Finite Group Databasebeta

← C109×#19178 #42137172

Subgroups — C109×#19178 #42137172

Order 27904.

648 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3182C211yesmaximal, characteristic, complemented
2C109×#3107C211yesmaximal, characteristic, complemented
3C109×#3035C211yesmaximal, characteristic
4C109×#2970C211yesmaximal, characteristic, complemented
5C109×#1702C211yesmaximal, characteristic, complemented
6C109×#1700C211yesmaximal, characteristic, complemented
7C109×#1694C211yesmaximal, characteristic, complemented
8C109×#1686C211yesmaximal, characteristic, complemented
9C109×#1681C211yesmaximal, characteristic, complemented
10C109×#1679C211yesmaximal, characteristic, complemented
11C109×#1673C211yesmaximal, characteristic, complemented
12C109×#1665C211yesmaximal, characteristic, complemented
13C109×#1565C211yesmaximal, characteristic, complemented
14C109×#1553C211yesmaximal, characteristic, complemented
15C109×#1552C211yesmaximal, characteristic, complemented
16C2×#135×C109—21no—
17#533×C109C2211yescharacteristic
18#532×C109C2211yescharacteristic
19C4×#41×C109C2211yescharacteristic
20#500×C109C2211yescharacteristic
21#492×C109C2211yescharacteristic
22#487×C109C2211yescharacteristic
23#486×C109C2211yescharacteristic
24#485×C109—21no—
25#475×C109C2211yescharacteristic
26#474×C109C2211yescharacteristic
27#468×C109—21no—
28#468×C109—21no—
29#464×C109—21no—
30#463×C109—21no—
31#462×C109C2211yescharacteristic
32#462×C109C2211yescharacteristic
33#461×C109C2211yescharacteristic
34#461×C109C2211yescharacteristic
35#460×C109C2211yescharacteristic
36#459×C109C2211yescharacteristic
37#452×C109—21no—
38#446×C109C2211yescharacteristic
39#446×C109C2211yescharacteristic
40#440×C109—21no—
41#440×C109—21no—
42C4×Q16×C109—21no—
43C4×SD16×C109—21no—
44#435×C109—21no—
45#435×C109—21no—
46C8×D4×C109C2211yescharacteristic
47C8×D4×C109C2211yescharacteristic
48#432×C109—21no—
49#432×C109C2211yescharacteristic
50#431×C109C2211yescharacteristic
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#332×C109C2211yescharacteristic
60#332×C109C2211yescharacteristic
61#332×C109C2211yescharacteristic
62#332×C109C2211yescharacteristic
63#332×C109C2211yescharacteristic
64#332×C109C2211yescharacteristic
65#331×C109C2211yescharacteristic
66#331×C109C2211yescharacteristic
67C2×#41×C109—21no—
68C2×#41×C109D411yescharacteristic
69#135×C109—44no—
70C2×Q16×C109—21no—
71C2×Q16×C109—21no—
72C2×SD16×C109—21no—
73C2×SD16×C109—21no—
74C2×SD16×C109—21no—
75C2×SD16×C109—21no—
76C2×SD16×C109—21no—
77C2×D8×C109—21no—
78C2×M16×C109D411yescharacteristic
79C2×M16×C109D411yescharacteristic
80C22×C8×C109—21no—
81C22×C8×C109—21no—
82C22×C8×C109—21no—
83C4⋊Q8×C109C2311yescharacteristic
84C4⋊Q8×C109C2311yescharacteristic
85C4⋊Q8×C109C2311yescharacteristic
86#127×C109C2311yescharacteristic
87#125×C109—21no—
88#124×C109—21no—
89C22⋊Q8×C109—21no—
90C22⋊Q8×C109—21no—
91#121×C109—21no—
92#121×C109—21no—
93C4×Q8×C109—21no—
94C4×Q8×C109—21no—
95C4×Q8×C109D411yescharacteristic
96C4×Q8×C109C2311yescharacteristic
97C4×D4×C109—21no—
98C4×D4×C109—21no—
99C4×D4×C109—21no—
100C4×D4×C109—21no—
101C4×D4×C109D411yescharacteristic
102C4×D4×C109C2311yescharacteristic
103#117×C109—21no—
104#117×C109—21no—
105#117×C109D411yescharacteristic
106C2×C42×C109—21no—
107C2×C42×C109C2311yescharacteristic
108#107×C109—21no—
109#107×C109—21no—
110#107×C109—21no—
111#106×C109—21no—
112C4⋊C8×C109—21no—
113C4⋊C8×C109—21no—
114C4⋊C8×C109—21no—
115C4⋊C8×C109C2311yescharacteristic
116C4⋊C8×C109C2311yescharacteristic
117C4⋊C8×C109C2311yescharacteristic
118C4⋊C8×C109C2311yescharacteristic
119C4⋊C8×C109C2311yescharacteristic
120C4⋊C8×C109C2311yescharacteristic
121#103×C109—21no—
122#103×C109—21no—
123#103×C109—21no—
124#103×C109—21no—
125#103×C109—21no—
126#103×C109—21no—
127#103×C109—21no—
128#102×C109—21no—
129#102×C109—21no—
130#102×C109—21no—
131#102×C109—21no—
132#102×C109—21no—
133C22⋊C8×C109—21no—
134C22⋊C8×C109—21no—
135C22⋊C8×C109—21no—
136C22⋊C8×C109—21no—
137#97×C109—21no—
138#97×C109—21no—
139#97×C109—21no—
140#97×C109D411yescharacteristic
141#97×C109D411yescharacteristic
142C4×C8×C109—21no—
143C4×C8×C109C2311yescharacteristic
144C4×C8×C109C2311yescharacteristic
145#41×C109—22no—
146#41×C109—41no—
147#41×C109—42no—
148#41×C109—42no—
149C2×Q8×C109—21no—
150C2×Q8×C109—21no—
151C2×Q8×C109—21no—
152C2×Q8×C109C2×D411yescharacteristic
153C2×D4×C109—21no—
154C2×D4×C109—21no—
155C2×D4×C109—21no—
156C2×D4×C109—21no—
157C2×D4×C109—41no—
158C2×D4×C109C2×D411yescharacteristic
159C22×C4×C109—21no—
160C22×C4×C109—21no—
161C22×C4×C109—21no—
162C22×C4×C109—41no—
163C22×C4×C109C2×D411yescharacteristic
164C22×C4×C109C2×D411yescharacteristic
165C22×C4×C109#4111yescharacteristic
166Q16×C109—42no—
167Q16×C109—42no—
168SD16×C109—42no—
169SD16×C109—42no—
170SD16×C109—42no—
171SD16×C109—42no—
172SD16×C109—42no—
173D8×C109—42no—
174M16×C109—22no—
175M16×C109—41no—
176C2×C8×C109—21no—
177C2×C8×C109—21no—
178C2×C8×C109—21no—
179C2×C8×C109—21no—
180C2×C8×C109—21no—
181C2×C8×C109—21no—
182C2×C8×C109—42no—
183C2×C8×C109—42no—
184C2×C8×C109—42no—
185C2×C8×C109C2×D411yescharacteristic
186C2×C8×C109C2×D411yescharacteristic
187C2×C8×C109C2×D411yescharacteristic
188C2×C8×C109C2×D411yescharacteristic
189C4⋊C4×C109—21no—
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—41no—
205C22⋊C4×C109—41no—
206C22⋊C4×C109—41no—
207C42×C109—21no—
208C42×C109—21no—
209C42×C109—21no—
210C42×C109—41no—
211C42×C109C2×D411yescharacteristic
212C42×C109C2×D411yescharacteristic
213C42×C109#4111yescharacteristic
214C42×C109C2411yescharacteristic
215C23×C109—21no—
216C23×C109—41no—
217C23×C109#12111yescharacteristic
218Q8×C109—21no—
219Q8×C109—21no—
220Q8×C109—41no—
221Q8×C109—41no—
222Q8×C109—41no—
223Q8×C109—41no—
224Q8×C109—41no—
225Q8×C109—41no—
226D4×C109—21no—
227D4×C109—42no—
228D4×C109—41no—
229D4×C109—41no—
230D4×C109—41no—
231D4×C109—41no—
232D4×C109—81no—
233D4×C109—82no—
234D4×C109AGL(1,ℤ/8)12yes—
235C2×C4×C109—21no—
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—42no—
244C2×C4×C109—41no—
245C2×C4×C109—41no—
246C2×C4×C109—41no—
247C2×C4×C109—41no—
248C2×C4×C109—41no—
249C2×C4×C109—81no—
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×C109#13512yescomplemented
267C22×C109—21no—
268C22×C109—21no—
269C22×C109—22no—
270C22×C109—21no—
271C22×C109—41no—
272C22×C109—41no—
273C22×C109—81no—
274C22×C109—81no—
275C22×C109—81no—
276C22×C109C2×#12111yescharacteristic
277C4×C109—21no—
278C4×C109—21no—
279C4×C109—21no—
280C4×C109—21no—
281C4×C109—41no—
282C4×C109—41no—
283C4×C109—41no—
284C4×C109—81no—
285C4×C109—81no—
286C4×C109—81no—
287C4×C109C2×#13511yescharacteristic
288C4×C109C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C109#57511yescharacteristic
290C4×C109#57511yescharacteristic
291#19178C10911yesmaximal, characteristic, direct product factor, Sylow
292C2×C109—41no—
293C2×C109—42no—
294C2×C109—161no—
295C2×C109#303511yescharacteristic
296C2×C109#305511yescharacteristic
297C2×C109#306911yescharacteristic
298#3182C2×C10911yescharacteristic, complemented
299#3107C2×C10911yescharacteristic, complemented
300#3035C2×C10911yescharacteristic
301#2970C2×C10911yescharacteristic, complemented
302#1702C2×C10911yescharacteristic, complemented
303#1700C2×C10911yescharacteristic, complemented
304#1694C2×C10911yescharacteristic, complemented
305#1686C2×C10911yescharacteristic, complemented
306#1681C2×C10911yescharacteristic, complemented
307#1679C2×C10911yescharacteristic, complemented
308#1673C2×C10911yescharacteristic, complemented
309#1665C2×C10911yescharacteristic, complemented
310#1565C2×C10911yescharacteristic, complemented
311#1553C2×C10911yescharacteristic, complemented
312#1552C2×C10911yescharacteristic, complemented
313C109#1917811yescharacteristic, direct product factor, Sylow
314C2×#135—21no—
315#533C22×C10911yescharacteristic
316#532C22×C10911yescharacteristic
317C4×#41C22×C10911yescharacteristic
318#500C22×C10911yescharacteristic
319#492C22×C10911yescharacteristic
320#487C22×C10911yescharacteristic
321#486C22×C10911yescharacteristic
322#485—21no—
323#475C22×C10911yescharacteristic
324#474C22×C10911yescharacteristic
325#468—21no—
326#468—21no—
327#464—21no—
328#463—21no—
329#462C22×C10911yescharacteristic
330#462C22×C10911yescharacteristic
331#461C22×C10911yescharacteristic
332#461C22×C10911yescharacteristic
333#460C22×C10911yescharacteristic
334#459C22×C10911yescharacteristic
335#452—21no—
336#446C22×C10911yescharacteristic
337#446C22×C10911yescharacteristic
338#440—21no—
339#440—21no—
340C4×Q16—21no—
341C4×SD16—21no—
342#435—21no—
343#435—21no—
344C8×D4C22×C10911yescharacteristic
345C8×D4C22×C10911yescharacteristic
346#432—21no—
347#432C22×C10911yescharacteristic
348#431C22×C10911yescharacteristic
349C2×C4⋊C8C22×C10911yescharacteristic
350#416—21no—
351C4×M16C22×C10911yescharacteristic
352C2×#97—21no—
353#335C22×C10911yescharacteristic
354#335C22×C10911yescharacteristic
355#334C22×C10911yescharacteristic
356#334C22×C10911yescharacteristic
357#332C22×C10911yescharacteristic
358#332C22×C10911yescharacteristic
359#332C22×C10911yescharacteristic
360#332C22×C10911yescharacteristic
361#332C22×C10911yescharacteristic
362#332C22×C10911yescharacteristic
363#331C22×C10911yescharacteristic
364#331C22×C10911yescharacteristic
365C2×#41—21no—
366C2×#41D4×C10911yescharacteristic
367#135—44no—
368C2×Q16—21no—
369C2×Q16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×D8—21no—
376C2×M16D4×C10911yescharacteristic
377C2×M16D4×C10911yescharacteristic
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C4⋊Q8C23×C10911yescharacteristic
382C4⋊Q8C23×C10911yescharacteristic
383C4⋊Q8C23×C10911yescharacteristic
384#127C23×C10911yescharacteristic
385#125—21no—
386#124—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389#121—21no—
390#121—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8D4×C10911yescharacteristic
394C4×Q8C23×C10911yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4D4×C10911yescharacteristic
400C4×D4C23×C10911yescharacteristic
401#117—21no—
402#117—21no—
403#117D4×C10911yescharacteristic
404C2×C42—21no—
405C2×C42C23×C10911yescharacteristic
406#107—21no—
407#107—21no—
408#107—21no—
409#106—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C23×C10911yescharacteristic
414C4⋊C8C23×C10911yescharacteristic
415C4⋊C8C23×C10911yescharacteristic
416C4⋊C8C23×C10911yescharacteristic
417C4⋊C8C23×C10911yescharacteristic
418C4⋊C8C23×C10911yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435#97—21no—
436#97—21no—
437#97—21no—
438#97D4×C10911yescharacteristic
439#97D4×C10911yescharacteristic
440C4×C8—21no—
441C4×C8C23×C10911yescharacteristic
442C4×C8C23×C10911yescharacteristic
443#41—22no—
444#41—41no—
445#41—42no—
446#41—42no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C10911yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4C2×D4×C10911yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4C2×D4×C10911yescharacteristic
462C22×C4C2×D4×C10911yescharacteristic
463C22×C4#41×C10911yescharacteristic
464Q16—42no—
465Q16—42no—
466SD16—42no—
467SD16—42no—
468SD16—42no—
469SD16—42no—
470SD16—42no—
471D8—42no—
472M16—22no—
473M16—41no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—42no—
481C2×C8—42no—
482C2×C8—42no—
483C2×C8C2×D4×C10911yescharacteristic
484C2×C8C2×D4×C10911yescharacteristic
485C2×C8C2×D4×C10911yescharacteristic
486C2×C8C2×D4×C10911yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4C2×D4×C10911yescharacteristic
498C4⋊C4C2×D4×C10911yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—41no—
509C42C2×D4×C10911yescharacteristic
510C42C2×D4×C10911yescharacteristic
511C42#41×C10911yescharacteristic
512C42C24×C10911yescharacteristic
513C23—21no—
514C23—41no—
515C23#121×C10911yescharacteristic
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524D4—21no—
525D4—42no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—81no—
531D4—82no—
532D4AGL(1,ℤ/8)×C10912yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—81no—
548C2×C4—82no—
549C2×C4#121×C10911yescharacteristic
550C2×C4#121×C10911yescharacteristic
551C2×C4#121×C10911yescharacteristic
552C2×C4C22×D4×C10911yescharacteristic
553C2×C4C22×D4×C10911yescharacteristic
554C2×C4C2×#41×C10911yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8#135×C10912yescomplemented
565C22—21no—
566C22—21no—
567C22—22no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22C2×#121×C10911yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4C2×#135×C10911yescharacteristic
586C4C2×AGL(1,ℤ/8)×C10911yescharacteristic
587C4#575×C10911yescharacteristic
588C4#575×C10911yescharacteristic
589C2—41no—
590C2—42no—
591C2—161no—
592C2C109×#303511yescharacteristic
593C2C109×#305511yescharacteristic
594C2C109×#306911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radicalC109×#3035C2
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
2. C109×#3107C2semidirect
4. C109×#2970C2semidirect
5. C109×#1702C2semidirect
6. C109×#1700C2semidirect
7. C109×#1694C2semidirect
8. C109×#1686C2semidirect
9. C109×#1681C2semidirect
10. C109×#1679C2semidirect
11. C109×#1673C2semidirect
12. C109×#1665C2semidirect
13. C109×#1565C2semidirect
14. C109×#1553C2semidirect
15. C109×#1552C2semidirect
266. C8×C109#135semidirect
291. #19178C109direct (N × H)
298. #3182C2×C109semidirect
299. #3107C2×C109semidirect
301. #2970C2×C109semidirect
302. #1702C2×C109semidirect
303. #1700C2×C109semidirect
304. #1694C2×C109semidirect
305. #1686C2×C109semidirect
306. #1681C2×C109semidirect
307. #1679C2×C109semidirect
308. #1673C2×C109semidirect
309. #1665C2×C109semidirect
310. #1565C2×C109semidirect
311. #1553C2×C109semidirect
312. #1552C2×C109semidirect
313. C109#19178direct (N × H)
564. C8#135×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#31822
C109×#31072
C109×#30352
C109×#29702
C109×#17022
C109×#17002
C109×#16942
C109×#16862
C109×#16812
C109×#16792
C109×#16732
C109×#16652
C109×#15652
C109×#15532
C109×#15522
#19178109