Finite Group Databasebeta

← C109×#14841 #42132835

Subgroups — C109×#14841 #42132835

Order 27904.

1534 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C109C211yesmaximal, characteristic, complemented
2C2×#385×C109C211yesmaximal, characteristic
3C2×#380×C109C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C109C211yesmaximal, characteristic
5C109×#1445C211yesmaximal, characteristic, complemented
6C109×#1442C211yesmaximal, characteristic, complemented
7C109×#1441C211yesmaximal, characteristic, complemented
8C109×#1440C212yesmaximal
9C109×#1440C212yesmaximal
10C109×#1436C212yesmaximal, complemented
11C109×#1434C212yesmaximal, complemented
12C24×C4×C109C2211yescharacteristic
13C22×C4⋊C4×C109C2211yescharacteristic
14C22×C4⋊C4×C109C2211yescharacteristic
15C22×C4⋊C4×C109C2211yescharacteristic
16C22×C4⋊C4×C109C2211yescharacteristic
17C22×C22⋊C4×C109C2212yes—
18C22×C22⋊C4×C109C2212yes—
19C22×C22⋊C4×C109C2211yescharacteristic
20C22×C22⋊C4×C109C2211yescharacteristic
21C22×C42×C109C2212yes—
22#400×C109—24no—
23#385×C109—24no—
24#380×C109—24no—
25C4×C22⋊C4×C109—24no—
26C2×#95×C109C2211yescharacteristic
27C2×#95×C109C2212yes—
28C2×#95×C109C2212yes—
29C2×#95×C109C2212yes—
30C2×#95×C109C2212yes—
31C2×#95×C109C2212yes—
32C2×#95×C109C2212yes—
33C2×#95×C109C2212yes—
34C2×#95×C109C2211yescharacteristic
35C2×#95×C109C2211yescharacteristic
36C2×#95×C109C2212yes—
37C2×#95×C109C2212yes—
38C2×#95×C109C2211yescharacteristic
39C25×C109C2311yescharacteristic
40C23×C4×C109—22no—
41C23×C4×C109—22no—
42C23×C4×C109—24no—
43C23×C4×C109—42no—
44C23×C4×C109D414yes—
45C23×C4×C109C2311yescharacteristic
46C23×C4×C109C2312yes—
47C23×C4×C109C2312yes—
48C23×C4×C109C2311yescharacteristic
49C23×C4×C109C2312yes—
50C23×C4×C109C2312yes—
51C23×C4×C109C2311yescharacteristic
52C23×C4×C109C2311yescharacteristic
53C23×C4×C109C2311yescharacteristic
54C23×C4×C109C2311yescharacteristic
55C2×C4⋊C4×C109—22no—
56C2×C4⋊C4×C109—22no—
57C2×C4⋊C4×C109—22no—
58C2×C4⋊C4×C109—22no—
59C2×C4⋊C4×C109—22no—
60C2×C4⋊C4×C109—22no—
61C2×C4⋊C4×C109—22no—
62C2×C4⋊C4×C109—22no—
63C2×C4⋊C4×C109—24no—
64C2×C4⋊C4×C109—42no—
65C2×C22⋊C4×C109—22no—
66C2×C22⋊C4×C109—24no—
67C2×C22⋊C4×C109—24no—
68C2×C22⋊C4×C109—24no—
69C2×C22⋊C4×C109—22no—
70C2×C22⋊C4×C109—22no—
71C2×C22⋊C4×C109—24no—
72C2×C22⋊C4×C109—22no—
73C2×C22⋊C4×C109—24no—
74C2×C22⋊C4×C109—24no—
75C2×C22⋊C4×C109—42no—
76C2×C42×C109—24no—
77C2×C42×C109—24no—
78C2×C42×C109—42no—
79#95×C109—22no—
80#95×C109—24no—
81#95×C109—22no—
82#95×C109—22no—
83#95×C109—24no—
84#95×C109—24no—
85#95×C109—24no—
86#95×C109—24no—
87#95×C109—24no—
88#95×C109—24no—
89#95×C109—42no—
90#95×C109—42no—
91#95×C109D414yes—
92C24×C109—21no—
93C24×C109—21no—
94C24×C109—21no—
95C24×C109—22no—
96C24×C109—21no—
97C24×C109—22no—
98C24×C109—22no—
99C24×C109—21no—
100C24×C109—21no—
101C24×C109C2×D412yes—
102C24×C109#4114yes—
103C24×C109C2411yescharacteristic
104C22×C4×C109—21no—
105C22×C4×C109—21no—
106C22×C4×C109—22no—
107C22×C4×C109—22no—
108C22×C4×C109—22no—
109C22×C4×C109—21no—
110C22×C4×C109—22no—
111C22×C4×C109—21no—
112C22×C4×C109—21no—
113C22×C4×C109—22no—
114C22×C4×C109—22no—
115C22×C4×C109—22no—
116C22×C4×C109—22no—
117C22×C4×C109—22no—
118C22×C4×C109—22no—
119C22×C4×C109—22no—
120C22×C4×C109—21no—
121C22×C4×C109—21no—
122C22×C4×C109—22no—
123C22×C4×C109—22no—
124C22×C4×C109—21no—
125C22×C4×C109—22no—
126C22×C4×C109—22no—
127C22×C4×C109—22no—
128C22×C4×C109—22no—
129C22×C4×C109—21no—
130C22×C4×C109—21no—
131C22×C4×C109—28no—
132C22×C4×C109—28no—
133C22×C4×C109—21no—
134C22×C4×C109—22no—
135C22×C4×C109—21no—
136C22×C4×C109—22no—
137C22×C4×C109—22no—
138C22×C4×C109—21no—
139C22×C4×C109—22no—
140C22×C4×C109—22no—
141C22×C4×C109—22no—
142C22×C4×C109—22no—
143C22×C4×C109—22no—
144C22×C4×C109—22no—
145C22×C4×C109—22no—
146C22×C4×C109—22no—
147C22×C4×C109—22no—
148C22×C4×C109—22no—
149C22×C4×C109—21no—
150C22×C4×C109—22no—
151C22×C4×C109—22no—
152C22×C4×C109—22no—
153C22×C4×C109—22no—
154C22×C4×C109—22no—
155C22×C4×C109—21no—
156C22×C4×C109—21no—
157C22×C4×C109—44no—
158C22×C4×C109—48no—
159C22×C4×C109—48no—
160C22×C4×C109C2×D414yes—
161C22×C4×C109C2×D412yes—
162C22×C4×C109C2×D412yes—
163C22×C4×C109C2×D412yes—
164C22×C4×C109#4112yes—
165C22×C4×C109#4114yes—
166C22×C4×C109#4112yes—
167C22×C4×C109#4112yes—
168C22×C4×C109#4114yes—
169C4⋊C4×C109—44no—
170C4⋊C4×C109—44no—
171C4⋊C4×C109—44no—
172C4⋊C4×C109—44no—
173C22⋊C4×C109—216no—
174C22⋊C4×C109—28no—
175C22⋊C4×C109—44no—
176C22⋊C4×C109—48no—
177C42×C109—48no—
178C23×C109—22no—
179C23×C109—22no—
180C23×C109—22no—
181C23×C109—24no—
182C23×C109—24no—
183C23×C109—22no—
184C23×C109—22no—
185C23×C109—22no—
186C23×C109—24no—
187C23×C109—24no—
188C23×C109—24no—
189C23×C109—24no—
190C23×C109—42no—
191C23×C109—42no—
192C23×C109—42no—
193C23×C109—42no—
194C23×C109—42no—
195C23×C109—41no—
196C23×C109—41no—
197C23×C109—42no—
198C23×C109—41no—
199C23×C109—41no—
200C23×C109#12414yes—
201C23×C109C22×D411yescharacteristic
202C23×C109C22×D411yescharacteristic
203C23×C109C2×#4111yescharacteristic
204C23×C109C2×#4112yes—
205C23×C109C2×#4112yes—
206C23×C109C2×#4112yes—
207C23×C109C2×#4111yescharacteristic
208C23×C109C2×#4111yescharacteristic
209C23×C109H(5,𝔽2)12yes—
210C23×C1092−1+411yescharacteristic
211C23×C1092−1+411yescharacteristic
212C2×C4×C109—22no—
213C2×C4×C109—22no—
214C2×C4×C109—22no—
215C2×C4×C109—22no—
216C2×C4×C109—24no—
217C2×C4×C109—24no—
218C2×C4×C109—24no—
219C2×C4×C109—24no—
220C2×C4×C109—24no—
221C2×C4×C109—22no—
222C2×C4×C109—22no—
223C2×C4×C109—24no—
224C2×C4×C109—24no—
225C2×C4×C109—24no—
226C2×C4×C109—24no—
227C2×C4×C109—24no—
228C2×C4×C109—24no—
229C2×C4×C109—22no—
230C2×C4×C109—22no—
231C2×C4×C109—416no—
232C2×C4×C109—41no—
233C2×C4×C109—41no—
234C2×C4×C109—42no—
235C2×C4×C109—42no—
236C2×C4×C109—41no—
237C2×C4×C109—41no—
238C2×C4×C109—42no—
239C2×C4×C109—42no—
240C2×C4×C109—41no—
241C2×C4×C109—42no—
242C2×C4×C109—42no—
243C2×C4×C109—42no—
244C2×C4×C109—42no—
245C2×C4×C109—42no—
246C2×C4×C109—41no—
247C2×C4×C109—42no—
248C2×C4×C109—41no—
249C2×C4×C109—41no—
250C2×C4×C109—42no—
251C2×C4×C109—42no—
252C2×C4×C109—42no—
253C2×C4×C109—42no—
254C2×C4×C109—42no—
255C2×C4×C109—42no—
256C2×C4×C109—42no—
257C2×C4×C109—42no—
258C2×C4×C109—41no—
259C2×C4×C109—41no—
260C2×C4×C109—41no—
261C2×C4×C109—42no—
262C2×C4×C109—41no—
263C2×C4×C109—42no—
264C2×C4×C109—42no—
265C2×C4×C109—42no—
266C2×C4×C109—42no—
267C2×C4×C109—42no—
268C2×C4×C109—42no—
269C2×C4×C109—42no—
270C2×C4×C109—42no—
271C2×C4×C109#12114yes—
272C2×C4×C109#12314yes—
273C22×C109—24no—
274C22×C109—24no—
275C22×C109—24no—
276C22×C109—44no—
277C22×C109—42no—
278C22×C109—42no—
279C22×C109—42no—
280C22×C109—42no—
281C22×C109—44no—
282C22×C109—44no—
283C22×C109—44no—
284C22×C109C2×#12111yescharacteristic
285C22×C109C2×#12311yescharacteristic
286C22×C109#52511yescharacteristic
287C22×C109#52512yes—
288C22×C109C2×#12411yescharacteristic
289C22×C109#52912yes—
290C22×C109#52912yes—
291C22×C109#52912yes—
292C22×C109#53211yescharacteristic
293C22×C109#53411yescharacteristic
294C22×C109#53611yescharacteristic
295C22×C109#53912yes—
296C22×C109#54212yes—
297C22×C109#54612yes—
298C22×C109#54711yescharacteristic
299C22×C109#54811yescharacteristic
300C22×C109#55112yes—
301C22×C109#55212yes—
302C22×C109#55211yescharacteristic
303C22×C109#55212yes—
304C22×C109#55312yes—
305C22×C109#55312yes—
306C22×C109#55611yescharacteristic
307C4×C109—24no—
308C4×C109—24no—
309C4×C109—42no—
310C4×C109—42no—
311C4×C109—44no—
312C4×C109—44no—
313C4×C109—82no—
314C4×C109—82no—
315C4×C109—81no—
316C4×C109—81no—
317#14841C10911yesmaximal, characteristic, direct product factor, Sylow
318C2×C109—44no—
319C2×C109#239511yescharacteristic
320C2×C109#241211yescharacteristic
321C2×C109#241511yescharacteristic
322C2×C109#246012yes—
323C2×C109#246812yes—
324C2×C109#250311yescharacteristic
325C2×C109#253012yes—
326C2×C109#257712yes—
327C2×C109#259111yescharacteristic
328C2×C109#266311yescharacteristic
329C2×C109#285011yescharacteristic
330C2×#400C2×C10911yescharacteristic, complemented
331C2×#385C2×C10911yescharacteristic
332C2×#380C2×C10911yescharacteristic
333C2×C4×C22⋊C4C2×C10911yescharacteristic
334#1445C2×C10911yescharacteristic, complemented
335#1442C2×C10911yescharacteristic, complemented
336#1441C2×C10911yescharacteristic, complemented
337#1440C2×C10912yes—
338#1440C2×C10912yes—
339#1436C2×C10912yescomplemented
340#1434C2×C10912yescomplemented
341C109#1484111yescharacteristic, direct product factor, Sylow
342C24×C4C22×C10911yescharacteristic
343C22×C4⋊C4C22×C10911yescharacteristic
344C22×C4⋊C4C22×C10911yescharacteristic
345C22×C4⋊C4C22×C10911yescharacteristic
346C22×C4⋊C4C22×C10911yescharacteristic
347C22×C22⋊C4C22×C10912yes—
348C22×C22⋊C4C22×C10912yes—
349C22×C22⋊C4C22×C10911yescharacteristic
350C22×C22⋊C4C22×C10911yescharacteristic
351C22×C42C22×C10912yes—
352#400—24no—
353#385—24no—
354#380—24no—
355C4×C22⋊C4—24no—
356C2×#95C22×C10912yes—
357C2×#95C22×C10912yes—
358C2×#95C22×C10911yescharacteristic
359C2×#95C22×C10912yes—
360C2×#95C22×C10912yes—
361C2×#95C22×C10912yes—
362C2×#95C22×C10912yes—
363C2×#95C22×C10912yes—
364C2×#95C22×C10911yescharacteristic
365C2×#95C22×C10911yescharacteristic
366C2×#95C22×C10912yes—
367C2×#95C22×C10912yes—
368C2×#95C22×C10911yescharacteristic
369C25C23×C10911yescharacteristic
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—24no—
373C23×C4—42no—
374C23×C4D4×C10914yes—
375C23×C4C23×C10911yescharacteristic
376C23×C4C23×C10912yes—
377C23×C4C23×C10912yes—
378C23×C4C23×C10911yescharacteristic
379C23×C4C23×C10912yes—
380C23×C4C23×C10911yescharacteristic
381C23×C4C23×C10911yescharacteristic
382C23×C4C23×C10912yes—
383C23×C4C23×C10911yescharacteristic
384C23×C4C23×C10911yescharacteristic
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—42no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—42no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—42no—
409#95—22no—
410#95—24no—
411#95—22no—
412#95—22no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—42no—
420#95—42no—
421#95D4×C10914yes—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—21no—
430C24—21no—
431C24C2×D4×C10912yes—
432C24#41×C10914yes—
433C24C24×C10911yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—44no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4C2×D4×C10914yes—
491C22×C4C2×D4×C10912yes—
492C22×C4C2×D4×C10912yes—
493C22×C4C2×D4×C10912yes—
494C22×C4#41×C10912yes—
495C22×C4#41×C10914yes—
496C22×C4#41×C10912yes—
497C22×C4#41×C10912yes—
498C22×C4#41×C10914yes—
499C4⋊C4—44no—
500C4⋊C4—44no—
501C4⋊C4—44no—
502C4⋊C4—44no—
503C22⋊C4—216no—
504C22⋊C4—28no—
505C22⋊C4—44no—
506C22⋊C4—48no—
507C42—48no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—24no—
512C23—24no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—41no—
530C23#124×C10914yes—
531C23C22×D4×C10911yescharacteristic
532C23C22×D4×C10911yescharacteristic
533C23C2×#41×C10911yescharacteristic
534C23C2×#41×C10912yes—
535C23C2×#41×C10912yes—
536C23C2×#41×C10912yes—
537C23C2×#41×C10911yescharacteristic
538C23C2×#41×C10911yescharacteristic
539C23H(5,𝔽2)×C10912yes—
540C232−1+4×C10911yescharacteristic
541C232−1+4×C10911yescharacteristic
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—416no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4#121×C10914yes—
602C2×C4#123×C10914yes—
603C22—24no—
604C22—24no—
605C22—24no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22C2×#121×C10911yescharacteristic
615C22C2×#123×C10911yescharacteristic
616C22#525×C10912yes—
617C22#525×C10911yescharacteristic
618C22C2×#124×C10911yescharacteristic
619C22#529×C10912yes—
620C22#529×C10912yes—
621C22#529×C10912yes—
622C22#532×C10911yescharacteristic
623C22#534×C10911yescharacteristic
624C22#536×C10911yescharacteristic
625C22#539×C10912yes—
626C22#542×C10912yes—
627C22#546×C10912yes—
628C22#547×C10911yescharacteristic
629C22#548×C10911yescharacteristic
630C22#551×C10912yes—
631C22#552×C10912yes—
632C22#552×C10912yes—
633C22#552×C10911yescharacteristic
634C22#553×C10912yes—
635C22#553×C10912yes—
636C22#556×C10911yescharacteristic
637C4—24no—
638C4—24no—
639C4—44no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—82no—
644C4—82no—
645C4—81no—
646C4—81no—
647C2—44no—
648C2C109×#239511yescharacteristic
649C2C109×#241211yescharacteristic
650C2C109×#241511yescharacteristic
651C2C109×#246012yes—
652C2C109×#246812yes—
653C2C109×#250311yescharacteristic
654C2C109×#253012yes—
655C2C109×#257712yes—
656C2C109×#259111yescharacteristic
657C2C109×#266311yescharacteristic
658C2C109×#285011yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC24C24×C109
prime radicalC25×C109C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#400×C109C2semidirect
5. C109×#1445C2semidirect
6. C109×#1442C2semidirect
7. C109×#1441C2semidirect
10. C109×#1436C2semidirect
11. C109×#1434C2semidirect
317. #14841C109direct (N × H)
330. C2×#400C2×C109semidirect
334. #1445C2×C109semidirect
335. #1442C2×C109semidirect
336. #1441C2×C109semidirect
339. #1436C2×C109semidirect
340. #1434C2×C109semidirect
341. C109#14841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#400×C1092
C2×#385×C1092
C2×#380×C1092
C2×C4×C22⋊C4×C1092
C109×#14452
C109×#14422
C109×#14412
C109×#14402
C109×#14362
C109×#14342
#14841109