Finite Group Databasebeta

← C109×#18418 #42136412

Subgroups — C109×#18418 #42136412

Order 27904.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3537C211yesmaximal, characteristic, complemented
2C109×#3192C211yesmaximal, characteristic, complemented
3C109×#3188C211yesmaximal, characteristic, complemented
4C109×#2656C211yesmaximal, characteristic, complemented
5C109×#1618C212yesmaximal, complemented
6C109×#1613C212yesmaximal, complemented
7C109×#1600C212yesmaximal, complemented
8C109×#1595C212yesmaximal, complemented
9C109×#1504C211yesmaximal, characteristic, complemented
10C2×#327×C109C211yesmaximal, characteristic, complemented
11C109×#1471C211yesmaximal, characteristic, complemented
12#560×C109—22no—
13#553×C109—21no—
14#553×C109—21no—
15D42×C109—22no—
16D42×C109—21no—
17D42×C109—21no—
18#540×C109—21no—
19#538×C109—21no—
20#538×C109C2212yes—
21#535×C109—21no—
22#534×C109—21no—
23#534×C109C2212yes—
24#525×C109C2211yescharacteristic
25C2×#121×C109—22no—
26C2×#121×C109C2211yescharacteristic
27C2×#121×C109C2211yescharacteristic
28C2×#121×C109C2211yescharacteristic, complemented
29#484×C109C2211yescharacteristic, complemented
30#482×C109—21no—
31#481×C109—21no—
32#481×C109C2211yescharacteristic, complemented
33#481×C109C2212yescomplemented
34#469×C109—22no—
35#466×C109—21no—
36#465×C109—21no—
37#450×C109C2211yescharacteristic, complemented
38#449×C109—21no—
39#447×C109—21no—
40#447×C109C2211yescharacteristic, complemented
41#447×C109C2212yescomplemented
42#407×C109C2211yescharacteristic, complemented
43C2×C22⋊C8×C109C2211yescharacteristic, complemented
44#399×C109—21no—
45#399×C109C2212yescomplemented
46#392×C109—21no—
47#392×C109C2212yescomplemented
48C2×#95×C109C2211yescharacteristic, complemented
49#328×C109C2212yescomplemented
50#327×C109C2212yescomplemented
51#327×C109C2212yescomplemented
52#327×C109C2212yescomplemented
53#323×C109C2212yescomplemented
54#323×C109C2212yescomplemented
55C2×#41×C109D411yescharacteristic, complemented
56C22×D4×C109—22no—
57C22×D4×C109—21no—
58C22×D4×C109—21no—
59C22×D4×C109—22no—
60C22×D4×C109—21no—
61C22×D4×C109—22no—
62C22×D4×C109D412yes—
63C22×D4×C109D411yescharacteristic
64C22×D4×C109D411yescharacteristic, complemented
65C22×D4×C109C2311yescharacteristic
66C23×C4×C109—21no—
67C23×C4×C109C2311yescharacteristic
68C2×SD16×C109—21no—
69C2×D8×C109—22no—
70C2×D8×C109—21no—
71C2×M16×C109—21no—
72C22×C8×C109—21no—
73#127×C109—22no—
74#127×C109—21no—
75#126×C109—22no—
76#126×C109—22no—
77#125×C109—21no—
78#124×C109—22no—
79#123×C109—22no—
80#123×C109—21no—
81#123×C109—22no—
82#123×C109—22no—
83#123×C109—22no—
84C22⋊Q8×C109D411yescharacteristic, complemented
85C22⋊Q8×C109C2311yescharacteristic
86#121×C109—22no—
87#121×C109—21no—
88#121×C109—21no—
89#121×C109—22no—
90#121×C109—22no—
91#121×C109—22no—
92#121×C109—22no—
93#121×C109—21no—
94#121×C109—21no—
95#121×C109—21no—
96#121×C109—21no—
97#121×C109—21no—
98#121×C109—21no—
99#121×C109—22no—
100#121×C109—21no—
101#121×C109—21no—
102#121×C109—21no—
103#121×C109—21no—
104#121×C109—48no—
105#121×C109D412yescomplemented
106#121×C109D411yescharacteristic, complemented
107#121×C109C2312yes—
108#121×C109C2311yescharacteristic
109#120×C109—22no—
110#120×C109—22no—
111#120×C109—22no—
112#120×C109—21no—
113#120×C109—22no—
114#120×C109—22no—
115#120×C109—22no—
116C4×D4×C109—22no—
117C4×D4×C109—21no—
118C4×D4×C109—21no—
119C4×D4×C109—21no—
120C4×D4×C109—21no—
121C4×D4×C109—22no—
122#117×C109—21no—
123#117×C109D411yescharacteristic, complemented
124C2×C4⋊C4×C109—22no—
125C2×C4⋊C4×C109D411yescharacteristic
126C2×C4⋊C4×C109D411yescharacteristic, complemented
127C2×C4⋊C4×C109C2311yescharacteristic
128C2×C22⋊C4×C109—21no—
129C2×C22⋊C4×C109—22no—
130C2×C22⋊C4×C109—22no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109C2312yes—
133#107×C109—21no—
134#106×C109—21no—
135#106×C109—22no—
136#103×C109—21no—
137#102×C109—22no—
138#102×C109—21no—
139#102×C109—21no—
140#102×C109—22no—
141#102×C109—21no—
142C22⋊C8×C109—21no—
143C22⋊C8×C109—21no—
144C22⋊C8×C109C2311yescharacteristic
145C22⋊C8×C109C2311yescharacteristic
146C22⋊C8×C109C2312yes—
147#95×C109—21no—
148#95×C109C2312yes—
149C24×C109—22no—
150C24×C109—21no—
151C24×C109—21no—
152C24×C109C2×D411yescharacteristic
153C24×C109C2×D412yes—
154#41×C109—81no—
155C2×Q8×C109C2×D411yescharacteristic
156C2×D4×C109—22no—
157C2×D4×C109—21no—
158C2×D4×C109—21no—
159C2×D4×C109—22no—
160C2×D4×C109—22no—
161C2×D4×C109—22no—
162C2×D4×C109—22no—
163C2×D4×C109—22no—
164C2×D4×C109—22no—
165C2×D4×C109—21no—
166C2×D4×C109—22no—
167C2×D4×C109—22no—
168C2×D4×C109—21no—
169C2×D4×C109—21no—
170C2×D4×C109—21no—
171C2×D4×C109—21no—
172C2×D4×C109—21no—
173C2×D4×C109—44no—
174C2×D4×C109—44no—
175C2×D4×C109—44no—
176C2×D4×C109—41no—
177C2×D4×C109—41no—
178C2×D4×C109—81no—
179C2×D4×C109—81no—
180C2×D4×C109—82no—
181C2×D4×C109—81no—
182C2×D4×C109—82no—
183C2×D4×C109—82no—
184C2×D4×C109—81no—
185C2×D4×C109—81no—
186C2×D4×C109—82no—
187C2×D4×C109—82no—
188C2×D4×C109—84no—
189C2×D4×C109C2×D411yescharacteristic
190C2×D4×C109C2×D412yes—
191C22×C4×C109—22no—
192C22×C4×C109—22no—
193C22×C4×C109—22no—
194C22×C4×C109—24no—
195C22×C4×C109—21no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—81no—
199C22×C4×C109—81no—
200C22×C4×C109—81no—
201C22×C4×C109C2×D412yes—
202C22×C4×C109C2×D411yescharacteristic
203C22×C4×C109C2×D411yescharacteristic
204C22×C4×C109C2×D411yescharacteristic
205C22×C4×C109C2×D411yescharacteristic
206C22×C4×C109C2×D411yescharacteristic
207C22×C4×C109C2411yescharacteristic
208SD16×C109—81no—
209D8×C109—81no—
210D8×C109—82no—
211M16×C109—81no—
212C2×C8×C109—21no—
213C2×C8×C109—22no—
214C2×C8×C109—21no—
215C2×C8×C109—81no—
216C4⋊C4×C109—22no—
217C4⋊C4×C109—22no—
218C4⋊C4×C109—21no—
219C4⋊C4×C109—21no—
220C4⋊C4×C109—21no—
221C4⋊C4×C109—21no—
222C4⋊C4×C109—21no—
223C4⋊C4×C109—21no—
224C4⋊C4×C109—21no—
225C4⋊C4×C109—44no—
226C4⋊C4×C109C2×D412yes—
227C4⋊C4×C109C2×D411yescharacteristic
228C4⋊C4×C109C2×D411yescharacteristic
229C22⋊C4×C109—22no—
230C22⋊C4×C109—22no—
231C22⋊C4×C109—22no—
232C22⋊C4×C109—22no—
233C22⋊C4×C109—22no—
234C22⋊C4×C109—21no—
235C22⋊C4×C109—21no—
236C22⋊C4×C109—21no—
237C22⋊C4×C109—22no—
238C22⋊C4×C109—21no—
239C22⋊C4×C109—22no—
240C22⋊C4×C109—22no—
241C22⋊C4×C109—22no—
242C22⋊C4×C109—21no—
243C22⋊C4×C109—44no—
244C22⋊C4×C109—44no—
245C22⋊C4×C109—41no—
246C22⋊C4×C109—41no—
247C42×C109—22no—
248C42×C109—21no—
249C23×C109—21no—
250C23×C109—21no—
251C23×C109—22no—
252C23×C109—22no—
253C23×C109—22no—
254C23×C109—21no—
255C23×C109—22no—
256C23×C109—22no—
257C23×C109—41no—
258C23×C109—42no—
259C23×C109—42no—
260C23×C109—42no—
261C23×C109—42no—
262C23×C109—42no—
263C23×C109—41no—
264C23×C109—41no—
265C23×C109—41no—
266C23×C109—81no—
267C23×C109—81no—
268C23×C109—82no—
269C23×C109—82no—
270C23×C109—82no—
271C23×C109#12011yescharacteristic
272C23×C109#12011yescharacteristic
273C23×C109C22×D411yescharacteristic
274Q8×C109—41no—
275D4×C109—42no—
276D4×C109—41no—
277D4×C109—42no—
278D4×C109—42no—
279D4×C109—42no—
280D4×C109—41no—
281D4×C109—41no—
282D4×C109—42no—
283D4×C109—41no—
284D4×C109—42no—
285D4×C109—41no—
286D4×C109—44no—
287D4×C109—42no—
288D4×C109—81no—
289D4×C109—82no—
290D4×C109—82no—
291D4×C109—81no—
292D4×C109—82no—
293D4×C109—82no—
294D4×C109—82no—
295D4×C109—82no—
296D4×C109—82no—
297D4×C109—88no—
298D4×C109—82no—
299D4×C109—82no—
300C2×C4×C109—24no—
301C2×C4×C109—21no—
302C2×C4×C109—22no—
303C2×C4×C109—22no—
304C2×C4×C109—21no—
305C2×C4×C109—21no—
306C2×C4×C109—41no—
307C2×C4×C109—41no—
308C2×C4×C109—41no—
309C2×C4×C109—41no—
310C2×C4×C109—41no—
311C2×C4×C109—41no—
312C2×C4×C109—42no—
313C2×C4×C109—42no—
314C2×C4×C109—42no—
315C2×C4×C109—42no—
316C2×C4×C109—42no—
317C2×C4×C109—41no—
318C2×C4×C109—81no—
319C2×C4×C109—84no—
320C2×C4×C109—82no—
321C2×C4×C109—82no—
322C2×C4×C109#12011yescharacteristic
323C2×C4×C109#12011yescharacteristic
324C2×C4×C109C22×D411yescharacteristic
325C2×C4×C109C22×D411yescharacteristic
326C8×C109—41no—
327C8×C109—41no—
328C8×C109—42no—
329C22×C109—21no—
330C22×C109—21no—
331C22×C109—21no—
332C22×C109—21no—
333C22×C109—21no—
334C22×C109—21no—
335C22×C109—21no—
336C22×C109—42no—
337C22×C109—42no—
338C22×C109—42no—
339C22×C109—42no—
340C22×C109—41no—
341C22×C109—42no—
342C22×C109—42no—
343C22×C109—41no—
344C22×C109—41no—
345C22×C109—42no—
346C22×C109—42no—
347C22×C109—82no—
348C22×C109—82no—
349C22×C109—82no—
350C22×C109—82no—
351C22×C109—81no—
352C22×C109—81no—
353C22×C109—81no—
354C22×C109—162no—
355C22×C109—164no—
356C22×C109#45312yes—
357C22×C109C2×#12011yescharacteristic
358C22×C109#57611yescharacteristic
359C22×C109#57711yescharacteristic
360C4×C109—21no—
361C4×C109—21no—
362C4×C109—21no—
363C4×C109—21no—
364C4×C109—44no—
365C4×C109—42no—
366C4×C109—41no—
367C4×C109—42no—
368C4×C109—41no—
369C4×C109—41no—
370C4×C109—81no—
371#18418C10911yesmaximal, characteristic, direct product factor, Sylow
372C2×C109—21no—
373C2×C109—21no—
374C2×C109—22no—
375C2×C109—41no—
376C2×C109—82no—
377C2×C109—82no—
378C2×C109—81no—
379C2×C109—161no—
380C2×C109#301211yescharacteristic
381C2×C109C2×#45311yescharacteristic
382C2×C109#302611yescharacteristic
383#3537C2×C10911yescharacteristic, complemented
384#3192C2×C10911yescharacteristic, complemented
385#3188C2×C10911yescharacteristic, complemented
386#2656C2×C10911yescharacteristic, complemented
387#1618C2×C10912yescomplemented
388#1613C2×C10912yescomplemented
389#1600C2×C10912yescomplemented
390#1595C2×C10912yescomplemented
391#1504C2×C10911yescharacteristic, complemented
392C2×#327C2×C10911yescharacteristic, complemented
393#1471C2×C10911yescharacteristic, complemented
394C109#1841811yescharacteristic, direct product factor, Sylow
395#560—22no—
396#553—21no—
397#553—21no—
398D42—22no—
399D42—21no—
400D42—21no—
401#540—21no—
402#538—21no—
403#538C22×C10912yes—
404#535—21no—
405#534—21no—
406#534C22×C10912yes—
407#525C22×C10911yescharacteristic
408C2×#121—22no—
409C2×#121C22×C10911yescharacteristic
410C2×#121C22×C10911yescharacteristic
411C2×#121C22×C10911yescharacteristic, complemented
412#484C22×C10911yescharacteristic, complemented
413#482—21no—
414#481—21no—
415#481C22×C10911yescharacteristic, complemented
416#481C22×C10912yescomplemented
417#469—22no—
418#466—21no—
419#465—21no—
420#450C22×C10911yescharacteristic, complemented
421#449—21no—
422#447—21no—
423#447C22×C10911yescharacteristic, complemented
424#447C22×C10912yescomplemented
425#407C22×C10911yescharacteristic, complemented
426C2×C22⋊C8C22×C10911yescharacteristic, complemented
427#399—21no—
428#399C22×C10912yescomplemented
429#392—21no—
430#392C22×C10912yescomplemented
431C2×#95C22×C10911yescharacteristic, complemented
432#328C22×C10912yescomplemented
433#327C22×C10912yescomplemented
434#327C22×C10912yescomplemented
435#327C22×C10912yescomplemented
436#323C22×C10912yescomplemented
437#323C22×C10912yescomplemented
438C2×#41D4×C10911yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C10912yes—
446C22×D4D4×C10911yescharacteristic
447C22×D4D4×C10911yescharacteristic, complemented
448C22×D4C23×C10911yescharacteristic
449C23×C4—21no—
450C23×C4C23×C10911yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C10911yescharacteristic, complemented
468C22⋊Q8C23×C10911yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C10912yescomplemented
489#121D4×C10911yescharacteristic, complemented
490#121C23×C10912yes—
491#121C23×C10911yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C10911yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C10911yescharacteristic
509C2×C4⋊C4D4×C10911yescharacteristic, complemented
510C2×C4⋊C4C23×C10911yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C10912yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C10911yescharacteristic
528C22⋊C8C23×C10911yescharacteristic
529C22⋊C8C23×C10912yes—
530#95—21no—
531#95C23×C10912yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C10911yescharacteristic
536C24C2×D4×C10912yes—
537#41—81no—
538C2×Q8C2×D4×C10911yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C10911yescharacteristic
573C2×D4C2×D4×C10912yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C10912yes—
585C22×C4C2×D4×C10911yescharacteristic
586C22×C4C2×D4×C10911yescharacteristic
587C22×C4C2×D4×C10911yescharacteristic
588C22×C4C2×D4×C10911yescharacteristic
589C22×C4C2×D4×C10911yescharacteristic
590C22×C4C24×C10911yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C10912yes—
610C4⋊C4C2×D4×C10911yescharacteristic
611C4⋊C4C2×D4×C10911yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C10911yescharacteristic
655C23#120×C10911yescharacteristic
656C23C22×D4×C10911yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—42no—
666D4—41no—
667D4—42no—
668D4—41no—
669D4—44no—
670D4—42no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C10911yescharacteristic
706C2×C4#120×C10911yescharacteristic
707C2×C4C22×D4×C10911yescharacteristic
708C2×C4C22×D4×C10911yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22#453×C10912yes—
740C22C2×#120×C10911yescharacteristic
741C22#576×C10911yescharacteristic
742C22#577×C10911yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2C109×#301211yescharacteristic
763C2C2×#453×C10911yescharacteristic
764C2C109×#302611yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3537C2semidirect
2. C109×#3192C2semidirect
3. C109×#3188C2semidirect
4. C109×#2656C2semidirect
5. C109×#1618C2semidirect
6. C109×#1613C2semidirect
7. C109×#1600C2semidirect
8. C109×#1595C2semidirect
9. C109×#1504C2semidirect
10. C2×#327×C109C2semidirect
11. C109×#1471C2semidirect
28. C2×#121×C109C22semidirect
29. #484×C109C22semidirect
32. #481×C109C22semidirect
33. #481×C109C22semidirect
37. #450×C109C22semidirect
40. #447×C109C22semidirect
41. #447×C109C22semidirect
42. #407×C109C22semidirect
43. C2×C22⋊C8×C109C22semidirect
45. #399×C109C22semidirect
47. #392×C109C22semidirect
48. C2×#95×C109C22semidirect
49. #328×C109C22semidirect
50. #327×C109C22semidirect
51. #327×C109C22semidirect
52. #327×C109C22semidirect
53. #323×C109C22semidirect
54. #323×C109C22semidirect
55. C2×#41×C109D4semidirect
64. C22×D4×C109D4semidirect
84. C22⋊Q8×C109D4semidirect
105. #121×C109D4semidirect
106. #121×C109D4semidirect
123. #117×C109D4semidirect
126. C2×C4⋊C4×C109D4semidirect
371. #18418C109direct (N × H)
383. #3537C2×C109semidirect
384. #3192C2×C109semidirect
385. #3188C2×C109semidirect
386. #2656C2×C109semidirect
387. #1618C2×C109semidirect
388. #1613C2×C109semidirect
389. #1600C2×C109semidirect
390. #1595C2×C109semidirect
391. #1504C2×C109semidirect
392. C2×#327C2×C109semidirect
393. #1471C2×C109semidirect
394. C109#18418direct (N × H)
411. C2×#121C22×C109semidirect
412. #484C22×C109semidirect
415. #481C22×C109semidirect
416. #481C22×C109semidirect
420. #450C22×C109semidirect
423. #447C22×C109semidirect
424. #447C22×C109semidirect
425. #407C22×C109semidirect
426. C2×C22⋊C8C22×C109semidirect
428. #399C22×C109semidirect
430. #392C22×C109semidirect
431. C2×#95C22×C109semidirect
432. #328C22×C109semidirect
433. #327C22×C109semidirect
434. #327C22×C109semidirect
435. #327C22×C109semidirect
436. #323C22×C109semidirect
437. #323C22×C109semidirect
438. C2×#41D4×C109semidirect
447. C22×D4D4×C109semidirect
467. C22⋊Q8D4×C109semidirect
488. #121D4×C109semidirect
489. #121D4×C109semidirect
506. #117D4×C109semidirect
509. C2×C4⋊C4D4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35372
C109×#31922
C109×#31882
C109×#26562
C109×#16182
C109×#16132
C109×#16002
C109×#15952
C109×#15042
C2×#327×C1092
C109×#14712
#18418109