Finite Group Databasebeta

← C109×#12958 #42130952

Subgroups — C109×#12958 #42130952

Order 27904.

728 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2358C211yesmaximal, characteristic
2C2×AΣL(1,𝔽16)×C109C211yesmaximal, characteristic
3C109×#1889C211yesmaximal, characteristic
4C109×#1867C211yesmaximal, characteristic, complemented
5C109×#1856C211yesmaximal, characteristic, complemented
6C109×#1393C211yesmaximal, characteristic, complemented
7C109×#1390C211yesmaximal, characteristic, complemented
8C2×#120×C109C2211yescharacteristic
9#518×C109C2211yescharacteristic
10C2×C4×D4×C109—21no—
11C22×C22⋊C4×C109—21no—
12#428×C109—21no—
13C2×#100×C109C2211yescharacteristic
14C2×#99×C109C2211yescharacteristic
15C2×#99×C109C2211yescharacteristic
16#390×C109C2211yescharacteristic
17#388×C109—21no—
18#386×C109—21no—
19#386×C109C2211yescharacteristic
20#385×C109—21no—
21#385×C109—21no—
22#379×C109—21no—
23C4×C22⋊C4×C109—21no—
24AΣL(1,𝔽16)×C109C414yescomplemented
25#342×C109—21no—
26#342×C109—21no—
27#339×C109—21no—
28C25×C109D411yescharacteristic
29C22×D4×C109—21no—
30C22×D4×C109C2311yescharacteristic
31C23×C4×C109—21no—
32C23×C4×C109—21no—
33C23×C4×C109D411yescharacteristic
34C2×M16×C109—21no—
35#120×C109—21no—
36#120×C109—21no—
37#120×C109C2×C412yes—
38#120×C109Q812yes—
39C4×D4×C109—44no—
40C4×D4×C109—41no—
41C4×D4×C109—41no—
42#117×C109—21no—
43C2×C4⋊C4×C109—21no—
44C2×C4⋊C4×C109—41no—
45C2×C4⋊C4×C109D411yescharacteristic
46C2×C22⋊C4×C109—21no—
47C2×C22⋊C4×C109—21no—
48C2×C22⋊C4×C109—21no—
49C2×C22⋊C4×C109—21no—
50C2×C22⋊C4×C109—21no—
51C2×C22⋊C4×C109—21no—
52C2×C22⋊C4×C109—21no—
53C2×C22⋊C4×C109—21no—
54C2×C22⋊C4×C109—21no—
55C2×C22⋊C4×C109—21no—
56C2×C22⋊C4×C109—44no—
57C2×C22⋊C4×C109—41no—
58C2×C22⋊C4×C109—41no—
59C2×C22⋊C4×C109D411yescharacteristic
60C2×C22⋊C4×C109D411yescharacteristic
61C2×C42×C109—21no—
62C2×C42×C109D411yescharacteristic
63#107×C109—41no—
64#106×C109—41no—
65#100×C109—21no—
66#100×C109C2×C412yescomplemented
67#99×C109—21no—
68#99×C109—21no—
69#99×C109—21no—
70#99×C109C2×C412yescomplemented
71#95×C109—21no—
72#95×C109—21no—
73#95×C109—21no—
74#95×C109—41no—
75C24×C109—21no—
76C24×C109—21no—
77C24×C109—42no—
78C24×C109—41no—
79C24×C109—42no—
80C24×C109—41no—
81C24×C109C4⋊C412yescomplemented
82C24×C109C2×D411yescharacteristic
83C24×C109C2×D411yescharacteristic
84C2×D4×C109—22no—
85C2×D4×C109—22no—
86C2×D4×C109—41no—
87C2×D4×C109—41no—
88C2×D4×C109—42no—
89C2×D4×C109—42no—
90C2×D4×C109C22×C411yescharacteristic
91C2×D4×C109C2×Q811yescharacteristic
92C2×D4×C109#4111yescharacteristic
93C2×D4×C109#4111yescharacteristic
94C22×C4×C109—21no—
95C22×C4×C109—21no—
96C22×C4×C109—21no—
97C22×C4×C109—21no—
98C22×C4×C109—21no—
99C22×C4×C109—21no—
100C22×C4×C109—21no—
101C22×C4×C109—21no—
102C22×C4×C109—21no—
103C22×C4×C109—42no—
104C22×C4×C109—42no—
105C22×C4×C109—42no—
106C22×C4×C109—41no—
107C22×C4×C109—41no—
108C22×C4×C109—42no—
109C22×C4×C109—42no—
110C22×C4×C109—41no—
111C22×C4×C109—81no—
112C22×C4×C109—81no—
113C22×C4×C109C2×D411yescharacteristic
114M16×C109—22no—
115M16×C109—41no—
116C2×C8×C109—41no—
117C4⋊C4×C109—21no—
118C4⋊C4×C109—21no—
119C4⋊C4×C109—41no—
120C4⋊C4×C109—42no—
121C4⋊C4×C109—82no—
122C22⋊C4×C109—24no—
123C22⋊C4×C109—21no—
124C22⋊C4×C109—22no—
125C22⋊C4×C109—22no—
126C22⋊C4×C109—22no—
127C22⋊C4×C109—42no—
128C22⋊C4×C109—42no—
129C22⋊C4×C109—42no—
130C22⋊C4×C109—41no—
131C22⋊C4×C109—42no—
132C22⋊C4×C109—41no—
133C22⋊C4×C109—41no—
134C22⋊C4×C109—41no—
135C22⋊C4×C109—41no—
136C22⋊C4×C109—41no—
137C22⋊C4×C109—41no—
138C22⋊C4×C109—82no—
139C22⋊C4×C109—82no—
140C22⋊C4×C109C4⋊C412yescomplemented
141C42×C109—41no—
142C42×C109—42no—
143C42×C109—41no—
144C23×C109—22no—
145C23×C109—22no—
146C23×C109—22no—
147C23×C109—21no—
148C23×C109—21no—
149C23×C109—21no—
150C23×C109—21no—
151C23×C109—41no—
152C23×C109—41no—
153C23×C109—41no—
154C23×C109—41no—
155C23×C109—41no—
156C23×C109—44no—
157C23×C109—42no—
158C23×C109—41no—
159C23×C109—44no—
160C23×C109—41no—
161C23×C109—41no—
162C23×C109—42no—
163C23×C109—42no—
164C23×C109—81no—
165C23×C109—84no—
166C23×C109—81no—
167C23×C109—81no—
168C23×C109C2×C4⋊C411yescharacteristic
169C23×C109C4×D411yescharacteristic
170C23×C109#12011yescharacteristic
171C23×C109C22⋊Q811yescharacteristic
172C23×C109#12311yescharacteristic
173D4×C109—41no—
174D4×C109—41no—
175D4×C109—41no—
176D4×C109—41no—
177D4×C109—44no—
178D4×C109—44no—
179C2×C4×C109—21no—
180C2×C4×C109—21no—
181C2×C4×C109—22no—
182C2×C4×C109—22no—
183C2×C4×C109—22no—
184C2×C4×C109—41no—
185C2×C4×C109—41no—
186C2×C4×C109—41no—
187C2×C4×C109—41no—
188C2×C4×C109—41no—
189C2×C4×C109—41no—
190C2×C4×C109—42no—
191C2×C4×C109—42no—
192C2×C4×C109—41no—
193C2×C4×C109—41no—
194C2×C4×C109—41no—
195C2×C4×C109—41no—
196C2×C4×C109—41no—
197C2×C4×C109—41no—
198C2×C4×C109—41no—
199C2×C4×C109—41no—
200C2×C4×C109—81no—
201C2×C4×C109—84no—
202C2×C4×C109—84no—
203C2×C4×C109—81no—
204C2×C4×C109—81no—
205C2×C4×C109—81no—
206C2×C4×C109—81no—
207C2×C4×C109—81no—
208C2×C4×C109—81no—
209C2×C4×C109—81no—
210C2×C4×C109—81no—
211C2×C4×C109—81no—
212C2×C4×C109C4×D411yescharacteristic
213C2×C4×C109C22⋊Q811yescharacteristic
214C8×C109—42no—
215C22×C109—21no—
216C22×C109—21no—
217C22×C109—24no—
218C22×C109—21no—
219C22×C109—21no—
220C22×C109—21no—
221C22×C109—21no—
222C22×C109—41no—
223C22×C109—41no—
224C22×C109—41no—
225C22×C109—41no—
226C22×C109—42no—
227C22×C109—42no—
228C22×C109—42no—
229C22×C109—44no—
230C22×C109—42no—
231C22×C109—41no—
232C22×C109—41no—
233C22×C109—42no—
234C22×C109—41no—
235C22×C109—41no—
236C22×C109—42no—
237C22×C109—81no—
238C22×C109—81no—
239C22×C109—82no—
240C22×C109—82no—
241C22×C109—82no—
242C22×C109#38511yescharacteristic
243C22×C109B(4,𝔽2)11yescharacteristic
244C22×C109#45811yescharacteristic
245C4×C109—21no—
246C4×C109—21no—
247C4×C109—42no—
248C4×C109—42no—
249C4×C109—42no—
250C4×C109—81no—
251C4×C109—82no—
252C4×C109—81no—
253C4×C109—81no—
254C4×C109—81no—
255C4×C109—161no—
256#12958C10911yesmaximal, characteristic, direct product factor, Sylow
257C2×C109—21no—
258C2×C109—21no—
259C2×C109—41no—
260C2×C109—41no—
261C2×C109—44no—
262C2×C109—41no—
263C2×C109—41no—
264C2×C109#186711yescharacteristic
265C2×C109#219611yescharacteristic
266C2×C109#219711yescharacteristic
267#2358C2×C10911yescharacteristic
268C2×AΣL(1,𝔽16)C2×C10911yescharacteristic
269#1889C2×C10911yescharacteristic
270#1867C2×C10911yescharacteristic, complemented
271#1856C2×C10911yescharacteristic, complemented
272#1393C2×C10911yescharacteristic, complemented
273#1390C2×C10911yescharacteristic, complemented
274C109#1295811yescharacteristic, direct product factor, Sylow
275C2×#120C22×C10911yescharacteristic
276#518C22×C10911yescharacteristic
277C2×C4×D4—21no—
278C22×C22⋊C4—21no—
279#428—21no—
280C2×#100C22×C10911yescharacteristic
281C2×#99C22×C10911yescharacteristic
282C2×#99C22×C10911yescharacteristic
283#390C22×C10911yescharacteristic
284#388—21no—
285#386—21no—
286#386C22×C10911yescharacteristic
287#385—21no—
288#385—21no—
289#379—21no—
290C4×C22⋊C4—21no—
291AΣL(1,𝔽16)C4×C10914yescomplemented
292#342—21no—
293#342—21no—
294#339—21no—
295C25D4×C10911yescharacteristic
296C22×D4—21no—
297C22×D4C23×C10911yescharacteristic
298C23×C4—21no—
299C23×C4—21no—
300C23×C4D4×C10911yescharacteristic
301C2×M16—21no—
302#120—21no—
303#120—21no—
304#120C2×C4×C10912yes—
305#120Q8×C10912yes—
306C4×D4—44no—
307C4×D4—41no—
308C4×D4—41no—
309#117—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4D4×C10911yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4D4×C10911yescharacteristic
327C2×C22⋊C4D4×C10911yescharacteristic
328C2×C42—21no—
329C2×C42D4×C10911yescharacteristic
330#107—41no—
331#106—41no—
332#100—21no—
333#100C2×C4×C10912yescomplemented
334#99—21no—
335#99—21no—
336#99—21no—
337#99C2×C4×C10912yescomplemented
338#95—21no—
339#95—21no—
340#95—21no—
341#95—41no—
342C24—21no—
343C24—21no—
344C24—42no—
345C24—41no—
346C24—42no—
347C24—41no—
348C24C4⋊C4×C10912yescomplemented
349C24C2×D4×C10911yescharacteristic
350C24C2×D4×C10911yescharacteristic
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4C22×C4×C10911yescharacteristic
358C2×D4C2×Q8×C10911yescharacteristic
359C2×D4#41×C10911yescharacteristic
360C2×D4#41×C10911yescharacteristic
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—41no—
378C22×C4—81no—
379C22×C4—81no—
380C22×C4C2×D4×C10911yescharacteristic
381M16—22no—
382M16—41no—
383C2×C8—41no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—42no—
388C4⋊C4—82no—
389C22⋊C4—24no—
390C22⋊C4—21no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4—41no—
398C22⋊C4—42no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—82no—
406C22⋊C4—82no—
407C22⋊C4C4⋊C4×C10912yescomplemented
408C42—41no—
409C42—42no—
410C42—41no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—44no—
424C23—42no—
425C23—41no—
426C23—44no—
427C23—41no—
428C23—41no—
429C23—42no—
430C23—42no—
431C23—81no—
432C23—84no—
433C23—81no—
434C23—81no—
435C23C2×C4⋊C4×C10911yescharacteristic
436C23C4×D4×C10911yescharacteristic
437C23#120×C10911yescharacteristic
438C23C22⋊Q8×C10911yescharacteristic
439C23#123×C10911yescharacteristic
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—44no—
445D4—44no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—81no—
468C2×C4—84no—
469C2×C4—84no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4C4×D4×C10911yescharacteristic
480C2×C4C22⋊Q8×C10911yescharacteristic
481C8—42no—
482C22—21no—
483C22—21no—
484C22—24no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—44no—
497C22—41no—
498C22—41no—
499C22—42no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—82no—
507C22—82no—
508C22—82no—
509C22#385×C10911yescharacteristic
510C22B(4,𝔽2)×C10911yescharacteristic
511C22#458×C10911yescharacteristic
512C4—21no—
513C4—21no—
514C4—42no—
515C4—42no—
516C4—42no—
517C4—81no—
518C4—82no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—161no—
523C2—21no—
524C2—21no—
525C2—41no—
526C2—41no—
527C2—44no—
528C2—41no—
529C2—41no—
530C2C109×#186711yescharacteristic
531C2C109×#219611yescharacteristic
532C2C109×#219711yescharacteristic
subgroupG/H
center, socleC22×C109B(4,𝔽2)
commutatorC2×D4C22×C4×C109
Frattini, cosocleC22×D4C23×C109
prime radicalC2×#120×C109C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C109 ◁ C22×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
4. C109×#1867C2semidirect
5. C109×#1856C2semidirect
6. C109×#1393C2semidirect
7. C109×#1390C2semidirect
24. AΣL(1,𝔽16)×C109C4semidirect
66. #100×C109C2×C4semidirect
70. #99×C109C2×C4semidirect
81. C24×C109C4⋊C4semidirect
140. C22⋊C4×C109C4⋊C4semidirect
256. #12958C109direct (N × H)
270. #1867C2×C109semidirect
271. #1856C2×C109semidirect
272. #1393C2×C109semidirect
273. #1390C2×C109semidirect
274. C109#12958direct (N × H)
291. AΣL(1,𝔽16)C4×C109semidirect
333. #100C2×C4×C109semidirect
337. #99C2×C4×C109semidirect
348. C24C4⋊C4×C109semidirect
407. 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×#23582
C2×AΣL(1,𝔽16)×C1092
C109×#18892
C109×#18672
C109×#18562
C109×#13932
C109×#13902
#12958109