Finite Group Databasebeta

← C109×#19155 #42137149

Subgroups — C109×#19155 #42137149

Order 27904.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3131C211yesmaximal, characteristic
2C109×#3104C211yesmaximal, characteristic, complemented
3C109×#3103C211yesmaximal, characteristic
4C2×#446×C109C211yesmaximal, characteristic, complemented
5C109×#1704C212yesmaximal, complemented
6C109×#1702C212yesmaximal, complemented
7C109×#1700C212yesmaximal, complemented
8C109×#1698C212yesmaximal, complemented
9C109×#1564C211yesmaximal, characteristic, complemented
10C109×#1542C211yesmaximal, characteristic, complemented
11C109×#1540C211yesmaximal, characteristic
12#533×C109C2211yescharacteristic
13#532×C109C2211yescharacteristic
14C2×C4×Q8×C109C2211yescharacteristic
15#488×C109—21no—
16#488×C109—21no—
17#487×C109C2211yescharacteristic
18#487×C109C2211yescharacteristic
19#486×C109C2211yescharacteristic
20#486×C109C2211yescharacteristic
21#484×C109—21no—
22#481×C109—21no—
23#477×C109C2212yes—
24#475×C109C2212yes—
25#462×C109C2212yes—
26#460×C109C2212yes—
27#451×C109—21no—
28#448×C109—21no—
29#446×C109—21no—
30#446×C109—21no—
31#446×C109C2212yes—
32#446×C109C2212yes—
33C4×Q16×C109—22no—
34C4×SD16×C109—22no—
35#431×C109C2211yescharacteristic
36#431×C109C2211yescharacteristic
37C2×C4⋊C8×C109—21no—
38C2×C4⋊C8×C109C2211yescharacteristic
39#416×C109—21no—
40#416×C109—21no—
41C2×#97×C109—21no—
42C2×C4×C8×C109C2211yescharacteristic
43#335×C109C2212yes—
44#334×C109C2212yes—
45#333×C109C2212yes—
46#332×C109C2212yes—
47#332×C109C2212yes—
48#331×C109C2212yes—
49C2×#41×C109—21no—
50C22×Q8×C109D411yescharacteristic
51C2×Q16×C109—22no—
52C2×SD16×C109—22no—
53C22×C8×C109—21no—
54C22×C8×C109D411yescharacteristic
55C22×C8×C109D411yescharacteristic
56C4⋊Q8×C109C2311yescharacteristic
57C4⋊Q8×C109C2311yescharacteristic
58C4⋊Q8×C109C2311yescharacteristic
59#127×C109C2311yescharacteristic
60#125×C109—21no—
61#124×C109—21no—
62C22⋊Q8×C109—21no—
63C22⋊Q8×C109—21no—
64#121×C109—21no—
65#121×C109—21no—
66C4×Q8×C109—21no—
67C4×Q8×C109—21no—
68C4×Q8×C109—21no—
69C4×Q8×C109—21no—
70C4×Q8×C109D412yes—
71C4×Q8×C109C2312yes—
72C4×D4×C109—21no—
73C4×D4×C109—21no—
74#117×C109—21no—
75C2×C4⋊C4×C109—21no—
76C2×C4⋊C4×C109D411yescharacteristic
77C2×C42×C109—21no—
78C2×C42×C109C2311yescharacteristic
79#107×C109—22no—
80#106×C109—22no—
81C4⋊C8×C109—22no—
82C4⋊C8×C109—22no—
83C4⋊C8×C109—21no—
84C4⋊C8×C109C2312yes—
85C4⋊C8×C109C2312yes—
86C4⋊C8×C109C2312yes—
87#103×C109—22no—
88#103×C109—22no—
89#103×C109—21no—
90#103×C109—21no—
91#103×C109—21no—
92#103×C109—21no—
93#103×C109—22no—
94#102×C109—21no—
95#102×C109—21no—
96#102×C109—21no—
97#102×C109—21no—
98#102×C109—22no—
99C22⋊C8×C109—21no—
100C22⋊C8×C109—21no—
101#97×C109—22no—
102#97×C109—22no—
103C4×C8×C109—21no—
104C4×C8×C109—21no—
105C4×C8×C109D411yescharacteristic
106C4×C8×C109D411yescharacteristic
107C4×C8×C109C2311yescharacteristic
108C4×C8×C109C2311yescharacteristic
109#41×C109—42no—
110#41×C109—42no—
111C2×Q8×C109—21no—
112C2×Q8×C109—21no—
113C2×Q8×C109—21no—
114C2×Q8×C109—21no—
115C2×Q8×C109—42no—
116C2×Q8×C109C2×D412yes—
117C2×D4×C109—21no—
118C2×D4×C109—21no—
119C2×D4×C109—21no—
120C2×D4×C109—41no—
121C22×C4×C109—21no—
122C22×C4×C109—21no—
123C22×C4×C109—41no—
124C22×C4×C109C2×D411yescharacteristic
125C22×C4×C109C2×D411yescharacteristic
126C22×C4×C109#4111yescharacteristic
127Q16×C109—44no—
128SD16×C109—44no—
129C2×C8×C109—22no—
130C2×C8×C109—22no—
131C2×C8×C109—22no—
132C2×C8×C109—22no—
133C2×C8×C109—22no—
134C2×C8×C109—42no—
135C2×C8×C109C2×D411yescharacteristic
136C2×C8×C109C2×D411yescharacteristic
137C2×C8×C109C2×D411yescharacteristic
138C2×C8×C109C2×D411yescharacteristic
139C4⋊C4×C109—22no—
140C4⋊C4×C109—21no—
141C4⋊C4×C109—22no—
142C4⋊C4×C109—21no—
143C4⋊C4×C109—21no—
144C4⋊C4×C109—21no—
145C4⋊C4×C109—21no—
146C4⋊C4×C109—21no—
147C4⋊C4×C109—21no—
148C4⋊C4×C109—41no—
149C4⋊C4×C109—41no—
150C4⋊C4×C109C2×D412yes—
151C22⋊C4×C109—41no—
152C22⋊C4×C109—41no—
153C22⋊C4×C109—41no—
154C42×C109—22no—
155C42×C109—22no—
156C42×C109—41no—
157C42×C109C2×D411yescharacteristic
158C42×C109C2×D411yescharacteristic
159C42×C109#4111yescharacteristic
160C42×C109C2411yescharacteristic
161C23×C109—41no—
162C23×C109#12111yescharacteristic
163Q8×C109—22no—
164Q8×C109—22no—
165Q8×C109—42no—
166Q8×C109—41no—
167Q8×C109—41no—
168Q8×C109—42no—
169Q8×C109—81no—
170D4×C109—41no—
171D4×C109—41no—
172D4×C109—42no—
173D4×C109—81no—
174D4×C109—82no—
175C2×C4×C109—22no—
176C2×C4×C109—22no—
177C2×C4×C109—22no—
178C2×C4×C109—41no—
179C2×C4×C109—42no—
180C2×C4×C109—42no—
181C2×C4×C109—41no—
182C2×C4×C109—41no—
183C2×C4×C109—41no—
184C2×C4×C109—82no—
185C2×C4×C109#12111yescharacteristic
186C2×C4×C109#12111yescharacteristic
187C2×C4×C109#12111yescharacteristic
188C2×C4×C109#13512yes—
189C2×C4×C109#13712yes—
190C2×C4×C109C22×D411yescharacteristic
191C2×C4×C109C22×D411yescharacteristic
192C2×C4×C109C2×#4111yescharacteristic
193C8×C109—21no—
194C8×C109—21no—
195C8×C109—21no—
196C8×C109—21no—
197C8×C109—42no—
198C8×C109—42no—
199C8×C109—42no—
200C22×C109—21no—
201C22×C109—21no—
202C22×C109—81no—
203C22×C109—81no—
204C22×C109—81no—
205C22×C109#46412yes—
206C22×C109C2×#12111yescharacteristic
207C4×C109—21no—
208C4×C109—21no—
209C4×C109—21no—
210C4×C109—42no—
211C4×C109—42no—
212C4×C109—81no—
213C4×C109—81no—
214C4×C109—81no—
215C4×C109#46412yes—
216C4×C109C2×#13511yescharacteristic
217C4×C109C2×#13711yescharacteristic
218C4×C109#57512yes—
219#19155C10911yesmaximal, characteristic, direct product factor, Sylow
220C2×C109—22no—
221C2×C109—161no—
222C2×C109C2×#46411yescharacteristic
223C2×C109#305411yescharacteristic
224C2×C109#306711yescharacteristic
225#3131C2×C10911yescharacteristic
226#3104C2×C10911yescharacteristic, complemented
227#3103C2×C10911yescharacteristic
228C2×#446C2×C10911yescharacteristic, complemented
229#1704C2×C10912yescomplemented
230#1702C2×C10912yescomplemented
231#1700C2×C10912yescomplemented
232#1698C2×C10912yescomplemented
233#1564C2×C10911yescharacteristic, complemented
234#1542C2×C10911yescharacteristic, complemented
235#1540C2×C10911yescharacteristic
236C109#1915511yescharacteristic, direct product factor, Sylow
237#533C22×C10911yescharacteristic
238#532C22×C10911yescharacteristic
239C2×C4×Q8C22×C10911yescharacteristic
240#488—21no—
241#488—21no—
242#487C22×C10911yescharacteristic
243#487C22×C10911yescharacteristic
244#486C22×C10911yescharacteristic
245#486C22×C10911yescharacteristic
246#484—21no—
247#481—21no—
248#477C22×C10912yes—
249#475C22×C10912yes—
250#462C22×C10912yes—
251#460C22×C10912yes—
252#451—21no—
253#448—21no—
254#446—21no—
255#446—21no—
256#446C22×C10912yes—
257#446C22×C10912yes—
258C4×Q16—22no—
259C4×SD16—22no—
260#431C22×C10911yescharacteristic
261#431C22×C10911yescharacteristic
262C2×C4⋊C8—21no—
263C2×C4⋊C8C22×C10911yescharacteristic
264#416—21no—
265#416—21no—
266C2×#97—21no—
267C2×C4×C8C22×C10911yescharacteristic
268#335C22×C10912yes—
269#334C22×C10912yes—
270#333C22×C10912yes—
271#332C22×C10912yes—
272#332C22×C10912yes—
273#331C22×C10912yes—
274C2×#41—21no—
275C22×Q8D4×C10911yescharacteristic
276C2×Q16—22no—
277C2×SD16—22no—
278C22×C8—21no—
279C22×C8D4×C10911yescharacteristic
280C22×C8D4×C10911yescharacteristic
281C4⋊Q8C23×C10911yescharacteristic
282C4⋊Q8C23×C10911yescharacteristic
283C4⋊Q8C23×C10911yescharacteristic
284#127C23×C10911yescharacteristic
285#125—21no—
286#124—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289#121—21no—
290#121—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8D4×C10912yes—
296C4×Q8C23×C10912yes—
297C4×D4—21no—
298C4×D4—21no—
299#117—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4D4×C10911yescharacteristic
302C2×C42—21no—
303C2×C42C23×C10911yescharacteristic
304#107—22no—
305#106—22no—
306C4⋊C8—22no—
307C4⋊C8—22no—
308C4⋊C8—21no—
309C4⋊C8C23×C10912yes—
310C4⋊C8C23×C10912yes—
311C4⋊C8C23×C10912yes—
312#103—22no—
313#103—22no—
314#103—21no—
315#103—21no—
316#103—21no—
317#103—21no—
318#103—22no—
319#102—21no—
320#102—21no—
321#102—21no—
322#102—21no—
323#102—22no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326#97—22no—
327#97—22no—
328C4×C8—21no—
329C4×C8—21no—
330C4×C8D4×C10911yescharacteristic
331C4×C8D4×C10911yescharacteristic
332C4×C8C23×C10911yescharacteristic
333C4×C8C23×C10911yescharacteristic
334#41—42no—
335#41—42no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C2×Q8C2×D4×C10912yes—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4C2×D4×C10911yescharacteristic
350C22×C4C2×D4×C10911yescharacteristic
351C22×C4#41×C10911yescharacteristic
352Q16—44no—
353SD16—44no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—42no—
360C2×C8C2×D4×C10911yescharacteristic
361C2×C8C2×D4×C10911yescharacteristic
362C2×C8C2×D4×C10911yescharacteristic
363C2×C8C2×D4×C10911yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4C2×D4×C10912yes—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C42—22no—
380C42—22no—
381C42—41no—
382C42C2×D4×C10911yescharacteristic
383C42C2×D4×C10911yescharacteristic
384C42#41×C10911yescharacteristic
385C42C24×C10911yescharacteristic
386C23—41no—
387C23#121×C10911yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—42no—
391Q8—41no—
392Q8—41no—
393Q8—42no—
394Q8—81no—
395D4—41no—
396D4—41no—
397D4—42no—
398D4—81no—
399D4—82no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—82no—
410C2×C4#121×C10911yescharacteristic
411C2×C4#121×C10911yescharacteristic
412C2×C4#121×C10911yescharacteristic
413C2×C4#135×C10912yes—
414C2×C4#137×C10912yes—
415C2×C4C22×D4×C10911yescharacteristic
416C2×C4C22×D4×C10911yescharacteristic
417C2×C4C2×#41×C10911yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—21no—
422C8—42no—
423C8—42no—
424C8—42no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22#464×C10912yes—
431C22C2×#121×C10911yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4#464×C10912yes—
441C4C2×#135×C10911yescharacteristic
442C4C2×#137×C10911yescharacteristic
443C4#575×C10912yes—
444C2—22no—
445C2—161no—
446C2C2×#464×C10911yescharacteristic
447C2C109×#305411yescharacteristic
448C2C109×#306711yescharacteristic
subgroupG/H
centerC2×C4×C109#121
commutator, Frattini, cosocleC42C24×C109
socleC22×C109C2×#121
prime radical#532×C109C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#3104C2semidirect
4. C2×#446×C109C2semidirect
5. C109×#1704C2semidirect
6. C109×#1702C2semidirect
7. C109×#1700C2semidirect
8. C109×#1698C2semidirect
9. C109×#1564C2semidirect
10. C109×#1542C2semidirect
219. #19155C109direct (N × H)
226. #3104C2×C109semidirect
228. C2×#446C2×C109semidirect
229. #1704C2×C109semidirect
230. #1702C2×C109semidirect
231. #1700C2×C109semidirect
232. #1698C2×C109semidirect
233. #1564C2×C109semidirect
234. #1542C2×C109semidirect
236. C109#19155direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#31312
C109×#31042
C109×#31032
C2×#446×C1092
C109×#17042
C109×#17022
C109×#17002
C109×#16982
C109×#15642
C109×#15422
C109×#15402
#19155109