Finite Group Databasebeta

← C109×#10283 #42128277

Subgroups — C109×#10283 #42128277

Order 27904.

626 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3227C211yesmaximal, characteristic
2C109×#3206C211yesmaximal, characteristic
3C109×#2868C211yesmaximal, characteristic, complemented
4C109×#1962C211yesmaximal, characteristic
5C109×#1549C211yesmaximal, characteristic, complemented
6C109×#1548C211yesmaximal, characteristic, complemented
7C109×#1276C211yesmaximal, characteristic, complemented
8#532×C109C2211yescharacteristic
9C2×C4⋊Q8×C109—22no—
10C2×C4⋊Q8×C109C2211yescharacteristic
11C2×C4⋊Q8×C109C2211yescharacteristic
12#498×C109—21no—
13#492×C109—21no—
14#487×C109—21no—
15#486×C109—21no—
16#481×C109—22no—
17#476×C109—22no—
18#461×C109—22no—
19#448×C109—22no—
20#431×C109C2211yescharacteristic
21#431×C109C2211yescharacteristic
22#423×C109C2211yescharacteristic
23C2×#104×C109—22no—
24#384×C109—22no—
25#384×C109—22no—
26C43×C109C2211yescharacteristic
27#333×C109—22no—
28#332×C109—22no—
29C2×#41×C109—21no—
30C22×Q8×C109—21no—
31C22×Q8×C109D412yes—
32C2×SD16×C109—24no—
33C2×M16×C109—21no—
34C4⋊Q8×C109—21no—
35C4⋊Q8×C109—21no—
36C4⋊Q8×C109—21no—
37C4⋊Q8×C109—21no—
38C4⋊Q8×C109—21no—
39C4⋊Q8×C109—21no—
40C4⋊Q8×C109—21no—
41C4⋊Q8×C109—21no—
42C4⋊Q8×C109—48no—
43C4⋊Q8×C109D411yescharacteristic
44#127×C109D411yescharacteristic
45#124×C109—21no—
46#121×C109—21no—
47#121×C109—21no—
48C4×D4×C109—21no—
49C4×D4×C109—21no—
50C2×C4⋊C4×C109—28no—
51C2×C4⋊C4×C109—21no—
52C2×C4⋊C4×C109—21no—
53C2×C4⋊C4×C109—21no—
54C2×C4⋊C4×C109D412yes—
55C2×C42×C109—21no—
56C2×C42×C109—21no—
57C2×C42×C109D412yes—
58C2×C42×C109C2311yescharacteristic
59#106×C109—24no—
60C4⋊C8×C109—21no—
61C4⋊C8×C109—21no—
62C4⋊C8×C109D412yes—
63C4⋊C8×C109D412yes—
64#104×C109—44no—
65#103×C109—24no—
66#102×C109—24no—
67C22⋊C8×C109—21no—
68C22⋊C8×C109—21no—
69C4×C8×C109—21no—
70C4×C8×C109—21no—
71#41×C109—42no—
72#41×C109—42no—
73C2×Q8×C109—22no—
74C2×Q8×C109—21no—
75C2×Q8×C109—22no—
76C2×Q8×C109—44no—
77C2×Q8×C109—44no—
78C2×Q8×C109—41no—
79C2×Q8×C109—41no—
80C2×D4×C109—21no—
81C2×D4×C109—21no—
82C2×D4×C109—21no—
83C2×D4×C109—41no—
84C22×C4×C109—22no—
85C22×C4×C109—22no—
86C22×C4×C109—22no—
87C22×C4×C109—41no—
88C22×C4×C109C2×D411yescharacteristic
89C22×C4×C109C2×D411yescharacteristic
90C22×C4×C109C2×D411yescharacteristic
91SD16×C109—84no—
92M16×C109—42no—
93C2×C8×C109—22no—
94C2×C8×C109—22no—
95C2×C8×C109—41no—
96C4⋊C4×C109—22no—
97C4⋊C4×C109—21no—
98C4⋊C4×C109—21no—
99C4⋊C4×C109—22no—
100C4⋊C4×C109—416no—
101C4⋊C4×C109—41no—
102C4⋊C4×C109—41no—
103C4⋊C4×C109—41no—
104C4⋊C4×C109—41no—
105C4⋊C4×C109—41no—
106C4⋊C4×C109—41no—
107C22⋊C4×C109—41no—
108C22⋊C4×C109—41no—
109C42×C109—24no—
110C42×C109—24no—
111C42×C109—22no—
112C42×C109SD1614yescomplemented
113C42×C109C2×D411yescharacteristic
114C42×C109C2×D411yescharacteristic
115C42×C109C2×D411yescharacteristic
116C42×C109#4111yescharacteristic
117C23×C109—41no—
118C23×C109#12011yescharacteristic
119Q8×C109—44no—
120Q8×C109—42no—
121Q8×C109—82no—
122Q8×C109—82no—
123Q8×C109—82no—
124D4×C109—42no—
125D4×C109—42no—
126D4×C109—42no—
127D4×C109—82no—
128C2×C4×C109—24no—
129C2×C4×C109—24no—
130C2×C4×C109—24no—
131C2×C4×C109—22no—
132C2×C4×C109—22no—
133C2×C4×C109—44no—
134C2×C4×C109—44no—
135C2×C4×C109—41no—
136C2×C4×C109—42no—
137C2×C4×C109—42no—
138C2×C4×C109—81no—
139C2×C4×C109—81no—
140C2×C4×C109#12011yescharacteristic
141C2×C4×C109#12011yescharacteristic
142C2×C4×C109#12111yescharacteristic
143C2×C4×C109#12111yescharacteristic
144C2×C4×C109#12111yescharacteristic
145C2×C4×C109#12711yescharacteristic
146C2×C4×C109C2×SD1612yes—
147C2×C4×C109#13712yes—
148C8×C109—42no—
149C8×C109—42no—
150C8×C109—81no—
151C22×C109—21no—
152C22×C109—21no—
153C22×C109—81no—
154C22×C109—81no—
155C22×C109—81no—
156C22×C109#39211yescharacteristic
157C22×C109#44812yes—
158C4×C109—28no—
159C4×C109—21no—
160C4×C109—21no—
161C4×C109—82no—
162C4×C109—82no—
163C4×C109—81no—
164C4×C109#45312yes—
165C4×C109#45612yes—
166C4×C109#46112yes—
167C4×C109#49211yescharacteristic
168C4×C109#49711yescharacteristic
169#10283C10911yesmaximal, characteristic, direct product factor, Sylow
170C2×C109—22no—
171C2×C109—161no—
172C2×C109#200211yescharacteristic
173C2×C109#200511yescharacteristic
174C2×C109#201311yescharacteristic
175#3227C2×C10911yescharacteristic
176#3206C2×C10911yescharacteristic
177#2868C2×C10911yescharacteristic, complemented
178#1962C2×C10911yescharacteristic
179#1549C2×C10911yescharacteristic, complemented
180#1548C2×C10911yescharacteristic, complemented
181#1276C2×C10911yescharacteristic, complemented
182C109#1028311yescharacteristic, direct product factor, Sylow
183#532C22×C10911yescharacteristic
184C2×C4⋊Q8—22no—
185C2×C4⋊Q8C22×C10911yescharacteristic
186C2×C4⋊Q8C22×C10911yescharacteristic
187#498—21no—
188#492—21no—
189#487—21no—
190#486—21no—
191#481—22no—
192#476—22no—
193#461—22no—
194#448—22no—
195#431C22×C10911yescharacteristic
196#431C22×C10911yescharacteristic
197#423C22×C10911yescharacteristic
198C2×#104—22no—
199#384—22no—
200#384—22no—
201C43C22×C10911yescharacteristic
202#333—22no—
203#332—22no—
204C2×#41—21no—
205C22×Q8—21no—
206C22×Q8D4×C10912yes—
207C2×SD16—24no—
208C2×M16—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—48no—
218C4⋊Q8D4×C10911yescharacteristic
219#127D4×C10911yescharacteristic
220#124—21no—
221#121—21no—
222#121—21no—
223C4×D4—21no—
224C4×D4—21no—
225C2×C4⋊C4—28no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C10912yes—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42D4×C10912yes—
233C2×C42C23×C10911yescharacteristic
234#106—24no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8D4×C10912yes—
238C4⋊C8D4×C10912yes—
239#104—44no—
240#103—24no—
241#102—24no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C4×C8—21no—
245C4×C8—21no—
246#41—42no—
247#41—42no—
248C2×Q8—22no—
249C2×Q8—21no—
250C2×Q8—22no—
251C2×Q8—44no—
252C2×Q8—44no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4C2×D4×C10911yescharacteristic
264C22×C4C2×D4×C10911yescharacteristic
265C22×C4C2×D4×C10911yescharacteristic
266SD16—84no—
267M16—42no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—416no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—24no—
285C42—24no—
286C42—22no—
287C42SD16×C10914yescomplemented
288C42C2×D4×C10911yescharacteristic
289C42C2×D4×C10911yescharacteristic
290C42C2×D4×C10911yescharacteristic
291C42#41×C10911yescharacteristic
292C23—41no—
293C23#120×C10911yescharacteristic
294Q8—44no—
295Q8—42no—
296Q8—82no—
297Q8—82no—
298Q8—82no—
299D4—42no—
300D4—42no—
301D4—42no—
302D4—82no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#120×C10911yescharacteristic
316C2×C4#120×C10911yescharacteristic
317C2×C4#121×C10911yescharacteristic
318C2×C4#121×C10911yescharacteristic
319C2×C4#121×C10911yescharacteristic
320C2×C4#127×C10911yescharacteristic
321C2×C4C2×SD16×C10912yes—
322C2×C4#137×C10912yes—
323C8—42no—
324C8—42no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22#392×C10911yescharacteristic
332C22#448×C10912yes—
333C4—28no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—82no—
338C4—81no—
339C4#453×C10912yes—
340C4#456×C10912yes—
341C4#461×C10912yes—
342C4#492×C10911yescharacteristic
343C4#497×C10911yescharacteristic
344C2—22no—
345C2—161no—
346C2C109×#200211yescharacteristic
347C2C109×#200511yescharacteristic
348C2C109×#201311yescharacteristic
subgroupG/H
center, socleC22×C109#392
commutator, Frattini, cosocleC2×C42C23×C109
prime radical#532×C109C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
3. C109×#2868C2semidirect
5. C109×#1549C2semidirect
6. C109×#1548C2semidirect
7. C109×#1276C2semidirect
112. C42×C109SD16semidirect
169. #10283C109direct (N × H)
177. #2868C2×C109semidirect
179. #1549C2×C109semidirect
180. #1548C2×C109semidirect
181. #1276C2×C109semidirect
182. C109#10283direct (N × H)
287. C42SD16×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#32272
C109×#32062
C109×#28682
C109×#19622
C109×#15492
C109×#15482
C109×#12762
#10283109