Finite Group Databasebeta

← C101×#8216 #38790367

Subgroups — C101×#8216 #38790367

Order 25856.

712 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
1C4×#121×C101C211yesmaximal, characteristic
2C101×#1749C211yesmaximal, characteristic, complemented
3C2×#327×C101C212yesmaximal
4C101×#1434C211yesmaximal, characteristic, complemented
5C101×#1294C212yesmaximal, complemented
6C2×#121×C101C2211yescharacteristic
7C2×C4×D4×C101—21no—
8C2×C4×D4×C101C411yescharacteristic, complemented
9C22×C42×C101C2211yescharacteristic
10C2×C22⋊C8×C101C2212yes—
11C2×#97×C101—21no—
12#390×C101C411yescharacteristic, complemented
13#389×C101C411yescharacteristic, complemented
14#388×C101—21no—
15#386×C101—21no—
16#380×C101C2211yescharacteristic
17C4×C4⋊C4×C101C411yescharacteristic, complemented
18C4×C22⋊C4×C101—21no—
19C2×#95×C101—21no—
20C2×#95×C101—21no—
21C2×#95×C101C2212yes—
22#336×C101—21no—
23#327×C101C418yescomplemented
24C22×D4×C101—21no—
25C22×D4×C101C2×C411yescharacteristic
26C23×C4×C101—22no—
27C23×C4×C101—21no—
28C23×C4×C101D411yescharacteristic
29C23×C4×C101D411yescharacteristic
30C23×C4×C101C2311yescharacteristic
31C22×C8×C101—22no—
32#121×C101—22no—
33#121×C101C2×C414yes—
34C4×D4×C101—42no—
35C4×D4×C101—44no—
36C2×C4⋊C4×C101—21no—
37C2×C4⋊C4×C101C2×C411yescharacteristic
38C2×C4⋊C4×C101C2×C411yescharacteristic
39C2×C4⋊C4×C101C2×C411yescharacteristic
40C2×C22⋊C4×C101—21no—
41C2×C22⋊C4×C101—21no—
42C2×C22⋊C4×C101—21no—
43C2×C22⋊C4×C101—21no—
44C2×C22⋊C4×C101—21no—
45C2×C42×C101—21no—
46C2×C42×C101—42no—
47C2×C42×C101C2×C411yescharacteristic
48C2×C42×C101C2×C411yescharacteristic
49C2×C42×C101D411yescharacteristic
50C2×C42×C101D411yescharacteristic
51C22⋊C8×C101—22no—
52C22⋊C8×C101C2×C414yescomplemented
53#97×C101—42no—
54#95×C101—21no—
55#95×C101—21no—
56#95×C101—21no—
57#95×C101—22no—
58#95×C101—42no—
59#95×C101—42no—
60#95×C101C2×C414yescomplemented
61C24×C101—21no—
62C24×C101C2×D411yescharacteristic
63C2×D4×C101—24no—
64C2×D4×C101—21no—
65C2×D4×C101—41no—
66C2×D4×C101—41no—
67C2×D4×C101—42no—
68C2×D4×C101—41no—
69C2×D4×C101—41no—
70C2×D4×C101C4212yes—
71C22×C4×C101—21no—
72C22×C4×C101—21no—
73C22×C4×C101—22no—
74C22×C4×C101—21no—
75C22×C4×C101—22no—
76C22×C4×C101—21no—
77C22×C4×C101—21no—
78C22×C4×C101—24no—
79C22×C4×C101—41no—
80C22×C4×C101—41no—
81C22×C4×C101—41no—
82C22×C4×C101—41no—
83C22×C4×C101—41no—
84C22×C4×C101—42no—
85C22×C4×C101—42no—
86C22×C4×C101—42no—
87C22×C4×C101—42no—
88C22×C4×C101—42no—
89C22×C4×C101—42no—
90C22×C4×C101—42no—
91C22×C4×C101—42no—
92C22×C4×C101—42no—
93C22×C4×C101C22⋊C411yescharacteristic
94C22×C4×C101C22⋊C411yescharacteristic
95C22×C4×C101C22⋊C411yescharacteristic
96C22×C4×C101C22⋊C411yescharacteristic
97C22×C4×C101C22×C411yescharacteristic
98C22×C4×C101C22×C412yes—
99C22×C4×C101C2×D411yescharacteristic
100C22×C4×C101#4112yes—
101C2×C8×C101—24no—
102C2×C8×C101—42no—
103C2×C8×C101—42no—
104C4⋊C4×C101—21no—
105C4⋊C4×C101—41no—
106C4⋊C4×C101—41no—
107C4⋊C4×C101—42no—
108C4⋊C4×C101C4212yes—
109C22⋊C4×C101—24no—
110C22⋊C4×C101—42no—
111C22⋊C4×C101—42no—
112C22⋊C4×C101—42no—
113C22⋊C4×C101—42no—
114C42×C101—22no—
115C42×C101—22no—
116C42×C101—41no—
117C42×C101—41no—
118C42×C101—42no—
119C23×C101—21no—
120C23×C101—21no—
121C23×C101—21no—
122C23×C101—21no—
123C23×C101—22no—
124C23×C101—41no—
125C23×C101—41no—
126C23×C101—41no—
127C23×C101—41no—
128C23×C101—41no—
129C23×C101—41no—
130C23×C101C2×C22⋊C411yescharacteristic
131C23×C101C4×D412yes—
132C23×C101AGL(1,ℤ/8)11yescharacteristic
133C23×C101AGL(1,ℤ/8)12yes—
134C23×C101#13711yescharacteristic
135D4×C101—42no—
136D4×C101—42no—
137D4×C101—44no—
138D4×C101—44no—
139C2×C4×C101—21no—
140C2×C4×C101—21no—
141C2×C4×C101—21no—
142C2×C4×C101—21no—
143C2×C4×C101—21no—
144C2×C4×C101—21no—
145C2×C4×C101—22no—
146C2×C4×C101—21no—
147C2×C4×C101—21no—
148C2×C4×C101—21no—
149C2×C4×C101—21no—
150C2×C4×C101—21no—
151C2×C4×C101—21no—
152C2×C4×C101—21no—
153C2×C4×C101—21no—
154C2×C4×C101—21no—
155C2×C4×C101—42no—
156C2×C4×C101—42no—
157C2×C4×C101—44no—
158C2×C4×C101—42no—
159C2×C4×C101—42no—
160C2×C4×C101—41no—
161C2×C4×C101—41no—
162C2×C4×C101—44no—
163C2×C4×C101—44no—
164C2×C4×C101—41no—
165C2×C4×C101—41no—
166C2×C4×C101—41no—
167C2×C4×C101—41no—
168C2×C4×C101—41no—
169C2×C4×C101—41no—
170C2×C4×C101—44no—
171C2×C4×C101—84no—
172C2×C4×C101—82no—
173C2×C4×C101—82no—
174C2×C4×C101—82no—
175C2×C4×C101—82no—
176C2×C4×C101#9912yes—
177C2×C4×C101C2×C4211yescharacteristic
178C2×C4×C101#11711yescharacteristic
179C2×C4×C101C4×D412yes—
180C8×C101—44no—
181C22×C101—22no—
182C22×C101—22no—
183C22×C101—22no—
184C22×C101—21no—
185C22×C101—21no—
186C22×C101—21no—
187C22×C101—21no—
188C22×C101—22no—
189C22×C101—42no—
190C22×C101—42no—
191C22×C101—42no—
192C22×C101—81no—
193C22×C101—81no—
194C22×C101—81no—
195C22×C101—81no—
196C22×C101C4×C22⋊C411yescharacteristic
197C22×C101C2×#9911yescharacteristic
198C22×C101#41011yescharacteristic
199C22×C101#41711yescharacteristic
200C22×C101#41811yescharacteristic
201C22×C101#42111yescharacteristic
202C22×C101#42111yescharacteristic
203C22×C101#44012yes—
204C22×C101#44212yes—
205C4×C101—22no—
206C4×C101—21no—
207C4×C101—21no—
208C4×C101—22no—
209C4×C101—42no—
210C4×C101—41no—
211C4×C101—41no—
212C4×C101—41no—
213C4×C101—84no—
214C4×C101—81no—
215C4×C101—81no—
216#8216C10111yesmaximal, characteristic, direct product factor, Sylow
217C2×C101—22no—
218C2×C101—22no—
219C2×C101—82no—
220C2×C101#151011yescharacteristic
221C2×C101#151211yescharacteristic
222C2×C101#151311yescharacteristic
223C2×C101#151411yescharacteristic
224C2×C101C4×#9911yescharacteristic
225C2×C101#175911yescharacteristic
226C2×C101#176211yescharacteristic
227C4×#121C2×C10111yescharacteristic
228#1749C2×C10111yescharacteristic, complemented
229C2×#327C2×C10112yes—
230#1434C2×C10111yescharacteristic, complemented
231#1294C2×C10112yescomplemented
232C101#821611yescharacteristic, direct product factor, Sylow
233C2×#121C22×C10111yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C4×C10111yescharacteristic, complemented
236C22×C42C22×C10111yescharacteristic
237C2×C22⋊C8C22×C10112yes—
238C2×#97—21no—
239#390C4×C10111yescharacteristic, complemented
240#389C4×C10111yescharacteristic, complemented
241#388—21no—
242#386—21no—
243#380C22×C10111yescharacteristic
244C4×C4⋊C4C4×C10111yescharacteristic, complemented
245C4×C22⋊C4—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95C22×C10112yes—
249#336—21no—
250#327C4×C10118yescomplemented
251C22×D4—21no—
252C22×D4C2×C4×C10111yescharacteristic
253C23×C4—22no—
254C23×C4—21no—
255C23×C4D4×C10111yescharacteristic
256C23×C4D4×C10111yescharacteristic
257C23×C4C23×C10111yescharacteristic
258C22×C8—22no—
259#121—22no—
260#121C2×C4×C10114yes—
261C4×D4—42no—
262C4×D4—44no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C2×C4×C10111yescharacteristic
265C2×C4⋊C4C2×C4×C10111yescharacteristic
266C2×C4⋊C4C2×C4×C10111yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C42—21no—
273C2×C42—42no—
274C2×C42C2×C4×C10111yescharacteristic
275C2×C42C2×C4×C10111yescharacteristic
276C2×C42D4×C10111yescharacteristic
277C2×C42D4×C10111yescharacteristic
278C22⋊C8—22no—
279C22⋊C8C2×C4×C10114yescomplemented
280#97—42no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—22no—
285#95—42no—
286#95—42no—
287#95C2×C4×C10114yescomplemented
288C24—21no—
289C24C2×D4×C10111yescharacteristic
290C2×D4—24no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4C42×C10112yes—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—24no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4C22⋊C4×C10111yescharacteristic
321C22×C4C22⋊C4×C10111yescharacteristic
322C22×C4C22⋊C4×C10111yescharacteristic
323C22×C4C22⋊C4×C10111yescharacteristic
324C22×C4C22×C4×C10111yescharacteristic
325C22×C4C22×C4×C10112yes—
326C22×C4C2×D4×C10111yescharacteristic
327C22×C4#41×C10112yes—
328C2×C8—24no—
329C2×C8—42no—
330C2×C8—42no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—42no—
335C4⋊C4C42×C10112yes—
336C22⋊C4—24no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C42—22no—
342C42—22no—
343C42—41no—
344C42—41no—
345C42—42no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—22no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23C2×C22⋊C4×C10111yescharacteristic
358C23C4×D4×C10112yes—
359C23AGL(1,ℤ/8)×C10111yescharacteristic
360C23AGL(1,ℤ/8)×C10112yes—
361C23#137×C10111yescharacteristic
362D4—42no—
363D4—42no—
364D4—44no—
365D4—44no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—44no—
398C2×C4—84no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4#99×C10112yes—
404C2×C4C2×C42×C10111yescharacteristic
405C2×C4#117×C10111yescharacteristic
406C2×C4C4×D4×C10112yes—
407C8—44no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—42no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22C4×C22⋊C4×C10111yescharacteristic
424C22C2×#99×C10111yescharacteristic
425C22#410×C10111yescharacteristic
426C22#417×C10111yescharacteristic
427C22#418×C10111yescharacteristic
428C22#421×C10111yescharacteristic
429C22#421×C10111yescharacteristic
430C22#440×C10112yes—
431C22#442×C10112yes—
432C4—22no—
433C4—21no—
434C4—21no—
435C4—22no—
436C4—42no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—84no—
441C4—81no—
442C4—81no—
443C2—22no—
444C2—22no—
445C2—82no—
446C2C101×#151011yescharacteristic
447C2C101×#151211yescharacteristic
448C2C101×#151311yescharacteristic
449C2C101×#151411yescharacteristic
450C2C4×#99×C10111yescharacteristic
451C2C101×#175911yescharacteristic
452C2C101×#176211yescharacteristic
subgroupG/H
center, socleC23×C101C2×C22⋊C4
commutatorC2×C4C2×C42×C101
Frattini, cosocleC23×C4C23×C101
prime radicalC2×#121×C101C22
LCSG ▷ C2×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×#1749C2semidirect
4. C101×#1434C2semidirect
5. C101×#1294C2semidirect
8. C2×C4×D4×C101C4semidirect
12. #390×C101C4semidirect
13. #389×C101C4semidirect
17. C4×C4⋊C4×C101C4semidirect
23. #327×C101C4semidirect
52. C22⋊C8×C101C2×C4semidirect
60. #95×C101C2×C4semidirect
216. #8216C101direct (N × H)
228. #1749C2×C101semidirect
230. #1434C2×C101semidirect
231. #1294C2×C101semidirect
232. C101#8216direct (N × H)
235. C2×C4×D4C4×C101semidirect
239. #390C4×C101semidirect
240. #389C4×C101semidirect
244. C4×C4⋊C4C4×C101semidirect
250. #327C4×C101semidirect
279. C22⋊C8C2×C4×C101semidirect
287. #95C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1012
C101×#17492
C2×#327×C1012
C101×#14342
C101×#12942
#8216101