Finite Group Databasebeta

← C109×#18254 #42136248

Subgroups — C109×#18254 #42136248

Order 27904.

1508 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3537C211yesmaximal, characteristic, complemented
2C109×#3003C211yesmaximal, characteristic, complemented
3C2×#447×C109C211yesmaximal, characteristic, complemented
4C109×#2433C211yesmaximal, characteristic, complemented
5C109×#1600C214yesmaximal, complemented
6C109×#1595C214yesmaximal, complemented
7C109×#1507C211yesmaximal, characteristic, complemented
8C109×#1501C211yesmaximal, characteristic, complemented
9C109×#1471C211yesmaximal, characteristic, complemented
10C23×D4×C109C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C109—21no—
12C22×D8×C109—21no—
13#560×C109—22no—
14#553×C109—21no—
15#553×C109—21no—
16D42×C109—22no—
17D42×C109—21no—
18D42×C109—21no—
19#540×C109—21no—
20#538×C109—21no—
21#538×C109C2212yescomplemented
22#535×C109—21no—
23#534×C109—21no—
24#534×C109C2212yescomplemented
25C2×#127×C109—21no—
26#525×C109C2211yescharacteristic
27C2×#121×C109C2211yescharacteristic
28C2×#121×C109C2211yescharacteristic
29C2×#120×C109—22no—
30#450×C109—21no—
31#450×C109C2212yescomplemented
32#447×C109—22no—
33#447×C109—21no—
34#447×C109C2214yescomplemented
35#447×C109C2212yescomplemented
36#418×C109—21no—
37C2×#102×C109—21no—
38#407×C109C2211yescharacteristic, complemented
39C2×C22⋊C8×C109C2211yescharacteristic, complemented
40#392×C109C2214yescomplemented
41#390×C109—21no—
42C4×C22⋊C4×C109C2211yescharacteristic, complemented
43#328×C109C2212yescomplemented
44#327×C109C2212yescomplemented
45#327×C109C2214yescomplemented
46#323×C109C2214yescomplemented
47C25×C109—21no—
48C2×#41×C109D411yescharacteristic, complemented
49C22×D4×C109—22no—
50C22×D4×C109—21no—
51C22×D4×C109—21no—
52C22×D4×C109—22no—
53C22×D4×C109—24no—
54C22×D4×C109—21no—
55C22×D4×C109—21no—
56C22×D4×C109—21no—
57C22×D4×C109—21no—
58C22×D4×C109—21no—
59C22×D4×C109—44no—
60C22×D4×C109D412yes—
61C22×D4×C109D411yescharacteristic
62C22×D4×C109D411yescharacteristic, complemented
63C22×D4×C109C2312yes—
64C23×C4×C109C2311yescharacteristic
65AGL(1,ℤ/8)×C109—44no—
66C2×SD16×C109—22no—
67C2×D8×C109—24no—
68C2×D8×C109—22no—
69C2×D8×C109—44no—
70C2×M16×C109—21no—
71C22×C8×C109—21no—
72#127×C109—22no—
73#127×C109—21no—
74#127×C109—44no—
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×C109D412yescomplemented
101#121×C109D411yescharacteristic, complemented
102#121×C109C2312yes—
103#121×C109C2311yescharacteristic
104#120×C109—22no—
105#120×C109—22no—
106#120×C109—22no—
107#120×C109—21no—
108#120×C109—22no—
109#120×C109—22no—
110#120×C109—22no—
111#120×C109—48no—
112C4×D4×C109—22no—
113C4×D4×C109—21no—
114C4×D4×C109—21no—
115C4×D4×C109—21no—
116C4×D4×C109—21no—
117C4×D4×C109—22no—
118#117×C109—21no—
119#117×C109D411yescharacteristic, complemented
120C2×C4⋊C4×C109D411yescharacteristic
121C2×C4⋊C4×C109D411yescharacteristic, complemented
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—24no—
125C2×C22⋊C4×C109C2312yes—
126C2×C42×C109—21no—
127#102×C109—24no—
128#102×C109—22no—
129#102×C109—22no—
130C22⋊C8×C109—21no—
131C22⋊C8×C109—21no—
132C22⋊C8×C109C2312yes—
133C22⋊C8×C109C2312yes—
134#95×C109C2312yes—
135C24×C109—22no—
136C24×C109—22no—
137C24×C109—21no—
138C24×C109—44no—
139C24×C109—44no—
140C24×C109—41no—
141C24×C109—41no—
142C24×C109—82no—
143C24×C109C2×D411yescharacteristic
144C24×C109C2×D412yes—
145#41×C109—42no—
146C2×Q8×C109C2×D411yescharacteristic
147C2×D4×C109—24no—
148C2×D4×C109—24no—
149C2×D4×C109—24no—
150C2×D4×C109—22no—
151C2×D4×C109—21no—
152C2×D4×C109—21no—
153C2×D4×C109—22no—
154C2×D4×C109—22no—
155C2×D4×C109—22no—
156C2×D4×C109—22no—
157C2×D4×C109—22no—
158C2×D4×C109—22no—
159C2×D4×C109—21no—
160C2×D4×C109—22no—
161C2×D4×C109—22no—
162C2×D4×C109—21no—
163C2×D4×C109—21no—
164C2×D4×C109—21no—
165C2×D4×C109—22no—
166C2×D4×C109—22no—
167C2×D4×C109—42no—
168C2×D4×C109—42no—
169C2×D4×C109—42no—
170C2×D4×C109—42no—
171C2×D4×C109—42no—
172C2×D4×C109—48no—
173C2×D4×C109—44no—
174C2×D4×C109—44no—
175C2×D4×C109—44no—
176C2×D4×C109—44no—
177C2×D4×C109—48no—
178C2×D4×C109—41no—
179C2×D4×C109—41no—
180C2×D4×C109—82no—
181C2×D4×C109—84no—
182C2×D4×C109—82no—
183C2×D4×C109—84no—
184C2×D4×C109—84no—
185C2×D4×C109C2×D411yescharacteristic
186C2×D4×C109C2×D412yes—
187C22×C4×C109—22no—
188C22×C4×C109—22no—
189C22×C4×C109—22no—
190C22×C4×C109—21no—
191C22×C4×C109—21no—
192C22×C4×C109—42no—
193C22×C4×C109C2×D411yescharacteristic
194C22×C4×C109C2×D411yescharacteristic
195C22×C4×C109C2×D411yescharacteristic
196C22×C4×C109C2×D412yes—
197C22×C4×C109C2×D411yescharacteristic
198C22×C4×C109C2×D411yescharacteristic
199C22×C4×C109C2411yescharacteristic
200SD16×C109—44no—
201D8×C109—48no—
202D8×C109—44no—
203M16×C109—42no—
204C2×C8×C109—22no—
205C2×C8×C109—22no—
206C2×C8×C109—42no—
207C4⋊C4×C109—22no—
208C4⋊C4×C109—22no—
209C4⋊C4×C109—21no—
210C4⋊C4×C109—21no—
211C4⋊C4×C109—21no—
212C4⋊C4×C109—21no—
213C4⋊C4×C109—21no—
214C4⋊C4×C109C2×D412yes—
215C4⋊C4×C109C2×D411yescharacteristic
216C4⋊C4×C109C2×D411yescharacteristic
217C22⋊C4×C109—24no—
218C22⋊C4×C109—22no—
219C22⋊C4×C109—22no—
220C22⋊C4×C109—22no—
221C22⋊C4×C109—22no—
222C22⋊C4×C109—22no—
223C22⋊C4×C109—21no—
224C22⋊C4×C109—21no—
225C22⋊C4×C109—21no—
226C22⋊C4×C109—22no—
227C22⋊C4×C109—21no—
228C22⋊C4×C109—22no—
229C22⋊C4×C109—22no—
230C22⋊C4×C109—22no—
231C22⋊C4×C109—21no—
232C22⋊C4×C109—48no—
233C42×C109—22no—
234C42×C109—21no—
235C42×C109—42no—
236C23×C109—22no—
237C23×C109—22no—
238C23×C109—24no—
239C23×C109—22no—
240C23×C109—22no—
241C23×C109—21no—
242C23×C109—24no—
243C23×C109—41no—
244C23×C109—44no—
245C23×C109—44no—
246C23×C109—44no—
247C23×C109—42no—
248C23×C109—42no—
249C23×C109—42no—
250C23×C109—42no—
251C23×C109—44no—
252C23×C109—42no—
253C23×C109—81no—
254C23×C109—81no—
255C23×C109—82no—
256C23×C109—82no—
257C23×C109—82no—
258C23×C109—82no—
259C23×C109—82no—
260C23×C109—82no—
261C23×C109—816no—
262C23×C109—82no—
263C23×C109#12011yescharacteristic
264C23×C109#12011yescharacteristic
265C23×C109C22×D411yescharacteristic
266Q8×C109—41no—
267D4×C109—24no—
268D4×C109—24no—
269D4×C109—42no—
270D4×C109—41no—
271D4×C109—42no—
272D4×C109—42no—
273D4×C109—44no—
274D4×C109—44no—
275D4×C109—42no—
276D4×C109—44no—
277D4×C109—42no—
278D4×C109—44no—
279D4×C109—42no—
280D4×C109—42no—
281D4×C109—81no—
282D4×C109—82no—
283D4×C109—82no—
284D4×C109—81no—
285D4×C109—82no—
286D4×C109—82no—
287D4×C109—82no—
288D4×C109—82no—
289D4×C109—82no—
290D4×C109—816no—
291C2×C4×C109—22no—
292C2×C4×C109—22no—
293C2×C4×C109—22no—
294C2×C4×C109—24no—
295C2×C4×C109—21no—
296C2×C4×C109—22no—
297C2×C4×C109—22no—
298C2×C4×C109—21no—
299C2×C4×C109—21no—
300C2×C4×C109—41no—
301C2×C4×C109—41no—
302C2×C4×C109—41no—
303C2×C4×C109—42no—
304C2×C4×C109—42no—
305C2×C4×C109—42no—
306C2×C4×C109—42no—
307C2×C4×C109—81no—
308C2×C4×C109—82no—
309C2×C4×C109—82no—
310C2×C4×C109#12011yescharacteristic
311C2×C4×C109#12011yescharacteristic
312C2×C4×C109C22×D411yescharacteristic
313C2×C4×C109C22×D411yescharacteristic
314C8×C109—42no—
315C8×C109—42no—
316C22×C109—21no—
317C22×C109—21no—
318C22×C109—21no—
319C22×C109—21no—
320C22×C109—21no—
321C22×C109—21no—
322C22×C109—21no—
323C22×C109—44no—
324C22×C109—48no—
325C22×C109—42no—
326C22×C109—42no—
327C22×C109—41no—
328C22×C109—42no—
329C22×C109—42no—
330C22×C109—41no—
331C22×C109—41no—
332C22×C109—44no—
333C22×C109—42no—
334C22×C109—42no—
335C22×C109—84no—
336C22×C109—84no—
337C22×C109—88no—
338C22×C109—88no—
339C22×C109—82no—
340C22×C109—82no—
341C22×C109—162no—
342C22×C109—164no—
343C22×C109#45312yes—
344C22×C109C2×#12011yescharacteristic
345C22×C109#57612yes—
346C4×C109—21no—
347C4×C109—21no—
348C4×C109—21no—
349C4×C109—44no—
350C4×C109—42no—
351C4×C109—41no—
352C4×C109—42no—
353C4×C109—41no—
354C4×C109—41no—
355C4×C109B(4,𝔽2)12yes—
356#18254C10911yesmaximal, characteristic, direct product factor, Sylow
357C2×C109—22no—
358C2×C109—22no—
359C2×C109—41no—
360C2×C109—84no—
361C2×C109—82no—
362C2×C109—82no—
363C2×C109—81no—
364C2×C109#300811yescharacteristic
365C2×C109C2×#45311yescharacteristic
366C2×C109C2×B(4,𝔽2)11yescharacteristic
367#3537C2×C10911yescharacteristic, complemented
368#3003C2×C10911yescharacteristic, complemented
369C2×#447C2×C10911yescharacteristic, complemented
370#2433C2×C10911yescharacteristic, complemented
371#1600C2×C10914yescomplemented
372#1595C2×C10914yescomplemented
373#1507C2×C10911yescharacteristic, complemented
374#1501C2×C10911yescharacteristic, complemented
375#1471C2×C10911yescharacteristic, complemented
376C109#1825411yescharacteristic, direct product factor, Sylow
377C23×D4C22×C10911yescharacteristic, complemented
378C2×AGL(1,ℤ/8)—21no—
379C22×D8—21no—
380#560—22no—
381#553—21no—
382#553—21no—
383D42—22no—
384D42—21no—
385D42—21no—
386#540—21no—
387#538—21no—
388#538C22×C10912yescomplemented
389#535—21no—
390#534—21no—
391#534C22×C10912yescomplemented
392C2×#127—21no—
393#525C22×C10911yescharacteristic
394C2×#121C22×C10911yescharacteristic
395C2×#121C22×C10911yescharacteristic
396C2×#120—22no—
397#450—21no—
398#450C22×C10912yescomplemented
399#447—22no—
400#447—21no—
401#447C22×C10912yescomplemented
402#447C22×C10914yescomplemented
403#418—21no—
404C2×#102—21no—
405#407C22×C10911yescharacteristic, complemented
406C2×C22⋊C8C22×C10911yescharacteristic, complemented
407#392C22×C10914yescomplemented
408#390—21no—
409C4×C22⋊C4C22×C10911yescharacteristic, complemented
410#328C22×C10912yescomplemented
411#327C22×C10912yescomplemented
412#327C22×C10914yescomplemented
413#323C22×C10914yescomplemented
414C25—21no—
415C2×#41D4×C10911yescharacteristic, complemented
416C22×D4—22no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4—22no—
420C22×D4—24no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—44no—
427C22×D4D4×C10912yes—
428C22×D4D4×C10911yescharacteristic
429C22×D4D4×C10911yescharacteristic, complemented
430C22×D4C23×C10912yes—
431C23×C4C23×C10911yescharacteristic
432AGL(1,ℤ/8)—44no—
433C2×SD16—22no—
434C2×D8—24no—
435C2×D8—22no—
436C2×D8—44no—
437C2×M16—21no—
438C22×C8—21no—
439#127—22no—
440#127—21no—
441#127—44no—
442#126—22no—
443#126—22no—
444#125—21no—
445#124—22no—
446#123—22no—
447#123—21no—
448#123—22no—
449#123—22no—
450#123—22no—
451C22⋊Q8D4×C10911yescharacteristic, complemented
452C22⋊Q8C23×C10911yescharacteristic
453#121—22no—
454#121—21no—
455#121—21no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121—22no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—22no—
467#121D4×C10912yescomplemented
468#121D4×C10911yescharacteristic, complemented
469#121C23×C10912yes—
470#121C23×C10911yescharacteristic
471#120—22no—
472#120—22no—
473#120—22no—
474#120—21no—
475#120—22no—
476#120—22no—
477#120—22no—
478#120—48no—
479C4×D4—22no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—22no—
485#117—21no—
486#117D4×C10911yescharacteristic, complemented
487C2×C4⋊C4D4×C10911yescharacteristic
488C2×C4⋊C4D4×C10911yescharacteristic, complemented
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4C23×C10912yes—
493C2×C42—21no—
494#102—24no—
495#102—22no—
496#102—22no—
497C22⋊C8—21no—
498C22⋊C8—21no—
499C22⋊C8C23×C10912yes—
500C22⋊C8C23×C10912yes—
501#95C23×C10912yes—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—44no—
506C24—44no—
507C24—41no—
508C24—41no—
509C24—82no—
510C24C2×D4×C10911yescharacteristic
511C24C2×D4×C10912yes—
512#41—42no—
513C2×Q8C2×D4×C10911yescharacteristic
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—21no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—48no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—48no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—82no—
548C2×D4—84no—
549C2×D4—82no—
550C2×D4—84no—
551C2×D4—84no—
552C2×D4C2×D4×C10911yescharacteristic
553C2×D4C2×D4×C10912yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4C2×D4×C10911yescharacteristic
561C22×C4C2×D4×C10911yescharacteristic
562C22×C4C2×D4×C10911yescharacteristic
563C22×C4C2×D4×C10912yes—
564C22×C4C2×D4×C10911yescharacteristic
565C22×C4C2×D4×C10911yescharacteristic
566C22×C4C24×C10911yescharacteristic
567SD16—44no—
568D8—48no—
569D8—44no—
570M16—42no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—42no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4C2×D4×C10912yes—
582C4⋊C4C2×D4×C10911yescharacteristic
583C4⋊C4C2×D4×C10911yescharacteristic
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—21no—
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—22no—
594C22⋊C4—21no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—21no—
599C22⋊C4—48no—
600C42—22no—
601C42—21no—
602C42—42no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—21no—
609C23—24no—
610C23—41no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—44no—
619C23—42no—
620C23—81no—
621C23—81no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—816no—
629C23—82no—
630C23#120×C10911yescharacteristic
631C23#120×C10911yescharacteristic
632C23C22×D4×C10911yescharacteristic
633Q8—41no—
634D4—24no—
635D4—24no—
636D4—42no—
637D4—41no—
638D4—42no—
639D4—42no—
640D4—44no—
641D4—44no—
642D4—42no—
643D4—44no—
644D4—42no—
645D4—44no—
646D4—42no—
647D4—42no—
648D4—81no—
649D4—82no—
650D4—82no—
651D4—81no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—82no—
657D4—816no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—81no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4#120×C10911yescharacteristic
678C2×C4#120×C10911yescharacteristic
679C2×C4C22×D4×C10911yescharacteristic
680C2×C4C22×D4×C10911yescharacteristic
681C8—42no—
682C8—42no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—44no—
691C22—48no—
692C22—42no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—44no—
700C22—42no—
701C22—42no—
702C22—84no—
703C22—84no—
704C22—88no—
705C22—88no—
706C22—82no—
707C22—82no—
708C22—162no—
709C22—164no—
710C22#453×C10912yes—
711C22C2×#120×C10911yescharacteristic
712C22#576×C10912yes—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—44no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—41no—
722C4B(4,𝔽2)×C10912yes—
723C2—22no—
724C2—22no—
725C2—41no—
726C2—84no—
727C2—82no—
728C2—82no—
729C2—81no—
730C2C109×#300811yescharacteristic
731C2C2×#453×C10911yescharacteristic
732C2C2×B(4,𝔽2)×C10911yescharacteristic
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×#3003C2semidirect
3. C2×#447×C109C2semidirect
4. C109×#2433C2semidirect
5. C109×#1600C2semidirect
6. C109×#1595C2semidirect
7. C109×#1507C2semidirect
8. C109×#1501C2semidirect
9. C109×#1471C2semidirect
10. C23×D4×C109C22semidirect
21. #538×C109C22semidirect
24. #534×C109C22semidirect
31. #450×C109C22semidirect
34. #447×C109C22semidirect
35. #447×C109C22semidirect
38. #407×C109C22semidirect
39. C2×C22⋊C8×C109C22semidirect
40. #392×C109C22semidirect
42. C4×C22⋊C4×C109C22semidirect
43. #328×C109C22semidirect
44. #327×C109C22semidirect
45. #327×C109C22semidirect
46. #323×C109C22semidirect
48. C2×#41×C109D4semidirect
62. C22×D4×C109D4semidirect
84. C22⋊Q8×C109D4semidirect
100. #121×C109D4semidirect
101. #121×C109D4semidirect
119. #117×C109D4semidirect
121. C2×C4⋊C4×C109D4semidirect
356. #18254C109direct (N × H)
367. #3537C2×C109semidirect
368. #3003C2×C109semidirect
369. C2×#447C2×C109semidirect
370. #2433C2×C109semidirect
371. #1600C2×C109semidirect
372. #1595C2×C109semidirect
373. #1507C2×C109semidirect
374. #1501C2×C109semidirect
375. #1471C2×C109semidirect
376. C109#18254direct (N × H)
377. C23×D4C22×C109semidirect
388. #538C22×C109semidirect
391. #534C22×C109semidirect
398. #450C22×C109semidirect
401. #447C22×C109semidirect
402. #447C22×C109semidirect
405. #407C22×C109semidirect
406. C2×C22⋊C8C22×C109semidirect
407. #392C22×C109semidirect
409. C4×C22⋊C4C22×C109semidirect
410. #328C22×C109semidirect
411. #327C22×C109semidirect
412. #327C22×C109semidirect
413. #323C22×C109semidirect
415. C2×#41D4×C109semidirect
429. C22×D4D4×C109semidirect
451. C22⋊Q8D4×C109semidirect
467. #121D4×C109semidirect
468. #121D4×C109semidirect
486. #117D4×C109semidirect
488. 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×#30032
C2×#447×C1092
C109×#24332
C109×#16002
C109×#15952
C109×#15072
C109×#15012
C109×#14712
#18254109