Finite Group Databasebeta

← C109×#11152 #42129146

Subgroups — C109×#11152 #42129146

Order 27904.

826 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#421×C109C211yesmaximal, characteristic
2C2×#417×C109C211yesmaximal, characteristic
3C2×#413×C109C211yesmaximal, characteristic
4C2×#344×C109C211yesmaximal, characteristic, complemented
5C2×#343×C109C211yesmaximal, characteristic, complemented
6C109×#1738C211yesmaximal, characteristic, complemented
7C109×#1736C211yesmaximal, characteristic, complemented
8C22×#41×C109C2211yescharacteristic
9C22×M16×C109C2211yescharacteristic
10C22×M16×C109C2211yescharacteristic
11C22×M16×C109C2211yescharacteristic
12C22×M16×C109C2211yescharacteristic
13C2×#117×C109C2211yescharacteristic
14C22×C4⋊C4×C109C2211yescharacteristic
15#421×C109—22no—
16#421×C109—22no—
17C2×#104×C109—22no—
18#417×C109—22no—
19#417×C109—22no—
20C2×#103×C109—21no—
21C2×#102×C109—21no—
22#413×C109—22no—
23#413×C109C414yescomplemented
24C2×#101×C109—21no—
25C2×#100×C109—21no—
26#344×C109—22no—
27#343×C109—22no—
28#341×C109—22no—
29#340×C109—22no—
30C2×#41×C109—21no—
31C2×#41×C109—21no—
32C2×#41×C109—21no—
33C2×#41×C109—21no—
34C2×#41×C109—21no—
35C2×#41×C109—21no—
36C2×#41×C109—21no—
37C2×#41×C109—21no—
38C2×#41×C109—21no—
39C2×#41×C109—21no—
40C2×#41×C109C2×C412yes—
41C2×#41×C109D412yes—
42C22×Q8×C109D411yescharacteristic
43C22×D4×C109—21no—
44C22×D4×C109D411yescharacteristic
45C23×C4×C109—21no—
46C23×C4×C109—21no—
47C23×C4×C109C2311yescharacteristic
48C2×M16×C109—21no—
49C2×M16×C109—21no—
50C2×M16×C109—21no—
51C2×M16×C109—21no—
52C2×M16×C109—21no—
53C2×M16×C109—21no—
54C2×M16×C109—21no—
55C2×M16×C109—21no—
56C2×M16×C109—21no—
57C2×M16×C109—21no—
58C2×M16×C109—21no—
59C2×M16×C109—21no—
60C2×M16×C109—21no—
61C2×M16×C109—21no—
62C2×M16×C109—21no—
63C2×M16×C109—21no—
64C2×M16×C109—21no—
65C2×M16×C109—21no—
66C2×M16×C109—21no—
67C2×M16×C109—21no—
68C2×M16×C109C2×C412yes—
69C2×M16×C109C2×C412yes—
70C2×M16×C109D412yes—
71C2×M16×C109D412yes—
72C22×C8×C109—21no—
73C22×C8×C109—21no—
74C22×C8×C109—21no—
75C22×C8×C109—21no—
76#117×C109—21no—
77#117×C109—21no—
78#117×C109—21no—
79#117×C109D412yes—
80C2×C4⋊C4×C109—21no—
81C2×C4⋊C4×C109—21no—
82C2×C4⋊C4×C109—21no—
83C2×C4⋊C4×C109—21no—
84C2×C4⋊C4×C109—21no—
85C2×C4⋊C4×C109—21no—
86C2×C4⋊C4×C109D412yes—
87C2×C22⋊C4×C109—21no—
88C2×C42×C109—21no—
89#104×C109—28no—
90#103×C109—24no—
91#102×C109—24no—
92#101×C109—24no—
93#100×C109—24no—
94C24×C109—21no—
95C24×C109#4111yescharacteristic
96#41×C109—22no—
97#41×C109—22no—
98#41×C109—22no—
99#41×C109—22no—
100#41×C109—22no—
101#41×C109—22no—
102#41×C109—22no—
103#41×C109—22no—
104#41×C109—41no—
105#41×C109—41no—
106#41×C109—41no—
107#41×C109—41no—
108#41×C109—41no—
109#41×C109—41no—
110#41×C109—41no—
111#41×C109—41no—
112C2×Q8×C109—21no—
113C2×Q8×C109—21no—
114C2×Q8×C109—21no—
115C2×Q8×C109—21no—
116C2×Q8×C109—21no—
117C2×Q8×C109C22⋊C412yes—
118C2×D4×C109—22no—
119C2×D4×C109—22no—
120C2×D4×C109—21no—
121C2×D4×C109—21no—
122C2×D4×C109—21no—
123C2×D4×C109—21no—
124C2×D4×C109—21no—
125C2×D4×C109—41no—
126C2×D4×C109—41no—
127C2×D4×C109—41no—
128C2×D4×C109—41no—
129C2×D4×C109C22⋊C412yes—
130C22×C4×C109—21no—
131C22×C4×C109—22no—
132C22×C4×C109—22no—
133C22×C4×C109—22no—
134C22×C4×C109—41no—
135C22×C4×C109—41no—
136C22×C4×C109—41no—
137C22×C4×C109—41no—
138C22×C4×C109—41no—
139C22×C4×C109—41no—
140C22×C4×C109—41no—
141C22×C4×C109—82no—
142C22×C4×C109C22×C411yescharacteristic
143C22×C4×C109C2×D411yescharacteristic
144C22×C4×C109C2×D411yescharacteristic
145C22×C4×C109C2×D411yescharacteristic
146C22×C4×C109C2×D411yescharacteristic
147C22×C4×C109C2×D411yescharacteristic
148C22×C4×C109C2×D411yescharacteristic
149C22×C4×C109#4111yescharacteristic
150C22×C4×C109#4111yescharacteristic
151C22×C4×C109#4111yescharacteristic
152C22×C4×C109#4111yescharacteristic
153C22×C4×C109#4111yescharacteristic
154C22×C4×C109#4111yescharacteristic
155C22×C4×C109#4111yescharacteristic
156M16×C109—22no—
157M16×C109—22no—
158M16×C109—22no—
159M16×C109—22no—
160M16×C109—22no—
161M16×C109—22no—
162M16×C109—22no—
163M16×C109—22no—
164M16×C109—41no—
165M16×C109—41no—
166M16×C109—41no—
167M16×C109—41no—
168M16×C109—41no—
169M16×C109—41no—
170M16×C109—41no—
171M16×C109—41no—
172C2×C8×C109—22no—
173C2×C8×C109—22no—
174C2×C8×C109—22no—
175C2×C8×C109—22no—
176C2×C8×C109—41no—
177C2×C8×C109—41no—
178C2×C8×C109—41no—
179C2×C8×C109—41no—
180C2×C8×C109—41no—
181C2×C8×C109—41no—
182C2×C8×C109—41no—
183C2×C8×C109—41no—
184C4⋊C4×C109—22no—
185C4⋊C4×C109—22no—
186C4⋊C4×C109—22no—
187C4⋊C4×C109—41no—
188C4⋊C4×C109—41no—
189C4⋊C4×C109—41no—
190C22⋊C4×C109—22no—
191C22⋊C4×C109—41no—
192C42×C109—22no—
193C42×C109—41no—
194C23×C109—22no—
195C23×C109—41no—
196C23×C109—41no—
197C23×C109—41no—
198C23×C109—41no—
199C23×C109—81no—
200C23×C109—81no—
201C23×C109#11711yescharacteristic
202C23×C109#12111yescharacteristic
203C23×C109#12311yescharacteristic
204C23×C109#12311yescharacteristic
205C23×C109#12311yescharacteristic
206C23×C109#12411yescharacteristic
207C23×C109#12611yescharacteristic
208Q8×C109—22no—
209Q8×C109—22no—
210Q8×C109—41no—
211Q8×C109—41no—
212D4×C109—22no—
213D4×C109—22no—
214D4×C109—42no—
215D4×C109—42no—
216D4×C109—42no—
217D4×C109—42no—
218D4×C109—41no—
219D4×C109—41no—
220C2×C4×C109—22no—
221C2×C4×C109—41no—
222C2×C4×C109—41no—
223C2×C4×C109—42no—
224C2×C4×C109—42no—
225C2×C4×C109—42no—
226C2×C4×C109—42no—
227C2×C4×C109—42no—
228C2×C4×C109—42no—
229C2×C4×C109—81no—
230C2×C4×C109—81no—
231C2×C4×C109—82no—
232C2×C4×C109—82no—
233C2×C4×C109—82no—
234C2×C4×C109C2×C22⋊C411yescharacteristic
235C2×C4×C109#11711yescharacteristic
236C2×C4×C109C4×D411yescharacteristic
237C2×C4×C109C4×D411yescharacteristic
238C2×C4×C109C4×D411yescharacteristic
239C2×C4×C109C4×D411yescharacteristic
240C2×C4×C109#12011yescharacteristic
241C2×C4×C109#12011yescharacteristic
242C2×C4×C109#12111yescharacteristic
243C2×C4×C109#12111yescharacteristic
244C2×C4×C109#12111yescharacteristic
245C2×C4×C109#12111yescharacteristic
246C2×C4×C109#12111yescharacteristic
247C2×C4×C109#12111yescharacteristic
248C2×C4×C109#12111yescharacteristic
249C2×C4×C109#12311yescharacteristic
250C2×C4×C109#12311yescharacteristic
251C2×C4×C109#12311yescharacteristic
252C2×C4×C109#12311yescharacteristic
253C2×C4×C109#12311yescharacteristic
254C2×C4×C109#12311yescharacteristic
255C2×C4×C109#12311yescharacteristic
256C2×C4×C109#12411yescharacteristic
257C2×C4×C109#12411yescharacteristic
258C2×C4×C109#12411yescharacteristic
259C2×C4×C109#12611yescharacteristic
260C2×C4×C109#12611yescharacteristic
261C2×C4×C109#12611yescharacteristic
262C8×C109—42no—
263C8×C109—42no—
264C8×C109—42no—
265C8×C109—42no—
266C22×C109—21no—
267C22×C109—21no—
268C22×C109—21no—
269C22×C109—21no—
270C22×C109—21no—
271C22×C109—21no—
272C22×C109—41no—
273C22×C109—41no—
274C22×C109—41no—
275C22×C109—41no—
276C22×C109—42no—
277C22×C109—82no—
278C22×C109—82no—
279C22×C109—81no—
280C22×C109—81no—
281C22×C109#38111yescharacteristic
282C22×C109#38811yescharacteristic
283C22×C109#38811yescharacteristic
284C22×C109#39411yescharacteristic
285C22×C109#39411yescharacteristic
286C22×C109#39711yescharacteristic
287C22×C109#39711yescharacteristic
288C4×C109—42no—
289C4×C109—82no—
290C4×C109—82no—
291C4×C109#38611yescharacteristic
292C4×C109#38611yescharacteristic
293C4×C109#38811yescharacteristic
294C4×C109#38811yescharacteristic
295C4×C109#39411yescharacteristic
296C4×C109#39411yescharacteristic
297C4×C109#39711yescharacteristic
298C4×C109#39711yescharacteristic
299#11152C10911yesmaximal, characteristic, direct product factor, Sylow
300C2×C109—21no—
301C2×C109—21no—
302C2×C109—21no—
303C2×C109—21no—
304C2×C109—21no—
305C2×C109—21no—
306C2×C109—82no—
307C2×C109#144011yescharacteristic
308C2×C109#204811yescharacteristic
309C2×C109#204911yescharacteristic
310C2×#421C2×C10911yescharacteristic
311C2×#417C2×C10911yescharacteristic
312C2×#413C2×C10911yescharacteristic
313C2×#344C2×C10911yescharacteristic, complemented
314C2×#343C2×C10911yescharacteristic, complemented
315#1738C2×C10911yescharacteristic, complemented
316#1736C2×C10911yescharacteristic, complemented
317C109#1115211yescharacteristic, direct product factor, Sylow
318C22×#41C22×C10911yescharacteristic
319C22×M16C22×C10911yescharacteristic
320C22×M16C22×C10911yescharacteristic
321C22×M16C22×C10911yescharacteristic
322C22×M16C22×C10911yescharacteristic
323C2×#117C22×C10911yescharacteristic
324C22×C4⋊C4C22×C10911yescharacteristic
325#421—22no—
326#421—22no—
327C2×#104—22no—
328#417—22no—
329#417—22no—
330C2×#103—21no—
331C2×#102—21no—
332#413—22no—
333#413C4×C10914yescomplemented
334C2×#101—21no—
335C2×#100—21no—
336#344—22no—
337#343—22no—
338#341—22no—
339#340—22no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41C2×C4×C10912yes—
351C2×#41D4×C10912yes—
352C22×Q8D4×C10911yescharacteristic
353C22×D4—21no—
354C22×D4D4×C10911yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4C23×C10911yescharacteristic
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16C2×C4×C10912yes—
379C2×M16C2×C4×C10912yes—
380C2×M16D4×C10912yes—
381C2×M16D4×C10912yes—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117D4×C10912yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4D4×C10912yes—
397C2×C22⋊C4—21no—
398C2×C42—21no—
399#104—28no—
400#103—24no—
401#102—24no—
402#101—24no—
403#100—24no—
404C24—21no—
405C24#41×C10911yescharacteristic
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C22⋊C4×C10912yes—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4C22⋊C4×C10912yes—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—82no—
452C22×C4C22×C4×C10911yescharacteristic
453C22×C4C2×D4×C10911yescharacteristic
454C22×C4C2×D4×C10911yescharacteristic
455C22×C4C2×D4×C10911yescharacteristic
456C22×C4C2×D4×C10911yescharacteristic
457C22×C4C2×D4×C10911yescharacteristic
458C22×C4C2×D4×C10911yescharacteristic
459C22×C4#41×C10911yescharacteristic
460C22×C4#41×C10911yescharacteristic
461C22×C4#41×C10911yescharacteristic
462C22×C4#41×C10911yescharacteristic
463C22×C4#41×C10911yescharacteristic
464C22×C4#41×C10911yescharacteristic
465C22×C4#41×C10911yescharacteristic
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—41no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16—41no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C22⋊C4—22no—
501C22⋊C4—41no—
502C42—22no—
503C42—41no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—81no—
510C23—81no—
511C23#117×C10911yescharacteristic
512C23#121×C10911yescharacteristic
513C23#123×C10911yescharacteristic
514C23#123×C10911yescharacteristic
515C23#123×C10911yescharacteristic
516C23#124×C10911yescharacteristic
517C23#126×C10911yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—22no—
524D4—42no—
525D4—42no—
526D4—42no—
527D4—42no—
528D4—41no—
529D4—41no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—82no—
544C2×C4C2×C22⋊C4×C10911yescharacteristic
545C2×C4#117×C10911yescharacteristic
546C2×C4C4×D4×C10911yescharacteristic
547C2×C4C4×D4×C10911yescharacteristic
548C2×C4C4×D4×C10911yescharacteristic
549C2×C4C4×D4×C10911yescharacteristic
550C2×C4#120×C10911yescharacteristic
551C2×C4#120×C10911yescharacteristic
552C2×C4#121×C10911yescharacteristic
553C2×C4#121×C10911yescharacteristic
554C2×C4#121×C10911yescharacteristic
555C2×C4#121×C10911yescharacteristic
556C2×C4#121×C10911yescharacteristic
557C2×C4#121×C10911yescharacteristic
558C2×C4#121×C10911yescharacteristic
559C2×C4#123×C10911yescharacteristic
560C2×C4#123×C10911yescharacteristic
561C2×C4#123×C10911yescharacteristic
562C2×C4#123×C10911yescharacteristic
563C2×C4#123×C10911yescharacteristic
564C2×C4#123×C10911yescharacteristic
565C2×C4#123×C10911yescharacteristic
566C2×C4#124×C10911yescharacteristic
567C2×C4#124×C10911yescharacteristic
568C2×C4#124×C10911yescharacteristic
569C2×C4#126×C10911yescharacteristic
570C2×C4#126×C10911yescharacteristic
571C2×C4#126×C10911yescharacteristic
572C8—42no—
573C8—42no—
574C8—42no—
575C8—42no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—82no—
588C22—82no—
589C22—81no—
590C22—81no—
591C22#381×C10911yescharacteristic
592C22#388×C10911yescharacteristic
593C22#388×C10911yescharacteristic
594C22#394×C10911yescharacteristic
595C22#394×C10911yescharacteristic
596C22#397×C10911yescharacteristic
597C22#397×C10911yescharacteristic
598C4—42no—
599C4—82no—
600C4—82no—
601C4#386×C10911yescharacteristic
602C4#386×C10911yescharacteristic
603C4#388×C10911yescharacteristic
604C4#388×C10911yescharacteristic
605C4#394×C10911yescharacteristic
606C4#394×C10911yescharacteristic
607C4#397×C10911yescharacteristic
608C4#397×C10911yescharacteristic
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—82no—
616C2C109×#144011yescharacteristic
617C2C109×#204811yescharacteristic
618C2C109×#204911yescharacteristic
subgroupG/H
center, socleC22×C109#394
commutatorC22×C4C22×C4×C109
Frattini, cosocleC23×C4C23×C109
prime radicalC22×#41×C109C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#344×C109C2semidirect
5. C2×#343×C109C2semidirect
6. C109×#1738C2semidirect
7. C109×#1736C2semidirect
23. #413×C109C4semidirect
299. #11152C109direct (N × H)
313. C2×#344C2×C109semidirect
314. C2×#343C2×C109semidirect
315. #1738C2×C109semidirect
316. #1736C2×C109semidirect
317. C109#11152direct (N × H)
333. #413C4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#421×C1092
C2×#417×C1092
C2×#413×C1092
C2×#344×C1092
C2×#343×C1092
C109×#17382
C109×#17362
#11152109