Finite Group Databasebeta

← C109×#14722 #42132716

Subgroups — C109×#14722 #42132716

Order 27904.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C109C211yesmaximal, characteristic, complemented
2C22×C4×D4×C109C211yesmaximal, characteristic, complemented
3C2×#394×C109C211yesmaximal, characteristic, complemented
4C2×#392×C109C212yesmaximal, complemented
5C2×#392×C109C211yesmaximal, characteristic, complemented
6C2×#386×C109C212yesmaximal, complemented
7C109×#1441C211yesmaximal, characteristic, complemented
8C109×#1439C211yesmaximal, characteristic, complemented
9C109×#1438C212yesmaximal, complemented
10C109×#1437C212yesmaximal, complemented
11C109×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C109C2211yescharacteristic
13C23×D4×C109C2212yes—
14C23×D4×C109C2212yes—
15C23×D4×C109C2211yescharacteristic
16C24×C4×C109C2211yescharacteristic
17C24×C4×C109C2211yescharacteristic
18C2×#121×C109—24no—
19C2×#121×C109—28no—
20C2×C4×D4×C109—24no—
21C2×C4×D4×C109—24no—
22C2×C4×D4×C109—24no—
23C22×C4⋊C4×C109C2211yescharacteristic
24C22×C4⋊C4×C109C2211yescharacteristic
25C22×C22⋊C4×C109C2212yes—
26C22×C22⋊C4×C109C2211yescharacteristic
27C22×C22⋊C4×C109C2212yes—
28C22×C22⋊C4×C109C2212yes—
29C22×C22⋊C4×C109C2212yes—
30C22×C22⋊C4×C109C2212yes—
31C22×C22⋊C4×C109C2212yes—
32C22×C22⋊C4×C109C2211yescharacteristic
33C22×C42×C109C2211yescharacteristic
34#394×C109—24no—
35#392×C109—28no—
36#392×C109—24no—
37#386×C109—28no—
38C2×#95×C109C2212yes—
39C2×#95×C109C2211yescharacteristic
40C2×#95×C109C2211yescharacteristic
41C2×#95×C109C2212yes—
42C2×#95×C109C2212yes—
43C2×#95×C109C2212yes—
44C25×C109C2312yes—
45C25×C109C2311yescharacteristic
46C25×C109C2311yescharacteristic
47C22×D4×C109—22no—
48C22×D4×C109—22no—
49C22×D4×C109—22no—
50C22×D4×C109—22no—
51C22×D4×C109—24no—
52C22×D4×C109—24no—
53C22×D4×C109—24no—
54C22×D4×C109—24no—
55C22×D4×C109—24no—
56C22×D4×C109—24no—
57C22×D4×C109—24no—
58C22×D4×C109—24no—
59C22×D4×C109—24no—
60C22×D4×C109—22no—
61C22×D4×C109—24no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—24no—
67C22×D4×C109—42no—
68C22×D4×C109—42no—
69C22×D4×C109—42no—
70C22×D4×C109—42no—
71C22×D4×C109—42no—
72C22×D4×C109D414yescomplemented
73C23×C4×C109—22no—
74C23×C4×C109—22no—
75C23×C4×C109—22no—
76C23×C4×C109—22no—
77C23×C4×C109—22no—
78C23×C4×C109—24no—
79C23×C4×C109—24no—
80C23×C4×C109—42no—
81C23×C4×C109—42no—
82C23×C4×C109D414yescomplemented
83C23×C4×C109C2312yes—
84C23×C4×C109C2311yescharacteristic
85C23×C4×C109C2311yescharacteristic
86C23×C4×C109C2312yes—
87C23×C4×C109C2312yes—
88C23×C4×C109C2311yescharacteristic
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91#121×C109—232no—
92C4×D4×C109—232no—
93C2×C4⋊C4×C109—22no—
94C2×C4⋊C4×C109—22no—
95C2×C4⋊C4×C109—24no—
96C2×C4⋊C4×C109—22no—
97C2×C4⋊C4×C109D414yescomplemented
98C2×C22⋊C4×C109—22no—
99C2×C22⋊C4×C109—22no—
100C2×C22⋊C4×C109—22no—
101C2×C22⋊C4×C109—22no—
102C2×C22⋊C4×C109—22no—
103C2×C22⋊C4×C109—24no—
104C2×C22⋊C4×C109—24no—
105C2×C22⋊C4×C109—24no—
106C2×C22⋊C4×C109—24no—
107C2×C22⋊C4×C109—24no—
108C2×C22⋊C4×C109—24no—
109C2×C22⋊C4×C109—24no—
110C2×C22⋊C4×C109—24no—
111C2×C22⋊C4×C109—24no—
112C2×C22⋊C4×C109—24no—
113C2×C22⋊C4×C109—24no—
114C2×C22⋊C4×C109—24no—
115C2×C22⋊C4×C109—24no—
116C2×C22⋊C4×C109—42no—
117C2×C22⋊C4×C109—42no—
118C2×C22⋊C4×C109—42no—
119C2×C22⋊C4×C109—42no—
120C2×C22⋊C4×C109D414yescomplemented
121C2×C22⋊C4×C109D418yescomplemented
122C2×C42×C109—22no—
123C2×C42×C109—22no—
124C2×C42×C109—22no—
125#95×C109—24no—
126#95×C109—24no—
127#95×C109—22no—
128#95×C109—24no—
129#95×C109—22no—
130#95×C109—42no—
131C24×C109—21no—
132C24×C109—21no—
133C24×C109—21no—
134C24×C109—21no—
135C24×C109—22no—
136C24×C109—22no—
137C24×C109—22no—
138C24×C109—21no—
139C24×C109—21no—
140C24×C109—21no—
141C24×C109—21no—
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—22no—
155C24×C109—22no—
156C24×C109—22no—
157C24×C109—22no—
158C24×C109—22no—
159C24×C109—22no—
160C24×C109—22no—
161C24×C109C2×D414yes—
162C24×C109C2×D412yes—
163C24×C109C2×D412yes—
164C24×C109C2×D412yes—
165C24×C109C2×D412yes—
166C24×C109#4112yes—
167C24×C109#4112yes—
168C24×C109C2411yescharacteristic
169C2×D4×C109—28no—
170C2×D4×C109—28no—
171C2×D4×C109—28no—
172C2×D4×C109—28no—
173C2×D4×C109—28no—
174C2×D4×C109—28no—
175C2×D4×C109—28no—
176C2×D4×C109—216no—
177C2×D4×C109—216no—
178C2×D4×C109—28no—
179C2×D4×C109—48no—
180C2×D4×C109—48no—
181C2×D4×C109—48no—
182C2×D4×C109—48no—
183C2×D4×C109—48no—
184C2×D4×C109—48no—
185C2×D4×C109—44no—
186C2×D4×C109—48no—
187C2×D4×C109—48no—
188C2×D4×C109—48no—
189C2×D4×C109—48no—
190C2×D4×C109—48no—
191C2×D4×C109—48no—
192C2×D4×C109—48no—
193C2×D4×C109—48no—
194C2×D4×C109—44no—
195C22×C4×C109—21no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—21no—
199C22×C4×C109—22no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—22no—
203C22×C4×C109—22no—
204C22×C4×C109—28no—
205C22×C4×C109—22no—
206C22×C4×C109—22no—
207C22×C4×C109—22no—
208C22×C4×C109—22no—
209C22×C4×C109—22no—
210C22×C4×C109—21no—
211C22×C4×C109—21no—
212C22×C4×C109—21no—
213C22×C4×C109—21no—
214C22×C4×C109—22no—
215C22×C4×C109—22no—
216C22×C4×C109—22no—
217C22×C4×C109—22no—
218C22×C4×C109—22no—
219C22×C4×C109—22no—
220C22×C4×C109—22no—
221C22×C4×C109—22no—
222C22×C4×C109—22no—
223C22×C4×C109—22no—
224C22×C4×C109—22no—
225C22×C4×C109—28no—
226C22×C4×C109—28no—
227C22×C4×C109—22no—
228C22×C4×C109—22no—
229C22×C4×C109—22no—
230C22×C4×C109—22no—
231C22×C4×C109—22no—
232C22×C4×C109—22no—
233C22×C4×C109—22no—
234C22×C4×C109—44no—
235C22×C4×C109—48no—
236C22×C4×C109—48no—
237C22×C4×C109—48no—
238C22×C4×C109—48no—
239C22×C4×C109—44no—
240C22×C4×C109—44no—
241C22×C4×C109C2×D414yes—
242C22×C4×C109C2×D412yes—
243C22×C4×C109C2×D412yes—
244C22×C4×C109C2×D414yes—
245C22×C4×C109C2×D412yes—
246C22×C4×C109C2×D412yes—
247C22×C4×C109C2×D412yes—
248C22×C4×C109C2×D412yes—
249C22×C4×C109C2×D412yes—
250C22×C4×C109C2×D412yes—
251C22×C4×C109#4114yes—
252C22×C4×C109#4112yes—
253C4⋊C4×C109—28no—
254C4⋊C4×C109—28no—
255C22⋊C4×C109—28no—
256C22⋊C4×C109—28no—
257C22⋊C4×C109—216no—
258C22⋊C4×C109—48no—
259C22⋊C4×C109—48no—
260C22⋊C4×C109—48no—
261C22⋊C4×C109—48no—
262C22⋊C4×C109—48no—
263C42×C109—28no—
264C23×C109—22no—
265C23×C109—22no—
266C23×C109—22no—
267C23×C109—22no—
268C23×C109—22no—
269C23×C109—22no—
270C23×C109—22no—
271C23×C109—22no—
272C23×C109—22no—
273C23×C109—22no—
274C23×C109—22no—
275C23×C109—22no—
276C23×C109—22no—
277C23×C109—24no—
278C23×C109—22no—
279C23×C109—22no—
280C23×C109—22no—
281C23×C109—24no—
282C23×C109—24no—
283C23×C109—24no—
284C23×C109—24no—
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—24no—
295C23×C109—24no—
296C23×C109—24no—
297C23×C109—41no—
298C23×C109—42no—
299C23×C109—42no—
300C23×C109—42no—
301C23×C109—41no—
302C23×C109—41no—
303C23×C109—41no—
304C23×C109—42no—
305C23×C109—42no—
306C23×C109—42no—
307C23×C109—42no—
308C23×C109—42no—
309C23×C109—42no—
310C23×C109—42no—
311C23×C109—42no—
312C23×C109—42no—
313C23×C109—42no—
314C23×C109—42no—
315C23×C109—42no—
316C23×C109—42no—
317C23×C109—42no—
318C23×C109—42no—
319C23×C109—42no—
320C23×C109—42no—
321C23×C109—42no—
322C23×C109—42no—
323C23×C109—42no—
324C23×C109—42no—
325C23×C109—42no—
326C23×C109—42no—
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#12114yes—
344C23×C109#12114yescomplemented
345C23×C109C22×D411yescharacteristic
346C23×C109C22×D411yescharacteristic
347C23×C109C22×D411yescharacteristic
348C23×C109C22×D412yes—
349C23×C109C22×D411yescharacteristic
350C23×C109C2×#4111yescharacteristic
351C23×C109C2×#4111yescharacteristic
352C23×C109C2×#4111yescharacteristic
353C23×C109C2×#4112yes—
354C23×C109H(5,𝔽2)12yes—
355C23×C109H(5,𝔽2)12yes—
356D4×C109—232no—
357D4×C109—416no—
358D4×C109—432no—
359D4×C109—432no—
360C2×C4×C109—22no—
361C2×C4×C109—22no—
362C2×C4×C109—22no—
363C2×C4×C109—22no—
364C2×C4×C109—22no—
365C2×C4×C109—22no—
366C2×C4×C109—22no—
367C2×C4×C109—22no—
368C2×C4×C109—22no—
369C2×C4×C109—22no—
370C2×C4×C109—24no—
371C2×C4×C109—24no—
372C2×C4×C109—24no—
373C2×C4×C109—24no—
374C2×C4×C109—22no—
375C2×C4×C109—22no—
376C2×C4×C109—24no—
377C2×C4×C109—24no—
378C2×C4×C109—24no—
379C2×C4×C109—24no—
380C2×C4×C109—24no—
381C2×C4×C109—24no—
382C2×C4×C109—24no—
383C2×C4×C109—24no—
384C2×C4×C109—416no—
385C2×C4×C109—416no—
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—42no—
393C2×C4×C109—42no—
394C2×C4×C109—42no—
395C2×C4×C109—42no—
396C2×C4×C109—42no—
397C2×C4×C109—42no—
398C2×C4×C109—42no—
399C2×C4×C109—42no—
400C2×C4×C109—42no—
401C2×C4×C109—42no—
402C2×C4×C109—42no—
403C2×C4×C109—42no—
404C2×C4×C109—42no—
405C2×C4×C109—42no—
406C2×C4×C109—42no—
407C2×C4×C109#12014yes—
408C2×C4×C109#12014yes—
409C2×C4×C109#12114yescomplemented
410C22×C109—24no—
411C22×C109—24no—
412C22×C109—24no—
413C22×C109—28no—
414C22×C109—24no—
415C22×C109—42no—
416C22×C109—42no—
417C22×C109—42no—
418C22×C109—42no—
419C22×C109—42no—
420C22×C109—42no—
421C22×C109—42no—
422C22×C109—44no—
423C22×C109—44no—
424C22×C109—44no—
425C22×C109—42no—
426C22×C109—42no—
427C22×C109—44no—
428C22×C109—44no—
429C22×C109—44no—
430C22×C109—44no—
431C22×C109—42no—
432C22×C109—44no—
433C22×C109—44no—
434C22×C109—44no—
435C22×C109—44no—
436C22×C109—44no—
437C22×C109—44no—
438C22×C109—44no—
439C22×C109—82no—
440C22×C109—82no—
441C22×C109—82no—
442C22×C109—82no—
443C22×C109—82no—
444C22×C109—82no—
445C22×C109—82no—
446C22×C109—82no—
447C22×C109C2×#12011yescharacteristic
448C22×C109C2×#12011yescharacteristic
449C22×C109C2×#12111yescharacteristic
450C22×C109C2×#12111yescharacteristic
451C22×C109C2×#12111yescharacteristic
452C22×C109#52511yescharacteristic
453C22×C109#52511yescharacteristic
454C22×C109#52511yescharacteristic
455C22×C109#52512yes—
456C22×C109#53212yes—
457C22×C109#53211yescharacteristic
458C22×C109#53411yescharacteristic
459C22×C109#53511yescharacteristic
460C22×C109#53812yes—
461C22×C109#54012yes—
462C22×C109D4212yes—
463C22×C109D4212yes—
464C22×C109D4212yes—
465C22×C109#54612yes—
466C22×C109#54612yes—
467C22×C109#54612yes—
468C22×C109#55012yes—
469C22×C109#55312yes—
470C4×C109—24no—
471C4×C109—24no—
472C4×C109—24no—
473C4×C109—42no—
474C4×C109—44no—
475C4×C109—44no—
476C4×C109—42no—
477C4×C109—82no—
478#14722C10911yesmaximal, characteristic, direct product factor, Sylow
479C2×C109—44no—
480C2×C109—44no—
481C2×C109—84no—
482C2×C109#238811yescharacteristic
483C2×C109#240311yescharacteristic
484C2×C109#240811yescharacteristic
485C2×C109#242412yes—
486C2×C109#242812yes—
487C2×C109#243111yescharacteristic
488C2×C109#245612yes—
489C2×C109#246412yes—
490C2×C109#254311yescharacteristic
491C2×C109#263511yescharacteristic
492C2×C109#284711yescharacteristic
493C22×#121C2×C10911yescharacteristic, complemented
494C22×C4×D4C2×C10911yescharacteristic, complemented
495C2×#394C2×C10911yescharacteristic, complemented
496C2×#392C2×C10912yescomplemented
497C2×#392C2×C10911yescharacteristic, complemented
498C2×#386C2×C10912yescomplemented
499#1441C2×C10911yescharacteristic, complemented
500#1439C2×C10911yescharacteristic, complemented
501#1438C2×C10912yescomplemented
502#1437C2×C10912yescomplemented
503C22⋊#95C2×C10911yescharacteristic, complemented
504C109#1472211yescharacteristic, direct product factor, Sylow
505C23×D4C22×C10911yescharacteristic
506C23×D4C22×C10912yes—
507C23×D4C22×C10911yescharacteristic
508C23×D4C22×C10912yes—
509C24×C4C22×C10911yescharacteristic
510C24×C4C22×C10911yescharacteristic
511C2×#121—24no—
512C2×#121—28no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C2×C4×D4—24no—
516C22×C4⋊C4C22×C10911yescharacteristic
517C22×C4⋊C4C22×C10911yescharacteristic
518C22×C22⋊C4C22×C10912yes—
519C22×C22⋊C4C22×C10911yescharacteristic
520C22×C22⋊C4C22×C10912yes—
521C22×C22⋊C4C22×C10912yes—
522C22×C22⋊C4C22×C10912yes—
523C22×C22⋊C4C22×C10912yes—
524C22×C22⋊C4C22×C10911yescharacteristic
525C22×C22⋊C4C22×C10912yes—
526C22×C42C22×C10911yescharacteristic
527#394—24no—
528#392—28no—
529#392—24no—
530#386—28no—
531C2×#95C22×C10911yescharacteristic
532C2×#95C22×C10912yes—
533C2×#95C22×C10911yescharacteristic
534C2×#95C22×C10912yes—
535C2×#95C22×C10912yes—
536C2×#95C22×C10912yes—
537C25C23×C10912yes—
538C25C23×C10911yescharacteristic
539C25C23×C10911yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C10914yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C10914yescomplemented
576C23×C4C23×C10912yes—
577C23×C4C23×C10911yescharacteristic
578C23×C4C23×C10911yescharacteristic
579C23×C4C23×C10912yes—
580C23×C4C23×C10912yes—
581C23×C4C23×C10911yescharacteristic
582C23×C4C23×C10911yescharacteristic
583C23×C4C23×C10911yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C10914yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C10914yescomplemented
614C2×C22⋊C4D4×C10918yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C10914yes—
655C24C2×D4×C10912yes—
656C24C2×D4×C10912yes—
657C24C2×D4×C10912yes—
658C24C2×D4×C10912yes—
659C24#41×C10912yes—
660C24#41×C10912yes—
661C24C24×C10911yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C10914yes—
735C22×C4C2×D4×C10912yes—
736C22×C4C2×D4×C10912yes—
737C22×C4C2×D4×C10914yes—
738C22×C4C2×D4×C10912yes—
739C22×C4C2×D4×C10912yes—
740C22×C4C2×D4×C10912yes—
741C22×C4C2×D4×C10912yes—
742C22×C4C2×D4×C10912yes—
743C22×C4C2×D4×C10912yes—
744C22×C4#41×C10914yes—
745C22×C4#41×C10912yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C10914yes—
837C23#121×C10914yescomplemented
838C23C22×D4×C10911yescharacteristic
839C23C22×D4×C10911yescharacteristic
840C23C22×D4×C10911yescharacteristic
841C23C22×D4×C10912yes—
842C23C22×D4×C10911yescharacteristic
843C23C2×#41×C10911yescharacteristic
844C23C2×#41×C10911yescharacteristic
845C23C2×#41×C10911yescharacteristic
846C23C2×#41×C10912yes—
847C23H(5,𝔽2)×C10912yes—
848C23H(5,𝔽2)×C10912yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C10914yes—
901C2×C4#120×C10914yes—
902C2×C4#121×C10914yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—44no—
909C22—44no—
910C22—42no—
911C22—42no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C10911yescharacteristic
941C22C2×#120×C10911yescharacteristic
942C22C2×#121×C10911yescharacteristic
943C22C2×#121×C10911yescharacteristic
944C22C2×#121×C10911yescharacteristic
945C22#525×C10911yescharacteristic
946C22#525×C10912yes—
947C22#525×C10911yescharacteristic
948C22#525×C10911yescharacteristic
949C22#532×C10912yes—
950C22#532×C10911yescharacteristic
951C22#534×C10911yescharacteristic
952C22#535×C10911yescharacteristic
953C22#538×C10912yes—
954C22#540×C10912yes—
955C22D42×C10912yes—
956C22D42×C10912yes—
957C22D42×C10912yes—
958C22#546×C10912yes—
959C22#546×C10912yes—
960C22#546×C10912yes—
961C22#550×C10912yes—
962C22#553×C10912yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—42no—
968C4—44no—
969C4—44no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C109×#238811yescharacteristic
975C2C109×#240311yescharacteristic
976C2C109×#240811yescharacteristic
977C2C109×#242412yes—
978C2C109×#242812yes—
979C2C109×#243111yescharacteristic
980C2C109×#245612yes—
981C2C109×#246412yes—
982C2C109×#254311yescharacteristic
983C2C109×#263511yescharacteristic
984C2C109×#284711yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC24C24×C109
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C109C2semidirect
2. C22×C4×D4×C109C2semidirect
3. C2×#394×C109C2semidirect
4. C2×#392×C109C2semidirect
5. C2×#392×C109C2semidirect
6. C2×#386×C109C2semidirect
7. C109×#1441C2semidirect
8. C109×#1439C2semidirect
9. C109×#1438C2semidirect
10. C109×#1437C2semidirect
11. C109×C22⋊#95C2semidirect
72. C22×D4×C109D4semidirect
82. C23×C4×C109D4semidirect
97. C2×C4⋊C4×C109D4semidirect
120. C2×C22⋊C4×C109D4semidirect
121. C2×C22⋊C4×C109D4semidirect
344. C23×C109#121semidirect
409. C2×C4×C109#121semidirect
478. #14722C109direct (N × H)
493. C22×#121C2×C109semidirect
494. C22×C4×D4C2×C109semidirect
495. C2×#394C2×C109semidirect
496. C2×#392C2×C109semidirect
497. C2×#392C2×C109semidirect
498. C2×#386C2×C109semidirect
499. #1441C2×C109semidirect
500. #1439C2×C109semidirect
501. #1438C2×C109semidirect
502. #1437C2×C109semidirect
503. C22⋊#95C2×C109semidirect
504. C109#14722direct (N × H)
565. C22×D4D4×C109semidirect
575. C23×C4D4×C109semidirect
590. C2×C4⋊C4D4×C109semidirect
613. C2×C22⋊C4D4×C109semidirect
614. C2×C22⋊C4D4×C109semidirect
837. C23#121×C109semidirect
902. C2×C4#121×C109semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1092
C22×C4×D4×C1092
C2×#394×C1092
C2×#392×C1092
C2×#386×C1092
C109×#14412
C109×#14392
C109×#14382
C109×#14372
C109×C22⋊#952
#14722109