Finite Group Databasebeta

← C109×#23972 #42141966

Subgroups — C109×#23972 #42141966

Order 27904.

1516 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
1C2×#547×C109C211yesmaximal, characteristic, complemented
2C2×#449×C109C211yesmaximal, characteristic, complemented
3C2×#417×C109C211yesmaximal, characteristic, complemented
4C109×#2407C211yesmaximal, characteristic, complemented
5C109×#2024C211yesmaximal, characteristic, complemented
6C109×#2023C211yesmaximal, characteristic, complemented
7C109×#2000C211yesmaximal, characteristic, complemented
8C109×#1999C211yesmaximal, characteristic, complemented
9C109×#1895C211yesmaximal, characteristic, complemented
10C109×#1879C211yesmaximal, characteristic, complemented
11C109×#1877C211yesmaximal, characteristic, complemented
12C109×#1874C211yesmaximal, characteristic, complemented
13C109×#1872C211yesmaximal, characteristic, complemented
14C109×#1870C211yesmaximal, characteristic, complemented
15C109×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C109—21no—
17C22×#41×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×M16×C109C2211yescharacteristic
21#547×C109—24no—
22#547×C109—24no—
23C2×C4⋊Q8×C109C2211yescharacteristic
24C2×#123×C109—21no—
25C2×#123×C109—21no—
26C2×C22⋊Q8×C109—21no—
27C2×C22⋊Q8×C109C2211yescharacteristic
28C2×#121×C109C2211yescharacteristic
29C2×#121×C109C2211yescharacteristic
30C2×#121×C109C2211yescharacteristic
31C2×C4×D4×C109C2211yescharacteristic
32C2×C4×D4×C109C2211yescharacteristic
33C22×C4⋊C4×C109C2211yescharacteristic
34C22×C4⋊C4×C109C2211yescharacteristic
35#449×C109—24no—
36#417×C109—24no—
37C2×#103×C109C2211yescharacteristic
38C2×#103×C109C2211yescharacteristic
39C2×#103×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×C22⋊C8×C109C2211yescharacteristic
46C2×C22⋊C8×C109C2211yescharacteristic
47C2×C22⋊C8×C109C2211yescharacteristic
48#394×C109—21no—
49#392×C109—21no—
50#391×C109C2211yescharacteristic
51#390×C109C2211yescharacteristic
52#386×C109—21no—
53#385×C109—21no—
54#380×C109C2211yescharacteristic
55#340×C109C2211yescharacteristic
56#340×C109C2211yescharacteristic
57#340×C109C2211yescharacteristic
58#340×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic
60#340×C109C2211yescharacteristic
61#336×C109C2211yescharacteristic
62#336×C109C2211yescharacteristic
63C2×#41×C109—28no—
64C2×#41×C109—22no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—41no—
69C2×#41×C109—41no—
70C2×#41×C109—44no—
71C2×#41×C109—44no—
72C22×Q8×C109—21no—
73C22×Q8×C109C2311yescharacteristic
74C22×D4×C109—21no—
75C22×D4×C109—21no—
76C22×D4×C109—21no—
77C22×D4×C109—21no—
78C22×D4×C109D411yescharacteristic
79C22×D4×C109C2311yescharacteristic
80C22×D4×C109C2311yescharacteristic
81C23×C4×C109—21no—
82C23×C4×C109—21no—
83C23×C4×C109—21no—
84C23×C4×C109—21no—
85C23×C4×C109C2311yescharacteristic
86C23×C4×C109C2311yescharacteristic
87C2×SD16×C109—22no—
88C2×SD16×C109—22no—
89C2×SD16×C109—41no—
90C2×D8×C109—22no—
91C2×D8×C109—22no—
92C2×D8×C109—41no—
93C2×M16×C109—22no—
94C2×M16×C109—41no—
95C2×M16×C109—41no—
96C22×C8×C109C2311yescharacteristic
97C22×C8×C109C2311yescharacteristic
98C22×C8×C109C2311yescharacteristic
99C22×C8×C109C2311yescharacteristic
100C4⋊Q8×C109—22no—
101C4⋊Q8×C109—22no—
102#123×C109—28no—
103#123×C109—28no—
104C22⋊Q8×C109—28no—
105C22⋊Q8×C109—22no—
106C22⋊Q8×C109—41no—
107#121×C109—22no—
108#121×C109—22no—
109#121×C109—22no—
110#121×C109—22no—
111#121×C109—41no—
112#121×C109D414yescomplemented
113C4×D4×C109—22no—
114C4×D4×C109—22no—
115C4×D4×C109—22no—
116C4×D4×C109—22no—
117C2×C4⋊C4×C109—21no—
118C2×C4⋊C4×C109—21no—
119C2×C4⋊C4×C109—22no—
120C2×C4⋊C4×C109—21no—
121C2×C4⋊C4×C109—22no—
122C2×C4⋊C4×C109—22no—
123C2×C4⋊C4×C109—21no—
124C2×C4⋊C4×C109D411yescharacteristic
125C2×C4⋊C4×C109D414yescomplemented
126C2×C4⋊C4×C109C2311yescharacteristic
127C2×C4⋊C4×C109C2311yescharacteristic
128C2×C4⋊C4×C109C2311yescharacteristic
129C2×C4⋊C4×C109C2311yescharacteristic
130C2×C4⋊C4×C109C2311yescharacteristic
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—21no—
134C2×C22⋊C4×C109—21no—
135C2×C22⋊C4×C109—21no—
136C2×C22⋊C4×C109—21no—
137C2×C22⋊C4×C109—21no—
138C2×C22⋊C4×C109—21no—
139C2×C22⋊C4×C109D411yescharacteristic
140C2×C22⋊C4×C109D411yescharacteristic
141C2×C42×C109C2311yescharacteristic
142#103×C109—22no—
143#103×C109—22no—
144#103×C109—22no—
145#102×C109—22no—
146#102×C109—22no—
147#102×C109—22no—
148#102×C109—41no—
149#102×C109—41no—
150C22⋊C8×C109—22no—
151C22⋊C8×C109—41no—
152C22⋊C8×C109—41no—
153#95×C109—21no—
154#95×C109—21no—
155#95×C109—21no—
156C24×C109—21no—
157C24×C109—21no—
158C24×C109C2×D411yescharacteristic
159C24×C109C2×D411yescharacteristic
160#41×C109—28no—
161#41×C109—44no—
162#41×C109—44no—
163#41×C109—44no—
164#41×C109—432no—
165C2×Q8×C109—24no—
166C2×Q8×C109—21no—
167C2×Q8×C109—21no—
168C2×Q8×C109—21no—
169C2×Q8×C109—21no—
170C2×Q8×C109—21no—
171C2×Q8×C109—42no—
172C2×Q8×C109—42no—
173C2×Q8×C109#4112yescomplemented
174C2×D4×C109—22no—
175C2×D4×C109—22no—
176C2×D4×C109—24no—
177C2×D4×C109—24no—
178C2×D4×C109—22no—
179C2×D4×C109—21no—
180C2×D4×C109—21no—
181C2×D4×C109—21no—
182C2×D4×C109—21no—
183C2×D4×C109—21no—
184C2×D4×C109—21no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—21no—
189C2×D4×C109—42no—
190C2×D4×C109—42no—
191C2×D4×C109—42no—
192C2×D4×C109—42no—
193C2×D4×C109—42no—
194C2×D4×C109—42no—
195C2×D4×C109—42no—
196C2×D4×C109—42no—
197C2×D4×C109—42no—
198C2×D4×C109—81no—
199C2×D4×C109C2×D412yes—
200C2×D4×C109#4112yescomplemented
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—24no—
206C22×C4×C109—24no—
207C22×C4×C109—24no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—21no—
211C22×C4×C109—21no—
212C22×C4×C109—21no—
213C22×C4×C109—21no—
214C22×C4×C109—21no—
215C22×C4×C109—21no—
216C22×C4×C109—21no—
217C22×C4×C109—21no—
218C22×C4×C109—21no—
219C22×C4×C109—21no—
220C22×C4×C109—42no—
221C22×C4×C109—42no—
222C22×C4×C109—42no—
223C22×C4×C109—42no—
224C22×C4×C109—42no—
225C22×C4×C109—42no—
226C22×C4×C109—42no—
227C22×C4×C109—42no—
228C22×C4×C109—42no—
229C22×C4×C109C2×D411yescharacteristic
230C22×C4×C109C2×D411yescharacteristic
231C22×C4×C109C2×D411yescharacteristic
232C22×C4×C109C2×D412yes—
233C22×C4×C109C2×D412yes—
234C22×C4×C109C2×D411yescharacteristic
235C22×C4×C109C2411yescharacteristic
236SD16×C109—44no—
237D8×C109—44no—
238M16×C109—44no—
239C2×C8×C109—21no—
240C2×C8×C109—21no—
241C2×C8×C109—21no—
242C2×C8×C109—21no—
243C2×C8×C109—21no—
244C2×C8×C109—21no—
245C2×C8×C109—21no—
246C2×C8×C109—21no—
247C2×C8×C109—21no—
248C2×C8×C109—21no—
249C2×C8×C109—21no—
250C2×C8×C109—21no—
251C4⋊C4×C109—24no—
252C4⋊C4×C109—24no—
253C4⋊C4×C109—24no—
254C4⋊C4×C109—22no—
255C4⋊C4×C109—21no—
256C4⋊C4×C109—21no—
257C4⋊C4×C109—21no—
258C4⋊C4×C109—21no—
259C4⋊C4×C109—21no—
260C4⋊C4×C109—21no—
261C4⋊C4×C109—21no—
262C4⋊C4×C109—42no—
263C4⋊C4×C109C2×D412yes—
264C4⋊C4×C109C2×D412yes—
265C4⋊C4×C109C2×D412yes—
266C22⋊C4×C109—24no—
267C22⋊C4×C109—24no—
268C22⋊C4×C109—22no—
269C22⋊C4×C109—24no—
270C22⋊C4×C109—22no—
271C22⋊C4×C109—42no—
272C22⋊C4×C109—42no—
273C22⋊C4×C109—42no—
274C22⋊C4×C109—81no—
275C22⋊C4×C109—81no—
276C42×C109—21no—
277C42×C109—21no—
278C23×C109—21no—
279C23×C109—21no—
280C23×C109—21no—
281C23×C109—21no—
282C23×C109—21no—
283C23×C109—21no—
284C23×C109—21no—
285C23×C109—21no—
286C23×C109—21no—
287C23×C109—21no—
288C23×C109—21no—
289C23×C109—21no—
290C23×C109—22no—
291C23×C109—22no—
292C23×C109—41no—
293C23×C109—41no—
294C23×C109—41no—
295C23×C109—41no—
296C23×C109—41no—
297C23×C109—41no—
298C23×C109—41no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109—41no—
302C23×C109—41no—
303C23×C109—41no—
304C23×C109#12012yes—
305C23×C109AGL(1,ℤ/8)12yes—
306C23×C109C22×D411yescharacteristic
307Q8×C109—22no—
308Q8×C109—22no—
309Q8×C109—48no—
310Q8×C109—41no—
311Q8×C109—41no—
312D4×C109—28no—
313D4×C109—22no—
314D4×C109—22no—
315D4×C109—22no—
316D4×C109—22no—
317D4×C109—48no—
318D4×C109—48no—
319D4×C109—48no—
320D4×C109—41no—
321D4×C109—41no—
322D4×C109—41no—
323D4×C109—41no—
324D4×C109—84no—
325C2×C4×C109—21no—
326C2×C4×C109—21no—
327C2×C4×C109—21no—
328C2×C4×C109—21no—
329C2×C4×C109—22no—
330C2×C4×C109—22no—
331C2×C4×C109—22no—
332C2×C4×C109—22no—
333C2×C4×C109—21no—
334C2×C4×C109—21no—
335C2×C4×C109—22no—
336C2×C4×C109—22no—
337C2×C4×C109—22no—
338C2×C4×C109—21no—
339C2×C4×C109—22no—
340C2×C4×C109—21no—
341C2×C4×C109—21no—
342C2×C4×C109—21no—
343C2×C4×C109—48no—
344C2×C4×C109—48no—
345C2×C4×C109—48no—
346C2×C4×C109—48no—
347C2×C4×C109—41no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—41no—
351C2×C4×C109—41no—
352C2×C4×C109—41no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—41no—
356C2×C4×C109—41no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109—41no—
360C2×C4×C109—41no—
361C2×C4×C109—41no—
362C2×C4×C109—41no—
363C2×C4×C109—41no—
364C2×C4×C109—41no—
365C2×C4×C109#12012yes—
366C2×C4×C109AGL(1,ℤ/8)12yes—
367C2×C4×C109C22×D411yescharacteristic
368C2×C4×C109C22×D411yescharacteristic
369C2×C4×C109C2×#4111yescharacteristic
370C2×C4×C109C2×#4111yescharacteristic
371C2×C4×C109H(5,𝔽2)11yescharacteristic
372C2×C4×C109H(5,𝔽2)11yescharacteristic
373C8×C109—41no—
374C8×C109—41no—
375C8×C109—41no—
376C8×C109—41no—
377C22×C109—22no—
378C22×C109—22no—
379C22×C109—22no—
380C22×C109—22no—
381C22×C109—22no—
382C22×C109—22no—
383C22×C109—41no—
384C22×C109—41no—
385C22×C109—41no—
386C22×C109—41no—
387C22×C109—41no—
388C22×C109—41no—
389C22×C109—41no—
390C22×C109—41no—
391C22×C109—42no—
392C22×C109—42no—
393C22×C109—42no—
394C22×C109—42no—
395C22×C109—42no—
396C22×C109—42no—
397C22×C109—81no—
398C22×C109—81no—
399C22×C109—81no—
400C22×C109—81no—
401C22×C109—81no—
402C22×C109—81no—
403C22×C109—81no—
404C22×C109—81no—
405C22×C109C2×#12011yescharacteristic
406C22×C109#54611yescharacteristic
407C22×C109#54611yescharacteristic
408C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C109#57711yescharacteristic
411C22×C109#57811yescharacteristic
412C4×C109—22no—
413C4×C109—22no—
414C4×C109—41no—
415C4×C109—42no—
416C4×C109—42no—
417C4×C109—42no—
418C4×C109—42no—
419C4×C109—41no—
420C4×C109—81no—
421C4×C109—81no—
422C4×C109#52511yescharacteristic
423C4×C109#53511yescharacteristic
424C4×C109#54611yescharacteristic
425C4×C109#54611yescharacteristic
426#23972C10911yesmaximal, characteristic, direct product factor, Sylow
427C2×C109—42no—
428C2×C109—42no—
429C2×C109—82no—
430C2×C109—82no—
431C2×C109#240411yescharacteristic
432C2×C109#300311yescharacteristic
433C2×C109#301311yescharacteristic
434C2×C109#330611yescharacteristic
435C2×C109#330811yescharacteristic
436C2×C109#333011yescharacteristic
437C2×C109#333211yescharacteristic
438C2×#547C2×C10911yescharacteristic, complemented
439C2×#449C2×C10911yescharacteristic, complemented
440C2×#417C2×C10911yescharacteristic, complemented
441#2407C2×C10911yescharacteristic, complemented
442#2024C2×C10911yescharacteristic, complemented
443#2023C2×C10911yescharacteristic, complemented
444#2000C2×C10911yescharacteristic, complemented
445#1999C2×C10911yescharacteristic, complemented
446#1895C2×C10911yescharacteristic, complemented
447#1879C2×C10911yescharacteristic, complemented
448#1877C2×C10911yescharacteristic, complemented
449#1874C2×C10911yescharacteristic, complemented
450#1872C2×C10911yescharacteristic, complemented
451#1870C2×C10911yescharacteristic, complemented
452#1824C2×C10911yescharacteristic, complemented
453C109#2397211yescharacteristic, direct product factor, Sylow
454C22×#41—21no—
455C22×#41C22×C10911yescharacteristic
456C22×SD16C22×C10911yescharacteristic
457C22×D8C22×C10911yescharacteristic
458C22×M16C22×C10911yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C10911yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C10911yescharacteristic
466C2×#121C22×C10911yescharacteristic
467C2×#121C22×C10911yescharacteristic
468C2×#121C22×C10911yescharacteristic
469C2×C4×D4C22×C10911yescharacteristic
470C2×C4×D4C22×C10911yescharacteristic
471C22×C4⋊C4C22×C10911yescharacteristic
472C22×C4⋊C4C22×C10911yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C10911yescharacteristic
476C2×#103C22×C10911yescharacteristic
477C2×#103C22×C10911yescharacteristic
478C2×#102C22×C10911yescharacteristic
479C2×#102C22×C10911yescharacteristic
480C2×#102C22×C10911yescharacteristic
481C2×#102C22×C10911yescharacteristic
482C2×#102C22×C10911yescharacteristic
483C2×C22⋊C8C22×C10911yescharacteristic
484C2×C22⋊C8C22×C10911yescharacteristic
485C2×C22⋊C8C22×C10911yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C10911yescharacteristic
489#390C22×C10911yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C10911yescharacteristic
493#340C22×C10911yescharacteristic
494#340C22×C10911yescharacteristic
495#340C22×C10911yescharacteristic
496#340C22×C10911yescharacteristic
497#340C22×C10911yescharacteristic
498#340C22×C10911yescharacteristic
499#336C22×C10911yescharacteristic
500#336C22×C10911yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C10911yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C10911yescharacteristic
517C22×D4C23×C10911yescharacteristic
518C22×D4C23×C10911yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C10911yescharacteristic
524C23×C4C23×C10911yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C10911yescharacteristic
535C22×C8C23×C10911yescharacteristic
536C22×C8C23×C10911yescharacteristic
537C22×C8C23×C10911yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C10914yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C10911yescharacteristic
563C2×C4⋊C4D4×C10914yescomplemented
564C2×C4⋊C4C23×C10911yescharacteristic
565C2×C4⋊C4C23×C10911yescharacteristic
566C2×C4⋊C4C23×C10911yescharacteristic
567C2×C4⋊C4C23×C10911yescharacteristic
568C2×C4⋊C4C23×C10911yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C10911yescharacteristic
578C2×C22⋊C4D4×C10911yescharacteristic
579C2×C42C23×C10911yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C10911yescharacteristic
597C24C2×D4×C10911yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C10912yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C10912yes—
638C2×D4#41×C10912yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C10911yescharacteristic
668C22×C4C2×D4×C10911yescharacteristic
669C22×C4C2×D4×C10911yescharacteristic
670C22×C4C2×D4×C10912yes—
671C22×C4C2×D4×C10912yes—
672C22×C4C2×D4×C10911yescharacteristic
673C22×C4C24×C10911yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C10912yes—
702C4⋊C4C2×D4×C10912yes—
703C4⋊C4C2×D4×C10912yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C10912yes—
743C23AGL(1,ℤ/8)×C10912yes—
744C23C22×D4×C10911yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C10912yes—
804C2×C4AGL(1,ℤ/8)×C10912yes—
805C2×C4C22×D4×C10911yescharacteristic
806C2×C4C22×D4×C10911yescharacteristic
807C2×C4C2×#41×C10911yescharacteristic
808C2×C4C2×#41×C10911yescharacteristic
809C2×C4H(5,𝔽2)×C10911yescharacteristic
810C2×C4H(5,𝔽2)×C10911yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C10911yescharacteristic
844C22#546×C10911yescharacteristic
845C22#546×C10911yescharacteristic
846C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
847C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
848C22#577×C10911yescharacteristic
849C22#578×C10911yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—41no—
856C4—41no—
857C4—42no—
858C4—81no—
859C4—81no—
860C4#525×C10911yescharacteristic
861C4#535×C10911yescharacteristic
862C4#546×C10911yescharacteristic
863C4#546×C10911yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C109×#240411yescharacteristic
869C2C109×#300311yescharacteristic
870C2C109×#301311yescharacteristic
871C2C109×#330611yescharacteristic
872C2C109×#330811yescharacteristic
873C2C109×#333011yescharacteristic
874C2C109×#333211yescharacteristic
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×#547×C109C2semidirect
2. C2×#449×C109C2semidirect
3. C2×#417×C109C2semidirect
4. C109×#2407C2semidirect
5. C109×#2024C2semidirect
6. C109×#2023C2semidirect
7. C109×#2000C2semidirect
8. C109×#1999C2semidirect
9. C109×#1895C2semidirect
10. C109×#1879C2semidirect
11. C109×#1877C2semidirect
12. C109×#1874C2semidirect
13. C109×#1872C2semidirect
14. C109×#1870C2semidirect
15. C109×#1824C2semidirect
112. #121×C109D4semidirect
125. C2×C4⋊C4×C109D4semidirect
173. C2×Q8×C109#41semidirect
200. C2×D4×C109#41semidirect
426. #23972C109direct (N × H)
438. C2×#547C2×C109semidirect
439. C2×#449C2×C109semidirect
440. C2×#417C2×C109semidirect
441. #2407C2×C109semidirect
442. #2024C2×C109semidirect
443. #2023C2×C109semidirect
444. #2000C2×C109semidirect
445. #1999C2×C109semidirect
446. #1895C2×C109semidirect
447. #1879C2×C109semidirect
448. #1877C2×C109semidirect
449. #1874C2×C109semidirect
450. #1872C2×C109semidirect
451. #1870C2×C109semidirect
452. #1824C2×C109semidirect
453. C109#23972direct (N × H)
550. #121D4×C109semidirect
563. C2×C4⋊C4D4×C109semidirect
611. C2×Q8#41×C109semidirect
638. C2×D4#41×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1092
C2×#449×C1092
C2×#417×C1092
C109×#24072
C109×#20242
C109×#20232
C109×#20002
C109×#19992
C109×#18952
C109×#18792
C109×#18772
C109×#18742
C109×#18722
C109×#18702
C109×#18242
#23972109