Finite Group Databasebeta

← C109×#24473 #42142467

Subgroups — C109×#24473 #42142467

Order 27904.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3586C211yesmaximal, characteristic, complemented
2C109×#3068C211yesmaximal, characteristic, complemented
3C109×#3040C211yesmaximal, characteristic, complemented
4C109×#3021C211yesmaximal, characteristic, complemented
5C2×#454×C109C211yesmaximal, characteristic, complemented
6C109×#2901C211yesmaximal, characteristic, complemented
7C109×#2050C211yesmaximal, characteristic, complemented
8C109×#2049C211yesmaximal, characteristic, complemented
9C109×#2008C211yesmaximal, characteristic, complemented
10C109×#2004C211yesmaximal, characteristic, complemented
11C109×#1906C211yesmaximal, characteristic, complemented
12C109×#1903C211yesmaximal, characteristic, complemented
13C109×#1902C211yesmaximal, characteristic, complemented
14C109×#1861C211yesmaximal, characteristic, complemented
15C109×#1796C211yesmaximal, characteristic, complemented
16#585×C109C2211yescharacteristic
17C2×2−1+4×C109C2211yescharacteristic
18#578×C109—22no—
19#578×C109—22no—
20#577×C109—22no—
21#577×C109—22no—
22#575×C109—22no—
23#575×C109C2211yescharacteristic
24#575×C109C2211yescharacteristic
25C2×#137×C109—22no—
26C2×#137×C109C2211yescharacteristic
27C2×#137×C109C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C109C2211yescharacteristic, complemented
31#568×C109C2211yescharacteristic
32#568×C109C2211yescharacteristic
33#535×C109C2211yescharacteristic
34C2×#124×C109C2211yescharacteristic, complemented
35C4×#41×C109C2211yescharacteristic
36#472×C109—22no—
37#471×C109—22no—
38#464×C109—22no—
39#463×C109—22no—
40#454×C109—22no—
41#454×C109—22no—
42#454×C109—22no—
43#453×C109—22no—
44#430×C109C2211yescharacteristic, complemented
45#423×C109C2211yescharacteristic, complemented
46#421×C109—22no—
47#421×C109C2211yescharacteristic
48#421×C109C2211yescharacteristic
49#421×C109C2211yescharacteristic
50#421×C109C2211yescharacteristic
51C2×#104×C109—22no—
52C2×#104×C109C2211yescharacteristic
53C2×#104×C109C2211yescharacteristic
54C2×#104×C109C2211yescharacteristic, complemented
55#419×C109C2211yescharacteristic, complemented
56#419×C109C2211yescharacteristic, complemented
57#418×C109C2211yescharacteristic, complemented
58#413×C109C2211yescharacteristic
59#413×C109C2211yescharacteristic, complemented
60C2×#101×C109C2211yescharacteristic, complemented
61C2×#100×C109C2211yescharacteristic, complemented
62#410×C109C2211yescharacteristic, complemented
63#344×C109C2211yescharacteristic, complemented
64#344×C109C2211yescharacteristic, complemented
65#339×C109C2211yescharacteristic, complemented
66#338×C109C2211yescharacteristic, complemented
672−1+4×C109—22no—
682−1+4×C109—22no—
692−1+4×C109—21no—
702−1+4×C109—21no—
712−1+4×C109—22no—
722−1+4×C109—41no—
732−1+4×C109D412yes—
74H(5,𝔽2)×C109—21no—
75H(5,𝔽2)×C109—21no—
76H(5,𝔽2)×C109—41no—
77H(5,𝔽2)×C109D412yes—
78C2×#41×C109—22no—
79C2×#41×C109—22no—
80C2×#41×C109—21no—
81C2×#41×C109—21no—
82C2×#41×C109—41no—
83C2×#41×C109—41no—
84C2×#41×C109C2311yescharacteristic
85C2×#41×C109C2311yescharacteristic
86C2×#41×C109C2311yescharacteristic
87C2×#41×C109C2311yescharacteristic
88C22×Q8×C109—21no—
89C22×Q8×C109—21no—
90C22×Q8×C109C2311yescharacteristic
91C22×D4×C109C2311yescharacteristic
92#137×C109—24no—
93#137×C109—24no—
94#137×C109—24no—
95#137×C109—22no—
96#137×C109—22no—
97#137×C109—21no—
98#137×C109—22no—
99#137×C109—21no—
100#137×C109—21no—
101#137×C109—22no—
102#137×C109D412yescomplemented
103AGL(1,ℤ/8)×C109—24no—
104AGL(1,ℤ/8)×C109—21no—
105AGL(1,ℤ/8)×C109—21no—
106AGL(1,ℤ/8)×C109—21no—
107AGL(1,ℤ/8)×C109—22no—
108AGL(1,ℤ/8)×C109—22no—
109AGL(1,ℤ/8)×C109—22no—
110AGL(1,ℤ/8)×C109—22no—
111AGL(1,ℤ/8)×C109—22no—
112AGL(1,ℤ/8)×C109—41no—
113AGL(1,ℤ/8)×C109D412yescomplemented
114#135×C109—24no—
115#135×C109—24no—
116#135×C109—22no—
117#135×C109—22no—
118C2×Q16×C109—24no—
119C2×Q16×C109—21no—
120C2×Q16×C109D412yescomplemented
121C2×SD16×C109—24no—
122C2×SD16×C109—21no—
123C2×SD16×C109—21no—
124C2×SD16×C109—21no—
125C2×SD16×C109—21no—
126C2×SD16×C109D412yescomplemented
127C2×D8×C109—21no—
128C2×D8×C109—21no—
129C2×D8×C109—21no—
130#131×C109—22no—
131#131×C109—22no—
132#131×C109—22no—
133#131×C109—41no—
134C2×M16×C109—22no—
135C2×M16×C109—22no—
136C2×M16×C109C2311yescharacteristic
137C2×M16×C109C2311yescharacteristic
138C2×M16×C109C2311yescharacteristic
139C2×M16×C109C2311yescharacteristic
140C2×M16×C109C2311yescharacteristic
141C2×M16×C109C2311yescharacteristic
142#127×C109—21no—
143#124×C109—22no—
144#124×C109—21no—
145#124×C109—21no—
146#124×C109—21no—
147#121×C109—41no—
148#120×C109—41no—
149C4×Q8×C109—21no—
150C4×D4×C109—21no—
151C4×D4×C109—41no—
152#117×C109—21no—
153#117×C109C2311yescharacteristic
154#117×C109C2311yescharacteristic
155C2×C22⋊C4×C109—41no—
156C2×C42×C109—21no—
157C2×C42×C109C2311yescharacteristic
158#108×C109—22no—
159C4⋊C8×C109—22no—
160#104×C109—22no—
161#104×C109—22no—
162#104×C109—22no—
163#104×C109—22no—
164#104×C109—21no—
165#104×C109—21no—
166#104×C109—21no—
167#104×C109—21no—
168#104×C109D412yescomplemented
169#104×C109D412yescomplemented
170#103×C109—22no—
171#103×C109—41no—
172#102×C109—22no—
173#101×C109—21no—
174#101×C109—21no—
175#101×C109—22no—
176#100×C109—21no—
177#100×C109—21no—
178#100×C109—22no—
179#99×C109—41no—
180C24×C109—21no—
181#41×C109—21no—
182#41×C109—21no—
183#41×C109—21no—
184#41×C109—21no—
185#41×C109—24no—
186#41×C109—22no—
187#41×C109—22no—
188#41×C109—22no—
189#41×C109—22no—
190#41×C109—21no—
191#41×C109—21no—
192#41×C109—21no—
193#41×C109—21no—
194#41×C109—21no—
195#41×C109—21no—
196#41×C109—21no—
197#41×C109—21no—
198#41×C109—42no—
199#41×C109—42no—
200#41×C109—42no—
201#41×C109—42no—
202#41×C109—42no—
203#41×C109—44no—
204#41×C109—42no—
205#41×C109—41no—
206#41×C109—41no—
207#41×C109—44no—
208#41×C109—42no—
209#41×C109C2×D412yes—
210#41×C109C2×D412yes—
211#41×C109C2×D412yes—
212#41×C109C2×D412yes—
213C2×Q8×C109—21no—
214C2×Q8×C109—24no—
215C2×Q8×C109—22no—
216C2×Q8×C109—22no—
217C2×Q8×C109—21no—
218C2×Q8×C109—21no—
219C2×Q8×C109—21no—
220C2×Q8×C109—21no—
221C2×Q8×C109—41no—
222C2×Q8×C109—42no—
223C2×Q8×C109—42no—
224C2×Q8×C109—41no—
225C2×Q8×C109—42no—
226C2×Q8×C109C2×D411yescharacteristic
227C2×Q8×C109C2×D411yescharacteristic
228C2×Q8×C109C2×D412yes—
229C2×Q8×C109C2×D411yescharacteristic
230C2×Q8×C109#4111yescharacteristic
231C2×D4×C109—21no—
232C2×D4×C109—21no—
233C2×D4×C109—22no—
234C2×D4×C109—22no—
235C2×D4×C109—21no—
236C2×D4×C109—21no—
237C2×D4×C109—21no—
238C2×D4×C109—21no—
239C2×D4×C109—21no—
240C2×D4×C109—21no—
241C2×D4×C109—21no—
242C2×D4×C109—21no—
243C2×D4×C109—42no—
244C2×D4×C109—41no—
245C2×D4×C109—42no—
246C2×D4×C109—42no—
247C2×D4×C109—41no—
248C2×D4×C109—42no—
249C2×D4×C109C2×D411yescharacteristic
250C2×D4×C109C2×D411yescharacteristic
251C2×D4×C109C2×D411yescharacteristic
252C2×D4×C109#4111yescharacteristic
253C22×C4×C109—21no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—21no—
257C22×C4×C109—21no—
258C22×C4×C109—21no—
259C22×C4×C109—42no—
260C22×C4×C109—41no—
261C22×C4×C109—41no—
262C22×C4×C109—41no—
263C22×C4×C109C2411yescharacteristic
264Q16×C109—24no—
265Q16×C109—22no—
266Q16×C109—22no—
267Q16×C109—24no—
268SD16×C109—24no—
269SD16×C109—22no—
270SD16×C109—22no—
271SD16×C109—22no—
272SD16×C109—22no—
273SD16×C109—24no—
274SD16×C109—42no—
275SD16×C109—42no—
276SD16×C109—42no—
277D8×C109—22no—
278D8×C109—22no—
279D8×C109—42no—
280D8×C109—42no—
281D8×C109—42no—
282M16×C109—24no—
283M16×C109—21no—
284M16×C109—21no—
285M16×C109—21no—
286M16×C109—21no—
287M16×C109—21no—
288M16×C109—21no—
289M16×C109—21no—
290M16×C109—21no—
291M16×C109—21no—
292M16×C109—21no—
293M16×C109—42no—
294M16×C109C2×D412yes—
295M16×C109C2×D412yes—
296C2×C8×C109—24no—
297C2×C8×C109—21no—
298C2×C8×C109—21no—
299C2×C8×C109—21no—
300C2×C8×C109—21no—
301C2×C8×C109—21no—
302C2×C8×C109—42no—
303C2×C8×C109C2×D412yes—
304C4⋊C4×C109—21no—
305C4⋊C4×C109—21no—
306C4⋊C4×C109—41no—
307C22⋊C4×C109—21no—
308C22⋊C4×C109—21no—
309C22⋊C4×C109—42no—
310C22⋊C4×C109—42no—
311C22⋊C4×C109—41no—
312C22⋊C4×C109—42no—
313C42×C109—21no—
314C42×C109—21no—
315C42×C109—21no—
316C42×C109—41no—
317C42×C109C2×D411yescharacteristic
318C42×C109C2×D411yescharacteristic
319C23×C109—21no—
320C23×C109—21no—
321C23×C109—21no—
322C23×C109—21no—
323C23×C109—42no—
324C23×C109—41no—
325C23×C109—41no—
326C23×C109—41no—
327C23×C109—82no—
328C23×C109H(5,𝔽2)11yescharacteristic
329Q8×C109—21no—
330Q8×C109—21no—
331Q8×C109—21no—
332Q8×C109—22no—
333Q8×C109—21no—
334Q8×C109—21no—
335Q8×C109—21no—
336Q8×C109—22no—
337Q8×C109—42no—
338Q8×C109—44no—
339Q8×C109—41no—
340Q8×C109—41no—
341Q8×C109#12012yes—
342Q8×C109#12112yes—
343D4×C109—22no—
344D4×C109—22no—
345D4×C109—22no—
346D4×C109—22no—
347D4×C109—21no—
348D4×C109—21no—
349D4×C109—21no—
350D4×C109—21no—
351D4×C109—21no—
352D4×C109—21no—
353D4×C109—42no—
354D4×C109—42no—
355D4×C109—42no—
356D4×C109—44no—
357D4×C109—41no—
358D4×C109—41no—
359D4×C109—41no—
360D4×C109—41no—
361D4×C109—41no—
362D4×C109—41no—
363D4×C109—41no—
364D4×C109—41no—
365D4×C109—162no—
366D4×C109#12012yes—
367D4×C109#12112yes—
368C2×C4×C109—21no—
369C2×C4×C109—21no—
370C2×C4×C109—22no—
371C2×C4×C109—22no—
372C2×C4×C109—22no—
373C2×C4×C109—22no—
374C2×C4×C109—21no—
375C2×C4×C109—21no—
376C2×C4×C109—21no—
377C2×C4×C109—22no—
378C2×C4×C109—21no—
379C2×C4×C109—42no—
380C2×C4×C109—42no—
381C2×C4×C109—42no—
382C2×C4×C109—44no—
383C2×C4×C109—44no—
384C2×C4×C109—41no—
385C2×C4×C109—41no—
386C2×C4×C109—41no—
387C2×C4×C109—41no—
388C2×C4×C109—41no—
389C2×C4×C109—41no—
390C2×C4×C109—41no—
391C2×C4×C109—41no—
392C2×C4×C109—81no—
393C2×C4×C109—82no—
394C2×C4×C109C22×D411yescharacteristic
395C2×C4×C109C22×D411yescharacteristic
396C2×C4×C109C22×D411yescharacteristic
397C2×C4×C109C22×D411yescharacteristic
398C2×C4×C109C2×#4111yescharacteristic
399C2×C4×C109H(5,𝔽2)11yescharacteristic
400C8×C109—22no—
401C8×C109—22no—
402C8×C109—22no—
403C8×C109—41no—
404C8×C109—41no—
405C8×C109—41no—
406C22×C109—22no—
407C22×C109—22no—
408C22×C109—41no—
409C22×C109—41no—
410C22×C109—41no—
411C22×C109—81no—
412C22×C109—81no—
413C22×C109—81no—
414C22×C109—81no—
415C22×C109—82no—
416C22×C109—82no—
417C22×C109—81no—
418C22×C109—161no—
419C22×C109—162no—
420C22×C109#53411yescharacteristic
421C22×C109D4211yescharacteristic
422C22×C109#54611yescharacteristic
423C4×C109—22no—
424C4×C109—22no—
425C4×C109—41no—
426C4×C109—41no—
427C4×C109—41no—
428C4×C109—42no—
429C4×C109—41no—
430C4×C109—81no—
431C4×C109—81no—
432C4×C109C2×#12011yescharacteristic
433C4×C109C2×#12111yescharacteristic
434C4×C109D4211yescharacteristic
435C4×C109#54611yescharacteristic
436#24473C10911yesmaximal, characteristic, direct product factor, Sylow
437C2×C109—21no—
438C2×C109—21no—
439C2×C109—21no—
440C2×C109—42no—
441C2×C109—42no—
442C2×C109—81no—
443C2×C109—81no—
444C2×C109—161no—
445C2×C109#241011yescharacteristic
446#3586C2×C10911yescharacteristic, complemented
447#3068C2×C10911yescharacteristic, complemented
448#3040C2×C10911yescharacteristic, complemented
449#3021C2×C10911yescharacteristic, complemented
450C2×#454C2×C10911yescharacteristic, complemented
451#2901C2×C10911yescharacteristic, complemented
452#2050C2×C10911yescharacteristic, complemented
453#2049C2×C10911yescharacteristic, complemented
454#2008C2×C10911yescharacteristic, complemented
455#2004C2×C10911yescharacteristic, complemented
456#1906C2×C10911yescharacteristic, complemented
457#1903C2×C10911yescharacteristic, complemented
458#1902C2×C10911yescharacteristic, complemented
459#1861C2×C10911yescharacteristic, complemented
460#1796C2×C10911yescharacteristic, complemented
461C109#2447311yescharacteristic, direct product factor, Sylow
462#585C22×C10911yescharacteristic
463C2×2−1+4C22×C10911yescharacteristic
464#578—22no—
465#578—22no—
466#577—22no—
467#577—22no—
468#575—22no—
469#575C22×C10911yescharacteristic
470#575C22×C10911yescharacteristic
471C2×#137—22no—
472C2×#137C22×C10911yescharacteristic
473C2×#137C22×C10911yescharacteristic
474C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
475C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
476C2×AGL(1,ℤ/8)C22×C10911yescharacteristic, complemented
477#568C22×C10911yescharacteristic
478#568C22×C10911yescharacteristic
479#535C22×C10911yescharacteristic
480C2×#124C22×C10911yescharacteristic, complemented
481C4×#41C22×C10911yescharacteristic
482#472—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#454—22no—
487#454—22no—
488#454—22no—
489#453—22no—
490#430C22×C10911yescharacteristic, complemented
491#423C22×C10911yescharacteristic, complemented
492#421—22no—
493#421C22×C10911yescharacteristic
494#421C22×C10911yescharacteristic
495#421C22×C10911yescharacteristic
496#421C22×C10911yescharacteristic
497C2×#104—22no—
498C2×#104C22×C10911yescharacteristic
499C2×#104C22×C10911yescharacteristic
500C2×#104C22×C10911yescharacteristic, complemented
501#419C22×C10911yescharacteristic, complemented
502#419C22×C10911yescharacteristic, complemented
503#418C22×C10911yescharacteristic, complemented
504#413C22×C10911yescharacteristic
505#413C22×C10911yescharacteristic, complemented
506C2×#101C22×C10911yescharacteristic, complemented
507C2×#100C22×C10911yescharacteristic, complemented
508#410C22×C10911yescharacteristic, complemented
509#344C22×C10911yescharacteristic, complemented
510#344C22×C10911yescharacteristic, complemented
511#339C22×C10911yescharacteristic, complemented
512#338C22×C10911yescharacteristic, complemented
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—21no—
5162−1+4—21no—
5172−1+4—22no—
5182−1+4—41no—
5192−1+4D4×C10912yes—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—21no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)D4×C10912yes—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41C23×C10911yescharacteristic
531C2×#41C23×C10911yescharacteristic
532C2×#41C23×C10911yescharacteristic
533C2×#41C23×C10911yescharacteristic
534C22×Q8—21no—
535C22×Q8—21no—
536C22×Q8C23×C10911yescharacteristic
537C22×D4C23×C10911yescharacteristic
538#137—24no—
539#137—24no—
540#137—24no—
541#137—22no—
542#137—22no—
543#137—21no—
544#137—22no—
545#137—21no—
546#137—21no—
547#137—22no—
548#137D4×C10912yescomplemented
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—22no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—41no—
559AGL(1,ℤ/8)D4×C10912yescomplemented
560#135—24no—
561#135—24no—
562#135—22no—
563#135—22no—
564C2×Q16—24no—
565C2×Q16—21no—
566C2×Q16D4×C10912yescomplemented
567C2×SD16—24no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16D4×C10912yescomplemented
573C2×D8—21no—
574C2×D8—21no—
575C2×D8—21no—
576#131—22no—
577#131—22no—
578#131—22no—
579#131—41no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16C23×C10911yescharacteristic
583C2×M16C23×C10911yescharacteristic
584C2×M16C23×C10911yescharacteristic
585C2×M16C23×C10911yescharacteristic
586C2×M16C23×C10911yescharacteristic
587C2×M16C23×C10911yescharacteristic
588#127—21no—
589#124—22no—
590#124—21no—
591#124—21no—
592#124—21no—
593#121—41no—
594#120—41no—
595C4×Q8—21no—
596C4×D4—21no—
597C4×D4—41no—
598#117—21no—
599#117C23×C10911yescharacteristic
600#117C23×C10911yescharacteristic
601C2×C22⋊C4—41no—
602C2×C42—21no—
603C2×C42C23×C10911yescharacteristic
604#108—22no—
605C4⋊C8—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—21no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104D4×C10912yescomplemented
615#104D4×C10912yescomplemented
616#103—22no—
617#103—41no—
618#102—22no—
619#101—21no—
620#101—21no—
621#101—22no—
622#100—21no—
623#100—21no—
624#100—22no—
625#99—41no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—42no—
645#41—42no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—44no—
650#41—42no—
651#41—41no—
652#41—41no—
653#41—44no—
654#41—42no—
655#41C2×D4×C10912yes—
656#41C2×D4×C10912yes—
657#41C2×D4×C10912yes—
658#41C2×D4×C10912yes—
659C2×Q8—21no—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8C2×D4×C10911yescharacteristic
673C2×Q8C2×D4×C10911yescharacteristic
674C2×Q8C2×D4×C10912yes—
675C2×Q8C2×D4×C10911yescharacteristic
676C2×Q8#41×C10911yescharacteristic
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—41no—
694C2×D4—42no—
695C2×D4C2×D4×C10911yescharacteristic
696C2×D4C2×D4×C10911yescharacteristic
697C2×D4C2×D4×C10911yescharacteristic
698C2×D4#41×C10911yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4C24×C10911yescharacteristic
710Q16—24no—
711Q16—22no—
712Q16—22no—
713Q16—24no—
714SD16—24no—
715SD16—22no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—42no—
721SD16—42no—
722SD16—42no—
723D8—22no—
724D8—22no—
725D8—42no—
726D8—42no—
727D8—42no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C10912yes—
741M16C2×D4×C10912yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C10912yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—41no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—41no—
763C42C2×D4×C10911yescharacteristic
764C42C2×D4×C10911yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—82no—
774C23H(5,𝔽2)×C10911yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—22no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—22no—
783Q8—42no—
784Q8—44no—
785Q8—41no—
786Q8—41no—
787Q8#120×C10912yes—
788Q8#121×C10912yes—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—21no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—162no—
812D4#120×C10912yes—
813D4#121×C10912yes—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—82no—
840C2×C4C22×D4×C10911yescharacteristic
841C2×C4C22×D4×C10911yescharacteristic
842C2×C4C22×D4×C10911yescharacteristic
843C2×C4C22×D4×C10911yescharacteristic
844C2×C4C2×#41×C10911yescharacteristic
845C2×C4H(5,𝔽2)×C10911yescharacteristic
846C8—22no—
847C8—22no—
848C8—22no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—161no—
865C22—162no—
866C22#534×C10911yescharacteristic
867C22D42×C10911yescharacteristic
868C22#546×C10911yescharacteristic
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—42no—
875C4—41no—
876C4—81no—
877C4—81no—
878C4C2×#120×C10911yescharacteristic
879C4C2×#121×C10911yescharacteristic
880C4D42×C10911yescharacteristic
881C4#546×C10911yescharacteristic
882C2—21no—
883C2—21no—
884C2—21no—
885C2—42no—
886C2—42no—
887C2—81no—
888C2—81no—
889C2—161no—
890C2C109×#241011yescharacteristic
subgroupG/H
center, socleC2×C109#2410
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C109 ◁ C22×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3586C2semidirect
2. C109×#3068C2semidirect
3. C109×#3040C2semidirect
4. C109×#3021C2semidirect
5. C2×#454×C109C2semidirect
6. C109×#2901C2semidirect
7. C109×#2050C2semidirect
8. C109×#2049C2semidirect
9. C109×#2008C2semidirect
10. C109×#2004C2semidirect
11. C109×#1906C2semidirect
12. C109×#1903C2semidirect
13. C109×#1902C2semidirect
14. C109×#1861C2semidirect
15. C109×#1796C2semidirect
30. C2×AGL(1,ℤ/8)×C109C22semidirect
34. C2×#124×C109C22semidirect
44. #430×C109C22semidirect
45. #423×C109C22semidirect
54. C2×#104×C109C22semidirect
55. #419×C109C22semidirect
56. #419×C109C22semidirect
57. #418×C109C22semidirect
59. #413×C109C22semidirect
60. C2×#101×C109C22semidirect
61. C2×#100×C109C22semidirect
62. #410×C109C22semidirect
63. #344×C109C22semidirect
64. #344×C109C22semidirect
65. #339×C109C22semidirect
66. #338×C109C22semidirect
102. #137×C109D4semidirect
113. AGL(1,ℤ/8)×C109D4semidirect
120. C2×Q16×C109D4semidirect
126. C2×SD16×C109D4semidirect
168. #104×C109D4semidirect
169. #104×C109D4semidirect
436. #24473C109direct (N × H)
446. #3586C2×C109semidirect
447. #3068C2×C109semidirect
448. #3040C2×C109semidirect
449. #3021C2×C109semidirect
450. C2×#454C2×C109semidirect
451. #2901C2×C109semidirect
452. #2050C2×C109semidirect
453. #2049C2×C109semidirect
454. #2008C2×C109semidirect
455. #2004C2×C109semidirect
456. #1906C2×C109semidirect
457. #1903C2×C109semidirect
458. #1902C2×C109semidirect
459. #1861C2×C109semidirect
460. #1796C2×C109semidirect
461. C109#24473direct (N × H)
476. C2×AGL(1,ℤ/8)C22×C109semidirect
480. C2×#124C22×C109semidirect
490. #430C22×C109semidirect
491. #423C22×C109semidirect
500. C2×#104C22×C109semidirect
501. #419C22×C109semidirect
502. #419C22×C109semidirect
503. #418C22×C109semidirect
505. #413C22×C109semidirect
506. C2×#101C22×C109semidirect
507. C2×#100C22×C109semidirect
508. #410C22×C109semidirect
509. #344C22×C109semidirect
510. #344C22×C109semidirect
511. #339C22×C109semidirect
512. #338C22×C109semidirect
548. #137D4×C109semidirect
559. AGL(1,ℤ/8)D4×C109semidirect
566. C2×Q16D4×C109semidirect
572. C2×SD16D4×C109semidirect
614. #104D4×C109semidirect
615. #104D4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35862
C109×#30682
C109×#30402
C109×#30212
C2×#454×C1092
C109×#29012
C109×#20502
C109×#20492
C109×#20082
C109×#20042
C109×#19062
C109×#19032
C109×#19022
C109×#18612
C109×#17962
#24473109