Finite Group Databasebeta

← C109×#25563 #42143557

Subgroups — C109×#25563 #42143557

Order 27904.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3490C211yesmaximal, characteristic, complemented
2C109×#2410C212yesmaximal, complemented
3C109×#2405C211yesmaximal, characteristic, complemented
4C109×#2062C211yesmaximal, characteristic, complemented
5C109×#2044C211yesmaximal, characteristic, complemented
6C109×#2029C211yesmaximal, characteristic, complemented
7C109×#2021C211yesmaximal, characteristic, complemented
8C109×#1898C212yesmaximal, complemented
9C109×#1889C212yesmaximal, complemented
10C109×#1867C212yesmaximal, complemented
11C2×#342×C109C211yesmaximal, characteristic, complemented
12C23×D4×C109C2211yescharacteristic
13#551×C109—22no—
14#551×C109—22no—
15#546×C109—22no—
16#546×C109—22no—
17#543×C109C2211yescharacteristic
18#538×C109—21no—
19#538×C109—21no—
20#534×C109C2211yescharacteristic
21#525×C109—21no—
22#525×C109—21no—
23C2×#123×C109—21no—
24C2×#121×C109—22no—
25C2×#120×C109C2212yes—
26C2×#120×C109C2212yes—
27#518×C109C2212yes—
28C22×C22⋊C4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2212yes—
30C2×#99×C109C2212yes—
31C2×#99×C109C2212yes—
32#394×C109—21no—
33#394×C109—21no—
34#394×C109—22no—
35#392×C109—22no—
36#386×C109—21no—
37#386×C109—22no—
38#386×C109C2212yes—
39#385×C109C2211yescharacteristic
40#385×C109C2212yes—
41#385×C109C2211yescharacteristic
42#379×C109C2211yescharacteristic
43#379×C109C2212yes—
44#379×C109C2211yescharacteristic
45#379×C109C2211yescharacteristic
46#342×C109C2211yescharacteristic
47#342×C109C2211yescharacteristic
48#342×C109C2212yes—
49#342×C109C2212yes—
50#342×C109C2212yes—
51C25×C109C2311yescharacteristic
52C25×C109C2311yescharacteristic
53C2×#41×C109—21no—
54C2×#41×C109—21no—
55C22×D4×C109—22no—
56C22×D4×C109—21no—
57C22×D4×C109—22no—
58C22×D4×C109—21no—
59C22×D4×C109—22no—
60C22×D4×C109—44no—
61C22×D4×C109D412yescomplemented
62C22×D4×C109D412yescomplemented
63C22×D4×C109C2312yes—
64C23×C4×C109—22no—
65C23×C4×C109D411yescharacteristic, complemented
66C23×C4×C109D411yescharacteristic, complemented
67C23×C4×C109C2311yescharacteristic
68#126×C109—22no—
69#126×C109—22no—
70#124×C109—22no—
71#124×C109—22no—
72#123×C109—22no—
73#123×C109—22no—
74#123×C109—22no—
75#123×C109—22no—
76#123×C109—22no—
77#123×C109—44no—
78C22⋊Q8×C109—21no—
79C22⋊Q8×C109—21no—
80C22⋊Q8×C109—21no—
81C22⋊Q8×C109—21no—
82C22⋊Q8×C109—22no—
83C22⋊Q8×C109—22no—
84#121×C109—21no—
85#121×C109—21no—
86#121×C109—22no—
87#121×C109—22no—
88#121×C109—21no—
89#121×C109—21no—
90#121×C109—48no—
91#120×C109—22no—
92#120×C109—22no—
93#120×C109—22no—
94#120×C109—22no—
95#120×C109—22no—
96#120×C109—24no—
97#120×C109—42no—
98C4×D4×C109—22no—
99C4×D4×C109—22no—
100C4×D4×C109—22no—
101C4×D4×C109—22no—
102C4×D4×C109—22no—
103C4×D4×C109—22no—
104#117×C109—21no—
105#117×C109—21no—
106#117×C109—22no—
107C2×C4⋊C4×C109—22no—
108C2×C4⋊C4×C109—21no—
109C2×C4⋊C4×C109—21no—
110C2×C22⋊C4×C109—22no—
111C2×C22⋊C4×C109—22no—
112C2×C22⋊C4×C109—22no—
113C2×C22⋊C4×C109—24no—
114C2×C22⋊C4×C109—22no—
115C2×C22⋊C4×C109—22no—
116C2×C22⋊C4×C109—21no—
117C2×C22⋊C4×C109—22no—
118C2×C22⋊C4×C109—22no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—22no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—42no—
126C2×C22⋊C4×C109D411yescharacteristic, complemented
127C2×C22⋊C4×C109D411yescharacteristic, complemented
128C2×C22⋊C4×C109D412yescomplemented
129C2×C22⋊C4×C109D412yescomplemented
130C2×C22⋊C4×C109C2312yes—
131C2×C22⋊C4×C109C2311yescharacteristic
132C2×C22⋊C4×C109C2311yescharacteristic
133C2×C22⋊C4×C109C2311yescharacteristic
134C2×C22⋊C4×C109C2311yescharacteristic
135C2×C22⋊C4×C109C2312yes—
136C2×C22⋊C4×C109C2312yes—
137#99×C109—24no—
138#99×C109—42no—
139#95×C109—22no—
140#95×C109—21no—
141#95×C109—21no—
142#95×C109—22no—
143C24×C109—22no—
144C24×C109—21no—
145C24×C109—21no—
146C24×C109—21no—
147C24×C109—22no—
148C24×C109—22no—
149C24×C109—21no—
150C24×C109—21no—
151C24×C109—42no—
152C24×C109—42no—
153C24×C109—81no—
154C24×C109—81no—
155C24×C109C2×D412yes—
156C24×C109C2×D411yescharacteristic
157C24×C109C2×D412yes—
158C24×C109C2×D412yes—
159C24×C109C2×D411yescharacteristic
160C24×C109C2411yescharacteristic
161#41×C109—82no—
162#41×C109—82no—
163C2×Q8×C109—21no—
164C2×Q8×C109—21no—
165C2×D4×C109—28no—
166C2×D4×C109—24no—
167C2×D4×C109—22no—
168C2×D4×C109—22no—
169C2×D4×C109—22no—
170C2×D4×C109—22no—
171C2×D4×C109—22no—
172C2×D4×C109—22no—
173C2×D4×C109—22no—
174C2×D4×C109—22no—
175C2×D4×C109—21no—
176C2×D4×C109—21no—
177C2×D4×C109—22no—
178C2×D4×C109—22no—
179C2×D4×C109—44no—
180C2×D4×C109—42no—
181C2×D4×C109—44no—
182C2×D4×C109—42no—
183C2×D4×C109—44no—
184C2×D4×C109—42no—
185C2×D4×C109—44no—
186C2×D4×C109—42no—
187C2×D4×C109—41no—
188C2×D4×C109—41no—
189C2×D4×C109—44no—
190C2×D4×C109—44no—
191C2×D4×C109—82no—
192C2×D4×C109—82no—
193C22×C4×C109—21no—
194C22×C4×C109—21no—
195C22×C4×C109—22no—
196C22×C4×C109—21no—
197C22×C4×C109—22no—
198C22×C4×C109—22no—
199C22×C4×C109—22no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—22no—
205C22×C4×C109—42no—
206C22×C4×C109—44no—
207C22×C4×C109—42no—
208C22×C4×C109—44no—
209C22×C4×C109—81no—
210C22×C4×C109—82no—
211C22×C4×C109C2×D412yes—
212C22×C4×C109C2×D411yescharacteristic
213C22×C4×C109C2×D412yes—
214C22×C4×C109C2×D411yescharacteristic
215C22×C4×C109C2×D411yescharacteristic
216C22×C4×C109C2×D412yes—
217C22×C4×C109C2×D411yescharacteristic
218C4⋊C4×C109—22no—
219C4⋊C4×C109—22no—
220C4⋊C4×C109—21no—
221C4⋊C4×C109—21no—
222C4⋊C4×C109—21no—
223C4⋊C4×C109—21no—
224C4⋊C4×C109—22no—
225C4⋊C4×C109—22no—
226C4⋊C4×C109—44no—
227C4⋊C4×C109—42no—
228C4⋊C4×C109—42no—
229C22⋊C4×C109—22no—
230C22⋊C4×C109—22no—
231C22⋊C4×C109—22no—
232C22⋊C4×C109—22no—
233C22⋊C4×C109—22no—
234C22⋊C4×C109—22no—
235C22⋊C4×C109—22no—
236C22⋊C4×C109—22no—
237C22⋊C4×C109—22no—
238C22⋊C4×C109—22no—
239C22⋊C4×C109—22no—
240C22⋊C4×C109—22no—
241C22⋊C4×C109—22no—
242C22⋊C4×C109—22no—
243C22⋊C4×C109—22no—
244C22⋊C4×C109—22no—
245C22⋊C4×C109—22no—
246C22⋊C4×C109—21no—
247C22⋊C4×C109—22no—
248C22⋊C4×C109—21no—
249C22⋊C4×C109—44no—
250C22⋊C4×C109—44no—
251C22⋊C4×C109—44no—
252C22⋊C4×C109—44no—
253C22⋊C4×C109—42no—
254C22⋊C4×C109—42no—
255C22⋊C4×C109—42no—
256C22⋊C4×C109—81no—
257C22⋊C4×C109—81no—
258C22⋊C4×C109—82no—
259C22⋊C4×C109—81no—
260C22⋊C4×C109#4114yescomplemented
261C42×C109—22no—
262C42×C109—22no—
263C23×C109—21no—
264C23×C109—21no—
265C23×C109—22no—
266C23×C109—22no—
267C23×C109—22no—
268C23×C109—24no—
269C23×C109—21no—
270C23×C109—21no—
271C23×C109—22no—
272C23×C109—22no—
273C23×C109—22no—
274C23×C109—24no—
275C23×C109—22no—
276C23×C109—22no—
277C23×C109—22no—
278C23×C109—41no—
279C23×C109—41no—
280C23×C109—42no—
281C23×C109—41no—
282C23×C109—41no—
283C23×C109—41no—
284C23×C109—42no—
285C23×C109—42no—
286C23×C109—41no—
287C23×C109—41no—
288C23×C109—42no—
289C23×C109—41no—
290C23×C109—42no—
291C23×C109—42no—
292C23×C109—42no—
293C23×C109—42no—
294C23×C109—41no—
295C23×C109—41no—
296C23×C109—41no—
297C23×C109—42no—
298C23×C109—42no—
299C23×C109—84no—
300C23×C109—84no—
301C23×C109—82no—
302C23×C109—82no—
303C23×C109—82no—
304C23×C109—82no—
305C23×C109#12012yes—
306C23×C109#12011yescharacteristic
307C23×C109#12011yescharacteristic
308C23×C109C22×D411yescharacteristic
309C23×C109C22×D412yes—
310C23×C109C2×#4112yes—
311C23×C109H(5,𝔽2)11yescharacteristic
312C23×C1092−1+411yescharacteristic
313Q8×C109—81no—
314Q8×C109—81no—
315D4×C109—44no—
316D4×C109—48no—
317D4×C109—44no—
318D4×C109—42no—
319D4×C109—42no—
320D4×C109—42no—
321D4×C109—42no—
322D4×C109—44no—
323D4×C109—44no—
324D4×C109—82no—
325D4×C109—82no—
326D4×C109—81no—
327D4×C109—81no—
328D4×C109—88no—
329C2×C4×C109—24no—
330C2×C4×C109—22no—
331C2×C4×C109—22no—
332C2×C4×C109—21no—
333C2×C4×C109—21no—
334C2×C4×C109—22no—
335C2×C4×C109—22no—
336C2×C4×C109—21no—
337C2×C4×C109—21no—
338C2×C4×C109—24no—
339C2×C4×C109—22no—
340C2×C4×C109—22no—
341C2×C4×C109—42no—
342C2×C4×C109—41no—
343C2×C4×C109—42no—
344C2×C4×C109—42no—
345C2×C4×C109—42no—
346C2×C4×C109—41no—
347C2×C4×C109—42no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—42no—
351C2×C4×C109—41no—
352C2×C4×C109—41no—
353C2×C4×C109—42no—
354C2×C4×C109—41no—
355C2×C4×C109—41no—
356C2×C4×C109—42no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109—42no—
360C2×C4×C109—41no—
361C2×C4×C109—41no—
362C2×C4×C109—42no—
363C2×C4×C109—81no—
364C2×C4×C109—81no—
365C2×C4×C109—82no—
366C2×C4×C109—82no—
367C2×C4×C109—88no—
368C22×C109—21no—
369C22×C109—21no—
370C22×C109—22no—
371C22×C109—21no—
372C22×C109—22no—
373C22×C109—21no—
374C22×C109—21no—
375C22×C109—22no—
376C22×C109—21no—
377C22×C109—22no—
378C22×C109—21no—
379C22×C109—22no—
380C22×C109—42no—
381C22×C109—41no—
382C22×C109—41no—
383C22×C109—44no—
384C22×C109—42no—
385C22×C109—42no—
386C22×C109—44no—
387C22×C109—44no—
388C22×C109—42no—
389C22×C109—42no—
390C22×C109—44no—
391C22×C109—42no—
392C22×C109—42no—
393C22×C109—42no—
394C22×C109—42no—
395C22×C109—82no—
396C22×C109—81no—
397C22×C109—81no—
398C22×C109—82no—
399C22×C109—82no—
400C22×C109—82no—
401C22×C109—82no—
402C22×C109—81no—
403C22×C109—81no—
404C22×C109—82no—
405C22×C109—81no—
406C22×C109—81no—
407C22×C109B(4,𝔽2)12yes—
408C22×C109C2×#12011yescharacteristic
409C22×C109#53211yescharacteristic
410C22×C109#53711yescharacteristic
411C22×C109#54612yes—
412C22×C109#54712yes—
413C4×C109—44no—
414C4×C109—42no—
415C4×C109—42no—
416C4×C109—41no—
417C4×C109—41no—
418C4×C109—42no—
419C4×C109—41no—
420C4×C109—41no—
421C4×C109—42no—
422C4×C109—81no—
423C4×C109—81no—
424C4×C109—82no—
425#25563C10911yesmaximal, characteristic, direct product factor, Sylow
426C2×C109—22no—
427C2×C109—21no—
428C2×C109—21no—
429C2×C109—22no—
430C2×C109—22no—
431C2×C109—41no—
432C2×C109—42no—
433C2×C109—82no—
434C2×C109—82no—
435C2×C109#243011yescharacteristic
436C2×C109C2×B(4,𝔽2)11yescharacteristic
437C2×C109#302611yescharacteristic
438#3490C2×C10911yescharacteristic, complemented
439#2410C2×C10912yescomplemented
440#2405C2×C10911yescharacteristic, complemented
441#2062C2×C10911yescharacteristic, complemented
442#2044C2×C10911yescharacteristic, complemented
443#2029C2×C10911yescharacteristic, complemented
444#2021C2×C10911yescharacteristic, complemented
445#1898C2×C10912yescomplemented
446#1889C2×C10912yescomplemented
447#1867C2×C10912yescomplemented
448C2×#342C2×C10911yescharacteristic, complemented
449C109#2556311yescharacteristic, direct product factor, Sylow
450C23×D4C22×C10911yescharacteristic
451#551—22no—
452#551—22no—
453#546—22no—
454#546—22no—
455#543C22×C10911yescharacteristic
456#538—21no—
457#538—21no—
458#534C22×C10911yescharacteristic
459#525—21no—
460#525—21no—
461C2×#123—21no—
462C2×#121—22no—
463C2×#120C22×C10912yes—
464C2×#120C22×C10912yes—
465#518C22×C10912yes—
466C22×C22⋊C4C22×C10911yescharacteristic
467C22×C22⋊C4C22×C10912yes—
468C2×#99C22×C10912yes—
469C2×#99C22×C10912yes—
470#394—21no—
471#394—21no—
472#394—22no—
473#392—22no—
474#386—21no—
475#386—22no—
476#386C22×C10912yes—
477#385C22×C10912yes—
478#385C22×C10911yescharacteristic
479#385C22×C10911yescharacteristic
480#379C22×C10911yescharacteristic
481#379C22×C10912yes—
482#379C22×C10911yescharacteristic
483#379C22×C10911yescharacteristic
484#342C22×C10912yes—
485#342C22×C10911yescharacteristic
486#342C22×C10912yes—
487#342C22×C10912yes—
488#342C22×C10911yescharacteristic
489C25C23×C10911yescharacteristic
490C25C23×C10911yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C10912yescomplemented
500C22×D4D4×C10912yescomplemented
501C22×D4C23×C10912yes—
502C23×C4—22no—
503C23×C4D4×C10911yescharacteristic, complemented
504C23×C4D4×C10911yescharacteristic, complemented
505C23×C4C23×C10911yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C10911yescharacteristic, complemented
565C2×C22⋊C4D4×C10911yescharacteristic, complemented
566C2×C22⋊C4D4×C10912yescomplemented
567C2×C22⋊C4D4×C10912yescomplemented
568C2×C22⋊C4C23×C10912yes—
569C2×C22⋊C4C23×C10911yescharacteristic
570C2×C22⋊C4C23×C10911yescharacteristic
571C2×C22⋊C4C23×C10911yescharacteristic
572C2×C22⋊C4C23×C10911yescharacteristic
573C2×C22⋊C4C23×C10912yes—
574C2×C22⋊C4C23×C10912yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C10912yes—
594C24C2×D4×C10911yescharacteristic
595C24C2×D4×C10912yes—
596C24C2×D4×C10912yes—
597C24C2×D4×C10911yescharacteristic
598C24C24×C10911yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C10912yes—
650C22×C4C2×D4×C10911yescharacteristic
651C22×C4C2×D4×C10912yes—
652C22×C4C2×D4×C10911yescharacteristic
653C22×C4C2×D4×C10911yescharacteristic
654C22×C4C2×D4×C10912yes—
655C22×C4C2×D4×C10911yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C10914yescomplemented
699C42—22no—
700C42—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C10912yes—
744C23#120×C10911yescharacteristic
745C23#120×C10911yescharacteristic
746C23C22×D4×C10911yescharacteristic
747C23C22×D4×C10912yes—
748C23C2×#41×C10912yes—
749C23H(5,𝔽2)×C10911yescharacteristic
750C232−1+4×C10911yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—44no—
761D4—44no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22B(4,𝔽2)×C10912yes—
846C22C2×#120×C10911yescharacteristic
847C22#532×C10911yescharacteristic
848C22#537×C10911yescharacteristic
849C22#546×C10912yes—
850C22#547×C10912yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C109×#243011yescharacteristic
873C2C2×B(4,𝔽2)×C10911yescharacteristic
874C2C109×#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×#3490C2semidirect
2. C109×#2410C2semidirect
3. C109×#2405C2semidirect
4. C109×#2062C2semidirect
5. C109×#2044C2semidirect
6. C109×#2029C2semidirect
7. C109×#2021C2semidirect
8. C109×#1898C2semidirect
9. C109×#1889C2semidirect
10. C109×#1867C2semidirect
11. C2×#342×C109C2semidirect
61. C22×D4×C109D4semidirect
62. C22×D4×C109D4semidirect
65. C23×C4×C109D4semidirect
66. C23×C4×C109D4semidirect
126. C2×C22⋊C4×C109D4semidirect
127. C2×C22⋊C4×C109D4semidirect
128. C2×C22⋊C4×C109D4semidirect
129. C2×C22⋊C4×C109D4semidirect
260. C22⋊C4×C109#41semidirect
425. #25563C109direct (N × H)
438. #3490C2×C109semidirect
439. #2410C2×C109semidirect
440. #2405C2×C109semidirect
441. #2062C2×C109semidirect
442. #2044C2×C109semidirect
443. #2029C2×C109semidirect
444. #2021C2×C109semidirect
445. #1898C2×C109semidirect
446. #1889C2×C109semidirect
447. #1867C2×C109semidirect
448. C2×#342C2×C109semidirect
449. C109#25563direct (N × H)
499. C22×D4D4×C109semidirect
500. C22×D4D4×C109semidirect
503. C23×C4D4×C109semidirect
504. C23×C4D4×C109semidirect
564. C2×C22⋊C4D4×C109semidirect
565. C2×C22⋊C4D4×C109semidirect
566. C2×C22⋊C4D4×C109semidirect
567. C2×C22⋊C4D4×C109semidirect
698. C22⋊C4#41×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#34902
C109×#24102
C109×#24052
C109×#20622
C109×#20442
C109×#20292
C109×#20212
C109×#18982
C109×#18892
C109×#18672
C2×#342×C1092
#25563109