Finite Group Databasebeta

← C107×#9054 #41035018

Subgroups — C107×#9054 #41035018

Order 27392.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3167C211yesmaximal, characteristic
2C107×#2962C211yesmaximal, characteristic, complemented
3C107×#1980C211yesmaximal, characteristic
4C107×#1503C211yesmaximal, characteristic, complemented
5C107×#1480C211yesmaximal, characteristic
6C107×#1279C211yesmaximal, characteristic, complemented
7C107×#1278C211yesmaximal, characteristic, complemented
8#533×C107C2211yescharacteristic
9#532×C107C2211yescharacteristic
10#498×C107C411yescharacteristic, complemented
11#492×C107C411yescharacteristic, complemented
12#487×C107C411yescharacteristic, complemented
13#486×C107C411yescharacteristic, complemented
14#465×C107—22no—
15#446×C107—22no—
16#446×C107—21no—
17C8×Q8×C107—21no—
18C4×SD16×C107—22no—
19#431×C107C2211yescharacteristic
20#424×C107—21no—
21C2×C4⋊C8×C107C2211yescharacteristic
22C2×#104×C107—21no—
23C2×#104×C107—21no—
24#405×C107—21no—
25C4×M16×C107C2211yescharacteristic
26C2×C4×C8×C107C2211yescharacteristic
27C4×C4⋊C4×C107C2211yescharacteristic
28#328×C107—22no—
29D4⋊C8×C107—21no—
30D4⋊C8×C107—21no—
31C2×#41×C107—21no—
32C2×SD16×C107—22no—
33C2×M16×C107D411yescharacteristic
34C2×M16×C107D411yescharacteristic
35C22×C8×C107—21no—
36C22×C8×C107—21no—
37C4⋊Q8×C107C2×C411yescharacteristic
38C4⋊Q8×C107C2×C411yescharacteristic
39C4⋊Q8×C107C2×C411yescharacteristic
40#127×C107C2×C411yescharacteristic
41#125×C107—21no—
42#124×C107—21no—
43C22⋊Q8×C107—21no—
44C22⋊Q8×C107D412yes—
45#121×C107—21no—
46#121×C107—21no—
47C4×Q8×C107—21no—
48C4×Q8×C107D412yes—
49C4×D4×C107—21no—
50C4×D4×C107—21no—
51#117×C107—21no—
52C2×C4⋊C4×C107—21no—
53C2×C42×C107—21no—
54C2×C42×C107C2311yescharacteristic
55#106×C107—22no—
56C4⋊C8×C107—22no—
57C4⋊C8×C107—22no—
58C4⋊C8×C107—21no—
59C4⋊C8×C107—21no—
60C4⋊C8×C107D411yescharacteristic
61C4⋊C8×C107D411yescharacteristic
62#104×C107—42no—
63#104×C107—42no—
64#103×C107—22no—
65#102×C107—22no—
66C22⋊C8×C107—21no—
67#97×C107—22no—
68#97×C107—21no—
69C4×C8×C107—22no—
70C4×C8×C107—21no—
71C4×C8×C107—21no—
72C4×C8×C107—21no—
73C4×C8×C107C2×C411yescharacteristic
74C4×C8×C107C2×C411yescharacteristic
75#95×C107—21no—
76#41×C107—41no—
77#41×C107—41no—
78#41×C107—41no—
79#41×C107—41no—
80C2×Q8×C107—21no—
81C2×Q8×C107—21no—
82C2×Q8×C107C22⋊C412yes—
83C2×D4×C107—21no—
84C2×D4×C107—21no—
85C2×D4×C107—21no—
86C2×D4×C107—41no—
87C22×C4×C107—41no—
88C22×C4×C107—41no—
89C22×C4×C107C2×D411yescharacteristic
90C22×C4×C107C2×D411yescharacteristic
91C22×C4×C107#4111yescharacteristic
92SD16×C107—44no—
93M16×C107—21no—
94M16×C107—21no—
95M16×C107—21no—
96M16×C107SD1612yescomplemented
97C2×C8×C107—21no—
98C2×C8×C107—21no—
99C2×C8×C107—21no—
100C2×C8×C107—21no—
101C2×C8×C107—21no—
102C2×C8×C107—21no—
103C2×C8×C107—42no—
104C2×C8×C107—41no—
105C2×C8×C107—41no—
106C2×C8×C107—41no—
107C4⋊C4×C107—21no—
108C4⋊C4×C107—21no—
109C4⋊C4×C107—21no—
110C4⋊C4×C107—22no—
111C4⋊C4×C107—22no—
112C4⋊C4×C107—22no—
113C4⋊C4×C107—21no—
114C4⋊C4×C107—21no—
115C4⋊C4×C107—41no—
116C4⋊C4×C107C22⋊C412yes—
117C22⋊C4×C107—22no—
118C22⋊C4×C107—41no—
119C22⋊C4×C107—41no—
120C42×C107—22no—
121C42×C107—41no—
122C42×C107—41no—
123C42×C107C22×C411yescharacteristic
124C42×C107C2×D411yescharacteristic
125C42×C107C2×D411yescharacteristic
126C42×C107#4111yescharacteristic
127C23×C107—41no—
128C23×C107#12111yescharacteristic
129Q8×C107—42no—
130Q8×C107—41no—
131Q8×C107—41no—
132Q8×C107—41no—
133Q8×C107—41no—
134D4×C107—42no—
135D4×C107—41no—
136D4×C107—41no—
137D4×C107—41no—
138D4×C107—41no—
139D4×C107—81no—
140D4×C107—81no—
141C2×C4×C107—21no—
142C2×C4×C107—21no—
143C2×C4×C107—22no—
144C2×C4×C107—22no—
145C2×C4×C107—41no—
146C2×C4×C107—42no—
147C2×C4×C107—41no—
148C2×C4×C107—81no—
149C2×C4×C107—81no—
150C2×C4×C107—81no—
151C2×C4×C107—81no—
152C2×C4×C107C2×C22⋊C411yescharacteristic
153C2×C4×C107C4×D411yescharacteristic
154C2×C4×C107C4×D411yescharacteristic
155C2×C4×C107#12011yescharacteristic
156C2×C4×C107#12111yescharacteristic
157C2×C4×C107#12311yescharacteristic
158C2×C4×C107C2×SD1611yescharacteristic
159C2×C4×C107#13511yescharacteristic
160C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C107#13711yescharacteristic
162C8×C107—22no—
163C8×C107—22no—
164C8×C107—41no—
165C8×C107—41no—
166C8×C107—41no—
167C8×C107—41no—
168C8×C107—81no—
169C22×C107—21no—
170C22×C107—21no—
171C22×C107—81no—
172C22×C107—81no—
173C22×C107—81no—
174C22×C107#38611yescharacteristic
175C22×C107#46011yescharacteristic
176C22×C107#46411yescharacteristic
177C4×C107—21no—
178C4×C107—21no—
179C4×C107—21no—
180C4×C107—42no—
181C4×C107—42no—
182C4×C107—82no—
183C4×C107—81no—
184C4×C107C4×SD1611yescharacteristic
185C4×C107#44011yescharacteristic
186C4×C107#44311yescharacteristic
187C4×C107#44411yescharacteristic
188C4×C107#44811yescharacteristic
189C4×C107#44911yescharacteristic
190#9054C10711yesmaximal, characteristic, direct product factor, Sylow
191C2×C107—21no—
192C2×C107—21no—
193C2×C107—161no—
194C2×C107#187611yescharacteristic
195C2×C107#188011yescharacteristic
196C2×C107#188411yescharacteristic
197#3167C2×C10711yescharacteristic
198#2962C2×C10711yescharacteristic, complemented
199#1980C2×C10711yescharacteristic
200#1503C2×C10711yescharacteristic, complemented
201#1480C2×C10711yescharacteristic
202#1279C2×C10711yescharacteristic, complemented
203#1278C2×C10711yescharacteristic, complemented
204C107#905411yescharacteristic, direct product factor, Sylow
205#533C22×C10711yescharacteristic
206#532C22×C10711yescharacteristic
207#498C4×C10711yescharacteristic, complemented
208#492C4×C10711yescharacteristic, complemented
209#487C4×C10711yescharacteristic, complemented
210#486C4×C10711yescharacteristic, complemented
211#465—22no—
212#446—22no—
213#446—21no—
214C8×Q8—21no—
215C4×SD16—22no—
216#431C22×C10711yescharacteristic
217#424—21no—
218C2×C4⋊C8C22×C10711yescharacteristic
219C2×#104—21no—
220C2×#104—21no—
221#405—21no—
222C4×M16C22×C10711yescharacteristic
223C2×C4×C8C22×C10711yescharacteristic
224C4×C4⋊C4C22×C10711yescharacteristic
225#328—22no—
226D4⋊C8—21no—
227D4⋊C8—21no—
228C2×#41—21no—
229C2×SD16—22no—
230C2×M16D4×C10711yescharacteristic
231C2×M16D4×C10711yescharacteristic
232C22×C8—21no—
233C22×C8—21no—
234C4⋊Q8C2×C4×C10711yescharacteristic
235C4⋊Q8C2×C4×C10711yescharacteristic
236C4⋊Q8C2×C4×C10711yescharacteristic
237#127C2×C4×C10711yescharacteristic
238#125—21no—
239#124—21no—
240C22⋊Q8—21no—
241C22⋊Q8D4×C10712yes—
242#121—21no—
243#121—21no—
244C4×Q8—21no—
245C4×Q8D4×C10712yes—
246C4×D4—21no—
247C4×D4—21no—
248#117—21no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42C23×C10711yescharacteristic
252#106—22no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8D4×C10711yescharacteristic
258C4⋊C8D4×C10711yescharacteristic
259#104—42no—
260#104—42no—
261#103—22no—
262#102—22no—
263C22⋊C8—21no—
264#97—22no—
265#97—21no—
266C4×C8—22no—
267C4×C8—21no—
268C4×C8—21no—
269C4×C8—21no—
270C4×C8C2×C4×C10711yescharacteristic
271C4×C8C2×C4×C10711yescharacteristic
272#95—21no—
273#41—41no—
274#41—41no—
275#41—41no—
276#41—41no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8C22⋊C4×C10712yes—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C2×D4×C10711yescharacteristic
287C22×C4C2×D4×C10711yescharacteristic
288C22×C4#41×C10711yescharacteristic
289SD16—44no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16SD16×C10712yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4C22⋊C4×C10712yes—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—22no—
318C42—41no—
319C42—41no—
320C42C22×C4×C10711yescharacteristic
321C42C2×D4×C10711yescharacteristic
322C42C2×D4×C10711yescharacteristic
323C42#41×C10711yescharacteristic
324C23—41no—
325C23#121×C10711yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—41no—
330Q8—41no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4C2×C22⋊C4×C10711yescharacteristic
350C2×C4C4×D4×C10711yescharacteristic
351C2×C4C4×D4×C10711yescharacteristic
352C2×C4#120×C10711yescharacteristic
353C2×C4#121×C10711yescharacteristic
354C2×C4#123×C10711yescharacteristic
355C2×C4C2×SD16×C10711yescharacteristic
356C2×C4#135×C10711yescharacteristic
357C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
358C2×C4#137×C10711yescharacteristic
359C8—22no—
360C8—22no—
361C8—41no—
362C8—41no—
363C8—41no—
364C8—41no—
365C8—81no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22#386×C10711yescharacteristic
372C22#460×C10711yescharacteristic
373C22#464×C10711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—82no—
380C4—81no—
381C4C4×SD16×C10711yescharacteristic
382C4#440×C10711yescharacteristic
383C4#443×C10711yescharacteristic
384C4#444×C10711yescharacteristic
385C4#448×C10711yescharacteristic
386C4#449×C10711yescharacteristic
387C2—21no—
388C2—21no—
389C2—161no—
390C2C107×#187611yescharacteristic
391C2C107×#188011yescharacteristic
392C2C107×#188411yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#386
prime radical#532×C107C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2962C2semidirect
4. C107×#1503C2semidirect
6. C107×#1279C2semidirect
7. C107×#1278C2semidirect
10. #498×C107C4semidirect
11. #492×C107C4semidirect
12. #487×C107C4semidirect
13. #486×C107C4semidirect
96. M16×C107SD16semidirect
190. #9054C107direct (N × H)
198. #2962C2×C107semidirect
200. #1503C2×C107semidirect
202. #1279C2×C107semidirect
203. #1278C2×C107semidirect
204. C107#9054direct (N × H)
207. #498C4×C107semidirect
208. #492C4×C107semidirect
209. #487C4×C107semidirect
210. #486C4×C107semidirect
293. M16SD16×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#31672
C107×#29622
C107×#19802
C107×#15032
C107×#14802
C107×#12792
C107×#12782
#9054107