Finite Group Databasebeta

← C109×#18277 #42136271

Subgroups — C109×#18277 #42136271

Order 27904.

934 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3559C211yesmaximal, characteristic
2C109×#3112C211yesmaximal, characteristic, complemented
3C109×#3108C211yesmaximal, characteristic, complemented
4C109×#2584C211yesmaximal, characteristic, complemented
5C109×#1610C212yesmaximal, complemented
6C109×#1609C212yesmaximal, complemented
7C109×#1604C212yesmaximal, complemented
8C109×#1603C212yesmaximal, complemented
9C109×#1509C211yesmaximal, characteristic, complemented
10C109×#1502C211yesmaximal, characteristic, complemented
11C109×#1470C211yesmaximal, characteristic, complemented
12#563×C109—21no—
13#562×C109—21no—
14#554×C109—21no—
15#553×C109—21no—
16#553×C109—21no—
17#547×C109—22no—
18#547×C109—21no—
19#544×C109—21no—
20#540×C109—21no—
21#539×C109—22no—
22#539×C109C2212yes—
23#537×C109C2212yes—
24#532×C109C2211yescharacteristic
25#529×C109C2211yescharacteristic
26C2×#125×C109C2211yescharacteristic
27C2×C4×Q8×C109C2211yescharacteristic
28#483×C109C2211yescharacteristic
29#480×C109C2211yescharacteristic
30#480×C109C2212yes—
31#479×C109—21no—
32#477×C109—21no—
33#464×C109—21no—
34#460×C109—21no—
35#451×C109C2211yescharacteristic
36#448×C109C2211yescharacteristic
37#448×C109C2212yes—
38#440×C109—22no—
39C4×Q16×C109—21no—
40C4×SD16×C109—21no—
41#432×C109C2211yescharacteristic
42#431×C109C2211yescharacteristic
43#398×C109C2212yes—
44#395×C109C2212yes—
45#389×C109—21no—
46#389×C109—22no—
47#389×C109—21no—
48C4×C4⋊C4×C109C2211yescharacteristic
49#328×C109C2212yes—
50#327×C109C2212yes—
51#327×C109C2212yes—
52#327×C109C2212yes—
53#324×C109C2212yes—
54#324×C109C2212yes—
55C2×#41×C109—21no—
56C2×#41×C109—22no—
57C22×Q8×C109C2311yescharacteristic
58C2×Q16×C109—21no—
59C2×SD16×C109—21no—
60C2×SD16×C109—22no—
61C4⋊Q8×C109—21no—
62C4⋊Q8×C109—22no—
63C4⋊Q8×C109D411yescharacteristic
64#127×C109D411yescharacteristic
65#126×C109—22no—
66#126×C109—22no—
67#126×C109—21no—
68#125×C109—21no—
69#125×C109—22no—
70#125×C109—21no—
71#125×C109—21no—
72#125×C109—21no—
73#125×C109—21no—
74#125×C109D411yescharacteristic
75#124×C109—21no—
76#124×C109D411yescharacteristic
77#123×C109—22no—
78#123×C109—22no—
79#123×C109—22no—
80#123×C109—22no—
81#123×C109—22no—
82#123×C109—21no—
83#123×C109—22no—
84C22⋊Q8×C109—22no—
85C22⋊Q8×C109—22no—
86C22⋊Q8×C109—22no—
87C22⋊Q8×C109—22no—
88C22⋊Q8×C109—22no—
89C22⋊Q8×C109—22no—
90C22⋊Q8×C109C2311yescharacteristic
91#121×C109—21no—
92#121×C109—22no—
93#121×C109—21no—
94#121×C109—22no—
95#121×C109—22no—
96#121×C109—21no—
97#121×C109—22no—
98#121×C109C2311yescharacteristic
99#121×C109C2312yes—
100C4×Q8×C109—21no—
101C4×Q8×C109—21no—
102C4×Q8×C109—21no—
103C4×Q8×C109—21no—
104C4×Q8×C109D411yescharacteristic
105C4×D4×C109—22no—
106C4×D4×C109—21no—
107C4×D4×C109—21no—
108C4×D4×C109—21no—
109C4×D4×C109—22no—
110C4×D4×C109—21no—
111C4×D4×C109D411yescharacteristic
112C4×D4×C109D412yes—
113#117×C109—21no—
114#117×C109—21no—
115C2×C4⋊C4×C109—22no—
116C2×C4⋊C4×C109—21no—
117C2×C4⋊C4×C109—21no—
118C2×C4⋊C4×C109—21no—
119C2×C4⋊C4×C109—22no—
120C2×C4⋊C4×C109—22no—
121C2×C4⋊C4×C109D411yescharacteristic
122C2×C4⋊C4×C109D412yes—
123C2×C4⋊C4×C109D411yescharacteristic
124C2×C4⋊C4×C109C2311yescharacteristic
125C2×C4⋊C4×C109C2312yes—
126C2×C42×C109—21no—
127C2×C42×C109—21no—
128C2×C42×C109C2311yescharacteristic
129#107×C109—21no—
130#107×C109—22no—
131#106×C109—21no—
132C4⋊C8×C109—21no—
133C4⋊C8×C109—21no—
134#103×C109—21no—
135#103×C109—21no—
136#103×C109—21no—
137#103×C109—22no—
138#102×C109—21no—
139#102×C109—22no—
140C22⋊C8×C109C2311yescharacteristic
141C22⋊C8×C109C2311yescharacteristic
142C22⋊C8×C109C2312yes—
143#97×C109—21no—
144C4×C8×C109—21no—
145#95×C109—22no—
146#95×C109—22no—
147#95×C109C2312yes—
148#41×C109—81no—
149#41×C109—81no—
150#41×C109—82no—
151#41×C109—82no—
152C2×Q8×C109—22no—
153C2×Q8×C109—21no—
154C2×Q8×C109—21no—
155C2×Q8×C109—21no—
156C2×Q8×C109—42no—
157C2×Q8×C109C2×D411yescharacteristic
158C2×D4×C109—21no—
159C2×D4×C109—22no—
160C2×D4×C109—22no—
161C2×D4×C109—22no—
162C2×D4×C109—21no—
163C2×D4×C109—21no—
164C2×D4×C109C2×D411yescharacteristic
165C2×D4×C109C2×D412yes—
166C22×C4×C109—22no—
167C22×C4×C109—21no—
168C22×C4×C109—22no—
169C22×C4×C109—22no—
170C22×C4×C109—22no—
171C22×C4×C109—21no—
172C22×C4×C109—22no—
173C22×C4×C109—21no—
174C22×C4×C109C2×D412yes—
175C22×C4×C109C2×D411yescharacteristic
176C22×C4×C109C2×D411yescharacteristic
177C22×C4×C109C2×D412yes—
178C22×C4×C109C2411yescharacteristic
179Q16×C109—42no—
180SD16×C109—44no—
181SD16×C109—42no—
182C2×C8×C109—21no—
183C2×C8×C109—21no—
184C2×C8×C109—22no—
185C4⋊C4×C109—24no—
186C4⋊C4×C109—22no—
187C4⋊C4×C109—22no—
188C4⋊C4×C109—22no—
189C4⋊C4×C109—22no—
190C4⋊C4×C109—21no—
191C4⋊C4×C109—21no—
192C4⋊C4×C109—22no—
193C4⋊C4×C109—21no—
194C4⋊C4×C109—21no—
195C4⋊C4×C109—22no—
196C4⋊C4×C109—21no—
197C4⋊C4×C109—21no—
198C4⋊C4×C109—21no—
199C4⋊C4×C109—21no—
200C4⋊C4×C109—22no—
201C4⋊C4×C109—22no—
202C4⋊C4×C109—21no—
203C4⋊C4×C109—21no—
204C4⋊C4×C109—21no—
205C4⋊C4×C109—44no—
206C4⋊C4×C109—41no—
207C4⋊C4×C109—41no—
208C4⋊C4×C109—82no—
209C4⋊C4×C109C2×D411yescharacteristic
210C4⋊C4×C109C2×D412yes—
211C4⋊C4×C109C2×D411yescharacteristic
212C22⋊C4×C109—22no—
213C22⋊C4×C109—22no—
214C22⋊C4×C109—22no—
215C22⋊C4×C109—22no—
216C22⋊C4×C109—22no—
217C22⋊C4×C109—21no—
218C22⋊C4×C109—21no—
219C22⋊C4×C109—21no—
220C22⋊C4×C109—21no—
221C22⋊C4×C109—22no—
222C22⋊C4×C109—21no—
223C22⋊C4×C109—22no—
224C42×C109—22no—
225C42×C109—21no—
226C42×C109—41no—
227C42×C109—41no—
228C42×C109—81no—
229C42×C109C2×D411yescharacteristic
230C42×C109C2×D411yescharacteristic
231C42×C109C2×D411yescharacteristic
232C42×C109C2×D411yescharacteristic
233C23×C109—21no—
234C23×C109—22no—
235C23×C109C22×D411yescharacteristic
236Q8×C109—22no—
237Q8×C109—22no—
238Q8×C109—41no—
239Q8×C109—41no—
240Q8×C109—41no—
241Q8×C109—81no—
242Q8×C109—82no—
243D4×C109—42no—
244D4×C109—41no—
245D4×C109—42no—
246D4×C109—41no—
247D4×C109—42no—
248D4×C109—41no—
249D4×C109—42no—
250D4×C109—81no—
251D4×C109—82no—
252D4×C109—82no—
253C2×C4×C109—21no—
254C2×C4×C109—21no—
255C2×C4×C109—22no—
256C2×C4×C109—24no—
257C2×C4×C109—22no—
258C2×C4×C109—21no—
259C2×C4×C109—21no—
260C2×C4×C109—22no—
261C2×C4×C109—22no—
262C2×C4×C109—21no—
263C2×C4×C109—22no—
264C2×C4×C109—22no—
265C2×C4×C109—22no—
266C2×C4×C109—41no—
267C2×C4×C109—42no—
268C2×C4×C109—41no—
269C2×C4×C109—41no—
270C2×C4×C109—42no—
271C2×C4×C109—42no—
272C2×C4×C109—42no—
273C2×C4×C109—41no—
274C2×C4×C109—41no—
275C2×C4×C109—41no—
276C2×C4×C109—82no—
277C2×C4×C109—82no—
278C2×C4×C109—82no—
279C2×C4×C109—82no—
280C2×C4×C109#12011yescharacteristic
281C2×C4×C109#12011yescharacteristic
282C2×C4×C109#12011yescharacteristic
283C2×C4×C109#12011yescharacteristic
284C2×C4×C109C22×D411yescharacteristic
285C2×C4×C109C22×D411yescharacteristic
286C8×C109—42no—
287C8×C109—41no—
288C8×C109—41no—
289C22×C109—21no—
290C22×C109—21no—
291C22×C109—42no—
292C22×C109—41no—
293C22×C109—41no—
294C22×C109—42no—
295C22×C109—42no—
296C22×C109—41no—
297C22×C109C2×#12011yescharacteristic
298C22×C109#57611yescharacteristic
299C22×C109#57711yescharacteristic
300C4×C109—21no—
301C4×C109—21no—
302C4×C109—21no—
303C4×C109—21no—
304C4×C109—21no—
305C4×C109—44no—
306C4×C109—42no—
307C4×C109—42no—
308C4×C109—41no—
309C4×C109—41no—
310C4×C109—42no—
311C4×C109—42no—
312C4×C109—41no—
313C4×C109—81no—
314C4×C109#45612yes—
315#18277C10911yesmaximal, characteristic, direct product factor, Sylow
316C2×C109—21no—
317C2×C109—21no—
318C2×C109—81no—
319C2×C109—82no—
320C2×C109#301211yescharacteristic
321C2×C109C2×#45611yescharacteristic
322C2×C109#302511yescharacteristic
323#3559C2×C10911yescharacteristic
324#3112C2×C10911yescharacteristic, complemented
325#3108C2×C10911yescharacteristic, complemented
326#2584C2×C10911yescharacteristic, complemented
327#1610C2×C10912yescomplemented
328#1609C2×C10912yescomplemented
329#1604C2×C10912yescomplemented
330#1603C2×C10912yescomplemented
331#1509C2×C10911yescharacteristic, complemented
332#1502C2×C10911yescharacteristic, complemented
333#1470C2×C10911yescharacteristic, complemented
334C109#1827711yescharacteristic, direct product factor, Sylow
335#563—21no—
336#562—21no—
337#554—21no—
338#553—21no—
339#553—21no—
340#547—22no—
341#547—21no—
342#544—21no—
343#540—21no—
344#539—22no—
345#539C22×C10912yes—
346#537C22×C10912yes—
347#532C22×C10911yescharacteristic
348#529C22×C10911yescharacteristic
349C2×#125C22×C10911yescharacteristic
350C2×C4×Q8C22×C10911yescharacteristic
351#483C22×C10911yescharacteristic
352#480C22×C10911yescharacteristic
353#480C22×C10912yes—
354#479—21no—
355#477—21no—
356#464—21no—
357#460—21no—
358#451C22×C10911yescharacteristic
359#448C22×C10911yescharacteristic
360#448C22×C10912yes—
361#440—22no—
362C4×Q16—21no—
363C4×SD16—21no—
364#432C22×C10911yescharacteristic
365#431C22×C10911yescharacteristic
366#398C22×C10912yes—
367#395C22×C10912yes—
368#389—21no—
369#389—22no—
370#389—21no—
371C4×C4⋊C4C22×C10911yescharacteristic
372#328C22×C10912yes—
373#327C22×C10912yes—
374#327C22×C10912yes—
375#327C22×C10912yes—
376#324C22×C10912yes—
377#324C22×C10912yes—
378C2×#41—21no—
379C2×#41—22no—
380C22×Q8C23×C10911yescharacteristic
381C2×Q16—21no—
382C2×SD16—21no—
383C2×SD16—22no—
384C4⋊Q8—21no—
385C4⋊Q8—22no—
386C4⋊Q8D4×C10911yescharacteristic
387#127D4×C10911yescharacteristic
388#126—22no—
389#126—22no—
390#126—21no—
391#125—21no—
392#125—22no—
393#125—21no—
394#125—21no—
395#125—21no—
396#125—21no—
397#125D4×C10911yescharacteristic
398#124—21no—
399#124D4×C10911yescharacteristic
400#123—22no—
401#123—22no—
402#123—22no—
403#123—22no—
404#123—22no—
405#123—21no—
406#123—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8C23×C10911yescharacteristic
414#121—21no—
415#121—22no—
416#121—21no—
417#121—22no—
418#121—22no—
419#121—21no—
420#121—22no—
421#121C23×C10911yescharacteristic
422#121C23×C10912yes—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8D4×C10911yescharacteristic
428C4×D4—22no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—22no—
433C4×D4—21no—
434C4×D4D4×C10911yescharacteristic
435C4×D4D4×C10912yes—
436#117—21no—
437#117—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4D4×C10911yescharacteristic
445C2×C4⋊C4D4×C10912yes—
446C2×C4⋊C4D4×C10911yescharacteristic
447C2×C4⋊C4C23×C10911yescharacteristic
448C2×C4⋊C4C23×C10912yes—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C10911yescharacteristic
452#107—21no—
453#107—22no—
454#106—21no—
455C4⋊C8—21no—
456C4⋊C8—21no—
457#103—21no—
458#103—21no—
459#103—21no—
460#103—22no—
461#102—21no—
462#102—22no—
463C22⋊C8C23×C10911yescharacteristic
464C22⋊C8C23×C10911yescharacteristic
465C22⋊C8C23×C10912yes—
466#97—21no—
467C4×C8—21no—
468#95—22no—
469#95—22no—
470#95C23×C10912yes—
471#41—81no—
472#41—81no—
473#41—82no—
474#41—82no—
475C2×Q8—22no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—42no—
480C2×Q8C2×D4×C10911yescharacteristic
481C2×D4—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×D4×C10911yescharacteristic
488C2×D4C2×D4×C10912yes—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4C2×D4×C10912yes—
498C22×C4C2×D4×C10911yescharacteristic
499C22×C4C2×D4×C10911yescharacteristic
500C22×C4C2×D4×C10912yes—
501C22×C4C24×C10911yescharacteristic
502Q16—42no—
503SD16—44no—
504SD16—42no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—22no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—44no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—82no—
532C4⋊C4C2×D4×C10911yescharacteristic
533C4⋊C4C2×D4×C10912yes—
534C4⋊C4C2×D4×C10911yescharacteristic
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—22no—
547C42—22no—
548C42—21no—
549C42—41no—
550C42—41no—
551C42—81no—
552C42C2×D4×C10911yescharacteristic
553C42C2×D4×C10911yescharacteristic
554C42C2×D4×C10911yescharacteristic
555C42C2×D4×C10911yescharacteristic
556C23—21no—
557C23—22no—
558C23C22×D4×C10911yescharacteristic
559Q8—22no—
560Q8—22no—
561Q8—41no—
562Q8—41no—
563Q8—41no—
564Q8—81no—
565Q8—82no—
566D4—42no—
567D4—41no—
568D4—42no—
569D4—41no—
570D4—42no—
571D4—41no—
572D4—42no—
573D4—81no—
574D4—82no—
575D4—82no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4#120×C10911yescharacteristic
604C2×C4#120×C10911yescharacteristic
605C2×C4#120×C10911yescharacteristic
606C2×C4#120×C10911yescharacteristic
607C2×C4C22×D4×C10911yescharacteristic
608C2×C4C22×D4×C10911yescharacteristic
609C8—42no—
610C8—41no—
611C8—41no—
612C22—21no—
613C22—21no—
614C22—42no—
615C22—41no—
616C22—41no—
617C22—42no—
618C22—42no—
619C22—41no—
620C22C2×#120×C10911yescharacteristic
621C22#576×C10911yescharacteristic
622C22#577×C10911yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—44no—
629C4—42no—
630C4—42no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—42no—
635C4—41no—
636C4—81no—
637C4#456×C10912yes—
638C2—21no—
639C2—21no—
640C2—81no—
641C2—82no—
642C2C109×#301211yescharacteristic
643C2C2×#456×C10911yescharacteristic
644C2C109×#302511yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#3559C2
LCSG ▷ C22×C4 ▷ 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×#3112C2semidirect
3. C109×#3108C2semidirect
4. C109×#2584C2semidirect
5. C109×#1610C2semidirect
6. C109×#1609C2semidirect
7. C109×#1604C2semidirect
8. C109×#1603C2semidirect
9. C109×#1509C2semidirect
10. C109×#1502C2semidirect
11. C109×#1470C2semidirect
315. #18277C109direct (N × H)
324. #3112C2×C109semidirect
325. #3108C2×C109semidirect
326. #2584C2×C109semidirect
327. #1610C2×C109semidirect
328. #1609C2×C109semidirect
329. #1604C2×C109semidirect
330. #1603C2×C109semidirect
331. #1509C2×C109semidirect
332. #1502C2×C109semidirect
333. #1470C2×C109semidirect
334. C109#18277direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#35592
C109×#31122
C109×#31082
C109×#25842
C109×#16102
C109×#16092
C109×#16042
C109×#16032
C109×#15092
C109×#15022
C109×#14702
#18277109