Finite Group Databasebeta

← C109×#24404 #42142398

Subgroups — C109×#24404 #42142398

Order 27904.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3484C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C109C211yesmaximal, characteristic, complemented
3C22×#99×C109C211yesmaximal, characteristic, complemented
4C109×#2410C212yesmaximal, complemented
5C109×#2403C211yesmaximal, characteristic, complemented
6C109×#2044C212yesmaximal, complemented
7C109×#2021C212yesmaximal, complemented
8C109×#1898C212yesmaximal, complemented
9C109×#1889C211yesmaximal, characteristic, complemented
10C109×#1867C211yesmaximal, characteristic, complemented
11C109×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C109C2211yescharacteristic
13C23×D4×C109C2211yescharacteristic
14C23×D4×C109C2211yescharacteristic, complemented
15#546×C109—22no—
16#546×C109—22no—
17D42×C109—22no—
18D42×C109—22no—
19#535×C109—21no—
20#534×C109—21no—
21#534×C109C2212yes—
22#525×C109—21no—
23C2×#121×C109—22no—
24C2×#120×C109—21no—
25C2×#120×C109—21no—
26C2×#120×C109C2211yescharacteristic
27C2×#120×C109C2212yes—
28C2×#120×C109C2212yescomplemented
29C2×#120×C109C2211yescharacteristic, complemented
30#518×C109C2211yescharacteristic
31C22×C22⋊C4×C109C2212yescomplemented
32B(4,𝔽2)×C109—24no—
33C2×#99×C109—24no—
34C2×#99×C109C2211yescharacteristic
35C2×#99×C109C2211yescharacteristic
36C2×#99×C109C2212yescomplemented
37C2×#99×C109C2212yescomplemented
38C2×#99×C109C2212yescomplemented
39#394×C109—22no—
40#392×C109—21no—
41#392×C109—21no—
42#392×C109—22no—
43#386×C109—21no—
44#386×C109—22no—
45#386×C109C2211yescharacteristic
46#386×C109C2211yescharacteristic, complemented
47#386×C109C2212yescomplemented
48#385×C109C2212yescomplemented
49#379×C109C2212yescomplemented
50#379×C109C2211yescharacteristic, complemented
51#342×C109C2212yescomplemented
52#342×C109C2212yescomplemented
53C25×C109D411yescharacteristic, complemented
54C25×C109C2311yescharacteristic
55C25×C109C2311yescharacteristic
56H(5,𝔽2)×C109—22no—
57H(5,𝔽2)×C109—22no—
58H(5,𝔽2)×C109—42no—
59C2×#41×C109—21no—
60C2×#41×C109—22no—
61C22×D4×C109—21no—
62C22×D4×C109—21no—
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—21no—
68C22×D4×C109—21no—
69C22×D4×C109—22no—
70C22×D4×C109—22no—
71C22×D4×C109—21no—
72C22×D4×C109—22no—
73C22×D4×C109—21no—
74C22×D4×C109—21no—
75C22×D4×C109—22no—
76C22×D4×C109—44no—
77C22×D4×C109—42no—
78C22×D4×C109D411yescharacteristic, complemented
79C22×D4×C109D411yescharacteristic, complemented
80C22×D4×C109D412yescomplemented
81C22×D4×C109D412yescomplemented
82C22×D4×C109C2312yes—
83C22×D4×C109C2311yescharacteristic
84C22×D4×C109C2311yescharacteristic
85C23×C4×C109—22no—
86C23×C4×C109D411yescharacteristic, complemented
87C23×C4×C109C2311yescharacteristic
88#127×C109—22no—
89#124×C109—22no—
90#123×C109—22no—
91#123×C109—22no—
92#123×C109—22no—
93C22⋊Q8×C109—21no—
94C22⋊Q8×C109—21no—
95#121×C109—21no—
96#121×C109—21no—
97#121×C109—22no—
98#121×C109—22no—
99#121×C109—22no—
100#121×C109—22no—
101#121×C109—22no—
102#121×C109—22no—
103#121×C109—48no—
104#120×C109—22no—
105#120×C109—22no—
106#120×C109—22no—
107#120×C109—22no—
108#120×C109—22no—
109#120×C109—22no—
110#120×C109—22no—
111#120×C109—22no—
112#120×C109—22no—
113#120×C109—22no—
114#120×C109—22no—
115#120×C109—24no—
116#120×C109—42no—
117#120×C109—42no—
118#120×C109—44no—
119C4×D4×C109—22no—
120C4×D4×C109—22no—
121C4×D4×C109—22no—
122C4×D4×C109—22no—
123#117×C109—21no—
124C2×C4⋊C4×C109—22no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109—24no—
129C2×C22⋊C4×C109—22no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—22no—
134C2×C22⋊C4×C109—21no—
135C2×C22⋊C4×C109—21no—
136C2×C22⋊C4×C109—22no—
137C2×C22⋊C4×C109—22no—
138C2×C22⋊C4×C109—21no—
139C2×C22⋊C4×C109—22no—
140C2×C22⋊C4×C109—42no—
141C2×C22⋊C4×C109D412yescomplemented
142C2×C22⋊C4×C109D412yescomplemented
143C2×C22⋊C4×C109C2312yes—
144C2×C22⋊C4×C109C2311yescharacteristic
145C2×C22⋊C4×C109C2311yescharacteristic
146C2×C22⋊C4×C109C2312yes—
147C2×C22⋊C4×C109C2312yes—
148#99×C109—22no—
149#99×C109—24no—
150#99×C109—24no—
151#99×C109—42no—
152#99×C109D414yescomplemented
153#95×C109—22no—
154#95×C109—21no—
155#95×C109—21no—
156#95×C109—22no—
157C24×C109—21no—
158C24×C109—21no—
159C24×C109—22no—
160C24×C109—21no—
161C24×C109—22no—
162C24×C109—21no—
163C24×C109—21no—
164C24×C109—21no—
165C24×C109—22no—
166C24×C109—21no—
167C24×C109—21no—
168C24×C109—22no—
169C24×C109—41no—
170C24×C109—42no—
171C24×C109—42no—
172C24×C109—42no—
173C24×C109—81no—
174C24×C109—81no—
175C24×C109—81no—
176C24×C109C2×D411yescharacteristic
177C24×C109C2×D412yes—
178C24×C109C2×D411yescharacteristic
179C24×C109C2×D412yes—
180C24×C109C2×D412yes—
181C24×C109C2×D411yescharacteristic
182C24×C109C2×D411yescharacteristic
183C24×C109C2411yescharacteristic
184#41×C109—44no—
185#41×C109—44no—
186#41×C109—42no—
187#41×C109—42no—
188C2×Q8×C109—21no—
189C2×D4×C109—22no—
190C2×D4×C109—22no—
191C2×D4×C109—22no—
192C2×D4×C109—24no—
193C2×D4×C109—21no—
194C2×D4×C109—28no—
195C2×D4×C109—22no—
196C2×D4×C109—22no—
197C2×D4×C109—22no—
198C2×D4×C109—22no—
199C2×D4×C109—22no—
200C2×D4×C109—21no—
201C2×D4×C109—22no—
202C2×D4×C109—22no—
203C2×D4×C109—22no—
204C2×D4×C109—22no—
205C2×D4×C109—21no—
206C2×D4×C109—22no—
207C2×D4×C109—22no—
208C2×D4×C109—22no—
209C2×D4×C109—22no—
210C2×D4×C109—22no—
211C2×D4×C109—22no—
212C2×D4×C109—22no—
213C2×D4×C109—22no—
214C2×D4×C109—22no—
215C2×D4×C109—41no—
216C2×D4×C109—41no—
217C2×D4×C109—42no—
218C2×D4×C109—44no—
219C2×D4×C109—44no—
220C2×D4×C109—44no—
221C2×D4×C109—44no—
222C2×D4×C109—44no—
223C2×D4×C109—44no—
224C2×D4×C109—44no—
225C2×D4×C109—44no—
226C2×D4×C109—44no—
227C2×D4×C109—42no—
228C2×D4×C109—42no—
229C2×D4×C109—44no—
230C2×D4×C109—42no—
231C2×D4×C109—41no—
232C2×D4×C109—42no—
233C2×D4×C109—41no—
234C2×D4×C109—42no—
235C2×D4×C109—44no—
236C2×D4×C109—42no—
237C2×D4×C109—42no—
238C2×D4×C109—42no—
239C2×D4×C109—44no—
240C2×D4×C109—42no—
241C2×D4×C109—82no—
242C2×D4×C109—82no—
243C2×D4×C109—81no—
244C2×D4×C109—81no—
245C2×D4×C109—82no—
246C2×D4×C109—82no—
247C2×D4×C109C2×D412yes—
248C2×D4×C109#4112yes—
249C22×C4×C109—21no—
250C22×C4×C109—22no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109—21no—
254C22×C4×C109—22no—
255C22×C4×C109—22no—
256C22×C4×C109—21no—
257C22×C4×C109—21no—
258C22×C4×C109—22no—
259C22×C4×C109—22no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—42no—
263C22×C4×C109—41no—
264C22×C4×C109—44no—
265C22×C4×C109—44no—
266C22×C4×C109—82no—
267C22×C4×C109C2×D412yes—
268C22×C4×C109C2×D411yescharacteristic
269C22×C4×C109C2×D411yescharacteristic
270C22×C4×C109C2×D412yes—
271C22×C4×C109C2×D412yes—
272C4⋊C4×C109—21no—
273C4⋊C4×C109—21no—
274C4⋊C4×C109—22no—
275C4⋊C4×C109—22no—
276C4⋊C4×C109—44no—
277C22⋊C4×C109—22no—
278C22⋊C4×C109—22no—
279C22⋊C4×C109—22no—
280C22⋊C4×C109—22no—
281C22⋊C4×C109—22no—
282C22⋊C4×C109—22no—
283C22⋊C4×C109—22no—
284C22⋊C4×C109—22no—
285C22⋊C4×C109—22no—
286C22⋊C4×C109—22no—
287C22⋊C4×C109—22no—
288C22⋊C4×C109—22no—
289C22⋊C4×C109—22no—
290C22⋊C4×C109—21no—
291C22⋊C4×C109—21no—
292C22⋊C4×C109—22no—
293C22⋊C4×C109—22no—
294C22⋊C4×C109—44no—
295C22⋊C4×C109—44no—
296C22⋊C4×C109—42no—
297C22⋊C4×C109—42no—
298C22⋊C4×C109—42no—
299C22⋊C4×C109—44no—
300C22⋊C4×C109—42no—
301C22⋊C4×C109—44no—
302C22⋊C4×C109—42no—
303C22⋊C4×C109—82no—
304C22⋊C4×C109—81no—
305C22⋊C4×C109C2×D414yescomplemented
306C42×C109—22no—
307C23×C109—21no—
308C23×C109—21no—
309C23×C109—21no—
310C23×C109—22no—
311C23×C109—22no—
312C23×C109—22no—
313C23×C109—24no—
314C23×C109—21no—
315C23×C109—21no—
316C23×C109—21no—
317C23×C109—22no—
318C23×C109—22no—
319C23×C109—24no—
320C23×C109—22no—
321C23×C109—21no—
322C23×C109—22no—
323C23×C109—21no—
324C23×C109—21no—
325C23×C109—22no—
326C23×C109—22no—
327C23×C109—41no—
328C23×C109—42no—
329C23×C109—41no—
330C23×C109—41no—
331C23×C109—41no—
332C23×C109—42no—
333C23×C109—41no—
334C23×C109—42no—
335C23×C109—42no—
336C23×C109—42no—
337C23×C109—41no—
338C23×C109—41no—
339C23×C109—41no—
340C23×C109—41no—
341C23×C109—42no—
342C23×C109—42no—
343C23×C109—41no—
344C23×C109—42no—
345C23×C109—41no—
346C23×C109—41no—
347C23×C109—42no—
348C23×C109—42no—
349C23×C109—42no—
350C23×C109—42no—
351C23×C109—41no—
352C23×C109—41no—
353C23×C109—41no—
354C23×C109—42no—
355C23×C109—42no—
356C23×C109—42no—
357C23×C109—81no—
358C23×C109—81no—
359C23×C109—82no—
360C23×C109—82no—
361C23×C109—82no—
362C23×C109—82no—
363C23×C109—84no—
364C23×C109—84no—
365C23×C109—81no—
366C23×C109—81no—
367C23×C109—84no—
368C23×C109—84no—
369C23×C109#12011yescharacteristic
370C23×C109#12012yes—
371C23×C109#12011yescharacteristic
372C23×C109#12112yescomplemented
373C23×C109C22×D411yescharacteristic
374C23×C109C22×D412yes—
375C23×C109C22×D411yescharacteristic
376C23×C109C2×#4111yescharacteristic
377C23×C109H(5,𝔽2)12yes—
378Q8×C109—42no—
379D4×C109—24no—
380D4×C109—24no—
381D4×C109—44no—
382D4×C109—42no—
383D4×C109—44no—
384D4×C109—48no—
385D4×C109—44no—
386D4×C109—44no—
387D4×C109—44no—
388D4×C109—42no—
389D4×C109—42no—
390D4×C109—42no—
391D4×C109—42no—
392D4×C109—42no—
393D4×C109—42no—
394D4×C109—44no—
395D4×C109—44no—
396D4×C109—82no—
397D4×C109—82no—
398D4×C109—82no—
399D4×C109—82no—
400D4×C109—88no—
401D4×C109—84no—
402D4×C109—84no—
403C2×C4×C109—21no—
404C2×C4×C109—21no—
405C2×C4×C109—22no—
406C2×C4×C109—24no—
407C2×C4×C109—22no—
408C2×C4×C109—22no—
409C2×C4×C109—22no—
410C2×C4×C109—21no—
411C2×C4×C109—21no—
412C2×C4×C109—21no—
413C2×C4×C109—24no—
414C2×C4×C109—22no—
415C2×C4×C109—22no—
416C2×C4×C109—42no—
417C2×C4×C109—42no—
418C2×C4×C109—44no—
419C2×C4×C109—42no—
420C2×C4×C109—42no—
421C2×C4×C109—41no—
422C2×C4×C109—42no—
423C2×C4×C109—42no—
424C2×C4×C109—41no—
425C2×C4×C109—42no—
426C2×C4×C109—42no—
427C2×C4×C109—42no—
428C2×C4×C109—41no—
429C2×C4×C109—41no—
430C2×C4×C109—42no—
431C2×C4×C109—41no—
432C2×C4×C109—41no—
433C2×C4×C109—41no—
434C2×C4×C109—41no—
435C2×C4×C109—42no—
436C2×C4×C109—81no—
437C2×C4×C109—81no—
438C2×C4×C109—88no—
439C2×C4×C109#12112yescomplemented
440C22×C109—21no—
441C22×C109—22no—
442C22×C109—21no—
443C22×C109—22no—
444C22×C109—21no—
445C22×C109—21no—
446C22×C109—21no—
447C22×C109—22no—
448C22×C109—22no—
449C22×C109—22no—
450C22×C109—21no—
451C22×C109—21no—
452C22×C109—22no—
453C22×C109—41no—
454C22×C109—41no—
455C22×C109—42no—
456C22×C109—44no—
457C22×C109—44no—
458C22×C109—42no—
459C22×C109—42no—
460C22×C109—42no—
461C22×C109—44no—
462C22×C109—42no—
463C22×C109—42no—
464C22×C109—42no—
465C22×C109—44no—
466C22×C109—41no—
467C22×C109—41no—
468C22×C109—42no—
469C22×C109—41no—
470C22×C109—42no—
471C22×C109—42no—
472C22×C109—41no—
473C22×C109—42no—
474C22×C109—41no—
475C22×C109—82no—
476C22×C109—81no—
477C22×C109—81no—
478C22×C109—81no—
479C22×C109—82no—
480C22×C109—84no—
481C22×C109—82no—
482C22×C109—82no—
483C22×C109—81no—
484C22×C109—82no—
485C22×C109—81no—
486C22×C109—81no—
487C22×C109—82no—
488C22×C109—84no—
489C22×C109—81no—
490C22×C109—81no—
491C22×C109—162no—
492C22×C109B(4,𝔽2)12yescomplemented
493C22×C109C2×#12011yescharacteristic
494C22×C109C2×#12111yescharacteristic
495C22×C109#53411yescharacteristic
496C22×C109D4212yes—
497C22×C109#54612yes—
498C4×C109—22no—
499C4×C109—44no—
500C4×C109—41no—
501C4×C109—42no—
502C4×C109—42no—
503C4×C109—42no—
504C4×C109—42no—
505C4×C109—82no—
506C4×C109—81no—
507C4×C109—81no—
508#24404C10911yesmaximal, characteristic, direct product factor, Sylow
509C2×C109—22no—
510C2×C109—21no—
511C2×C109—21no—
512C2×C109—22no—
513C2×C109—22no—
514C2×C109—42no—
515C2×C109—41no—
516C2×C109—42no—
517C2×C109—82no—
518C2×C109—81no—
519C2×C109—82no—
520C2×C109#241011yescharacteristic
521C2×C109C2×B(4,𝔽2)11yescharacteristic
522C2×C109#302611yescharacteristic
523#3484C2×C10911yescharacteristic, complemented
524C2×B(4,𝔽2)C2×C10911yescharacteristic, complemented
525C22×#99C2×C10911yescharacteristic, complemented
526#2410C2×C10912yescomplemented
527#2403C2×C10911yescharacteristic, complemented
528#2044C2×C10912yescomplemented
529#2021C2×C10912yescomplemented
530#1898C2×C10912yescomplemented
531#1889C2×C10911yescharacteristic, complemented
532#1867C2×C10911yescharacteristic, complemented
533#1790C2×C10911yescharacteristic, complemented
534C109#2440411yescharacteristic, direct product factor, Sylow
535C2×H(5,𝔽2)C22×C10911yescharacteristic
536C23×D4C22×C10911yescharacteristic
537C23×D4C22×C10911yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C10912yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C10911yescharacteristic
550C2×#120C22×C10912yes—
551C2×#120C22×C10912yescomplemented
552C2×#120C22×C10911yescharacteristic, complemented
553#518C22×C10911yescharacteristic
554C22×C22⋊C4C22×C10912yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C10911yescharacteristic
558C2×#99C22×C10911yescharacteristic
559C2×#99C22×C10912yescomplemented
560C2×#99C22×C10912yescomplemented
561C2×#99C22×C10912yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C10911yescharacteristic
569#386C22×C10911yescharacteristic, complemented
570#386C22×C10912yescomplemented
571#385C22×C10912yescomplemented
572#379C22×C10912yescomplemented
573#379C22×C10911yescharacteristic, complemented
574#342C22×C10912yescomplemented
575#342C22×C10912yescomplemented
576C25D4×C10911yescharacteristic, complemented
577C25C23×C10911yescharacteristic
578C25C23×C10911yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C10911yescharacteristic, complemented
602C22×D4D4×C10911yescharacteristic, complemented
603C22×D4D4×C10912yescomplemented
604C22×D4D4×C10912yescomplemented
605C22×D4C23×C10912yes—
606C22×D4C23×C10911yescharacteristic
607C22×D4C23×C10911yescharacteristic
608C23×C4—22no—
609C23×C4D4×C10911yescharacteristic, complemented
610C23×C4C23×C10911yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C10912yescomplemented
665C2×C22⋊C4D4×C10912yescomplemented
666C2×C22⋊C4C23×C10912yes—
667C2×C22⋊C4C23×C10911yescharacteristic
668C2×C22⋊C4C23×C10911yescharacteristic
669C2×C22⋊C4C23×C10912yes—
670C2×C22⋊C4C23×C10912yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C10914yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C10911yescharacteristic
700C24C2×D4×C10912yes—
701C24C2×D4×C10911yescharacteristic
702C24C2×D4×C10912yes—
703C24C2×D4×C10912yes—
704C24C2×D4×C10911yescharacteristic
705C24C2×D4×C10911yescharacteristic
706C24C24×C10911yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C10912yes—
771C2×D4#41×C10912yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C10912yes—
791C22×C4C2×D4×C10911yescharacteristic
792C22×C4C2×D4×C10911yescharacteristic
793C22×C4C2×D4×C10912yes—
794C22×C4C2×D4×C10912yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C10914yescomplemented
829C42—22no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—24no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C10911yescharacteristic
893C23#120×C10912yes—
894C23#120×C10911yescharacteristic
895C23#121×C10912yescomplemented
896C23C22×D4×C10911yescharacteristic
897C23C22×D4×C10912yes—
898C23C22×D4×C10911yescharacteristic
899C23C2×#41×C10911yescharacteristic
900C23H(5,𝔽2)×C10912yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—44no—
918D4—44no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C10912yescomplemented
963C22—22no—
964C22—21no—
965C22—22no—
966C22—21no—
967C22—21no—
968C22—21no—
969C22—22no—
970C22—21no—
971C22—21no—
972C22—22no—
973C22—21no—
974C22—22no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—42no—
993C22—41no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C10912yescomplemented
1016C22C2×#120×C10911yescharacteristic
1017C22C2×#121×C10911yescharacteristic
1018C22#534×C10911yescharacteristic
1019C22D42×C10912yes—
1020C22#546×C10912yes—
1021C4—22no—
1022C4—44no—
1023C4—42no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C109×#241011yescharacteristic
1043C2C2×B(4,𝔽2)×C10911yescharacteristic
1044C2C109×#302611yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC24C24×C109
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C25×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3484C2semidirect
2. C2×B(4,𝔽2)×C109C2semidirect
3. C22×#99×C109C2semidirect
4. C109×#2410C2semidirect
5. C109×#2403C2semidirect
6. C109×#2044C2semidirect
7. C109×#2021C2semidirect
8. C109×#1898C2semidirect
9. C109×#1889C2semidirect
10. C109×#1867C2semidirect
11. C109×#1790C2semidirect
14. C23×D4×C109C22semidirect
28. C2×#120×C109C22semidirect
29. C2×#120×C109C22semidirect
31. C22×C22⋊C4×C109C22semidirect
36. C2×#99×C109C22semidirect
37. C2×#99×C109C22semidirect
38. C2×#99×C109C22semidirect
46. #386×C109C22semidirect
47. #386×C109C22semidirect
48. #385×C109C22semidirect
49. #379×C109C22semidirect
50. #379×C109C22semidirect
51. #342×C109C22semidirect
52. #342×C109C22semidirect
53. C25×C109D4semidirect
78. C22×D4×C109D4semidirect
79. C22×D4×C109D4semidirect
80. C22×D4×C109D4semidirect
81. C22×D4×C109D4semidirect
86. C23×C4×C109D4semidirect
141. C2×C22⋊C4×C109D4semidirect
142. C2×C22⋊C4×C109D4semidirect
152. #99×C109D4semidirect
305. C22⋊C4×C109C2×D4semidirect
372. C23×C109#121semidirect
439. C2×C4×C109#121semidirect
492. C22×C109B(4,𝔽2)semidirect
508. #24404C109direct (N × H)
523. #3484C2×C109semidirect
524. C2×B(4,𝔽2)C2×C109semidirect
525. C22×#99C2×C109semidirect
526. #2410C2×C109semidirect
527. #2403C2×C109semidirect
528. #2044C2×C109semidirect
529. #2021C2×C109semidirect
530. #1898C2×C109semidirect
531. #1889C2×C109semidirect
532. #1867C2×C109semidirect
533. #1790C2×C109semidirect
534. C109#24404direct (N × H)
537. C23×D4C22×C109semidirect
551. C2×#120C22×C109semidirect
552. C2×#120C22×C109semidirect
554. C22×C22⋊C4C22×C109semidirect
559. C2×#99C22×C109semidirect
560. C2×#99C22×C109semidirect
561. C2×#99C22×C109semidirect
569. #386C22×C109semidirect
570. #386C22×C109semidirect
571. #385C22×C109semidirect
572. #379C22×C109semidirect
573. #379C22×C109semidirect
574. #342C22×C109semidirect
575. #342C22×C109semidirect
576. C25D4×C109semidirect
601. C22×D4D4×C109semidirect
602. C22×D4D4×C109semidirect
603. C22×D4D4×C109semidirect
604. C22×D4D4×C109semidirect
609. C23×C4D4×C109semidirect
664. C2×C22⋊C4D4×C109semidirect
665. C2×C22⋊C4D4×C109semidirect
675. #99D4×C109semidirect
828. C22⋊C4C2×D4×C109semidirect
895. C23#121×C109semidirect
962. C2×C4#121×C109semidirect
1015. C22B(4,𝔽2)×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#34842
C2×B(4,𝔽2)×C1092
C22×#99×C1092
C109×#24102
C109×#24032
C109×#20442
C109×#20212
C109×#18982
C109×#18892
C109×#18672
C109×#17902
#24404109