Finite Group Databasebeta

← C109×#12796 #42130790

Subgroups — C109×#12796 #42130790

Order 27904.

512 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2322C211yesmaximal, characteristic
2C2×#352×C109C212yesmaximal
3C109×#1800C211yesmaximal, characteristic
4C109×#1799C211yesmaximal, characteristic
5C109×#1390C212yesmaximal
6C2×#123×C109C2211yescharacteristic
7C2×C4×D4×C109C2211yescharacteristic
8C22×C4⋊C4×C109C411yescharacteristic, complemented
9#423×C109—21no—
10C2×#100×C109C2212yes—
11C2×#99×C109C2212yes—
12#389×C109—21no—
13#388×C109—21no—
14#387×C109—21no—
15#386×C109C2211yescharacteristic
16#385×C109—21no—
17#385×C109C411yescharacteristic, complemented
18#381×C109C411yescharacteristic, complemented
19#380×C109—21no—
20C4×C22⋊C4×C109C411yescharacteristic, complemented
21#352×C109—24no—
22#343×C109—21no—
23#342×C109—21no—
24C22×D4×C109C2311yescharacteristic
25C23×C4×C109C2×C411yescharacteristic
26C23×C4×C109C2×C411yescharacteristic
27C23×C4×C109C2×C411yescharacteristic
28C23×C4×C109D411yescharacteristic
29C2×M16×C109—22no—
30#123×C109—21no—
31#123×C109—21no—
32#123×C109D412yes—
33#123×C109Q812yes—
34C4×D4×C109—41no—
35C4×D4×C109—41no—
36C2×C4⋊C4×C109—21no—
37C2×C4⋊C4×C109—21no—
38C2×C4⋊C4×C109—21no—
39C2×C4⋊C4×C109—21no—
40C2×C4⋊C4×C109—41no—
41C2×C4⋊C4×C109—41no—
42C2×C4⋊C4×C109—41no—
43C2×C4⋊C4×C109D411yescharacteristic
44C2×C22⋊C4×C109—21no—
45C2×C22⋊C4×C109—22no—
46C2×C22⋊C4×C109—21no—
47C2×C22⋊C4×C109C2×C411yescharacteristic
48C2×C22⋊C4×C109C2×C411yescharacteristic
49C2×C22⋊C4×C109C2×C411yescharacteristic
50C2×C22⋊C4×C109D411yescharacteristic
51C2×C42×C109—21no—
52C2×C42×C109D411yescharacteristic
53C4⋊C8×C109—41no—
54C4⋊C8×C109—41no—
55#100×C109—22no—
56#100×C109—22no—
57#99×C109—22no—
58#99×C109—22no—
59#95×C109—21no—
60#95×C109—21no—
61#95×C109—21no—
62#95×C109—21no—
63#95×C109—21no—
64#95×C109—41no—
65C24×C109C22×C411yescharacteristic
66C24×C109C2×D411yescharacteristic
67C2×D4×C109—41no—
68C2×D4×C109—41no—
69C2×D4×C109C2×D411yescharacteristic
70C2×D4×C109C2×Q811yescharacteristic
71C2×D4×C109#4111yescharacteristic
72C2×D4×C109#4111yescharacteristic
73C22×C4×C109—21no—
74C22×C4×C109—21no—
75C22×C4×C109—21no—
76C22×C4×C109—21no—
77C22×C4×C109—21no—
78C22×C4×C109—21no—
79C22×C4×C109—21no—
80C22×C4×C109—21no—
81C22×C4×C109—21no—
82C22×C4×C109—41no—
83C22×C4×C109—41no—
84C22×C4×C109—41no—
85C22×C4×C109—42no—
86C22×C4×C109—81no—
87C22×C4×C109—81no—
88C22×C4×C109—81no—
89C22×C4×C109C22⋊C411yescharacteristic
90C22×C4×C109C22⋊C411yescharacteristic
91C22×C4×C109C22⋊C411yescharacteristic
92C22×C4×C109C22⋊C411yescharacteristic
93C22×C4×C109C4⋊C412yescomplemented
94C22×C4×C109C2×D411yescharacteristic
95M16×C109—42no—
96M16×C109—42no—
97C2×C8×C109—42no—
98C4⋊C4×C109—22no—
99C4⋊C4×C109—22no—
100C4⋊C4×C109—41no—
101C4⋊C4×C109—42no—
102C4⋊C4×C109—41no—
103C4⋊C4×C109—41no—
104C4⋊C4×C109—81no—
105C4⋊C4×C109—82no—
106C22⋊C4×C109—21no—
107C22⋊C4×C109—22no—
108C22⋊C4×C109—22no—
109C22⋊C4×C109—41no—
110C22⋊C4×C109—41no—
111C22⋊C4×C109—41no—
112C22⋊C4×C109—42no—
113C22⋊C4×C109—42no—
114C22⋊C4×C109—81no—
115C22⋊C4×C109C4⋊C412yescomplemented
116C42×C109—21no—
117C42×C109—21no—
118C42×C109—81no—
119C23×C109—21no—
120C23×C109—21no—
121C23×C109—21no—
122C23×C109—21no—
123C23×C109—41no—
124C23×C109—41no—
125C23×C109—41no—
126C23×C109—41no—
127C23×C109C2×C22⋊C411yescharacteristic
128C23×C109C2×C4⋊C411yescharacteristic
129C23×C109#11711yescharacteristic
130C23×C109#12111yescharacteristic
131C23×C109C22⋊Q811yescharacteristic
132D4×C109—41no—
133D4×C109—41no—
134D4×C109—41no—
135D4×C109—41no—
136C2×C4×C109—21no—
137C2×C4×C109—21no—
138C2×C4×C109—22no—
139C2×C4×C109—22no—
140C2×C4×C109—21no—
141C2×C4×C109—21no—
142C2×C4×C109—21no—
143C2×C4×C109—41no—
144C2×C4×C109—42no—
145C2×C4×C109—41no—
146C2×C4×C109—41no—
147C2×C4×C109—42no—
148C2×C4×C109—41no—
149C2×C4×C109—41no—
150C2×C4×C109—41no—
151C2×C4×C109—41no—
152C2×C4×C109—42no—
153C2×C4×C109—41no—
154C2×C4×C109—41no—
155C2×C4×C109—41no—
156C2×C4×C109—41no—
157C2×C4×C109—41no—
158C2×C4×C109—41no—
159C2×C4×C109—41no—
160C2×C4×C109—81no—
161C2×C4×C109—81no—
162C2×C4×C109—81no—
163C2×C4×C109—82no—
164C2×C4×C109—82no—
165C2×C4×C109—82no—
166C2×C4×C109—82no—
167C2×C4×C109#9911yescharacteristic
168C2×C4×C109#9911yescharacteristic
169C2×C4×C109#12111yescharacteristic
170C2×C4×C109C22⋊Q811yescharacteristic
171C8×C109—82no—
172C22×C109—21no—
173C22×C109—21no—
174C22×C109—21no—
175C22×C109—21no—
176C22×C109—21no—
177C22×C109—21no—
178C22×C109—41no—
179C22×C109—41no—
180C22×C109—41no—
181C22×C109—41no—
182C22×C109—42no—
183C22×C109—41no—
184C22×C109—41no—
185C22×C109—41no—
186C22×C109—41no—
187C22×C109—81no—
188C22×C109#38011yescharacteristic
189C22×C109C2×#9911yescharacteristic
190C22×C109#41011yescharacteristic
191C4×C109—21no—
192C4×C109—21no—
193C4×C109—21no—
194C4×C109—21no—
195C4×C109—42no—
196C4×C109—42no—
197C4×C109—41no—
198C4×C109—41no—
199C4×C109—41no—
200C4×C109—81no—
201C4×C109—81no—
202C4×C109—162no—
203#12796C10911yesmaximal, characteristic, direct product factor, Sylow
204C2×C109—21no—
205C2×C109—21no—
206C2×C109—41no—
207C2×C109—41no—
208C2×C109—41no—
209C2×C109—41no—
210C2×C109#179911yescharacteristic
211C2×C109#212111yescharacteristic
212C2×C109#212311yescharacteristic
213#2322C2×C10911yescharacteristic
214C2×#352C2×C10912yes—
215#1800C2×C10911yescharacteristic
216#1799C2×C10911yescharacteristic
217#1390C2×C10912yes—
218C109#1279611yescharacteristic, direct product factor, Sylow
219C2×#123C22×C10911yescharacteristic
220C2×C4×D4C22×C10911yescharacteristic
221C22×C4⋊C4C4×C10911yescharacteristic, complemented
222#423—21no—
223C2×#100C22×C10912yes—
224C2×#99C22×C10912yes—
225#389—21no—
226#388—21no—
227#387—21no—
228#386C22×C10911yescharacteristic
229#385—21no—
230#385C4×C10911yescharacteristic, complemented
231#381C4×C10911yescharacteristic, complemented
232#380—21no—
233C4×C22⋊C4C4×C10911yescharacteristic, complemented
234#352—24no—
235#343—21no—
236#342—21no—
237C22×D4C23×C10911yescharacteristic
238C23×C4C2×C4×C10911yescharacteristic
239C23×C4C2×C4×C10911yescharacteristic
240C23×C4C2×C4×C10911yescharacteristic
241C23×C4D4×C10911yescharacteristic
242C2×M16—22no—
243#123—21no—
244#123—21no—
245#123D4×C10912yes—
246#123Q8×C10912yes—
247C4×D4—41no—
248C4×D4—41no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4—41no—
255C2×C4⋊C4—41no—
256C2×C4⋊C4D4×C10911yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4C2×C4×C10911yescharacteristic
261C2×C22⋊C4C2×C4×C10911yescharacteristic
262C2×C22⋊C4C2×C4×C10911yescharacteristic
263C2×C22⋊C4D4×C10911yescharacteristic
264C2×C42—21no—
265C2×C42D4×C10911yescharacteristic
266C4⋊C8—41no—
267C4⋊C8—41no—
268#100—22no—
269#100—22no—
270#99—22no—
271#99—22no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—41no—
278C24C22×C4×C10911yescharacteristic
279C24C2×D4×C10911yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4C2×D4×C10911yescharacteristic
283C2×D4C2×Q8×C10911yescharacteristic
284C2×D4#41×C10911yescharacteristic
285C2×D4#41×C10911yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—81no—
300C22×C4—81no—
301C22×C4—81no—
302C22×C4C22⋊C4×C10911yescharacteristic
303C22×C4C22⋊C4×C10911yescharacteristic
304C22×C4C22⋊C4×C10911yescharacteristic
305C22×C4C22⋊C4×C10911yescharacteristic
306C22×C4C4⋊C4×C10912yescomplemented
307C22×C4C2×D4×C10911yescharacteristic
308M16—42no—
309M16—42no—
310C2×C8—42no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—81no—
318C4⋊C4—82no—
319C22⋊C4—21no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—81no—
328C22⋊C4C4⋊C4×C10912yescomplemented
329C42—21no—
330C42—21no—
331C42—81no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23C2×C22⋊C4×C10911yescharacteristic
341C23C2×C4⋊C4×C10911yescharacteristic
342C23#117×C10911yescharacteristic
343C23#121×C10911yescharacteristic
344C23C22⋊Q8×C10911yescharacteristic
345D4—41no—
346D4—41no—
347D4—41no—
348D4—41no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4#99×C10911yescharacteristic
381C2×C4#99×C10911yescharacteristic
382C2×C4#121×C10911yescharacteristic
383C2×C4C22⋊Q8×C10911yescharacteristic
384C8—82no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22#380×C10911yescharacteristic
402C22C2×#99×C10911yescharacteristic
403C22#410×C10911yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—42no—
409C4—42no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—81no—
414C4—81no—
415C4—162no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2—41no—
421C2—41no—
422C2C109×#179911yescharacteristic
423C2C109×#212111yescharacteristic
424C2C109×#212311yescharacteristic
subgroupG/H
center, socleC22×C109C2×#99
commutatorC24C22×C4×C109
Frattini, cosocleC22×D4C23×C109
prime radicalC22×D4×C109C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C22×C4×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
8. C22×C4⋊C4×C109C4semidirect
17. #385×C109C4semidirect
18. #381×C109C4semidirect
20. C4×C22⋊C4×C109C4semidirect
93. C22×C4×C109C4⋊C4semidirect
115. C22⋊C4×C109C4⋊C4semidirect
203. #12796C109direct (N × H)
218. C109#12796direct (N × H)
221. C22×C4⋊C4C4×C109semidirect
230. #385C4×C109semidirect
231. #381C4×C109semidirect
233. C4×C22⋊C4C4×C109semidirect
306. C22×C4C4⋊C4×C109semidirect
328. C22⋊C4C4⋊C4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#23222
C2×#352×C1092
C109×#18002
C109×#17992
C109×#13902
#12796109