Finite Group Databasebeta

← C109×#19369 #42137363

Subgroups — C109×#19369 #42137363

Order 27904.

644 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3253C211yesmaximal, characteristic
2C109×#3235C211yesmaximal, characteristic, complemented
3C109×#3182C211yesmaximal, characteristic, complemented
4C109×#2935C211yesmaximal, characteristic, complemented
5C109×#1703C211yesmaximal, characteristic, complemented
6C109×#1697C211yesmaximal, characteristic, complemented
7C109×#1695C211yesmaximal, characteristic, complemented
8C109×#1685C211yesmaximal, characteristic, complemented
9C109×#1683C211yesmaximal, characteristic, complemented
10C109×#1677C211yesmaximal, characteristic, complemented
11C109×#1675C211yesmaximal, characteristic, complemented
12C109×#1665C211yesmaximal, characteristic, complemented
13C109×#1569C211yesmaximal, characteristic, complemented
14C109×#1551C211yesmaximal, characteristic, complemented
15C109×#1550C211yesmaximal, characteristic, complemented
16C2×#131×C109—21no—
17#533×C109C2211yescharacteristic
18#532×C109C2211yescharacteristic
19#532×C109C2211yescharacteristic
20#501×C109—21no—
21#500×C109C2211yescharacteristic
22#492×C109C2211yescharacteristic
23#490×C109—21no—
24#487×C109C2211yescharacteristic
25#486×C109C2211yescharacteristic
26#482×C109—21no—
27#482×C109—21no—
28#476×C109—21no—
29#476×C109C2211yescharacteristic
30#476×C109C2211yescharacteristic
31#476×C109C2211yescharacteristic
32#476×C109C2211yescharacteristic
33#474×C109C2211yescharacteristic
34#474×C109C2211yescharacteristic
35#469×C109—21no—
36#469×C109—21no—
37#468×C109—21no—
38#468×C109—21no—
39#459×C109—21no—
40#459×C109C2211yescharacteristic
41#459×C109C2211yescharacteristic
42#440×C109—21no—
43#440×C109—21no—
44#436×C109C2211yescharacteristic
45#436×C109C2211yescharacteristic
46#435×C109—21no—
47#435×C109—21no—
48C8×D4×C109C2211yescharacteristic
49C8×D4×C109C2211yescharacteristic
50#432×C109C2211yescharacteristic
51#423×C109C2211yescharacteristic
52C2×C4⋊C8×C109C2211yescharacteristic
53#408×C109—21no—
54C4×M16×C109C2211yescharacteristic
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×C109—21no—
69C2×SD16×C109—21no—
70C2×SD16×C109—21no—
71C2×D8×C109—21no—
72C2×D8×C109—21no—
73#131×C109—44no—
74C2×M16×C109—21no—
75C2×M16×C109—21no—
76C2×M16×C109—21no—
77C2×M16×C109D411yescharacteristic
78C2×M16×C109D411yescharacteristic
79C22×C8×C109—21no—
80C22×C8×C109—21no—
81C22×C8×C109—21no—
82C4⋊Q8×C109D411yescharacteristic
83C4⋊Q8×C109C2311yescharacteristic
84C4⋊Q8×C109C2311yescharacteristic
85C4⋊Q8×C109C2311yescharacteristic
86#127×C109D411yescharacteristic
87#127×C109C2311yescharacteristic
88#125×C109—21no—
89#124×C109—21no—
90#124×C109—21no—
91C22⋊Q8×C109—21no—
92C22⋊Q8×C109—21no—
93#121×C109—21no—
94#121×C109—21no—
95#121×C109—21no—
96#121×C109D411yescharacteristic
97#121×C109D411yescharacteristic
98C4×Q8×C109—21no—
99C4×Q8×C109—21no—
100C4×D4×C109—21no—
101C4×D4×C109—21no—
102C4×D4×C109—21no—
103C4×D4×C109C2311yescharacteristic
104C4×D4×C109C2311yescharacteristic
105#117×C109—21no—
106C2×C42×C109C2311yescharacteristic
107#107×C109—21no—
108#107×C109—21no—
109#107×C109—21no—
110#107×C109—21no—
111#106×C109—21no—
112#106×C109—21no—
113#106×C109—21no—
114#106×C109—21no—
115C4⋊C8×C109—21no—
116C4⋊C8×C109—21no—
117C4⋊C8×C109C2311yescharacteristic
118C4⋊C8×C109C2311yescharacteristic
119C4⋊C8×C109C2311yescharacteristic
120C4⋊C8×C109C2311yescharacteristic
121C4⋊C8×C109C2311yescharacteristic
122C4⋊C8×C109C2311yescharacteristic
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—
132#102×C109—21no—
133#102×C109—21no—
134#102×C109—21no—
135C22⋊C8×C109—21no—
136C22⋊C8×C109—21no—
137C22⋊C8×C109—21no—
138C22⋊C8×C109—21no—
139C22⋊C8×C109—21no—
140#97×C109—21no—
141#97×C109D411yescharacteristic
142#97×C109D411yescharacteristic
143C4×C8×C109C2311yescharacteristic
144C4×C8×C109C2311yescharacteristic
145#41×C109—42no—
146#41×C109—42no—
147#41×C109—82no—
148C2×Q8×C109—21no—
149C2×Q8×C109—21no—
150C2×Q8×C109—21no—
151C2×Q8×C109—21no—
152C2×D4×C109—21no—
153C2×D4×C109—21no—
154C2×D4×C109—21no—
155C2×D4×C109—21no—
156C2×D4×C109—21no—
157C2×D4×C109—21no—
158C2×D4×C109—21no—
159C2×D4×C109—41no—
160C2×D4×C109C2×D411yescharacteristic
161C2×D4×C109C2×D411yescharacteristic
162C22×C4×C109—21no—
163C22×C4×C109—21no—
164C22×C4×C109—41no—
165C22×C4×C109C2×D411yescharacteristic
166C22×C4×C109C2×D411yescharacteristic
167C22×C4×C109#4111yescharacteristic
168SD16×C109—42no—
169SD16×C109—42no—
170D8×C109—81no—
171D8×C109—81no—
172M16×C109—22no—
173M16×C109—41no—
174M16×C109—42no—
175M16×C109—42no—
176M16×C109—81no—
177C2×C8×C109—21no—
178C2×C8×C109—21no—
179C2×C8×C109—21no—
180C2×C8×C109—21no—
181C2×C8×C109—21no—
182C2×C8×C109—21no—
183C2×C8×C109—42no—
184C2×C8×C109—42no—
185C2×C8×C109—42no—
186C2×C8×C109C2×D411yescharacteristic
187C2×C8×C109C2×D411yescharacteristic
188C2×C8×C109C2×D411yescharacteristic
189C2×C8×C109C2×D411yescharacteristic
190C4⋊C4×C109—21no—
191C4⋊C4×C109—21no—
192C4⋊C4×C109—21no—
193C4⋊C4×C109—21no—
194C4⋊C4×C109—21no—
195C4⋊C4×C109—21no—
196C4⋊C4×C109—21no—
197C4⋊C4×C109—41no—
198C4⋊C4×C109—41no—
199C4⋊C4×C109C2×D411yescharacteristic
200C4⋊C4×C109C2×D411yescharacteristic
201C22⋊C4×C109—21no—
202C22⋊C4×C109—21no—
203C22⋊C4×C109—21no—
204C22⋊C4×C109—21no—
205C22⋊C4×C109—41no—
206C22⋊C4×C109—41no—
207C22⋊C4×C109—41no—
208C42×C109—41no—
209C42×C109C2×D411yescharacteristic
210C42×C109C2×D411yescharacteristic
211C42×C109#4111yescharacteristic
212C42×C109C2411yescharacteristic
213C23×C109—21no—
214C23×C109—21no—
215C23×C109—41no—
216C23×C109#12111yescharacteristic
217Q8×C109—42no—
218Q8×C109—41no—
219Q8×C109—41no—
220Q8×C109—81no—
221Q8×C109—81no—
222D4×C109—21no—
223D4×C109—21no—
224D4×C109—21no—
225D4×C109—21no—
226D4×C109—42no—
227D4×C109—42no—
228D4×C109—42no—
229D4×C109—41no—
230D4×C109—41no—
231D4×C109—41no—
232D4×C109—41no—
233D4×C109—81no—
234D4×C109—81no—
235D4×C109—82no—
236C2×C4×C109—21no—
237C2×C4×C109—21no—
238C2×C4×C109—21no—
239C2×C4×C109—21no—
240C2×C4×C109—21no—
241C2×C4×C109—21no—
242C2×C4×C109—41no—
243C2×C4×C109—41no—
244C2×C4×C109—41no—
245C2×C4×C109—41no—
246C2×C4×C109—41no—
247C2×C4×C109—41no—
248C2×C4×C109—41no—
249C2×C4×C109—41no—
250C2×C4×C109—82no—
251C2×C4×C109#12111yescharacteristic
252C2×C4×C109#12111yescharacteristic
253C2×C4×C109#12111yescharacteristic
254C2×C4×C109C22×D411yescharacteristic
255C2×C4×C109C22×D411yescharacteristic
256C2×C4×C109C2×#4111yescharacteristic
257C8×C109—21no—
258C8×C109—21no—
259C8×C109—21no—
260C8×C109—41no—
261C8×C109—41no—
262C8×C109—41no—
263C8×C109—41no—
264C8×C109—41no—
265C8×C109—41no—
266C8×C109AGL(1,ℤ/8)12yes—
267C22×C109—21no—
268C22×C109—21no—
269C22×C109—21no—
270C22×C109—41no—
271C22×C109—41no—
272C22×C109—41no—
273C22×C109—41no—
274C22×C109—41no—
275C22×C109—41no—
276C22×C109—81no—
277C22×C109—81no—
278C22×C109—81no—
279C22×C109C2×#12111yescharacteristic
280C4×C109—21no—
281C4×C109—21no—
282C4×C109—21no—
283C4×C109—21no—
284C4×C109—41no—
285C4×C109—41no—
286C4×C109—81no—
287C4×C109—81no—
288C4×C109—81no—
289C4×C109C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C109#57511yescharacteristic
291C4×C109#57711yescharacteristic
292C4×C109#57811yescharacteristic
293#19369C10911yesmaximal, characteristic, direct product factor, Sylow
294C2×C109—41no—
295C2×C109—81no—
296C2×C109—81no—
297C2×C109—161no—
298C2×C109#303611yescharacteristic
299C2×C109#306311yescharacteristic
300C2×C109#306811yescharacteristic
301#3253C2×C10911yescharacteristic
302#3235C2×C10911yescharacteristic, complemented
303#3182C2×C10911yescharacteristic, complemented
304#2935C2×C10911yescharacteristic, complemented
305#1703C2×C10911yescharacteristic, complemented
306#1697C2×C10911yescharacteristic, complemented
307#1695C2×C10911yescharacteristic, complemented
308#1685C2×C10911yescharacteristic, complemented
309#1683C2×C10911yescharacteristic, complemented
310#1677C2×C10911yescharacteristic, complemented
311#1675C2×C10911yescharacteristic, complemented
312#1665C2×C10911yescharacteristic, complemented
313#1569C2×C10911yescharacteristic, complemented
314#1551C2×C10911yescharacteristic, complemented
315#1550C2×C10911yescharacteristic, complemented
316C109#1936911yescharacteristic, direct product factor, Sylow
317C2×#131—21no—
318#533C22×C10911yescharacteristic
319#532C22×C10911yescharacteristic
320#532C22×C10911yescharacteristic
321#501—21no—
322#500C22×C10911yescharacteristic
323#492C22×C10911yescharacteristic
324#490—21no—
325#487C22×C10911yescharacteristic
326#486C22×C10911yescharacteristic
327#482—21no—
328#482—21no—
329#476—21no—
330#476C22×C10911yescharacteristic
331#476C22×C10911yescharacteristic
332#476C22×C10911yescharacteristic
333#476C22×C10911yescharacteristic
334#474C22×C10911yescharacteristic
335#474C22×C10911yescharacteristic
336#469—21no—
337#469—21no—
338#468—21no—
339#468—21no—
340#459—21no—
341#459C22×C10911yescharacteristic
342#459C22×C10911yescharacteristic
343#440—21no—
344#440—21no—
345#436C22×C10911yescharacteristic
346#436C22×C10911yescharacteristic
347#435—21no—
348#435—21no—
349C8×D4C22×C10911yescharacteristic
350C8×D4C22×C10911yescharacteristic
351#432C22×C10911yescharacteristic
352#423C22×C10911yescharacteristic
353C2×C4⋊C8C22×C10911yescharacteristic
354#408—21no—
355C4×M16C22×C10911yescharacteristic
356#335C22×C10911yescharacteristic
357#335C22×C10911yescharacteristic
358#334C22×C10911yescharacteristic
359#334C22×C10911yescharacteristic
360#333C22×C10911yescharacteristic
361#333C22×C10911yescharacteristic
362#333C22×C10911yescharacteristic
363#333C22×C10911yescharacteristic
364#332C22×C10911yescharacteristic
365#332C22×C10911yescharacteristic
366#331C22×C10911yescharacteristic
367#331C22×C10911yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×D8—21no—
373C2×D8—21no—
374#131—44no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16D4×C10911yescharacteristic
379C2×M16D4×C10911yescharacteristic
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8D4×C10911yescharacteristic
384C4⋊Q8C23×C10911yescharacteristic
385C4⋊Q8C23×C10911yescharacteristic
386C4⋊Q8C23×C10911yescharacteristic
387#127D4×C10911yescharacteristic
388#127C23×C10911yescharacteristic
389#125—21no—
390#124—21no—
391#124—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121D4×C10911yescharacteristic
398#121D4×C10911yescharacteristic
399C4×Q8—21no—
400C4×Q8—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C23×C10911yescharacteristic
405C4×D4C23×C10911yescharacteristic
406#117—21no—
407C2×C42C23×C10911yescharacteristic
408#107—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C10911yescharacteristic
419C4⋊C8C23×C10911yescharacteristic
420C4⋊C8C23×C10911yescharacteristic
421C4⋊C8C23×C10911yescharacteristic
422C4⋊C8C23×C10911yescharacteristic
423C4⋊C8C23×C10911yescharacteristic
424#103—21no—
425#103—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441#97—21no—
442#97D4×C10911yescharacteristic
443#97D4×C10911yescharacteristic
444C4×C8C23×C10911yescharacteristic
445C4×C8C23×C10911yescharacteristic
446#41—42no—
447#41—42no—
448#41—82no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4C2×D4×C10911yescharacteristic
462C2×D4C2×D4×C10911yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×D4×C10911yescharacteristic
467C22×C4C2×D4×C10911yescharacteristic
468C22×C4#41×C10911yescharacteristic
469SD16—42no—
470SD16—42no—
471D8—81no—
472D8—81no—
473M16—22no—
474M16—41no—
475M16—42no—
476M16—42no—
477M16—81no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8C2×D4×C10911yescharacteristic
488C2×C8C2×D4×C10911yescharacteristic
489C2×C8C2×D4×C10911yescharacteristic
490C2×C8C2×D4×C10911yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C10911yescharacteristic
501C4⋊C4C2×D4×C10911yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—41no—
510C42C2×D4×C10911yescharacteristic
511C42C2×D4×C10911yescharacteristic
512C42#41×C10911yescharacteristic
513C42C24×C10911yescharacteristic
514C23—21no—
515C23—21no—
516C23—41no—
517C23#121×C10911yescharacteristic
518Q8—42no—
519Q8—41no—
520Q8—41no—
521Q8—81no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—81no—
535D4—81no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4#121×C10911yescharacteristic
553C2×C4#121×C10911yescharacteristic
554C2×C4#121×C10911yescharacteristic
555C2×C4C22×D4×C10911yescharacteristic
556C2×C4C22×D4×C10911yescharacteristic
557C2×C4C2×#41×C10911yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8AGL(1,ℤ/8)×C10912yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C10911yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4C2×AGL(1,ℤ/8)×C10911yescharacteristic
591C4#575×C10911yescharacteristic
592C4#577×C10911yescharacteristic
593C4#578×C10911yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—161no—
598C2C109×#303611yescharacteristic
599C2C109×#306311yescharacteristic
600C2C109×#306811yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radicalC109×#3253C2
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
2. C109×#3235C2semidirect
3. C109×#3182C2semidirect
4. C109×#2935C2semidirect
5. C109×#1703C2semidirect
6. C109×#1697C2semidirect
7. C109×#1695C2semidirect
8. C109×#1685C2semidirect
9. C109×#1683C2semidirect
10. C109×#1677C2semidirect
11. C109×#1675C2semidirect
12. C109×#1665C2semidirect
13. C109×#1569C2semidirect
14. C109×#1551C2semidirect
15. C109×#1550C2semidirect
293. #19369C109direct (N × H)
302. #3235C2×C109semidirect
303. #3182C2×C109semidirect
304. #2935C2×C109semidirect
305. #1703C2×C109semidirect
306. #1697C2×C109semidirect
307. #1695C2×C109semidirect
308. #1685C2×C109semidirect
309. #1683C2×C109semidirect
310. #1677C2×C109semidirect
311. #1675C2×C109semidirect
312. #1665C2×C109semidirect
313. #1569C2×C109semidirect
314. #1551C2×C109semidirect
315. #1550C2×C109semidirect
316. C109#19369direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#32532
C109×#32352
C109×#31822
C109×#29352
C109×#17032
C109×#16972
C109×#16952
C109×#16852
C109×#16832
C109×#16772
C109×#16752
C109×#16652
C109×#15692
C109×#15512
C109×#15502
#19369109