Finite Group Databasebeta

← C109×#9449 #42127443

Subgroups — C109×#9449 #42127443

Order 27904.

490 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2973C211yesmaximal, characteristic
2C109×#2566C211yesmaximal, characteristic
3C109×#1534C212yesmaximal, complemented
4C109×#1466C211yesmaximal, characteristic
5C109×#1285C212yesmaximal, complemented
6C2×#125×C109C2211yescharacteristic
7C2×C4×D4×C109C2211yescharacteristic
8#435×C109—24no—
9#432×C109C2212yes—
10#432×C109C2212yes—
11#407×C109—21no—
12C2×C22⋊C8×C109—21no—
13#396×C109—21no—
14#396×C109—21no—
15#390×C109C411yescharacteristic
16#390×C109C411yescharacteristic
17#385×C109—21no—
18#385×C109—21no—
19#384×C109C411yescharacteristic
20#382×C109C411yescharacteristic
21C4×C4⋊C4×C109C2211yescharacteristic
22#330×C109—24no—
23#323×C109—21no—
24#323×C109—21no—
25C22×D4×C109C2×C411yescharacteristic
26C23×C4×C109D411yescharacteristic
27C23×C4×C109D411yescharacteristic
28C2×M16×C109—22no—
29C22×C8×C109—22no—
30#125×C109—22no—
31#125×C109—22no—
32C4×D4×C109—22no—
33C4×D4×C109—22no—
34C2×C4⋊C4×C109—21no—
35C2×C4⋊C4×C109—21no—
36C2×C4⋊C4×C109—21no—
37C2×C4⋊C4×C109—21no—
38C2×C4⋊C4×C109—21no—
39C2×C4⋊C4×C109C2×C411yescharacteristic
40C2×C4⋊C4×C109C2×C411yescharacteristic
41C2×C4⋊C4×C109C2×C411yescharacteristic
42C2×C22⋊C4×C109—21no—
43C2×C22⋊C4×C109—21no—
44C2×C22⋊C4×C109—21no—
45C2×C22⋊C4×C109—21no—
46C2×C22⋊C4×C109D411yescharacteristic
47C2×C22⋊C4×C109D411yescharacteristic
48C2×C42×C109C2×C411yescharacteristic
49C2×C42×C109C2×C411yescharacteristic
50C2×C42×C109C2311yescharacteristic
51C4⋊C8×C109—22no—
52C4⋊C8×C109—22no—
53C22⋊C8×C109—22no—
54C22⋊C8×C109—22no—
55C22⋊C8×C109—22no—
56C22⋊C8×C109—22no—
57#97×C109—22no—
58#97×C109D414yes—
59#95×C109—21no—
60#95×C109—21no—
61#95×C109—21no—
62C24×C109C22⋊C411yescharacteristic
63C24×C109C22⋊C411yescharacteristic
64C2×D4×C109—22no—
65C2×D4×C109—22no—
66C2×D4×C109—41no—
67C22×C4×C109—21no—
68C22×C4×C109—21no—
69C22×C4×C109—21no—
70C22×C4×C109—21no—
71C22×C4×C109—21no—
72C22×C4×C109—21no—
73C22×C4×C109—21no—
74C22×C4×C109—21no—
75C22×C4×C109—81no—
76C22×C4×C109—81no—
77C22×C4×C109C22⋊C411yescharacteristic
78C22×C4×C109C22⋊C411yescharacteristic
79C22×C4×C109C22×C411yescharacteristic
80C22×C4×C109C2×D411yescharacteristic
81C22×C4×C109C2×D411yescharacteristic
82M16×C109—82no—
83C2×C8×C109—24no—
84C2×C8×C109—42no—
85C2×C8×C109—82no—
86C4⋊C4×C109—22no—
87C4⋊C4×C109—22no—
88C4⋊C4×C109—22no—
89C4⋊C4×C109—42no—
90C4⋊C4×C109—41no—
91C4⋊C4×C109—42no—
92C4⋊C4×C109—41no—
93C4⋊C4×C109—81no—
94C4⋊C4×C109—81no—
95C22⋊C4×C109—22no—
96C22⋊C4×C109—22no—
97C22⋊C4×C109—42no—
98C22⋊C4×C109—42no—
99C22⋊C4×C109—81no—
100C22⋊C4×C109—81no—
101C42×C109—41no—
102C42×C109—41no—
103C42×C109C2×D412yes—
104C42×C109#4112yes—
105C23×C109—21no—
106C23×C109—21no—
107C23×C109—21no—
108C23×C109—21no—
109C23×C109—21no—
110C23×C109—41no—
111C23×C109—41no—
112C23×C109—41no—
113C23×C109—41no—
114C23×C109#10112yes—
115C23×C109C2×C22⋊C411yescharacteristic
116D4×C109—44no—
117C2×C4×C109—21no—
118C2×C4×C109—21no—
119C2×C4×C109—22no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—41no—
123C2×C4×C109—41no—
124C2×C4×C109—42no—
125C2×C4×C109—42no—
126C2×C4×C109—41no—
127C2×C4×C109—41no—
128C2×C4×C109—41no—
129C2×C4×C109—41no—
130C2×C4×C109—41no—
131C2×C4×C109—41no—
132C2×C4×C109—41no—
133C2×C4×C109—41no—
134C2×C4×C109—41no—
135C2×C4×C109—41no—
136C2×C4×C109—41no—
137C2×C4×C109—41no—
138C2×C4×C109—41no—
139C2×C4×C109—81no—
140C2×C4×C109—81no—
141C2×C4×C109C4×D412yes—
142C2×C4×C109#12011yescharacteristic
143C2×C4×C109#12112yes—
144C2×C4×C109#12311yescharacteristic
145C8×C109—44no—
146C8×C109—82no—
147C22×C109—21no—
148C22×C109—21no—
149C22×C109—22no—
150C22×C109—42no—
151C22×C109—42no—
152C22×C109—41no—
153C22×C109—41no—
154C22×C109—41no—
155C22×C109—41no—
156C22×C109—41no—
157C22×C109—81no—
158C22×C109—81no—
159C22×C109#38611yescharacteristic
160C22×C109C2×#10111yescharacteristic
161C22×C109#41311yescharacteristic
162C4×C109—22no—
163C4×C109—22no—
164C4×C109—21no—
165C4×C109—21no—
166C4×C109—42no—
167C4×C109—41no—
168C4×C109—41no—
169C4×C109—81no—
170C4×C109—81no—
171C4×C109—81no—
172#9449C10911yesmaximal, characteristic, direct product factor, Sylow
173C2×C109—21no—
174C2×C109—21no—
175C2×C109—42no—
176C2×C109—81no—
177C2×C109#188411yescharacteristic
178C2×C109#190111yescharacteristic
179C2×C109#191111yescharacteristic
180#2973C2×C10911yescharacteristic
181#2566C2×C10911yescharacteristic
182#1534C2×C10912yescomplemented
183#1466C2×C10911yescharacteristic
184#1285C2×C10912yescomplemented
185C109#944911yescharacteristic, direct product factor, Sylow
186C2×#125C22×C10911yescharacteristic
187C2×C4×D4C22×C10911yescharacteristic
188#435—24no—
189#432C22×C10912yes—
190#432C22×C10912yes—
191#407—21no—
192C2×C22⋊C8—21no—
193#396—21no—
194#396—21no—
195#390C4×C10911yescharacteristic
196#390C4×C10911yescharacteristic
197#385—21no—
198#385—21no—
199#384C4×C10911yescharacteristic
200#382C4×C10911yescharacteristic
201C4×C4⋊C4C22×C10911yescharacteristic
202#330—24no—
203#323—21no—
204#323—21no—
205C22×D4C2×C4×C10911yescharacteristic
206C23×C4D4×C10911yescharacteristic
207C23×C4D4×C10911yescharacteristic
208C2×M16—22no—
209C22×C8—22no—
210#125—22no—
211#125—22no—
212C4×D4—22no—
213C4×D4—22no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×C4×C10911yescharacteristic
220C2×C4⋊C4C2×C4×C10911yescharacteristic
221C2×C4⋊C4C2×C4×C10911yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4D4×C10911yescharacteristic
227C2×C22⋊C4D4×C10911yescharacteristic
228C2×C42C2×C4×C10911yescharacteristic
229C2×C42C2×C4×C10911yescharacteristic
230C2×C42C23×C10911yescharacteristic
231C4⋊C8—22no—
232C4⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237#97—22no—
238#97D4×C10914yes—
239#95—21no—
240#95—21no—
241#95—21no—
242C24C22⋊C4×C10911yescharacteristic
243C24C22⋊C4×C10911yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4C22⋊C4×C10911yescharacteristic
258C22×C4C22⋊C4×C10911yescharacteristic
259C22×C4C22×C4×C10911yescharacteristic
260C22×C4C2×D4×C10911yescharacteristic
261C22×C4C2×D4×C10911yescharacteristic
262M16—82no—
263C2×C8—24no—
264C2×C8—42no—
265C2×C8—82no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—42no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—81no—
274C4⋊C4—81no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—81no—
280C22⋊C4—81no—
281C42—41no—
282C42—41no—
283C42C2×D4×C10912yes—
284C42#41×C10912yes—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#101×C10912yes—
295C23C2×C22⋊C4×C10911yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4C4×D4×C10912yes—
322C2×C4#120×C10911yescharacteristic
323C2×C4#121×C10912yes—
324C2×C4#123×C10911yescharacteristic
325C8—44no—
326C8—82no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#386×C10911yescharacteristic
340C22C2×#101×C10911yescharacteristic
341C22#413×C10911yescharacteristic
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2C109×#188411yescharacteristic
357C2C109×#190111yescharacteristic
358C2C109×#191111yescharacteristic
subgroupG/H
center, socleC22×C109#386
commutatorC22×C4C22×C4×C109
Frattini, cosocleC2×C42C23×C109
prime radicalC22×D4×C109C2×C4
LCSG ▷ C22×C4 ▷ 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×#1534C2semidirect
5. C109×#1285C2semidirect
172. #9449C109direct (N × H)
182. #1534C2×C109semidirect
184. #1285C2×C109semidirect
185. C109#9449direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#29732
C109×#25662
C109×#15342
C109×#14662
C109×#12852
#9449109