101—42no—
59C2×D4×C101—42no—
60C2×D4×C101—42no—
61C22×C4×C101—22no—
62C22×C4×C101—22no—
63C22×C4×C101—22no—
64C22×C4×C101—22no—
65C22×C4×C101—22no—
66C22×C4×C101—22no—
67C22×C4×C101—21no—
68C22×C4×C101—21no—
69C22×C4×C101—21no—
70C22×C4×C101—41no—
71C22×C4×C101—41no—
72C22×C4×C101—41no—
73C22×C4×C101C22⋊C411yescharacteristic
74C22×C4×C101C22⋊C411yescharacteristic
75C22×C4×C101C22⋊C411yescharacteristic
76C22×C4×C101C22×C411yescharacteristic
77C22×C4×C101C2×D411yescharacteristic
78C22×C4×C101C2×D411yescharacteristic
79C2×C8×C101—42no—
80C2×C8×C101—42no—
81C2×C8×C101—42no—
82C2×C8×C101—42no—
83C2×C8×C101—42no—
84C2×C8×C101—42no—
85C4⋊C4×C101—22no—
86C4⋊C4×C101—41no—
87C4⋊C4×C101—41no—
88C4⋊C4×C101—42no—
89C4⋊C4×C101—42no—
90C22⋊C4×C101—42no—
91C22⋊C4×C101—42no—
92C22⋊C4×C101—42no—
93C22⋊C4×C101—42no—
94C22⋊C4×C101—42no—
95C22⋊C4×C101—42no—
96C42×C101—41no—
97C42×C101—41no—
98C42×C101—41no—
99C42×C101—41no—
100C23×C101—21no—
101C23×C101—21no—
102C23×C101—21no—
103C23×C101—21no—
104C23×C101—21no—
105C23×C101—21no—
106C23×C101—41no—
107C23×C101—41no—
108C23×C101—41no—
109C23×C101—41no—
110C23×C101—41no—
111C23×C101—41no—
112C23×C101—41no—
113C23×C101#9912yes—
114C23×C101C2×C22⋊C411yescharacteristic
115D4×C101—82no—
116D4×C101—84no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
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—21no—
132C2×C4×C101—44no—
133C2×C4×C101—44no—
134C2×C4×C101—44no—
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#13112yes—
145C2×C4×C101#13512yes—
146C2×C4×C101AGL(1,ℤ/8)12yes—
147C8×C101—82no—
148C8×C101—82no—
149C22×C101—22no—
150C22×C101—22no—
151C22×C101—22no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101—41no—
155C22×C101—41no—
156C22×C101—81no—
157C22×C101—81no—
158C22×C101—81no—
159C22×C101—81no—
160C22×C101—81no—
161C22×C101—81no—
162C22×C101—81no—
163C22×C101#40811yescharacteristic
164C22×C101C2×#9911yescharacteristic
165C22×C101#41311yescharacteristic
166C22×C101#41611yescharacteristic
167C22×C101#41811yescharacteristic
168C22×C101#42111yescharacteristic
169C22×C101#42111yescharacteristic
170C4×C101—22no—
171C4×C101—22no—
172C4×C101—22no—
173C4×C101—41no—
174C4×C101—41no—
175C4×C101—41no—
176C4×C101—81no—
177C4×C101—81no—
178C4×C101—81no—
179#7718C10111yesmaximal, characteristic, direct product factor, Sylow
180C2×C101—42no—
181C2×C101—161no—
182C2×C101#146811yescharacteristic
183C2×C101#148211yescharacteristic
184C2×C101#149611yescharacteristic
185C2×C101#151011yescharacteristic
186C2×C101#151611yescharacteristic
187C2×C101#153511yescharacteristic
188C2×C101#155311yescharacteristic
189#2854C2×C10111yescharacteristic
190#1817C2×C10111yescharacteristic, complemented
191#1817C2×C10111yescharacteristic, complemented
192#1271C2×C10112yescomplemented
193#1270C2×C10112yescomplemented
194C101#771811yescharacteristic, direct product factor, Sylow
195C2×#123—21no—
196C2×#121C4×C10111yescharacteristic
197C22×C42C22×C10111yescharacteristic
198C2×C22⋊C8—21no—
199C2×C22⋊C8—21no—
200#390C4×C10111yescharacteristic
201#390C22×C10111yescharacteristic
202#389C4×C10111yescharacteristic
203#389C22×C10111yescharacteristic
204#388—21no—
205#388—21no—
206#386—21no—
207#380C4×C10111yescharacteristic
208#336—21no—
209#336—21no—
210#336C22×C10112yes—
211#336C22×C10112yes—
212C22×D4—21no—
213C22×D4C2×C4×C10111yescharacteristic
214C23×C4C2×C4×C10111yescharacteristic
215C23×C4D4×C10111yescharacteristic
216C23×C4D4×C10111yescharacteristic
217C22×C8—22no—
218C22×C8—22no—
219#123—44no—
220#121—42no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4C2×C4×C10111yescharacteristic
224C2×C4⋊C4C2×C4×C10111yescharacteristic
225C2×C4⋊C4C2×C4×C10111yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C42—42no—
233C2×C42C2×C4×C10111yescharacteristic
234C2×C42D4×C10111yescharacteristic
235C2×C42D4×C10111yescharacteristic
236C2×C42C23×C10111yescharacteristic
237C22⋊C8—42no—
238C22⋊C8—42no—
239#95—21no—
240#95—21no—
241#95—21no—
242C24—21no—
243C24C22⋊C4×C10111yescharacteristic
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C22⋊C4×C10111yescharacteristic
263C22×C4C22⋊C4×C10111yescharacteristic
264C22×C4C22⋊C4×C10111yescharacteristic
265C22×C4C22×C4×C10111yescharacteristic
266C22×C4C2×D4×C10111yescharacteristic
267C22×C4C2×D4×C10111yescharacteristic
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—41no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23#99×C10112yes—
303C23C2×C22⋊C4×C10111yescharacteristic
304D4—82no—
305D4—84no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4#131×C10112yes—
334C2×C4#135×C10112yes—
335C2×C4AGL(1,ℤ/8)×C10112yes—
336C8—82no—
337C8—82no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#408×C10111yescharacteristic
353C22C2×#99×C10111yescharacteristic
354C22#413×C10111yescharacteristic
355C22#416×C10111yescharacteristic
356C22#418×C10111yescharacteristic
357C22#421×C10111yescharacteristic
358C22#421×C10111yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—81no—
368C2—42no—
369C2—161no—
370C2C101×#146811yescharacteristic
371C2C101×#148211yescharacteristic
372C2C101×#149611yescharacteristic
373C2C101×#151011yescharacteristic
374C2C101×#151611yescharacteristic
375C2C101×#153511yescharacteristic
376C2C101×#155311yescharacteristic
subgroupG/H
center, socleC23×C101C2×C22⋊C4
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC2×#121×C101C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C22×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#1817C2semidirect
3. C101×#1817C2semidirect
4. C101×#1271C2semidirect
5. C101×#1270C2semidirect
179. #7718C101direct (N × H)
190. #1817C2×C101semidirect
191. #1817C2×C101semidirect
192. #1271C2×C101semidirect
193. #1270C2×C101semidirect
194. C101#7718direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#28542
C101×#18172
C101×#12712
C101×#12702
#7718101