Finite Group Databasebeta

← C109×#24434 #42142428

Subgroups — C109×#24434 #42142428

Order 27904.

1674 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C109C211yesmaximal, characteristic, complemented
2C2×#465×C109C211yesmaximal, characteristic, complemented
3C2×#449×C109C211yesmaximal, characteristic, complemented
4C2×#447×C109C211yesmaximal, characteristic, complemented
5C22×#102×C109C211yesmaximal, characteristic, complemented
6C109×#2416C211yesmaximal, characteristic, complemented
7C109×#2042C211yesmaximal, characteristic, complemented
8C109×#2034C211yesmaximal, characteristic, complemented
9C109×#2012C211yesmaximal, characteristic, complemented
10C109×#1999C211yesmaximal, characteristic, complemented
11C109×#1879C211yesmaximal, characteristic, complemented
12C109×#1872C211yesmaximal, characteristic, complemented
13C109×#1869C211yesmaximal, characteristic, complemented
14C109×#1864C211yesmaximal, characteristic, complemented
15C109×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic, complemented
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C23×C8×C109C2211yescharacteristic
22#546×C109—24no—
23#546×C109—24no—
24C2×#124×C109C2211yescharacteristic
25C2×#123×C109—21no—
26C2×C22⋊Q8×C109C2211yescharacteristic
27C2×#121×C109—21no—
28C2×#121×C109—21no—
29C2×#121×C109C2211yescharacteristic
30C2×#121×C109C2211yescharacteristic
31C2×#121×C109C2211yescharacteristic, complemented
32C2×#120×C109—21no—
33C2×C4×D4×C109C2211yescharacteristic
34C2×C4×D4×C109C2211yescharacteristic
35C22×C4⋊C4×C109C2211yescharacteristic
36C22×C22⋊C4×C109—21no—
37#465×C109—24no—
38#449×C109—24no—
39#447×C109—24no—
40C2×#106×C109C2211yescharacteristic, complemented
41C2×#103×C109C2211yescharacteristic, complemented
42C2×#103×C109C2211yescharacteristic, complemented
43C2×#103×C109C2211yescharacteristic, complemented
44C2×#102×C109—24no—
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49C2×#102×C109C2211yescharacteristic
50C2×#102×C109C2211yescharacteristic
51C2×#102×C109C2211yescharacteristic, complemented
52C2×C22⋊C8×C109C2211yescharacteristic
53C2×C22⋊C8×C109C2211yescharacteristic, complemented
54C2×C22⋊C8×C109C2211yescharacteristic, complemented
55#396×C109—21no—
56#394×C109—21no—
57#390×C109C2211yescharacteristic, complemented
58#389×C109C2211yescharacteristic, complemented
59#386×C109—21no—
60#380×C109C2211yescharacteristic, complemented
61#340×C109C2211yescharacteristic, complemented
62#340×C109C2211yescharacteristic, complemented
63#336×C109C2211yescharacteristic, complemented
64#336×C109C2211yescharacteristic, complemented
65C25×C109—21no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—22no—
69C2×#41×C109—22no—
70C2×#41×C109—41no—
71C2×#41×C109—41no—
72C22×Q8×C109C2311yescharacteristic
73C22×D4×C109—22no—
74C22×D4×C109—22no—
75C22×D4×C109—21no—
76C22×D4×C109—21no—
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—22no—
81C22×D4×C109—41no—
82C22×D4×C109—41no—
83C22×D4×C109D411yescharacteristic
84C22×D4×C109D414yescomplemented
85C22×D4×C109C2311yescharacteristic
86C22×D4×C109C2311yescharacteristic
87C22×D4×C109C2311yescharacteristic
88C23×C4×C109—21no—
89C23×C4×C109—21no—
90C23×C4×C109—21no—
91C23×C4×C109C2311yescharacteristic
92C23×C4×C109C2311yescharacteristic
93C2×SD16×C109—22no—
94C2×SD16×C109—22no—
95C2×SD16×C109—41no—
96C2×D8×C109—22no—
97C2×D8×C109—22no—
98C2×D8×C109—22no—
99C2×D8×C109—22no—
100C2×D8×C109—41no—
101C2×D8×C109—41no—
102C22×C8×C109—22no—
103C22×C8×C109—22no—
104C22×C8×C109—41no—
105C22×C8×C109C2311yescharacteristic
106C22×C8×C109C2311yescharacteristic
107C22×C8×C109C2311yescharacteristic
108C22×C8×C109C2311yescharacteristic
109#124×C109—22no—
110#124×C109—22no—
111#123×C109—28no—
112C22⋊Q8×C109—22no—
113C22⋊Q8×C109D414yescomplemented
114#121×C109—28no—
115#121×C109—22no—
116#121×C109—22no—
117#121×C109—22no—
118#121×C109—22no—
119#121×C109—22no—
120#121×C109—41no—
121#121×C109—44no—
122#120×C109—28no—
123C4×D4×C109—22no—
124C4×D4×C109—22no—
125C4×D4×C109—22no—
126C4×D4×C109—22no—
127C2×C4⋊C4×C109—21no—
128C2×C4⋊C4×C109—22no—
129C2×C4⋊C4×C109—21no—
130C2×C4⋊C4×C109—21no—
131C2×C4⋊C4×C109—41no—
132C2×C4⋊C4×C109D411yescharacteristic
133C2×C4⋊C4×C109C2311yescharacteristic
134C2×C4⋊C4×C109C2311yescharacteristic
135C2×C4⋊C4×C109C2311yescharacteristic
136C2×C4⋊C4×C109C2311yescharacteristic
137C2×C22⋊C4×C109—28no—
138C2×C22⋊C4×C109—21no—
139C2×C22⋊C4×C109—21no—
140C2×C22⋊C4×C109—21no—
141C2×C22⋊C4×C109—21no—
142C2×C22⋊C4×C109—21no—
143C2×C22⋊C4×C109—21no—
144C2×C22⋊C4×C109—21no—
145C2×C22⋊C4×C109—21no—
146C2×C22⋊C4×C109—21no—
147C2×C22⋊C4×C109—21no—
148C2×C22⋊C4×C109D411yescharacteristic
149C2×C22⋊C4×C109D411yescharacteristic
150C2×C42×C109C2311yescharacteristic
151#106×C109—22no—
152#103×C109—22no—
153#103×C109—22no—
154#103×C109—41no—
155#102×C109—22no—
156#102×C109—22no—
157#102×C109—22no—
158#102×C109—22no—
159#102×C109—22no—
160#102×C109—22no—
161#102×C109D414yescomplemented
162C22⋊C8×C109—22no—
163C22⋊C8×C109—22no—
164C22⋊C8×C109—41no—
165#95×C109—21no—
166#95×C109—21no—
167C24×C109—21no—
168C24×C109—21no—
169C24×C109—24no—
170C24×C109—21no—
171C24×C109—42no—
172C24×C109—42no—
173C24×C109—42no—
174C24×C109—42no—
175C24×C109—81no—
176C24×C109—81no—
177C24×C109C2×D411yescharacteristic
178C24×C109C2×D411yescharacteristic
179#41×C109—44no—
180#41×C109—44no—
181#41×C109—44no—
182#41×C109—44no—
183C2×Q8×C109—21no—
184C2×Q8×C109—21no—
185C2×Q8×C109—21no—
186C2×Q8×C109—21no—
187C2×Q8×C109—21no—
188C2×Q8×C109C2×D412yes—
189C2×D4×C109—28no—
190C2×D4×C109—24no—
191C2×D4×C109—22no—
192C2×D4×C109—22no—
193C2×D4×C109—22no—
194C2×D4×C109—24no—
195C2×D4×C109—24no—
196C2×D4×C109—21no—
197C2×D4×C109—21no—
198C2×D4×C109—21no—
199C2×D4×C109—21no—
200C2×D4×C109—21no—
201C2×D4×C109—21no—
202C2×D4×C109—21no—
203C2×D4×C109—21no—
204C2×D4×C109—21no—
205C2×D4×C109—21no—
206C2×D4×C109—21no—
207C2×D4×C109—21no—
208C2×D4×C109—21no—
209C2×D4×C109—21no—
210C2×D4×C109—44no—
211C2×D4×C109—44no—
212C2×D4×C109—44no—
213C2×D4×C109—42no—
214C2×D4×C109—42no—
215C2×D4×C109—42no—
216C2×D4×C109—42no—
217C2×D4×C109—42no—
218C2×D4×C109—42no—
219C2×D4×C109—42no—
220C2×D4×C109—42no—
221C2×D4×C109—42no—
222C2×D4×C109—81no—
223C2×D4×C109—81no—
224C2×D4×C109—81no—
225C2×D4×C109C2×D412yes—
226C2×D4×C109C2×D412yes—
227C2×D4×C109C2×D412yes—
228C2×D4×C109#4112yes—
229C22×C4×C109—21no—
230C22×C4×C109—21no—
231C22×C4×C109—21no—
232C22×C4×C109—21no—
233C22×C4×C109—24no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—21no—
237C22×C4×C109—24no—
238C22×C4×C109—21no—
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
245C22×C4×C109—21no—
246C22×C4×C109—42no—
247C22×C4×C109—42no—
248C22×C4×C109—42no—
249C22×C4×C109—42no—
250C22×C4×C109—81no—
251C22×C4×C109—81no—
252C22×C4×C109—81no—
253C22×C4×C109C2×D411yescharacteristic
254C22×C4×C109C2×D411yescharacteristic
255C22×C4×C109C2×D411yescharacteristic
256C22×C4×C109C2×D411yescharacteristic
257C22×C4×C109C2×D412yes—
258C22×C4×C109C2×D412yes—
259C22×C4×C109C2411yescharacteristic
260SD16×C109—44no—
261D8×C109—44no—
262D8×C109—44no—
263C2×C8×C109—21no—
264C2×C8×C109—21no—
265C2×C8×C109—21no—
266C2×C8×C109—21no—
267C2×C8×C109—21no—
268C2×C8×C109—21no—
269C2×C8×C109—21no—
270C2×C8×C109—21no—
271C2×C8×C109—21no—
272C2×C8×C109—21no—
273C2×C8×C109—21no—
274C2×C8×C109—44no—
275C2×C8×C109C2×D412yes—
276C4⋊C4×C109—24no—
277C4⋊C4×C109—22no—
278C4⋊C4×C109—21no—
279C4⋊C4×C109—21no—
280C4⋊C4×C109—21no—
281C4⋊C4×C109—21no—
282C4⋊C4×C109—21no—
283C4⋊C4×C109—21no—
284C4⋊C4×C109—42no—
285C4⋊C4×C109—42no—
286C4⋊C4×C109C2×D412yes—
287C4⋊C4×C109C2×D412yes—
288C22⋊C4×C109—24no—
289C22⋊C4×C109—24no—
290C22⋊C4×C109—24no—
291C22⋊C4×C109—24no—
292C22⋊C4×C109—22no—
293C22⋊C4×C109—24no—
294C22⋊C4×C109—22no—
295C22⋊C4×C109—42no—
296C22⋊C4×C109—42no—
297C22⋊C4×C109—42no—
298C22⋊C4×C109—42no—
299C22⋊C4×C109—81no—
300C42×C109—21no—
301C42×C109—21no—
302C23×C109—21no—
303C23×C109—21no—
304C23×C109—21no—
305C23×C109—21no—
306C23×C109—22no—
307C23×C109—22no—
308C23×C109—22no—
309C23×C109—22no—
310C23×C109—21no—
311C23×C109—21no—
312C23×C109—21no—
313C23×C109—21no—
314C23×C109—21no—
315C23×C109—21no—
316C23×C109—21no—
317C23×C109—48no—
318C23×C109—41no—
319C23×C109—41no—
320C23×C109—41no—
321C23×C109—41no—
322C23×C109—41no—
323C23×C109—41no—
324C23×C109—41no—
325C23×C109—41no—
326C23×C109—41no—
327C23×C109—41no—
328C23×C109—48no—
329C23×C109—41no—
330C23×C109—41no—
331C23×C109—41no—
332C23×C109—41no—
333C23×C109—41no—
334C23×C109—41no—
335C23×C109—41no—
336C23×C109—84no—
337C23×C109—84no—
338C23×C109—84no—
339C23×C109—84no—
340C23×C109—84no—
341C23×C109#12012yes—
342C23×C109#13512yes—
343C23×C109AGL(1,ℤ/8)12yes—
344C23×C109C22×D411yescharacteristic
345Q8×C109—22no—
346Q8×C109—22no—
347Q8×C109—41no—
348Q8×C109—41no—
349D4×C109—22no—
350D4×C109—22no—
351D4×C109—22no—
352D4×C109—22no—
353D4×C109—22no—
354D4×C109—48no—
355D4×C109—48no—
356D4×C109—44no—
357D4×C109—41no—
358D4×C109—41no—
359D4×C109—41no—
360D4×C109—41no—
361D4×C109—41no—
362D4×C109—41no—
363D4×C109—84no—
364D4×C109—84no—
365D4×C109—84no—
366D4×C109#12114yescomplemented
367C2×C4×C109—21no—
368C2×C4×C109—21no—
369C2×C4×C109—22no—
370C2×C4×C109—22no—
371C2×C4×C109—22no—
372C2×C4×C109—22no—
373C2×C4×C109—21no—
374C2×C4×C109—21no—
375C2×C4×C109—22no—
376C2×C4×C109—21no—
377C2×C4×C109—22no—
378C2×C4×C109—21no—
379C2×C4×C109—22no—
380C2×C4×C109—21no—
381C2×C4×C109—21no—
382C2×C4×C109—21no—
383C2×C4×C109—21no—
384C2×C4×C109—21no—
385C2×C4×C109—48no—
386C2×C4×C109—41no—
387C2×C4×C109—41no—
388C2×C4×C109—41no—
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—41no—
396C2×C4×C109—41no—
397C2×C4×C109—41no—
398C2×C4×C109—41no—
399C2×C4×C109—41no—
400C2×C4×C109—41no—
401C2×C4×C109—41no—
402C2×C4×C109—84no—
403C2×C4×C109—84no—
404C2×C4×C109#12012yes—
405C2×C4×C109C22×D411yescharacteristic
406C2×C4×C109C22×D411yescharacteristic
407C2×C4×C109C22×D411yescharacteristic
408C2×C4×C109C2×#4111yescharacteristic
409C2×C4×C109H(5,𝔽2)11yescharacteristic
410C2×C4×C109H(5,𝔽2)11yescharacteristic
411C8×C109—22no—
412C8×C109—41no—
413C8×C109—41no—
414C8×C109—41no—
415C22×C109—22no—
416C22×C109—22no—
417C22×C109—22no—
418C22×C109—22no—
419C22×C109—22no—
420C22×C109—22no—
421C22×C109—24no—
422C22×C109—42no—
423C22×C109—42no—
424C22×C109—42no—
425C22×C109—42no—
426C22×C109—42no—
427C22×C109—42no—
428C22×C109—41no—
429C22×C109—42no—
430C22×C109—41no—
431C22×C109—42no—
432C22×C109—41no—
433C22×C109—41no—
434C22×C109—42no—
435C22×C109—41no—
436C22×C109—41no—
437C22×C109—41no—
438C22×C109—816no—
439C22×C109—81no—
440C22×C109—81no—
441C22×C109—81no—
442C22×C109—81no—
443C22×C109—81no—
444C22×C109—81no—
445C22×C109—81no—
446C22×C109—81no—
447C22×C109—81no—
448C22×C109—81no—
449C22×C109—81no—
450C22×C109#44914yescomplemented
451C22×C109C2×#12011yescharacteristic
452C22×C109D4211yescharacteristic
453C22×C109#54611yescharacteristic
454C22×C109C2×#13511yescharacteristic
455C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C109#57611yescharacteristic
457C22×C109#57711yescharacteristic
458C4×C109—22no—
459C4×C109—41no—
460C4×C109—42no—
461C4×C109—41no—
462C4×C109—42no—
463C4×C109—41no—
464C4×C109—42no—
465C4×C109—81no—
466C4×C109—81no—
467C4×C109C2×#12111yescharacteristic
468C4×C109#53411yescharacteristic
469C4×C109D4211yescharacteristic
470C4×C109#54611yescharacteristic
471#24434C10911yesmaximal, characteristic, direct product factor, Sylow
472C2×C109—24no—
473C2×C109—44no—
474C2×C109—81no—
475C2×C109—82no—
476C2×C109—161no—
477C2×C109#241011yescharacteristic
478C2×C109C2×#44911yescharacteristic
479C2×C109#301211yescharacteristic
480C2×C109#326411yescharacteristic
481C2×C109#328211yescharacteristic
482C2×C109#329711yescharacteristic
483C2×C109#330611yescharacteristic
484C2×#546C2×C10911yescharacteristic, complemented
485C2×#465C2×C10911yescharacteristic, complemented
486C2×#449C2×C10911yescharacteristic, complemented
487C2×#447C2×C10911yescharacteristic, complemented
488C22×#102C2×C10911yescharacteristic, complemented
489#2416C2×C10911yescharacteristic, complemented
490#2042C2×C10911yescharacteristic, complemented
491#2034C2×C10911yescharacteristic, complemented
492#2012C2×C10911yescharacteristic, complemented
493#1999C2×C10911yescharacteristic, complemented
494#1879C2×C10911yescharacteristic, complemented
495#1872C2×C10911yescharacteristic, complemented
496#1869C2×C10911yescharacteristic, complemented
497#1864C2×C10911yescharacteristic, complemented
498#1788C2×C10911yescharacteristic, complemented
499C109#2443411yescharacteristic, direct product factor, Sylow
500C22×#41C22×C10911yescharacteristic
501C23×D4C22×C10911yescharacteristic
502C22×SD16C22×C10911yescharacteristic, complemented
503C22×D8C22×C10911yescharacteristic
504C22×D8C22×C10911yescharacteristic
505C23×C8C22×C10911yescharacteristic
506#546—24no—
507#546—24no—
508C2×#124C22×C10911yescharacteristic
509C2×#123—21no—
510C2×C22⋊Q8C22×C10911yescharacteristic
511C2×#121—21no—
512C2×#121—21no—
513C2×#121C22×C10911yescharacteristic
514C2×#121C22×C10911yescharacteristic
515C2×#121C22×C10911yescharacteristic, complemented
516C2×#120—21no—
517C2×C4×D4C22×C10911yescharacteristic
518C2×C4×D4C22×C10911yescharacteristic
519C22×C4⋊C4C22×C10911yescharacteristic
520C22×C22⋊C4—21no—
521#465—24no—
522#449—24no—
523#447—24no—
524C2×#106C22×C10911yescharacteristic, complemented
525C2×#103C22×C10911yescharacteristic, complemented
526C2×#103C22×C10911yescharacteristic, complemented
527C2×#103C22×C10911yescharacteristic, complemented
528C2×#102—24no—
529C2×#102C22×C10911yescharacteristic
530C2×#102C22×C10911yescharacteristic
531C2×#102C22×C10911yescharacteristic
532C2×#102C22×C10911yescharacteristic
533C2×#102C22×C10911yescharacteristic
534C2×#102C22×C10911yescharacteristic
535C2×#102C22×C10911yescharacteristic, complemented
536C2×C22⋊C8C22×C10911yescharacteristic
537C2×C22⋊C8C22×C10911yescharacteristic, complemented
538C2×C22⋊C8C22×C10911yescharacteristic, complemented
539#396—21no—
540#394—21no—
541#390C22×C10911yescharacteristic, complemented
542#389C22×C10911yescharacteristic, complemented
543#386—21no—
544#380C22×C10911yescharacteristic, complemented
545#340C22×C10911yescharacteristic, complemented
546#340C22×C10911yescharacteristic, complemented
547#336C22×C10911yescharacteristic, complemented
548#336C22×C10911yescharacteristic, complemented
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—41no—
555C2×#41—41no—
556C22×Q8C23×C10911yescharacteristic
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C10911yescharacteristic
568C22×D4D4×C10914yescomplemented
569C22×D4C23×C10911yescharacteristic
570C22×D4C23×C10911yescharacteristic
571C22×D4C23×C10911yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C10911yescharacteristic
576C23×C4C23×C10911yescharacteristic
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C22×C8—22no—
587C22×C8—22no—
588C22×C8—41no—
589C22×C8C23×C10911yescharacteristic
590C22×C8C23×C10911yescharacteristic
591C22×C8C23×C10911yescharacteristic
592C22×C8C23×C10911yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8D4×C10914yescomplemented
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—41no—
605#121—44no—
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C10911yescharacteristic
617C2×C4⋊C4C23×C10911yescharacteristic
618C2×C4⋊C4C23×C10911yescharacteristic
619C2×C4⋊C4C23×C10911yescharacteristic
620C2×C4⋊C4C23×C10911yescharacteristic
621C2×C22⋊C4—28no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C10911yescharacteristic
633C2×C22⋊C4D4×C10911yescharacteristic
634C2×C42C23×C10911yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—41no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102D4×C10914yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—21no—
653C24—24no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C10911yescharacteristic
662C24C2×D4×C10911yescharacteristic
663#41—44no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C10912yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C10912yes—
710C2×D4C2×D4×C10912yes—
711C2×D4C2×D4×C10912yes—
712C2×D4#41×C10912yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C10911yescharacteristic
738C22×C4C2×D4×C10911yescharacteristic
739C22×C4C2×D4×C10911yescharacteristic
740C22×C4C2×D4×C10911yescharacteristic
741C22×C4C2×D4×C10912yes—
742C22×C4C2×D4×C10912yes—
743C22×C4C24×C10911yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—44no—
759C2×C8C2×D4×C10912yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C10912yes—
771C4⋊C4C2×D4×C10912yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—24no—
778C22⋊C4—22no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—48no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—48no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23#120×C10912yes—
826C23#135×C10912yes—
827C23AGL(1,ℤ/8)×C10912yes—
828C23C22×D4×C10911yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—44no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C10914yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C10912yes—
889C2×C4C22×D4×C10911yescharacteristic
890C2×C4C22×D4×C10911yescharacteristic
891C2×C4C22×D4×C10911yescharacteristic
892C2×C4C2×#41×C10911yescharacteristic
893C2×C4H(5,𝔽2)×C10911yescharacteristic
894C2×C4H(5,𝔽2)×C10911yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22#449×C10914yescomplemented
935C22C2×#120×C10911yescharacteristic
936C22D42×C10911yescharacteristic
937C22#546×C10911yescharacteristic
938C22C2×#135×C10911yescharacteristic
939C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
940C22#576×C10911yescharacteristic
941C22#577×C10911yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C10911yescharacteristic
952C4#534×C10911yescharacteristic
953C4D42×C10911yescharacteristic
954C4#546×C10911yescharacteristic
955C2—24no—
956C2—44no—
957C2—81no—
958C2—82no—
959C2—161no—
960C2C109×#241011yescharacteristic
961C2C2×#449×C10911yescharacteristic
962C2C109×#301211yescharacteristic
963C2C109×#326411yescharacteristic
964C2C109×#328211yescharacteristic
965C2C109×#329711yescharacteristic
966C2C109×#330611yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#546×C109C2semidirect
2. C2×#465×C109C2semidirect
3. C2×#449×C109C2semidirect
4. C2×#447×C109C2semidirect
5. C22×#102×C109C2semidirect
6. C109×#2416C2semidirect
7. C109×#2042C2semidirect
8. C109×#2034C2semidirect
9. C109×#2012C2semidirect
10. C109×#1999C2semidirect
11. C109×#1879C2semidirect
12. C109×#1872C2semidirect
13. C109×#1869C2semidirect
14. C109×#1864C2semidirect
15. C109×#1788C2semidirect
18. C22×SD16×C109C22semidirect
31. C2×#121×C109C22semidirect
40. C2×#106×C109C22semidirect
41. C2×#103×C109C22semidirect
42. C2×#103×C109C22semidirect
43. C2×#103×C109C22semidirect
51. C2×#102×C109C22semidirect
53. C2×C22⋊C8×C109C22semidirect
54. C2×C22⋊C8×C109C22semidirect
57. #390×C109C22semidirect
58. #389×C109C22semidirect
60. #380×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
63. #336×C109C22semidirect
64. #336×C109C22semidirect
84. C22×D4×C109D4semidirect
113. C22⋊Q8×C109D4semidirect
161. #102×C109D4semidirect
366. D4×C109#121semidirect
450. C22×C109#449semidirect
471. #24434C109direct (N × H)
484. C2×#546C2×C109semidirect
485. C2×#465C2×C109semidirect
486. C2×#449C2×C109semidirect
487. C2×#447C2×C109semidirect
488. C22×#102C2×C109semidirect
489. #2416C2×C109semidirect
490. #2042C2×C109semidirect
491. #2034C2×C109semidirect
492. #2012C2×C109semidirect
493. #1999C2×C109semidirect
494. #1879C2×C109semidirect
495. #1872C2×C109semidirect
496. #1869C2×C109semidirect
497. #1864C2×C109semidirect
498. #1788C2×C109semidirect
499. C109#24434direct (N × H)
502. C22×SD16C22×C109semidirect
515. C2×#121C22×C109semidirect
524. C2×#106C22×C109semidirect
525. C2×#103C22×C109semidirect
526. C2×#103C22×C109semidirect
527. C2×#103C22×C109semidirect
535. C2×#102C22×C109semidirect
537. C2×C22⋊C8C22×C109semidirect
538. C2×C22⋊C8C22×C109semidirect
541. #390C22×C109semidirect
542. #389C22×C109semidirect
544. #380C22×C109semidirect
545. #340C22×C109semidirect
546. #340C22×C109semidirect
547. #336C22×C109semidirect
548. #336C22×C109semidirect
568. C22×D4D4×C109semidirect
597. C22⋊Q8D4×C109semidirect
645. #102D4×C109semidirect
850. D4#121×C109semidirect
934. C22#449×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1092
C2×#465×C1092
C2×#449×C1092
C2×#447×C1092
C22×#102×C1092
C109×#24162
C109×#20422
C109×#20342
C109×#20122
C109×#19992
C109×#18792
C109×#18722
C109×#18692
C109×#18642
C109×#17882
#24434109