Finite Group Databasebeta

← C109×#8847 #42126841

Subgroups — C109×#8847 #42126841

Order 27904.

516 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#436×C109C211yesmaximal, characteristic
2C109×#1939C211yesmaximal, characteristic, complemented
3C4×#102×C109C211yesmaximal, characteristic
4C2×#335×C109C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C109C211yesmaximal, characteristic
6C109×#1279C211yesmaximal, characteristic, complemented
7C109×#1273C211yesmaximal, characteristic, complemented
8C22×M16×C109—21no—
9C2×C4×D4×C109C2211yescharacteristic
10#436×C109—22no—
11#436×C109—22no—
12C2×C4⋊C8×C109—21no—
13C2×C4⋊C8×C109C2211yescharacteristic
14C2×C4⋊C8×C109C2211yescharacteristic
15C2×#102×C109C411yescharacteristic
16C2×#102×C109C411yescharacteristic
17C2×C22⋊C8×C109—21no—
18C2×C4×C8×C109C2211yescharacteristic
19C2×C4×C8×C109C2211yescharacteristic
20C2×C4×C8×C109C2211yescharacteristic
21C4×C4⋊C4×C109C2211yescharacteristic
22#340×C109C411yescharacteristic
23#340×C109C411yescharacteristic
24#336×C109—21no—
25#335×C109—22no—
26D4⋊C8×C109—22no—
27C22×D4×C109C2×C411yescharacteristic
28C23×C4×C109—21no—
29C2×M16×C109—24no—
30C2×M16×C109—42no—
31C2×M16×C109—42no—
32C22×C8×C109—21no—
33C22×C8×C109—21no—
34C22×C8×C109—21no—
35C22×C8×C109C2×C411yescharacteristic
36C22×C8×C109C2×C411yescharacteristic
37C22×C8×C109D411yescharacteristic
38C22×C8×C109D411yescharacteristic
39C4×D4×C109—21no—
40C4×D4×C109—21no—
41C4×D4×C109D412yes—
42C4×D4×C109Q812yes—
43C2×C4⋊C4×C109C2×C411yescharacteristic
44C2×C4⋊C4×C109C2×C411yescharacteristic
45C2×C4⋊C4×C109C2×C411yescharacteristic
46C2×C22⋊C4×C109—21no—
47C2×C42×C109—21no—
48C2×C42×C109C2311yescharacteristic
49C4⋊C8×C109—21no—
50C4⋊C8×C109—21no—
51C4⋊C8×C109—21no—
52C4⋊C8×C109—42no—
53C4⋊C8×C109D412yes—
54#102×C109—22no—
55#102×C109—22no—
56C22⋊C8×C109—24no—
57C4×C8×C109—21no—
58C4×C8×C109—21no—
59C4×C8×C109—21no—
60C4×C8×C109—21no—
61C4×C8×C109—21no—
62C4×C8×C109—21no—
63#95×C109—21no—
64C24×C109—21no—
65C2×D4×C109—21no—
66C2×D4×C109—21no—
67C2×D4×C109—21no—
68C2×D4×C109—21no—
69C2×D4×C109—21no—
70C2×D4×C109C4⋊C412yes—
71C22×C4×C109—21no—
72C22×C4×C109—21no—
73C22×C4×C109—22no—
74C22×C4×C109—22no—
75C22×C4×C109—21no—
76C22×C4×C109—41no—
77C22×C4×C109—41no—
78C22×C4×C109—41no—
79C22×C4×C109—41no—
80C22×C4×C109C22×C411yescharacteristic
81C22×C4×C109C2×D411yescharacteristic
82C22×C4×C109#4111yescharacteristic
83M16×C109—48no—
84C2×C8×C109—21no—
85C2×C8×C109—21no—
86C2×C8×C109—21no—
87C2×C8×C109—21no—
88C2×C8×C109—22no—
89C2×C8×C109—21no—
90C2×C8×C109—21no—
91C2×C8×C109—22no—
92C2×C8×C109—21no—
93C2×C8×C109—21no—
94C2×C8×C109—21no—
95C2×C8×C109—21no—
96C2×C8×C109—41no—
97C2×C8×C109—41no—
98C2×C8×C109—41no—
99C2×C8×C109—41no—
100C2×C8×C109—41no—
101C2×C8×C109—41no—
102C2×C8×C109—41no—
103C2×C8×C109M1612yescomplemented
104C2×C8×C109D812yes—
105C4⋊C4×C109—21no—
106C4⋊C4×C109—21no—
107C4⋊C4×C109—21no—
108C4⋊C4×C109—21no—
109C4⋊C4×C109C4⋊C412yes—
110C4⋊C4×C109M1612yescomplemented
111C22⋊C4×C109—22no—
112C22⋊C4×C109—22no—
113C42×C109—41no—
114C42×C109—41no—
115C42×C109C2×D411yescharacteristic
116C42×C109C2×D411yescharacteristic
117C42×C109C2×Q811yescharacteristic
118C42×C109#4111yescharacteristic
119C23×C109—22no—
120C23×C109—41no—
121C23×C109—41no—
122C23×C109—41no—
123C23×C109—41no—
124C23×C109—41no—
125C23×C109—41no—
126C23×C109C4×D411yescharacteristic
127D4×C109—22no—
128D4×C109—22no—
129D4×C109—41no—
130D4×C109—41no—
131C2×C4×C109—21no—
132C2×C4×C109—21no—
133C2×C4×C109—22no—
134C2×C4×C109—22no—
135C2×C4×C109—41no—
136C2×C4×C109—41no—
137C2×C4×C109—41no—
138C2×C4×C109—41no—
139C2×C4×C109—42no—
140C2×C4×C109—42no—
141C2×C4×C109—42no—
142C2×C4×C109—42no—
143C2×C4×C109—41no—
144C2×C4×C109—41no—
145C2×C4×C109—41no—
146C2×C4×C109C2×C4⋊C411yescharacteristic
147C2×C4×C109C4×D411yescharacteristic
148C2×C4×C109#12011yescharacteristic
149C2×C4×C109C22⋊Q811yescharacteristic
150C2×C4×C109C22⋊Q811yescharacteristic
151C2×C4×C109#12311yescharacteristic
152C2×C4×C109C2×M1611yescharacteristic
153C2×C4×C109C2×M1611yescharacteristic
154C2×C4×C109#13111yescharacteristic
155C2×C4×C109#13111yescharacteristic
156C2×C4×C109C2×D811yescharacteristic
157C2×C4×C109#13511yescharacteristic
158C2×C4×C109AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C109#13711yescharacteristic
160C8×C109—22no—
161C8×C109—22no—
162C8×C109—42no—
163C8×C109—41no—
164C8×C109—42no—
165C8×C109—41no—
166C8×C109—81no—
167C22×C109—42no—
168C22×C109—42no—
169C22×C109—42no—
170C22×C109—81no—
171C22×C109—81no—
172C22×C109—81no—
173C22×C109—81no—
174C22×C109#38511yescharacteristic
175C22×C109#43511yescharacteristic
176C22×C109#43611yescharacteristic
177C22×C109C4×D811yescharacteristic
178C22×C109#44011yescharacteristic
179C22×C109#44311yescharacteristic
180C22×C109#44411yescharacteristic
181C4×C109—21no—
182C4×C109—21no—
183C4×C109—42no—
184C4×C109—42no—
185C4×C109—81no—
186C4×C109#42311yescharacteristic
187C4×C109#42411yescharacteristic
188C4×C109#43511yescharacteristic
189C4×C109#43611yescharacteristic
190C4×C109#44711yescharacteristic
191C4×C109#45211yescharacteristic
192C4×C109#47411yescharacteristic
193C4×C109#47811yescharacteristic
194#8847C10911yesmaximal, characteristic, direct product factor, Sylow
195C2×C109—82no—
196C2×C109#158111yescharacteristic
197C2×C109#158811yescharacteristic
198C2×C109#158911yescharacteristic
199C2×C109#159211yescharacteristic
200C2×C109#185111yescharacteristic
201C2×C109#186211yescharacteristic
202C2×C109#186611yescharacteristic
203C2×#436C2×C10911yescharacteristic
204#1939C2×C10911yescharacteristic, complemented
205C4×#102C2×C10911yescharacteristic
206C2×#335C2×C10911yescharacteristic, complemented
207C2×D4⋊C8C2×C10911yescharacteristic
208#1279C2×C10911yescharacteristic, complemented
209#1273C2×C10911yescharacteristic, complemented
210C109#884711yescharacteristic, direct product factor, Sylow
211C22×M16—21no—
212C2×C4×D4C22×C10911yescharacteristic
213#436—22no—
214#436—22no—
215C2×C4⋊C8—21no—
216C2×C4⋊C8C22×C10911yescharacteristic
217C2×C4⋊C8C22×C10911yescharacteristic
218C2×#102C4×C10911yescharacteristic
219C2×#102C4×C10911yescharacteristic
220C2×C22⋊C8—21no—
221C2×C4×C8C22×C10911yescharacteristic
222C2×C4×C8C22×C10911yescharacteristic
223C2×C4×C8C22×C10911yescharacteristic
224C4×C4⋊C4C22×C10911yescharacteristic
225#340C4×C10911yescharacteristic
226#340C4×C10911yescharacteristic
227#336—21no—
228#335—22no—
229D4⋊C8—22no—
230C22×D4C2×C4×C10911yescharacteristic
231C23×C4—21no—
232C2×M16—24no—
233C2×M16—42no—
234C2×M16—42no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8C2×C4×C10911yescharacteristic
239C22×C8C2×C4×C10911yescharacteristic
240C22×C8D4×C10911yescharacteristic
241C22×C8D4×C10911yescharacteristic
242C4×D4—21no—
243C4×D4—21no—
244C4×D4D4×C10912yes—
245C4×D4Q8×C10912yes—
246C2×C4⋊C4C2×C4×C10911yescharacteristic
247C2×C4⋊C4C2×C4×C10911yescharacteristic
248C2×C4⋊C4C2×C4×C10911yescharacteristic
249C2×C22⋊C4—21no—
250C2×C42—21no—
251C2×C42C23×C10911yescharacteristic
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—42no—
256C4⋊C8D4×C10912yes—
257#102—22no—
258#102—22no—
259C22⋊C8—24no—
260C4×C8—21no—
261C4×C8—21no—
262C4×C8—21no—
263C4×C8—21no—
264C4×C8—21no—
265C4×C8—21no—
266#95—21no—
267C24—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4C4⋊C4×C10912yes—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4C22×C4×C10911yescharacteristic
284C22×C4C2×D4×C10911yescharacteristic
285C22×C4#41×C10911yescharacteristic
286M16—48no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—22no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8M16×C10912yescomplemented
307C2×C8D8×C10912yes—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4C4⋊C4×C10912yes—
313C4⋊C4M16×C10912yescomplemented
314C22⋊C4—22no—
315C22⋊C4—22no—
316C42—41no—
317C42—41no—
318C42C2×D4×C10911yescharacteristic
319C42C2×D4×C10911yescharacteristic
320C42C2×Q8×C10911yescharacteristic
321C42#41×C10911yescharacteristic
322C23—22no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23C4×D4×C10911yescharacteristic
330D4—22no—
331D4—22no—
332D4—41no—
333D4—41no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4C2×C4⋊C4×C10911yescharacteristic
350C2×C4C4×D4×C10911yescharacteristic
351C2×C4#120×C10911yescharacteristic
352C2×C4C22⋊Q8×C10911yescharacteristic
353C2×C4C22⋊Q8×C10911yescharacteristic
354C2×C4#123×C10911yescharacteristic
355C2×C4C2×M16×C10911yescharacteristic
356C2×C4C2×M16×C10911yescharacteristic
357C2×C4#131×C10911yescharacteristic
358C2×C4#131×C10911yescharacteristic
359C2×C4C2×D8×C10911yescharacteristic
360C2×C4#135×C10911yescharacteristic
361C2×C4AGL(1,ℤ/8)×C10911yescharacteristic
362C2×C4#137×C10911yescharacteristic
363C8—22no—
364C8—22no—
365C8—42no—
366C8—41no—
367C8—42no—
368C8—41no—
369C8—81no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22#385×C10911yescharacteristic
378C22#435×C10911yescharacteristic
379C22#436×C10911yescharacteristic
380C22C4×D8×C10911yescharacteristic
381C22#440×C10911yescharacteristic
382C22#443×C10911yescharacteristic
383C22#444×C10911yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—42no—
388C4—81no—
389C4#423×C10911yescharacteristic
390C4#424×C10911yescharacteristic
391C4#435×C10911yescharacteristic
392C4#436×C10911yescharacteristic
393C4#447×C10911yescharacteristic
394C4#452×C10911yescharacteristic
395C4#474×C10911yescharacteristic
396C4#478×C10911yescharacteristic
397C2—82no—
398C2C109×#158111yescharacteristic
399C2C109×#158811yescharacteristic
400C2C109×#158911yescharacteristic
401C2C109×#159211yescharacteristic
402C2C109×#185111yescharacteristic
403C2C109×#186211yescharacteristic
404C2C109×#186611yescharacteristic
subgroupG/H
centerC22×C4×C109C2×D4
commutatorC22×C4C22×C4×C109
Frattini, cosocleC2×C42C23×C109
socleC23×C109C4×D4
prime radicalC22×D4×C109C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C109 ◁ C2×C4×C8×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#1939C2semidirect
4. C2×#335×C109C2semidirect
6. C109×#1279C2semidirect
7. C109×#1273C2semidirect
103. C2×C8×C109M16semidirect
110. C4⋊C4×C109M16semidirect
194. #8847C109direct (N × H)
204. #1939C2×C109semidirect
206. C2×#335C2×C109semidirect
208. #1279C2×C109semidirect
209. #1273C2×C109semidirect
210. C109#8847direct (N × H)
306. C2×C8M16×C109semidirect
313. C4⋊C4M16×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#436×C1092
C109×#19392
C4×#102×C1092
C2×#335×C1092
C2×D4⋊C8×C1092
C109×#12792
C109×#12732
#8847109