Finite Group Databasebeta

← C109×#19377 #42137371

Subgroups — C109×#19377 #42137371

Order 27904.

658 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×#3251C211yesmaximal, characteristic
2C109×#3239C211yesmaximal, characteristic, complemented
3C109×#3152C211yesmaximal, characteristic, complemented
4C109×#2969C211yesmaximal, characteristic, complemented
5C109×#1690C211yesmaximal, characteristic, complemented
6C109×#1689C211yesmaximal, characteristic, complemented
7C109×#1686C211yesmaximal, characteristic, complemented
8C109×#1685C211yesmaximal, characteristic, complemented
9C109×#1670C211yesmaximal, characteristic, complemented
10C109×#1669C211yesmaximal, characteristic, complemented
11C109×#1666C211yesmaximal, characteristic, complemented
12C109×#1665C211yesmaximal, characteristic, complemented
13C109×#1569C211yesmaximal, characteristic, complemented
14C109×#1553C211yesmaximal, characteristic, complemented
15C109×#1549C211yesmaximal, characteristic, complemented
16C2×#137×C109—21no—
17C2×#137×C109—21no—
18#532×C109C2211yescharacteristic
19C2×C4⋊Q8×C109C2211yescharacteristic
20#529×C109C2211yescharacteristic
21#501×C109—21no—
22#497×C109—21no—
23#497×C109—21no—
24#494×C109C2211yescharacteristic
25#494×C109C2211yescharacteristic
26#492×C109C2211yescharacteristic
27#492×C109C2211yescharacteristic
28#489×C109—21no—
29#484×C109—21no—
30#481×C109—21no—
31#478×C109—21no—
32#475×C109C2211yescharacteristic
33#475×C109C2211yescharacteristic
34#475×C109C2211yescharacteristic
35#474×C109C2211yescharacteristic
36#474×C109C2211yescharacteristic
37#474×C109C2211yescharacteristic
38#469×C109—21no—
39#468×C109—21no—
40#463×C109—21no—
41#460×C109C2211yescharacteristic
42#459×C109C2211yescharacteristic
43#446×C109C2211yescharacteristic
44C8×Q8×C109C2211yescharacteristic
45#436×C109—21no—
46#436×C109C2211yescharacteristic
47#435×C109—21no—
48C8×D4×C109C2211yescharacteristic
49#433×C109—21no—
50#432×C109C2211yescharacteristic
51#431×C109C2211yescharacteristic
52#423×C109C2211yescharacteristic
53#405×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—
68C22×Q8×C109—21no—
69#137×C109—44no—
70#137×C109—44no—
71C2×Q16×C109—21no—
72C2×Q16×C109—21no—
73C2×Q16×C109—21no—
74C2×Q16×C109—21no—
75C2×SD16×C109—21no—
76C2×SD16×C109—21no—
77C2×SD16×C109—21no—
78C2×SD16×C109—21no—
79C2×SD16×C109—21no—
80C2×D8×C109—21no—
81C2×M16×C109—21no—
82C2×M16×C109—21no—
83C2×M16×C109D411yescharacteristic
84C2×M16×C109D411yescharacteristic
85C22×C8×C109—21no—
86C4⋊Q8×C109—21no—
87C4⋊Q8×C109—21no—
88C4⋊Q8×C109—21no—
89C4⋊Q8×C109C2311yescharacteristic
90C4⋊Q8×C109C2311yescharacteristic
91C4⋊Q8×C109C2311yescharacteristic
92#127×C109C2311yescharacteristic
93#126×C109—21no—
94#125×C109D411yescharacteristic
95#124×C109—21no—
96#124×C109D411yescharacteristic
97#123×C109—21no—
98C22⋊Q8×C109D411yescharacteristic
99#121×C109—21no—
100#121×C109—21no—
101#121×C109D411yescharacteristic
102C4×Q8×C109C2311yescharacteristic
103C4×D4×C109—21no—
104C4×D4×C109—21no—
105C4×D4×C109—21no—
106C4×D4×C109C2311yescharacteristic
107#117×C109—21no—
108C2×C4⋊C4×C109—21no—
109C2×C4⋊C4×C109—21no—
110C2×C42×C109C2311yescharacteristic
111#107×C109—21no—
112#107×C109—21no—
113#107×C109—21no—
114#106×C109—21no—
115#106×C109—21no—
116#106×C109—21no—
117C4⋊C8×C109—21no—
118C4⋊C8×C109—21no—
119C4⋊C8×C109—21no—
120C4⋊C8×C109C2311yescharacteristic
121C4⋊C8×C109C2311yescharacteristic
122C4⋊C8×C109C2311yescharacteristic
123C4⋊C8×C109C2311yescharacteristic
124C4⋊C8×C109C2311yescharacteristic
125C4⋊C8×C109C2311yescharacteristic
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—
134C22⋊C8×C109—21no—
135C22⋊C8×C109—21no—
136C22⋊C8×C109—21no—
137C22⋊C8×C109—21no—
138#97×C109—21no—
139#97×C109—21no—
140#97×C109D411yescharacteristic
141#97×C109D411yescharacteristic
142C4×C8×C109—21no—
143C4×C8×C109—21no—
144C4×C8×C109C2311yescharacteristic
145C4×C8×C109C2311yescharacteristic
146#41×C109—42no—
147#41×C109—42no—
148C2×Q8×C109—21no—
149C2×Q8×C109—21no—
150C2×Q8×C109—21no—
151C2×Q8×C109—42no—
152C2×Q8×C109—42no—
153C2×Q8×C109—41no—
154C2×Q8×C109C2×D411yescharacteristic
155C2×D4×C109—21no—
156C2×D4×C109—21no—
157C2×D4×C109—21no—
158C2×D4×C109—21no—
159C2×D4×C109—41no—
160C2×D4×C109C2×D411yescharacteristic
161C22×C4×C109—21no—
162C22×C4×C109—41no—
163C22×C4×C109—41no—
164C22×C4×C109C2×D411yescharacteristic
165C22×C4×C109C2×D411yescharacteristic
166C22×C4×C109#4111yescharacteristic
167Q16×C109—42no—
168Q16×C109—42no—
169Q16×C109—42no—
170Q16×C109—42no—
171SD16×C109—42no—
172SD16×C109—42no—
173SD16×C109—42no—
174SD16×C109—42no—
175SD16×C109—81no—
176D8×C109—81no—
177M16×C109—22no—
178M16×C109—22no—
179M16×C109—42no—
180M16×C109—81no—
181C2×C8×C109—21no—
182C2×C8×C109—21no—
183C2×C8×C109—21no—
184C2×C8×C109—21no—
185C2×C8×C109—21no—
186C2×C8×C109—21no—
187C2×C8×C109—42no—
188C2×C8×C109C2×D411yescharacteristic
189C2×C8×C109C2×D411yescharacteristic
190C2×C8×C109C2×D411yescharacteristic
191C2×C8×C109C2×D411yescharacteristic
192C4⋊C4×C109—21no—
193C4⋊C4×C109—21no—
194C4⋊C4×C109—21no—
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—21no—
211C22⋊C4×C109—41no—
212C22⋊C4×C109—41no—
213C42×C109—21no—
214C42×C109C2×D411yescharacteristic
215C42×C109C2×D411yescharacteristic
216C42×C109#4111yescharacteristic
217C42×C109C2411yescharacteristic
218C23×C109—21no—
219C23×C109—41no—
220C23×C109#12111yescharacteristic
221Q8×C109—21no—
222Q8×C109—21no—
223Q8×C109—41no—
224Q8×C109—41no—
225Q8×C109—41no—
226Q8×C109—41no—
227Q8×C109—41no—
228Q8×C109—41no—
229Q8×C109—82no—
230D4×C109—21no—
231D4×C109—21no—
232D4×C109—41no—
233D4×C109—41no—
234D4×C109—41no—
235D4×C109—41no—
236D4×C109—81no—
237D4×C109—81no—
238D4×C109—82no—
239C2×C4×C109—21no—
240C2×C4×C109—21no—
241C2×C4×C109—21no—
242C2×C4×C109—21no—
243C2×C4×C109—21no—
244C2×C4×C109—21no—
245C2×C4×C109—21no—
246C2×C4×C109—41no—
247C2×C4×C109—41no—
248C2×C4×C109—41no—
249C2×C4×C109—41no—
250C2×C4×C109—41no—
251C2×C4×C109—41no—
252C2×C4×C109—82no—
253C2×C4×C109—82no—
254C2×C4×C109#12111yescharacteristic
255C2×C4×C109#12111yescharacteristic
256C2×C4×C109#12111yescharacteristic
257C2×C4×C109C22×D411yescharacteristic
258C2×C4×C109C22×D411yescharacteristic
259C2×C4×C109C2×#4111yescharacteristic
260C8×C109—21no—
261C8×C109—21no—
262C8×C109—41no—
263C8×C109—41no—
264C8×C109—41no—
265C8×C109—41no—
266C8×C109—41no—
267C8×C109—41no—
268C8×C109AGL(1,ℤ/8)12yes—
269C8×C109AGL(1,ℤ/8)12yes—
270C22×C109—21no—
271C22×C109—21no—
272C22×C109—21no—
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—41no—
287C4×C109—81no—
288C4×C109—81no—
289C4×C109—81no—
290C4×C109C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C109C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C109#57711yescharacteristic
293C4×C109#57811yescharacteristic
294#19377C10911yesmaximal, characteristic, direct product factor, Sylow
295C2×C109—41no—
296C2×C109—81no—
297C2×C109—161no—
298C2×C109#303811yescharacteristic
299C2×C109#306311yescharacteristic
300C2×C109#306911yescharacteristic
301#3251C2×C10911yescharacteristic
302#3239C2×C10911yescharacteristic, complemented
303#3152C2×C10911yescharacteristic, complemented
304#2969C2×C10911yescharacteristic, complemented
305#1690C2×C10911yescharacteristic, complemented
306#1689C2×C10911yescharacteristic, complemented
307#1686C2×C10911yescharacteristic, complemented
308#1685C2×C10911yescharacteristic, complemented
309#1670C2×C10911yescharacteristic, complemented
310#1669C2×C10911yescharacteristic, complemented
311#1666C2×C10911yescharacteristic, complemented
312#1665C2×C10911yescharacteristic, complemented
313#1569C2×C10911yescharacteristic, complemented
314#1553C2×C10911yescharacteristic, complemented
315#1549C2×C10911yescharacteristic, complemented
316C109#1937711yescharacteristic, direct product factor, Sylow
317C2×#137—21no—
318C2×#137—21no—
319#532C22×C10911yescharacteristic
320C2×C4⋊Q8C22×C10911yescharacteristic
321#529C22×C10911yescharacteristic
322#501—21no—
323#497—21no—
324#497—21no—
325#494C22×C10911yescharacteristic
326#494C22×C10911yescharacteristic
327#492C22×C10911yescharacteristic
328#492C22×C10911yescharacteristic
329#489—21no—
330#484—21no—
331#481—21no—
332#478—21no—
333#475C22×C10911yescharacteristic
334#475C22×C10911yescharacteristic
335#475C22×C10911yescharacteristic
336#474C22×C10911yescharacteristic
337#474C22×C10911yescharacteristic
338#474C22×C10911yescharacteristic
339#469—21no—
340#468—21no—
341#463—21no—
342#460C22×C10911yescharacteristic
343#459C22×C10911yescharacteristic
344#446C22×C10911yescharacteristic
345C8×Q8C22×C10911yescharacteristic
346#436—21no—
347#436C22×C10911yescharacteristic
348#435—21no—
349C8×D4C22×C10911yescharacteristic
350#433—21no—
351#432C22×C10911yescharacteristic
352#431C22×C10911yescharacteristic
353#423C22×C10911yescharacteristic
354#405—21no—
355C4×M16C22×C10911yescharacteristic
356#335C22×C10911yescharacteristic
357#335C22×C10911yescharacteristic
358#334C22×C10911yescharacteristic
359#334C22×C10911yescharacteristic
360#332C22×C10911yescharacteristic
361#332C22×C10911yescharacteristic
362#332C22×C10911yescharacteristic
363#332C22×C10911yescharacteristic
364#332C22×C10911yescharacteristic
365#332C22×C10911yescharacteristic
366#331C22×C10911yescharacteristic
367#331C22×C10911yescharacteristic
368C2×#41—21no—
369C22×Q8—21no—
370#137—44no—
371#137—44no—
372C2×Q16—21no—
373C2×Q16—21no—
374C2×Q16—21no—
375C2×Q16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×D8—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16D4×C10911yescharacteristic
385C2×M16D4×C10911yescharacteristic
386C22×C8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8C23×C10911yescharacteristic
391C4⋊Q8C23×C10911yescharacteristic
392C4⋊Q8C23×C10911yescharacteristic
393#127C23×C10911yescharacteristic
394#126—21no—
395#125D4×C10911yescharacteristic
396#124—21no—
397#124D4×C10911yescharacteristic
398#123—21no—
399C22⋊Q8D4×C10911yescharacteristic
400#121—21no—
401#121—21no—
402#121D4×C10911yescharacteristic
403C4×Q8C23×C10911yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C10911yescharacteristic
408#117—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C42C23×C10911yescharacteristic
412#107—21no—
413#107—21no—
414#107—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8C23×C10911yescharacteristic
422C4⋊C8C23×C10911yescharacteristic
423C4⋊C8C23×C10911yescharacteristic
424C4⋊C8C23×C10911yescharacteristic
425C4⋊C8C23×C10911yescharacteristic
426C4⋊C8C23×C10911yescharacteristic
427#103—21no—
428#103—21no—
429#103—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440#97—21no—
441#97D4×C10911yescharacteristic
442#97D4×C10911yescharacteristic
443C4×C8—21no—
444C4×C8—21no—
445C4×C8C23×C10911yescharacteristic
446C4×C8C23×C10911yescharacteristic
447#41—42no—
448#41—42no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8—41no—
455C2×Q8C2×D4×C10911yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4C2×D4×C10911yescharacteristic
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4C2×D4×C10911yescharacteristic
466C22×C4C2×D4×C10911yescharacteristic
467C22×C4#41×C10911yescharacteristic
468Q16—42no—
469Q16—42no—
470Q16—42no—
471Q16—42no—
472SD16—42no—
473SD16—42no—
474SD16—42no—
475SD16—42no—
476SD16—81no—
477D8—81no—
478M16—22no—
479M16—22no—
480M16—42no—
481M16—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—42no—
489C2×C8C2×D4×C10911yescharacteristic
490C2×C8C2×D4×C10911yescharacteristic
491C2×C8C2×D4×C10911yescharacteristic
492C2×C8C2×D4×C10911yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C10911yescharacteristic
506C4⋊C4C2×D4×C10911yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42C2×D4×C10911yescharacteristic
516C42C2×D4×C10911yescharacteristic
517C42#41×C10911yescharacteristic
518C42C24×C10911yescharacteristic
519C23—21no—
520C23—41no—
521C23#121×C10911yescharacteristic
522Q8—21no—
523Q8—21no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—82no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—81no—
538D4—81no—
539D4—82no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4#121×C10911yescharacteristic
556C2×C4#121×C10911yescharacteristic
557C2×C4#121×C10911yescharacteristic
558C2×C4C22×D4×C10911yescharacteristic
559C2×C4C22×D4×C10911yescharacteristic
560C2×C4C2×#41×C10911yescharacteristic
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8AGL(1,ℤ/8)×C10912yes—
570C8AGL(1,ℤ/8)×C10912yes—
571C22—21no—
572C22—21no—
573C22—21no—
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—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C2×AGL(1,ℤ/8)×C10911yescharacteristic
592C4C2×AGL(1,ℤ/8)×C10911yescharacteristic
593C4#577×C10911yescharacteristic
594C4#578×C10911yescharacteristic
595C2—41no—
596C2—81no—
597C2—161no—
598C2C109×#303811yescharacteristic
599C2C109×#306311yescharacteristic
600C2C109×#306911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC42C24×C109
prime radicalC109×#3251C2
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×#3239C2semidirect
3. C109×#3152C2semidirect
4. C109×#2969C2semidirect
5. C109×#1690C2semidirect
6. C109×#1689C2semidirect
7. C109×#1686C2semidirect
8. C109×#1685C2semidirect
9. C109×#1670C2semidirect
10. C109×#1669C2semidirect
11. C109×#1666C2semidirect
12. C109×#1665C2semidirect
13. C109×#1569C2semidirect
14. C109×#1553C2semidirect
15. C109×#1549C2semidirect
294. #19377C109direct (N × H)
302. #3239C2×C109semidirect
303. #3152C2×C109semidirect
304. #2969C2×C109semidirect
305. #1690C2×C109semidirect
306. #1689C2×C109semidirect
307. #1686C2×C109semidirect
308. #1685C2×C109semidirect
309. #1670C2×C109semidirect
310. #1669C2×C109semidirect
311. #1666C2×C109semidirect
312. #1665C2×C109semidirect
313. #1569C2×C109semidirect
314. #1553C2×C109semidirect
315. #1549C2×C109semidirect
316. C109#19377direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#32512
C109×#32392
C109×#31522
C109×#29692
C109×#16902
C109×#16892
C109×#16862
C109×#16852
C109×#16702
C109×#16692
C109×#16662
C109×#16652
C109×#15692
C109×#15532
C109×#15492
#19377109