Finite Group Databasebeta

← C109×#19360 #42137354

Subgroups — C109×#19360 #42137354

Order 27904.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3252C212yesmaximal
2C109×#3160C211yesmaximal, characteristic, complemented
3C109×#2966C211yesmaximal, characteristic
4C109×#1696C211yesmaximal, characteristic, complemented
5C109×#1695C211yesmaximal, characteristic, complemented
6C109×#1694C211yesmaximal, characteristic, complemented
7C109×#1693C211yesmaximal, characteristic, complemented
8C109×#1672C212yesmaximal, complemented
9C109×#1671C212yesmaximal, complemented
10C109×#1566C211yesmaximal, characteristic, complemented
11C109×#1559C212yesmaximal, complemented
12#533×C109C2212yes—
13#529×C109C2211yescharacteristic
14#500×C109C2211yescharacteristic
15#500×C109C2211yescharacteristic
16#499×C109—21no—
17#499×C109—21no—
18#498×C109C2212yes—
19#479×C109—22no—
20#477×C109C2212yes—
21#476×C109C2212yes—
22#470×C109—22no—
23#468×C109—22no—
24#464×C109—22no—
25#462×C109C2212yes—
26#461×C109C2212yes—
27#446×C109C2211yescharacteristic
28C8×Q8×C109C2211yescharacteristic
29#436×C109C2211yescharacteristic
30#435×C109—21no—
31C8×D4×C109—21no—
32C8×D4×C109C2211yescharacteristic
33#433×C109—21no—
34#432×C109C2211yescharacteristic
35#427×C109—21no—
36#427×C109—21no—
37#423×C109C2212yes—
38#405×C109—21no—
39C2×C4×C8×C109C2211yescharacteristic
40#334×C109C2212yes—
41#334×C109C2211yescharacteristic
42#334×C109C2211yescharacteristic
43#333×C109C2212yes—
44#333×C109C2212yes—
45#332×C109C2212yes—
46#332×C109C2212yes—
47C2×Q16×C109—22no—
48C2×SD16×C109—22no—
49C2×M16×C109—22no—
50C2×M16×C109—21no—
51C22×C8×C109—21no—
52C22×C8×C109D411yescharacteristic
53C22×C8×C109D411yescharacteristic
54C4⋊Q8×C109C2312yes—
55C4⋊Q8×C109C2312yes—
56#126×C109—21no—
57#125×C109—22no—
58#125×C109D411yescharacteristic
59#124×C109D411yescharacteristic
60#123×C109—21no—
61C22⋊Q8×C109—22no—
62C22⋊Q8×C109—22no—
63C22⋊Q8×C109D411yescharacteristic
64#121×C109D411yescharacteristic
65C4×Q8×C109—22no—
66C4×Q8×C109—22no—
67C4×Q8×C109C2311yescharacteristic
68C4×D4×C109—21no—
69C4×D4×C109C2311yescharacteristic
70#117×C109—21no—
71#117×C109—22no—
72C2×C42×C109C2311yescharacteristic
73#107×C109—21no—
74#107×C109—21no—
75#107×C109—21no—
76#107×C109—21no—
77#107×C109—22no—
78#106×C109—22no—
79#106×C109—22no—
80#106×C109—22no—
81C4⋊C8×C109—21no—
82C4⋊C8×C109—21no—
83C4⋊C8×C109—22no—
84C4⋊C8×C109C2311yescharacteristic
85C4⋊C8×C109C2311yescharacteristic
86C4⋊C8×C109C2312yes—
87C4⋊C8×C109C2312yes—
88#103×C109—22no—
89#103×C109—22no—
90#103×C109—22no—
91#102×C109—22no—
92C22⋊C8×C109—21no—
93C22⋊C8×C109—21no—
94C22⋊C8×C109—21no—
95#97×C109—21no—
96#97×C109—21no—
97C4×C8×C109—21no—
98C4×C8×C109D411yescharacteristic
99C4×C8×C109D411yescharacteristic
100C4×C8×C109C2311yescharacteristic
101C4×C8×C109C2311yescharacteristic
102C2×Q8×C109—22no—
103C2×Q8×C109—22no—
104C2×Q8×C109C2×D411yescharacteristic
105C2×D4×C109—21no—
106C2×D4×C109C2×D411yescharacteristic
107C22×C4×C109—21no—
108C22×C4×C109C2×D411yescharacteristic
109C22×C4×C109C2×D411yescharacteristic
110C22×C4×C109#4111yescharacteristic
111Q16×C109—82no—
112SD16×C109—82no—
113M16×C109—42no—
114M16×C109—82no—
115C2×C8×C109—22no—
116C2×C8×C109—22no—
117C2×C8×C109—21no—
118C2×C8×C109—21no—
119C2×C8×C109—22no—
120C2×C8×C109—22no—
121C2×C8×C109—42no—
122C2×C8×C109C2×D411yescharacteristic
123C2×C8×C109C2×D411yescharacteristic
124C2×C8×C109C2×D411yescharacteristic
125C2×C8×C109C2×D411yescharacteristic
126C4⋊C4×C109—21no—
127C4⋊C4×C109—21no—
128C4⋊C4×C109—21no—
129C4⋊C4×C109—21no—
130C4⋊C4×C109—22no—
131C4⋊C4×C109—22no—
132C4⋊C4×C109—22no—
133C4⋊C4×C109—22no—
134C4⋊C4×C109—42no—
135C4⋊C4×C109—42no—
136C4⋊C4×C109C2×D411yescharacteristic
137C4⋊C4×C109C2×D411yescharacteristic
138C22⋊C4×C109—21no—
139C22⋊C4×C109—21no—
140C22⋊C4×C109—21no—
141C22⋊C4×C109—21no—
142C22⋊C4×C109—21no—
143C22⋊C4×C109—42no—
144C42×C109—21no—
145C42×C109—42no—
146C42×C109C2×D411yescharacteristic
147C42×C109C2×D411yescharacteristic
148C42×C109#4111yescharacteristic
149C42×C109C2411yescharacteristic
150C23×C109—21no—
151C23×C109#12111yescharacteristic
152Q8×C109—22no—
153Q8×C109—42no—
154Q8×C109—42no—
155Q8×C109—82no—
156D4×C109—22no—
157D4×C109—42no—
158C2×C4×C109—21no—
159C2×C4×C109—21no—
160C2×C4×C109—22no—
161C2×C4×C109—21no—
162C2×C4×C109—21no—
163C2×C4×C109—21no—
164C2×C4×C109—41no—
165C2×C4×C109—41no—
166C2×C4×C109—41no—
167C2×C4×C109—42no—
168C2×C4×C109—42no—
169C2×C4×C109#12111yescharacteristic
170C2×C4×C109#12111yescharacteristic
171C2×C4×C109#12111yescharacteristic
172C2×C4×C109C22×D411yescharacteristic
173C2×C4×C109C22×D411yescharacteristic
174C2×C4×C109C2×#4111yescharacteristic
175C8×C109—21no—
176C8×C109—21no—
177C8×C109—41no—
178C8×C109—41no—
179C8×C109—42no—
180C8×C109—42no—
181C8×C109#13712yes—
182C8×C109#13712yes—
183C22×C109—21no—
184C22×C109—21no—
185C22×C109—21no—
186C22×C109—41no—
187C22×C109—41no—
188C22×C109—41no—
189C22×C109C2×#12111yescharacteristic
190C4×C109—21no—
191C4×C109—21no—
192C4×C109—21no—
193C4×C109—21no—
194C4×C109—41no—
195C4×C109—41no—
196C4×C109—41no—
197C4×C109—82no—
198C4×C109—82no—
199C4×C109C2×#13711yescharacteristic
200C4×C109C2×#13711yescharacteristic
201C4×C109#57712yes—
202#19360C10911yesmaximal, characteristic, direct product factor, Sylow
203C2×C109—41no—
204C2×C109—81no—
205C2×C109#303911yescharacteristic
206C2×C109#306011yescharacteristic
207C2×C109#306711yescharacteristic
208#3252C2×C10912yes—
209#3160C2×C10911yescharacteristic, complemented
210#2966C2×C10911yescharacteristic
211#1696C2×C10911yescharacteristic, complemented
212#1695C2×C10911yescharacteristic, complemented
213#1694C2×C10911yescharacteristic, complemented
214#1693C2×C10911yescharacteristic, complemented
215#1672C2×C10912yescomplemented
216#1671C2×C10912yescomplemented
217#1566C2×C10911yescharacteristic, complemented
218#1559C2×C10912yescomplemented
219C109#1936011yescharacteristic, direct product factor, Sylow
220#533C22×C10912yes—
221#529C22×C10911yescharacteristic
222#500C22×C10911yescharacteristic
223#500C22×C10911yescharacteristic
224#499—21no—
225#499—21no—
226#498C22×C10912yes—
227#479—22no—
228#477C22×C10912yes—
229#476C22×C10912yes—
230#470—22no—
231#468—22no—
232#464—22no—
233#462C22×C10912yes—
234#461C22×C10912yes—
235#446C22×C10911yescharacteristic
236C8×Q8C22×C10911yescharacteristic
237#436C22×C10911yescharacteristic
238#435—21no—
239C8×D4—21no—
240C8×D4C22×C10911yescharacteristic
241#433—21no—
242#432C22×C10911yescharacteristic
243#427—21no—
244#427—21no—
245#423C22×C10912yes—
246#405—21no—
247C2×C4×C8C22×C10911yescharacteristic
248#334C22×C10912yes—
249#334C22×C10911yescharacteristic
250#334C22×C10911yescharacteristic
251#333C22×C10912yes—
252#333C22×C10912yes—
253#332C22×C10912yes—
254#332C22×C10912yes—
255C2×Q16—22no—
256C2×SD16—22no—
257C2×M16—22no—
258C2×M16—21no—
259C22×C8—21no—
260C22×C8D4×C10911yescharacteristic
261C22×C8D4×C10911yescharacteristic
262C4⋊Q8C23×C10912yes—
263C4⋊Q8C23×C10912yes—
264#126—21no—
265#125—22no—
266#125D4×C10911yescharacteristic
267#124D4×C10911yescharacteristic
268#123—21no—
269C22⋊Q8—22no—
270C22⋊Q8—22no—
271C22⋊Q8D4×C10911yescharacteristic
272#121D4×C10911yescharacteristic
273C4×Q8—22no—
274C4×Q8—22no—
275C4×Q8C23×C10911yescharacteristic
276C4×D4—21no—
277C4×D4C23×C10911yescharacteristic
278#117—21no—
279#117—22no—
280C2×C42C23×C10911yescharacteristic
281#107—21no—
282#107—21no—
283#107—21no—
284#107—21no—
285#107—22no—
286#106—22no—
287#106—22no—
288#106—22no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—22no—
292C4⋊C8C23×C10911yescharacteristic
293C4⋊C8C23×C10911yescharacteristic
294C4⋊C8C23×C10912yes—
295C4⋊C8C23×C10912yes—
296#103—22no—
297#103—22no—
298#103—22no—
299#102—22no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303#97—21no—
304#97—21no—
305C4×C8—21no—
306C4×C8D4×C10911yescharacteristic
307C4×C8D4×C10911yescharacteristic
308C4×C8C23×C10911yescharacteristic
309C4×C8C23×C10911yescharacteristic
310C2×Q8—22no—
311C2×Q8—22no—
312C2×Q8C2×D4×C10911yescharacteristic
313C2×D4—21no—
314C2×D4C2×D4×C10911yescharacteristic
315C22×C4—21no—
316C22×C4C2×D4×C10911yescharacteristic
317C22×C4C2×D4×C10911yescharacteristic
318C22×C4#41×C10911yescharacteristic
319Q16—82no—
320SD16—82no—
321M16—42no—
322M16—82no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—42no—
330C2×C8C2×D4×C10911yescharacteristic
331C2×C8C2×D4×C10911yescharacteristic
332C2×C8C2×D4×C10911yescharacteristic
333C2×C8C2×D4×C10911yescharacteristic
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4C2×D4×C10911yescharacteristic
345C4⋊C4C2×D4×C10911yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—42no—
352C42—21no—
353C42—42no—
354C42C2×D4×C10911yescharacteristic
355C42C2×D4×C10911yescharacteristic
356C42#41×C10911yescharacteristic
357C42C24×C10911yescharacteristic
358C23—21no—
359C23#121×C10911yescharacteristic
360Q8—22no—
361Q8—42no—
362Q8—42no—
363Q8—82no—
364D4—22no—
365D4—42no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4#121×C10911yescharacteristic
378C2×C4#121×C10911yescharacteristic
379C2×C4#121×C10911yescharacteristic
380C2×C4C22×D4×C10911yescharacteristic
381C2×C4C22×D4×C10911yescharacteristic
382C2×C4C2×#41×C10911yescharacteristic
383C8—21no—
384C8—21no—
385C8—41no—
386C8—41no—
387C8—42no—
388C8—42no—
389C8#137×C10912yes—
390C8#137×C10912yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22C2×#121×C10911yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—82no—
406C4—82no—
407C4C2×#137×C10911yescharacteristic
408C4C2×#137×C10911yescharacteristic
409C4#577×C10912yes—
410C2—41no—
411C2—81no—
412C2C109×#303911yescharacteristic
413C2C109×#306011yescharacteristic
414C2C109×#306711yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radical#121×C109D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#3160C2semidirect
4. C109×#1696C2semidirect
5. C109×#1695C2semidirect
6. C109×#1694C2semidirect
7. C109×#1693C2semidirect
8. C109×#1672C2semidirect
9. C109×#1671C2semidirect
10. C109×#1566C2semidirect
11. C109×#1559C2semidirect
202. #19360C109direct (N × H)
209. #3160C2×C109semidirect
211. #1696C2×C109semidirect
212. #1695C2×C109semidirect
213. #1694C2×C109semidirect
214. #1693C2×C109semidirect
215. #1672C2×C109semidirect
216. #1671C2×C109semidirect
217. #1566C2×C109semidirect
218. #1559C2×C109semidirect
219. C109#19360direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#32522
C109×#31602
C109×#29662
C109×#16962
C109×#16952
C109×#16942
C109×#16932
C109×#16722
C109×#16712
C109×#15662
C109×#15592
#19360109