Finite Group Databasebeta

← C101×#19158 #38801309

Subgroups — C101×#19158 #38801309

Order 25856.

596 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3170C211yesmaximal, characteristic, complemented
2C101×#3076C212yesmaximal
3C101×#2965C211yesmaximal, characteristic
4C101×#1704C212yesmaximal, complemented
5C101×#1703C212yesmaximal, complemented
6C101×#1696C211yesmaximal, characteristic, complemented
7C101×#1695C211yesmaximal, characteristic, complemented
8C101×#1690C211yesmaximal, characteristic, complemented
9C101×#1689C211yesmaximal, characteristic, complemented
10C2×#334×C101C211yesmaximal, characteristic, complemented
11C101×#1542C212yesmaximal, complemented
12#533×C101C2212yes—
13C4×#41×C101C2211yescharacteristic
14#500×C101C2211yescharacteristic
15#494×C101C2211yescharacteristic
16#487×C101C2212yes—
17#479×C101—22no—
18#478×C101—22no—
19#477×C101C2212yes—
20#476×C101C2212yes—
21#475×C101C2212yes—
22#474×C101C2212yes—
23#467×C101—21no—
24#467×C101—21no—
25#446×C101C2211yescharacteristic
26#446×C101C2211yescharacteristic
27C4×Q16×C101—21no—
28C4×Q16×C101—21no—
29#436×C101C2211yescharacteristic
30#436×C101C2211yescharacteristic
31#435×C101—21no—
32#435×C101—21no—
33#431×C101—21no—
34#431×C101C2211yescharacteristic
35#427×C101—22no—
36C2×C4⋊C8×C101C2212yes—
37#416×C101—22no—
38C4×M16×C101—21no—
39C2×C4×C8×C101C2211yescharacteristic
40#334×C101C2211yescharacteristic
41#334×C101C2211yescharacteristic
42#334×C101C2212yes—
43#333×C101C2212yes—
44#333×C101C2212yes—
45#332×C101C2212yes—
46#332×C101C2212yes—
47C2×#41×C101D411yescharacteristic
48C2×Q16×C101—21no—
49C2×Q16×C101—21no—
50C2×M16×C101—21no—
51C2×M16×C101—21no—
52C22×C8×C101—22no—
53C22×C8×C101D411yescharacteristic
54C22×C8×C101D411yescharacteristic
55C4⋊Q8×C101C2312yes—
56C4⋊Q8×C101C2312yes—
57#125×C101—22no—
58C22⋊Q8×C101—22no—
59C22⋊Q8×C101—22no—
60C4×Q8×C101—22no—
61C4×Q8×C101—22no—
62C4×Q8×C101D411yescharacteristic
63C4×Q8×C101C2311yescharacteristic
64C4×D4×C101—21no—
65C4×D4×C101—21no—
66C4×D4×C101D411yescharacteristic
67C4×D4×C101C2311yescharacteristic
68#117×C101—21no—
69#117×C101—22no—
70#117×C101D411yescharacteristic
71C2×C42×C101—21no—
72C2×C42×C101C2311yescharacteristic
73#107×C101—21no—
74#107×C101—21no—
75#107×C101—22no—
76#107×C101—22no—
77#106×C101—22no—
78#106×C101—22no—
79C4⋊C8×C101—21no—
80C4⋊C8×C101—21no—
81C4⋊C8×C101—22no—
82C4⋊C8×C101C2312yes—
83C4⋊C8×C101C2312yes—
84C4⋊C8×C101C2311yescharacteristic
85C4⋊C8×C101C2311yescharacteristic
86#103×C101—22no—
87#103×C101—22no—
88#103×C101—22no—
89#103×C101—22no—
90#102×C101—22no—
91#102×C101—22no—
92C22⋊C8×C101—21no—
93C22⋊C8×C101—21no—
94C22⋊C8×C101—21no—
95#97×C101—21no—
96#97×C101—21no—
97C4×C8×C101—21no—
98C4×C8×C101D411yescharacteristic
99C4×C8×C101D411yescharacteristic
100C4×C8×C101C2311yescharacteristic
101C4×C8×C101C2311yescharacteristic
102#41×C101—24no—
103C2×Q8×C101—22no—
104C2×Q8×C101—22no—
105C2×Q8×C101C2×D411yescharacteristic
106C2×D4×C101—21no—
107C2×D4×C101C2×D411yescharacteristic
108C22×C4×C101—21no—
109C22×C4×C101—21no—
110C22×C4×C101—21no—
111C22×C4×C101C2×D411yescharacteristic
112C22×C4×C101C2×D411yescharacteristic
113C22×C4×C101#4111yescharacteristic
114Q16×C101—42no—
115Q16×C101—42no—
116M16×C101—42no—
117M16×C101—42no—
118C2×C8×C101—22no—
119C2×C8×C101—21no—
120C2×C8×C101—21no—
121C2×C8×C101—22no—
122C2×C8×C101—22no—
123C2×C8×C101—41no—
124C2×C8×C101—44no—
125C2×C8×C101C2×D411yescharacteristic
126C2×C8×C101C2×D411yescharacteristic
127C2×C8×C101C2×D411yescharacteristic
128C2×C8×C101C2×D411yescharacteristic
129C4⋊C4×C101—21no—
130C4⋊C4×C101—21no—
131C4⋊C4×C101—22no—
132C4⋊C4×C101—22no—
133C4⋊C4×C101—22no—
134C4⋊C4×C101—22no—
135C4⋊C4×C101—42no—
136C4⋊C4×C101—42no—
137C4⋊C4×C101C2×D411yescharacteristic
138C4⋊C4×C101C2×D411yescharacteristic
139C22⋊C4×C101—21no—
140C22⋊C4×C101—21no—
141C22⋊C4×C101—21no—
142C22⋊C4×C101—42no—
143C42×C101—21no—
144C42×C101—21no—
145C42×C101—21no—
146C42×C101—42no—
147C42×C101C2×D411yescharacteristic
148C42×C101C2×D411yescharacteristic
149C42×C101#4111yescharacteristic
150C42×C101C2411yescharacteristic
151C23×C101—21no—
152C23×C101#12111yescharacteristic
153Q8×C101—22no—
154Q8×C101—42no—
155Q8×C101—42no—
156Q8×C101—82no—
157D4×C101—22no—
158D4×C101—42no—
159C2×C4×C101—21no—
160C2×C4×C101—21no—
161C2×C4×C101—21no—
162C2×C4×C101—21no—
163C2×C4×C101—21no—
164C2×C4×C101—41no—
165C2×C4×C101—42no—
166C2×C4×C101—41no—
167C2×C4×C101—41no—
168C2×C4×C101—42no—
169C2×C4×C101—42no—
170C2×C4×C101—42no—
171C2×C4×C101#12111yescharacteristic
172C2×C4×C101#12111yescharacteristic
173C2×C4×C101#12111yescharacteristic
174C2×C4×C101#13714yes—
175C2×C4×C101C22×D411yescharacteristic
176C2×C4×C101C22×D411yescharacteristic
177C2×C4×C101C2×#4111yescharacteristic
178C8×C101—21no—
179C8×C101—21no—
180C8×C101—21no—
181C8×C101—41no—
182C8×C101—42no—
183C8×C101—42no—
184C8×C101—41no—
185C8×C101#13512yes—
186C22×C101—21no—
187C22×C101—21no—
188C22×C101—41no—
189C22×C101—41no—
190C22×C101—41no—
191C22×C101#47012yes—
192C22×C101C2×#12111yescharacteristic
193C4×C101—21no—
194C4×C101—21no—
195C4×C101—21no—
196C4×C101—41no—
197C4×C101—41no—
198C4×C101—41no—
199C4×C101—82no—
200C4×C101—82no—
201C4×C101#47012yes—
202C4×C101C2×#13511yescharacteristic
203C4×C101C2×#13712yes—
204C4×C101#57511yescharacteristic
205#19158C10111yesmaximal, characteristic, direct product factor, Sylow
206C2×C101—22no—
207C2×C101—81no—
208C2×C101#303511yescharacteristic
209C2×C101C2×#47011yescharacteristic
210C2×C101#306711yescharacteristic
211#3170C2×C10111yescharacteristic, complemented
212#3076C2×C10112yes—
213#2965C2×C10111yescharacteristic
214#1704C2×C10112yescomplemented
215#1703C2×C10112yescomplemented
216#1696C2×C10111yescharacteristic, complemented
217#1695C2×C10111yescharacteristic, complemented
218#1690C2×C10111yescharacteristic, complemented
219#1689C2×C10111yescharacteristic, complemented
220C2×#334C2×C10111yescharacteristic, complemented
221#1542C2×C10112yescomplemented
222C101#1915811yescharacteristic, direct product factor, Sylow
223#533C22×C10112yes—
224C4×#41C22×C10111yescharacteristic
225#500C22×C10111yescharacteristic
226#494C22×C10111yescharacteristic
227#487C22×C10112yes—
228#479—22no—
229#478—22no—
230#477C22×C10112yes—
231#476C22×C10112yes—
232#475C22×C10112yes—
233#474C22×C10112yes—
234#467—21no—
235#467—21no—
236#446C22×C10111yescharacteristic
237#446C22×C10111yescharacteristic
238C4×Q16—21no—
239C4×Q16—21no—
240#436C22×C10111yescharacteristic
241#436C22×C10111yescharacteristic
242#435—21no—
243#435—21no—
244#431—21no—
245#431C22×C10111yescharacteristic
246#427—22no—
247C2×C4⋊C8C22×C10112yes—
248#416—22no—
249C4×M16—21no—
250C2×C4×C8C22×C10111yescharacteristic
251#334C22×C10111yescharacteristic
252#334C22×C10111yescharacteristic
253#334C22×C10112yes—
254#333C22×C10112yes—
255#333C22×C10112yes—
256#332C22×C10112yes—
257#332C22×C10112yes—
258C2×#41D4×C10111yescharacteristic
259C2×Q16—21no—
260C2×Q16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C22×C8—22no—
264C22×C8D4×C10111yescharacteristic
265C22×C8D4×C10111yescharacteristic
266C4⋊Q8C23×C10112yes—
267C4⋊Q8C23×C10112yes—
268#125—22no—
269C22⋊Q8—22no—
270C22⋊Q8—22no—
271C4×Q8—22no—
272C4×Q8—22no—
273C4×Q8D4×C10111yescharacteristic
274C4×Q8C23×C10111yescharacteristic
275C4×D4—21no—
276C4×D4—21no—
277C4×D4D4×C10111yescharacteristic
278C4×D4C23×C10111yescharacteristic
279#117—21no—
280#117—22no—
281#117D4×C10111yescharacteristic
282C2×C42—21no—
283C2×C42C23×C10111yescharacteristic
284#107—21no—
285#107—21no—
286#107—22no—
287#107—22no—
288#106—22no—
289#106—22no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—22no—
293C4⋊C8C23×C10111yescharacteristic
294C4⋊C8C23×C10111yescharacteristic
295C4⋊C8C23×C10112yes—
296C4⋊C8C23×C10112yes—
297#103—22no—
298#103—22no—
299#103—22no—
300#103—22no—
301#102—22no—
302#102—22no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306#97—21no—
307#97—21no—
308C4×C8—21no—
309C4×C8D4×C10111yescharacteristic
310C4×C8D4×C10111yescharacteristic
311C4×C8C23×C10111yescharacteristic
312C4×C8C23×C10111yescharacteristic
313#41—24no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8C2×D4×C10111yescharacteristic
317C2×D4—21no—
318C2×D4C2×D4×C10111yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4C2×D4×C10111yescharacteristic
323C22×C4C2×D4×C10111yescharacteristic
324C22×C4#41×C10111yescharacteristic
325Q16—42no—
326Q16—42no—
327M16—42no—
328M16—42no—
329C2×C8—22no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—44no—
336C2×C8C2×D4×C10111yescharacteristic
337C2×C8C2×D4×C10111yescharacteristic
338C2×C8C2×D4×C10111yescharacteristic
339C2×C8C2×D4×C10111yescharacteristic
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4C2×D4×C10111yescharacteristic
349C4⋊C4C2×D4×C10111yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—42no—
354C42—21no—
355C42—21no—
356C42—21no—
357C42—42no—
358C42C2×D4×C10111yescharacteristic
359C42C2×D4×C10111yescharacteristic
360C42#41×C10111yescharacteristic
361C42C24×C10111yescharacteristic
362C23—21no—
363C23#121×C10111yescharacteristic
364Q8—22no—
365Q8—42no—
366Q8—42no—
367Q8—82no—
368D4—22no—
369D4—42no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4#121×C10111yescharacteristic
383C2×C4#121×C10111yescharacteristic
384C2×C4#121×C10111yescharacteristic
385C2×C4#137×C10114yes—
386C2×C4C22×D4×C10111yescharacteristic
387C2×C4C22×D4×C10111yescharacteristic
388C2×C4C2×#41×C10111yescharacteristic
389C8—21no—
390C8—21no—
391C8—21no—
392C8—41no—
393C8—42no—
394C8—42no—
395C8—41no—
396C8#135×C10112yes—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22#470×C10112yes—
403C22C2×#121×C10111yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—82no—
411C4—82no—
412C4#470×C10112yes—
413C4C2×#135×C10111yescharacteristic
414C4C2×#137×C10112yes—
415C4#575×C10111yescharacteristic
416C2—22no—
417C2—81no—
418C2C101×#303511yescharacteristic
419C2C2×#470×C10111yescharacteristic
420C2C101×#306711yescharacteristic
subgroupG/H
centerC2×C4×C101#121
commutator, Frattini, cosocleC42C24×C101
socleC22×C101C2×#121
prime radicalC2×#41×C101D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3170C2semidirect
4. C101×#1704C2semidirect
5. C101×#1703C2semidirect
6. C101×#1696C2semidirect
7. C101×#1695C2semidirect
8. C101×#1690C2semidirect
9. C101×#1689C2semidirect
10. C2×#334×C101C2semidirect
11. C101×#1542C2semidirect
205. #19158C101direct (N × H)
211. #3170C2×C101semidirect
214. #1704C2×C101semidirect
215. #1703C2×C101semidirect
216. #1696C2×C101semidirect
217. #1695C2×C101semidirect
218. #1690C2×C101semidirect
219. #1689C2×C101semidirect
220. C2×#334C2×C101semidirect
221. #1542C2×C101semidirect
222. C101#19158direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#31702
C101×#30762
C101×#29652
C101×#17042
C101×#17032
C101×#16962
C101×#16952
C101×#16902
C101×#16892
C2×#334×C1012
C101×#15422
#19158101