Finite Group Databasebeta

← C109×#14725 #42132719

Subgroups — C109×#14725 #42132719

Order 27904.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C109C211yesmaximal, characteristic
2C23×C22⋊C4×C109C211yesmaximal, characteristic, complemented
3C2×#394×C109C212yesmaximal, complemented
4C2×#386×C109C211yesmaximal, characteristic, complemented
5C2×#386×C109C211yesmaximal, characteristic, complemented
6C2×#380×C109C211yesmaximal, characteristic, complemented
7C2×#379×C109C211yesmaximal, characteristic, complemented
8C109×#1440C212yesmaximal, complemented
9C109×#1439C212yesmaximal, complemented
10C109×#1438C212yesmaximal, complemented
11C109×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C109C2211yescharacteristic
13C23×D4×C109C2211yescharacteristic
14C23×D4×C109C2212yes—
15C24×C4×C109C2211yescharacteristic
16C24×C4×C109C2211yescharacteristic
17C2×#120×C109—24no—
18C2×#120×C109—24no—
19C2×#120×C109—24no—
20C22×C4⋊C4×C109C2212yescomplemented
21C22×C22⋊C4×C109—24no—
22C22×C22⋊C4×C109—28no—
23C22×C22⋊C4×C109C2211yescharacteristic
24C22×C22⋊C4×C109C2212yes—
25C22×C22⋊C4×C109C2212yes—
26C22×C22⋊C4×C109C2212yes—
27C22×C22⋊C4×C109C2211yescharacteristic
28C22×C22⋊C4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2212yes—
30C22×C22⋊C4×C109C2212yes—
31C22×C22⋊C4×C109C2211yescharacteristic, complemented
32C22×C22⋊C4×C109C2212yescomplemented
33C22×C22⋊C4×C109C2211yescharacteristic, complemented
34#394×C109—28no—
35#386×C109—24no—
36#386×C109—24no—
37#380×C109—24no—
38#379×C109—24no—
39C2×#95×C109C2212yescomplemented
40C2×#95×C109C2212yescomplemented
41C2×#95×C109C2211yescharacteristic, complemented
42C2×#95×C109C2212yescomplemented
43C2×#95×C109C2211yescharacteristic, complemented
44C2×#95×C109C2212yescomplemented
45C25×C109—24no—
46C25×C109—22no—
47C25×C109—24no—
48C25×C109—22no—
49C25×C109—22no—
50C25×C109—22no—
51C25×C109—22no—
52C25×C109—22no—
53C25×C109—42no—
54C25×C109—42no—
55C25×C109D414yes—
56C25×C109C2311yescharacteristic
57C25×C109C2312yes—
58C25×C109C2311yescharacteristic
59C22×D4×C109—24no—
60C22×D4×C109—24no—
61C22×D4×C109—22no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—24no—
68C22×D4×C109—24no—
69C22×D4×C109—24no—
70C22×D4×C109—42no—
71C22×D4×C109—42no—
72C22×D4×C109D414yes—
73C23×C4×C109—22no—
74C23×C4×C109—22no—
75C23×C4×C109—22no—
76C23×C4×C109—24no—
77C23×C4×C109—24no—
78C23×C4×C109—22no—
79C23×C4×C109—22no—
80C23×C4×C109—42no—
81C23×C4×C109—42no—
82C23×C4×C109D414yescomplemented
83C23×C4×C109C2312yes—
84C23×C4×C109C2311yescharacteristic
85C23×C4×C109C2311yescharacteristic
86C23×C4×C109C2311yescharacteristic
87C23×C4×C109C2312yes—
88C23×C4×C109C2312yes—
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91#120×C109—232no—
92C2×C4⋊C4×C109—24no—
93C2×C4⋊C4×C109—24no—
94C2×C4⋊C4×C109—42no—
95C2×C22⋊C4×C109—232no—
96C2×C22⋊C4×C109—24no—
97C2×C22⋊C4×C109—24no—
98C2×C22⋊C4×C109—22no—
99C2×C22⋊C4×C109—22no—
100C2×C22⋊C4×C109—24no—
101C2×C22⋊C4×C109—24no—
102C2×C22⋊C4×C109—24no—
103C2×C22⋊C4×C109—24no—
104C2×C22⋊C4×C109—24no—
105C2×C22⋊C4×C109—24no—
106C2×C22⋊C4×C109—24no—
107C2×C22⋊C4×C109—22no—
108C2×C22⋊C4×C109—24no—
109C2×C22⋊C4×C109—22no—
110C2×C22⋊C4×C109—22no—
111C2×C22⋊C4×C109—22no—
112C2×C22⋊C4×C109—22no—
113C2×C22⋊C4×C109—24no—
114C2×C22⋊C4×C109—24no—
115C2×C22⋊C4×C109—24no—
116C2×C22⋊C4×C109—22no—
117C2×C22⋊C4×C109—22no—
118C2×C22⋊C4×C109—22no—
119C2×C22⋊C4×C109—24no—
120C2×C22⋊C4×C109—24no—
121C2×C22⋊C4×C109—42no—
122C2×C22⋊C4×C109—42no—
123C2×C22⋊C4×C109—42no—
124C2×C22⋊C4×C109—42no—
125C2×C22⋊C4×C109D414yes—
126C2×C22⋊C4×C109D418yescomplemented
127#95×C109—24no—
128#95×C109—22no—
129#95×C109—22no—
130#95×C109—24no—
131#95×C109—24no—
132#95×C109—42no—
133C24×C109—22no—
134C24×C109—22no—
135C24×C109—22no—
136C24×C109—22no—
137C24×C109—28no—
138C24×C109—28no—
139C24×C109—216no—
140C24×C109—216no—
141C24×C109—28no—
142C24×C109—22no—
143C24×C109—22no—
144C24×C109—22no—
145C24×C109—22no—
146C24×C109—22no—
147C24×C109—22no—
148C24×C109—22no—
149C24×C109—22no—
150C24×C109—22no—
151C24×C109—22no—
152C24×C109—22no—
153C24×C109—22no—
154C24×C109—28no—
155C24×C109—28no—
156C24×C109—21no—
157C24×C109—22no—
158C24×C109—21no—
159C24×C109—21no—
160C24×C109—21no—
161C24×C109—21no—
162C24×C109—21no—
163C24×C109—22no—
164C24×C109—22no—
165C24×C109—22no—
166C24×C109—48no—
167C24×C109—48no—
168C24×C109—48no—
169C24×C109—48no—
170C24×C109—48no—
171C24×C109—48no—
172C24×C109—48no—
173C24×C109—48no—
174C24×C109—48no—
175C24×C109—44no—
176C24×C109—44no—
177C24×C109—48no—
178C24×C109—44no—
179C24×C109—44no—
180C24×C109—44no—
181C24×C109—44no—
182C24×C109C2×D412yes—
183C24×C109C2×D414yes—
184C24×C109C2×D414yes—
185C24×C109C2×D412yes—
186C24×C109C2×D412yes—
187C24×C109C2×D412yes—
188C24×C109C2×D412yes—
189C24×C109#4114yes—
190C24×C109#4112yes—
191C24×C109#4112yes—
192C24×C109#4112yes—
193C24×C109C2411yescharacteristic
194C2×D4×C109—216no—
195C2×D4×C109—28no—
196C2×D4×C109—28no—
197C2×D4×C109—28no—
198C2×D4×C109—48no—
199C2×D4×C109—48no—
200C2×D4×C109—48no—
201C2×D4×C109—48no—
202C2×D4×C109—48no—
203C2×D4×C109—48no—
204C2×D4×C109—44no—
205C2×D4×C109—44no—
206C2×D4×C109—44no—
207C2×D4×C109—44no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—22no—
211C22×C4×C109—28no—
212C22×C4×C109—28no—
213C22×C4×C109—21no—
214C22×C4×C109—21no—
215C22×C4×C109—22no—
216C22×C4×C109—22no—
217C22×C4×C109—22no—
218C22×C4×C109—22no—
219C22×C4×C109—22no—
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—22no—
223C22×C4×C109—22no—
224C22×C4×C109—21no—
225C22×C4×C109—22no—
226C22×C4×C109—21no—
227C22×C4×C109—21no—
228C22×C4×C109—21no—
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—28no—
236C22×C4×C109—21no—
237C22×C4×C109—22no—
238C22×C4×C109—22no—
239C22×C4×C109—21no—
240C22×C4×C109—22no—
241C22×C4×C109—22no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—22no—
245C22×C4×C109—21no—
246C22×C4×C109—22no—
247C22×C4×C109—21no—
248C22×C4×C109—22no—
249C22×C4×C109—22no—
250C22×C4×C109—22no—
251C22×C4×C109—22no—
252C22×C4×C109—22no—
253C22×C4×C109—44no—
254C22×C4×C109—48no—
255C22×C4×C109—48no—
256C22×C4×C109—48no—
257C22×C4×C109—48no—
258C22×C4×C109—44no—
259C22×C4×C109—44no—
260C22×C4×C109C2×D412yes—
261C22×C4×C109C2×D412yes—
262C22×C4×C109C2×D414yes—
263C22×C4×C109C2×D414yes—
264C22×C4×C109C2×D412yes—
265C22×C4×C109C2×D414yes—
266C4⋊C4×C109—48no—
267C22⋊C4×C109—216no—
268C22⋊C4×C109—216no—
269C22⋊C4×C109—28no—
270C22⋊C4×C109—216no—
271C22⋊C4×C109—48no—
272C22⋊C4×C109—44no—
273C22⋊C4×C109—48no—
274C22⋊C4×C109—44no—
275C22⋊C4×C109—48no—
276C22⋊C4×C109—44no—
277C22⋊C4×C109—44no—
278C23×C109—22no—
279C23×C109—24no—
280C23×C109—22no—
281C23×C109—24no—
282C23×C109—22no—
283C23×C109—24no—
284C23×C109—22no—
285C23×C109—24no—
286C23×C109—24no—
287C23×C109—24no—
288C23×C109—24no—
289C23×C109—24no—
290C23×C109—24no—
291C23×C109—24no—
292C23×C109—24no—
293C23×C109—24no—
294C23×C109—232no—
295C23×C109—24no—
296C23×C109—24no—
297C23×C109—24no—
298C23×C109—24no—
299C23×C109—24no—
300C23×C109—24no—
301C23×C109—24no—
302C23×C109—24no—
303C23×C109—24no—
304C23×C109—24no—
305C23×C109—24no—
306C23×C109—24no—
307C23×C109—24no—
308C23×C109—24no—
309C23×C109—24no—
310C23×C109—24no—
311C23×C109—24no—
312C23×C109—24no—
313C23×C109—22no—
314C23×C109—22no—
315C23×C109—22no—
316C23×C109—24no—
317C23×C109—24no—
318C23×C109—432no—
319C23×C109—432no—
320C23×C109—416no—
321C23×C109—416no—
322C23×C109—416no—
323C23×C109—416no—
324C23×C109—432no—
325C23×C109—432no—
326C23×C109—416no—
327C23×C109—42no—
328C23×C109—42no—
329C23×C109—42no—
330C23×C109—42no—
331C23×C109—42no—
332C23×C109—42no—
333C23×C109—42no—
334C23×C109—42no—
335C23×C109—42no—
336C23×C109—42no—
337C23×C109—42no—
338C23×C109—42no—
339C23×C109—42no—
340C23×C109—42no—
341C23×C109—42no—
342C23×C109—42no—
343C23×C109—416no—
344C23×C109—41no—
345C23×C109—41no—
346C23×C109—41no—
347C23×C109—42no—
348C23×C109—41no—
349C23×C109—42no—
350C23×C109—41no—
351C23×C109—41no—
352C23×C109—41no—
353C23×C109—42no—
354C23×C109—41no—
355C23×C109—42no—
356C23×C109—42no—
357C23×C109—42no—
358C23×C109—42no—
359C23×C109—42no—
360C23×C109—42no—
361C23×C109—42no—
362C23×C109#12014yes—
363C23×C109#12118yes—
364C23×C109#12114yes—
365C23×C109#12114yes—
366C23×C109#12114yes—
367C23×C109#12314yes—
368C23×C109#12314yes—
369C23×C109#12414yes—
370C23×C109C22×D411yescharacteristic
371C23×C109C22×D411yescharacteristic
372C23×C109C22×D411yescharacteristic
373C23×C109C22×D412yes—
374C23×C109C22×D411yescharacteristic
375C23×C109C2×#4111yescharacteristic
376C23×C109C2×#4111yescharacteristic
377C23×C109C2×#4111yescharacteristic
378C23×C109C2×#4112yes—
379C23×C109H(5,𝔽2)12yes—
380C23×C109H(5,𝔽2)12yes—
381D4×C109—432no—
382D4×C109—416no—
383C2×C4×C109—22no—
384C2×C4×C109—22no—
385C2×C4×C109—24no—
386C2×C4×C109—24no—
387C2×C4×C109—24no—
388C2×C4×C109—22no—
389C2×C4×C109—22no—
390C2×C4×C109—24no—
391C2×C4×C109—22no—
392C2×C4×C109—22no—
393C2×C4×C109—22no—
394C2×C4×C109—22no—
395C2×C4×C109—24no—
396C2×C4×C109—24no—
397C2×C4×C109—24no—
398C2×C4×C109—24no—
399C2×C4×C109—416no—
400C2×C4×C109—416no—
401C2×C4×C109—42no—
402C2×C4×C109—41no—
403C2×C4×C109—41no—
404C2×C4×C109—42no—
405C2×C4×C109—41no—
406C2×C4×C109—41no—
407C2×C4×C109—42no—
408C2×C4×C109—42no—
409C2×C4×C109—42no—
410C2×C4×C109—42no—
411C2×C4×C109—42no—
412C2×C4×C109—42no—
413C2×C4×C109—42no—
414C2×C4×C109—42no—
415C2×C4×C109—41no—
416C2×C4×C109—42no—
417C2×C4×C109—41no—
418C2×C4×C109—42no—
419C2×C4×C109—41no—
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—41no—
427C2×C4×C109—42no—
428C2×C4×C109—42no—
429C2×C4×C109—42no—
430C2×C4×C109—42no—
431C2×C4×C109—42no—
432C2×C4×C109#12014yescomplemented
433C22×C109—24no—
434C22×C109—24no—
435C22×C109—24no—
436C22×C109—24no—
437C22×C109—28no—
438C22×C109—24no—
439C22×C109—28no—
440C22×C109—28no—
441C22×C109—28no—
442C22×C109—24no—
443C22×C109—28no—
444C22×C109—28no—
445C22×C109—28no—
446C22×C109—464no—
447C22×C109—44no—
448C22×C109—44no—
449C22×C109—44no—
450C22×C109—44no—
451C22×C109—44no—
452C22×C109—44no—
453C22×C109—44no—
454C22×C109—44no—
455C22×C109—44no—
456C22×C109—44no—
457C22×C109—44no—
458C22×C109—44no—
459C22×C109—42no—
460C22×C109—42no—
461C22×C109—44no—
462C22×C109—44no—
463C22×C109—42no—
464C22×C109—81no—
465C22×C109—81no—
466C22×C109—81no—
467C22×C109—81no—
468C22×C109—82no—
469C22×C109—82no—
470C22×C109#39418yescomplemented
471C22×C109C2×#12011yescharacteristic
472C22×C109C2×#12011yescharacteristic
473C22×C109C2×#12111yescharacteristic
474C22×C109C2×#12112yes—
475C22×C109C2×#12111yescharacteristic
476C22×C109C2×#12111yescharacteristic
477C22×C109C2×#12311yescharacteristic
478C22×C109C2×#12311yescharacteristic
479C22×C109#52511yescharacteristic
480C22×C109#52512yes—
481C22×C109C2×#12411yescharacteristic
482C22×C109#53412yes—
483C22×C109#53411yescharacteristic
484C22×C109#53511yescharacteristic
485C22×C109#53812yes—
486C22×C109D4212yes—
487C22×C109D4212yes—
488C22×C109#54612yes—
489C22×C109#54612yes—
490C22×C109#54612yes—
491C22×C109#54612yes—
492C22×C109#55112yes—
493C22×C109#55112yes—
494C4×C109—24no—
495C4×C109—42no—
496C4×C109—44no—
497C4×C109—42no—
498C4×C109—44no—
499C4×C109—81no—
500C4×C109—81no—
501C4×C109—82no—
502#14725C10911yesmaximal, characteristic, direct product factor, Sylow
503C2×C109—28no—
504C2×C109—48no—
505C2×C109—82no—
506C2×C109C2×#39411yescharacteristic
507C2×C109#240811yescharacteristic
508C2×C109#241011yescharacteristic
509C2×C109#241012yes—
510C2×C109#241111yescharacteristic
511C2×C109#241212yes—
512C2×C109#241812yes—
513C2×C109#247212yes—
514C2×C109#253411yescharacteristic
515C2×C109#261711yescharacteristic
516C2×C109#284711yescharacteristic
517C22×#120C2×C10911yescharacteristic
518C23×C22⋊C4C2×C10911yescharacteristic, complemented
519C2×#394C2×C10912yescomplemented
520C2×#386C2×C10911yescharacteristic, complemented
521C2×#386C2×C10911yescharacteristic, complemented
522C2×#380C2×C10911yescharacteristic, complemented
523C2×#379C2×C10911yescharacteristic, complemented
524#1440C2×C10912yescomplemented
525#1439C2×C10912yescomplemented
526#1438C2×C10912yescomplemented
527C22⋊#95C2×C10911yescharacteristic, complemented
528C109#1472511yescharacteristic, direct product factor, Sylow
529C26C22×C10911yescharacteristic
530C23×D4C22×C10911yescharacteristic
531C23×D4C22×C10912yes—
532C24×C4C22×C10911yescharacteristic
533C24×C4C22×C10911yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C10912yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C10912yes—
541C22×C22⋊C4C22×C10912yes—
542C22×C22⋊C4C22×C10912yes—
543C22×C22⋊C4C22×C10911yescharacteristic
544C22×C22⋊C4C22×C10911yescharacteristic
545C22×C22⋊C4C22×C10911yescharacteristic
546C22×C22⋊C4C22×C10912yes—
547C22×C22⋊C4C22×C10912yes—
548C22×C22⋊C4C22×C10911yescharacteristic, complemented
549C22×C22⋊C4C22×C10912yescomplemented
550C22×C22⋊C4C22×C10911yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C10912yescomplemented
557C2×#95C22×C10912yescomplemented
558C2×#95C22×C10911yescharacteristic, complemented
559C2×#95C22×C10912yescomplemented
560C2×#95C22×C10911yescharacteristic, complemented
561C2×#95C22×C10912yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C10914yes—
573C25C23×C10911yescharacteristic
574C25C23×C10912yes—
575C25C23×C10911yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C10914yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C10914yescomplemented
600C23×C4C23×C10912yes—
601C23×C4C23×C10911yescharacteristic
602C23×C4C23×C10911yescharacteristic
603C23×C4C23×C10911yescharacteristic
604C23×C4C23×C10912yes—
605C23×C4C23×C10912yes—
606C23×C4C23×C10911yescharacteristic
607C23×C4C23×C10911yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C10914yes—
643C2×C22⋊C4D4×C10918yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C10912yes—
700C24C2×D4×C10914yes—
701C24C2×D4×C10914yes—
702C24C2×D4×C10912yes—
703C24C2×D4×C10912yes—
704C24C2×D4×C10912yes—
705C24C2×D4×C10912yes—
706C24#41×C10914yes—
707C24#41×C10912yes—
708C24#41×C10912yes—
709C24#41×C10912yes—
710C24C24×C10911yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C10912yes—
778C22×C4C2×D4×C10912yes—
779C22×C4C2×D4×C10914yes—
780C22×C4C2×D4×C10914yes—
781C22×C4C2×D4×C10912yes—
782C22×C4C2×D4×C10914yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—432no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—416no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C10914yes—
880C23#121×C10918yes—
881C23#121×C10914yes—
882C23#121×C10914yes—
883C23#121×C10914yes—
884C23#123×C10914yes—
885C23#123×C10914yes—
886C23#124×C10914yes—
887C23C22×D4×C10911yescharacteristic
888C23C22×D4×C10911yescharacteristic
889C23C22×D4×C10911yescharacteristic
890C23C22×D4×C10912yes—
891C23C22×D4×C10911yescharacteristic
892C23C2×#41×C10911yescharacteristic
893C23C2×#41×C10911yescharacteristic
894C23C2×#41×C10911yescharacteristic
895C23C2×#41×C10912yes—
896C23H(5,𝔽2)×C10912yes—
897C23H(5,𝔽2)×C10912yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C10914yescomplemented
950C22—28no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—28no—
957C22—24no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—82no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22#394×C10918yescomplemented
988C22C2×#120×C10911yescharacteristic
989C22C2×#120×C10911yescharacteristic
990C22C2×#121×C10911yescharacteristic
991C22C2×#121×C10911yescharacteristic
992C22C2×#121×C10912yes—
993C22C2×#121×C10911yescharacteristic
994C22C2×#123×C10911yescharacteristic
995C22C2×#123×C10911yescharacteristic
996C22#525×C10912yes—
997C22#525×C10911yescharacteristic
998C22C2×#124×C10911yescharacteristic
999C22#534×C10911yescharacteristic
1000C22#534×C10912yes—
1001C22#535×C10911yescharacteristic
1002C22#538×C10912yes—
1003C22D42×C10912yes—
1004C22D42×C10912yes—
1005C22#546×C10912yes—
1006C22#546×C10912yes—
1007C22#546×C10912yes—
1008C22#546×C10912yes—
1009C22#551×C10912yes—
1010C22#551×C10912yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C10911yescharacteristic
1023C2C109×#240811yescharacteristic
1024C2C109×#241011yescharacteristic
1025C2C109×#241012yes—
1026C2C109×#241111yescharacteristic
1027C2C109×#241212yes—
1028C2C109×#241812yes—
1029C2C109×#247212yes—
1030C2C109×#253411yescharacteristic
1031C2C109×#261711yescharacteristic
1032C2C109×#284711yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC24C24×C109
prime radicalC22×#120×C109C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C109C2semidirect
3. C2×#394×C109C2semidirect
4. C2×#386×C109C2semidirect
5. C2×#386×C109C2semidirect
6. C2×#380×C109C2semidirect
7. C2×#379×C109C2semidirect
8. C109×#1440C2semidirect
9. C109×#1439C2semidirect
10. C109×#1438C2semidirect
11. C109×C22⋊#95C2semidirect
20. C22×C4⋊C4×C109C22semidirect
31. C22×C22⋊C4×C109C22semidirect
32. C22×C22⋊C4×C109C22semidirect
33. C22×C22⋊C4×C109C22semidirect
39. C2×#95×C109C22semidirect
40. C2×#95×C109C22semidirect
41. C2×#95×C109C22semidirect
42. C2×#95×C109C22semidirect
43. C2×#95×C109C22semidirect
44. C2×#95×C109C22semidirect
82. C23×C4×C109D4semidirect
126. C2×C22⋊C4×C109D4semidirect
432. C2×C4×C109#120semidirect
470. C22×C109#394semidirect
502. #14725C109direct (N × H)
518. C23×C22⋊C4C2×C109semidirect
519. C2×#394C2×C109semidirect
520. C2×#386C2×C109semidirect
521. C2×#386C2×C109semidirect
522. C2×#380C2×C109semidirect
523. C2×#379C2×C109semidirect
524. #1440C2×C109semidirect
525. #1439C2×C109semidirect
526. #1438C2×C109semidirect
527. C22⋊#95C2×C109semidirect
528. C109#14725direct (N × H)
537. C22×C4⋊C4C22×C109semidirect
548. C22×C22⋊C4C22×C109semidirect
549. C22×C22⋊C4C22×C109semidirect
550. C22×C22⋊C4C22×C109semidirect
556. C2×#95C22×C109semidirect
557. C2×#95C22×C109semidirect
558. C2×#95C22×C109semidirect
559. C2×#95C22×C109semidirect
560. C2×#95C22×C109semidirect
561. C2×#95C22×C109semidirect
599. C23×C4D4×C109semidirect
643. C2×C22⋊C4D4×C109semidirect
949. C2×C4#120×C109semidirect
987. C22#394×C109semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1092
C23×C22⋊C4×C1092
C2×#394×C1092
C2×#386×C1092
C2×#380×C1092
C2×#379×C1092
C109×#14402
C109×#14392
C109×#14382
C109×C22⋊#952
#14725109