Finite Group Databasebeta

← C109×#32696 #42150690

Subgroups — C109×#32696 #42150690

Order 27904.

552 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2102C211yesmaximal, characteristic, complemented
2C109×#2082C211yesmaximal, characteristic, complemented
3C109×#2082C211yesmaximal, characteristic, complemented
4C109×#2069C211yesmaximal, characteristic, complemented
5C109×#2049C211yesmaximal, characteristic, complemented
6C109×#2004C211yesmaximal, characteristic
7C109×#1967C211yesmaximal, characteristic, complemented
8C109×#1932C211yesmaximal, characteristic, complemented
9C109×#1914C211yesmaximal, characteristic
10C109×#1911C211yesmaximal, characteristic
11C109×#1902C211yesmaximal, characteristic, complemented
12C109×#1885C211yesmaximal, characteristic, complemented
13C109×#1861C211yesmaximal, characteristic, complemented
14C109×#1841C211yesmaximal, characteristic, complemented
15C109×#1829C211yesmaximal, characteristic, complemented
16C2×#137×C109C2211yescharacteristic
17#568×C109C2211yescharacteristic
18#535×C109C2211yescharacteristic
19C2×#124×C109C2211yescharacteristic
20#518×C109C2211yescharacteristic
21#430×C109C2211yescharacteristic
22#430×C109C2211yescharacteristic
23#430×C109C2211yescharacteristic
24#423×C109C2211yescharacteristic
25#421×C109C2211yescharacteristic
26#421×C109C2211yescharacteristic
27C2×#104×C109C2211yescharacteristic
28#419×C109C2211yescharacteristic
29#419×C109C2211yescharacteristic
30#419×C109C2211yescharacteristic
31#413×C109C2211yescharacteristic
32C2×#101×C109C2211yescharacteristic
33C2×#101×C109C2211yescharacteristic
34C2×#100×C109C2211yescharacteristic
35C2×#100×C109C2211yescharacteristic
36C2×#100×C109C2211yescharacteristic
37C2×#100×C109C2211yescharacteristic
38C4×M16×C109C2211yescharacteristic
39#344×C109C2211yescharacteristic
40#344×C109C2211yescharacteristic
41#344×C109C2211yescharacteristic
42#344×C109C2211yescharacteristic
43#344×C109C2211yescharacteristic
44#344×C109C2211yescharacteristic
45#339×C109C2211yescharacteristic
46#339×C109C2211yescharacteristic
47#339×C109C2211yescharacteristic
48#338×C109C2211yescharacteristic
49H(3,ℤ/4)×C109C2211yescharacteristic
50H(3,ℤ/4)×C109C2211yescharacteristic
51C2×#41×C109C2311yescharacteristic
52C22×Q8×C109C2311yescharacteristic
53C22×D4×C109C2311yescharacteristic
54#137×C109—41no—
55#137×C109—41no—
56C2×Q16×C109—21no—
57C2×SD16×C109—21no—
58#131×C109—41no—
59#131×C109—41no—
60C2×M16×C109—41no—
61C2×M16×C109C2311yescharacteristic
62C2×M16×C109C2311yescharacteristic
63C2×M16×C109C2311yescharacteristic
64C2×M16×C109C2311yescharacteristic
65C2×M16×C109C2311yescharacteristic
66C2×M16×C109C2311yescharacteristic
67C2×M16×C109C2311yescharacteristic
68C2×M16×C109C2311yescharacteristic
69#127×C109—21no—
70#124×C109—21no—
71#124×C109—21no—
72#124×C109—21no—
73#124×C109—41no—
74#121×C109—41no—
75#120×C109—22no—
76C4×D4×C109—41no—
77C4×D4×C109—41no—
78#117×C109C2311yescharacteristic
79#117×C109C2311yescharacteristic
80#117×C109C2311yescharacteristic
81C2×C22⋊C4×C109—22no—
82C2×C22⋊C4×C109—22no—
83C2×C42×C109C2311yescharacteristic
84#108×C109—41no—
85#108×C109—41no—
86#108×C109—41no—
87C4⋊C8×C109—41no—
88#104×C109—21no—
89#104×C109—21no—
90#104×C109—41no—
91#104×C109—41no—
92#103×C109—41no—
93#103×C109—41no—
94#103×C109—41no—
95#101×C109—21no—
96#101×C109—41no—
97#101×C109—41no—
98#100×C109—21no—
99#100×C109—41no—
100#100×C109—41no—
101#100×C109—41no—
102#100×C109—41no—
103#97×C109—21no—
104C4×C8×C109—21no—
105C24×C109#4112yes—
106#41×C109—21no—
107#41×C109—21no—
108#41×C109—21no—
109#41×C109—21no—
110C2×Q8×C109—21no—
111C2×Q8×C109—21no—
112C2×Q8×C109—21no—
113C2×Q8×C109—21no—
114C2×Q8×C109—21no—
115C2×Q8×C109—21no—
116C2×Q8×C109#4111yescharacteristic
117C2×D4×C109—21no—
118C2×D4×C109—21no—
119C2×D4×C109—21no—
120C2×D4×C109—21no—
121C2×D4×C109—21no—
122C2×D4×C109—21no—
123C2×D4×C109—21no—
124C2×D4×C109—42no—
125C2×D4×C109#4111yescharacteristic
126C22×C4×C109—21no—
127C22×C4×C109—21no—
128C22×C4×C109—21no—
129C22×C4×C109—42no—
130C22×C4×C109C2411yescharacteristic
131Q16×C109—42no—
132SD16×C109—42no—
133M16×C109—21no—
134M16×C109—21no—
135M16×C109—21no—
136M16×C109—21no—
137M16×C109—21no—
138M16×C109—21no—
139M16×C109—21no—
140M16×C109—21no—
141M16×C109—21no—
142M16×C109—21no—
143M16×C109—21no—
144M16×C109—21no—
145M16×C109—21no—
146M16×C109—21no—
147M16×C109—21no—
148M16×C109—21no—
149M16×C109—42no—
150C2×C8×C109—21no—
151C2×C8×C109—21no—
152C2×C8×C109—21no—
153C2×C8×C109—21no—
154C2×C8×C109—21no—
155C2×C8×C109—21no—
156C2×C8×C109—21no—
157C2×C8×C109—21no—
158C2×C8×C109—42no—
159C4⋊C4×C109—21no—
160C4⋊C4×C109—21no—
161C4⋊C4×C109—21no—
162C22⋊C4×C109—21no—
163C22⋊C4×C109—21no—
164C22⋊C4×C109—21no—
165C22⋊C4×C109—42no—
166C22⋊C4×C109—42no—
167C22⋊C4×C109—42no—
168C22⋊C4×C109—42no—
169C42×C109—21no—
170C42×C109—21no—
171C42×C109—21no—
172C42×C109—21no—
173C42×C109#4111yescharacteristic
174C42×C109#4111yescharacteristic
175C23×C109—22no—
176C23×C109—22no—
177C23×C109—22no—
178C23×C109—21no—
179C23×C109—82no—
180C23×C109C2×#4111yescharacteristic
181Q8×C109—21no—
182Q8×C109—21no—
183Q8×C109—41no—
184Q8×C109—41no—
185Q8×C109—41no—
186Q8×C109—41no—
187D4×C109—21no—
188D4×C109—21no—
189D4×C109—41no—
190D4×C109—41no—
191D4×C109—41no—
192D4×C109—41no—
193D4×C109—41no—
194D4×C109—41no—
195D4×C109—162no—
196C2×C4×C109—21no—
197C2×C4×C109—21no—
198C2×C4×C109—21no—
199C2×C4×C109—41no—
200C2×C4×C109—41no—
201C2×C4×C109—41no—
202C2×C4×C109—41no—
203C2×C4×C109—41no—
204C2×C4×C109—41no—
205C2×C4×C109—41no—
206C2×C4×C109—41no—
207C2×C4×C109—81no—
208C2×C4×C109—162no—
209C2×C4×C109C2×#4111yescharacteristic
210C2×C4×C109C2×#4111yescharacteristic
211C2×C4×C109H(5,𝔽2)11yescharacteristic
212C2×C4×C109H(5,𝔽2)11yescharacteristic
213C2×C4×C109H(5,𝔽2)11yescharacteristic
214C2×C4×C109H(5,𝔽2)11yescharacteristic
215C8×C109—41no—
216C8×C109—41no—
217C8×C109—41no—
218C8×C109—41no—
219C8×C109—41no—
220C8×C109—41no—
221C8×C109—41no—
222C8×C109—41no—
223C22×C109—41no—
224C22×C109—41no—
225C22×C109—42no—
226C22×C109—82no—
227C22×C109—81no—
228C22×C109—82no—
229C22×C109—82no—
230C22×C109#53811yescharacteristic
231C22×C109#55111yescharacteristic
232C22×C109#55111yescharacteristic
233C4×C109—41no—
234C4×C109—41no—
235C4×C109—41no—
236C4×C109—81no—
237C4×C109—81no—
238C4×C109—81no—
239C4×C109—81no—
240C4×C109#53811yescharacteristic
241C4×C109#54011yescharacteristic
242C4×C109#55311yescharacteristic
243C4×C109#56011yescharacteristic
244#32696C10911yesmaximal, characteristic, direct product factor, Sylow
245C2×C109—21no—
246C2×C109—21no—
247C2×C109—21no—
248C2×C109—81no—
249C2×C109—82no—
250C2×C109#274911yescharacteristic
251#2102C2×C10911yescharacteristic, complemented
252#2082C2×C10911yescharacteristic, complemented
253#2082C2×C10911yescharacteristic, complemented
254#2069C2×C10911yescharacteristic, complemented
255#2049C2×C10911yescharacteristic, complemented
256#2004C2×C10911yescharacteristic
257#1967C2×C10911yescharacteristic, complemented
258#1932C2×C10911yescharacteristic, complemented
259#1914C2×C10911yescharacteristic
260#1911C2×C10911yescharacteristic
261#1902C2×C10911yescharacteristic, complemented
262#1885C2×C10911yescharacteristic, complemented
263#1861C2×C10911yescharacteristic, complemented
264#1841C2×C10911yescharacteristic, complemented
265#1829C2×C10911yescharacteristic, complemented
266C109#3269611yescharacteristic, direct product factor, Sylow
267C2×#137C22×C10911yescharacteristic
268#568C22×C10911yescharacteristic
269#535C22×C10911yescharacteristic
270C2×#124C22×C10911yescharacteristic
271#518C22×C10911yescharacteristic
272#430C22×C10911yescharacteristic
273#430C22×C10911yescharacteristic
274#430C22×C10911yescharacteristic
275#423C22×C10911yescharacteristic
276#421C22×C10911yescharacteristic
277#421C22×C10911yescharacteristic
278C2×#104C22×C10911yescharacteristic
279#419C22×C10911yescharacteristic
280#419C22×C10911yescharacteristic
281#419C22×C10911yescharacteristic
282#413C22×C10911yescharacteristic
283C2×#101C22×C10911yescharacteristic
284C2×#101C22×C10911yescharacteristic
285C2×#100C22×C10911yescharacteristic
286C2×#100C22×C10911yescharacteristic
287C2×#100C22×C10911yescharacteristic
288C2×#100C22×C10911yescharacteristic
289C4×M16C22×C10911yescharacteristic
290#344C22×C10911yescharacteristic
291#344C22×C10911yescharacteristic
292#344C22×C10911yescharacteristic
293#344C22×C10911yescharacteristic
294#344C22×C10911yescharacteristic
295#344C22×C10911yescharacteristic
296#339C22×C10911yescharacteristic
297#339C22×C10911yescharacteristic
298#339C22×C10911yescharacteristic
299#338C22×C10911yescharacteristic
300H(3,ℤ/4)C22×C10911yescharacteristic
301H(3,ℤ/4)C22×C10911yescharacteristic
302C2×#41C23×C10911yescharacteristic
303C22×Q8C23×C10911yescharacteristic
304C22×D4C23×C10911yescharacteristic
305#137—41no—
306#137—41no—
307C2×Q16—21no—
308C2×SD16—21no—
309#131—41no—
310#131—41no—
311C2×M16—41no—
312C2×M16C23×C10911yescharacteristic
313C2×M16C23×C10911yescharacteristic
314C2×M16C23×C10911yescharacteristic
315C2×M16C23×C10911yescharacteristic
316C2×M16C23×C10911yescharacteristic
317C2×M16C23×C10911yescharacteristic
318C2×M16C23×C10911yescharacteristic
319C2×M16C23×C10911yescharacteristic
320#127—21no—
321#124—21no—
322#124—21no—
323#124—21no—
324#124—41no—
325#121—41no—
326#120—22no—
327C4×D4—41no—
328C4×D4—41no—
329#117C23×C10911yescharacteristic
330#117C23×C10911yescharacteristic
331#117C23×C10911yescharacteristic
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C42C23×C10911yescharacteristic
335#108—41no—
336#108—41no—
337#108—41no—
338C4⋊C8—41no—
339#104—21no—
340#104—21no—
341#104—41no—
342#104—41no—
343#103—41no—
344#103—41no—
345#103—41no—
346#101—21no—
347#101—41no—
348#101—41no—
349#100—21no—
350#100—41no—
351#100—41no—
352#100—41no—
353#100—41no—
354#97—21no—
355C4×C8—21no—
356C24#41×C10912yes—
357#41—21no—
358#41—21no—
359#41—21no—
360#41—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8#41×C10911yescharacteristic
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—42no—
376C2×D4#41×C10911yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—42no—
381C22×C4C24×C10911yescharacteristic
382Q16—42no—
383SD16—42no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16—21no—
389M16—21no—
390M16—21no—
391M16—21no—
392M16—21no—
393M16—21no—
394M16—21no—
395M16—21no—
396M16—21no—
397M16—21no—
398M16—21no—
399M16—21no—
400M16—42no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—42no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42#41×C10911yescharacteristic
425C42#41×C10911yescharacteristic
426C23—22no—
427C23—22no—
428C23—22no—
429C23—21no—
430C23—82no—
431C23C2×#41×C10911yescharacteristic
432Q8—21no—
433Q8—21no—
434Q8—41no—
435Q8—41no—
436Q8—41no—
437Q8—41no—
438D4—21no—
439D4—21no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—162no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—81no—
459C2×C4—162no—
460C2×C4C2×#41×C10911yescharacteristic
461C2×C4C2×#41×C10911yescharacteristic
462C2×C4H(5,𝔽2)×C10911yescharacteristic
463C2×C4H(5,𝔽2)×C10911yescharacteristic
464C2×C4H(5,𝔽2)×C10911yescharacteristic
465C2×C4H(5,𝔽2)×C10911yescharacteristic
466C8—41no—
467C8—41no—
468C8—41no—
469C8—41no—
470C8—41no—
471C8—41no—
472C8—41no—
473C8—41no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—82no—
478C22—81no—
479C22—82no—
480C22—82no—
481C22#538×C10911yescharacteristic
482C22#551×C10911yescharacteristic
483C22#551×C10911yescharacteristic
484C4—41no—
485C4—41no—
486C4—41no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4#538×C10911yescharacteristic
492C4#540×C10911yescharacteristic
493C4#553×C10911yescharacteristic
494C4#560×C10911yescharacteristic
495C2—21no—
496C2—21no—
497C2—21no—
498C2—82no—
499C2—81no—
500C2C109×#274911yescharacteristic
subgroupG/H
center, socleC2×C109#2749
commutator, Frattini, cosocleC22×C4C24×C109
prime radical#535×C109C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C109 ◁ C22×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#2102C2semidirect
2. C109×#2082C2semidirect
3. C109×#2082C2semidirect
4. C109×#2069C2semidirect
5. C109×#2049C2semidirect
7. C109×#1967C2semidirect
8. C109×#1932C2semidirect
11. C109×#1902C2semidirect
12. C109×#1885C2semidirect
13. C109×#1861C2semidirect
14. C109×#1841C2semidirect
15. C109×#1829C2semidirect
244. #32696C109direct (N × H)
251. #2102C2×C109semidirect
252. #2082C2×C109semidirect
253. #2082C2×C109semidirect
254. #2069C2×C109semidirect
255. #2049C2×C109semidirect
257. #1967C2×C109semidirect
258. #1932C2×C109semidirect
261. #1902C2×C109semidirect
262. #1885C2×C109semidirect
263. #1861C2×C109semidirect
264. #1841C2×C109semidirect
265. #1829C2×C109semidirect
266. C109#32696direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#21022
C109×#20822
C109×#20692
C109×#20492
C109×#20042
C109×#19672
C109×#19322
C109×#19142
C109×#19112
C109×#19022
C109×#18852
C109×#18612
C109×#18412
C109×#18292
#32696109