Finite Group Databasebeta

← C109×#19368 #42137362

Subgroups — C109×#19368 #42137362

Order 27904.

656 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3254C211yesmaximal, characteristic, complemented
2C109×#3214C211yesmaximal, characteristic
3C109×#3182C211yesmaximal, characteristic, complemented
4C109×#2935C211yesmaximal, characteristic, complemented
5C109×#1701C211yesmaximal, characteristic, complemented
6C109×#1699C211yesmaximal, characteristic, complemented
7C109×#1693C211yesmaximal, characteristic, complemented
8C109×#1685C211yesmaximal, characteristic, complemented
9C109×#1681C211yesmaximal, characteristic, complemented
10C109×#1679C211yesmaximal, characteristic, complemented
11C109×#1673C211yesmaximal, characteristic, complemented
12C109×#1665C211yesmaximal, characteristic, complemented
13C109×#1569C211yesmaximal, characteristic, complemented
14C109×#1552C211yesmaximal, characteristic, complemented
15C109×#1547C211yesmaximal, characteristic, complemented
16C2×#131×C109—21no—
17#533×C109C2211yescharacteristic
18#532×C109C2211yescharacteristic
19#532×C109C2211yescharacteristic
20#500×C109C2211yescharacteristic
21#496×C109—21no—
22#492×C109C2211yescharacteristic
23#489×C109—21no—
24#487×C109C2211yescharacteristic
25#486×C109C2211yescharacteristic
26#477×C109—21no—
27#474×C109C2211yescharacteristic
28#474×C109C2211yescharacteristic
29#468×C109—21no—
30#468×C109—21no—
31#468×C109—21no—
32#468×C109—21no—
33#461×C109C2211yescharacteristic
34#461×C109C2211yescharacteristic
35#461×C109C2211yescharacteristic
36#461×C109C2211yescharacteristic
37#460×C109—21no—
38#459×C109C2211yescharacteristic
39#459×C109C2211yescharacteristic
40#449×C109—21no—
41#449×C109—21no—
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#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×C109—21no—
69C2×SD16×C109—21no—
70C2×SD16×C109—21no—
71C2×SD16×C109—21no—
72C2×SD16×C109—21no—
73C2×SD16×C109—21no—
74C2×SD16×C109—21no—
75C2×D8×C109—21no—
76C2×D8×C109—21no—
77#131×C109—44no—
78C2×M16×C109—21no—
79C2×M16×C109—21no—
80C2×M16×C109—21no—
81C2×M16×C109D411yescharacteristic
82C2×M16×C109D411yescharacteristic
83C22×C8×C109—21no—
84C22×C8×C109—21no—
85C22×C8×C109—21no—
86C4⋊Q8×C109D411yescharacteristic
87C4⋊Q8×C109C2311yescharacteristic
88C4⋊Q8×C109C2311yescharacteristic
89C4⋊Q8×C109C2311yescharacteristic
90#127×C109D411yescharacteristic
91#127×C109C2311yescharacteristic
92#125×C109—21no—
93#124×C109—21no—
94#124×C109—21no—
95C22⋊Q8×C109—21no—
96C22⋊Q8×C109—21no—
97#121×C109—21no—
98#121×C109—21no—
99#121×C109—21no—
100#121×C109D411yescharacteristic
101#121×C109D411yescharacteristic
102C4×Q8×C109—21no—
103C4×Q8×C109—21no—
104C4×D4×C109—21no—
105C4×D4×C109—21no—
106C4×D4×C109—21no—
107C4×D4×C109C2311yescharacteristic
108C4×D4×C109C2311yescharacteristic
109#117×C109—21no—
110C2×C42×C109C2311yescharacteristic
111#107×C109—21no—
112#107×C109—21no—
113#107×C109—21no—
114#107×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#103×C109—21no—
126#103×C109—21no—
127#103×C109—21no—
128#103×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—81no—
148#41×C109—81no—
149C2×Q8×C109—21no—
150C2×Q8×C109—21no—
151C2×Q8×C109—21no—
152C2×Q8×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—21no—
160C2×D4×C109—41no—
161C2×D4×C109C2×D411yescharacteristic
162C2×D4×C109C2×D411yescharacteristic
163C22×C4×C109—21no—
164C22×C4×C109—21no—
165C22×C4×C109—41no—
166C22×C4×C109C2×D411yescharacteristic
167C22×C4×C109C2×D411yescharacteristic
168C22×C4×C109#4111yescharacteristic
169SD16×C109—42no—
170SD16×C109—42no—
171SD16×C109—81no—
172SD16×C109—81no—
173SD16×C109—81no—
174SD16×C109—81no—
175D8×C109—81no—
176D8×C109—81no—
177M16×C109—22no—
178M16×C109—41no—
179M16×C109—42no—
180M16×C109—42no—
181M16×C109—81no—
182C2×C8×C109—21no—
183C2×C8×C109—21no—
184C2×C8×C109—21no—
185C2×C8×C109—21no—
186C2×C8×C109—21no—
187C2×C8×C109—21no—
188C2×C8×C109—42no—
189C2×C8×C109—42no—
190C2×C8×C109—42no—
191C2×C8×C109C2×D411yescharacteristic
192C2×C8×C109C2×D411yescharacteristic
193C2×C8×C109C2×D411yescharacteristic
194C2×C8×C109C2×D411yescharacteristic
195C4⋊C4×C109—21no—
196C4⋊C4×C109—21no—
197C4⋊C4×C109—21no—
198C4⋊C4×C109—21no—
199C4⋊C4×C109—21no—
200C4⋊C4×C109—21no—
201C4⋊C4×C109—21no—
202C4⋊C4×C109—41no—
203C4⋊C4×C109—41no—
204C4⋊C4×C109C2×D411yescharacteristic
205C4⋊C4×C109C2×D411yescharacteristic
206C22⋊C4×C109—21no—
207C22⋊C4×C109—21no—
208C22⋊C4×C109—21no—
209C22⋊C4×C109—21no—
210C22⋊C4×C109—41no—
211C22⋊C4×C109—41no—
212C22⋊C4×C109—41no—
213C42×C109—41no—
214C42×C109C2×D411yescharacteristic
215C42×C109C2×D411yescharacteristic
216C42×C109#4111yescharacteristic
217C42×C109C2411yescharacteristic
218C23×C109—21no—
219C23×C109—21no—
220C23×C109—41no—
221C23×C109#12111yescharacteristic
222Q8×C109—42no—
223Q8×C109—41no—
224Q8×C109—41no—
225Q8×C109—41no—
226Q8×C109—41no—
227Q8×C109—41no—
228Q8×C109—41no—
229D4×C109—21no—
230D4×C109—21no—
231D4×C109—21no—
232D4×C109—21no—
233D4×C109—42no—
234D4×C109—42no—
235D4×C109—42no—
236D4×C109—41no—
237D4×C109—41no—
238D4×C109—41no—
239D4×C109—41no—
240D4×C109—81no—
241D4×C109—81no—
242D4×C109—82no—
243C2×C4×C109—21no—
244C2×C4×C109—21no—
245C2×C4×C109—21no—
246C2×C4×C109—21no—
247C2×C4×C109—21no—
248C2×C4×C109—21no—
249C2×C4×C109—41no—
250C2×C4×C109—41no—
251C2×C4×C109—41no—
252C2×C4×C109—41no—
253C2×C4×C109—41no—
254C2×C4×C109—41no—
255C2×C4×C109—41no—
256C2×C4×C109—41no—
257C2×C4×C109—82no—
258C2×C4×C109#12111yescharacteristic
259C2×C4×C109#12111yescharacteristic
260C2×C4×C109#12111yescharacteristic
261C2×C4×C109C22×D411yescharacteristic
262C2×C4×C109C22×D411yescharacteristic
263C2×C4×C109C2×#4111yescharacteristic
264C8×C109—21no—
265C8×C109—21no—
266C8×C109—21no—
267C8×C109—41no—
268C8×C109—41no—
269C8×C109—41no—
270C8×C109—41no—
271C8×C109—41no—
272C8×C109—41no—
273C8×C109AGL(1,ℤ/8)12yes—
274C22×C109—21no—
275C22×C109—21no—
276C22×C109—21no—
277C22×C109—41no—
278C22×C109—41no—
279C22×C109—41no—
280C22×C109—41no—
281C22×C109—41no—
282C22×C109—41no—
283C22×C109—81no—
284C22×C109—81no—
285C22×C109—81no—
286C22×C109C2×#12111yescharacteristic
287C4×C109—21no—
288C4×C109—21no—
289C4×C109—21no—
290C4×C109—21no—
291C4×C109—41no—
292C4×C109—41no—
293C4×C109—81no—
294C4×C109—81no—
295C4×C109—81no—
296C4×C109C2×AGL(1,ℤ/8)11yescharacteristic
297C4×C109#57511yescharacteristic
298C4×C109#57611yescharacteristic
299C4×C109#57711yescharacteristic
300#19368C10911yesmaximal, characteristic, direct product factor, Sylow
301C2×C109—41no—
302C2×C109—81no—
303C2×C109—81no—
304C2×C109—161no—
305C2×C109#303611yescharacteristic
306C2×C109#306211yescharacteristic
307C2×C109#306911yescharacteristic
308#3254C2×C10911yescharacteristic, complemented
309#3214C2×C10911yescharacteristic
310#3182C2×C10911yescharacteristic, complemented
311#2935C2×C10911yescharacteristic, complemented
312#1701C2×C10911yescharacteristic, complemented
313#1699C2×C10911yescharacteristic, complemented
314#1693C2×C10911yescharacteristic, complemented
315#1685C2×C10911yescharacteristic, complemented
316#1681C2×C10911yescharacteristic, complemented
317#1679C2×C10911yescharacteristic, complemented
318#1673C2×C10911yescharacteristic, complemented
319#1665C2×C10911yescharacteristic, complemented
320#1569C2×C10911yescharacteristic, complemented
321#1552C2×C10911yescharacteristic, complemented
322#1547C2×C10911yescharacteristic, complemented
323C109#1936811yescharacteristic, direct product factor, Sylow
324C2×#131—21no—
325#533C22×C10911yescharacteristic
326#532C22×C10911yescharacteristic
327#532C22×C10911yescharacteristic
328#500C22×C10911yescharacteristic
329#496—21no—
330#492C22×C10911yescharacteristic
331#489—21no—
332#487C22×C10911yescharacteristic
333#486C22×C10911yescharacteristic
334#477—21no—
335#474C22×C10911yescharacteristic
336#474C22×C10911yescharacteristic
337#468—21no—
338#468—21no—
339#468—21no—
340#468—21no—
341#461C22×C10911yescharacteristic
342#461C22×C10911yescharacteristic
343#461C22×C10911yescharacteristic
344#461C22×C10911yescharacteristic
345#460—21no—
346#459C22×C10911yescharacteristic
347#459C22×C10911yescharacteristic
348#449—21no—
349#449—21no—
350#440—21no—
351#440—21no—
352#436C22×C10911yescharacteristic
353#436C22×C10911yescharacteristic
354#435—21no—
355#435—21no—
356C8×D4C22×C10911yescharacteristic
357C8×D4C22×C10911yescharacteristic
358#432C22×C10911yescharacteristic
359#423C22×C10911yescharacteristic
360C2×C4⋊C8C22×C10911yescharacteristic
361#408—21no—
362C4×M16C22×C10911yescharacteristic
363#335C22×C10911yescharacteristic
364#335C22×C10911yescharacteristic
365#334C22×C10911yescharacteristic
366#334C22×C10911yescharacteristic
367#332C22×C10911yescharacteristic
368#332C22×C10911yescharacteristic
369#332C22×C10911yescharacteristic
370#332C22×C10911yescharacteristic
371#332C22×C10911yescharacteristic
372#332C22×C10911yescharacteristic
373#331C22×C10911yescharacteristic
374#331C22×C10911yescharacteristic
375C2×#41—21no—
376C2×#41—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×D8—21no—
384C2×D8—21no—
385#131—44no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16D4×C10911yescharacteristic
390C2×M16D4×C10911yescharacteristic
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—21no—
394C4⋊Q8D4×C10911yescharacteristic
395C4⋊Q8C23×C10911yescharacteristic
396C4⋊Q8C23×C10911yescharacteristic
397C4⋊Q8C23×C10911yescharacteristic
398#127D4×C10911yescharacteristic
399#127C23×C10911yescharacteristic
400#125—21no—
401#124—21no—
402#124—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121D4×C10911yescharacteristic
409#121D4×C10911yescharacteristic
410C4×Q8—21no—
411C4×Q8—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C23×C10911yescharacteristic
416C4×D4C23×C10911yescharacteristic
417#117—21no—
418C2×C42C23×C10911yescharacteristic
419#107—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8C23×C10911yescharacteristic
426C4⋊C8C23×C10911yescharacteristic
427C4⋊C8C23×C10911yescharacteristic
428C4⋊C8C23×C10911yescharacteristic
429C4⋊C8C23×C10911yescharacteristic
430C4⋊C8C23×C10911yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—21no—
436#103—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448#97—21no—
449#97D4×C10911yescharacteristic
450#97D4×C10911yescharacteristic
451C4×C8C23×C10911yescharacteristic
452C4×C8C23×C10911yescharacteristic
453#41—42no—
454#41—42no—
455#41—81no—
456#41—81no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4C2×D4×C10911yescharacteristic
470C2×D4C2×D4×C10911yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—41no—
474C22×C4C2×D4×C10911yescharacteristic
475C22×C4C2×D4×C10911yescharacteristic
476C22×C4#41×C10911yescharacteristic
477SD16—42no—
478SD16—42no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482SD16—81no—
483D8—81no—
484D8—81no—
485M16—22no—
486M16—41no—
487M16—42no—
488M16—42no—
489M16—81no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—42no—
497C2×C8—42no—
498C2×C8—42no—
499C2×C8C2×D4×C10911yescharacteristic
500C2×C8C2×D4×C10911yescharacteristic
501C2×C8C2×D4×C10911yescharacteristic
502C2×C8C2×D4×C10911yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4C2×D4×C10911yescharacteristic
513C4⋊C4C2×D4×C10911yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—41no—
522C42C2×D4×C10911yescharacteristic
523C42C2×D4×C10911yescharacteristic
524C42#41×C10911yescharacteristic
525C42C24×C10911yescharacteristic
526C23—21no—
527C23—21no—
528C23—41no—
529C23#121×C10911yescharacteristic
530Q8—42no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—81no—
550D4—82no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4#121×C10911yescharacteristic
567C2×C4#121×C10911yescharacteristic
568C2×C4#121×C10911yescharacteristic
569C2×C4C22×D4×C10911yescharacteristic
570C2×C4C22×D4×C10911yescharacteristic
571C2×C4C2×#41×C10911yescharacteristic
572C8—21no—
573C8—21no—
574C8—21no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8AGL(1,ℤ/8)×C10912yes—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22C2×#121×C10911yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4C2×AGL(1,ℤ/8)×C10911yescharacteristic
605C4#575×C10911yescharacteristic
606C4#576×C10911yescharacteristic
607C4#577×C10911yescharacteristic
608C2—41no—
609C2—81no—
610C2—81no—
611C2—161no—
612C2C109×#303611yescharacteristic
613C2C109×#306211yescharacteristic
614C2C109×#306911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radicalC109×#3214C2
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×#3254C2semidirect
3. C109×#3182C2semidirect
4. C109×#2935C2semidirect
5. C109×#1701C2semidirect
6. C109×#1699C2semidirect
7. C109×#1693C2semidirect
8. C109×#1685C2semidirect
9. C109×#1681C2semidirect
10. C109×#1679C2semidirect
11. C109×#1673C2semidirect
12. C109×#1665C2semidirect
13. C109×#1569C2semidirect
14. C109×#1552C2semidirect
15. C109×#1547C2semidirect
300. #19368C109direct (N × H)
308. #3254C2×C109semidirect
310. #3182C2×C109semidirect
311. #2935C2×C109semidirect
312. #1701C2×C109semidirect
313. #1699C2×C109semidirect
314. #1693C2×C109semidirect
315. #1685C2×C109semidirect
316. #1681C2×C109semidirect
317. #1679C2×C109semidirect
318. #1673C2×C109semidirect
319. #1665C2×C109semidirect
320. #1569C2×C109semidirect
321. #1552C2×C109semidirect
322. #1547C2×C109semidirect
323. C109#19368direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#32542
C109×#32142
C109×#31822
C109×#29352
C109×#17012
C109×#16992
C109×#16932
C109×#16852
C109×#16812
C109×#16792
C109×#16732
C109×#16652
C109×#15692
C109×#15522
C109×#15472
#19368109