Finite Group Databasebeta

← C109×#19179 #42137173

Subgroups — C109×#19179 #42137173

Order 27904.

616 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3182C211yesmaximal, characteristic, complemented
2C109×#3106C211yesmaximal, characteristic
3C109×#3076C211yesmaximal, characteristic, complemented
4C109×#2970C211yesmaximal, characteristic, complemented
5C109×#1704C211yesmaximal, characteristic, complemented
6C109×#1698C211yesmaximal, characteristic, complemented
7C109×#1696C211yesmaximal, characteristic, complemented
8C109×#1686C211yesmaximal, characteristic, complemented
9C109×#1683C211yesmaximal, characteristic, complemented
10C109×#1677C211yesmaximal, characteristic, complemented
11C109×#1675C211yesmaximal, characteristic, complemented
12C109×#1665C211yesmaximal, characteristic, complemented
13C109×#1565C211yesmaximal, characteristic, complemented
14C109×#1554C211yesmaximal, characteristic, complemented
15C109×#1551C211yesmaximal, characteristic, complemented
16#533×C109C2211yescharacteristic
17#532×C109C2211yescharacteristic
18C4×#41×C109C2211yescharacteristic
19#500×C109C2211yescharacteristic
20#492×C109C2211yescharacteristic
21#487×C109C2211yescharacteristic
22#486×C109C2211yescharacteristic
23#482×C109—21no—
24#479×C109—21no—
25#478×C109—21no—
26#477×C109C2211yescharacteristic
27#477×C109C2211yescharacteristic
28#476×C109C2211yescharacteristic
29#476×C109C2211yescharacteristic
30#475×C109C2211yescharacteristic
31#474×C109C2211yescharacteristic
32#468×C109—21no—
33#468×C109—21no—
34#460×C109C2211yescharacteristic
35#459×C109C2211yescharacteristic
36#449×C109—21no—
37#446×C109C2211yescharacteristic
38#446×C109C2211yescharacteristic
39#440×C109—21no—
40#440×C109—21no—
41C4×SD16×C109—21no—
42C4×D8×C109—21no—
43#435×C109—21no—
44#435×C109—21no—
45C8×D4×C109C2211yescharacteristic
46C8×D4×C109C2211yescharacteristic
47#432×C109—21no—
48#432×C109C2211yescharacteristic
49#431×C109C2211yescharacteristic
50#427×C109—21no—
51C2×C4⋊C8×C109C2211yescharacteristic
52#416×C109—21no—
53C4×M16×C109C2211yescharacteristic
54C2×#97×C109—21no—
55#335×C109C2211yescharacteristic
56#335×C109C2211yescharacteristic
57#334×C109C2211yescharacteristic
58#334×C109C2211yescharacteristic
59#333×C109C2211yescharacteristic
60#333×C109C2211yescharacteristic
61#333×C109C2211yescharacteristic
62#333×C109C2211yescharacteristic
63#332×C109C2211yescharacteristic
64#332×C109C2211yescharacteristic
65#331×C109C2211yescharacteristic
66#331×C109C2211yescharacteristic
67C2×#41×C109—21no—
68C2×#41×C109D411yescharacteristic
69C2×SD16×C109—21no—
70C2×SD16×C109—21no—
71C2×SD16×C109—21no—
72C2×D8×C109—21no—
73C2×M16×C109D411yescharacteristic
74C2×M16×C109D411yescharacteristic
75C22×C8×C109—21no—
76C22×C8×C109—21no—
77C22×C8×C109—21no—
78C4⋊Q8×C109C2311yescharacteristic
79C4⋊Q8×C109C2311yescharacteristic
80C4⋊Q8×C109C2311yescharacteristic
81#127×C109C2311yescharacteristic
82#125×C109—21no—
83#124×C109—21no—
84C22⋊Q8×C109—21no—
85C22⋊Q8×C109—21no—
86#121×C109—21no—
87#121×C109—21no—
88C4×Q8×C109—21no—
89C4×Q8×C109—21no—
90C4×Q8×C109D411yescharacteristic
91C4×Q8×C109C2311yescharacteristic
92C4×D4×C109—21no—
93C4×D4×C109—21no—
94C4×D4×C109—21no—
95C4×D4×C109—21no—
96C4×D4×C109D411yescharacteristic
97C4×D4×C109C2311yescharacteristic
98#117×C109—21no—
99#117×C109—21no—
100#117×C109D411yescharacteristic
101C2×C42×C109—21no—
102C2×C42×C109C2311yescharacteristic
103#107×C109—21no—
104#107×C109—21no—
105#107×C109—21no—
106#107×C109—21no—
107#107×C109—21no—
108#106×C109—21no—
109#106×C109—21no—
110#106×C109—21no—
111C4⋊C8×C109—21no—
112C4⋊C8×C109—21no—
113C4⋊C8×C109—21no—
114C4⋊C8×C109C2311yescharacteristic
115C4⋊C8×C109C2311yescharacteristic
116C4⋊C8×C109C2311yescharacteristic
117C4⋊C8×C109C2311yescharacteristic
118C4⋊C8×C109C2311yescharacteristic
119C4⋊C8×C109C2311yescharacteristic
120#103×C109—21no—
121#103×C109—21no—
122#103×C109—21no—
123#103×C109—21no—
124#103×C109—21no—
125#102×C109—21no—
126#102×C109—21no—
127#102×C109—21no—
128#102×C109—21no—
129#102×C109—21no—
130#102×C109—21no—
131#102×C109—21no—
132C22⋊C8×C109—21no—
133C22⋊C8×C109—21no—
134C22⋊C8×C109—21no—
135C22⋊C8×C109—21no—
136#97×C109—21no—
137#97×C109—21no—
138#97×C109—21no—
139#97×C109D411yescharacteristic
140#97×C109D411yescharacteristic
141C4×C8×C109—21no—
142C4×C8×C109C2311yescharacteristic
143C4×C8×C109C2311yescharacteristic
144#41×C109—22no—
145#41×C109—41no—
146#41×C109—82no—
147C2×Q8×C109—21no—
148C2×Q8×C109—21no—
149C2×Q8×C109—21no—
150C2×Q8×C109C2×D411yescharacteristic
151C2×D4×C109—21no—
152C2×D4×C109—21no—
153C2×D4×C109—21no—
154C2×D4×C109—21no—
155C2×D4×C109—41no—
156C2×D4×C109C2×D411yescharacteristic
157C22×C4×C109—21no—
158C22×C4×C109—21no—
159C22×C4×C109—21no—
160C22×C4×C109—41no—
161C22×C4×C109C2×D411yescharacteristic
162C22×C4×C109C2×D411yescharacteristic
163C22×C4×C109#4111yescharacteristic
164SD16×C109—42no—
165SD16×C109—42no—
166SD16×C109—42no—
167D8×C109—42no—
168M16×C109—22no—
169M16×C109—41no—
170C2×C8×C109—21no—
171C2×C8×C109—21no—
172C2×C8×C109—21no—
173C2×C8×C109—21no—
174C2×C8×C109—21no—
175C2×C8×C109—21no—
176C2×C8×C109—42no—
177C2×C8×C109—42no—
178C2×C8×C109—42no—
179C2×C8×C109C2×D411yescharacteristic
180C2×C8×C109C2×D411yescharacteristic
181C2×C8×C109C2×D411yescharacteristic
182C2×C8×C109C2×D411yescharacteristic
183C4⋊C4×C109—21no—
184C4⋊C4×C109—21no—
185C4⋊C4×C109—21no—
186C4⋊C4×C109—21no—
187C4⋊C4×C109—21no—
188C4⋊C4×C109—21no—
189C4⋊C4×C109—21no—
190C4⋊C4×C109—21no—
191C4⋊C4×C109—41no—
192C4⋊C4×C109—41no—
193C4⋊C4×C109C2×D411yescharacteristic
194C4⋊C4×C109C2×D411yescharacteristic
195C22⋊C4×C109—21no—
196C22⋊C4×C109—21no—
197C22⋊C4×C109—21no—
198C22⋊C4×C109—41no—
199C22⋊C4×C109—41no—
200C22⋊C4×C109—41no—
201C42×C109—21no—
202C42×C109—21no—
203C42×C109—21no—
204C42×C109—41no—
205C42×C109C2×D411yescharacteristic
206C42×C109C2×D411yescharacteristic
207C42×C109#4111yescharacteristic
208C42×C109C2411yescharacteristic
209C23×C109—21no—
210C23×C109—41no—
211C23×C109#12111yescharacteristic
212Q8×C109—21no—
213Q8×C109—21no—
214Q8×C109—41no—
215Q8×C109—41no—
216Q8×C109—81no—
217Q8×C109—81no—
218D4×C109—21no—
219D4×C109—42no—
220D4×C109—41no—
221D4×C109—41no—
222D4×C109—41no—
223D4×C109—41no—
224D4×C109—81no—
225D4×C109—82no—
226D4×C109#13712yes—
227C2×C4×C109—21no—
228C2×C4×C109—21no—
229C2×C4×C109—21no—
230C2×C4×C109—21no—
231C2×C4×C109—21no—
232C2×C4×C109—21no—
233C2×C4×C109—21no—
234C2×C4×C109—41no—
235C2×C4×C109—42no—
236C2×C4×C109—41no—
237C2×C4×C109—41no—
238C2×C4×C109—41no—
239C2×C4×C109—41no—
240C2×C4×C109—41no—
241C2×C4×C109—81no—
242C2×C4×C109—82no—
243C2×C4×C109#12111yescharacteristic
244C2×C4×C109#12111yescharacteristic
245C2×C4×C109#12111yescharacteristic
246C2×C4×C109C22×D411yescharacteristic
247C2×C4×C109C22×D411yescharacteristic
248C2×C4×C109C2×#4111yescharacteristic
249C8×C109—21no—
250C8×C109—21no—
251C8×C109—21no—
252C8×C109—41no—
253C8×C109—41no—
254C8×C109—41no—
255C8×C109—41no—
256C8×C109—41no—
257C8×C109—41no—
258C8×C109#13512yes—
259C22×C109—21no—
260C22×C109—21no—
261C22×C109—22no—
262C22×C109—21no—
263C22×C109—41no—
264C22×C109—41no—
265C22×C109—81no—
266C22×C109—81no—
267C22×C109—81no—
268C22×C109C2×#12111yescharacteristic
269C4×C109—21no—
270C4×C109—21no—
271C4×C109—21no—
272C4×C109—21no—
273C4×C109—41no—
274C4×C109—41no—
275C4×C109—41no—
276C4×C109—81no—
277C4×C109—81no—
278C4×C109—81no—
279C4×C109C2×#13511yescharacteristic
280C4×C109C2×#13711yescharacteristic
281C4×C109#57511yescharacteristic
282C4×C109#57511yescharacteristic
283#19179C10911yesmaximal, characteristic, direct product factor, Sylow
284C2×C109—41no—
285C2×C109—42no—
286C2×C109—161no—
287C2×C109#303511yescharacteristic
288C2×C109#305611yescharacteristic
289C2×C109#306811yescharacteristic
290#3182C2×C10911yescharacteristic, complemented
291#3106C2×C10911yescharacteristic
292#3076C2×C10911yescharacteristic, complemented
293#2970C2×C10911yescharacteristic, complemented
294#1704C2×C10911yescharacteristic, complemented
295#1698C2×C10911yescharacteristic, complemented
296#1696C2×C10911yescharacteristic, complemented
297#1686C2×C10911yescharacteristic, complemented
298#1683C2×C10911yescharacteristic, complemented
299#1677C2×C10911yescharacteristic, complemented
300#1675C2×C10911yescharacteristic, complemented
301#1665C2×C10911yescharacteristic, complemented
302#1565C2×C10911yescharacteristic, complemented
303#1554C2×C10911yescharacteristic, complemented
304#1551C2×C10911yescharacteristic, complemented
305C109#1917911yescharacteristic, direct product factor, Sylow
306#533C22×C10911yescharacteristic
307#532C22×C10911yescharacteristic
308C4×#41C22×C10911yescharacteristic
309#500C22×C10911yescharacteristic
310#492C22×C10911yescharacteristic
311#487C22×C10911yescharacteristic
312#486C22×C10911yescharacteristic
313#482—21no—
314#479—21no—
315#478—21no—
316#477C22×C10911yescharacteristic
317#477C22×C10911yescharacteristic
318#476C22×C10911yescharacteristic
319#476C22×C10911yescharacteristic
320#475C22×C10911yescharacteristic
321#474C22×C10911yescharacteristic
322#468—21no—
323#468—21no—
324#460C22×C10911yescharacteristic
325#459C22×C10911yescharacteristic
326#449—21no—
327#446C22×C10911yescharacteristic
328#446C22×C10911yescharacteristic
329#440—21no—
330#440—21no—
331C4×SD16—21no—
332C4×D8—21no—
333#435—21no—
334#435—21no—
335C8×D4C22×C10911yescharacteristic
336C8×D4C22×C10911yescharacteristic
337#432—21no—
338#432C22×C10911yescharacteristic
339#431C22×C10911yescharacteristic
340#427—21no—
341C2×C4⋊C8C22×C10911yescharacteristic
342#416—21no—
343C4×M16C22×C10911yescharacteristic
344C2×#97—21no—
345#335C22×C10911yescharacteristic
346#335C22×C10911yescharacteristic
347#334C22×C10911yescharacteristic
348#334C22×C10911yescharacteristic
349#333C22×C10911yescharacteristic
350#333C22×C10911yescharacteristic
351#333C22×C10911yescharacteristic
352#333C22×C10911yescharacteristic
353#332C22×C10911yescharacteristic
354#332C22×C10911yescharacteristic
355#331C22×C10911yescharacteristic
356#331C22×C10911yescharacteristic
357C2×#41—21no—
358C2×#41D4×C10911yescharacteristic
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×D8—21no—
363C2×M16D4×C10911yescharacteristic
364C2×M16D4×C10911yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C4⋊Q8C23×C10911yescharacteristic
369C4⋊Q8C23×C10911yescharacteristic
370C4⋊Q8C23×C10911yescharacteristic
371#127C23×C10911yescharacteristic
372#125—21no—
373#124—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8D4×C10911yescharacteristic
381C4×Q8C23×C10911yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4D4×C10911yescharacteristic
387C4×D4C23×C10911yescharacteristic
388#117—21no—
389#117—21no—
390#117D4×C10911yescharacteristic
391C2×C42—21no—
392C2×C42C23×C10911yescharacteristic
393#107—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8C23×C10911yescharacteristic
405C4⋊C8C23×C10911yescharacteristic
406C4⋊C8C23×C10911yescharacteristic
407C4⋊C8C23×C10911yescharacteristic
408C4⋊C8C23×C10911yescharacteristic
409C4⋊C8C23×C10911yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427#97—21no—
428#97—21no—
429#97D4×C10911yescharacteristic
430#97D4×C10911yescharacteristic
431C4×C8—21no—
432C4×C8C23×C10911yescharacteristic
433C4×C8C23×C10911yescharacteristic
434#41—22no—
435#41—41no—
436#41—82no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×D4×C10911yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4C2×D4×C10911yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C10911yescharacteristic
452C22×C4C2×D4×C10911yescharacteristic
453C22×C4#41×C10911yescharacteristic
454SD16—42no—
455SD16—42no—
456SD16—42no—
457D8—42no—
458M16—22no—
459M16—41no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—42no—
467C2×C8—42no—
468C2×C8—42no—
469C2×C8C2×D4×C10911yescharacteristic
470C2×C8C2×D4×C10911yescharacteristic
471C2×C8C2×D4×C10911yescharacteristic
472C2×C8C2×D4×C10911yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4C2×D4×C10911yescharacteristic
484C4⋊C4C2×D4×C10911yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—41no—
495C42C2×D4×C10911yescharacteristic
496C42C2×D4×C10911yescharacteristic
497C42#41×C10911yescharacteristic
498C42C24×C10911yescharacteristic
499C23—21no—
500C23—41no—
501C23#121×C10911yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—81no—
508D4—21no—
509D4—42no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—82no—
516D4#137×C10912yes—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—82no—
533C2×C4#121×C10911yescharacteristic
534C2×C4#121×C10911yescharacteristic
535C2×C4#121×C10911yescharacteristic
536C2×C4C22×D4×C10911yescharacteristic
537C2×C4C22×D4×C10911yescharacteristic
538C2×C4C2×#41×C10911yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8#135×C10912yes—
549C22—21no—
550C22—21no—
551C22—22no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22C2×#121×C10911yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C2×#135×C10911yescharacteristic
570C4C2×#137×C10911yescharacteristic
571C4#575×C10911yescharacteristic
572C4#575×C10911yescharacteristic
573C2—41no—
574C2—42no—
575C2—161no—
576C2C109×#303511yescharacteristic
577C2C109×#305611yescharacteristic
578C2C109×#306811yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radicalC109×#3106C2
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
1. C109×#3182C2semidirect
3. C109×#3076C2semidirect
4. C109×#2970C2semidirect
5. C109×#1704C2semidirect
6. C109×#1698C2semidirect
7. C109×#1696C2semidirect
8. C109×#1686C2semidirect
9. C109×#1683C2semidirect
10. C109×#1677C2semidirect
11. C109×#1675C2semidirect
12. C109×#1665C2semidirect
13. C109×#1565C2semidirect
14. C109×#1554C2semidirect
15. C109×#1551C2semidirect
283. #19179C109direct (N × H)
290. #3182C2×C109semidirect
292. #3076C2×C109semidirect
293. #2970C2×C109semidirect
294. #1704C2×C109semidirect
295. #1698C2×C109semidirect
296. #1696C2×C109semidirect
297. #1686C2×C109semidirect
298. #1683C2×C109semidirect
299. #1677C2×C109semidirect
300. #1675C2×C109semidirect
301. #1665C2×C109semidirect
302. #1565C2×C109semidirect
303. #1554C2×C109semidirect
304. #1551C2×C109semidirect
305. C109#19179direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#31822
C109×#31062
C109×#30762
C109×#29702
C109×#17042
C109×#16982
C109×#16962
C109×#16862
C109×#16832
C109×#16772
C109×#16752
C109×#16652
C109×#15652
C109×#15542
C109×#15512
#19179109