Finite Group Databasebeta

← C109×#24405 #42142399

Subgroups — C109×#24405 #42142399

Order 27904.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3484C211yesmaximal, characteristic
2C2×#458×C109C211yesmaximal, characteristic, complemented
3C22×#99×C109C211yesmaximal, characteristic, complemented
4C109×#2412C212yesmaximal, complemented
5C109×#2405C211yesmaximal, characteristic, complemented
6C109×#2044C212yesmaximal, complemented
7C109×#2022C212yesmaximal, complemented
8C109×#1898C212yesmaximal, complemented
9C109×#1890C211yesmaximal, characteristic, complemented
10C109×#1867C211yesmaximal, characteristic, complemented
11C109×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C109C2211yescharacteristic
13C23×D4×C109C2211yescharacteristic
14#546×C109—22no—
15#546×C109—22no—
16D42×C109—22no—
17D42×C109—22no—
18#535×C109—21no—
19#534×C109—21no—
20#534×C109C2212yes—
21#525×C109—21no—
22C2×#123×C109C2211yescharacteristic
23C2×#123×C109C2212yescomplemented
24C2×#123×C109C2211yescharacteristic, complemented
25C2×#120×C109—21no—
26C2×#120×C109C2212yes—
27#518×C109C2211yescharacteristic
28C22×C22⋊C4×C109C2211yescharacteristic, complemented
29C22×C22⋊C4×C109C2212yescomplemented
30#458×C109—24no—
31C2×#99×C109—24no—
32C2×#99×C109C2211yescharacteristic
33C2×#99×C109C2211yescharacteristic
34C2×#99×C109C2212yescomplemented
35C2×#99×C109C2212yescomplemented
36C2×#99×C109C2212yescomplemented
37#397×C109—22no—
38#394×C109—21no—
39#394×C109—21no—
40#394×C109—22no—
41#386×C109—22no—
42#386×C109C2211yescharacteristic
43#386×C109C2211yescharacteristic, complemented
44#386×C109C2212yescomplemented
45#385×C109—21no—
46#385×C109C2212yescomplemented
47#381×C109C2212yescomplemented
48#380×C109—22no—
49#379×C109—21no—
50#379×C109C2211yescharacteristic, complemented
51#342×C109C2212yescomplemented
52#342×C109C2212yescomplemented
53C25×C109D411yescharacteristic
54C25×C109C2311yescharacteristic
55H(5,𝔽2)×C109—22no—
56H(5,𝔽2)×C109—22no—
57H(5,𝔽2)×C109—42no—
58C2×#41×C109—21no—
59C2×#41×C109—22no—
60C22×D4×C109—21no—
61C22×D4×C109—22no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—21no—
65C22×D4×C109—21no—
66C22×D4×C109—22no—
67C22×D4×C109—22no—
68C22×D4×C109—42no—
69C22×D4×C109D411yescharacteristic
70C22×D4×C109D411yescharacteristic
71C22×D4×C109D412yes—
72C22×D4×C109D412yes—
73C22×D4×C109C2312yes—
74C22×D4×C109C2311yescharacteristic
75C22×D4×C109C2311yescharacteristic
76C23×C4×C109—22no—
77C23×C4×C109D411yescharacteristic
78C23×C4×C109C2311yescharacteristic
79C23×C4×C109C2311yescharacteristic
80#127×C109—22no—
81#124×C109—22no—
82#123×C109—22no—
83#123×C109—22no—
84#123×C109—22no—
85#123×C109—22no—
86#123×C109—22no—
87#123×C109—24no—
88#123×C109—42no—
89#123×C109—42no—
90C22⋊Q8×C109—21no—
91C22⋊Q8×C109—21no—
92#121×C109—21no—
93#121×C109—21no—
94#121×C109—22no—
95#121×C109—22no—
96#121×C109—22no—
97#121×C109—22no—
98#121×C109—22no—
99#121×C109—22no—
100#120×C109—22no—
101#120×C109—22no—
102#120×C109—22no—
103#120×C109—22no—
104#120×C109—22no—
105#120×C109—22no—
106#120×C109—22no—
107#120×C109—22no—
108#120×C109—22no—
109C4×D4×C109—22no—
110C4×D4×C109—22no—
111C4×D4×C109—22no—
112C4×D4×C109—22no—
113#117×C109—21no—
114C2×C4⋊C4×C109—21no—
115C2×C4⋊C4×C109—22no—
116C2×C4⋊C4×C109—21no—
117C2×C4⋊C4×C109—22no—
118C2×C22⋊C4×C109—21no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—24no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—22no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—22no—
126C2×C22⋊C4×C109—22no—
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109—21no—
129C2×C22⋊C4×C109—22no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—21no—
134C2×C22⋊C4×C109—22no—
135C2×C22⋊C4×C109—42no—
136C2×C22⋊C4×C109D412yes—
137C2×C22⋊C4×C109D412yes—
138C2×C22⋊C4×C109C2312yes—
139C2×C22⋊C4×C109C2311yescharacteristic
140C2×C22⋊C4×C109C2311yescharacteristic
141C2×C22⋊C4×C109C2312yes—
142C2×C22⋊C4×C109C2312yes—
143#99×C109—22no—
144#99×C109—24no—
145#99×C109—24no—
146#99×C109—42no—
147#99×C109D414yescomplemented
148#95×C109—22no—
149#95×C109—22no—
150#95×C109—22no—
151#95×C109—21no—
152#95×C109—21no—
153#95×C109—22no—
154C24×C109—21no—
155C24×C109—21no—
156C24×C109—22no—
157C24×C109—21no—
158C24×C109—21no—
159C24×C109—21no—
160C24×C109—22no—
161C24×C109—41no—
162C24×C109—42no—
163C24×C109—42no—
164C24×C109—81no—
165C24×C109—81no—
166C24×C109C2×D411yescharacteristic
167C24×C109C2×D412yes—
168C24×C109C2×D411yescharacteristic
169C24×C109C2×D412yes—
170C24×C109C2×D412yes—
171C24×C109C2×D411yescharacteristic
172C24×C109C2×D411yescharacteristic
173C24×C109C2411yescharacteristic
174#41×C109—44no—
175#41×C109—44no—
176#41×C109—42no—
177#41×C109—42no—
178C2×Q8×C109—21no—
179C2×D4×C109—22no—
180C2×D4×C109—22no—
181C2×D4×C109—22no—
182C2×D4×C109—21no—
183C2×D4×C109—22no—
184C2×D4×C109—22no—
185C2×D4×C109—22no—
186C2×D4×C109—22no—
187C2×D4×C109—22no—
188C2×D4×C109—21no—
189C2×D4×C109—22no—
190C2×D4×C109—22no—
191C2×D4×C109—22no—
192C2×D4×C109—22no—
193C2×D4×C109—21no—
194C2×D4×C109—22no—
195C2×D4×C109—22no—
196C2×D4×C109—22no—
197C2×D4×C109—22no—
198C2×D4×C109—22no—
199C2×D4×C109—22no—
200C2×D4×C109—22no—
201C2×D4×C109—22no—
202C2×D4×C109—22no—
203C2×D4×C109—41no—
204C2×D4×C109—41no—
205C2×D4×C109—44no—
206C2×D4×C109—44no—
207C2×D4×C109—44no—
208C2×D4×C109—44no—
209C2×D4×C109—44no—
210C2×D4×C109—44no—
211C2×D4×C109—42no—
212C2×D4×C109—42no—
213C2×D4×C109—44no—
214C2×D4×C109—82no—
215C2×D4×C109—82no—
216C2×D4×C109—82no—
217C2×D4×C109C2×D412yes—
218C2×D4×C109#4112yes—
219C22×C4×C109—21no—
220C22×C4×C109—22no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—22no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—22no—
227C22×C4×C109—22no—
228C22×C4×C109—21no—
229C22×C4×C109—22no—
230C22×C4×C109—22no—
231C22×C4×C109—21no—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—22no—
237C22×C4×C109—41no—
238C22×C4×C109—44no—
239C22×C4×C109—44no—
240C22×C4×C109—81no—
241C22×C4×C109—82no—
242C22×C4×C109C2×D412yes—
243C22×C4×C109C2×D411yescharacteristic
244C22×C4×C109C2×D411yescharacteristic
245C22×C4×C109C2×D412yes—
246C22×C4×C109C2×D412yes—
247C4⋊C4×C109—21no—
248C4⋊C4×C109—21no—
249C4⋊C4×C109—22no—
250C4⋊C4×C109—22no—
251C4⋊C4×C109—44no—
252C4⋊C4×C109—42no—
253C4⋊C4×C109—42no—
254C4⋊C4×C109—82no—
255C22⋊C4×C109—22no—
256C22⋊C4×C109—22no—
257C22⋊C4×C109—22no—
258C22⋊C4×C109—22no—
259C22⋊C4×C109—22no—
260C22⋊C4×C109—22no—
261C22⋊C4×C109—22no—
262C22⋊C4×C109—22no—
263C22⋊C4×C109—22no—
264C22⋊C4×C109—22no—
265C22⋊C4×C109—22no—
266C22⋊C4×C109—22no—
267C22⋊C4×C109—22no—
268C22⋊C4×C109—21no—
269C22⋊C4×C109—21no—
270C22⋊C4×C109—22no—
271C22⋊C4×C109—22no—
272C22⋊C4×C109—44no—
273C22⋊C4×C109—44no—
274C22⋊C4×C109—42no—
275C22⋊C4×C109—42no—
276C22⋊C4×C109—41no—
277C22⋊C4×C109—42no—
278C22⋊C4×C109—41no—
279C22⋊C4×C109—42no—
280C22⋊C4×C109—81no—
281C22⋊C4×C109—81no—
282C22⋊C4×C109—81no—
283C22⋊C4×C109—82no—
284C22⋊C4×C109C2×D414yescomplemented
285C42×C109—22no—
286C23×C109—21no—
287C23×C109—21no—
288C23×C109—21no—
289C23×C109—22no—
290C23×C109—22no—
291C23×C109—22no—
292C23×C109—24no—
293C23×C109—21no—
294C23×C109—21no—
295C23×C109—21no—
296C23×C109—22no—
297C23×C109—22no—
298C23×C109—21no—
299C23×C109—22no—
300C23×C109—21no—
301C23×C109—21no—
302C23×C109—22no—
303C23×C109—22no—
304C23×C109—42no—
305C23×C109—41no—
306C23×C109—41no—
307C23×C109—41no—
308C23×C109—41no—
309C23×C109—42no—
310C23×C109—42no—
311C23×C109—41no—
312C23×C109—42no—
313C23×C109—42no—
314C23×C109—41no—
315C23×C109—41no—
316C23×C109—41no—
317C23×C109—41no—
318C23×C109—42no—
319C23×C109—42no—
320C23×C109—42no—
321C23×C109—42no—
322C23×C109—42no—
323C23×C109—81no—
324C23×C109—81no—
325C23×C109—82no—
326C23×C109—82no—
327C23×C109—84no—
328C23×C109—81no—
329C23×C109—81no—
330C23×C109—84no—
331C23×C109—84no—
332C23×C109#12011yescharacteristic
333C23×C109#12012yes—
334C23×C109#12011yescharacteristic
335C23×C109#12112yes—
336C23×C109C22×D411yescharacteristic
337C23×C109C22×D412yes—
338C23×C109C22×D411yescharacteristic
339C23×C109C2×#4111yescharacteristic
340C23×C109H(5,𝔽2)12yes—
341Q8×C109—42no—
342D4×C109—24no—
343D4×C109—24no—
344D4×C109—44no—
345D4×C109—42no—
346D4×C109—44no—
347D4×C109—44no—
348D4×C109—44no—
349D4×C109—42no—
350D4×C109—42no—
351D4×C109—42no—
352D4×C109—42no—
353D4×C109—42no—
354D4×C109—42no—
355D4×C109—44no—
356D4×C109—82no—
357D4×C109—82no—
358D4×C109—82no—
359D4×C109—82no—
360C2×C4×C109—21no—
361C2×C4×C109—21no—
362C2×C4×C109—22no—
363C2×C4×C109—22no—
364C2×C4×C109—22no—
365C2×C4×C109—21no—
366C2×C4×C109—21no—
367C2×C4×C109—21no—
368C2×C4×C109—24no—
369C2×C4×C109—22no—
370C2×C4×C109—22no—
371C2×C4×C109—42no—
372C2×C4×C109—42no—
373C2×C4×C109—44no—
374C2×C4×C109—42no—
375C2×C4×C109—42no—
376C2×C4×C109—42no—
377C2×C4×C109—42no—
378C2×C4×C109—42no—
379C2×C4×C109—41no—
380C2×C4×C109—41no—
381C2×C4×C109—41no—
382C2×C4×C109—41no—
383C2×C4×C109—42no—
384C2×C4×C109—42no—
385C2×C4×C109—41no—
386C2×C4×C109—41no—
387C2×C4×C109—42no—
388C2×C4×C109—42no—
389C2×C4×C109—41no—
390C2×C4×C109—41no—
391C2×C4×C109—41no—
392C2×C4×C109—41no—
393C2×C4×C109—41no—
394C2×C4×C109—41no—
395C2×C4×C109—42no—
396C2×C4×C109—42no—
397C2×C4×C109—42no—
398C2×C4×C109—81no—
399C2×C4×C109—81no—
400C2×C4×C109—88no—
401C2×C4×C109#12112yes—
402C22×C109—21no—
403C22×C109—22no—
404C22×C109—21no—
405C22×C109—22no—
406C22×C109—21no—
407C22×C109—21no—
408C22×C109—21no—
409C22×C109—22no—
410C22×C109—22no—
411C22×C109—22no—
412C22×C109—21no—
413C22×C109—21no—
414C22×C109—22no—
415C22×C109—41no—
416C22×C109—41no—
417C22×C109—42no—
418C22×C109—44no—
419C22×C109—44no—
420C22×C109—42no—
421C22×C109—42no—
422C22×C109—42no—
423C22×C109—42no—
424C22×C109—41no—
425C22×C109—41no—
426C22×C109—42no—
427C22×C109—41no—
428C22×C109—42no—
429C22×C109—41no—
430C22×C109—42no—
431C22×C109—41no—
432C22×C109—82no—
433C22×C109—81no—
434C22×C109—81no—
435C22×C109—81no—
436C22×C109—82no—
437C22×C109—84no—
438C22×C109—82no—
439C22×C109—82no—
440C22×C109—81no—
441C22×C109—84no—
442C22×C109—162no—
443C22×C109#45812yescomplemented
444C22×C109C2×#12011yescharacteristic
445C22×C109C2×#12111yescharacteristic
446C22×C109#53411yescharacteristic
447C22×C109D4212yes—
448C22×C109#54612yes—
449C4×C109—22no—
450C4×C109—44no—
451C4×C109—41no—
452C4×C109—42no—
453C4×C109—42no—
454C4×C109—42no—
455C4×C109—81no—
456C4×C109—81no—
457C4×C109—82no—
458C4×C109—81no—
459C4×C109—81no—
460#24405C10911yesmaximal, characteristic, direct product factor, Sylow
461C2×C109—22no—
462C2×C109—21no—
463C2×C109—21no—
464C2×C109—22no—
465C2×C109—22no—
466C2×C109—42no—
467C2×C109—41no—
468C2×C109—42no—
469C2×C109—81no—
470C2×C109—82no—
471C2×C109#241011yescharacteristic
472C2×C109C2×#45811yescharacteristic
473C2×C109#302611yescharacteristic
474#3484C2×C10911yescharacteristic
475C2×#458C2×C10911yescharacteristic, complemented
476C22×#99C2×C10911yescharacteristic, complemented
477#2412C2×C10912yescomplemented
478#2405C2×C10911yescharacteristic, complemented
479#2044C2×C10912yescomplemented
480#2022C2×C10912yescomplemented
481#1898C2×C10912yescomplemented
482#1890C2×C10911yescharacteristic, complemented
483#1867C2×C10911yescharacteristic, complemented
484#1790C2×C10911yescharacteristic, complemented
485C109#2440511yescharacteristic, direct product factor, Sylow
486C2×H(5,𝔽2)C22×C10911yescharacteristic
487C23×D4C22×C10911yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C10912yes—
495#525—21no—
496C2×#123C22×C10911yescharacteristic
497C2×#123C22×C10912yescomplemented
498C2×#123C22×C10911yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C10912yes—
501#518C22×C10911yescharacteristic
502C22×C22⋊C4C22×C10911yescharacteristic, complemented
503C22×C22⋊C4C22×C10912yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C10911yescharacteristic
507C2×#99C22×C10911yescharacteristic
508C2×#99C22×C10912yescomplemented
509C2×#99C22×C10912yescomplemented
510C2×#99C22×C10912yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C10911yescharacteristic
517#386C22×C10911yescharacteristic, complemented
518#386C22×C10912yescomplemented
519#385—21no—
520#385C22×C10912yescomplemented
521#381C22×C10912yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C10911yescharacteristic, complemented
525#342C22×C10912yescomplemented
526#342C22×C10912yescomplemented
527C25D4×C10911yescharacteristic
528C25C23×C10911yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C10911yescharacteristic
544C22×D4D4×C10911yescharacteristic
545C22×D4D4×C10912yes—
546C22×D4D4×C10912yes—
547C22×D4C23×C10912yes—
548C22×D4C23×C10911yescharacteristic
549C22×D4C23×C10911yescharacteristic
550C23×C4—22no—
551C23×C4D4×C10911yescharacteristic
552C23×C4C23×C10911yescharacteristic
553C23×C4C23×C10911yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C10912yes—
611C2×C22⋊C4D4×C10912yes—
612C2×C22⋊C4C23×C10912yes—
613C2×C22⋊C4C23×C10911yescharacteristic
614C2×C22⋊C4C23×C10911yescharacteristic
615C2×C22⋊C4C23×C10912yes—
616C2×C22⋊C4C23×C10912yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C10914yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C10911yescharacteristic
641C24C2×D4×C10912yes—
642C24C2×D4×C10911yescharacteristic
643C24C2×D4×C10912yes—
644C24C2×D4×C10912yes—
645C24C2×D4×C10911yescharacteristic
646C24C2×D4×C10911yescharacteristic
647C24C24×C10911yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C10912yes—
692C2×D4#41×C10912yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C10912yes—
717C22×C4C2×D4×C10911yescharacteristic
718C22×C4C2×D4×C10911yescharacteristic
719C22×C4C2×D4×C10912yes—
720C22×C4C2×D4×C10912yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C10914yescomplemented
759C42—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—24no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C10911yescharacteristic
807C23#120×C10912yes—
808C23#120×C10911yescharacteristic
809C23#121×C10912yes—
810C23C22×D4×C10911yescharacteristic
811C23C22×D4×C10912yes—
812C23C22×D4×C10911yescharacteristic
813C23C2×#41×C10911yescharacteristic
814C23H(5,𝔽2)×C10912yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—44no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C10912yes—
876C22—22no—
877C22—21no—
878C22—22no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C10912yescomplemented
918C22C2×#120×C10911yescharacteristic
919C22C2×#121×C10911yescharacteristic
920C22#534×C10911yescharacteristic
921C22D42×C10912yes—
922C22#546×C10912yes—
923C4—22no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—41no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C109×#241011yescharacteristic
945C2C2×#458×C10911yescharacteristic
946C2C109×#302611yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC24C24×C109
prime radicalC109×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C25×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#458×C109C2semidirect
3. C22×#99×C109C2semidirect
4. C109×#2412C2semidirect
5. C109×#2405C2semidirect
6. C109×#2044C2semidirect
7. C109×#2022C2semidirect
8. C109×#1898C2semidirect
9. C109×#1890C2semidirect
10. C109×#1867C2semidirect
11. C109×#1790C2semidirect
23. C2×#123×C109C22semidirect
24. C2×#123×C109C22semidirect
28. C22×C22⋊C4×C109C22semidirect
29. C22×C22⋊C4×C109C22semidirect
34. C2×#99×C109C22semidirect
35. C2×#99×C109C22semidirect
36. C2×#99×C109C22semidirect
43. #386×C109C22semidirect
44. #386×C109C22semidirect
46. #385×C109C22semidirect
47. #381×C109C22semidirect
50. #379×C109C22semidirect
51. #342×C109C22semidirect
52. #342×C109C22semidirect
147. #99×C109D4semidirect
284. C22⋊C4×C109C2×D4semidirect
443. C22×C109#458semidirect
460. #24405C109direct (N × H)
475. C2×#458C2×C109semidirect
476. C22×#99C2×C109semidirect
477. #2412C2×C109semidirect
478. #2405C2×C109semidirect
479. #2044C2×C109semidirect
480. #2022C2×C109semidirect
481. #1898C2×C109semidirect
482. #1890C2×C109semidirect
483. #1867C2×C109semidirect
484. #1790C2×C109semidirect
485. C109#24405direct (N × H)
497. C2×#123C22×C109semidirect
498. C2×#123C22×C109semidirect
502. C22×C22⋊C4C22×C109semidirect
503. C22×C22⋊C4C22×C109semidirect
508. C2×#99C22×C109semidirect
509. C2×#99C22×C109semidirect
510. C2×#99C22×C109semidirect
517. #386C22×C109semidirect
518. #386C22×C109semidirect
520. #385C22×C109semidirect
521. #381C22×C109semidirect
524. #379C22×C109semidirect
525. #342C22×C109semidirect
526. #342C22×C109semidirect
621. #99D4×C109semidirect
758. C22⋊C4C2×D4×C109semidirect
917. C22#458×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#34842
C2×#458×C1092
C22×#99×C1092
C109×#24122
C109×#24052
C109×#20442
C109×#20222
C109×#18982
C109×#18902
C109×#18672
C109×#17902
#24405109